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WORLD METEOROLOGICAL ORGANIZATION

TECHNICAL NOTE No. 195

METHODS OF INTERPRETING NUMERICALWEATHER PREDICTION OUTPUT FOR

AERONAUTICAL METEOROLOGY

by the

CAeM Working Group on Advanced Techniques Applied to Aeronautical Meteorology

Second Edition

Secretariat of the World Meteorological Organization – Geneva – Switzerland

WMO–No. 770

The World Meteorological Organization

The World Meteorological Organization (WMO), of which 185* States and Territories are Members, is a specialized agencyof the United Nations. The purposes of the Organization are:

(a) To facilitate world-wide cooperation in the establishment of networks of stations for the making of meteorological obser-vations as well as hydrological and other geophysical observations related to meteorology, and to promote theestablishment and maintenance of centres charged with the provision of meteorological and related services;

(b) To promote the establishment and maintenance of systems for the rapid exchange of meteorological and related informa-tion;

(c) To promote standardization of meteorological and related observations and to ensure the uniform publication of observa-tions and statistics;

(d) To further the application of meteorology to aviation, shipping, water problems, agriculture and other human activities;(e) To promote activities in operational hydrology and to further close cooperation between Meteorological and Hydrological

Services; and(f) To encourage research and training in meteorology and, as appropriate, in related fields and to assist in

coordinating the international aspects of such research and training.

(Convention of the World Meteorological Organization, Article 2)

The Organization consists of the following:

The World Meteorological Congress, the supreme body of the Organization, brings together the delegates of Members onceevery four years to determine general policies for the fulfilment of the purposes of the Organization, to approve long-termplans, to authorize maximum expenditures for the following financial period, to adopt Technical Regulations relating to inter-national meteorological and operational hydrological practice, to elect the President and Vice-Presidents of the Organizationand members of the Executive Council and to appoint the Secretary-General;

The Executive Council, composed of 36 directors of national Meteorological or Hydrometeorological Services, meets at leastonce a year to review the activities of the Organization and to implement the programmes approved by Congress;

The six regional associations (Africa, Asia, South America, North and Central America, South-West Pacific and Europe),composed of Members, coordinate meteorological and related activities within their respective Regions;

The eight technical commissions, composed of experts designated by Members, study matters within their specific areas ofcompetence (technical commissions have been established for basic systems, instruments and methods of observation, atmo-spheric sciences, aeronautical meteorology, agricultural meteorology, marine meteorology, hydrology, and climatology);

The Secretariat, headed by the Secretary-General, serves as the administrative, documentation and information centre of theOrganization. It prepares, edits, produces and distributes the publications of the Organization, carries out the duties specifiedin the Convention and other Basic Documents and provides secretariat support to the work of the constituent bodies of WMOdescribed above.

________* On 1 February 1999

WORLD METEOROLOGICAL ORGANIZATION

Secretariat of the World Meteorological Organization – Geneva – Switzerland1999

WMO–No. 770

TECHNICAL NOTE No. 195

METHODS OF INTERPRETING NUMERICALWEATHER PREDICTION OUTPUT FOR

AERONAUTICAL METEOROLOGY

by the

CAeM Working Group on Advanced Techniques Applied to Aeronautical Meteorology

Second Edition

© 1999, World Meteorological Organization

ISBN: 92-63-12770-2

NOTE

The designations employed and the presentation of material in this publication do not implythe expression of any opinion whatsoever on the part of the Secretariat of the World Meteorological Organization concerning the legal status of any country, territory, city or area, or of its authorities, or concerning the delimitation of its frontiers or boundaries.

Page

FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

CHAPTER 1 — GLOBAL MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Historical background to numerical weather prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 From von Helmholtz to Richardson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 Barotropic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3 Baroclinic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.4 The primitive equation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.5 Objective analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Global atmospheric models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 The basic equations of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.2 Spatial resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.3 The numerical formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Parameterization of physical processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.2 Planetary boundary layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.3 The surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.3.1 Orography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.3.2 Land-sea mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.3.3 Sea-surface temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.3.4 Sea ice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.3.5 Surface albedo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.3.6 Ground cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.4 Gravity wave drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3.5 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3.6 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3.7 Clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3.8 The hydrological cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.9 Types of parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 Data assimilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4.1 Availability of conventional data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4.2 Variational analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

CHAPTER 2 — MESOSCALE MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Dynamical framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.1 Computer capability and model resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.2 Topography and vertical coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.3 Problems of the hydrostatic assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.3.1 Cumulus parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.3.2 Parameterization of non-convective cloud and precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3.3 Boundary layer processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3.4 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4 Data assimilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.4.1 Spin-up problems and initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.4.2 Use of asynoptic observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.4.3 Four-dimensional data assimilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

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iv METHODS OF INTERPRETING NUMERICAL WEATHER PREDICTION OUTPUT FOR AERONAUTICAL METEOROLOGY

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CHAPTER 3 — DIRECT USE OF MODEL OUTPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.1 Use of direct model output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1.2 Using locally produced displays of numerical weather prediction data . . . . . . . . . . . . . . . . . . . . . 313.1.3 Simplifying the use of interactive graphics systems in operational forcasting . . . . . . . . . . . . . . . . 36

3.2 Deriving meteorological diagnostics from the gridded data in forecast offices . . . . . . . . . . . . . . . . . . . . . . . . . 363.2.1 Deriving numerical weather prediction performance information . . . . . . . . . . . . . . . . . . . . . . . . 383.2.2 Detecting and monitoring development of tropical weather systems . . . . . . . . . . . . . . . . . . . . . . 403.2.2.1 Tropical upper-tropospheric trough . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.2.2.2 Upper-level cyclones in the tropics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.2.3 Phenomena affecting terminal forecasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.2.3.1 Diagnosing the development of diurnally foreced convection . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.2.3.2 Detecting interaction between sea breeze and mountain circulations in global model guidance 463.2.4 Phenomenological examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2.4.1 En-route icing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2.4.2 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2.4.2.1 Classical clear air turbulence forecasting techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2.4.2.2 Forecasting turbulence caused by other sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.2.4.3 Developing a new diagnostic forecasting tool for sandstorms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.2.4.4 Diagnosing severe weather potential using numerical model outputs — stability indices and

isentropic coordinate interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.3 Statistical interpreation of model output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.3.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.3.2 Statistical processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733.3.2.1 Defining the weather element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743.3.2.2 Selecting formulation methods and statistical analysis techniques . . . . . . . . . . . . . . . . . . . . . . . . 743.3.2.2.1 Formulation methods — PPM and MOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743.3.2.2.2 Statistical processing methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.3.2.2.2.1 Multivariate linear regression (MLR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.3.2.2.2.2 Regression estimation of event probabilities (REEP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.3.2.2.2.3 Multiple discriminant analysis (MDA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773.3.2.2.2.4 Classification and regression trees (CART) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783.3.2.2.2.5 Adaptive procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783.3.2.3 Preparing the dataset; choosing the predictors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.3.2.4 Testing the performance of the equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813.3.2.5 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813.3.3 Interpretation of statistical guidance products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813.3.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.3.4.1 Ceiling and visibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.3.4.2 Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.3.4.3 Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853.3.4.4 Clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863.3.4.5 Thunderstorms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.3.4.6 Turbulence — Clear air turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Appendix — Gridded meteorological guidance data through the World Area Forecast System (WAFS) . . . . . . . . 91

CHAPTER 4 — VALIDATION AND VERIFICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.1 Introduction: purpose of verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.1.1 Main areas of verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.1.2 Concept of “useful lead time” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.2 Methods of verification, underlying philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.2.1 Verification of gridded numerical weather prediction forecast fields . . . . . . . . . . . . . . . . . . . . . . 944.2.1.1 Ground truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.2.1.2 Standards of comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954.2.1.3 Aspects of forecast quality and verification of measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

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4.2.1.4 Verification measures for continuous variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.2.1.5 Verification scores for categorical variables (after Stanski, Wilson and Burrows, 1989) . . . . . . . 984.2.2 Validation of internal model fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.2.3 Verification of “weather parameters” (direct model output or derived parameters) . . . . . . . . . . . 994.2.3.1 Methods of verifying “weather parameters” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.2.3.2 Ground truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.2.3.3 Quality measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.2.3.4 Examples of the evaluation of individual parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.3 Guidelines for interpretation of systematic model behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054.3.1 Horizontal discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.3.2 Vertical discretization and coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.3.3 Advection schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.3.4 Hydrostatic versus non-hydrostatic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.3.5 Extra fields (cloud water, cloud ice, turbulent kinetic energy, etc.) . . . . . . . . . . . . . . . . . . . . . . . 1074.3.6 Evaluation of prediciton of rare events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.4 Evaluation of the prediction of hazard potential (aviation impact variables) . . . . . . . . . . . . . . . . . . . . . . . . . . 1084.4.1 Icing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1084.4.2 Clear air turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1094.4.3 Gravity wave activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

4.5 Evaluation of station forecasts for ceiling/visibility based on post-processed model output . . . . . . . . . . . . . . . 110

CHAPTER 5 — FUTURE TRENDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.1 Future observing system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115.1.1 Ground-based systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115.1.2 Airborne systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125.1.3 Satellite systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.2 Model and post-processing improvement trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135.2.2 Global models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135.2.3 Regional models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1145.2.4 Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.2.5 Computing power and communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.2.6 User feeback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

In view of the rapid developments in modern forecasting techniques and the potential benefit for the improvement of aero-nautical meteorological services in their application, the Commission for Aeronautical Meteorology at its eighth session inGeneva, November 1986, established a Working Group on Advanced Techniques Applied to Aeronautical Meteorology(ATEAM). In its terms of reference, the group was tasked to prepare and review guidance material on advanced techniquesand to advise on the use of numerical model outputs and also on the use of statistical methods and artificial intelligence inaeronautical forecasting.

In line with this mandate, the ATEAM working group agreed that this advice could take the form of a WMOTechnical Note. The Commission, at its ninth session in Montreal, September 1990, noted this suggestion with approvaland agreed that the proposed Technical Note would fill a perceived need, in particular in developing countries.

The first edition of Technical Note No. 195, Methods of Interpreting Numerical Weather Prediction Outputs forAeronautical Meteorology, was developed by ATEAM working group members and invited experts, and was published in1992.

The tenth session of the Commission for Aeronautical Meteorology which met in 1994 agreed with the view of theATEAM working group that Technical Note No. 195 should be reviewed in the time frame 1995-1996. As a result, theATEAM working group, composed of Mr Carr McLeod (Canada), Dr Herbert Pümpel (Austria), Mrs Masanori Obayashi(Japan), Mr Samuel Raboqha (Lesotho), Mr Gill H. Ross (United Kingdom) and Dr Ralph Petersen (United States ofAmerica), conducted an in-depth review and update of the first edition of Technical Note No. 195, which resulted in thissecond edition.

I thank all ATEAM working group members who gave much of their time and effort to develop this second editionof the Technical Note. I trust that this Technical Note will provide a most valuable contribution to the science of aeronau-tical meteorology and will continue to be a reference for aeronautical meteorology forecasters.

(G.O.P. Obasi)Secretary-General

FOREWORD

CHAPTER 1

GLOBAL MODELS

1.1 HISTORICAL BACKGROUND TO NUMERICAL WEATHER PREDICTION

In 1888 the hydrodynamicist H. von Helmholtz formulated the fundamental lawsof atmospheric motion necessary to describe atmospheric motion. These mathe-matical laws make up the complete set of hydrodynamic and thermodynamicequations. At the turn of the century, another hydrodynamicist, V. Bjerknes, sug-gested that the weather could be quantitatively predicted by applying thesephysical laws to a carefully analysed initial atmospheric state.

Bjerknes’s vision inspired a young mathematician and meteorologist,L.F. Richardson, to endeavour to compute weather forecasts along these purelymathematical lines. Very much ahead of his time, Richardson defined a primitiveequation model with a 300-kilometre grid and five vertical layers in which he setout to integrate the basic atmospheric equations. The result, published in 1922,was a disappointment. Not only did the flow pattern forecast appear to be a totalfailure, but Richardson determined that it would require 64 000 individuals toperform the manual computations just to keep pace with the weather itself. Theways of weather forecasting took other directions during the 1920s and 1930s,based to a large degree on conceptual models of the structure and evolution ofmid-latitude weather systems developed by Bjerknes and his colleagues at the“Bergen School”.

The period around World War II had a major impact on the future of modernmeteorology, and aviation forecasting in particular. Because the role of aircraft wasso extremely critical to the outcome of the conflict, extraordinary efforts were madeto improve aviation forecasting. The existence of the Jet Stream was first docu-mented and forecast products were routinely produced at constant pressure surfaces,since aeroplanes flew at these levels. Taking advantage of the new emphasis on theuse of constant pressure coordinates, Sutcliffe and Petterssen developed the firsttheory of cyclone development and atmospheric flow based on pressure coordi-nates, to provide the first of a series of more theoretically-based forecast tools.

After the end of the Second World War, the renewed exchange of meteoro-logical observations and the development of a hemispheric network of upper-airstations made daily analyses of the global circulation possible. At the same time,J. Charney and A. Eliassen extended the work of Sutcliffe and Petterssen in apply-ing the quasi-geostrophic equations to describe the large-scale evolution of abaroclinic atmosphere. Coincident with these observational and theoreticaladvances, the construction of the first electronic computer made the solution oflarge numbers of complex mathematical calculations feasible. The time was ripe fora new onslaught on the problem of computing the weather.

In 1946, the physicist and mathematician John von Neumann suggested to startfrom the simplest of all models — the barotropic equations of atmospheric motionwhere the evolution of the flow is determined by the effect of the conservation ofabsolute vorticity of an air parcel. This was taken as too simplistic an approach bythe theoretical meteorologists, who regarded it necessary to take account of thebaroclinic nature of the atmospheric flow if reliable forecasts were to be possible.Since all other approaches were too demanding on the computers available at thattime, the first experiments with a vorticity-conserving, barotropic model were madeand found to be surprisingly successful: the general mid-tropospheric flow patternwas forecast 2–3 days in advance with greater skill in mid-latitudes than previoussubjective methods. Even evolutions which looked baroclinic often turned out tobe mainly barotropic in nature. From the mid-1950s, with improved computerssome countries started operational numerical weather prediction (NWP) at500 hPa three days ahead using this simple barotropic model.

1.1.2BAROTROPIC MODELS

1.1.1FROM VON HELMHOLTZ TO

RICHARDSON

Though the barotropic model could produce useful forecasts at 500 hPa up to threedays ahead, its disadvantages were its restriction to the movement of existingstorms in the middle atmosphere and its inability to develop new storms in a baro-clinic environment. The 1950s saw intense efforts in several countries to explorethe baroclinic nature of the atmosphere. Several quasi-geostrophic models weredesigned where the computations were, in principle, made for the geopotentialheight fields, the winds and temperatures being derived as spatial derivatives. Thisallowed simple modelling of heating from below, friction and orography. Theincreased complexity introduced new problems and it was not until the 1960s thatthe baroclinic quasi-geostrophic models began to show operational utility, and thenonly for 1–2 days; longer forecasts were still made by barotropic models. By thattime, work was already under way, with the introduction, or rather the reintroduc-tion, of the primitive-equation model, Richardson’s old invention, though nowrefined and enlarged.

In the primitive equation (PE) model changes in wind, temperature and moistureare explicitly forecast using the equations of motion. Physical parameterizationssuch as convection, which are difficult to handle in the quasi-geostrophic model,are more realistically incorporated, so that the forecast domain can be extended tothe entire globe.

The first operational PE model was implemented in 1966, with approximatelya 300-km grid and six layers in the vertical. During the 1970s and 1980s severalother PE models were implemented, either hemispheric or global, or as limited areamodels, which ran on a higher resolution over a smaller area and took boundaryvalues from a larger hemispheric or global model.

A fundamental limitation of early NWP systems which both decreased the accuracyof the products and delayed their availability to forecasters was the lack of an auto-mated means of providing the initial height, temperature, wind and moistureanalyses necessary to run the model. In the early years, model initial conditionswere obtained by laboriously interpolating manually analysed charts onto pre-defined grid points. It was not until the mid-1950s that the current concept ofcorrecting short-range model forecasts (so-called “first-guess” fields) with observa-tional data was suggested and successfully tried. The impetus came from thecombined efforts of mathematicians and meteorologists who were inspired by newlyderived estimation theories and by conceptual models of the likely evolution of theatmosphere. Though their methods were refined during the 1960s and early 1970s,reducing errors in the numerical forecast first-guess fields was given greatest empha-sis. Today, the quality of the short-range model forecasts has reached the levelwhere the observations, in general, make only small changes to the first-guess fieldin most areas. In general, the analyses undergo substantial change only in data-sparse areas or in regions downstream of these areas, or when smaller-scale featuresare missing from the short-range model forecasts.

Present data assimilation and analysis systems have been further refined tomake better use of “unconventional” types of data (including satellite data and air-craft reports) and also better account for known forecast model behaviour.

The continued improvement both in forecast models and in better use of anincreasing number of total observations has led to a steady improvement in NWPforecast accuracy. The impact of these improvements on aviation forecast is, inmany respects, reflected by the 35 per cent decreases in 200 hPa vector wind rootmean square errors for verification of forecast versus observations between 1980 andthe present, as shown in Figure 1.1.

1.2 GLOBAL ATMOSPHERIC MODELS

Global models with similar overall characteristics are running at a number of NWPcentres around the world, including the United Kingdom Meteorological Office(UKMO), the United States National Centers for Environmental Prediction

1.1.5OBJECTIVE ANALYSIS

1.1.4THE PRIMITIVE EQUATION MODEL

1.1.3BAROCLINIC MODELS

2 METHODS OF INTERPRETING NUMERICAL WEATHER PREDICTION OUTPUT FOR AERONAUTICAL METEOROLOGY

(NCEP), the European Centre for Medium-range Weather Forecasts (ECMWF),the Canadian Meteorological Centre (CMC) and the Japan MeteorologicalAgency (JMA), among others. The degree to which they are used to support avia-tion forecasting varies, both for national and international users. In what follows,the typical characteristics of those models available in support of aviation forecast-ing is described.

Every model consists of two parts; the first consists of solving the equations ofmotion (called the dynamics part) and the second involves the parameterizationsof other processes that cannot be calculated explicitly (called the physics part). Amodel is characterized by its spatial resolution and the way in which the numericalcomputations are carried out.

The solution of six equations is required to determine future state of flow in theatmosphere. These equations are:

(a) The Gas Law of dry air, which gives the relation between pressure, density andtemperature;

(b) The equations of motion, which describe how changes in the wind velocity arecaused by the pressure gradient and the Coriolis force and friction;

(c) The thermodynamic equation, which expresses how a change in the temperature ofan air parcel is brought about by adiabatic cooling or warming due to vertical dis-placements, latent heat release, radiational heating and cooling, and frictional orturbulent processes;

(d) The equation of continuity for dry air, which ensures that its mass is conserved andmakes it possible to determine the vertical velocity and changes in the surface pressure;

(e) The continuity equation for moisture, which assures that the moisture content ofan air parcel remains constant, except for losses due to precipitation and conden-sation or gains by evaporation from clouds, rain or moisture on the Earth’s surface;

(f) The hydrostatic equation, which shows the relationship between the density of theair and the change of pressure with height and removes vertically propagatingsound waves from the model solution in hydrostatic models. The hydrostaticassumption eliminates the vertical component of the equations of motion.

Numerical weather prediction models use either grid point representation for all oftheir computation or a combination of spectral representations of some horizontalfield along with certain grid point fields. The advantage of the spectral technique isthat computational errors are reduced for certain calculations, most notably

1.2.2SPATIAL RESOLUTION

Horizontal resolution

1.2.1THE BASIC EQUATIONS OF MOTION

CHAPTER 1 — GLOBAL MODELS 3

Figure 1.1North Atlantic

200 hPa root mean square wind vector error

Against analysisAgainst observation

Kno

ts

advection, than when using the conceptually more straightforward grid pointmodels. In the spectral technique, horizontal atmospheric waves around the globeare divided into series of longer and shorter wavelength components and thenrepresented as a series of trigonometric functions. In the spectral system, it is stillnecessary to perform many calculations in grid point coordinates. For example,vertical motion and precipitation, though forced by effects calculated in the spectralcoordinate, are still calculated at grid points. Likewise, radiation calculations areperformed on this same grid.

Current global grid point models have grid spacings of about 60 km measuredin mid-latitudes. Since approximately five grid points are needed to define thesmallest features on scalar fields that can be predicted accurately with the models(see Chapter 2, Figure 2.3), this corresponds to a minimum resolvable wavelengthof about 300 km. Current operating spectral models use from 126 to 240 waves todescribe the flow in the atmosphere thus resolving similar scale features as the gridpoint models.

Within all NWP models, the atmosphere is divided into a series of layers, more than30 in most models. The vertical resolution is usually highest in the planetaryboundary layer, where the levels follow the Earth’s surface and must be closelyspaced to realistically simulate the diurnal effects of surface heating and cooling,and in the upper troposphere/lower stratosphere. In between, a smooth transition isrequired to retain maximum computational accuracy. In spectral models, where thetime step can be much larger than in grid point models, the vertical spacing must beleast in the region of maximum vertical motion — usually between 250 and500 hPa, the general level of the polar jet/front. This coarseness can affect theability of spectral models to preserve upper-level frontal systems and their associatedwind maxima. Vertical discretization is usually done in so-called sigma coordinateswhereby sigma is defined as the ratio of pressure to surface pressure thus followingterrain elevation.

The sigma-pressure hybrid vertical coordinate was introduced to solve theproblem in the sigma coordinate that terrain-following surfaces are used even in theupper level, where the atmospheric flows are generally not affected by the topo-graphy. The hybrid coordinate is identical to the sigma coordinate in the lowerlevels at which topographic effects are large, but gradually changes toward the pres-sure coordinate as the levels go up (Figure 1.2).

Another inherent disadvantage of all terrain-following coordinates is that thepressure gradient force calculation may contain large errors in steep mountain areasleading to significant wind errors. This problem in the calculation of the pressuregradient force along the terrain-following surfaces becomes serious as the horizon-tal resolution increases, since higher resolution means steeper mountains.

In order to solve the six basic equations numerically, they have to be expressed ina finite difference form in the time dimension as well as horizontal and vertical. Inother words, the NWP model calculates the tendency of forecast variables based on

1.2.3THE NUMERICAL FORMULATION

Vertical resolution


1000850700

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Figure 1.2Sigma and hybrid vertical coordinates Sigma vertical coordinate

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the current (t = T) state of the model atmosphere, and estimates the value of thesevariables at a future time (t = T + Dt). The model repeats the same calculation untilthe accumulation of the time reaches the target forecast time. The longer the timestep interval, the fewer number of computation procedures required, and thereforeless computation time is needed. However, too long a time step interval causes acomputational instability.

The maximum time step is theoretically defined as:

Dt < Dx/c (1)

where c represents the speed of the movement of the disturbances and Dx is the gridinterval. A conceptual explanation of this is that the time step cannot exceed thetime needed for an air parcel to travel from one grid point or from one level to thenext.

Semi-Lagrangian approaches were proposed to increase the time step used ingrid point calculations and thus to reduce computing costs. In a semi-Lagrangianscheme, at each step, a backward trajectory is computed from every grid point. Thepoint reached defines where the air parcel was at the beginning of the time step.The value of the variable in that point is then carried forward to the grid point,applying various physical processes. The time step of the semi-Lagrangian model isdefined not by the computational stability constraints but by the accuracy require-ments. In current operational models, the time step can be four times longer usingthe semi-Lagrangian method than the pure Eulerian method.

The speed of the movement of the disturbances, c, does not have to be theadvection speed, but could be the speed of any disturbance in the horizontal or thevertical. Primitive equation models have disturbances called gravity waves. Thesewaves may travel much faster than typical maximum wind speeds. A semi-implicitscheme is used in most of the models to treat these waves separately in a stablemanner, and thus the time steps in real models are bound by the maximum windspeeds and the grid spacing.

1.3 PARAMETERIZATION OF PHYSICAL PROCESSES

Physical processes such as the hydrological cycle, convection or surface fluxes need tobe included in forecast models to ensure realistic simulations of the atmosphere, andthey can be used operationally to predict weather parameters required for public orterminal area forecasting. A global circulation type model makes it absolutely neces-sary to include processes with relatively long timescales including major effects such assolar radiation and minor effects such as evaporation from vegetation, in order tohandle the flow pattern in the large scale correctly. The different timescales and feed-back mechanisms between individual processes make the computations extremelycomplex and time-consuming. The mechanisms for some of these processes are relatedto scales which are much finer than those resolved by the model grid and their effectson the large-scale properties can only be estimated by parameterization, i.e. relatingthem to the values of the known variables at the grid points.

The planetary boundary layer (PBL), the lowest part of the atmosphere, plays a fun-damental role for the whole atmosphere-earth system. It is through the surfaceexchanges of momentum, heat and moisture that the atmosphere “feels” that itmoves over a rough land surface or a wet smooth sea. It is mostly through the trans-fer of heat and moisture at the surface that the energy of the sun is injected into theatmosphere, fueling the atmospheric motion.

In all global models the vertical resolution is highest near the surface. Even withthis fairly high resolution the vertical gradients of temperature, wind, moisture, etc. inthe PBL cannot be described very accurately, let alone the turbulent transports ofmomentum, heat and moisture. For the estimation of these parameters the model usesthe larger-scale variables such as wind, temperature and specific humidity, with theassumption that the transports are proportional to the vertical gradients. At the Earth’s

1.3.2PLANETARY BOUNDARY LAYER

1.3.1INTRODUCTION


surface, the turbulent transports of momentum, heat and moisture are computed as afunction of air-surface differences and surface characteristics.

Characteristics of the Earth’s surface such as roughness, vegetation, snow cover,sea-ice distribution, surface albedo, etc. strongly influence the fluxes of momentum,heat and moisture in the lowest model layers. Therefore, soil properties are requiredfor a realistic simulation of PBL. Over land areas, snow depth, soil temperature andwetness are forecast variables, typically calculated by a model of the soil compris-ing several layers.

The mountain massifs of the Earth are known to influence the circulation patternthrough dynamic and thermal forcing. In coarse mesh global models, averaging theheight of the orography over a grid square can lead to an underestimation of barriereffects and introduce exaggerated thermal forcing from elevated sources of heat andmoisture. Spectral fitting of steep orography in coastal areas (e.g. off the Chilean coast)may lead to unrealistically undulating surface fields over the adjacent oceans.

With increasing horizontal resolution the need to artificially enhance the oro-graphy is reduced, and artful algorithms have been devised to reduce the unwantedthermal effects of steep topography (‘heat islands’) particularly on convection.Model orography is adapted from very-high-resolution databases of approximatelyone kilometre resolution.

While the grid is chosen for a numerical model effectively by the amount of avail-able computer time, the accuracy of the surface representation is dependent on theresolution of the geographical data which are available. Land surface parametershave to be identified from these data, but at a coastal boundary a decision usuallyhas to be taken whether the grid point is a land or a sea point, although the gridsquare may be part land and part sea. Whilst at the boundary between sea and ice,the ratio of sea to ice can give a good representation of the partition of the heat andmoisture transport, the land-sea fraction is less useful since, for example, it cannoteasily represent different soil types.

A sea-surface temperature (SST) analysis is required to run a model, but not allcentres running global models perform their own SST analysis. Such an analysis istypically based on ship, buoy and satellite observations. It is generally of high qual-ity, but in small bodies of water rapid changes in SST can take place during the coldseason, thus the real SST can sometimes differ by as much as five degrees from theanalysis. Also in areas where there are few data, there can be large differencesbetween real and assumed SST. The SST over ice-free water is kept constant duringthe forecast for short- to medium-range forecasts.

Sea-surface temperatures are updated approximately every three to six days andare analysed at approximately 60 km resolution.

The sea-ice distribution typically obtained from a separate, independent, sea-iceanalysis is updated every week. The temperature at the surface of the ice is variable,according to a simple energy balance/heat budget scheme. The distribution of sea-ice points is often kept constant during the forecast; no freezing of the water ormelting of the ice is allowed.

Typically, a seasonally varying background climate field is used, according to which thealbedo is set to specific values over sea ice and over open water. The model is able toalter the surface albedo during the run only in response to changes in snow cover.

The parameterizations of the exchange of heat, moisture and momentum betweenthe Earth’s surface and the bottom of the atmosphere take into account many fine-scale processes. These include, inter alia, the distribution of soil and water, as wellas soil type, vegetation type and snow cover. The soil itself can be represented by amultiple layer model, including soil hydrology and evapotranspiration of waterfrom below ground to the atmosphere by plants.

1.3.3.6Ground cover

1.3.3.5Surface albedo

1.3.3.4Sea ice

1.3.3.3Sea-surface temperature

1.3.3.2Land-sea mask

1.3.3.1Orography

1.3.3THE SURFACE


The temperature in the topmost portion of the soil can change due to the com-bined effects of solar heating, subsurface heat flux and infrared cooling. In snowcovered areas, however, the soil temperature is typically constrained to the freezinglevel whenever snow cover is present. The snow cover itself is allowed to changeduring a forecast run, depending on the initial analysis, predicted snowfall accu-mulation and melting. In other areas, the amount of heating of the atmosphere dueto solar radiation depends on soil colour (which affects the reflection of incomingsolar radiation), the soil moisture content and vegetative growth.

Moisture is allowed both to accumulate on the Earth’s surface, to filter down-ward into the soil, to evaporate into the lowest atmosphere, and to be transportedfrom below the Earth’s surface into the atmosphere through parameterization ofparts of the photosynthesis process within plants. The degree of evapotranspirationis regulated by knowledge of vegetation type and growth activity, with activelygrowing plants using the greatest amount of solar radiation for growth (resulting insmaller atmospheric temperature changes) and transporting substantial amounts ofmoisture into the atmosphere. Surface water is allowed to change from the initialanalysis by including forecast rainfall and runoff into streams. In areas of wet soil,the primary use of daytime solar radiation is to evaporate water, especially overbare, dark soil.

Over large bodies of water, exchanges of both heat and moisture are allowed,depending on the surface temperature of the water and the amount of wave actioncaused by surface wind stresses. Once ice-covered, the bodies of water act the sameas snow-covered land. In the near future, both global and regional models mayinclude coupled ocean models to allow the sea-surface temperature and wave fieldsto vary during a forecast period.

Gravity waves excited in stably stratified air flowing over mountains are able toexchange momentum between the ground and higher layers of the atmosphere.Changes in vertical stability and cross-barrier wind speed may cause wave breaking,thus greatly amplifying the pressure drag exerted on the surface. Proper representa-tion of these processes is necessary to correctly represent the slowing down of theupper-level flow and typical surface pressure pattern. Operational gravity wave dragschemes are parameterized depending on static stability and wind profile, thusshowing a marked seasonal variation (strong damping in winter, weak effect insummer). There is also potential to implement algorithms for the detection of gravity-wave turbulence for aviation forecasting.

In view of the importance of cloud-radiation interaction for the surface energy budget,high emphasis has been placed on the treatment of the absorption and scattering byclouds of solar and terrestrial radiation. About one-fifth of the overall computationaltime is devoted to the radiation scheme, as much as for the dynamics.

The radiation spectrum is divided into a number of frequency bands, both in theshort-wave (incoming sunlight) and long-wave (outgoing Earth’s radiation) portionsof the spectrum. Both the upward and downward radiation are computed for each spec-tral band. The forecast parameters influencing the emission and absorption are pressure,moisture, cloud cover and cloud water content. Other input parameters that can affectradiation processes include the ground albedo (modified according to the snow cover),the solar radiation flux (which varies with time of year and time of day) and theconcentrations of carbon dioxide, ozone and other aerosols. The radiation schemes arealso designed to take the cloud-radiation interactions into account in considerabledetail, allowing for variable cloud cover in any layer of the model.

Convection processes move heat and moisture from near the surface up into theatmosphere. Simple convective adjustment schemes detect the stability of the airat each grid point, and adjust the temperature and humidity in each layer above thepoint which is reached by the convection. The adjustments are based on the vigourof the convection and estimates of the cloud coverage within the grid box and arebound by conservation of energy and moisture laws. More recent schemes are ratherbetter at modelling the physics of the process, as parameterizations developed for

1.3.6CONVECTION

1.3.5RADIATION

1.3.4GRAVITY WAVE DRAG


mesoscale models are adopted for increasingly higher resolution global models.Column convection is set off by surface evaporation and the contribution of areasaround the column using moisture convergence at low levels and the entrainmentof air at higher levels. The more realistic physics modelled in the sub-grid convec-tion gives a more accurate estimate of convective precipitation and a betterestimate of the amount of convective cloud.

There are three classes of convective parameterization schemes in common usein NWP and general circulation models. In order of increasing complexity andincreasing physical realism these are: convective adjustment schemes, the Kuoscheme (and variations such as the Anthes-Kuo scheme) and variations of theArakawa-Schubert scheme. A survey of all three may be found in Washington andParkinson (1986). In addition, there are many mesoscale convective schemeswhich are under development.

Convective adjustment has been used in atmospheric models since the mid-1960s. It attempts to model convective overturning caused by verticalthermodynamic instability in the atmosphere. The scheme accomplishes this byidentifying layers of the model atmosphere that are unstable with respect to eitherdry or moist convection, depending on the moisture in the layer. If an unstablelayer is found, then the lapse rate is modified to remove the instability. In thisprocess, the moisture profile must be altered to prevent supersaturation, with theexcess moisture falling out as precipitation, the latent heat of condensation warm-ing the column. The entire procedure is constrained by the requirement that thesum of the internal, potential and latent energies is constant.

The main advantages of this scheme is that it is simple to apply, easyto understand and computationally rapid. However, it often producesexcessive precipitation and overcools the lower troposphere. Also, the schemeoversimplifies the physics of the problem. Attempts have been made to improve theresults by empirically altering the thresholds for adjustment, but this approach is notphysical.

The Kuo scheme is based on the observation that significant precipitation isassociated with low-level moisture convergence. The diabatic heating due to cumu-lus convection is proportional to the product of the column moisture convergenceand surface evaporation, the low-level relative humidity and the convective parcelexcess temperature (a measure of the degree of instability) including the effects ofentrainment of dry air into the rising parcel. A coincidence of strong moisture con-vergence, evaporation, high humidity and convective instability results in strongconvection and latent heat release. Thus, the Kuo scheme captures the essentialphysics of large-scale cumulus convection. In comparison with convective adjust-ment schemes, the improved physics of the Kuo scheme results in improvedmoisture, temperature and precipitation forecasts, but still either underforecasts oroverforecasts many convective weather systems.

The Arakawa-Schubert scheme was devised as a means of more realistic mod-elling of the interaction between the cumulus and the environment. It tries toaccount for more processes by introducing a number of unique cloud models.Shallow and deep convection models are created and interact with each other andthe environment. Each cloud component has a mass budget, heat budget and mois-ture budget, entrainment of dry air and each component is strongly coupled to theboundary layer. Ascent within the cloud, compensating subsidence between cloudsand the evaporation of detrained cloudy air are all included.

About half of the globe is covered with clouds at any one time. They reflect around20 per cent of the solar radiation to the Earth and absorb two per cent of it. Thelong-wave radiation from the Earth cannot penetrate the clouds and is absorbed.Instead the clouds emit long-wave radiation according to their temperature, whichaltogether counts for more than a quarter of the long-wave radiation from the Earthto the space. It is therefore important to estimate the impact of the cloud to simu-late the radiation process properly within a model.

The radiation characteristics of clouds depend on the cloud amount and thecloud type, such as whether the cloud is formed of water droplets or ice, and the size

1.3.7CLOUDS


distribution of the cloud particles. However, most current operational globalmodels, which do not simulate the cloud processes in such detail, simply determinethe cloud amount and optical thickness using the relative humidity and verticalvelocity at each grid point. It may also be estimated using the amount and type ofcondensate if the model explicitly deals with cloud processes. In either case, thecloud parameters are determined by their empirical relationship with the predictedmeteorological elements.

In order to simulate the radiation processes associated with clouds as realisti-cally as possible, different relationships between the cloud parameters and thepredicted elements are employed at different vertical levels, in different convectiveenvironments, etc. Thus the model distinguishes among, for example, outflow fromdeep convection, low and high clouds associated with fronts, and low clouds linkedto the boundary layer.

When there are clouds at more than one layer at the same grid point, the totalcloud amount is computed taking into account the nature of overlapping. Again,the overlapping property is determined empirically, typically as a combination ofmaximum and random overlap of the model layers. Maximum overlap meansselecting the largest value in the cloud amount, assuming that clouds at differentlevels are overlapped with each other at maximum.

Random overlap assumes that the portions of cloud cover at different levels areindependent of each other, and gives the total cloud as the addition of independentprobabilities: for example, two layers with cloud amounts of 50 per cent and 50 percent constitute a total amount of 75 per cent.

Mechanisms to generate both convective and stratiform (frontal or dynamical) pre-cipitation are included in NWP models. When convection occurs, it is assumed tomove directly to the ground as either rain or snow. No ice crystals or liquid waterare stored in clouds or allowed to float in the air as cloud particles. A portion of thefalling precipitation can moisten the atmospheric environment below by evapora-tion, but the remainder falls out of the cloud as precipitation.

Stratiform precipitation, both in the forms of rain and snow, is produced oncethe relative humidity reaches a certain threshold, typically ranging from 90 to 100per cent. The type of precipitation depends on the temperature of the layer wherecondensation takes place. Again, condensation is generally not stored as clouddrops or ice crystals, but a portion can evaporate as it falls to the ground. Transitionfrom ice to water can also occur when the precipitation passes through layers withtemperatures sufficiently warm to melt the failing snow. In general, freezing waterto ice pellets is not considered in the model.

Evaporation: It is assumed that precipitation falling from a saturated layer satu-rates the first layer underneath before reaching the next layer below. This maysubstantially reduce the precipitation on the ground. Evaporation of the precipita-tion is not assumed to take place within the cloud, only between the cloud base andthe ground. The layer below a precipitating, non-convective cloud is always almostsaturated.

Figures 1.3 and 1.4 depict the types of parameterization which must be modelledfor a simple ground surface (Figure 1.3) and a more complex vegetation surface(Figure 1.4).

The processes involve solar radiation which is reflected by the surface or scat-tered upwards or downwards from clouds or absorbed within the clouds, heatingthem up. Heat is transmitted into the soil or transferred by conduction to the air incontact with the ground where, through mixing, it is transferred to higher levels.Long-wave radiation is transmitted from the surface and is absorbed by clouds orescapes to space. In the cloud, long-wave radiation at the cloud temperature isretransmitted upwards to space or back down to the surface.

For more complex surfaces, other mechanisms must also be modelled. Solarradiation is absorbed by leaves and, through conduction, warms the air.

From the ground, moisture is extracted through the root system and, throughevapotranspiration, moistens the air.

1.3.9TYPES OF PARAMETERIZATION

1.3.8THE HYDROLOGICAL CYCLE


1.4 DATA ASSIMILATION

Since the introduction of the first objective analysis techniques in the 1950s, theprocess of obtaining the initial conditions for NWP models has evolved from oneof analysing the full data values themselves, thus limiting the analyses primarily todata-rich areas and using interpolation to “fill in” the regions between data points.Today’s procedures of modifying short-range forecast “first-guess” fields withcorrections dictated by the observations have several advantages, including:

(a) The ability to provide initial conditions in data-sparse areas;(b) The ability of short-range forecasts used as first-guess fields to “remember” and

move previous observations, so areas between observations can contain betterinformation than available through interpolation alone; and

(c) The ability to account for differences in quality and utility using different observ-ing systems, as well as the expected error in the forecast first-guess fields.

The following discussion provides more detailed information on the full analysisprocess.

In many areas of the globe, the density of available conventional observations (pri-marily rawinsondes) is adequate in order to capture the structure of synoptic scale

1.4.1AVAILABILITY OF CONVENTIONAL DATA


A

BB

E

LG

K

N

M

H

K

Figure 1.3If a moist layer is predicted, some ofthe incoming solar radiation will bescattered upward and downward,

reducing the net incoming radiationand surface heating. Likewise,

outgoing long-wave radiation will beabsorbed and retransmitted upward

and downward

Figure 1.4Accurate radiation requires detailed

boundary layer information

A

B

C

C

D

E

F

G

HH

D

J

JJ

I,

J

systems. In other areas, however, the types of data available, the spacing and the timeinterval between observations fall far below what is needed to drive the analysis withthe required accuracy. In those areas, the assimilation must rely on a number of lessconventional data sources, including pibals, aircraft reports, satellite temperature,humidity and wind data, etc.

Before being passed on for analysis, the observations are decoded and are sub-jected to quality control procedures. The quality control checks that the reportedvalues are realistic and makes corrections for data transcription and communicationerrors, such as inverted digits, incorrect temperature signs, etc. These checksinclude hydrostatic and superadiabatic temperature checks, checks for supersatura-tion, check of the displacement of ships, aircraft and drifting buoys, etc., asconforming to WMO recommendations.

Serious difficulties can arise from the highly varying quality of the data thatcan occur from one station to another and from one time period to another. Regularmonitoring of all observations used in the data assimilation is performed at allNWP centres. Statistics on the differences between the observed values and thefirst-guess fields are regularly accumulated to identify potential problems either inthe data (in which case the observation site is informed of the problem) or theshort-range forecasts used as the analysis first-guess (in which case attempts aremade to improve the model performance). Consistently large differences or largerandom differences between the observations and the first-guess field are used asindicators of observational errors, as are large differences in comparisons of theobservations with neighbouring reports, while most other types of error are due tomodel limitations.

Figures 1.5 to 1.11 show the global distributions of different types of data.Figure 1.5 shows the spread of rawinsonde reporting sites which report at 1200

UTC and 0000 UTC. The spread reflects population density as well as communi-cation difficulties. There are large areas of Africa (and at different times, SouthAmerica) which either do not have rawinsondes or have difficulty communicatingresults to the Global Telecommunication System.

Figure 1.6 shows the distribution of sea-surface reports. The ship observationshave the highest density in the commercial shipping areas, but this is augmentedby drifting and static buoys.

Figure 1.7 shows the location of aircraft reports (AIREPS and AMDAR) for asix-hour period around 1200 UTC. The long lines of reports are modern ASDARand the isolated reports which clutter around longitude lines are manually generatedAIREPS. At different times of the day there are other long-haul tracks betweenAustralia and Europe and across Africa.


Figure 1.51200 Z global

rawinsondes

Figure 1.8 shows the very high density automatic aircraft reports over theUnited States where the observations are gathered on VHF.

Figure 1.9 shows the distribution of satellite cloud tracked winds from geo-stationary satellites. Most of these observations are over the sea where clouds canbe identified from one satellite picture to the next.

Figure 1.10 shows the range of polar satellite temperature and humidity sound-ings on a typical day around 1200 UTC. The soundings come to swathes below thesatellite track.

Figure 1.11 is a typical day’s value of Defence Meteorological SatelliteProgram (DMSP) microwave precipitable water and surface wind from an orbitingsatellite.

In recent years, the variational method has replaced the older optimum interpola-tion as the preferred method of data assimilation for global models. Variationalmethods have the advantage of flexibility, particularly for the assimilation of

1.4.2VARIATIONAL ANALYSIS


Figure 1.6 (top)Northern hemisphere marine

observations — 12-hour total

Figure 1.7 (bottom)1200 Z aircraft wind/temperature

reports

White = Buoy observationsBlack = Ship and C-MAN observations

remotely sensed data. The basic concept is to blend model and data together in anoptimal way, extracting information about the weather element from both sources.

Variational assimilation involves two steps, the forward step and the variationalstep. In the forward step, the model first-guess field (usually a short-term forecastvalid at the analysis time) is used to estimate the observation at the observationlocation. For standard observations such as geopotential heights, this may simplymean interpolating the trial geopotential height to the observation location.However, for remotely sensed data, where the physical parameter is not observeddirectly, the forward step is more complicated. For example, satellites measure radi-ances. The forward step then involves translating the trial field of the model intoan estimate of the satellite radiance at the observation location, which means thatthe relationship between satellite radiances and the physical fields represented by


Figure 1.80000 Z North American automated

aircraft reports

Figure 1.91 200 Z geostationary satellite cloud

tracked winds

the model must be used. The goal is always the same — to obtain the model coun-terpart of the data at the observation location.

Once the forward step is completed, the differences between the trial and theobservation can be computed. These differences are then used, along with priorknowledge of the accuracy of the model and the observations, to obtain a “best”analysis. This is the variational step and it is iterative, which means it can beexpensive in terms of computer time. The prior knowledge of model and observa-tion errors acts as a weight in the variational step. If, for example, the observationis known to have large errors (it is unreliable), it will be given relatively low weightand the analysed value will be nudged toward the model trial value in the varia-tional step. If the observation is considered highly accurate and representative, themethod will move the analysed value toward the observation.

Variational techniques come in two different formulations, three-dimensionaland four-dimensional variational analysis.


Figure 1.10 (top)12 000 polar satellite

temperature/humidity soundings

Figure 1.11 (bottom)12 000 DMSP microwave

precipitable water/surface winds

The 3DVAR method is set up in much the same way as older analysis methods, that is,data are assimilated at a particular time, usually prior to each run of the model, to provideinitial conditions for the model. Three-dimensional refers to the three spatial dimen-sions, but also indicates that all the data that contain information about a particularweather element are considered at once. Such a formulation automatically considersthree-dimensional correlations that exist in both the observation and the model datasets. All the available data and all the model grid points are analysed together.

Although 3DVAR can automatically account for spatial relationships (correla-tions) among the variables, there is no guarantee that two analyses separated by, forexample, six hours would represent a physically reasonable evolution of the atmos-phere over six hours. Four-dimensional variational analysis takes into account thetime dimension in the analysis. It does this by using the model as a constraint onthe variational step of the analysis. For example, the estimate of the “best” analysismust now be determined in light of whether the analysed value of the variable rep-resents a consistent evolution of the atmospheric state. Once again, all the data andall the model grid points are analysed together, but with 4DVAR, data can beinserted at any observation time.

Four-dimensional variational analysis has not been used operationally becauseit has been prohibitively expensive in computer time up until now. Including themodel as constraints means essentially that the model (or a simplified form of it) isrun during the variational step. However, 4DVAR is regarded as the most flexibleway of optimally merging data and models together.

Four-dimensional variational analysis(4DVAR)

Three-dimensional variational analysis (3DVAR)


CHAPTER 2

MESOSCALE MODELS

2.1 INTRODUCTION

Weather at an airport is affected by complex combinations of phenomena of differ-ent scales. Take winds, for example. Winds on average over a few hundredkilometres around the airport are determined by the synoptic scale features. If thereis a low pressure to the south of the airport in the northern mid-latitude, the pre-vailing wind around the airport is easterly. However, local phenomena may alterwinds immediately at the airport. Figure 2.1 shows the horizontal and temporalscales of various atmospheric phenomena. For example, land and sea breezes cansignificantly change the wind direction and speed between mid-day and evening.The terrain of various scales around the airport can also produce significant localvariations to the flow expected from the synoptic features. A small mountain nearthe airport may strengthen, weaken or affect the direction of the wind in its vicin-ity. Furthermore, the wind over the runway may not be the same as that over itssurroundings due to the different nature of the surface.

Global numerical prediction models have been successfully applied to aviation,mainly to the wind and temperature forecasts for flight planning purposes and tosupport en-route flight decision-making. However, current global models are stillunable to give sufficiently detailed guidance for terminal area forecasts. Local fore-casts require even higher resolution to represent small atmospheric structureswhich have crucial influence on the weather at the airport. High-resolutionmodels, which are capable of simulating an increasing number of small-scale atmos-pheric phenomena, are expected to become increasingly important in providingguidance for terminal forecasts.

The basic formulation of high-resolution models is the same as that for globalmodels, except that to predict the smallest scale phenomena possible, such models musthave increased spatial and temporal resolution and more detailed parameterizationschemes. The dynamical framework of high-resolution models is discussed in 2.2.

Even in a high-resolution model, parameterization of unresolvable processes isnecessary. However, different schemes may have to be employed in a high-resolu-tion model than those used in global modelling. Some topics related to theparameterization problems in high-resolution models are introduced in 2.3.

The quality and detail of initial fields used for numerical prediction play anespecially important role at the small scale. Detailed and precise short-term fore-casts are required for safe and efficient aircraft operations. Therefore, muchattention must be paid to the initial condition of the numerical models, which havea very large impact on the forecasts both over the first few hours and the next sev-eral days. The initialization problem of the models is discussed in 2.4.

Figure 2.1Various atmospheric phenomena and

their scales

10 000 km

1 000 km

100 km

10 km

1 km

100 m

Second Minute Hour Day Week

Mid-latitudeLow and High

Easterly waveTropical cyclone

Wake turbulence

Cloud clusterSea land breeze

Thunderstorm

Monsoon

2.2 DYNAMICAL FRAMEWORK

High-resolution models require powerful computers. For example, if the grid inter-val in a model is reduced by half for both horizontal and vertical directions, sixteentimes more speed and eight times more memory are required in the computer toproduce forecasts for the same domain within the same elapsed time. In order tomake the best use of the available computer resources, most high-resolution modelsare limited area models.

Unlike global models, limited area models must deal with the problem of thelateral boundary conditions. In experimental simulation models, artificial or idealboundary conditions, such as cyclic conditions, are often given. However, in oper-ational forecasting, the lateral boundary conditions are usually obtained from alarger scale model, such as a global model. These data are necessary to account fordisturbances which are outside the forecast domain at the initial time, but whichcan affect the forecasts as the model integration proceeds. It should be noted thatappropriate boundary conditions need to be carefully considered to assure stableintegration and to avoid inconsistencies due to the different nature of the modelwhich provides them.

A different approach is now used in the ARPEGE model at Météo-France.This model is a global model, but with a variable horizontal resolution in which thegrid points are distributed so that resolution is highest in France and decreasessteadily going away from it. Thus, this approach to high-resolution models reduceslateral boundary problems. A similar approach was also taken at the CanadianMeteorological Centre (Figure 2.2).

Currently most operational high-resolution models are grid point models with gridintervals of around 10 to 50 km. As indicated in Figure 2.3, a disturbance in the atmos-phere should only be included in a forecast if its wavelength is five or six times as longas the grid interval. A model sometimes produces waves of shorter wavelength thanthis. However, these waves are only computational artifacts and are not meteorologi-cally meaningful. Therefore, in interpreting the NWP products, features with

2.2.1COMPUTER CAPABILITY AND MODEL

RESOLUTION


Figure 2.2The Canadian Meteorological Centre

variable horizontal model

Figure 2.3Demonstrates the effect of grid

interval on the model’s ability toresolve atmospheric phenomena of

varying wavelengths

grid interval

Scale of the disturbance

grid interval

wavelength less than the five or six grid intervals should be neglected and not be under-stood as very small-scale weather patterns.

Spectral mesoscale regional models are also in operation at the JapanMeteorological Agency and have been tested at the NCEP in the USA. The spectralapproach has the advantage of high accuracy in mathematical calculation and theabsence of the dispersion problem since the phase speed of the waves at all the resolv-able wavelengths are realistically calculated, unlike the grid model showing delay inthe propagation of small-scale waves.

It is normal to choose a projection of the Earth’s surface which minimizes distor-tion of the model grid. In mid-latitudes, the model grid system is often laid on apolar-stereographics, Lambert conic conformal or rotated latitude-longitude grid. Intropical areas, latitude-longitude or Mercator projection are more common.

The treatment of topography in a model has a large impact on its forecasts. Theresolvable scale of the model topography is basically limited in the same way as theresolvable phenomena. Higher resolution models do particularly well in represent-ing topographically forced changes to flow patterns including enhancedprecipitation on the windward side of mountain chains. The influence of topo-graphy on local convection appears to be more complex and difficult to model.

A good example to show the impact of the resolution of topography on theforecasts is illustrated in Figures 2.4 to 2.8. In this experiment, a forecast withdetailed topography is compared with that using smoothed topography. All theremaining features of the model are identical; the grid interval of both models is10 km, and the two models have the same physical parameterizations. Figure 2.4depicts the surface wind fields observed in Kanto Plain in Japan, and a clear shearline is seen. Figure 2.5 presents the surface winds forecasted by the model withsmoothed topography shown in Figure 2.6. Figure 2.7 shows the surface predictedwinds by the model grid interval with the high-resolution topography shown inFigure 2.8. The position of the predicted shear line with high-resolution topography

2.2.2TOPOGRAPHY AND VERTICAL

COORDINATE

CHAPTER 2 — MESOSCALE MODELS 19

Figure 2.4Surface wind fields observed in

Kanto Plain, Japan. A clearsheer line is seen


Figure 2.5Surface winds forecasted by the model

with smoothed topography shown inFigure 2.6

Figure 2.6Smoothed topography used for

calculations in Figure 2.5


Figure 2.7Surface predicted winds by the model

grid interval with high-resolutiontopography shown in Figure 2.8

Figure 2.8High-resolution topography

used for calculations in Figure 2.7

is closer to the observation than that with smoothed topography, which has aneastward shift of the shear line.

In order to make the model calculations agree better with what is actually hap-pening, some advanced vertical coordinates have been proposed and used inoperational models. Where sigma or hybrid coordinates (Figure 1.2) are used inmesoscale models, errors in mountainous areas increase as the resolution increases.A ‘step-mountain’ coordinate was developed as a solution to this problem and nowis used in some operational high-resolution models. In this coordinate, the coordi-nate surfaces are quasi-horizontal and the mountains are depicted in ‘step-like’shapes (see Figure 2.9).

Isentropic coordinates have been recognized to have advantages over pressurecoordinates in areas of nearly adiabatic flow, near frontal zones and around the levelof the jet stream. (This will be discussed further in 3.2.4.4.) In an isentropic model,vertical structure around fronts and the tropopause is automatically well resolved,and the advection is calculated with high accuracy along the model surfaces whichare, in the absence of diabatic processes, the surfaces that the atmosphere parcelsfollow. The first operational model using the isentropic coordinate is the RapidUpdate Cycle (RUC) of the National Oceanic and Atmospheric Administration(NOAA), USA. The inherent difficulty of the isentropic coordinate in neutral orunstable boundary layers was solved by introducing a hybrid isentropic-sigma co-ordinate in which the isentropic surfaces aloft merge with a high-resolutionterrain-following coordinate near the Earth’s surface (Figure 2.10).

Virtually all of the current operational numerical prediction models are hydrostaticmodels. These models assume that the vertical acceleration has little impact on theatmospheric motions that it can be ignored. The vertical velocities are, instead,diagnosed from horizontal divergence and convergence using the equation of

2.2.3PROBLEMS OF THE HYDROSTATIC

ASSUMPTION


ps ps

ps

psu

u u

uu

u

u u u u u

u u

u

T T T T

TT

T

T

T

η N-5/2

N-3/2

N-1/2

N+1/2

η

η

η =1

Figure 2.9The coordinate surfacesare quasi-horizontal and

the mountains are depicted in "step-like" shapes

100

200

300

400

500

600

700

800

900

1000

410

380

360350

304

300

296

292

281280

342335330325320316

312

308

286

Figure 2.10A cross-section of RUC hybrid

isentropic-sigma surfaces from Texas(left) to North Dakota (right) for

1200 UTC 4 March 1992

θ – σ hybrid-b – 25 levels1200 UTC, 4 March 1992

Texas to North Dakota

continuity. This assumption applies very well to the synoptic scale phenomena,thus the approximation has worked without any performance deterioration inglobal models. However, at grid resolutions finer than 10 km, the validity of thisapproximation becomes uncertain.

The non-hydrostatic effect associated with mountain waves under adiabatic condi-tions has been studied by many researchers. This effect plays a significant role inthe mountain waves with a horizontal scale of a few kilometres. However, hydro-static simulations with a grid size larger than 10 km usually reproduce the samewave structures as those in non-hydrostatic ones. Research has indicated that, inthe absence of latent heat release, the hydrostatic approximation is generally suit-able unless the grid size falls below 10 km. Wave breaking phenomena can only becaptured explicitly by non-hydrostatic models.

The non-hydrostatic effect on baroclinic disturbances has also been studied. In gen-eral, hydrostatic and non-hydrostatic models produce similar simulation results,again unless the grid size is less than 10 km (see Dudhia (1993), for example).

The non-hydrostatic effect is considered to be large in mesoscale phenomenainvolving moist convection. Kato and Saito (1995) showed that a hydrostaticmodel overdevelops moist convection and overestimates the total amount and thearea of precipitation as the grid interval decreases. Non-hydrostatic effects are,however, found not to be crucial in the simulation with 10–20 km models if hydro-static water loading effect is considered within the model. In fact, recent evidencesuggests that inclusion of non-hydrostatic effects at grid resolutions greater than2–3 km may misrepresent the structures within individual thunderstorms.

2.3 PARAMETERIZATION

There are important processes that are not resolved by the model grid. As the res-olution of a model increases, the number of physical processes that need to beincluded in the computational scheme increases. The net effect of these sub-gridscale processes are parametrized in similar ways to those used in global models.

Convective parameterization schemes used in global models (see 1.3.6) are alsoused in more elaborate forms for mesoscale models. Recent work has focused onmodelling processes which are critical to the generation of mesoscale featurestypical of the forecast area (Wang and Seaman, 1997). For example, model inter-comparisons show that the inclusion of parameterized moist downdrafts allowssurface features related to intense convection to form. In particular, the predictionof the position and timing of wind shifts, mesoscale frontal features and pressurecentres are greatly improved. Typically, these features appear in the predictions ifthe grid length is less than 40 km.

Model predictions of rainfall amount, feature location and timing have been veri-fied for a variety of convective parameterization schemes. Some common performancecharacteristics emerge (Wang and Seaman, 1997), though one must realize that it isoften difficult to separate the effects of convective parameterization schemes from othercomponents of the prediction model. Frequently, the rainfall prediction in the warmseason is poorer than in the cold season owing to the more stochastic nature of summer-time convection. The convective adjustment schemes may have the most difficulty inwarm season events. The rainfall amount predictions tend to be better in the higherresolution models, as long as the convective scheme used is capable of simulatingprocesses at the appropriate scale. In addition, studies show that predictions by a partic-ular model running slightly different convective schemes can diverge significantly asthe grid size changes. Some schemes predict rainfall extent and amount better thanothers, presumably because they are capturing the essential processes and features. Anumber of schemes have difficulty simulating convection in dry climates (such as highcloud based convection in the US Great Plains).

2.3.1CUMULUS PARAMETERIZATION

Moist convection

Baroclinic disturbances

Mountain waves


An interesting aspect in the cumulus parameterization in the high-resolutionmodel is seen in the effect of model resolution on the “realism” of the forecastcumulus convection. Individual cumulus convection includes important internalprocesses which occur with the horizontal scales of a few kilometres. Therefore themodels with a greater than 1-km grid spacing inherently cannot express individualcumulus process. Hence parameterization is necessary. However, as the grid spacingdecreases, the validity of cumulus parameterization becomes unclear. In a modelusing both a non-convective cloud parameterization and a cumulus parameteriza-tion, the two scheme may form clouds at the same time, leading to errors in cloudamount estimate. Furthermore, in the case of the mesoscale convective system, themuch more complex interaction between the convective and stratiform precipita-tion processes may play an important role. Therefore, a simple cumulusparameterization may have difficulties in reproducing realistic circulations.Attempts have been made to solve this problem, including hybrid parameterizationmethods and cloud schemes to allow the interaction between the parameterizedand grid scale cloud processes.

Convective parameterization schemes require a thorough and accurateknowledge of the processes involved in the phenomena. Many of the importantquantities (such as liquid water and soil humidity) are still poorly observed. Thishas hampered the implementation of more complex schemes. However, the hope isthat observational studies will improve the knowledge of cloud physical processesenough to allow progress in the development of more realistic models of convection.

Since many mesoscale phenomena affecting aviation are dependent on the presenceof clouds, it is imperative to express the cloud physics processes as accurately aspossible. Early numerical models predicted relative humidity as the only moistureparameter and had a simple scheme for producing stratiform precipitation.Whenever the water vapour content exceeded the saturation value, the residualwater vapour was immediately removed from the atmosphere as rain, and calculatedas the rainfall at the surface. For the model radiation scheme, clouds were diagnosedfrom relative humidity and upward motion of the atmosphere.

More complex schemes are now being used in many operational mesoscalemodels. In these advanced schemes, the phases of the water (liquid, super-cooledliquid and ice) and particle size distribution are estimated or explicitly predictedaccording to theoretical and empirical rules (see Figure 2.11).

The use of sophisticated parameterization schemes of cloud physics is essentialfor the accurate reproduction of a variety of weather elements. The output from thecloud parameterization schemes are particularly interesting to aeronauticalapplication because these processes are closely related to the aeronauticallyimportant parameters. For example, predicted cloud water content and the sizedistribution of the water droplets are valuable in forecasting visibility, cloud baseheight and icing.

In the planetary boundary layer, which can extend as high as 2 000 m above thesurface, the atmospheric motions are turbulent and characterized by the verticalmixing of momentum, heat and moisture, which changes throughout the day.However, these processes are of such small scale that this cannot be resolved evenwith high-resolution NWP models. Therefore, the effect of the transport of heat,momentum and water vapour by the turbulence is expressed by parameterizationschemes in the model that can be more realistic for the smaller grid squaresinvolved than those for global models.

Momentum flux (or the drag effect of the ground surface) is usually a functionof the surface properties and atmospheric conditions such as vertical stability, windshear and winds at the lowest level. The parameter to determine the momentumflux in a given atmospheric condition is often predefined according to the land useover the land, and it is calculated based on an empirical relation with the surfacewind speed over the water.

Sensible and latent heat fluxes are also calculated using atmospheric condi-tions and surface properties. Surface properties include the albedo (or the

2.3.3BOUNDARY LAYER PROCESSES

2.3.2PARAMETERIZATION OF

NON-CONVECTIVE CLOUD AND

PRECIPITATION


reflectivity) and soil wetness. Soil wetness is an important parameter to determinethe ratio of sensible versus latent heat fluxes. It is estimated in the model using theprescribed land use, the “past” precipitation and run-off and, in some models, thebiological response to the environment.

Parameters used in the boundary layer processes are also used to diagnose theforecast values between the lowest model level and the surface. One such productfrom high-resolution models often used by aviation users is the 10-m wind speed. Aproblem in this calculation is to determine the parameters for the surface condi-tions. Different land utilization gives different friction, but the parameter for amodel grid representing a 10-km by 10-km area, for example, can only express theaveraged or prevailing type of surface of the area. Thus, when such products areused, the difference between the surface conditions of the airport and the sur-rounding area should be considered.

Radiation schemes used in high-resolution models are similar to those in globalmodels. However, when calculating radiation heat flux, consideration of the slantshade of cumulus becomes necessary as the grid interval comes close to the heightof cumulus.

Some phenomena affecting aviation are closely related to the radiationprocess. Land and sea breeze is one such example. This phenomenon is caused bythe differential warming of land and water surfaces. At the same time, the spatialextent of the simulated land and sea breeze circulation depends on the model’s hor-izontal resolution. Therefore, the model must have a high enough resolution andappropriate radiation and boundary layer process schemes in order to properly sim-ulate this phenomena, or else the effects will be seen too far inland in the model guidance.

Another example is the formation of low stratus ceilings. Low stratus is often formedand maintained by positive feedback of condensation and enhanced radiative coolingat the top of the cloud. It is therefore necessary to have sophisticated cloud and radiation parameterization schemes for the prediction of this important aviation variable.

2.3.4RADIATION


PRECIPITATION ON GROUND

PGMLT

PGACR , PIACR ,

PGFR , PSACR ,

PR

AU

T , P

RA

CW

, P

SA

CW

P SMLT

PR

EV

P

P IAC

R ,

P SAC

R

P SAU

T , P SA

CI

P RA

CI ,

PS

FI

PSA

CW

, P

SFW

PG

AUT

, PG

ACS

,

PR

ACS

PG

AC

W

PG

AC

I , P

RA

CI P

SS

UB

, P

SD

EP

PG

SU

B

PIDW , PIHOM

PIMLT

RAIN

SNOW

GRAUPEL/HAILWET (PGWET) ORDRY GROWTH

WATER VAPOUR

CLOUDWATER

CLOUDICE

Symbol MeaningPIMLT Melting of cloud ice to form cloud water, T≥T0PIDW Despositional growth of cloud ice at expense of cloud waterPIHOM Homogeneous freezing of cloud water to form cloud icePIACR Accretion of rain by cloud ice; produces snow or graupel depending on

the amount of rainPRACI Accretion of cloud ice by rain; produces snow or graupel depending on

the amount of rainPRAUT Autoconversion of cloud water to form rainPRACW Accretion of cloud water by rainPREVP Evaporation of rainPRACS Accretion of snow by rain; produces graupel if rain of snow exceeds

threshold and T<T0PSACW Accretion of cloud water by snow; produces snow if T<T0 or rain if

T≥T0. Also enhances snow meltng for T≥T0PSACR Accretion of rain by snow; For T<T0, produces graupel if rain or snow

exceeds threshold; if not, produces snow. For T≥T0, accreted waterenhances snow melting

PSACI Accretion of cloud ice by snowPSAUT Autoconversion (aggregation) of cloud ice to form snowPSFW Bergeron process (desposition and riming) — transfer of cloud water

to form snowPSFI Transfer rate of cloud ice to snow through growth of Bergeron process

embryosPSDEP Despositional growth of snowPSSUB Sublimation of snowPSMLT Melting of snow to form rain, T≥T0PGAUT Autoconversion (aggregation) of snow to form graupelPGFR Probalistic freezing of rain to form graupelPGACW Accretion of cloud water by graupelPGACI Accretion of cloud ice by graupelPGACR Accretion of rain by graupelPGACS Accretion of snow by graupelPGSUB Sublimation of graupelPGMLT Melting of graupel to form rain, T≥T0. (In this regime, PGACW is

assumed to be shed as rain)PGWET Wet growth of graupel; may involve PGACS and PGACI and must include

PGACW or PGACR, or both. The amount of PGACW which is not able tofreeze is shed to rain.

Figure 2.11Cloud physics processes simulated in

the model with the snow fieldincluded. An explanation of the

symbols is on the right

2.4 DATA ASSIMILATION

Although some of the benefits from mesoscale models come from improved explicitprediction of topographically forced phemonena (for example orographic precipi-tation, sea breezes), much of the improvement in very-short-range forecastsdepends upon the accuracy of detailed mesoscale analyses.

Initial conditions of an NWP model are expressed by temperatures, winds,pressures and water vapours at grid points. A number of approaches have been usedto optimize the impact of the measurements of these parameters, while generatingthe initial conditions. Recently, other information such as the precipitation andwind measured from weather radar and high density automated aircraft observa-tions are also used in mesoscale data assimilation systems.

An experiment to assess the improvement in the forecast performance due tochanges in the initial conditions is summarized in Figures 2.12 to 2.14. This exper-iment compares two forecasts by an identical model, but using different initialconditions. One initial condition is through a forecast-analysis cycle (first-guess forthe analysis is given by the same model as that used for forecast), with the use ofradar data in water vapour analysis, and through a scheme to account for the effectsof the diabatic heating implied by the precipitation observations. The otheremploys none of these, but uses a first-guess from a coarser resolution global model.Figure 2.12 shows the observed precipitation over the west part of Japan with a net-work comprising weather radars and automatic surface weather stations. Figure 2.13is the numerical prediction output from the mesoscale model with these initial con-ditions. The model needed 15 hours to produce the mesoscale system that broughtheavy precipitation clearly seen in Figure 2.12, and the simulated system is muchweaker than in reality. Figure 2.14 shows the forecasts from the forecast-analysis

2.4.1SPIN-UP PROBLEMS AND

INITIALIZATION


Figure 2.12Observed precipitation over the west part of Japan with anetwork comprising weather radars and automatic surfaceweather stations

cycle including the improved water vapour analysis and the diabatic initialization.The mesoscale precipitation system was simulated well from the beginning of theforecast, and was maintained properly for 12 hours.

Conventional meteorological observations such as radiosonde observations havebeen made at 0000 UTC and 1200 UTC and used to initialize the twice daily runsof numerical prediction models. New types of observations are now introduced tocontinuous weather monitoring and these observations provide a new opportunityfor mesoscale modelling.

Meteorological observations by aircraft are a valuable complement to thesparse radiosonde observations over the ocean. These observations have beenreported by the pilot using radio communications to the ground and relayed to thenumerical prediction centres through various aeronautical and meteorologicaltelecommunication facilities. Meteorological data observed by airborne sensors cannow be automatically downlinked to the ground. This has substantially increasedthe number of the meteorological reports from aircraft. Particularly interesting forthe mesoscale modelling is the data from aircraft during ascent and descent at theairport, the interval being around 2 000 ft or less. In fact, Benjamin et al. (1997)showed that the increased amount of ascent/descent data was a source of the per-formance improvement of the RUC in the USA.

A Doppler radar observes the winds around the radar site by measuring theDoppler shift in the radio wave reflected by raindrops and small particles in theatmosphere. These data provide important dynamical information, and are expected

2.4.2USE OF ASYNOPTIC OBSERVATIONS


Figure 2.13Numerical prediction output from the

mesoscale model with the initial conditionsfrom Figure 2.12

to improve aerodrome forecasts when applied appropriately in the initialization ofa model for the surrounding area.

A wind profiler observes winds aloft by measuring the Doppler shift in thereflected radio wave from turbulence in the atmosphere. This new remote sensingtechnology has an advantage over the conventional radiosonde observations inthat it provides nearly continuous wind data. The Wind Profiler DemonstrationNetwork in the United States is an example of a semi-operational network of suchwind profiler observations. When combined with aircraft observations, these twosystems have shown a large impact on short-range “off-time” forecasts.

Since the timescale of the mesoscale disturbances are usually relatively short,twice daily operation of the model is not sufficient to provide full coverage of


Figure 2.14Forecasts from the forecast-analysis cycle

including the improved water vapouranalysis and the diabatic initialization

mesoscale phenomena. The new observations described above have enabled us todevelop numerical analysis and forecast systems which allow more frequent updat-ing and shorter time interval forecasts. These systems have a capability to producehigher quality products for aviation use than twice daily products. For example, theRUC in the United States has been developed in order to provide hourly analysisand short-term prediction using non-synoptic data such as automated observationsfrom commercial aircraft. The three- to six-hour forecasts, which had the benefit ofasynoptic aircraft data in the initial conditions, showed large improvements overthe 12-hour forecasts for the same valid time (Figure 2.15). This advantage is par-ticularly important because the products are delivered to the users within one hourof the observation time.

Methods have also been developed for high-resolution models to improve the useof asynoptic data. They are called four-dimensional data assimilation. The methodsare similar to those for global models explained in 1.4.2. However, on themesoscale, the increased importance of parameterized and irreversible processesmakes the problem of four-dimensional assimilation even more difficult to solvethan for global models.

2.4.3FOUR-DIMENSIONAL DATA ASSIMILATION


Figure 2.15Vector differences (m s-1) (analysis minus forecast) at 250 hPa for wind forecasts valid at 0000 UTC 20 January and theverifying MAPS analysis (Figure 2.5). Wind plotting convention as in Figure 2.5, only differences > 5 m s-1 are plotted, contourinterval is 10 m s-1 and shaded area is for differences ≥ 10 m s-1. The heavy wind barbs are for rawinsonde minus forecastdifferences that exceed 10 m s-1. (a) For MAPS 3-hour forecast, (b) for NGM 12-hour forecast, (c) for operational MAPS12-hour forecast with old boundary conditions, and (d) for MAPS 12-hour forecast with new boundary conditions.

CHAPTER 3

DIRECT USE OF MODEL OUTPUT

3.1 USE OF DIRECT MODEL OUTPUT

For the past several decades, the primary access to NWP model output has beenthrough restricted sets of centrally produced graphical charts transmitted via fac-simile. In many instances, this has restricted operational meteorologists to use“cookbook” approaches to many aviation forecasting problems. Recent advances incommunications and reduced costs of on-site computers, however, are now provid-ing operational forecasters the opportunity to improve processing of aviationforecasts through more extensive use of NWP. Forecasters can benefit from acombination of local computing capability and access to digital NWP guidanceproducts in a number of ways, by:

(a) Better diagnosing and understanding the physical processes affecting a wide varietyof meteorological phenomena;

(b) Appreciating the strengths and weaknesses of the NWP tools;(c) Concentrating their time and expertise on the most important problems affecting

the aviation user on any particular day; and(d) Using a combination of real-time observations (including especially satellite data)

and NWP based diagnostics as a continuous monitor of model performance andongoing weather.

The following sections provide examples of how forecasters can use digitalNWP guidance to improve their daily forecasting processes. First, a review of gen-erally available workstation display capabilities illustrates how locally generateddisplays of the digital model output can provide additional information to the fore-caster. This is followed by more detailed discussions of how the digital NWP outputcan be used to diagnose the physical processes responsible for a variety of differentaviation weather phenomena. Case studies are included for both tropical and extra-tropical events. This is followed by a discussion of additional statistical techniquesthat can help forecasters take full advantage of the NWP guidance that is becom-ing readily available. (See the Appendix for further details on data availability.)

The availability of gridded NWP output presents field forecasters with a new sourceof guidance information for improving their aviation services. However, to usethese data to advantage, forecasters must be able to manipulate and display thegridded model forecast guidance in ways which are suited to a wide variety of mete-orological events and specific local forecast problems. As a means of expanding theutility of digital NWP guidance data beyond conventional map presentations, sev-eral national weather services and vendors have developed (and in some casesprovided to WMO and the International Civil Aviation Organization (ICAO)) avariety of computer software tools to display and manipulate gridded data, such asPCGRIDDS, RETIM, GEMPAK and Micro-Magics, among others. With these sys-tems, forecasters can not only ingest the NWP output data and produce many moregraphical display fields directly from the gridded data, but also can derive a widevariety of diagnostic products essential for understanding the dynamical evolutionof a broad spectrum of different meteorological problems. Several of these systemsare already being used in forecast offices as an effective means of introducing fore-casters to the use of gridded data in their daily operations.

With any of these systems, forecasters can produce displays over any portion ofthe area covered by the gridded NWP guidance data by specifying a unique combi-nation of parameter name, vertical level and forecast time. For the World AreaForecast System (WAFS) data sets, this means that displays can be generated forany part of the globe and at almost any resolution, from full global plots to detaileddisplays of specific regions. Figure 3.1, for example, shows a series of temperatureand wind plots generated with increasing detail for successively more localized areas

3.1.2USING LOCALLY PRODUCED DISPLAYS

OF NUMERICAL WEATHER

PREDICTION DATA

3.1.1INTRODUCTION


Figure 3.1Example of increasingly detailed

displays of mean sea level pressure(solid, hPa), 2-m temperature (°C)and 10-m winds (barbs, knots) over

the Middle East for 1200 UTC1 October 1997

at the time of a cold frontal passage over the Middle East. Forward and/or back-wards animation of the plots in time can also be produced to provide a much bettergrasp of changes anticipated to occur at any level in the atmosphere.

It can often be advantageous to alter the displays to highlight distinct aspectsof the displays which may be more pertinent to specific forecasting applications.The highlighting can be done by changing contour intervals and colours, dashed ordotted patterns, and maximum and minimum ranges, the number of digits in datadisplays, whether wind arrows or barbs are to be used, and if they are to be displayedin knots or m s-1. These options offer meteorologists greater freedom in siftingthrough the large volumes of model guidance available and improved focus by usingproducts tailored for the problem at hand. For example, when interpreting the windfield over large geographical areas, it can be more useful to combined displays ofwind arrows which are proportional in length to the wind speed and dashed con-tours of wind speed (as in Figure 3.2, right) than to use conventional wind barbplots alone. Whilst this “streamline-like” presentation of the wind fields can beuseful in assessing the overall flow regime, details of local flow patterns can often beviewed more clearly using wind barbs, either alone or in combination with the iso-tach field (Figure 3.2, left).

In addition to displaying parameters contained directly in the data set (e.g.temperature, relative humidity, wind, geopotential height, vertical velocity andprecipitation), forecasters can easily calculate a wide variety of additionalmeteorological variables from the gridded data which in the past could only, at best,be inferred from the facsimile charts. Many of these parameters are especiallyimportant in diagnosing hazardous aviation weather. These parameters includepotential temperature, equivalent potential temperature, specific humidity, dewpoint

CHAPTER 3 — DIRECT USE OF MODEL OUTPUT 33

Figure 3.2Example of two different wind display

options using 12-hour, 250 hPaforecast valid at 1200 UTC 6 June

1994. Wind barbs are shown inupper left portion of display, whilstwind velocity arrows and isotachs

(presenting a more "streamline-like"display) are shown in the lower right

temperature and vorticity. Vector quantities, such as the geostrophic andageostrophic winds, can also be calculated from the gridded numerical weatherprediction guidance data, a capability which can be especially useful for a number ofdiagnostic applications related to jet stream dynamics and precipitationdevelopment.

Although the majority of meteorological charts traditionally used in operationshave been quasi-horizontal maps, it is often beneficial to study vertical cross-sectional or time-sectional displays for specific locations, especially when forecastinglocal weather phenomena that are difficult to predict. Cross-sections and time-sections of any field or derived parameter can in general be produced by specifyingthe orientation of the display using either latitude/longitude or station identifierspecifications.

Figure 3.4a, for example, shows a display of winds, wind speed and temperaturealong a path normal to the jet streak shown in Figure 3.3. Figure 3.4b shows thesame information, except with potential temperature displayed instead of tempera-ture, whilst Figure 3.4c shows the same isentropic depiction, but including isotachsand wind barbs directed into and out of the cross-section path. The cross-sectionaldisplays reveals not one jet, as evident on the single level quasi-horizontal display,but three distinct wind maxima, one near 250 hPa, an equatorward extension near150 hPa, and one at low levels, near 850 hPa. The origin of these jets is furtherunderstood by studying the potential temperature information. The lower of thetwo upper-level jets (the Polar Jet) is supported by a major polar front, attested toby the temperature gradient below it. This front is particularly apparent in the isen-tropic representation in 3.4b. In this case, the location of the frontal zone isindicated by close vertical packing of the potential temperature surfaces slopingdownward from north to south between 250 and 500 hPa. Above and equatorwardof this Polar Jet, a second, weaker frontal zone can be noted between 150 and 250hPa supporting the higher altitude and more equatorial Subtropical Jet found near15 hPa. Above both jets, the location of the tropopause is also clearly identified inthe isentropic display by the demarcation between the more statically stable air inthe stratosphere (characterized by strong static stability and large vertical change ofpotential temperature) and the less stable tropospheric air below. At low levels, thearea of strong easterly flow is related to an area of strong cold air advection belowthe surface front sloping upward from near the surface to near 700 hPa going pole-ward. As will be shown in 3.2.4.2, the ability to isolate areas with specificcombinations of vertical static stability structure and vertical wind shear can becritical in diagnosing the potential for clear air turbulence (CAT).


Figure 3.3Display of 250 hPa grid point windbarbs (knots) and isotachs (knots)

over southern Africa for 0000 UTC18 October 1997. Line indicates path

of cross-sections in Figure 3.4

It should be noted that a number of conventions are normally used to simplifythe interpretation of cross-sectional displays. For example, the wind flags displayedin the preceding figures have been rotated to be displayed in a direction relative tothe path of the cross-section. By orientating the cross-section perpendicular to thefrontal zone, a southwesterly wind (flowing into the plane of the cross-section) isdepicted pointing from the bottom to the top of the display and along the baro-clinic (frontal) zone indicated by the potential temperature gradient. Similarly,winds flowing across the plane of the cross-section (in this case southeasterlywinds) are oriented from right-to-left or left-to-right across the cross-section. Thistype of display can be useful in detecting areas of “over-running” or lifting along thefrontal zone. The “flow-relative” nature of the display also allows forecasters to con-centrate on the structure of the meteorological processes relative to the directionof the atmospheric flow affecting that process, rather than having to extrapolatebetween a group of different-level, geographically-fixed displays.

A number of cross-sectional products including rotated wind displays can alsobe especially useful for forecasters to provide to pilots. Figure 3.5 contrasts a con-ventional horizontal display of flight level temperatures and winds (top) with across-sectional depiction of the head- and tail-winds along a flight path (bottom).In this case, the wind barbs have been rotated along the flight path from left-to-right on the product to show the direction and strength of the wind at all levels.Different shadings (or colours on the video display) can also be used to furtherhighlight different wind speed ranges. Overlaid on this are contours of the tail-windcomponent, a feature which can be particularly beneficial to pilots when makingdecisions about changing flight level. As will be discussed in 3.2.4.1 and 3.2.4.2,icing and turbulence indicators can also be displayed along the flight path to pro-vide more complete en-route guidance for pilots.


Figure 3.4A) North-to-south cross-section of temperature (°C) from1 000 to 100 hPa along path in Figure 3.3. Latitude andlongitude locations along cross-section path given at bottom ofdisplay. B) Same as A, except potential temperature (°K). C)Same as B, but with isotachs (dashed, knots) and wind barbs(knots) overlaid on isentropes (dotted, °K). Winds have beenrotated relative to the plane of the cross-section, with"upward" and "downward" pointed barbs indicating air flowinto and out of the cross-sectional plane respectively, etc.

A

B C

As the number of display options increases, forecasters can soon become over-whelmed by the complexity of the computer display system and divert their timeaway from applying the new tools to the forecast problem at hand by spending aninordinate amount of time remembering display and diagnostic options. To addressthis problem, many graphics display systems have incorporated both flexibility andsimplicity in the way in which forecasters can organize and access these new andessential diagnostic tools. Some considerations include:• Shorthand notations and abbreviated command name;• Multilingual commands;• Menus organized by basic product categories, including:

– commonly used products;– seasonal needs; and– specific forecast phenomena;

• Pre-generation of basic product displays and loops;• Pre-defined display areas and cross-/time-section locations; and• On-line “help” documentation.

The illustrations shown in the following sections exemplify the types of graphicsand forecaster products that can be generated using software systems and databasescurrently available through ICAO, WMO, individual meteorological services andprivate vendors.

3.2 DERIVING METEOROLOGICAL DIAGNOSTICS FROM THE GRIDDED DATA IN FORECAST OFFICES

Interactive meteorological display systems offer forecasters an opportunity to performa large number of calculations useful in diagnosing a variety of different weather events.The computations available on these systems include the following:

3.1.3SIMPLIFYING THE USE OF

INTERACTIVE GRAPHICS SYSTEMS IN

OPERATIONAL FORECASTING


Figure 3.5Standard ICAO plan-view of

12-hour forecast FL340 wind andtemperature data (top) and vertical

cross-section of flight path relativewinds and tailwind component

(bottom) at 1200 UTC 6 June 1994for route from Buenos Aires to Paris

(a) Simple numerical manipulation of individual or multiple grids (e.g. adding or sub-tracting two grids);

(b) More complex mathematical calculations (e.g. advection, vorticity, vorticityadvection, moisture fluxes and divergence) needed for many diagnostic forecastingparameters; as well as

(c) A variety of meteorologically significant indices and diagnostic parameters, includ-ing lifted index, convective condensation level, etc.

The results of the diagnostic calculations can either be displayed separately oroverlaid on other displays of model output parameter or diagnostic calculations. Anexample can be shown for detecting areas of mid-level cyclonic vorticity advection.Quasi-geostrophic theory suggests these areas should both be associated with risingvertical motions and be conducive for cyclogenesis. The conventional subjectiveprocess used to infer these areas of cyclonic vorticity advection involves overlayingthe geopotential height with the vorticity and noting where the contours intersectusing conventional facsimile charts as shown in Figure 3.6 over eastern Asia. Thisprocedure imposes another hidden approximation in that the direction and strengthof the winds are estimated by the geostrophic flow as defined by the direction andspacing of geopotential height contours. A much more precise picture can beobtained by displaying the predicted geopotential heights, wind and vorticity fieldsand overlaying these fields with vorticity advection calculated directly from thedigital model guidance (Figure 3.7). The area of strong cyclonic vorticity advectionahead and north of the upper level trough is delineated much more clearly than canbe achieved by inference alone. The forecaster can go one step further, if desired,and retrospectively assess whether the quasi-geostrophic approximation has meritsfor the particular forecast problem at hand. This can be done by overlaying thepredicted and/or observed vertical motion fields (Figure 3.8) or satellite imagery andcomparing these products with the lifting inferred from the areas of vorticityadvection to determine if the approximation is valid for use in other similarforecasting situations in the future. In this case, the approximation was generallysimilar to the predicted uplift in areas of strong vorticity advection to the north ofthe cyclone, but differed in other areas, such as ahead of the storm centre, wherethe region of cyclonic vorticity advection lags behind the predicted upward motions.

The previous example demonstrated only one of a large number of differentdiagnostic tools which have been developed to help in forecasting a variety of dif-ferent weather events. The following sections contain a number of differentexamples of how meteorologists can improve their understanding (and therefore


Figure 3.6Example of 500 hPa geopotential

height (dashed, m × 10) and vorticity(dashed, 10-5 s-1) as shown on

facsimile charts. Note cyclone centrenorth of Japan. Area of subsequent

figures outlined

their forecasts) of a variety of meteorological phenomena that affect aviation oper-ations and safety using techniques based on the results of recent research.

The ability to interrogate digital NWP output affords operational forecasters theopportunity to monitor the quality of NWP products, a process which in the pasthad been, at best, a very subjective one. This capability can be useful for a numberof purposes. The most elementary type of assessment can be accomplished by cal-culating the differences between forecasts and analyses valid at the forecast lengthand then accumulating the results over a period of time. For example, in short-range forecasting, areas where the NWP guidance has changed from one forecastcycle to the next can be identified very quickly, as shown in Figure 3.9. By usingtools like this, forecasters can focus their attention on those areas where inconsis-tency in the guidance may bring the validity of the NWP guidance into question.

Systematic assessment of sets of forecast verifications gathered for periods ofdays, weeks, months or years (see Figure 3.10) can also provide an understanding of

3.2.1DERIVING NUMERICAL WEATHER

PREDICTION PERFORMANCE

INFORMATION


Figure 3.7Same as Figure 3.6, but with wind

vectors and computed vorticityadvection (positive — think solid,

10-9 s-2) added

Figure 3.8500 hPa vorticity advection

(dotted, 10-9 s-2) and correspondingpredicted upward vertical motion

(10-3 hPa s-1)


Figure 3.9Display of 36-hour forecast of

250 hPa geopotential heights (solid,m) valid at 1200 UTC 30 January

1998 with dashed contours andshading to indicate the consistency

(RMS difference, m) within a set ofsix forecasts from three successive

days, all valid at the same time

Figure 3.10Monthly mean 250 hPa five-daywind forecasts (m s-1) for January1997 (top), compared with RMSvector errors and mean wind speederror (m s-1) for same period (bottom)

both large-scale and local biases in model forecast skills depending among otherthings, on season, flow regime or forecast problem. These techniques are most valu-able when using a “mature” NWP model, since changes or modifications to themodel’s dynamics and physics can greatly alter systematic model errors. (Additionalinformation on forecast verification is also provided in Chapter 4.)

Tropical weather systems can have large impacts on public and aviation forecasts.However, since these systems often have very weak synoptic scale signatures duringtheir early development, they can be difficult to detect on large area, quasi-hori-zontal displays of conventional data. In these instances, it is often advantageous forforecasters to isolate these small-scale and transient phenomena from the more sta-tionary large-scale flow regime and monitor their movement. A variety oftechniques can be used, including spatial and temporal filters. The following twoexamples show how forecasters in equatorial regions can recognize detailed infor-mation about the vertical structure and fine-scale flow pattern present in NWPanalyses and forecast guidance to help predict the evolution of different tropical systems.

The tropical upper-tropospheric trough (TUTT) has been identified as a majorclimatic control feature over the Atlantic Ocean during the warm/wet season.Characteristically, TUTTs are found in the region from the extreme northwest coastof Africa to the southwestern Caribbean. The trough is bounded by the subtropicalridge to the north and the sub-equatorial ridge to the south. The subtropical ridgediverts cold air and energy from extratropical sources into the TUTT, giving it cold-core characteristics. TUTTs appear most frequently in the upper atmosphere (above500 hPa), and some occasionally extend downward into the lower atmosphere. Thetrough axis typically appears as a wind-shear line, supporting primarily shallowconvective development. When manifested at lower levels, the convective activitybecomes deeper and better organized.

The following case illustrates how NWP analyses and forecast guidance wereused in forecasting the impact of a TUTT which developed in late August 1995and subsequently interacted with Hurricane/Tropical Storm (TS) Iris over the areashown in Figure 3.11. (The NWP analyses and guidance data used in this case arefrom a collection of operational WAFS data sets, as described in the Appendix.)

At 250 hPa (Figure 3.12), the TUTT extended along 40°N/45°W and28°N/55°W and then south of Hispaniola to near 15°N/74°W. The decrease oftemperature toward the trough axis identifies this as a possible cold-core system.

3.2.2.1Tropical upper-tropospheric trough

3.2.2DETECTING AND MONITORING

DEVELOPMENT OF TROPICAL

WEATHER SYSTEMS


Figure 3.11Mean sea level pressure (dashed,hPa) and 250 geopotential height

(solid, m × 10) analysed for0000 UTC 28 September 1995.

Area of displays in subsequent figuresoutlined

Figure 3.13 is a cross-section of the TUTT axis along 30°N. The cross-section con-firms the initial observation of a cold-core system, evident by the upward bulge inthe isentropes near the centre of the system. It should be noted that the trough isvery shallow, isolated mainly to the area above 300 hPa. This restricts the verticalextent of the upper level wind shear. It should also be noted that the global analy-sis and prediction system used in this case was able to resolve the structure of asynoptic scale feature extremely well.

Tropical cyclones will typically try to follow the path of least resistance. If acyclone moves west under a TUTT, the storm will cross both an area of wind shearand then an area of upper-level convergence, resulting in the disorganization of thecyclone and associated convection. The preferable path for continued storm devel-opment would be to travel along the east side of the TUTT where upper divergenceis maximized. With this in mind, it should be remembered that even though globalNWP models might not be able to fully resolve the mesoscale features of the trop-ical cyclones themselves, they do have the capability to depict synoptic scale


Figure 3.12250 hPa geopotential heights (dashed,

m × 10), temperatures (solid, °C)and wind vectors from analyses valid

0000 UTC 28 September 1995.Path of cross-section in following

figures shown

Figure 3.13Northwest to southeast cross-sectionof potential temperatures (thin solid,

°K), cross-section relative winds(knots) and relative vorticity (thicklines, 10-5 s-1) from analyses valid

0000 UTC 28 September 1995 alongpath extending from northwest to

southeast across axis of TUTT

features, such as TUTTs, that might have influence on the possible growth or dis-sipation of these systems.

The plot of mean sea level pressure and 850 hPa winds in Figure 3.14 showsseveral well-organized tropical cyclones: TS Iris is located just west of the LeewardIslands; TS Humberto is near 25°N/49°W; whilst a third developing storm is foundfarther to the east near 17°N/40°W. Although the global WAFS data for this caseresolved the closed circulation, the approximate 95-km resolution of the modellimited how well it could represent subsynoptic scale features. As a result, it failedto preserve the intensity of the associated winds and the corresponding centralpressures. Nevertheless, it did provide important guidance about how the TUTTwould interact with both Hurricanes Humberto and Iris. In each case, the TUTTprovided an outflow channel for organizing the convection, thereby helping sustainthe primary source of energy forcing the storms’ subsequent growth and movement.

As shown in this example, experienced forecasters can take advantage of thesynoptic scale information in global scale numerical models to improve theirdetailed local forecasts as long as they are aware of the models’ capabilities and lim-itations. In the situation shown here, the TUTT played an important role in theweather over the Tropical Atlantic and Caribbean Sea, interacting constructivelywith several smaller-scale, lower-level tropical systems by supporting their develop-ment and persistence. In other cases, the TUTT might have built downward overtime and provided support for organized convection itself, or in other flow regimesmight have inhibited growth of the smaller-scale systems.

Tropical upper-tropospheric troughs can, in some cases, also provide an environ-ment conducive for the development of closed circulations. Like the TUTTsthemselves, these upper-level cyclones are often limited to the upper atmosphere.Occasionally, however, they manifest themselves into the lower levels with muchmore dramatic influence on local weather conditions. Unlike most tropicalcyclones, these systems are generally cold core in nature. The circulations are mostoften sloped towards the west, but can also appear as being almost verticallystacked. This structure typically results in an area of upper-level divergence in theeastward and poleward quadrants of the systems. When coupled with low-levelconvergence, the combined structure is conducive to the development of an areaof dense cloud cover, with deep vertical development mainly east of the centre.However, there are rarer cases in which the cold cyclone slopes towards the eastwith height, shifting the most favourable area for deep convection to the west ofthe closed upper low.

3.2.2.2Upper-level cyclones in the tropics


Figure 3.14Mean sea level pressure (solid, hPa)

and 850 hPa winds (knots) from24-hour forecast valid 0000 UTC

26 September 1995

The following case depicts an eastward sloping closed upper low that affectedthe central Caribbean in September 1995. At 250 hPa, a closed cyclone was locatednorth of the Virgin Islands, near 24°N/64°W, as shown in Figure 3.15. The mini-mum temperatures of –45°C in the centre of the upper low in Figure 3.16 suggestsa cold-core structure. Figure 3.17a provides a northwest-to-southeast vertical cross-section across the trough, which extends between 60°W and 70°W. The upwardbulge of the isentropes along the trough axis, with temperature decreasing horizon-tally toward the centre, verifies the initial observation of a cold-core system, andalso suggests a slight tilt of the trough to the east. The extension of the potentialvorticity below 400 hPa further attests to the deep vertical depth of the system. Acorresponding cross-section of potential temperature, ageostrophic circulation andvertical velocities (Figure 3.17b) clearly shows cold air sinking in the centre of thecyclone (between 64°W and 66°W) and warm air rising east of the trough, a con-figuration which favours deep vertical development east of the cyclone centre.


Figure 3.15250 hPa geopotential heights

(solid, m) from 12-hour forecast valid1200 UTC 25 September 1995

Figure 3.16250 hPa geopotential heights (solid,m) and temperatures (dashed, °C)

from 12-hour forecast valid1200 UTC 25 September 1995. Pathof cross-section in Figure 3.17 shown

By 36 hours into the forecast cycle, the 250 hPa system (Figure 3.18) was predictedto move just to the north of the Virgin Islands, near 20°N/66°W. The temperatureanalysis still suggests a cold-core centre with a temperature, again of about –45°C. Thecross-section in Figure 3.19 verifies this observation, with the isentropes near the stormcentre again bulging upward. However, the vertical extent of the low is now reduced,with the lowest manifestation of the system reaching 500 hPa. The slope of the troughhas also become more pronounced towards the east. The temperature and verticalvelocity patterns shown in Figure 3.20 indicate that the circulation within the stormsystem remains primarily direct, but in contrast to 24 hours earlier, the circulationpattern is rotated such that cold air is sinking near the centre of the low, whilst warmair in found rising to the southwest. These changes in cyclone structure should nowfavour deep vertical development on the southwestern quadrant of the upper cyclone,but only if relatively strong low-level convergence is present to interact with the moreelevated upper-level cyclone.

In this example, having an understanding of the evaluation of the vertical andthree-dimensional structure of the upper-level cyclone provided a fuller apprecia-tion of the dynamics involved in this case and how they evolved over time.Although most tropic systems will follow theoretical models about the behaviourof warm-core systems, external forces can cause some to deviate from the generalexpectations, as this case demonstrated. In data-sparse areas, these systems can onlybe detected through careful examination of numerical model analyses and forecastguidance materials. Advances in data systems, computer-generated guidance andinteractive display systems are beginning to provide forecasters with a reliable capa-bility to dissect and interrogate a wide variety of tropical weather systems, offeringa new and far more complete perspective of the atmosphere.

In many ways, the process of producing accurate terminal forecasts represents a summa-tion of a large number of different meteorological phenomena that affect aviation. Thephenomena which must be considered can range from wind shifts to dust storms tosevere convection and heavy rainfall events. Unfortunately, some of these phenom-ena are forced by extremely small-scale circulations that can only be detected in localobservations or possibly simulated by extreme high-resolution forecast models whichare beyond the scope of today’s operational NWP. Other factors affecting the aviationenvironment, however, are much more predictable using currently operationalmodels — either through direct prediction of the phenomena by the NWP system orby prediction of the environment in which the event is likely to develop. Thesephenomena can include cyclone-scale frontal systems, larger-scale orographic flowpatterns and diurnally forced convection, among many others.

3.2.3PHENOMENA AFFECTING TERMINAL

FORECASTS


Figure 3.17A) Cross-section of potential

temperatures (solid, °K) and potentialvorticity (dashed) from

12-hour forecast valid 1200 UTC25 September 1995 along path

extending from northwest to southeastacross axis of upper-level cyclone. B)Same as A, except includes combined

vectors of vertical motion andageostrophic flow along plane of cross-section, and vertical motion contours(upward motions solid, 10-3 hPa s-1)

A B

Figure 3.21 shows an example of two particularly useful tools for diagnosing thepotential, severity and timing of thunderstorm development. To illustrate the diur-nal variability of the parameters present in current NWP systems, results are shownfor an 18-hour forecast period using WAFS data. In the left column, the 850 hPamoisture flux divergence has been calculated (solid contours indicate convergence)and overlaid on a schematic depiction of local topography. Moisture flux conver-gence, the combination of the moisture weighted velocity convergence and themoisture advection, provides a measure of the rate at which the moisture needed tosupport convective storms is being accumulated at low levels. In the right column,the temperature difference between the environment and a parcel lifted from

3.2.3.1Diagnosing the development of

diurnally forced convection


Figure 3.18250 hPa geopotential heights(solid, m) and temperatures

(dashed, °C) from 36-hour forecastvalid 1200 UTC 26 September

1995. Path of cross-section inFigure 3.19 shown

Figure 3.19Cross-section of potential

temperatures (solid, °K) and potentialvorticity (dashed) from 36-hour

forecast valid 1200 UTC26 September 1995 along path

extending from northwest to southeastacross axis of upper-level cyclone

850 to 250 hPa has been calculated to provide a measure of the buoyancy at thatlevel. This parameter, which is similar to the more traditional Showalter Index,represents what could occur if parcels of air are lifted dry adiabatically from 850 hPauntil they reached saturation and then moist adiabatically until they reached250 hPa. As a complement to the Showalter Index for mid-tropospheric buoyancy,this parameter represents the buoyancy of parcels nearing the tropopause and pro-vides a measure of both potential thunderstorm height and severity.

The time sequence of diagnosed 850 hPa moisture-flux convergence displaysprovides useful guidance as to both where and when topographically induced low-levelmoisture convergence needed to support convection should be expected. (Note thatthe NWP system used to produce the guidance shown here took into considerationinformation about forecast cloud cover. This factor could affect incoming solar radia-tion heating and moistening locally in the lowest portion of the atmosphere.) Theguidance evolution captures two factors critical to the formation of convection:

(a) The direct influences of diurnal processes on the low-level temperature and mois-ture fields, showing reductions in stability during daytime hours; and

(b) The combined effects of differential heating between land and ocean and theeffects of terrain in creating areas of on-shore flow and low-level moisture flux con-vergence during the daytime, first on the eastern slopes of Central America in themorning and then later in the afternoon along the western slopes.

The low-level moisture flux convergence is a necessary component in providingthe lift to start the convection and to supply the moisture to support it thereafter.Simultaneously, the diagnosed parcel buoyancy fields provide guidance as to how thechanges not only in the low-level temperature and moisture content, but also in thestructure of the tropopause (as modified by upper-level temperature advectionpatterns), could influence the vertical development of convection once it occurs.

Guidance about the overall height of the convection can also be obtained bycalculating the buoyancy of parcels lifted to a number of different levels in theupper level. The level at which the parcels are no longer buoyant and the strengthof the convective inhibition once the parcels penetrate the stratosphere (as indi-cated by negative values of buoyancy) can be used as a judge of probablethunderstorm heigh, as will be shown in the next section.

As noted in 2.1, the smallest phenomena that can be reliably predicted by anyNWP system must have a half wavelength (distance from minimum to maximum)of at least three to four grid points. Although this restriction prevents a number ofimportant local weather phenomena from being predicted directly using NWP,

3.2.3.2Detecting interaction between seabreeze and mountain circulations

in global model guidance


Figure 3.20300 hPa geopotential heights

(solid, m), temperatures(dashed, °C) and vertical motion

(upward motions solid, 10-3 hPa s-1)from 36-hour forecast valid

1200 UTC 26 September 1995


Figure 3.21 — Six-hourly sequencesof 850 hPa moisture flux convergence

(left, 10-7 s-1) and 250 hPa parcelbuoyancy (right, difference in

temperature between parcel andenvironment negative values indicate

buoyant parcels (°C)) for region ofCentral America shown in top panel

Moisture Flux Convergence Parcel Buoyancy

0600 UTC

1200 UTC

1800 UTC(~ Local Noon)

0000 UTC

recent advances in computer speed and model resolution allow global forecastingsystems to include not only the effects of larger-scale, continuous mountain ranges,but also the impact of large bodies of inland water and smaller areas of mountainsin their forecast guidance products. An example of where two such features inter-act regularly to affect local weather conditions is in the interior of eastern Africaaround Lake Victoria.

Figure 3.22 shows a schematic display of topography in eastern Africa, overlaidwith plots of 850 hPa moisture flux vectors. Lake Victoria appears in a plateau, sur-rounded on three sides by local areas of higher terrain. This is followed inFigure 3.23 by a six-hourly sequence of forecasts of the same parameter plus mois-ture flux divergence (divergence dashed). The case provides an example of theinfluence that even relatively small-scale geographic features can have on WAFSproducts from current, 90–100 km resolution global NWP systems.

Throughout the day, the southerly monsoonal flow over the Indian Oceanpersists at a relatively constant intensity. By contrast, the low-level flow over andaround Lake Victoria on this June day shows substantial variation during the 24-hour period. At sunrise (~0600 GMT), nocturnal drainage flows are dominating the850 hPa circulation, forcing local areas of divergence along the mountain ridges andweak moisture flux convergence along and immediately to the south and north ofthe lake. By local noon (~1200 GMT), however, the forecast low-level wind flowhas nearly reversed in response to the combined effects of the cooler lake surfaceand heated elevated terrain. Low-level convergence is now forecast for the elevatedareas, especially to the east of the lake, with low-level divergence inhibiting thedevelopment of convection in the intervening lowlands. The correspondingdiagnosed parcel buoyancy patterns provide further support for the development ofdeep convection over high elevations, with positive buoyancy noted over theeastern mountains at both 500 and 250 hPa (negative values in Figure 3.24) at thistime. The pattern of terrain induced low-level convergence continued to amplifyduring the afternoon (~1800 GMT), but now with the low-level divergence (andsinking) dominating the area immediately east of Lake Victoria itself and moreintense moisture flux convergence now situated over the mountains to thesouthwest, indicative of the development of convection in that area. More detailedinvestigation of the wind field shows that the enhancement of the local convergencepattern is the combined result of both continued heating of the elevated terrain andthe formation of a lake-breeze circulation along the western shores of the lake, witheasterly flow over the lake and westerly flow over land. By midnight (~0000 UTC),the pattern has again reversed, with low-level moisture flux convergence dominating


Figure 3.22Schematic display of local topographyover eastern Africa (increasing size of

boxes indicates higher elevation) atpoints on 1.25° latitude/longitude

WAFS output grid and 12-hourforecast, 850 hPa moisture flux

(arrows) valid at 1200 UTC 6 June1994. Area in subsequent figures

outlined

and supporting the development of nocturnal convection in the previous area ofsinking to the northeast of the lake. In the morning (~0600 GMT), the pattern isagain very similar to that of the previous day.

The forecast guidance shown here demonstrates that the current and futuregenerations of operational global-scale models can indeed forecast local circulationsthat mimic diurnally forced local circulation patterns that can impact daily aviationforecasts. However, it must be remembered that the scales of these phenomena inthe large-scale model output will be much larger than is observed locally. Forexample, the lake-breeze circulation noted at 1800 GMT along the west coast ofLake Victoria in the WAFS guidance shown in Figure 3.23c was the combinedresult of an easterly wind in the middle of the lake and a westerly wind 280 km to


Figure 3.23A) Schematic local topography surrounding Lake Victoria,with 6-hour forecast of 850 hPa moisture flux and moistureflux divergence (convergence solid, divergence dashed, 10-7 s-1)valid at 0600 UTC 6 June 1994. B) Same as A, except12-hour forecast valid 1200 UTC. C) Same as A, except18-hour forecast valid 1800 UTC. D) Same as A, except24-hour forecast valid 0000 UTC 7 June 1994. E)Same as A, except 30-hour forecast valid 0600 UTC7 June 1994

A B

C D

E

the west. Consequently, the on-shore convergence zone was forecast to be morethan 300 km wide, as opposed to the 10–20 km width noted in climatologicalstudies of the area. This does not mean that the forecast model output is of little usein forecasting local phenomena. Instead, it should serve as a warning that althoughNWP guidance may show the potential for the development of local weatherphenomena, it is the forecaster’s responsibility to interpret the model guidance andmodify it as necessary to the known local circumstances and all availableobservations, including satellite data — building upon the strengths of the modelphysics, but recognizing the limitations imposed by the resolution of the NWPsystem being used.

Two meteorological events which can sometime have devastating effects on aircraftoperating efficiency and passenger safety are icing and turbulence. Although we donot fully understand the physical mechanism responsible for creating these distur-bances and cannot forecast their development explicitly with present-day NWPmodels, we are beginning to understand more completely the evolutions of theenvironments that can be conducive for their development, both in the real atmos-phere and in NWP forecast guidance. Although modern NWP systems cannotsimulate the events themselves, even currently operational global models can pro-vide extremely valuable information about changing details in atmosphericstructure that can be used to identify areas where these events are most likely tooccur. The following discussion focuses on using NWP guidance to improve fore-casting of these two events and then explores ways in which forecasts of severalother hazardous weather phenomena could be aided using digital NWP guidance.

Ice accumulation during flight can have devastating effects on aircraft performance,ranging from adding large amounts of weight to small aircraft to disturbing the air-flow pattern over wings on many classes of aircraft — resulting in reduction of liftand sudden loss of altitude. Research conducted in the past ten years has begun toidentify an increasing number of factors that contribute to the formation of ice onaircraft surfaces. These include droplet size, ambient temperature and verticalmotion patterns, among others.

The most basic research shows that icing is most prone to develop when air-craft strike relatively large super-cooled drizzle droplets in areas where thetemperature ranges between 0° and –14°C. The greatest icing accumulation typi-cally occurs between –5°C and –9°C. Although all NWP models produce forecastsof upper-level temperatures, few models, especially on the global scale, include thedetailed micro-physical cloud simulations that are needed to forecast hydro-meteortype, size and evolution explicitly. Instead, many operational models and diagnos-tic icing forecast procedures infer the presence of clouds from the forecast relativehumidity fields. Values less than about 50 per cent are generally assumed to repre-sent cloud-free atmospheres and values near 100 per cent are assumed to be cloudyand likely to be precipitating. (This upper limit can vary from model to model,

3.2.4.1En-route icing

3.2.4PHENOMENOLOGICAL EXAMPLES


Figure 3.24A) Schematic local topography

surrounding Lake Victoria with 12-hourforecasts of 850 hPa wind and buoy-

ancy (negative values indicate buoyancy(°C) diagnosed for parcels lifted from

850 to 500 hPa at each grid point) validat 1200 UTC 6 June 1994. B) Same

as A, except buoyancy (°C) for parcelslifted from 850 to 250 hPa

A B

depending on the relative humidity threshold imposed for formation of large-scaleprecipitation discussed earlier.)

The same assumptions about cloud coverage can be used diagnostically to inferareas of icing potential from gridded NWP guidance. Although these calculationswould not have been possible using traditional facsimile map products, the abilityto manipulate the digital model guidance data makes it possible for forecasters totest for icing potential at many levels in the atmosphere, and at finer time intervalsthroughout the forecast period.

To create a display of the temperature weighted relative humidity values in theranges described above, the diagnostic display system can be instructed to performthe following calculation:

Icing Index = ((RH – 50) × 2) × (T × (T + 14)/–49)

where RH = relative humidity and T = temperature. Positive values are thendisplayed to isolate areas of icing potential, with the highest icing potential in areaswhere the index value approaches 100. The first half of this icing index representsdroplet numbers and size and increases linearly from 0 to 100 as the relativehumidity rises from 50 to 100 per cent. The second half of the equation simulatesobserved accretion rates using a quadratic temperature weighting which ranges froma maximum of 1 at –7°C to 0 at 0° and –14°C. Temperatures outside this range areassigned values of 0.

In the example shown in Figure 3.25, areas where high relative humidity isconcentrated in the 0° to –14°C range in panel A are clearly delineated by the icingindex values in panel B, with the highest values located near 100 per cent RH and–7°C.

Because the most difficult problem presented by pilots is often one of deter-mining at which level icing is likely to occur for a particular flight, the icingdiagnostic lends itself extremely well to cross-sectional display along a proposedflight path, rather than looking at a large sequence of plan view charts. Plots canbe generated for any or all of the expected flight routes in an area of interest, withdisplays of the icing potential guidance included at all data levels along the flightroutes, as in Figure 3.26 along the route shown in Figure 3.25b.

Another factor in the production of icing involves the vertical motion, specif-ically the decrease in upward vertical motion with height. This ingredient isnecessary both to promote the growth of supercooled water droplets through liftingand then to allow these droplets to be suspended in the areas of weaker verticalmotion and sub-freezing temperatures. If the vertical motion is too strong, thedroplets will continue to grow in size and weight and eventually become big enoughto precipitate. The cross-sectional displays of icing index can be enhanced toaccount for this factor by overlaying the vertical motion field on the combinedparameter displays discussed above (Figure 3.27). Forecasters can then identify


Figure 3.25A) 24-hour forecast of 700 hPa

temperature (dashed, °C) andrelative humidity (values ≥50 per cent

solid) valid 1200 UTC 23 March1991 over central North America.

Temperatures in 0° to -14° rangehighlighted by thick dashes. B) Sameas A), except relative humidity ≥50

per cent shaded and icing index solid.Flight path from northern Lake

Winnipeg to Saint Louis also shown

A B

areas where high values of the icing index are coincident with decreases in upwardvertical motion with height, in this case near 700 hPa at 42°N/92°W.

Vertical time-sections help forecasters to focus on the weather affecting a par-ticular location throughout a forecast period. These types of displays of icingpotential and variations in vertical motion can provide quickly understood guid-ance as to the likely onset and termination of an icing threat in specific areas. Inthe example in Figure 3.28, the model guidance suggests that an icing potentialexists at 42°N/92°W between 24 and 36 hours in the future, with the greatestpotential near 36 hours, when the vertical motion in this area has weakened.

Although global models do not as yet have sufficient horizontal or vertical reso-lution nor computation speed to include direct forecast of cloud droplet and ice crystalconcentration, regional and mesoscale models are beginning to include these charac-teristics as explicit prognostic parameters. Although the experience using these newtools has to date not exceeded the skill of techniques using relative humidity baseddiagnostic tools, the similarity of the forecast cloud patterns to satellite cloud images


Figure 3.26Cross-sectional

display of temperature(dotted, °C, except

0° to -14° rangedashed), relative

humidity ≥ 50 percent (shaded) andicing index (solid)

along flight pathshown in

Figure 3.25b

Figure 3.27Same as Figure 3.26,

but with wind flagsadded to depict

forecast verticalmotion (short flag is

1 × 10-3 hPa s-1, longflag is 2 × 10-3 hPa s-1)

along flight path inFigure 3.25b

bodes well for the use of these data. As continued development occurs, researchers andforecasters must work together to develop a better understanding of the algorithmsneeded to translate liquid cloud water concentrations (the model forecast parameter)into droplet size and concentration information. These in turn must then be relateddiagnostically to icing occurrence, potentially developing different formulations fordifferent aircraft class and flight altitudes.

Although turbulence affects more aircraft of all classes than almost any other mete-orological phenomenon, very little is yet understood about the many processes thatcontribute to its generation. It is highly dependent on weight, speed, wing span andphase of flight. Researchers have had a very difficult task merely studying the tur-bulence events themselves or quantifying the environments in which turbulenceforms. Unlike icing, where direct samples of cloud droplets can be collected byresearch aircraft, measurements of turbulence are much more difficult to obtain,since it is both generally invisible and very short-lived.

Turbulence in the atmosphere can form as a response to a variety of dynamicalinstabilities, analogous in the same way to convective clouds forming as a consequenceof thermal imbalance in the vertical structure of the atmosphere. In each instance,after an instability forms, a weather events occurs which attempts to return the atmos-phere to a more stable condition. As such, both convection and turbulence occurabruptly, are relatively short-lived and subject to a wide variety of causes.

Distinct types of turbulence should be treated as separate forecast entities.Turbulence events within or around deep convective storms are much differentfrom those generated over mountainous areas. Clear air turbulence (CAT) overmany areas is different from turbulence often found above areas of heavy stratoformprecipitation with imbedded convection. All of these are different from the turbu-lence which forms near the Earth’s surface due to daytime heating. Although wewill address several types of turbulence here, the reader should remember that dif-ferent tools will be needed to diagnose each type and that by performing only apartial diagnosis, major turbulence events may be overlooked. It should also benoted that because the physical mechanisms involved in producing turbulence arenot well understood and because the observations needed to detect the environ-ment in which it occurs are seldom adequate, statistical approaches can continueto play an especially important role in this area. Additional statistical techniquesfor forecasting turbulence are discussed in 4.5.

The parameter describing the potential for turbulence that has been in the meteo-rological literature for the longest period is the Richardson Number (Ri):

Ri = (g/θ)(∂θ/∂z) /|∂v/∂z|2

3.2.4.2.1Classical clear air turbulence

forecasting techniques

3.2.4.2Turbulence


Figure 3.28Same as Figure 3.27, except vertical

time section at 42°N/92°W fromanalysis through 48-hour forecasts

begun at 1200 UTC 22 March1991. Time increases from right to

left as noted at bottom of display,emulating the general easterly

progression of mid-latitude systems

where (g/θ)(∂θ/∂z) is the static stability in that layer and |∂v/∂z|2 is the magni-tude of the vertical wind shear across the layer of the atmosphere in questionsquared. Low values of Ri indicate the potential for turbulence by isolating areaswhere large vertical wind shear (either in wind speed or wind direction) occurs inconjunction with relatively weak static stability. The theory supporting this para-meter suggests that vertical variations for wind speed from one level of theatmosphere to another can reach limits where, if the static stability in the atmos-phere is weak enough, vertical overturning of the layer will occur in an attempt toreduce the vertical wind shear. This concept is especially applicable for diagnosingenvironments where CAT may form near the jet stream due to strong vertical windshears and where boundary layer turbulence may develop due to diurnal heatingand destabilization of the lowest levels of the atmosphere in the presence of strongwinds slightly above the surface.

Unfortunately, early attempts to use the Ri with NWP output failed to producemeaningful results. This to a large extent was due to the relatively coarse verticalresolution in the models then available. These models were unable to depict eitherthin layers of strong wind shear or extremes of static stability, both near the jetstream and near the Earth’s surface. More recent models have produced more reli-able results. Whilst the theoretical limit of Ri at which turbulence should form inthe real atmosphere is less than one, experience shows that Ri values diagnosedfrom current global scale models of five or less are often associated with areas whereturbulence forms. Because turbulence in the real atmosphere develops over a verysmall area and lasts for only very short periods of time, the fact that the NWP guid-ance does not reach the theoretical limit points to three factors:

(a) The inability of NWP systems to fully depict processes at these small scales;(b) Because the NWP grid point output often represents some form of areal averaging

and is only valid for specific time instants within the forecast period, the models’products seldom capture the most extreme conditions that occur in the modelbetween output times; and

(c) Parameterizations are included within the models which attempt to reduce dynami-cal instabilities before they reach levels which could otherwise jeopardize overallmodel performance.

Figure 3.30a shows cross-sectional displays of potential temperature (isen-tropes), wind barbs and wind speed (isotachs) through the jet streak shown inFigure 3.29. The inverse of the Richardson Number calculated using WAFS data isoverlaid in Figure 3.30b. The inverse of the Ri is shown in the display to empha-size areas of high turbulence potential with large values. The displays indicate threeseparate areas of maximum potential for CAT, one near the surface and two othersabove and below the jet stream, one located along the tropopause (indicated bytight vertical packing of isentropes at high levels in the cross-section) and the otherfound along the mid-level front (indicated by the sloping area of packed isentropesat mid-levels). At the level of the jet stream itself, where the vertical shear is min-imized, the risk of turbulence is less, even though the static stability (representedby the wide vertical spacing between isentropes) near the jet core is weak.

It should be noted that since several different levels of large turbulence poten-tial may exist at any time, it is often advantageous to use cross-sectional displays toidentify the levels most susceptible to CAT. For example, neither the spatial exten-sion or vertical locations of these areas of larger Ri near the jet stream would havebeen easy to detect using single level, horizontal displays alone, as shown inFigure 3.31, a, b and c. In addition, the area of CAT associated with the strong direc-tional wind shear near the surface front (near 700 hPa in Figure 3.30b and inFigure 3.31c) could easily have gone undetected by a forecaster concentrating onlyon conditions at jet stream levels.

Although the Ri has proven useful in detecting CAT, it often produces forecastsof regions of turbulence that are much larger than observed. To avoid this tendency tocreate false alarms, this technique can be extended to monitor areas where the Ri isboth approaching its critical value and expected to decrease over time — thus provid-ing guidance as to areas where the atmosphere is likely to be changing from dynamicallystable to unstable conditions, but where turbulence is unlikely to have removed the


instability already. The Ri change can be determined in several ways. One optionwould be to display time sections of the Ri at a particular location and note areas wherethe index is expected to change. Although useful in determining the locations of multi-ple layers of turbulence and for forecasting at specific sites, it is very difficult to knowahead of time where to locate the time section when forecasting for large areas. Asecond alternative is to calculate the Ri at each 3-, 6- or 12-hour model output timeand then display both the Ri and Ri tendencies for different levels overlaid on eachother, using different colours for each level or forecast times. By isolating areas whereRi and Ri change are both positive and taking the product of the two terms, the areasof possible CAT development may become more specific. A third option is to deter-mine the instantaneous Ri tendency directly by solving the equations of motion forchanges in wind and stability by computing the ageostrophic wind and difference intemperature advection across the layer directly and again overlaying this on the Ri.Although this may seem to duplicate the previous option, calculated instantaneouschanges can often be much larger at a specific point than when using time averagedcalculations.

A different method of delineating areas where CAT can be expected is to cal-culate the Ellrod Index (EI), which correlates the occurrence of CAT to thecombination of vertical wind shear and horizontal deformation through:

EI = VWS × (DEF + DIV)


Figure 3.29250 hPa wind barbs and isotachs

(solid, knots) from 0000 UTC18 October 1997 analyses over

southern Africa. Path of cross-sectionin Figure 3.30 shown

Figure 3.30A) Cross-section of potential

temperature (dotted, °K), wind barbsand isotachs (dashed, knots) throughthe jet streak shown in Figure 3.29.

B) Similar to A, but with inverseRichardson Number (solid, 10-2)

A B

where VWS is the magnitude of the vector wind difference across a layer in the atmos-phere and DEF is the magnitude of the total deformation (combined shearing andstretching deformation) of the wind in the layer and DIV is the divergence in the layer.Like the Inverse Ri, larger values of EI indicate greater likelihood for the developmentof turbulence. Unlike the Ri, which is based on a theoretical development, the EI wasdeveloped more empirically and verified statistically by relating areas where cloud struc-tures typically associated with CAT on satellite imagery with any number of kinematicvariables. In many cases, the EI and Ri show very similar patterns, as in Figure 3.32.This should not be unexpected since, although the EI is more convenient to calculatethan the Ri, both indices can be shown to be mathematically very similar, except thatstability term of the Ri is approximated through deformation and divergences terms of


Figure 3.31A) Same as Figure 3.29, except150 hPa wind barbs and isotachs

(dotted, knots) and inverse Ri (solid,10-2). B) Same as A, except 250 hPa.

C) Same as A, except 400 hPa.D) Same as A, except 700 hPa

Figure 3.32Same as Figure 3.30b, except with

Ellrod Index (solid) replacing inverse Ri

A B

C D

the EI via the geostrophic approximation. Work by Keller (1990) in isentropic co-ordinates has further validated this approach, showing that vertical compression ofisentropes which occurs in association with moving jet streaks enhances the potentialfor CAT by both changing the static stability and increasing wind shear.

More complex techniques for predicting other sources of CAT are also being investi-gated. In one of these, it is hypothesized that gravity waves can form (and then break)in the outflow regions of jet streaks due to a concentration of momentum in areas withmarked vertical change in density or static stability. When the dynamical forcesproducing these gravity waves are sufficiently strong, the waves which form along thedensity gradient will increase in amplitude until they reach a point where they break,in much the same way that waves on a lake break when they reach a certain height.The forces that create these breaking waves are produced by the along-stream advec-tion of momentum in the exit region of jet streaks, as shown mathematically in:

V •∇ V

where V is the wind vector and ∇ V is the gradient in momentum (wind speed) alongthe air flow. (It can also be shown that this formulation is also equivalent to the gradi-ent of kinetic energy.)

Gravity waves are assumed to be most likely to form in areas 1) where the jetstream is strong; and 2) where the wind speed decreasing rapidly in front of the jetstream maximum (called the exit region of the jet streak) is large. For example,Figure 3.33 shows the NWP guidance for a jet stream maximum entering SouthAmerica. Figure 3.34 indicates a dynamical environment conducive for gravitywave development ahead and slightly to the cyclonic side of the jet streak. It shouldalso be noted that this parameter can be approximated simply by calculating theadvection of the wind speed. Since the gravity waves tend to form along areas ofstrong vertical stability change, such as near the tropopause, it is again often advan-tageous to view this parameter in cross-section (Figure 3.35) along with the staticstability (potential temperature) field, but in this case orienting the cross-sectionalong the direction of the wind flow (along path shown in Figure 3.33).

Another form of turbulence that can have devastating effects on aircraft at highaltitudes is often found within, above or near thunderstorms. In either case, theturbulence can be anticipated by predicting the areas where convection is likely tooccur and monitoring the strength of the tropopause in those regions. Whilst it isstraightforward to expect turbulence within areas where the NWP guidance

3.2.4.2.2Forecasting turbulence caused by

other sources


Figure 3.3312-hour forecast of 300 hPa wind

vectors and isotachs (dashed, m s-1)for 3 September 1996 over southern

South America. Cross-section path inFigure 3.35 included

indicates significant amounts of convective precipitation, gravity waves can also beproduced when the parcels within the storms impact the tropopause. These wavescan then move away from the storms and break in clear air if the vertical motion inthe convection and the tropopause inversion are strong enough. Other techniquesfor forecasting the timing and location of severe convection are discussed later.

Breaking of gravity waves in the lee of mountains may cause structural damageto aircraft both at flight level and during descent into airports in valley regions. Inthis case, the gravity waves are produced in situations in the proximity of strongstable layers where very high speed winds extend downward from jet level to themountain tops. Although current operational NWP systems cannot forecast thesewaves explicitly, the availability of mesoscale model guidance may provide sufficienttools to better isolate areas when mountain waves are most likely to occur.

Near the Earth’s surface, turbulence can also occur when strong surface heatingproduces superadiabatic lapse rates near the surface, especially when the vertical windshear is strong. Again, the dependence of the Ri on both the vertical wind shear andthe static stability makes it a good tool for forecasting areas of strong turbulent mixingnear the surface.


Figure 3.34Same as Figure 3.33, except isotachs

(dashed, m s-1) and along-streamadvection of momentum

(solid, 10-5 m s-2)

Figure 3.35Southwest to northeast cross-section

along flow in jet streak exit regionshowing isentropes (dotted, °K),

cross-section relative wind arrows,isotachs (thin solid, m s-1) and along-stream advection of momentum (thick

solid, 10-5 m s-2)

Two final methods of detecting turbulence are based on the direct forecastingof turbulent kinetic energy (TKE) dissipation within mesoscale models, eitherthrough direct calculation within the models themselves or through diagnostic cal-culations from the model output. Although these techniques may show the bestlong-term promise for forecasting CAT in the future, the fact that current opera-tional models do contain sufficient resolution to depict turbulence at the scales atwhich it actually occurs has prevented the widespread application of these TKE-based techniques to date.

Sandstorms (and duststorms) can be prominent hazards to aviation in many partsof the world, yet they continue to be very difficult to forecast. Not only can theyreduce visibility greatly and often very suddenly, but they can also produce seriousdamage by scouring the surfaces of aircraft and damaging the combustion systemsof jet aircraft.

Although less research has been conducted on these systems than on other avi-ation hazards like turbulence and icing, the primary dynamical and physicalconditions favourable for their development are fairly well understood. The essen-tial ingredients include:

(a) Dry soil and strong winds — usually associated with nearly adiabatic lapse rates;and

(b) A deep, well-mixed boundary layer — to allow the sand to be lifted and then sus-pended for long periods.

In many localities where sandstorms are prevalent, forecasters have had littleor no access to digital NWP output, and as such, have had few opportunities toinvestigate the full potential of the NWP guidance in indicating where and whenthese storms are likely to develop. Experiences with severe weather forecasting sug-gest that an index which captures the conditions favourable for storm developmentcould be useful in detecting and monitoring the formation, intensity and progres-sion of the storms. The following discussion demonstrates how forecasters cancombine gridded data with physically sound reasoning to produce such an index.The case involves a situation in early autumn where the first cold front of theseason was moving southeastward into Saudi Arabia from the Mediterranean(Figures 3.36 and 3.37, and Figure 3.1 shown earlier).

The fundamental characteristics that need to be isolated and co-located are:(a) Areas with deep layers of weak static stability or nearly adiabatic lapse rates near the sur-

face. These can be detected by calculating the change in potential temperaturebetween the Earth’s surface and the top of a deep boundary, for example at 700 hPa.

3.2.4.3Developing a new diagnostic

forecasting tool for sandstorms


Figure 3.36Map highlighting area of Middle East

discussed in Figures 3.37 to 3.43

Figure 3.38 illustrates this parameter, with an area of weak static stability (smallpotential temperature difference in the vertical) across much of Saudi Arabia.

(b) Areas which have deeply mixed boundary layers. Typically, these regions have nearlyuniform winds throughout the lowest 150 to 200 hPa of the atmosphere. The ver-tical wind variability can be determined by calculating magnitude of the wind shearacross the layer. The wind shear vectors and their magnitude are shown in Figure3.39, in this case showing small values across the central part of the country.

(c) Areas of strong winds. These can be isolated easily by displaying the wind speed inthe boundary layer, as shown by the 10 m to 700 hPa layer average data inFigure 3.40. In this case, the major wind maximum stretches west-to-east acrossnorth-central Saudi Arabia, a different orientation from the previous two fields.

The dilemma now becomes one of determining the best way to display thecombination of these three components of the proposed index. If all threecomponents had indicated high storm potential with either high or low values, acombined index could have been derived by simply multiplying the three values


Figure 3.3712-hour forecast of near-surface

winds (10 m) and equivalent potentialtemperature (2 m θe, °K, cooler airmass solid, warmer air mass dotted)

valid 1200 UTC 1 October 1997

Figure 3.3812-hour forecast of 2-m (surface)

potential temperature (dotted, °K)and lapse rate (vertical change of

potential temperature, 10-2 °K hPa-1)in boundary layer between 2 m and

700 hPa valid 1200 UTC 1 October1997. Solid contours highlight

unstable stratification

together. This would have yielded a maximum or minimum where the three factorsoverlapped. However, since in this case the wind speed must be maximized in areaswhere the other two components are minimized, another tactic must be used. Themost straightforward approach would be to inverse either the wind speed or theother two factors before taking the product. In this case, the inverses of the stabilityand shear terms (Figures 3.41 and 3.42) were calculated in order to maximize theindex value where sandstorm potential is large. (Since care must be taken to avoiddivision by zero, it is advisable to replace very small numbers with a reasonably smalllimit when taking the inverse — i.e. removing superadiabatic values.)

The resulting index field in Figure 3.43 shows a narrow band of maximumvalues extending across north-central Saudi Arabia, encompassing both the areasof weakest stability and greatest winds. Indeed, observations for this day showedvisibilities of 1.5 km and less, caused by blowing sand associated with the first sub-stantial cold frontal passage of autumn.


Figure 3.4012-hour forecast layer mean wind

(m s-1) in boundary layer between10-m and 700 hPa valid 1200 UTC1 October 1997. Contours highlight

areas of highest wind speeds

Figure 3.3912-hour forecast vector wind shear

and magnitude of vertical wind shear(10-2 m s-1 hPa-1) in boundary layer

between 10 m and 700 hPa valid1200 UTC 1 October 1997. Solid

contours highlight areas of largestshear

Although the index proposed here used a strictly linear combination of the threecomponent fields, different non-linear weights could have been applied to the compo-nents if empirical or statistical data indicated that certain factors were more importantthan others. Likewise, the weighting used for each term could vary if particular factorshad different influences during distinct stages of development or varied betweenseasons. Tests could also be made to determine whether, in different situations or loca-tions, the kinetic energy (one half the wind speed squared) would provide betterguidance than the layer average momentum. In any event, meteorologists need to takeinto account local details about soil type and conditions across the regions and thento develop different thresholds for the NWP guidance applicable to the problem athand.


Figure 3.41Same as Figure 3.38, except

proportional to inverse lapse ratebetween 2 m and 700 hPa valid

1200 UTC 1 October 1997. Solidcontours highlight areas of least stable

stratification

Figure 3.42Same as Figure 3.39, except

proportional to inverse of verticalwind shear magnitude between 10 m

and 700 hPa valid 1200 UTC1 October 1997. Solid contours

highlight areas of least shear

Although NWP models are becoming more and more sophisticated, it is unlikelythat the forecast guidance will be correct in every respect — especially whendealing with extreme or especially violent weather events, such as warm-seasonconvection. Numerical weather prediction models were designed to perform theirmost fundamental functions best — these being the transports of heat and mois-ture and the change of wind speed and direction dictated by the equations ofmotion. In general, somewhere between 80 and 90 per cent of numerical fore-cast’s skill away from the tropics can be attributed to these basic processes. Atfiner scale, however, the remainder of the NWP calculations (especially the phys-ical parameterizations) can be extremely important in adding detail andlonger-range skill to the computer guidance, but often with less reliability.Forecasters must therefore learn to understand the capabilities and limitations ofthe NWP guidance, especially at smaller scales. This can be done very effectivelyby performing detailed post-analyses of especially difficult forecasting situations,such as described below.

Many examples exist of situations where NWP guidance which seems ques-tionable at face value could have provided forecasters with important informationabout changes which would occur in the wind, temperature and moisture patterns,especially prior to the onset of severe weather events. For example, in manyinstances where the precipitation forecasts were entirely in error, forecasters couldhave diagnosed dynamical and physical pre-cursor signatures of environmentsfavourable to heavy rainfall and severe weather events. In these cases, forecasterscould have made substantial improvements to their products by using diagnostictools designed to investigate the NWP guidance in the most advantageous way.

The following example shows how a technique developed for the prediction ofsevere weather in North America was applied with great success to a case of severethunderstorm development over southern Africa (see Figure 3.44). Even though thestandard level and precipitation guidance showed little or no sign of the potential forsevere convection, key indicators of the potential for severe weather were clearly iden-tified when the conventional gridded model output was properly manipulated. Thiswas done by converting the conventional isobaric model output into isentropic coor-dinates to better trace the flow of moisture and the effects of fronts in the loweratmosphere. The technique can also be useful in understanding the evolution of thefundamental atmospheric processes in other situations where traditional forecast toolsgive ambiguous or contradictory results.

Nocturnal convection was observed between Johannesburg and Pretoria shortlyafter 0000 UTC on 21 November 1996, associated with the movement of a weak surface

3.2.4.4Diagnosing severe weather

potential using numerical modeloutputs — stability indices and

isentropic coordinateinterpretation


Figure 3.4312-hour forecast sand storm index,

calculated as product of stability, windshear and wind speed products shown

in Figures 3.40 to 3.42. Solidcontours highlight areas of highest risk

circulation which formed in central South Africa and was translating slowly toward thesoutheast (Figure 3.45). The 12-hour accumulated precipitation forecast guidance(Figure 3.46) valid from the 80-km regional forecast guidance showed two areas ofprecipitation, one along the southern coast and the other along the northern border.Although the southern area of precipitation was verified, little if any rainfall was fore-cast over the area where the severe thunderstorms occurred shortly after 0000 UTC.

A traditional way of assessing the potential for the development of severeweather is to apply some of the many severe weather indices developed for theinterpretation of radiosonde observations to the NWP guidance. These indices caninclude the Lifted Index, the Total-Totals Index, the K-Index, the Showalter Indexand the SWEAT Index. In this case, however, the 12-hour forecast severe weatherindices showed the weakest stability (as represented by the Lifted Index guidancein Figure 3.46) in the areas of forecast precipitation and over the Indian Ocean,with relatively stable values encroaching the area of observed convection from thewest. By contrast, the 85 hPa Mixing Ratio guidance (Figure 3.47) showed a pattern


Figure 3.44Map highlighting area of Southern

Africa discussed in Figures 3.45 to3.60 and location of Johannesburg

and Pretoria (J/P)

Figure 3.45Mean sea level pressure analysis

(hPa) for 1200 UTC20 November 1996

which in general was favourable for convection, with a ridge of maximum moisturehaving already overtaken Pretoria from the northwest. Winds in this area of thestorm’s warm sector were from the north (Figure 3.48), with the largest shears alongthe moisture gradient in the central part of the country.

A measure of the amount of moisture being made available to supportconvection can be obtained from the moisture flux fields, which is calculated as theproduct of the gridded wind and moisture data. Although the 850 hPa moisture fluxin Figure 3.49 showed a well-defined stream of moisture crossing South Africa fromthe north and northwest, the areas of moisture flux convergence required to fuel theconvection once it began were located away from the convective outbreak, andinstead were co-located with the areas of forecast precipitation. In fact, relativelystrong moisture flux divergence was predicted at 850 hPa in the area of observedconvection. (It should be noted that the convective parameterization used in thismodel was developed, like most others, to simulate tropical, oceanic convection. Assuch, the convective precipitation in this model tends to form in areas where there


Figure 3.4612-hour precipitation forecast (mm)

valid 0000 UTC 21 November1996. Areas of any precipitation

shaded, ≥ 5 mm contoured

Figure 3.4712-hour forecast of lifted index (°C,

least stable values solid) valid0000 UTC 21 November 1996

is substantial low-level isobaric moisture flux convergence and often fails to capturesevere weather events which form in drier, mid-latitude, baroclinic environments.)

Aloft, the 300-hPa flow (Figure 3.50) showed a jet streak extending southeast-ward across the country, with the direct circulation in its entrance regionsupporting the eastward progression of the surface cold front. The cross-sectionalong the line through the exit region of the jet streak in Figure 3.51 reveals moredetail about the frontal structures and low-level moisture regimes. The potentialtemperature field shows a deep baroclinic zone supporting the jet streak, above asurface front separating a dome of colder and drier air to the south (lower potentialtemperature) from the warmer and moister air confined primarily to the north-eastof the surface front.

Because in the majority of situations parcels of air move along atmosphericlayers in which they retain their potential temperature (as opposed to flowing alongconstant pressure surfaces as is often inferred when using isobaric charts), transfor-


Figure 3.4812-hour forecast of 850 hPa

geopotential height (dashed, m × 10),wind flags (m s-1) and mixing ratio

(g kg-1) valid 0000 UTC21 November 1996

Figure 3.4912-hour forecast of 850 hPa moisture

flux (arrow length proportionalto moisture transport at grid

points) and moisture flux divergence(× 10-7 g kg-1 s-1, convergence solid)valid 0000 UTC 21 November 1996

mation of the NWP guidance from isobaric coordinates can be especially useful inanalyzing difficult forecast situations.

Of particular importance in this case was the ability to obtain a more detailedunderstanding of how the low-level moisture flow patterns evolved to produce anenvironment conducive for severe convection (i.e. localized increase in low-levelmoisture and existence of a lifting mechanism). In order to assess these effects, sev-eral low-level isentropic surfaces were derived from the standard, isobaric levelgridded model output. The 305°K and 310°K isentropic surfaces were selectedbased upon the potential temperatures forecast for the bottom and top of theboundary layer in the cyclone’s warm sector, as noted in Figure 3.51.


Figure 3.5012-hour forecast of 300 hPa

geopotential height (solid, m × 10),wind arrows and isotachs (dashed,≥ 50 knots) valid 0000 UTC 21

November 1996. Path ofcross-section in Figure 3.51 shown

Figure 3.51Cross-section of

potentialtemperature (solid,

°K), isotachs(dotted, ≥ 50 knots)

and mixing ratio(dashed, g kg-1)

valid 0000 UTC21 November 1996

extending fromcentre of the upper-level low, southwest

to northeast andcrossing

Johannesburg andPretoria

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The 12-hour forecast of isentropic pressure, moisture and wind guidance for0000 UTC (Figure 3.52) shows a well defined cold front extending southeastwardacross the western third of the country, as delineated by the upward slope (decreas-ing pressure) of the 305°K isentropic surface, from below 900 hPa in the warmestair to above 500 hPa above the cold air to the southwest. The primary source ofmoisture emanates from the Indian Ocean, moving gradually from the equator,southward and upward along the 305–310°K isentropic layer into the warm sectorof the cyclone in central South Africa. Although the winds in the warm region areweaker than at 850 hPa, both the source of the low-level moisture near the Equatorand the primary areas of moisture transport along the weak surface front extendingacross South Africa are readily apparent and paint a dynamically and physicallyconsistent picture of the atmospheric motions taking place.

Unlike constant pressure coordinates, where the volumetric moisture mea-surement is the mixing ratio itself, the total volume of moisture in an isentropiclayer depends not only on the mixing ratio (water vapour per unit mass) in the


Figure 3.5212-hour forecast of pressure (dashed,

hPa) on 305°K isentropic surface,overlaid with mean wind arrows and

mixing ratio (dashed, g kg-1) for305–310°K isentropic layer valid0000 UTC 21 November 1996

Figure 3.5312-hour forecast of pressure depth

(hPa) for 305–310°K isentropic layervalid 0000 UTC 21 November

1996. Areas of weaker staticstability (isentropic lapse rate

≤ 5°K / 100 hPa) solid

layer, but also the inverse of the static stability, which represents the atmosphericmass holding moisture in the layer. In this instance, the area of greatest mass inFigure 3.53 in the isentropic boundary layer (and correspondingly weakest low-level static stability) is clearly isolated in the warm sector of the cyclone, just to thenorth of Pretoria, whilst the minimum immediately to the west was associated withthe stable air within the surface cold front.

By calculating the total moisture in the layer from the product of the mixingratio and mass in the isentropic flow layer (Figure 3.54), a much more distinctmaxima of low-level moisture becomes apparent than had been present in the iso-baric display — with a clear concentration of moisture in the area immediatelyupwind of Pretoria. Although the average winds in the moist region are relativelyweak compared with areas at higher elevation along the cold front, the presence ofa distinct maximum of moisture causes the low-level adiabatic moisture transport(calculated as the product of the wind and total moisture content and shown inFigure 3.55) to become exceedingly strong in the storm’s warm sector. The axis of


Figure 3.5412-hour forecast of total moisture

content (10-1 g cm-2) 305–310°Kisentropic layer valid 0000 UTC

21 November 1996

Figure 3.5512-hour forecast of total moisture

content (≥ 8 × 10-1 g cm-2) and totalmoisture flux (arrow length

proportional to moisture transport inlayer) in 305–310°K isentropic layervalid 0000 UTC 21 November 1996

the largest moisture transport is again extending through the Johannesburg/Pretoriaarea, but unlike the situation at 850 hPa, significant variations are observed alongthe path of the moisture transport.

When the adiabatic moisture flux convergence is computed from the moisturetransport grid to obtain a measure of moisture accumulation necessary to supportconvection (Figure 3.56), clear localized signals of this process are apparent in threeareas, one along the coast and one along the northern border in areas where pre-cipitation was forecast to occur by the model, and one in the area where convectionwas observed later. The question remains as to which of these areas also contains alifting mechanism sufficient to initiate precipitation. This can be addressed bymanipulating the NWP guidance further to determine regions where both moistureconvergence and low-level lifting are present.

Adiabatic lifting can be calculated from the combination of the upwardmotion (pressure advection) along the bottom level of the isentropic layer and themass convergence below that level. The results in Figure 3.57 not only indicate the


Figure 3.5612-hour forecast of total moisture flux

(arrows) and adiabatic moisture fluxdivergence (solid, 10-5 g cm-2 s-1,

only areas of convergence shown) in305–310°K isentropic layer valid0000 UTC 21 November 1996

Figure 3.5712-hour forecast of pressure (hPa),

wind arrows and adiabatic ascent(10-3 hPa s-1) at bottom of

305–310°K isentropic layer valid0000 UTC 21 November 1996

development of localized lifting near Pretoria just prior to the observed onset of theconvection, but also reinforce the NWP forecast of precipitation along the coast.The support for convection becomes more apparent if the fields of moisture fluxconvergence and low-level ascent are combined to generate a single “isentropicconvective potential” product as in Figure 3.58. It should also be noted that thelack of a low-level lifting mechanism in the area of forecast precipitation along thenorthern border should serve as an indicator of inconsistency within the models’dynamics and convective parameterization and thereby should reduce forecasterconfidence in the NWP guidance for that region.

One additional ingredient can be studied to gauge the rapidity of the potentialconvective development. This is the presence of convective instability (decrease ofequivalent potential temperature with height), a vertical stratification of the lowertroposphere which allows a layer of the atmosphere to overturn automatically if liftedsufficiently and thereby support rapid storm growth. This can be determined either bycalculating the difference in equivalent potential temperature across the isentropiclayer (Figure 3.59) or by displaying a cross-section in the area of suspected convection(Figure 3.60). Again, an area of strong convective instability is found ahead of the coldfront in the cyclone’s warm sector over Johannesburg and Pretoria.

When all three of the isentropic diagnostic tools are viewed in combination, itbecomes clear that even though the conventional NWP forecast guidance did notindicate significant amounts of precipitation in the area of observed severe con-vection, fine-scale signatures of the potential for convective development werecontained in the NWP guidance which could have been valuable to forecasters ifdiagnosed properly. Even though the traditional synoptic-scale forecasting toolsshowed little evidence of this possibility, the isentropic tools designed to diagnosethe likelihood of convection combined to indicate a strong potential for rapiddevelopment localized specifically around Johannesburg and Pretoria. Althoughconventional techniques will provide very useful guidance in many cases, the avail-ability of more sophisticated derived tools, such as can be produced by convertingthe conventional model guidance into isentropic displays, can be particularly valu-able for forecasters dealing with many difficult forecasting situations. However, it isimperative to remember that, in all short-range forecasting situations, forecastersmust take constant vigil of real-time observations (including satellite imagery) bothto make fine-scale adjustments to the NWP guidance and to avoid being “surprised”by rapidly developing local weather events that are not depicted by the computerguidance.


Figure 3.5812-hour forecast of "isentropic

convective potential" (negative valuesindicate increased potential forconvection) based on adiabaticmoisture flux convergence andadiabatic ascent computed for

305–310°K isentropic layer valid0000 UTC 21 November 1996

3.3 STATISTICAL INTERPRETATION OF MODEL OUTPUT

The potential benefits of the application of statistics to weather forecasting problemshave been recognized for almost as long as the complexity of weather forecastinghas been appreciated. Dines (1902) pointed out the irregularity of meteorologicalevents and suggested that the laws of probability should be used in forecasting. Hisview was that the laws of statistics would put forecasting on an objective footing inthe absence of understanding of the physics and dynamics of the atmosphere and in

3.3.1HISTORY


Figure 3.59 12-hour forecast of convectiveinstability (°K, negative values

indicate unstable air masses) across305–310°K isentropic layer valid0000 UTC 21 November 1996

Figure 3.60Southwest to northeast

cross-section forecastof equivalent potential

temperature (°K)along path shown in

Figure 3.59 valid0000 UTC

21 November 1996

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the absence of sufficiently detailed observations. He quoted Laplace as saying thatstatistical laws are “common sense reduced to objective computation”.

By 1950, after the first numerical model had been successfully integrated, theperspective began to change. Wadsworth (1951) still considered statistical weatherforecasting to be a rival of dynamic models as the best way to generate weather fore-casts. He foresaw the trends of the next decades by stating: “There is no doubt thatthe ideal way to solve any dynamical problem is to set up a physical model in termsof mathematical symbols and, after having solved the resulting mathematicalmodel, to use statistical methods to solve for the basic parameters”.

The first widespread use of model output in operational statistical forecasttechniques followed the “perfect prognosis” method (perfect prog, or PPM) (Kleinet al., 1959). Within a few years, the idea of incorporating model output directlyinto the statistical relationships evolved. Named model output statistics (MOS)(Glahn and Lowry, 1972), the latter method has gained in popularity and now bothMOS and PPM are in widespread use in countries which have routine access to theoutput of numerical models.

It is now the common view that NWP models are preferred to purely statisti-cal methods for short-range forecasting at least; it is also recognized that statisticalmethods will have a role for the foreseeable future as a way of adding value to NWPforecasts, and anchoring their forecasts in reality as represented by historical obser-vational data.

The basic purpose of statistical techniques is to quantify relationships betweenweather elements of interest and other meteorological variables which can be read-ily forecast. If these meteorological variables (called predictors) are chosen not onlybecause they are expected to be related to a surface weather element but alsobecause they can easily be predicted, for example by a model, then the statisticalrelationship can be used to predict the weather element.

All statistical processing begins with a data set of historical data. First, one ormore quantitative relationships between the predictors and the weather elementare developed from the historical data set, which is sometimes called the “develop-ment” or “dependent” sample, or the “training sample”. The second stage ofdevelopment is to test the statistical equation on another data set, called the “inde-pendent data set”. The second step is necessary because statistical methods alwayswork better on the sample for which they were developed. Testing on independentdata gives a more realistic idea of performance levels in operations.

In statistical applications, sample size is very important, since small samplesgive rise to unstable forecast techniques. For meteorological problems it is oftendesirable that there be at least 250 events in the sample. In meteorological appli-cations, independent data samples are rare as samples often consist of time series ofevents which exhibit serial correlation. In general, the greater the correlationamong the events of the sample, the smaller the amount of new information con-tributed by each event, and the larger the sample must be to provide a gooddefinition of the relationship between predictors and the weather element.

The reliance on historical data is both an advantage and a disadvantage of sta-tistical processing. It is an advantage because it ensures that forecasts are related torecent climatology, since the statistical relationships are built using observationaldata. Products which come directly from an NWP model must depend on the detailand accuracy of the model’s representation of the physical processes for accuratesimulation of time series of observations at a site. Direct verification of model fore-casts against observations helps with understanding the deficiencies of the modelforecast.

The use of historical data is a disadvantage because it limits statistical applica-tions to locations where historical data sets are available. This is the mostimportant reason statistical processing has not often been applied to upper-air phe-nomena such as CAT: it is difficult to obtain enough data to develop statisticalrelationships.

The steps of development of an operational statistical forecast product may besummarized as follows:

3.3.2STATISTICAL PROCESSING


(a) Define the weather element;(b) Select the formulation methods and the statistical analysis method and prepare the

data set;(c) Develop the statistical relationships;(d) Test the equation performance on the development data, on independent data, and

on a case-by-case basis;(e) Implement the equation into operations, if the results of tests are positive;(f) Post-process the forecasts as needed.

Each of these steps is discussed in the sections which follow.

To select the appropriate statistical technique, it is useful to classify weather ele-ments into two types, continuous and categorical. Continuous weather elementsare those where the forecast can take any value, for example, a temperature of 15degrees or a windspeed of 15 knots. Of the surface weather elements, normally onlytemperature and dewpoint, and sometimes windspeed and direction, are treated ascontinuous variables.

Other elements are inherently categorical, or are treated as such. For example,obstructions to vision are already categorical: Fog can be classified according towhether visibility is above or below 1 000 m. Similarly, precipitation can bereduced to a categorical variable; it is or it is not raining, and amounts can begrouped into classes too. Categorical variables are usually forecast using a probabil-ity of occurrence, that is a probability of precipitation or of fog.

Precipitation type is a weather element that may have several distinct cate-gories, e.g. frozen (consisting of snow, snow grains, ice pellets, etc.), liquid(consisting of rain or showers) and freezing (freezing rain). How the categories aredivided is a matter of individual application, but they must be kept distinct.

Elements such as ceiling, visibility and cloud amount are continuous to theextent that they may take on many different values in any observation, but they areusually categorized in operational use. This is partly because of the unusual data dis-tribution exhibited by some weather elements.

Observation may be replaced by a set of categorical variables, one for each cat-egory. The categorical variable is set to one if the observation falls into the categoryrepresented by that variable; otherwise it is set to zero.

For example, the ceiling height might be divided into five categories: less than200 feet (ft), 200 to 400 ft inclusive, 500 to 900 ft inclusive, 1 000 to 2 900 ftinclusive, and 3 000 ft or more. An observation of 700 ft would be replaced by thefive values (0,0,1,0,0) since the observed ceiling height falls within the thirdcategory.

The output of statistical development for categorical elements is usually theprobability of occurrence of the event within each category, for example 20 percent probability the ceiling will be between 200 and 500 ft. Of course if everythingis working correctly, the set of probabilities for all categories of an element will addup to 100 per cent for every forecast.

There are two formulation methods used in statistical interpretation of NWP, PPMand MOS. It is the source of the data set used in development that distinguishesthem. Tables 3.1 and 3.2 summarize the characteristics of both techniques. It iscustomary to classify a method as MOS if any of the predictors used in thedevelopment are from model output. In practice, MOS methods are usually acombination of all types of predictors. For example, a prediction equation for ceilingmight include a low-level moisture predictor from a model (MOS), the observeddew point depression at 850 hPa (PPM) and the ceiling six hours ago (classical).Perfect prog methods also may contain classical predictors such as the ceiling heightsix hours ago.

Persistence predictors are used for short-range forecasting and are most usefulin situations where the variability of the weather is low. However, they have littlevalue in predicting changing weather, such as predicting clearance of fog.

3.3.2.2Selecting formulation methods and

statistical analysis techniques3.3.2.2.1

Formulation methods — PPM andMOS

3.3.2.1Defining the weather element


The choice of statistical processing method depends on the weather element pri-marily, but may also depend on what is available. Regression, for example, iscommonly available in commercial packages, and can be used, with care, for mostweather elements. Discriminant analysis, while more suitable than regression forsevere weather elements, is less accessible and more complicated to apply thanregression. Tree-based methods are relatively new, which means that the necessarysoftware may be even harder to obtain or more expensive, or both. Several statisti-cal processing methods that are applied to weather element processing are brieflydescribed in this section.

Multivariate linear regression (MLR) is the most widely used statistical tech-nique and probably the easiest to apply. It works best for continuous weatherelements. A complete description of MLR, with many worked examples is givenin Draper and Smith (1981). The basic idea of linear regression is shown inFigure 3.61. In the figure, a set of values of the 850 hPa wind speed (a predictor)are plotted against the corresponding observed surface wind speed. A straightline has been fitted so as to minimize the total of the squares of the distancesbetween the points and the line (the “least squares method”). The fitting pro-cedure finds the two coefficients which define the equation of the line, the pointwhere it crosses the Y axis (the intercept) and the multiplier for the predictor

3.3.2.2.2.1Multivariate linear regression (MLR)

3.3.2.2.2Statistical processing methods


Table 3.1Comparison of

formulation methods

Table 3.2Characteristics of

formulation methods

Development of equations

Application inoperational forecastmode

Comments

PPM

Weather element —observed at T; predictors— observed (analyzed) atT

Predictor values valid forT + dt from prog issuednow, to give forecast validat T + dt

dt can take any value forwhich forecast predictorsare available

MOS

Weather element —observed at T; predictors— forecast values valid atT from prog issued atT – dt

Predictor values valid forT + dt from prog issuednow, to give forecast validat T + dt

Same application as PPMbut separate equationsused for each dt

Strength of statisticalrelationship

Model dependence

Treatment of bias(average error)of model

Development sample size

Types of variables

PPM

Strong because uses onlyobserved data concurrentin time

Model-independent

Does not account formodel bias — modelerrors decrease accuracy

Large developmentsample possible

Must have access toobserved or analysedvariables

MOS

Weaken with increasingprojection time due toincreasing model errorvariance

Model-dependent

Partially accounts formodel bias (provideddevelopment sample biassimilar to operationalmodel bias)

Generally small develop-ment samples — dependson frequency of modelchange

Must have access tomodel output variables.Can use variables that arenot observed

(the slope). Once the line is defined, any value of the 850 mb wind speed canbe substituted into the equation to give an estimate of the surface wind speed.In meteorological applications of regression there is usually more than one pre-dictor and the procedure is generalized to find the best overall linear fit betweenall the predictors and the weather element (hence the name “multivariate linearregression”). The output is a set of coefficients, one coefficient for each predic-tor and one intercept.

The element wind is treated a little differently in regression applicationsbecause it is a vector quantity (Glahn, 1970). Normally, equations are developedseparately for the speed, and the west and the south components of the surfacewind. Forecasts of the west and south components are combined to estimate thewind direction and the equation for speed is used directly to estimate the wind-speed. Although one could use the west and south components to estimate thespeed as well, this tends to produce speed forecasts that are too low on average.Similarly, in difficult sites, wind direction from individually derived componentscan conflict with climatology.

The linear nature of MLR can be modified by transforming the variable intoan approximately linear one. For example, wind speed stops at zero, and is morevariable the larger the average wind speed. A logarithmic transform creates anapproximately linear variable, whose variability remains constant across the range.Similarly there are extensions to linear regression such as regression estimation ofevent probabilities described below and logistic regression (Lemcke and Kruizinga,1988) which are designed for probabilistic forecasts of categorical variables.

Regression estimation of event probabilities (REEP) (Miller, 1964) is a variation ofregression designed for use with categorical weather elements. The weather ele-ment, and if necessary the predictors, are replaced with sets of categorical variables,one for each category, as described above. Figure 3.62 is a plot of precipitationoccurrence after conversion to a categorical variable versus vertical velocity as apredictor. Non-precipitation events correspond mostly to negative vertical velocity(subsidence) and precipitation events tend to occur for positive vertical velocitycases (ascent). The line shows what might be obtained from a linear regression pro-cedure applied to such a data set. Forecast values of the categorical form of theweather element that are obtained from the equation will usually but not always liebetween 0 and 1 and must be truncated to this interval. The output of a REEP pro-cedure is interpreted as the probability of occurrence of the weather event categoryrepresented by the categorical variable.

REEP is widely used in the United States for forecasting precipitation proba-bilities, for thunderstorm forecasting (Glahn, 1985), and for forecasting ceiling,visibility, cloud amount and obstructions to vision. REEP is used in Canada also forprecipitation forecasting (Yacowar et al., 1985).

3.3.2.2.2.2Regression estimation of event

probabilities (REEP)


Yes = 1

No = 0

-5 0 +5

Y = 0,65

Y = a + bx

Vertical velocity (cm s-1)

Intercept

Y =

Pre

cip

itatio

n

Figure 3.61An example of linear regression. X is

the predictor (850 hPa windspeed, forexample) and Y represents the

weather element to be predicted(surface windspeed). The regression

line is fitted by minimizing the sum ofthe squares of the distances ei between

the data points and the line. Theplotted points represent the

observations of the surface windspeedmatched to corresponding values ofthe 850 hPa windspeed, which maycome from a model (MOS) or from

observations (PPM)

Like the REEP method described above, multiple discriminant analysis (MDA) isintended for use with categorized weather elements and is a linear technique.However, it has a slightly different focus. MDA is designed to define relationshipsbetween predictors and a weather element that optimizes the ability to reliably predict to which category of the weather element an observation belongs. It usesthe development data set to seek information which distinguishes one categoryfrom another. Applications of MDA to some meteorological problems, includingceiling and visibility, are described in Miller (1962) and in Wilson (1983, 1987,1988). The form of MDA that is usually used in operations is the parametricmethod described by Miller (1962). Figure 3.63 illustrates the generalidea of MDA. A data set consisting of values of two predictors, vertical velocityand relative humidity is plotted. As expected, rain events are associatedwith higher (positive) vertical velocity and higher relative humidity. Any new fore-cast event found on the scatter plot can be assigned a probability of belonging toeach of the categories by a formula related to the distance from the centre of eachgroup.

3.3.2.2.2.3Multiple discriminant analysis

(MDA)


Yes = 1

No = 0

-5 0 +5

Y = 0,65

Y = a + bx

Vertical velocity (cm s-1)

Intercept

Y =

Pre

cip

itatio

n

X

X

XX

X

XX

X

X

X

X

X

X

X

XX

X X

XX

XXX

XXX X

X

X

X

XX

XX

X

X

X X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X X

X

X

X

XX

X

X X

X

X

X

XX

XXX

X

X

XX

X

X

X

X

X

XX

X

X

XX

XX

X

X

XX

X

XX

XX X

X

XX

X

X

X

X

X XX

XXX

X

Precipitation

No precipitation

Relative humidity

Vert

ical

vel

ocity

Discriminant

function

Figure 3.62An example of REEP. The ordinate is

a binary variable representing theoccurrence of precipitation. All cases

where precipitation occurred areassigned the value 1 and all cases whereprecipitation did not occur are assignedthe value 0. A straight line is fit to the

data. Given values of the verticalvelocity predictor, the line can be used

to estimate the probability ofprecipitation. The data are represented

by the dots. The size of the dots isproportional to the number of cases at

each plotting point(after Gilhousen, 1976)

Figure 3.63A schematic bivariate plot of verticalvelocity and relative humidity. Caseswhere rain occurred are representedby crosses and cases where rain didnot occur are represented by dots.The large symbols are the category

averages. The discriminant function isshown by the straight line

Output from MDA procedures is a set of probability values for all the categoriesof the weather element, obtained using the discriminant functions as describedabove. MDA has been applied successfully in Switzerland (Altherr et al., 1982); inCanada, Stanski (1987) used it in precipitation type, ceiling and visibility fore-casting; and it has also been applied to probability of precipitation amountforecasting (Wilson and Yacowar, 1980; Wilson and Stanski, 1984). MDA is aslightly more complicated procedure to design and implement into operation, buthas been shown to produce sharper forecasts (i.e. more capable of forecastingextremes in the distribution), but less reliable probability forecasts than REEP(Wilson and Stanski, 1983). Experience with MDA indicates that it is a goodmethod to use when an “alarm” is wanted for extreme events.

Classification and regression trees (CART) is a statistical method that has becomepopular with forecasters in Canada in recent years because it mimics a commonapproach to the weather element forecasting process. Like MDA, REEP and logis-tic regression, it is intended for categorical variables. However, unlike the otherstatistical methods, CART sets up a decision-tree structure for classification of theforecast variable into one of several categories defined by the user (Figure 3.64).

The CART technique is fully described by Breiman et al. (1984). New predic-tor values are fed to the categorical decision rules and control passes through thetree until a terminal point (node) is reached. There will be a confidence factor(probability) associated with each terminal point which depends on how well thetree was able to classify the events of the development sample. CART’s mainadvantages are that it is fully non-parametric (no assumptions need be made aboutthe data distribution) and it is non-linear. CART can handle situations where thephysical relationship between predictors and weather element change over therange of values of the weather element.

Recent enhancements have been made to the CART technique to improve itsresponse. One of these is to use neural nets to improve the resolution of the pre-diction. CART has so far been applied to MOS forecasts of heavy local snowfalls(“snowsqualls”) and surface ozone pollution episodes (Burrows, 1990a, 1990b,Burrows et al., 1995).

When forecasters verify their forecasts from yesterday, and decide on that basis toadjust ideas about their forecasts today, they are using an adaptive technique.Adaptive statistical techniques are designed so that the relationship is built up asthe data are collected. They are most useful in situations where not enough datahave been collected to develop a reliable statistical forecast equation. The need towait for enough data to be collected is a weakness of all the statistical methodsdescribed above, because they cannot respond immediately to changes in the fore-cast system. Adaptive techniques offer the potential of more rapid response to

3.3.2.2.2.5Adaptive procedures

3.3.2.2.2.4Classification and regression trees

(CART)


Vertical velocity< 07

850 mbRelative humidity

> 70%


> 90%

Vertical velocity> 5 cm s-1

SCT

SCT SCT

OVC

BKN BKN BKN OVC

500 mbVorticity

advection > 0


> 80%

850 mbVorticity

> 10 x 10-5

Yes No

Yes No No

No

YesNo

Yes

Yes

No NoYesYes

Figure 3.64A schematic example of a

classification tree. The binary decisionrules are contained in the rectanglesand the terminal nodes representing

decisions are encircled. The weatherelement is cloud amount in three

categories, scattered (SCT), broken(BKN) and overcast (OVC)

changes in the forecast system or the model and include the Kalman Filter, whichis a simple recursive updating procedure and updateable MOS, which is any MOSdevelopment that is designed to permit frequent updating of the equation.Adaptive techniques are described briefly below.

The Kalman Filter (KF) is an adaptive technique for correcting the systematicerrors in forecasts of specific weather elements that come from any source.“Systematic” means that part of the error can be modelled as a linear expression offorecast weather elements. Originally developed for signal processing applications,it has been used in a simple form for statistical weather forecasting applications.The KF is most often applied to direct model output forecasts of weather elements,but may be applied to forecasts from any source. The KF could be used to correctsystematic errors in statistical forecasts, for example arising from prolonged periodsof abnormal weather which were not contained in the development sample for thestatistical procedure.

Basically, the KF method is a prediction–correction process. To implement aKF, one must first choose predictors and formulate the linear model that will beused to explain the errors in the forecast. For example, one might consider thaterrors in temperature are greater when the temperature is far from the climatologi-cal normal, and choose the temperature anomaly as a variable to explain (linearly)the errors. Unlike automatic statistical methods, the developer of a KF must choosethe model. There are no automatic statistical selection methods to choose predic-tive variables and, for example, the developer must choose a set of variables whichcommonly have high predictive weights.

Each time a KF forecast is produced, using the latest version of the linearmodel, it is then verified with the corresponding observation, and the error is com-puted and used to estimate updates to the coefficients of the linear model. The KFis thus a recursive procedure that “learns” from its own errors. Compared to statis-tical techniques, which can be used only to update the forecast, until a new data setis available for redevelopment of the equations, the KF procedure uses the latestdata to update both the forecast and the equation.

In an operational context, the KF is quick and easy to implement and use,especially if the linear model is kept simple. However, it has been appliedsuccessfully mainly to “continuous” surface variables such as temperature, windspeed and direction, although it is now being used for probability of precipitation(POP). Some adaptation of the model is necessary to make it work effectively forcategorized variables such as precipitation type or occurrence or ceiling height. If aKF were to be started during a prolonged dry period, for example, it would quicklylearn to forecast no rain all the time, then be caught by surprise when rain wouldoccur.

Figure 3.65 is an example of a KF forecast of temperature for Montreal, for 83days in 1995. This was a three-parameter Kalman model consisting of a constant,the model output temperature and a PPM statistical forecast of temperature. It canbe seen that there are sometimes relatively large errors during the first few days ofthe period, as the filter learns how to adjust for the characteristic errors. The verticaldotted line represents a change in the NWP model. After this change, the KF has toreadjust to a new set of error characteristics, which it evidently does within a fewdays. Once again the user is in control: after a model change when errorcharacteristics are unknown, the confidence factor can be changed in the filter. Thatis, it can be told to respond more cautiously after a model change or, if desired, torespond more quickly to the more relevant recent errors from the new model.

This example illustrates two advantages of the KF. First, it can be used to blendforecasts from different sources. The filter will quickly learn which is the morereliable forecast tool and set the coefficients accordingly. In this sense the KFbecomes a convenient consensus forecasting tool. Second, it automatically andquickly responds to systematic changes in error characteristics, such as occur after amodel change. The KF therefore may be seen as an early response tool, for useimmediately following model changes, before sufficient data are available forapplication of more comprehensive techniques such as MOS.

The Kalman Filter


Updateable MOS (Ross, 1987) is a method of developing MOS equations, whileensuring a capability to respond quickly to changes in the NWP model. It is thusan optimization of the MOS development procedure to make it more responsive inan environment of frequently changing models. Updateable MOS has formed thebasis for the MOS forecast system in the UK, and is under development in Canada(Vallée et al., 1996).

Updateable MOS represents an “operational” development system for statisticalforecast equations; there is nothing new compared to MOS. Forecast equations areredeveloped monthly or so, especially after a model change. To maintain continuityin the forecasts and ensure stable equations with small samples, the data from thenew model may be blended with data from the old model in a weighted scheme.Higher weights would be assigned to cases from the new model and, as the samplebecomes larger, cases from the old model are eventually dropped altogether.

Updateable MOS is similar to the KF in many respects. Important differencesare:

(a) Updateable MOS can be applied to any weather element, continuous or categorical;(b) Objective screening methods are available for updateable MOS; the developer

must specify the linear model in advance for the KF;(i) The blending of information from old and new models is explicitly specified

through the weighting scheme in updateable MOS. The KF “weights” histor-ical data through the response factor;

(ii) The KF is simpler to set up and apply.In practice, there are advantages to using the KF for early adaptation of weather

element forecasts immediately after a model change, within the first month or so,then using updateable MOS to update the full statistical forecast guidance system.

Once the methodology has been chosen and the exact form of the weather elementto be forecast has been defined, one is able to prepare the data set for statistical pro-cessing. This is the time to decide which predictors to use in the equation. Thefollowing are three qualities of a good predictor.

There should be a good meteorological reason to choose a predictor. It shouldbe physically and preferably linearly related to the weather element to be forecast.The parameters should be interpolated to the station position, and then a selectionprocess is applied to choose which parameters to use in the equation. Althoughthere may be many parameters to choose from, in the final equation, the number

3.3.2.3Preparing the data set;

choosing the predictors

Updateable MOS


Figure 3.65Time series of surface temperature

observations (circles), 48-hour modelforecasts (open diamonds) and KF

forecasts (squares) for Montreal(Quebec, Canada), 7 June to

2 September 1995

Day

T (OBS)T (Kalman)T (modelo)

Tem

per

atur

e (C

elsi

us)

Jun. Jul. Aug. Sept.

must be limited. Equations with more than about 15 parameters are never stable,and are often unstable with less.

If the statistical model is fitted using a standard package, then there are many diag-nostic statistics which help to decide how good a fit the equation is.

However, unless the model is recursive, like the KF, it must be tested on anindependent set of data. It is often too easy to choose many predictors, becauseincreasing the number of predictors on a development set always reduces theremaining error. If the performace of the equation on an independent set is poor,then this is a good indication of overfitting.

Ultimately, and indeed the only reasonable way for recursive models, it is nec-essary to put these into practice. The performance of the statistical model inoperation must be monitored in a variety of synoptic situations and seasons.

Before the statistical weather element forecasts are incorporated into operationalweather forecast products that are sent to users, they may need to be processed orconverted for forecaster use. Post-processing refers to any systematic method ofaltering the output of the statistical weather forecast technique before that outputis sent to users.

There are a number of methods for post-processing statistical forecasts. Each isbriefly discussed below A complete discussion of the various post-processing strate-gies is given in Glahn et al. (1991).

Forecast products that are in the form of probabilities may be accompanied orreplaced by a suggested “best” category obtained from the probabilities. However,important warning information contained in less likely categories may be lost ifonly the best category is sent out.

Sometimes it is desirable to increase the spread of the forecasts, to try to capturemore extreme events, or to deal with inconsistent forecasts of different parameters(for example, forecasts of high probability of precipitation with clear skies). Thiscan run the risk of introducing gross errors.

Forecasts of a weather element from different sources may contribute some differ-ent information to our knowledge of the forecast weather element. They can becombined to result in a forecast that is superior to any of the component forecasts.Ways of combining forecasts include the following:

(a) Averaging them;(b) Developing selection rules;(c) Taking a weighted combination of the component forecasts by subjective weight-

ing based on physical reasoning, or by regression.An example of a consensus forecast system that was used operationally is the

blended perfect prog and MOS POP forecasts that were run in Canada (Verret andYacowar, 1989).

There are always time lags before forecasters receive products from NWP runs every12 hours. This may be overcome by updating the products with recent locally avail-able data. The Local AWIPS MOS Programme (LAMP) (Unger et al., 1989) is anexample of one such updating system designed to be run at local offices where thelatest observations are available.

Statistical interpretation of NWP model output is generally considered to add valueto that output. It is also believed that forecasters can improve on the forecasts ofstatistical guidance products, especially for the first day of the forecast. The followingare some suggestions on how to ensure that changes are beneficial.

In general, the best way to improve on statistical guidance is to capitalize onwhat the forecaster knows, and that the statistical product does not show. It istherefore first of all important to be aware of what the statistical product shows.

3.3.3INTERPRETATION OF STATISTICAL

GUIDANCE PRODUCTS

3.3.2.5Post-processing

3.3.2.4Testing the performance

of the equation


Best category selection

Consensus forecasting

Short-range updating systems

Correcting for limitations in thestatistical method

Is it representative of a point or an area? Is it valid for a specific time or a period oftime? Is it a maximum, minimum or average over an area or over a period of time?This is of fundamental importance in matching the guidance output to the actualforecast that is wanted.

While it is often not feasible to know all the predictors for a large number ofequations, it is worth being aware of the relationships that are represented in theequation since these will give clues to information that can be added. As anexample, equations for ceiling sometimes avoid moisture parameters because theyare not reliably forecast by the model. If the forecaster has a better forecast ofmoisture available, this information can be used to modify the statistical forecasts.

This will determine how the forecasts are assessed in terms of the model output.MOS forecasts account for most systematic errors, but not if the NWP model has noskill in forecasting a parameter. For example, if the model has incorrect informationabout snow cover, or does not forecast layer cloud well, MOS temperature forecastwill still be wrong. Since the MOS guidance knows only the average performance,forecasters should be able to improve on the guidance in cases where the model per-formance is known to be poor. Knowledge of the predictors is useful here as well. Itis not worthwhile to modify the statistical forecasts on the basis of a bad model mois-ture forecast if moisture predictors are not in the equation.

Most development samples are stratified by season. This means the skill of theequation is with respect to the season average. Situations where the weather isclearly abnormal for the season should be watched carefully. Statistical forecast sys-tems, especially MOS systems, may try to move the forecast back towards normalwith increasing lead time as persistence loses influence if the initial situation isabnormal. Conversely, trends away from normal are likely to be dampened by aMOS system. Apparent trends away from extreme values may be due more to thefact that at longer time ranges the correlations are weaker.

Diurnal variations can also be modified if they are not well represented in themodel predictors. Knowledge of the model characteristics is useful in this sense too.

Perhaps the forecast is a blend of two or more techniques; perhaps it is a perfectprog forecast that has already been corrected for bias error on the current model.Common types of post-processing are described above.

To interpret verification statistics, the most important characteristics to know are:sample size, sample stratification and type of verification measure used. It is impor-tant to know the sample stratification to ensure that the results are representativeof the conditions which apply in the current situation. Seasonal stratification ismost common; verification statistics from winter forecasts will not necessarily sayanything useful about performance in summer. Of more interest are sample stratifi-cations based on the values of the weather element. For instance, verificationinformation could be computed for a sub-sample consisting of all cases where ceil-ings less than 200 ft were forecast. The verification statistics then could say, forexample, that forecasts of ceilings less than 200 ft tend to be one category too high75 per cent of the time and two categories too high 20 per cent of the time. A wordof caution, however: subdividing the sample reduces the sample size — the benefitsof stratified sample verification may be lost if the sub-sample is too small to givestable results.

The characteristics of the different types of verification measures in general useare briefly described in Chapter 4.

In summary, it is generally not worthwhile to make small adjustments to sta-tistical guidance products. Overall, this tends to add variance to the forecast, andis more likely to lower the performance than to raise it. It is better to identify situ-ations where changes are clearly needed (model in error, extreme event situations,etc.) and concentrate on those.


The exact definition of the weatherelement

The predictors, at least generally

The formulation method

The characteristics of thedevelopment sample, especially the

way it is stratified

What if any post-processing has beendone to the forecasts

Understand the general level ofperformance of the product

Forecasts for some aviation elements such as ceiling and visibility are requiredin considerably more detail than for other elements. The requirements generallyexceed the capabilities of the resolution of current models, and as a result, ceilingand visibility are widely regarded as the hardest elements to show skill in forecast-ing. Extreme values of these parameters are of the highest importance to aviation.As they are rare, sample sizes are small and lead to unstable equations.

Figure 3.66 is an example output of a MOS, MDA-based ceiling height forecasttechnique. The weather element in this case is defined as the lowest ceiling expectedover a six-hour period beginning at the valid time. The output is presentedgraphically in terms of probabilities of occurrence of the five categories. Forecastswere run operationally for a period of two months in support of the airbornecomponent of a field experiment over the east coast of Canada. Predictor valueswere taken from the Canadian spectral model, forecasts were run centrally andtransmitted to a personal computer at the forecaster’s desk for display. Theoperational forecasters were pleased with the graphical presentation.

The US Technique Development Laboratory has run MOS ceiling height fore-casts based on the nested grid model (NGM) operationally since 1993. The latestversion of the operational forecasts is described in Miller (1995). Ceiling heightsare predicted as categorical variables, in seven categories, < 200, 200–400,500–900, 1 000–3 000, 3 100–6 500, 6 600–12 000 ft and > 12 000 ft, which areselected according to LIFR, IFR, MVFR and VFR limits for aviation. Predictorsinclude a large array of basic and computed variables from the NGM, along withpersistence predictors (the latest available observation) and geoclimatic predictors.Development of the equations was by forward selection regression, and the devel-opment sample consisted of five to six years of data. Separate equations weredeveloped for warm and cool seasons, and for each three-hour forecast projectionto 48 hours.

The current US MOS guidance system based on the NGM also containsforecasts of visibility, which were developed jointly with statistical guidance forecastsfor obstructions to vision. A complete description of the visibility/obstructions tovision forecasts is contained in Meyer et al. (1996). As for the ceiling forecasts, theforecast variable is treated categorically, and the method produces probability

3.3.4EXAMPLES

3.3.4.1Ceiling and visibility


Figure 3.66Sample output of a

24-hour MDA ceilingforecast valid 0000

UTC 3 February1986 for the

Maritimes region ofCanada. Probabilities

of the five categoriesare represented by the

bar graphs plotted atthe location of each

station. This is aMOS product.

Verifying categoriesare shown by the

hand-plotted figures(after MacAfee,

1986)

MOS –MIN. CEILINGT + 24 PROGV-00Z 03 FEB.

OBSERVEDCATEGORY

PROBABILITY OF(5) 5000+(4) 3000 - 5000(3) 1000 - 3000(2) 500 - 1000(1) 0 - 500 pies

forecasts of the categories. For visibility, there are five categories, < 1/2, 1/2 to 7/8, 1 to23/4, 3 to 5, and > 5 miles. Obstructions to vision consist of three categories: haze,fog, and neither fog nor haze. To ensure consistency in the forecasts, the equationsfor visibility and obstructions to vision contain the same predictors. The predictorsets and development method are generally the same as for the ceiling forecasts.

The MOS probability forecasts of ceiling, visibility and obstructions to visionare further processed to determine the “best” categorical forecast. This is an exampleof a type of post-processing of statistical forecasts. The purpose is generally to reducethe work involved in the assessment of large numbers of probability forecasts, butthe cost is that some of the information contained in the sets of probabilities willbe lost to the forecaster. For the ceiling, visibility and obstructions-to-visionforecasts, the development sample was used in an iterative procedure to selectthreshold probability values which both maximize the threat score (see Chapter 4)and maintain the frequency bias reasonably close to one.

The operational output of the ceiling/visibility/obstructions-to-vision forecastsincludes both numerical and graphical formats. Only the categorical output isavailable. The ceiling and visibility forecasts are combined according to aviationflight weather categories and plotted as numbers on a chart, 1 for LIFR or IFR, 2 forMVFR and 3 for VFR conditions. The charts also contain statistical forecast outputfor cloud amount and wind.

Surface winds (usually observed at 10 m) are often available directly from an NWPmodel, unlike ceiling height and visibility. Nevertheless, it has been shown(Wilson and Vallée, 1996) that statistical processing can still improve on directmodel output forecasts of winds. Since wind is highly influenced by local topo-graphical and thermal effects which operate on scales smaller than can be resolvedin numerical models, statistical processing can produce an effective link betweenthe local climatology of wind and the larger scale model output.

Surface wind forecasts are part of the operational US NGM-based MOSsystem. The forecasts are for specific times, for one minute averaged winds, forthree-hour projection intervals to 60 hours. Predictors used for development ofwind forecast equations include low-level model wind forecasts, geostrophic winds,low-level relative vorticity, vertical velocity and the K index. Persistence predictors(T + 2 observation) were used for projections up to 12 hours. The US MOS windsare described in detail in Miller (1993).

Figure 3.67 shows a sample verification of six months of MOS wind speed fore-casts averaged over 68 US stations, compared to local manual forecasts. Meanabsolute errors are in the range of 3 knots at all three forecast ranges. Only at thelongest range, 24 hours, are the MOS forecasts superior to the local forecasts.Differences, however are small at all forecast ranges.

3.3.4.2Wind


12 18 00

4

3

3

1

0

0000 UTC 68 Stations

Local

NGM MOS

Forecast valid time (UTC)

Mea

n ab

solu

te e

rror

(Kt)

Figure 3.67Mean absolute error (in knots) ofwind speed forecasts produced by

National Weather Service forecasters(LOCAL) and by a MOS approach

applied to the nested grid model(NGM MOS). Forecasts for 68

stations in the contiguous US wereverified during the warm season of

1 April through 30 September 1993.The NGM MOS guidance wasproduced from the 0000 UTC

initialization of the NGM and wasvalid for 12-, 18- and 24-hour

projections. The local forecasts weretaken from the 0900 UTC issuanceof the aviation terminal forecast and

represent projections of approximately3, 9 and 15 hours, respectively. Theabscissa of the diagram represents the

valid time of the forecast

The Canadian operational statistical surface wind forecasts are based on a PPMtechnique. During development of the PPM equations, special consideration wasgiven to the design of the predictor set. Predictors were added on the basis of earlierstudies of the relationship of winds to atmospheric boundary layer structure, forexample. Details of the development are contained in Glahn et al. (1991).

For aviation applications, precipitation type is of great interest. As a variable, pre-cipitation type is non-numerical and inherently categorical. Furthermore, thehighly significant but relatively rare freezing rain event poses special problems forstatistical interpretation.

Figure 3.68 comprises three maps showing experimental MOS-MDA condi-tional probability of precipitation type forecasts produced using the Canadianspectral model. The three maps are 24-, 30- and 36-hour forecasts for the Maritimesarea of Canada, all generated from initial data at 1200 UTC on 4 February 1986.“Conditional” means that the forecast probabilities are conditional on the occur-rence of precipitation. Thus, a value of 20 per cent for liquid precipitation means“assuming it is precipitating” there is a 20 per cent chance that it will be in the formof rain.

The three forecasts suggest that a significant band of freezing rain spreadsnorthward from southern Nova Scotia then changes to rain over all of NovaScotia except in the extreme north. The precipitation remains as snow in thenorthwestern area over New Brunswick. The forecasts show the change to rainsharply between the first and second period, but it is too soon; most of southernNova Scotia is reporting freezing rain when the probability of precipitation type(POPT) forecasts suggest rain (Figure 3.68b). However, there is a hint of freezingrain at YQI on Figure 3.68a and YZX on Figure 3.68b, indicated by the relativelyhigh probability of freezing rain and the nearly equal probabilities assigned to rainand snow. Since the probability forecasts are modulated by the climatological fre-quencies, the probability assigned to the freezing rain category will rarely be high.The best example of the ability of the system to represent sharp spatial transitionsis in Figure 3.68c where the probabilities change from 80 per cent for rain at YAWto 90 per cent for snow at YZX, a distance of about 50 miles. This sharp delineationof the rain/snow boundary verified well in this case.

This product was developed using MDA, which is known to clearly separatethe categories.

In the US, technique developers took a different approach to the problem offorecasting precipitation type. POPT is included in the central MOS system, butthat procedure is not accurate enough or complete enough for use in the interactivecomputer worded forecast system. Thus, using the national forecasts, local modeloutput and recent observations, an enhanced system was developed for local use inthe context of the local MOS programme. The categories of the weather elementare defined as:

FREEZING = freezing rain/drizzle, alone or mixed with snow, or ice pellets;FROZEN = snow; andLIQUID = rain alone or mixed with snow.

These categories are the same as used in the current NGM-based centralizedforecasts. The national system is described in Erikson (1995).

Since the local forecast system uses the output of other statistical processing asinput, this method can be categorized as a forecast combination algorithm, asdefined above. The technique is REEP, using eight winters of data. The forecasts aresubjected to a best-category selection procedure which distinguishes mixed typesfrom the three pure types leading to a five-category system. Assessment of thissystem demonstrated some skill (Carroll, 1992).

3.3.4.3Precipitation


In addition to ceiling and visibility forecasts described above, “cloud amount”,“total cloud amount” or “total cloud opacity” are often treated to statistical inter-pretation. This weather element is usually treated categorically, with the categoriescorresponding to the designations sky clear (SKC), scattered (SCT), broken(BKN) and overcast (OVC). The climatological frequency distribution of cloudi-ness sometimes presents problems for statistical processing. In this case thedistribution tends to be U-shaped, with maximum frequencies near the extremes ofSKC or OVC. The tendency of regression methods to smooth toward the mean(SCT or BKN) makes it difficult to reproduce the climatological distribution in theforecasts.

3.3.4.4Clouds


MOS CONDITIONALPRECIPITATION

TYPET + 24 PROG12Z 05 FEB.





Observed categoryNo precipitation



(3) Snow(2) FRZ rain(1) Rain

Probability of Probability of

Probability of



The US system is based on the NGM forecasts and is described in Jacks et al.(1990). Development of the equations is completely analogous to the method usedfor other elements. The probability forecasts are subjected to a “category selection”procedure which is designed to guarantee unbiased predictions, meaning that eachcategory is forecast as often as observed on average and the climatological distrib-ution is reproduced.

Figure 3.69 shows a time series of three-hourly MOS (regression) forecasts ofcloud cover, ceiling, visibility, wind, weather, temperature and dewpoint, comparedwith the corresponding observation time series. The cloud amount verifies well inthis case; both forecast and observation are overcast or nearly overcast throughout.The ceiling forecasts are generally more pessimistic than observed; with oneexception MOS has predicted a lower or equal ceiling category than was observed.There is a gradual windshift from southwest to northwest during the period, whichwas forecast well by MOS. Also notable in this case is that MOS has accuratelypredicted the changes in precipitation type from snow to rain and back to snowagain.

Thunderstorms are rarely forecast statistically, not because information is not avail-able from models to forecast them but mainly because the station-specific

3.3.4.5Thunderstorms


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MOS MOSOBSERVED OBSERVED

Legend1 = < 1/2 miles2 = 1/2 – 7/8 miles3 = 1 – 2 3/4 miles4 = 3 – 5 miles5 = > 5 miles

wind (degrees)

(Kts)

Cloudcover

Temperature (F)

VisibilityCurrentweather

Dewpt (F)

Ceiling1 = < 200 ft2 = 200 – 400 ft3 = 500 – 900 ft4 = 1000 – 3000 ft5 = 3100 – 6500 ft6 = 6600 – 12000 ft7 = > 12000 ftN/A = No forecasts produced for this projection; corresponding observation not plotted.

Figure 3.69MOS forecasts and verifying

observations for International Falls,Minnesota (INL), produced from the

1200 UTC initialization of the NGMon 27 October 1993. Forecasts of

temperature, dew point, conditionalprecipitation type, visibility, wind

direction and speed, and ceiling heightare plotted in a station plot model (see

Legend) for projections every threehours from six through 60 hours afterinitial model time. Note that forecasts

of the precipitation type (plotted ascurrent weather) are conditional upon

precipitation occurring. Note, too,that no current weather is shown in

the observed station plot whenprecipitation was not occurring at

INL. Finally, note that theprecipitation type forecasts are

available only at 6-hour intervals,rather than 3-hour intervals, after the

36-hour projection (29 October,0000 UTC); similarly, the ceiling

height and visibility forecasts are onlyavailable for the 42- and 48-hour

forecasts, rather than the remainingprojections after 36 hours

observation data sets that are available are usually inadequate to describe the occur-rence of such spatially discrete phenomena. There are too many occurrences ofthunderstorms between stations that are missed in the data.

Because of this, the most successful attempts to forecast thunderstorms statis-tically have used special data sets to help give a better definition of the occurrenceof storms. An example is the MOS thunderstorm forecasting system in the USwhich makes use of lightning data. The technique is briefly described below; moreinformation is available from Reap (1994).

For equation development, the weather element “thunderstorm occurrence” isdefined as the occurrence of two or more lightning flashes in a 48-km grid block,over the contiguous US, during 24-hour periods from 12–36 hours and 36–60 hoursfollowing 0000 UTC and 6- to 24-hour and 24- to 48-hour periods following1200 UTC. Predictors include over 100 basic and derived variables from the NGM.

Some severe weather indices were also included as predictors. The statisticalmethod is MOS-REEP. Following development of the thunderstorm relationshipsadditional relationships were developed to predict the conditional probability ofsevere convective weather, using a data set of reports from the National SevereStorms Forecast Centre. The forecast probabilities of severe weather are condi-tional on the occurrence of a thunderstorm. Output products include maps of theprobabilities of thunderstorm occurrence and severe weather, and a convective out-look map derived from the probabilities.

Figure 3.70 is an example of the MOS forecast probability of thunderstormoccurrence for the 6- to 24-hour forecast period after 1200 UTC on 22 July 1997.This product is available operationally in the US, based on statistical interpretationof the output of the NGM.

Clear air turbulence is difficult to treat statistically because of a lack of sufficientlylarge data sets to use in the development of statistical relationships. Nevertheless,at least two statistical procedures have been successfully used in operations. Theseare described below.

Detailed accounts of this method are contained in Dutton (1980) and Forrester (1986).The data set for technique development was built actively through the cooperation ofpilots on North Atlantic, European and mid-Eastern routes. Pilots on these routes wereasked to report CAT occurrence per 100 km segment of flight path, corresponding tothe grid length of the (then) operational UK model. Two data sets were built, oneduring 1976 and the other during 1984–1985. The statistical development formula-tion was MOS. Predictors used included eleven meteorological synoptic scale indicesthought to be associated with the occurrence of CAT. All were computed from theoutput of the operational model, and optimal matching with the observations wasassured by the match of the reports with the grid length of the operational model. Theobservations were expressed as a categorical variable and equations were developedusing forward stepwise regression. The output is the probability of light, moderate orsevere CAT. Forecasts are run operationally and are presented in chart form withcontours of probabilities of moderate or severe CAT.

Although the systematic collection of special data sets is tedious andlabour-intensive, the experience in the UK shows that important contributions tothe ability to forecast particular weather parameters can be made through suchefforts.

The US Techniques Development Laboratory has recently developed a statisticalCAT forecasting technique. This development is different in important respectsfrom the UK approach. Because the observational data collection was done“passively” (only routine reports of CAT were used), certain assumptions had to bemade both in the development and in the use of the products. The US method isdescribed in detail in Reap (1996). The development sample consisted of three yearsof PIREP data. These data have three important limitations. First, they areintermittent in space and time, and contain a strong diurnal bias due to the relativeinfrequency of night-time flights. Second, cases of “no turbulence” cannot be

US method

UK method

3.3.4.6 Turbulence — clear air turbulence

Statistical methods


separated from situations where no aircraft were present. Third, the reportsthemselves are the pilot’s subjective estimate of the intensity of the turbulence,which will depend to a large extent on the weight, speed and aerodynamiccharacteristics of the aircraft.

The observations were pre-processed as follows: First, a CAT event was definedas “light to moderate” (category 3) or greater for aircraft of 10 000 lb or greater, or“moderate to severe” (category 5) for all aircraft. Second, events were counted andtabulated for a grid of 48-km blocks covering the contiguous US. Events over theocean were not included. Third, lightning data was used to remove turbulenceevents that appeared to be associated with convective weather. The predictors usedin development consisted of combinations of model output variables which havebeen shown to be related to CAT occurrence. These include stability indices,shearing and stretching deformation, total deformation, and the TI1 and TI2 indices(Mancuso and Endlich, 1966; Ellrod and Knapp, 1992), along with more basicpredictors such as winds at various levels, temperature advection, and gradients.Equations were developed separately for high (above 15 000 ft) and low flight levels,for warm and cool seasons, and for east and western US regions. The laststratification of the data is in recognition of the special turbulence conditions whicharise in the vicinity of the western mountain ranges.

The statistical technique used is regression in a MOS formulation, and theforecast output of the method is the probability of moderate (category 3 or greater)


Figure 3.70MOS forecast of the probability of

thunderstorms occurring in the6-through 24-hour period after

1200 UTC on 22 July 1997. TheMOS forecasts were produced fromthe 1200 UTC initialization of theNGM. The contours shown are in

tens of per cent, with the lowest valueof 10 per cent for the first contour

10 20 30 40 50 60 70 80 90

970723/1200V024 NGM MOS 18HR THUNDERSTORM PROBABILITY

or severe (category 5 or greater) non-convectively induced CAT, for six-hour validperiods. The output is presented in mapped form with the probabilities contoured,except that the probabilities have been scaled. This was deemed necessary becauseof the low relative frequency of CAT over the full sample. Also, because of thelimitations of the development sample described above, the forecasts are furtherprocessed to try to remove the diurnal bias. Thus Reap (1996) recommends thatthey not be considered true probabilities but rather an index of CAT occurrence.An example of the CAT forecasts is shown in Figure 3.71.


Figure 3.71Example of MOS forecast of

probability of occurrence of category 3or greater CAT for high altitudes

(above 15 000 ft), valid for 8 to 14hours after 1200 UTC 14 January

1995 (solid lines). Probabilitycontours are multiplied by 20;

500 mb height contours for initial datatime are also shown (dashed lines)

(after Reap, 1996)

APPENDIX

GRIDDED METEOROLOGICAL GUIDANCE DATA THROUGH THEWORLD AREA FORECAST SYSTEM (WAFS)

Gridded numerical forecast guidance information is available from major interna-tional centres through global communications systems and/or from national orregional meteorological services via local communications networks. For aviationpurposes, the two World Area Forecast Centres (WAFCs) at the UKMO and theNCEP in the USA have recently established operational satellite broadcasts of avia-tion weather information as part of the World Area Forecast System (WAFS). Thesesatellite broadcasts provide global wind and temperature forecasts for internationalaviation operations and disseminate these data both as chart and digital grid pointdata. Additional gridded parameter fields are also included. They are necessary todescribe the complete evolution of atmosphere and are particularly useful in fore-casting a much broader range of meteorological conditions affecting aviation.

Although the WAFS data sets will provide global coverage, additional NWPoutput may also be available from various regional NWP centres, such as theNCEP, UKMO, CMC, JMA, etc. These higher resolution NWP forecast guidancefields could include a wider variety of guidance parameters. They could also con-tain detailed hourly vertical profiles of conditions projected for specific sites,allowing forecasters to focus on local and very small-scale phenomena. Whilst theavailability of these data can vary greatly from one centre to another, the advent ofthe Internet offers the promise of making these high-resolution data available to amuch broader community within the next decade.

Due to its global availability, the following discussion availability only detailsthe gridded data contents typical of the two WAFS broadcast systems.

WAFS DATA TRANSMISSION The WAFS gridded data broadcasts consist of two parts. The first data setincludes the ICAO required 12-, 18-, 24- and 30-hour forecasts of winds and tem-peratures at all mandatory levels up to 70 hPa and the tropopause and maximumwind levels. The forecast fields are provided at least twice daily at a minimum,including guidance based on the normal 0000 and 1200 UTC upper air observ-ing and forecasting schedule. Each of these broadcasts contains about 3.5megabytes of data, requiring approximately 15–20 minutes to receive using thetypical 38 400 bit/second (baud) transmission rate. These data are then aug-mented with a second set of global grid point fields of mandatory levelgeopotential height, humidity and vertical velocity, along with precipitation andsurface fields, as well as all parameters at 6- and 36-hour forecast times. The com-bined data sets provide as a complete description of the state of the atmosphereas possible during all phases of flight. In the future, 0600 and 1800 UTC forecastupdates may also be added to the broadcast data set.

The gridded data are transmitted in the WMO-approved gridded binary (GRIB)format on a ‘thinned’ 1.25° × 1.25° latitude/longitude grid. At the equator, the gridspacing is exactly 1.25° × 1.25°, but the east-west grid longitudinal increment increasesnear the pole to avoid unnecessary repetition of the data. In no case is the model-output grid spacing greater than 140 km. Use of this ‘thinned’ data distribution gridreduces the total volume of data transmission (and thereby shortens the time requiredto receive the data) by about 35 per cent when compared with a uniformly spaced 1.25°× 1.25° grid, without any loss of data precision. Although the grid spacing used in NWPmodels themselves may be less than that of the output grid, the highest resolution(smallest scale) features predicted by modern NWP systems contain a high degree of“noise” and as such provide very little valuable forecast guidance information. Thoughcoarser that the prediction models themselves, the resolution of the WAFS grids isexpected to be adequate to describe the useful information contained in operationalglobal forecast models relevant to aviation for at least the next decade.

To simplify communications, the WAFS data sets are subdivided further intoeight different subset areas covering the globe (see Figure A.1). Computer programsare available to merge data from each of the eight different data communicationareas and expand the ‘thinned’ data onto various sized rectangular 1.25° × 1.25°grids for display and deriving diagnostic tools important for aviation forecasting.

The full array of products planned for transmission by WAFS is summarized inTable A.1. The primary (P) transmission of gridded ICAO required data begins atabout 3.5–4.0 hours after the normal data observation times (0000 and 1200 UTC).This is followed by a supplementary (S) transmission of the additional meteorolog-ical fields and forecast projections, requiring about 25 minutes of extra transmissiontime. This may be followed by a repeated (R) transmission of the ICAO requireddata to provide a second opportunity for local forecast offices to collect the data inthe event of temporary problems with the satellite data receiver.

The WAFS satellite broadcast uses existing commercial satellite communica-tions systems. More detailed information is available through ICAO or from thespecific satellite data providers.


Level Temp Wind Hght RH VVel Pres Prcp Cprcp

Max wind P, R P, R PTropopause P, R P, R PFL600 P, R P, R S S SFL530 P, R P, R S S SFL450 P, R P, R S S SFL390 P, R P, R S S SFL340 P, R P, R S S SFL300 P, R P, R S S SFL240 P, R P, R S S SFL180 P, R P, R S S SFL100 P, R P, R S S SFL050 P, R P, R S S S2 metre S S10 metre SMean sea level SSurface S S SFreezing level S

Table A.1Summary of WAFS satellite

broadcast products

Parameters:Temp = TemperatureWind = Wind speeds and directionsHght = HeightRH = Relative humidityVvel = Vertical velocityPres = PressurePrcp = Accumulated precipitationCprcp = Convective precipitationTransmission priority:P = Primary transmissionR = Repeat of primary

transmissionS = Supplementary (secondary)

transmission

Figure A.1Display of eight global subsections

used to transmit WAFS griddedproducts; labels refer to

communications identifiers used foreach octet

Thinned 1.25-degree resolution grid (global)

CHAPTER 4

VALIDATION AND VERFICATION

4.1 INTRODUCTION: PURPOSE OF VERIFICATION

There are numerous valid reasons and purposes to undertake validation and qualitycontrol of weather forecast products, from both the producers’ and users’ points ofview. For an NWP centre, there are three main areas of verification required:

In a competitive world, you need to prove that your output is up to agreed stan-dards, that it keeps improving with time and that the investment in newtechnologies and developments is reflected by some increase in agreed measures offorecast quality:

• It allows comparisons to other centres working in the same field;• It may help to show that your forecasts have a beneficial impact on the operations

of your customers, e.g. that fuel savings of air carriers using wind forecasts exceedthe cost of providing them.

It should be kept in mind, however, that this type of verification tends to bemeasure-oriented and often relies on single measures, i.e. for a specific forecastapplication such summary figures seldom reflect the overall quality of the forecastsystem relevant to the problem at hand.

In general, NWP models exhibit some deficiencies which need to be identified bysystematic evaluation. Progress in numerical modelling is demonstrably less spec-tacular and unambiguous now as massive computing resources have been availablefor some time and scientists have to make reasoned decisions where to concentratetheir efforts in system upgrades (data assimilation, horizontal versus vertical resolu-tion, non-hydrostatic models, advection schemes, coordinate systems or explicitphysics). Such decisions have to be based on reliable and meaningful quality mea-sures, and require in general extensive series of comparisons of model integrationsusing different formulations and techniques.

The choice of numerical techniques and physical parameterization schemeshas a wide-ranging impact on the resulting forecasts. Only thorough evaluation ofall model fields will ensure that systematic deficiencies in techniques are identifiedand eliminated. Where improvements are seen in some parameters or regions, theremay be a negative effects on others, thereby reducing the net benefit from a users’point of view of a proposed model upgrade.

Operational forecasters and end users often have a choice of guidance productsfrom different centres and models available for their specific forecasting problem.Systematic evaluation of such guidance products should be done using appropriatemeasures of forecast quality, reflecting the specific needs and applications of theuser.

Land users of numerical output need to know the dependability of these prod-ucts if they are to base critical decisions on weather forecasts in a cost-lossenvironment (see Murphy and Ehrendorfer, 1987).

The verification method and scores used need to be chosen carefully in orderto ensure that a better (higher) value of a score truly corresponds to a forecast thatis of greater value to the user. To this end, close cooperation with the end user isneeded during the process of choosing or designing the verification system.

For the presentation of quality of NWP products to users, it appears sensible toexpress this quality in terms of useful lead time. This measure would indicate forhow many hours (days) of lead time the forecasts contain useful informationexceeding that of a trivial competitor such as climatology or persistence. Thethresholds to be used for individual scores will necessarily have a degree of

4.1.2CONCEPT OF “USEFUL LEAD TIME”

4.1.1MAIN AREAS OF VERIFICATION

Administrative verification

‘Scientific’ verification

User-oriented product evaluation

arbitrariness, but the method can be used very well to demonstrate progress in time(such as five-day forecasts in 1996 have the quality of two-day forecasts in 1975) oradvantages of particular model designs over others.

Typical measures for height and wind fields would be, for example, 0.60 foranomaly correlation coefficient.

Scores used in categorical verification, such as the Heidke skill score, necessarilyinvolve a standard of comparison such as chance, climatology or persistence andtherefor have a clear cut-off value, where forecasts fall below that chosen standard.

4.2 METHODS OF VERIFICATION, UNDERLYING PHILOSOPHY

Mathematical formulations of different verification measures have been describedelsewhere in great detail and are summarized only briefly in 4.2.1.5. Here we willconcentrate on the merits and pitfalls of the methods described.

Forecast verification is the attempt to quantify the degree of correspondencebetween observations and forecasts. In the most general sense, the forecast qualityconsists of the statistical characteristics revealed by the joint distribution of fore-casts and observations (Murphy and Winkler, 1987). Such a distribution-orientedapproach lays the foundations for developing, choosing and applying particularmethods or measures of quality (Murphy, 1996).

Closer scrutiny of the verification problem in most cases reveals a high degreeof complexity or dimensionality, which makes it quite clear that a single measureof forecast performance, such as a mean square error, will not provide a complete oreven meaningful description of forecast quality.

Since the beginning of numerical weather prediction, verification of the griddedNWP model output has been performed on a regular basis. Results from these ver-ification exercises have marked the progress achieved over the last four decades. Inorder to understand the meaning and significance of such measures, a few generalconsiderations are required.

Any verification of forecasts requires some ground truth that is independent fromthe forecast, is objectively defined and is available for all forecast regions and times.Where raw observations are to be used as ground truth, an uneven distribution ofdata used may introduce an unwanted stronger weighting of the forecast qualityover areas of denser data. This could be avoided by artificially thinning observa-tions in data dense areas.

For fields such as geopotential height, temperature and wind, a comparison offorecasts against analyses is not using a strictly independent source of information, asthe finer structure of atmospheric fields in the analysis such as jet streams or frontaltemperature gradients are strongly influenced by the model, be it through a first-guess in the optimum interpolation technique or a variational method. This isparticularly true for data-sparse regions or model levels in the stratosphere, whereobservations are also scarce. For longer-range forecasts, however, this limitation isnot considered too serious. A further problem area would be mean sea level pressurefields near steep topography (e.g. Greenland, Andes, etc.), where the effect ofinterpolation from model levels to pressure levels exceeds the natural variablitiy ofthe field. Verification results obtained under such circumstances should beconsidered doubtful and may not be used for model comparison or evaluation ofpractical usefulness of model output. At mid-levels and in reasonably data-denseareas, verification against analyses provides reliable information on forecast quality.An effect well known to modellers in verifying fields against analyses is theparadoxical increase in verification scores using higher resolution fields. Here thegreater variability possible at higher resolutions counts against the verification scorebecause fine detail in the analysis is not replicated exactly in the forecast. Thisweighs against any better representation of mid-scale features made possible byhigher resolution.

Verification against analysed fields

4.2.1.1Ground truth

4.2.1VERIFICATION OF GRIDDED

NUMERICAL WEATHER PREDICTION

FORECAST FIELDS


When analysed parameters are interpolated to observing sites and statistics arecollected over a long period of time, these statistics may be used to identify doubt-ful individual observing platforms where systematic biases of observations againstanalyses or first-guess fields are found.

This method has the advantage of being completely uninfluenced by any modelcharacteristics filtering through into the analysed fields. It further avoids anysmoothing effects common to most analysis schemes: strong vertical gradients, clearjet maxima, or strong variations in vertical stability will be found in undiluted formonly in data from aircraft or radiosondes. Some provisions are rather essential forthis method that is best suited for short-range forecasts of geopotential height andwind fields.

Observing platforms to be used in verification methods should fulfil stringentcriteria:

• Availability. They need to be evenly distributed over the area to be verified in orderto avoid higher weighting of data-dense areas;

• Absence of systematic errors;• They should be representative of a volume corresponding to the grid scale of the

system;• They should not be interdependent (e.g. temperature retrievals from a satellite swathe);• They should not use forecast values for generating the data (e.g. model temperature

profiles used for the height assignment for satellite cloud motion vectors).Regular data monitoring permits the elimination of chronically malfunction-

ing observing platforms from the verification data set. This may be time consumingand labour intensive, but clean data sets are a prerequisite for meaningful verifica-tion results.

For verification results to be more meaningful, the forecast skill of an NWP systemmay be calculated against an available standard of comparison, such as climatology,persistence or classical statistical forecasts.

All verification statistics vary with the actual weather experience during theverification period. Weather patterns which have a greater variability tend to haveworse forecast verification statistics — in terms of absolute value — than quietweather. In relative terms the quiet weather forecasts are likely to be of poorerquality and may be much less valuable. This can show up as diurnal or seasonalcycles in verification scores. This weather dependency is difficult to remove andimpossible to remove entirely. One solution is to scale the statistical score againstanother standard forecast made during the same weather to give a relativeverification statistic — usually termed a skill score. However, this may not alwaysbe feasible. Comparison against another forecast centre or another model may notbe comparing like with like. Comparison against climatology or persistence may becomparing with a very poor forecast indeed. Another solution can be to averageover a cycle, such as an annual average score. For whole globe average winds,summer in the northern hemisphere can balance out against winter in the south. Itis usual, unfortunately, that not all the weather dependency can be removed. Usersof verification statistics still have to consider the complications which remain.

Some aspects of forecast quality are commonly used in the relevant literature and ashort list of the most widely used is as follows:

Bias: This relates to the degree of agreement between the average forecast andthe average observation. It may be expressed in terms of difference between thesetwo measures or a ratio of them. Remember that bias — like all mean values —does not reveal whether it is caused by a uniform shift (inviting simple correctivemeasures) or by a limited number of “outliers” (which can be mitigated by Robuststatistics).

Association: This expresses the strength of the linear relationship between theseries of observations and forecasts. It may be measured by correlation coefficient

4.2.1.3Aspects of forecast quality and

verification measures

4.2.1.2Standards of comparison

Platform selection

Verification against observations

CHAPTER 4 — VALIDATION AND VERIFICATION 95

and represents the proportion of the variance of the observations explained by theforecast — but is utterly insensitive to bias!

Accuracy: the spread of the forecasts about the observations usually expessed byeither absolute or mean square error in the case of continuous variables or thenumber of correct forecasts for discrete (categorical) variables.

Skill accuracy: skill accuracy of the forecasts to be evaluated normalized by the accu-racy of some “trivial” standard of this comparison, such as climatologal values orpersisence forecast.

Statistical resolution: is expressed by the mean observation found for a particu-lar forecast value (e.g. the mean temperature on all days when +5°C werepredicted), and the overall mean temperature. Thus, larger differences (of observedmeans) for different sample forecast means indicate higher resolution; no differencewould correspond to a total lack of resolution.

Based on these aspects of forecast quality, different measures can be defined.For the scalar fields of geopotential height, temperature and moisture — all

available on regular grids from numerical model output — several objective verifi-cation measures have established themselves as quasi-standards. These measures aremostly quadratic scoring rules, where the square of the difference between a fore-cast field and some accepted ground truth is calculated. The argument goes thatover a large number of comparisons, the forecasts showing the smallest overall devi-ation would be rated highest.

Looking at some at the most commonly used measures, we find as favouritesthe root mean square error (RMSE), standard deviation, bias and correlation co-efficients as “first-order-measures”, supplemented by a variety of higher-ordermeasures testing not only the deviations of the original fields, but also gradients,advection terms or tendencies.

The mathematical definition of the root mean square error:

with n the number of grid points, f the forecast value of a parameter, and t the truevalue at the grid point i is straightforward, its interpretation probably less so.

For all quadratic scoring rules, smoothing of the forecast field will improve theverification results particularly for the medium range, where stronger features maybe out of phase with reality. This is evident in the case of small developing lows,where missing the feature will be less penalized than misplacing it by a small measure. Any constant bias in the model will be reflected in this score, even thoughit may be less of a practical problem, e.g. for geopotential fields. In such cases, cor-relation would be a more practical measure. RMSE is probably best used forcontinuous parameters with a high predictability in the shorter forecast ranges,where it will truly reflect the success of forecasting relevant features.

For the verification of the vector fields of horizontal wind, RMSE is commonlyused, as it penalizes deviations from truth both in direction and speed. For the cal-culation of vector wind error, both component errors for u and v are to be summedunder the root to accommodate the directional dependence of wind errors. Again,the measure is more apt for shorter forecast ranges, where the main features (jetstreams, polar and subtropic fronts) are predicted in the correct position and rela-tively small errors dominate. Incorrect positioning of a jet stream would be heaviliypenalized, which appears reasonable from an aviation user’s point of view. Areas forwhich an RMSE is calculated should not cover too disparate climatological zonesif the results are to be used as a yardstick for model development. Selecting identi-fiable areas (e.g. the mid-latitudes for 60–90 degree longitude sections, tropical belt,Antarctic area, the region of very high topography near the Himalayas or Andes)will help to identify deficiencies in the treatment of physical processes such as grav-ity wave drag, deep convection or frontogenetic processes.

RMSEN

f ti ii

n= −( )

=∑1 2

1

4.2.1.4Verification measures for

continuous variables


For intercomparisons of verification results, the regional and seasonal characterof most meteorological parameters needs to be taken into account. Where RMSE isused as a single resulting number for a whole hemisphere and a year, it may only beused to show long-term trends. For individual areas and seasons, this measure will be more meaningful, but it then obviously reflects the varianceof the predicted parameter, i.e. the 1 000 hPa height field for January and the area ofthe North Atlantic will necessarily show larger RMSEs than for July over NorthAfrica.

In order to identify problem areas, the RMSE may be calculated for each gridpoint over a season, thus depicting geographically the distribution of errors.Cyclone paths, but also areas with incorrectly handled orography, will be highlightedby such graphs. The fact that different underlying sample climatologies make theinterpretation of such graphs difficult could be overcome by subtracting the samplebias from the data before calculation of the RMSE.

For moisture fields, in particular for the lower layers of the atmosphere, RMSEmay be difficult to interpret: the patchy nature and small-scale structure of suchfields would require very large data sets to deliver reliable verification results.Biases, uncertainty of the ground truth and high temporal variability of moisture inindividual layers all contribute to this problem.

The time trend of the mean error or bias is a valuable tool in identifying sys-tematic errors in models. It can identify problems with the discretization scheme(e.g. loss of mass or energy), in the case of temperature and moisture it will showup deficiencies in the physical parameterization. Again, if calculated on a seasonalbasis for individual grid points, problem areas (e.g. near orography, coastal effects,ice boundary) can de depicted in map form.

Correlation coefficients have for a long time been the favourite measure of skillin representing synoptic-scale features, particularly in the short to medium range.

Its value r, with fip being forecast value at grid point i, ri the value of a refer-ence field (e.g. climatology, persistence or similar), ti the true value at point i isgiven as follows:

The interpretation of correlation coefficients can be helped by considering a simplemathematical problem: Assuming we have a forecast and a verifying sinusoidalwave, both with the same amplitude and wavelength, the correlation will be thecosine of the phase-shift between the forecast and the true wave.

Correlation coefficients require some standard of comparison to be reallymeaningful. The natural structure of meteorological fields tends to impose a highcorrelation between, for example, hemispheric fields of geopotential height as theoverall gradient from polar to subtropic areas explains a large proportion of thevariance. To overcome this problem, most verification systems use either:

— the anomaly correlation coefficient, whereby climatology is subtracted both fromthe forecast and the verifying field, or

— tendency correlation, whereby the initial field is subtracted to give a true represen-tation of the model’s ability to predict the temporal changes of the field.

Anomaly correlation favours large-scale features (e.g. blocking highs, Omegapatterns, etc.) as the phase error becomes small in comparison to the wavelengthand amplitude of the quasi-stationary feature. Months and areas where large Rossbywavelengths are a dominating feature very high scores in this measure. Tendencycorrelation will provide a good measure for short-range forecasting, wherepersistence is a formidable competitor. Variable and generally low scores would befound in stagnant situations with blocking highs showing little development,tropical areas in the absence of significant easterly waves or cyclones. Highly mobile

r

f r t t

f f t t

ip i i ii

n

ip ir i ri n

n

i

n=

−( ) −( )

−( ) • −( )=

==

∑

∑∑1

2 2

1


situations with fast travelling waves in mid-latitudes are the best suited to tendencycorrelation as a yardstick of forecast quality.

During the early years of numerical weather forecasting, balanced models werecommonly used. They did not explicitly forecast wind fields, but derived them fromthe mass field. Also analysed wind fields were not commonly available before thelate 1970s. In order to assess the model’s ability to predict the wind field,geostrophicity was used to represent model winds in the concept of the S1-score(Teweles and Wobusa, 1954) in use mostly in the USA and Canada. It is very sen-sitive to the correct intensity of gradients, so even correctly placed low pressurecentres with underestimated gradients will be reflected by a worse S1 score. Thiswas done to discourage hedged (smoothed) forecast fields that would be rewardedby an RMSE measure.

A seasonal dependence is given by the varying strength of observed gradientsin summer and winter hemispheres, and if applied to a limited region, depends onthe existence of strong systems there. All these factors make a direct comparison ofindividual forecasts for different times or areas very difficult, as the interpretationof its numerical value is difficult.

A useful summary of the forecast and observed weather events can be presentedin the form of a contingency table. Such a table doese not constitute a verifica-tion method itself, but provides the basis from which a number of useful scorescan be obtained. A contingency table is nothing more nor less than a scatter plotfor a categorical variable. As with scatter plots, the entries of the table simplyrepresent a convenient presentation of the raw verification data set from whichmany statistical inferences can be drawn, and different scores can be computed.

The utility of verification databases often suffers more from a lack ofinformation saved than from the actual storage space required.

The contingency table for categorical forecasts is formed in such a way thateach event adds one to the grid element of contingency table according to theintersection of the forecast category and observed category.

The following subsections describe scores often computed from the entries ina contingency table. Table 4.1 is used for demonstration purposes.

Per cent correct is the summation of the diagonal elements divided by the totalnumber of events:

Per cent correct = 100*(a+e+i)/Twhere a, e, i are the number of correct forecasts in each category, and T is the totalnumber of forecasts.

FAR is the number correct divided by the number forecast for each category.Post agreement = a/M, e/N, i/O for the three categories.Ideal situation… value of one.FAR falls into the category of verification measures that imply stratification by fore-cast, and therefore, as the name implies, is sensitive only to false predictions of thesevere event, not to missed events. The term false alarm ratio is usually used whenreferring to a contingency table for severe weather forecasts; the ratio is (1 – postagreement (of a severe event)). This score can always be increased by underfore-casting the number of severe events, but only at the cost of more missed events,which are not seen by the score.

This is the number correct divided by the number observed in each category. It isa measure of the ability to correctly forecast a certain category, and is sometimesreferred to as “hit rate”, especially when applied to severe weather verification.Prefigurance = a/J, e/K, i/L for the three categories.Ideal situation… value of one.Like the FAR, it is not a complete score. It is in the class of verification measures thatimply stratification by observation, and thus is sensitive only to missed events, notfalse alarms. Thus the POD can be increased by issuing a larger number of forecasts

Probability of detection (POD)

False alarm ratio (FAR)

Per cent correct

4.2.1.5Verification scores for categorical

variables (after Stanski, Wilsonand Burrows, 1989)

Gradient-oriented verification ofheight fields


Table 4.1Contingency table

Forecast category: 1 2 3 Total

Observation 1 a b c JObservation 2 d e f KObservation 3 g h i LTOTAL M N O T

on the assumption that a greater number will then be correct, usually at the cost ofmore false alarms. This is similar to a rifleman using a shotgun instead of a rifle toincrease his target accuracy. In short, the POD can always be increased by crying wolf.

Bias is the number forecast divided by the number observed for each category. Itmeasures the ability to forecast events at the same frequency as found in the samplewithout regard to forecast accuracy.Bias = M/J, N/K, O/L for the three categories.where:Bias = 1 implies no bias;Bias > 1 implies overforecasting the event;Bias <1 implies underforecasting the event.

The threat score is the number correct divided by the number of cases forecastand/or observed for that category. It is a measure of relative accuracy.Threat score = a/(M+J–a), e/(N+K–e), i/(O+L–i)The range is from zero to one.Ideal situation… values close to one preferred.

The advantage of the threat score over the FAR and the POD is that it is sen-sitive to both false alarms and missed events. Thus it gives a more representativeidea of real accuracy both in situations where the climatological frequencies of thecategories are nearly equal. However, this discussion shows quite clearly that nosingle statistic can describe all these effects.

In general, it is difficult to describe statistically or to assign statistical confi-dence measures to a large contingency table. It can be difficult to do so for even a2 × 2 table (two categories excluding margins). Large tables have to be further sum-marized and described by the person creating the table so that users can quicklyunderstand the importance of the results. The larger the table, the more difficultthat is to do.

Physical parametrization packages deliver several fields, such as kinetic energy dis-sipation rate, outgoing long-wave radiation, precipitable water content, etc. whichare not routinely presented to users as graphical output. These fields, however, playan important role in the generation of user-oriented products such as precipitation,turbulence or cloudiness in different layers. In model development, validation ofsuch fields against suitable observing systems (satellite radiances, gravity wave drag,radiosondes) is a main objective of large scientific experiments such as Pyrex,Totex, MAP and others. Although their methods are not yet operational, insightinto strengths and weaknesses of particular parameterization schemes can be gainedfrom such procedures. A detailed study of the influence of land-surface parameter-ization can be found in Noilhan et al. (1992).

As already mentioned above, modern forecast systems produce output directly relatedto weather elements needed in a routine forecasting environment. Among these areprecipitation, temperature and dewpoint at screen height, winds at 8–10 m abovethe surface and cloudiness. The increase both in horizontal and vertical resolution,in particular for regional models, promises to deliver information on a scale rele-vant to regional and even local forecasting. The critical dependence on a properrepresentation of the planetary boundary layer and a realistic treatment of topo-graphic effects makes thorough verification a prerequisite for the use of suchparameters in operational forecasting. Many of the predicted parameters may be bynature continuous, but their values are suitably divided into meaningful categories.Similarily, many parameters which appear continuous in practice are not (e.g.height of cloud ceiling is determined by levels).

In order to verify these so-called “weather parameters” from direct model output,dedicated verification systems need to be set up. Although similar methods to thoseemployed for regular upper-air fields are available, it is worthwile to emphasize thedifferences.

4.2.3.1Methods of verifying “weather parameters”

4.2.3VERIFICATION OF “WEATHER

PARAMETERS” (DIRECT MODEL

OUTPUT OR DERIVED PARAMETERS)

4.2.2VALIDATION OF INTERNAL MODEL

FIELDS

Threat score or critical success index(CSI)

Bias or frequency bias


Unlike fields of geopotential height or wind in the free atmosphere, these para-meters are not routinely analysed in operational forecasting systems. Forverification purposes, only the comparison to observations is therefore available.Several critical considerations are required in order to set up a verification system:

Most NWP centres are predicting such parameters for an area far exceeding theirown observing network. While main synoptic data are usually exchanged world-wide, data from denser networks of climatological or hydrological stations are notalways easy to obtain.

Oberservations of wind and temperature as well as relative humidity taken at syn-optic stations may be strongly influenced by local physiography, sea breeze effectsor urban heat islands. Accumulated precipitation in mountainous terrain may varyby more than 100 per cent even in annual sums between stations separated by lessthan 10 km.

For accumulated precipitation, it is sometimes necessary to have more than oneobservation time available to derive rainfall totals for intermediate periods. Missingobservations are a major problem.

Especially for highly variable parameters such as rainfall, a dense observing networkis required.

One “bad apple” in a large sample may corrupt the entire verification result.

These depend on both the nature of the parameter to be verified (e.g. continuouslyvarying, event-type) and the purpose of the verification.

For continuously varying parameters such as temperature or wind speed, stan-dard tools such as RMSE, bias, standard deviation and bias may be adequate foradministrative verification. For user-oriented verification, the forecasting problemat hand will influence the chosen methodology. Usually, the full range of values ofthe predictand (say, temperature) is divided up into meaningful categories orientedtowards the user’s situation; the ability of the forecasting system to predict theoccurrence of temperatures in extreme categories is then evaluated based on con-tingency tables. In aviation meteorology, forecasting strong crosswinds can becrucial for operations; where long runways exist, the component along the runwaywould only be of interest if a change of runway direction became necessary. In sucha situation, user-oriented validation would try to structure the distribution of datainto categories to give the most meaningful results, i.e. a forecasting system reliablypredicting runway changes or marked crosswinds would have to score higher thana competing system, where the RMSE of wind is smaller but fails to predict theabove.

The operational introduction of interactive cloud-radiation schemes, boundarylayer processes and improved data sets for physiographical properties such as soiltype and vegetation cover have led to quite realistic model forecasts of screen-height temperature. Regular evaluations of these forecasts are being carried out bynearly all NWP centres. Some examples given for a verification exercise under-taken at ECMWF for a dense network of 1 800 synoptic stations over Europe mayserve as an example. The results presented in Figure 4.1 (left) are for wintertime 72-hour tendencies of 2-m temperature for a range of observed temperature changesfrom –20 to +25°C, the length of the error bars indicating standard deviation.

Looking at predicted temperature tendency avoids systematic bias problemsover areas with different vegetation type. The mean tendency error shown exhibitsa clear underestimate of observed temperature change. Figure 4.1 (right) forsummer shows a reduction both of mean error and standard deviation compared tothe cold season, which can be explained both by a smaller atmospheric variance insummer and the absence of snow cover. The regional nature of the errors is demon-strated in Figure 4.2. More recently, a thorough verification exercise undertaken by

4.2.3.4Examples of the evaluation of

individual parametersScreen height temperature

4.2.3.3Quality measures

Data quality control

Data density

Reliability of observations and communications

Representativity of data

Availability of data

4.2.3.2Ground truth


Deutscher Wetterdienst verifies 2-m temperatures for its limited area model forEurope and its high-resolution Deutschland model. The susceptibility of near-surface temperatures to soil fluxes was shown in an experiment, where only theassumption of root length in the vegetation was changed, resulting in a dramaticchange in the diurnal cycle of temperature (see Figure 4.3, D. Majevski, personalcommunication).

Near-surface winds in high-resolution models can provide very accurate estimatesof observed values under certain circumstances:

— reasonably homogenous terrain (topography and roughness variations small withinone grid box)

— no abrupt changes in stability, both horizontally and vertically— absence of strong, localized convection.

Verification results obtained by ECMWF (not shown) are similar to thoseobtained for 2-m temperature in one respect; a high initial error increasing veryslowly for the first two days suggests a systematic nature of the error for most sta-tions. Random errors introduced by the degrading of the forecasts with time arebeginning to dominate only after three days. A comparison to a verification donein 1982 for 10-m winds from the ECMWF model for the Ocean Weather Ship Lima(where both uniform “terrain” and a well-mixed boundary layer are guaranteed)shows the high skill of such a product in forecasting rapid changes from day to day(Figure 4.4).

The strong diurnal variation and dependence on very localized physiography suchas soil moisture, soil penetrability, vegetation (density, type, current stage of vege-tation cycle, root depth) make a meaningful operational verification of near-surfacemoisture questionable for the time being. Dedicated experiments as presented inFigure 4.5, a to c from Beljaars and Betts (1992) indicate a very high sensitivity oflow-level moisture to the chosen boundary layer scheme (here “old” versus “new”ECMWF).

This is one of the more difficult elements to predict. Cloudiness can be derivedfrom relative humidity or ideally from a cloud water parameter in most currentoperational models. Some models discern between so-called “large-scale” cloudassociated with dynamic lifting and “convective” cloud as a by-product of the con-vection scheme producing precipitation. Global models used for aviation purposestend to gear their convection schemes towards correctly representing tropical con-vection and display some weaknesses in mid-latitudes. High-resolution regionalmodels hold some promise to predict large convective systems and orographicenhancement of precipitation and cloudiness. In general, however, one should notexpect comparable levels of skill as in more conventional fields like temperature. Inparticular, thin cloud layers not filling a substantial proportion of a model layer willremain difficult to predict.

Cloudiness

Screen-height moisture

10-m wind


15.0

10.0

5.0

0.0

-5.0

-10.0

-15.0-20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 25.0-20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 25.0

15.0

10.0

5.0

0.0

-5.0

-10.0

-15.0

Figure 4.1Forecast error of 72-h 2-m

temperature tendency as a function ofobserved tendency, with standard

deviation (error bars) for Europe forJanuary 1992 (left) and July 1992

(right) (from Strauss and Lanzinger,1992)

Observed tendency

Fore

cast

ten

denc

y m

ean

erro

r an

d S

t. D

ev.

Observed tendency

Fore

cast

ten

denc

y m

ean

erro

r an

d S

t. D

ev.


Figure 4.2Temperature mean t + 72 h forecast

errors at observation locations:a) April 1990; b) April 1992

(from Strauss and Lanzinger, 1992)

a)

b)

The ground truth for cloudiness observations also has some limitations, asobservations during night-time are sometimes unreliable, and in convective situa-tions the temporal fluctuation is high.

Measures of skill to be used for cloudiness necessarily follow the observingpractice at aeodromes, where cloudiness is reported as “few” (1–2 octa), “sct”(3–4 octa), “bkn” (5–7 octa) or “ovc” (8 octa). They are based on contingencytables for these observed categories. Such contingency tables can then be evaluatedusing scoring systems like Heidke skill score, Brier score or True Skill statistics.Further interesting measures would be the false alarm ratio, probability of detec-tion, threat and prefigurance. They are most appropriate where the events in aparticular category are very important to predict, such as overcast sky at low ceil-ing heights.

Winter months tend to be even more difficult, as low stratus is dominating thepicture for many stations in the lowlands. Verification results for low stratus are


14

12

10

8

6

4

24 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76

8

6

4

2

0

-2

4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76

14

12

10

8

6

4

2

4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76

16

Figure 4.3Temporal evolution of the surface temperature (bottom left),temperature at 2 m (top right) and dewpoint at 2 m (bottom

right) at a grid point near Braunschweig (Northern Germany)on 13 April 1993 (from Majevski and Schrodin, 1994)

30

20

10

020 40 60 80 100

Figure 4.4Forecast and observed

10-m windspeed at Ocean WeatherShip Lima, spring 1982 for 24-h

forecast time. Forecast winds (dashedline), observed winds (solid line)

(from Pumpel, 1982)

EMR: New EM version

EMX: Old EM version

Forecast time (h)

Tem

pera

ture

_ 2

m (°

C)

Dew

poin

t _

2 m

(°C

)

Sur

face

tem

pera

ture

(°C

)

Forecast time (h)

Forecast time (h)

EMREMX

EMREMX

EMREMX

Event

Win

dspe

ed _

10 m

(m/s

)

currently hard to come by, as boundary layer moisture is structured on a scale stillbeyond even high-resolution models.

Accumulated precipitation is a highly important parameter in nearly all forecastingproblems and has been verified by many centres on a regular basis. The behaviourof precipitation scores tends to vary wildly with resolution changes both in model-ling and observation networks. Again, precipitation produced by synoptic-scalesystems or fronts has a higher degree of predictability than convective-type precip-itation from individual cells or events. Precipitation enhancement due totopography is still not well resolved even by fairly high-resolution models, althoughthe overall effect of large orography can be clearly identified in monthly averageresults. Precipitation forecasts by the 14-km resolution Deutschland model com-pared to the European limited area model indicate an increase in accuracy gainedthrough higher resolution. Finer detail revealed in regional climatologies, however,cannot now be expected to be resolved. Recent progress in high-resolution model-ling would promise significantly improved forecasts of intense precipitationenhanced by local topography. Studies of severe flooding events in France (Vaison-la-Romaine, 1992) and Switzerland (Brig, 1994) showed surprisingly good resultsfor the French Peridot-model and the Swiss model. A dedicated version of aCanadian limited area model MC2 prepared by A. Robert was also tested on theBrig case and revealed remarkable success both in predicting location and amountof the observed rainfall maxima (over 400 mm/2 days).

Verification of very high-resolution models needs to be undertaken using a verydense network of raingauges, if results are to be meaningful. Warm season convec-tive precipitation is by nature very localized and may show high variability on ascale of a few kilometres. Orographically enhanced precipitation leads to verylocalized maxima that are visible in high-resolution rainfall climatologies, such ashave been derived from the Alpine region by Schaer et al. (1997).

For individual strong precipitation events, case studies may be a useful tool toinvestigate the model’s ability to predict such events.

Precipitation


Figure 4.5Mixing ration of level 18 (ECMWF model) at about

150 m (a) level 19 at about 30 m (b) and 2 m (c)(from Beljaars and Betts, 1992)

q LE

V. 1

8 (g

kg-

1 )

DAYNR

OBSNEWOLD

OBSNEWOLD

OBSNEWOLD

DAYNRDAYNR

q LE

V. 1

9 (g

kg-

1 )q

2m

b)

c)a)

4.3 GUIDELINES FOR INTERPRETATION OF SYSTEMATIC MODELBEHAVIOUR

The design of an NWP model to some extent determines its strenghts and weak-nesses. In some cases, it may be possible to identify meteorological phenomena, forwhich a particular model does especially well or shows deficiencies on a statisticallysignificant number of occasions. With the ongoing improvement of models, trendto higher resolution and more complete physics, the number of clearly identifiedproblem areas will be reduced, but for some years to come, there is a benefit to beexpected if users attempt to identify these areas and incorporate this knowledge intheir operational practices. It would not be feasible in this context to name but afew examples of typical problem areas.

The formation of small cold pools and cut-off lows at mid-level or higher levels usedto be a particularly weak point for many coarse-mesh global models. Despite someimprovement seen during the first half of the 1990s, the location and intensity ofsuch processes is still a source of large errors beyond a range of 24-hour lead time inmany global models.

In cases of strong baroclinic zones found in areas of poor data coverage, the onsetof rapidly developing lows may be misplaced in space or time.

Such systems may extend for several hundreds of kilometres and have an influencenot only on fields such as precipitation, but also horizontal wind fields, convergencezones, etc. Only very high-resolution regional models can be expected to show skillin the prediction of such systems.

The current generation of global models used for aviation purposes is not designedto predict onset and development of tropical cyclones. If information on the loca-tion of already existing tropical storms is inserted by bogussing in the initialsituation, these models may predict the track of the cyclone with some limited suc-cess. Nevertheless, specialized centres running dedicated models are doing muchbetter in predicting tracks and evolution of tropical cyclones.

Air mass boundaries, and cold fronts in particular, are subject to retardation, accel-eration or deformation whenever they are steered towards steep orography.Figure 4.6 gives an example of a detailed study of a cold frontal passage over the

Orographic deformation of fronts

Tropical storms

Formation of mesoscale convectivesystems

Explosive developments in data-sparse areas

Small cut-off processes


Figure 4.6Isochromes of a coldfront in the Alpsfrom 23 June 1978 0000 UTC until

25 June 1978 1200 UTC(from Steinacker, 1981)

Alps, showing clearly the acceleration of the front on the northern side of themassif, the retardation over the Western Alps, and the penetration of cold air intothe Mediterranean area on both sides of these mountain ranges.

Coastal effects and wind systems in large valleys cannot be properly represented inmodels of a grid scale much coarser than the structure of the regional topography.These wind systems, however, may play an important role in the prediction of ceil-ing, visibility and precipitation.

Designing NWP models is not only an art in itself, but is a formidable chal-lenge to one’s ability to compromise. Decisions have to be made on where to puthow much of the development team’s human resources, how to share the availablecomputer power, and how much emphasis should be given to data selection andassimilation.

It may not be obvious how these decisions should influence the working prac-tices of a (probably remote) user of the forecast products. In many forecast officesaround the world, a selection of forecast products from quite diverse models andcentres are available for the forecaster. Such a choice can be a mixed blessing forthose cases where products differ considerably in the predicted weather parameters.Reasoned arguments about the merits of individual models or systems, in particularforecasting problems, will support the reliability and speed of the decision-makingprocess and improve over purely personal preferences or “gut feeling”. Thoroughinformation on the conceptual strenghts and weaknesses of individual models is afirst step towards making an informed choice in a given situation.

The characteristics of a forecasting system are determined by its basic designproperties, such as described below.

The merits of higher horizontal resolution have been stressed (and maybeoverstressed) by the modelling community for a long time. Direct comparisonsbetween models of widely different horizontal resolution become rather tricky.Verifying models of, for example, 15-km resolution against a radiosonde networkwith average spacing of 150 km is less than satisfying when it comes to assessingdetails of frontal structure, orographic and land/sea effects. Verification againstanalyses, particularly in the very short range, has to take into acount the extent towhich smaller scales in the analyses are determined by the first guess. The penaltyincurred by high-resolution models in terms of a low signal/noise ratio both inobservations and forecasts is high. The meteorologically significant pressuredifference between two closely situated observing platforms is in the order of themeasurement accuracy and representativity.

There seems to be general agreement that for global models a further increasein horizontal resolution towards the 30-km range appears both feasible and desir-able in the near- to medium-term. For such resolutions, the choice of qualitymeasures observing platforms for verification becomes even more crucial. Withincreased detail in the mesoscale of forecast fields, traditional summary measuressuch as root mean square index (RMSI) are likely to increase with resolution.Thorough quality control procedures will be required for the observational dataused in the ground truth; 4DVAR data assimilation schemes may offer new ways ofmeasuring forecast quality against off-time observations.

Current operational models can be found in three groups of vertical coordinate systems:

Sigma-system with:

This system results in terrain-following coordinates, thus avoiding problemswith the interface between atmospheric grid points and points falling within theground. Among the drawbacks of a pure sigma system are the frequent intersectionsof sigma surfaces and the tropopause over high orography. Spurious temperature

σ = p

pa

4.3.2VERTICAL DISCRETIZATION AND

COORDINATE SYSTEM

4.3.1HORIZONTAL DISCRETIZATION

Local and regional wind systems


gradients there may be hard to compensate by smoothing algorithms. A popular fixfor this problem is a hybrid coordinate system, in which a smooth transition fromsigma coordinates near the ground to purely p-coordinates at the top of the atmos-phere is chosen.

These systems are typically designed as:

with a varying from 1 at the surface to 0 at p = 0, and b varying inversely.Such hybrid coordinates are currently used in most global operational models.

They tend to represent mountains as rather rounded hills with an exaggerated foot-print (a problem exacerbated by the use of spectral techniques in horizontaldiscretization). Cold air damming will therefore be reduced and upslope effects onprecipitation may be spread over larger areas than expected. The heating effect ofthese large elevated surfaces on convection should not be underestimated. Usersshould be aware that the effect of increased cloudiness and precipitation observedover individual peaks in nature will be spread over large areas.

For limited area models, where blocking effects of steep topography are one ofthe hot topics to be resolved properly, the step-mountain formulation in theη-model in use at the National Meteorological Centre (NMC) in Washington hasbeen shown to perform well in this respect.

Despite the notorious problems with treating boundary layer problems in isen-tropic coordinates, this natural coordinate system has great advantages when itcomes to resolving the structure of wind fields near the tropopause. The high staticstability at the tropopause level leads to a dense packing of isentropic levels there,thus ensuring a very high vertical resolution of the model where it is most neededin aviation. No other coordinate system could deliver the same “natural” increasein resolution anywhere on the globe, as the tropopause level varies from aroundFL 240 near the poles to FL 500 in the tropical belt.

Verification against observations is influenced by the necessary interpolationsteps that are needed to calculate forecast values of atmospheric variables at the siteof observation. The use of terrain-following coordinate systems often involves several interpolation steps which may add additional variance particularly in thevicinity of steep orography, near the tropopause or in frontal zones.

Some numerical schemes are prone to produce relatively noisy height and windfields, leading to higher values in RMSE and standard deviation in verification.This information content may, however, be rather unaffected by these “cosmetic”problems.

With the foreseeable transition to horizontal resolutions below the 10-km thresholdin specialized models, the hydrostatic assumption becomes invalid in explicitly sim-ulated convection. First attempts in explicit modelling of physical processes such asconvection, water cycle and turbulence (Schultz, 1995) would indicate a consider-able potential for improved forecasts of aviation impact variables. Forecastersshould be encouraged, however, to regard output from very high-resolution localmodels as an indication of what could happen, not necessarily of what will happen.

The prediction of hazardous weather phenomena purely from model data reliesheavily on fields such as cloud liquid water content, cloud ice or dissipation of TKE.These predictions are a prerequisite for the automated generation of aviation prod-ucts such as significant weather (SIGWX) charts. Validation of such specializedfields normally requires dedicated field experiments, as the required parameters arenot routinely observed by standard observing networks. The high cost of suchexperiments, for example WRIPEP (Winterstorm Project 94 Real-time IcingPrediction and Evaluation Program (Brown et al., 1995)), precludes standard sta-tistical methods with large sample sizes, but in-depth case studies are invaluable to

4.3.5EXTRA FIELDS (CLOUD WATER,

CLOUD ICE, TURBULENT KINETIC

ENERGY, ETC.)

4.3.4HYDROSTATIC VERSUS

NON-HYDROSTATIC MODELS

4.3.3ADVECTIVE SCHEMES

ζ σ= +a b * p*


highlight strengths and weaknesses of individual models or parameterizationschemes. In many instances, it is difficult to verify fields such as TKE even usingspecialized research aircraft. In such cases, only the resulting combination of modelprediction and algorithm performance can be monitored.

Continuing improvements in the technology of all-weather flying have led to thesituation that weather events causing severe disruption to air traffic have becomefairly rare. Most of the verification scores and evaluation schemes discussed so farrequire large sample sizes to be statistically significant. The time-honoured way ofrerunning severe weather cases with fine-tuned parameterization schemes could bedangerous: different situations with a new mix of dynamical ingredients usuallyrequire different sets of tuning parameters in order to simulate the course of eventsa posteriori.

4.4 EVALUATION OF THE PREDICTION OF HAZARD POTENTIAL(AVIATION IMPACT VARIABLES)

Recent events — airliner crashes in both Europe and the US — have heightenedthe industry’s awareness of the continuing risk.

Systematic evaluations of the currently used operational algorithms for predic-tion of icing potential as undertaken in WRIPEP compare the performance ofindivual model-algorithm combinations based on PIREPs. In order to penalizeoverforecasting, the successfully predicted icing events have to be normalized bythe volume of airspace impacted by the algorithm.

A comparison of algorithms in use by the National Weather Advisory Unit,Kansas, US, the US Air Force and NMC Washington (RAP 3.0, B.-F.) in Figure 4.7shows the close relationship between probability of detection and affected volume.The precision of an algorithm can be enhanced by adding extra conditions such asa switch for upslope or downslope component, shear at the cloud top or similar fac-tors. Any implementation of icing algorithm in an operational forecastingenvironment should be preceded or at least accompanied by a well-documentedevaluation exercise.

4.4.1ICING

4.3.6EVALUATION OF PREDICTION OF

RARE EVENTS


Eta_40 Icing, National Analysis (All)Forecast Issue Dates: 25Jan 94 to 25Mar94

Lead Time = 0 hours, Issue Time = 0

25

20

15

10

5

0

RAP3.0 Air Force B–F NAWAU–2 NAWAU–3

Algorithm

Vol

ume

(10*

*6 k

m**

3)

Figure 4.7Average volume affected by different

icing algorithms(from Brown et al., 1995)

This display is a clever indication ofthe distribution of the air volume(horizontal and vertical extent)

affected by different icing algorithmsfor events which were correctly

detected by each algorithm. Obviouslyforecasting a large volume increases

the chance of correctly forecasting anicing event, but it grossly increases the

false alarm rate (i.e. increases theoverforcasting). So the smaller the

volume the better the forecast tends tobe. Each part of the bobbin symbol

depicts a parameter of the distribution.The narrow waist is the median

(50%), the nearby dot is the mean.At each end of the bobbin are the

upper and lower quartiles (75 and25%) and the limits on the spindles

are the 2 sigma (approximately 95 and5%) values. The outside dots reflect

the highest and lowest pairs of values.The whole symbol gives a good

representation of the whole distribution

As in icing, most algorithms for CAT prediction suffer from a scale problem as men-tioned in 4.3.2. The lack of vertical resolution near the tropopause limits themodel’s ability to capture strong vertical shear and variations in static stability asinput for calculating the Richardson number, defined as the ratio of static stabilityand the square of vertical wind shear as a source of mechanical turbulence. The sto-chastic nature of CAT makes verification against PIREPs difficult, and avoidanceof marked CAT areas further reduces the number of available reports.

Systematic evaluation exercises of individual algorithms are now being under-taken at several institutions. The following example of ongoing work atNOAA-FSL may serve as a proof of principle (Marroquin and Cairns, 1995).

In a comparison of a diagnostic scheme for dissipation of TKE (DTF-1, DTF-2)based on the MAPS and ETA models, both PODs for Turbulence (=yes) and Noturbulence (=no) are shown in Figure 4.8. Note the sharp deterioration of theperformance above FL 350, where a low vertical model resolution in the ETA modelmay contribute to this result, whereas good results in the lower tropospherecorrespond well with the high number of model layers there. To what extentconvective turbulence is contributing to the number there would have to beresolved. A region of low skill is found in the middle troposphere, where turbulencemechanisms in the absence of jets are not well understood as yet.

A further valuable verification study comparing the UKMO’s Empirical Index(based on Richardson number and developed by Dutton, Met. Mag; 1976) and theTI-Index by Ellrod is found in Ellrod and Knapp, 1992. They find that both indiceshave skill in detecting CAT associated with frontogenetic processes ahead of asharp upper level trough, but that the inclusion of divergence contributes to a slightedge of the TI over the Emprical Index.

Further research in this field is sorely needed, and with the multiplication ofautomated PIREPs the availability of large databases of observed turbulence willfoster such work at least over the US, and hopefully help to speed the building ofsimilar databases over other regions.

There is general agreement that breaking gravity waves pose one of the remainingfatal meteorological hazards for aircraft en route; loss of control or even structuraldamage (not to mention passenger injuries) are a real threat in severe breakingwave situations. Strong and breaking mountain waves can be observed over anymountain ridge exposed to cross-barrier flow, and is not restricted to the very highranges such as the Rockies, the Andes or the Himalayas. Severe mountain waveactivity has been reported over unspectacular terrain such as the Welsh Hills or theEifel region in Germany.

A body of literature (e.g. Smith, 1977, Hoinka, 1984 and many others) haveshown the relationship between the gravity wave pressure drag and the intensity ofmountain wave activity, and McCann (1995) has demonstrated a practicalapproach to deducing this measure from model-generated profiles. Further

4.4.3GRAVITY WAVE ACTIVITY

4.4.2CLEAR AIR TURBULENCE


40 – 45

35 – 40

30 – 35

25 – 30

20 – 25

15 – 20

10 – 15

5 – 10

Stc – 5

2 24

70 82

137 87

26 19

26 5

11 13

32 28

77 67

76 32

1.00.80.60.40.20.0

Figure 4.8Probability of detection (POD) for

PIREP turbulence versus ETAanalysis turbulence from DTF-2. Thetwo columns to the right show the total

number of Yes/No turbulence reportsfrom PIREPs selected for the

STORM-FEST period(from Marroquin and Cairns et al.,

1995)

POD

Leve

l (10

00 h

)

Yes NoPositive = Yes Negative = No only

Legend POD of No POD of Yes

enhancements of the method allow the inclusion of hydraulic-jump-type flow andreflection and resonance phenomena associated with sudden changes in verticalstability. Table 4.2 (from McCann (1995)) demonstrates the potential of themethod and the viability of the contingency table for such problems.

4.5 EVALUATION OF STATION FORECASTS FOR CEILING/VISIBILITYBASED ON POST-PROCESSED MODEL OUTPUT

Several meteorological authorities are currently attempting to objectively generateaviation forecasts such as aerodrome forecasts (TAFs) or aviation terminal forecasts(FTs) based on statistical forecasting techniques using NWP output. Evaluationand verification of such forecasts is a particularly sensitive issue; as planningminima for operators are becoming lower, the critical range of ceiling and visibili-ty is getting very narrow. Traditional verification scores frequently used in otherforecast domains (e.g. RMSE for temperature or wind) are at best meaningless andsometimes utterly misleading. The forecast problem of predicting a visibility below500 m is not really solved by methods performing well in average fair-weather con-ditions; such cases need to be specifically addressed by the verification system. Verylow visibility and ceiling values are furthermore influenced by strictly localized con-ditions such as soil moisture, snow cover, terrain features, vicinity to river beds, etc.

Strong inversions in the boundary layer are a typical feature in low visibility/ceiling conditions and they indicate nearly complete de-coupling of upper-levelflow and near-surface conditions. The covariance of model-generated parameters inthe free atmosphere and moisture near the ground is therefore necessarily low andunreliable in such conditions.

Low visibility and ceilings associated with strong frontal or mesoscale systems,particularly in the cold season with snow prevalent, can be well captured by models(Porter and Seaman, 1995) and profit from statistical adaptation to take local ter-rain features into account (typical convergences, coastal or upslope effects).

Evaluation schemes designed to monitor the performance of any automatedproducts obviously need to take this into account. Possible solutions would be tostratify the data sample into purely localized and advectively driven events. Forlocally driven events, methods with mostly local predictors, auto-regressiveschemes, Markov-chains or one-dimensional models (see for example Keller, 1995)hold more promise than MOS-type systems, particularly in complex terrain. MOS-type systems have been shown to provide valuable guidance in coastal areas andlarge, homogeneous regions with slowly varying soil conditions, for exampleCanada and Finland.

Seasonal variations are strong in middle and higher latitudes and require sep-arate investigations for warm and cold seasons, and regime-dependent stratification(see Clark, 1995) helps to identify physically-based weaknesses.


Pressure drag (mb)

Intensity 0.0–0.1 1.0–2.0 2.0–3.0 3.0–4.0 >4.0 Total

Smooth 13 5 0 0 0 18Light 8 7 1 0 0 16Light-moderate 14 4 3 0 0 21Moderate 3 8 0 0 0 11Moderate-severe 2 2 1 1 2 8Severe 1 1 1 4 12 19

Total 41 27 6 5 14 93

Table 4.2A 6 × 5 contingency table of turbulence

intensity reports with ranges of MWAVEpressure drag

(from McCann, 1995)

CHAPTER 5

FUTURE TRENDS

5.1 FUTURE OBSERVING SYSTEM

The task of an NWP model is to solve a set of complicated differential equations,using observational data as initial conditions, to produce a weather forecast in a shortperiod of time. With the advance of computer technology, models have become morerefined in terms of resolution and the details of physics. To make more accurate fore-casts, precise observational data at the model resolution are needed. At present,global models need three-dimensional fields of temperature, humidity and wind at 50-to 100-km resolution in the horizontal and 1-km resolution in the vertical from thesurface to about 30-km altitude. Observations are needed every three to 12 hours.Evolving mesoscale models require even greater resolution: 15–35 km horizontal and1–3 hours temporal. Other data such as snow depth, snow cover, ice cover, soil tem-perature profile, soil moisture profile and water temperatures are also essential inputs.These are unlikely to be achieved from the current land-based systems (such as thesurface synoptic observational network, the rawinsonde network, etc.), because thecost of establishing and maintaining such networks would be astronomical. Othersources of data are essential to supplement the current database. The new three- andfour-dimensional data assimilation techniques (for example, 4DVAR), would enablemodels to integrate data from other non-traditional platforms effectively. In thefuture, composite observing systems consisting of ground-based remote sensing, air-borne in situ and remote sensing, and satellite remote sensing systems are likely toprovide the observational data for NWP models. Some of the potential future in situand remotely sensed systems will be described briefly here.

The usefulness of radar for summer severe storm monitoring has been proven. SomeNWP models are planning to incorporate these data in their initialization schemes.Their impacts on NWP will be evaluated.

Networks of lightning detectors will be installed in North America. These arecritical for summer severe storm detection, especially in data-sparse areas, but theirimpacts on NWP have yet to be validated.

In many parts of the world a number of institutions, which include the nationalweather services, operate observing networks for specialized purposes. Power com-panies often have extensive raingauge networks, and road maintenance authorities,schools and tourism industries, among others, operate surface observing systems.Although some of these data may not get to be calibrated to NWS standards, manyof them would go a long way towards ensuring a vastly improved observation den-sity both for data assimilation and for verification of high-resolution models.

One of the ground-based remote sensing systems that would be important forboth the global and mesoscale NWP initialization is the wind profiler. Networks ofthis instrument are planned for some areas of the world. This instrument provideshigh temporal and vertical resolution wind profile data for the troposphere andlower stratosphere. Typically, these profilers operate at 0.33 to 6.0 metre wave-lengths and use gradients in atmospheric refractive index to scatter energy back tothe receiver. They can operate unattended for long periods and provide wind pro-files every 30 or 60 minutes. Used in combination with an acoustic sounder system(or Sodar), the profiler can also reliably calculate virtual temperature profiles.Experiments are also under way to infer the humidity profile from the surface toabout 3-km altitude.

Currently, profilers used in the lower atmosphere (to 3 km) are showing morepotential than those designed to operate at higher levels. This is due to a combi-nation of cost and effectiveness. With variational assimilation techniques, thesedata are becoming increasingly useful to NWP models.

Improved use of existing observationnetworks

5.1.1GROUND-BASED SYSTEMS

Commercial aircraft are excellent platforms for upper air in situ measurement ofmeteorological variables. The VHF data link provides reliable two-way air-to-ground digital communication. This enables automatic transmission of wind andair temperature observed onboard the aircraft to ground stations. The AircraftCommunications Addressing and Recording System (ACARS) is used in NorthAmerica and similar systems are being installed worldwide. Tests are being carriedout in the US on aircraft humidity sensing system (e.g. the Water Vapour SensingSystem, WVSS). Nintey-five per cent of the data obtained from these two systemsare flight level data around 20 000 ft above ground. An increasing number areascent/descent (profile type) data. The vertical resolution of these data is currentlynot as high as the rawinsonde though higher-frequency data may be available infuture. Also, commercial aircraft flight paths cover mainly populated areas of theworld. Despite these drawbacks, the combined ACARS and CASH measurementswould augment the current upper air network tremendously and would likely havea positive impact on NWP analysis. Turbulence observing systems are currentlybeing implemented.

The newly developed aerosonde (autopilot lightweight aircraft) is an afford-able method to obtain in situ meteorological data in remote areas such as overoceans and deserts. The aerosonde’s flight path can be controlled remotely via satel-lite and the Global Positioning System (GPS). This platform provides high spatialand temporal resolution data at non-standard times. It has been demonstrated thataircraft data have positive impacts on meteorological analysis and prediction.There is an increased interest in the use of balloons as observational platforms. Oneuse is as constant level platforms, used over the oceans to help fill data voids. Asecond use is as a platform from which to deploy drop-sondes for atmospheric pro-filing.

Work is under way to adapt current research aircraft remote sensing instru-ments to fit into commercial aircraft. These instruments have to be compact,lightweight, automatic, have low power consumption and be almost maintenancefree to minimize operational cost. Also, they need to have built-in processing powerto perform onboard real-time calculations to reduce the volume of data to be trans-mitted via VHF or satellite to ground receiving stations.

Satellite is going to be a versatile future meteorological observational platform.Many prediction models incorporate satellite radiance data in their analysesalready. Other models will do so soon. Whether these data will improve the NWPis to be determined.

There have been steady improvements in the quality of satellite temperatureand moisture soundings. A new sensor, the Advanced TIROS Operational VerticalSounder (ATOVS), is onboard the new generation of NOAA polar-orbiting satel-lites. The biggest deficiency of these data is the lack of vertical resolution. Recentexperience with variational assimilation shows that an increased benefit of incor-porating these data in NWP models show that they provide no greater benefit toNWP in the Northern Hemisphere. The above conclusion has to be tested with thenew 4DVAR techniques.

Estimates of surface wind over oceans from a satellite-borne scatterometer weremade in the late 1970s and is available from NSCAT (NASA Scatterometer)onboard the ADEOS (Japan’s Advanced Earth Observing Satellite) in 1996. Asimilar instrument, the ASCAT (Advanced Scatterometer) will be flown on thenext generation NOAA polar-orbiting satellites. They should greatly help surfaceanalysis over the oceans, but the benefit to NWP in general is as yet unclear.

The new Doppler wind lidar (DWL) is under evaluation to see whether it iscost-effective to include with the next generation polar-orbiting satellites. Itmeasures the Doppler shift of a refracted signal due to moving aerosol and cloudparticles along the line of sight. A vertical wind component profile can be inferred.By probing in different directions, the full horizontal wind vector field may beresolved. Such an instrument can profile the atmosphere from 20-km height to thesurface with high vertical resolution. The use of lidar to measure the vertical profile

5.1.3SATELLITE SYSTEMS

5.1.2AIRBORNE SYSTEMS


of wind at a land station has been demonstrated to give accurate values. They havethe potential of providing a massive increase in valuable data for NWP.

The GPS consists of 24 satellites. They transmit L-band radio signals (~ 19 and22 cm wavelength) to Earth for navigation, time transfer and relative positioningpurposes. This platform provides opportunities for active sensing of the Earth’satmosphere. The radio source aboard the satellite is very stable and the signalstrength is constant and strong. With a dual frequency GPS ground receiver, surfacetemperature and pressure measurements, and the time delay of the signal by theionosphere, an estimate of the vertically integrated water vapour overlying thereceiver can be derived. Integrated water vapour represents the total latent heatavailable in the air column. It provides a powerful constraint to NWP models andweather analysis. The vertical resolution of these data is comparable to the ground-based water vapour radiometer. Depending on the number of ground-based receivingsites, horizontal resolution can be good.

The GPS receiver can also be installed aboard a low earth-orbiting satellite, andperforms limb scanning of the atmosphere. The occultation technique can be used todeduce the atmospheric temperature and pressure profile. The accuracy of the tempera-ture recovered in the troposphere is limited by the uncertainty of the moisturedistribution and other factors. Because of the sub-horizontal nature of its samplinggeometry, the retrieved data are subject to obstruction by mountain ranges. From aproof of concept study in 1995 accurate vertical temperature profiles from an altitudeof 40 km to about 5 km were obtained in dry atmospheres. The vertical resolution isabout 1 km. Research is under way to improve temperature retrievals above 40 km andbelow 5 km altitude.

Accurate measurements of surface properties such as snow depth, snow coverarea, ice cover, soil temperature profile, soil moisture profile and water temperaturesare very difficult. By nature, these data have large spatial and temporal variability.These data are of course of great interest to other communities such as agricultureand forestry. Cooperative efforts are required. Research is under way to use satelliteobservations to recover these data.

5.2 MODEL AND POST-PROCESSING IMPROVEMENT TRENDS

Some trends in NWP, post-processing of data and infrastructure support systems areclear. Others are less so as they depend on the intense research being conducted atmany institutes and national Meteorological and Hydrological Services (NMHSs).The trends that are more likely to become reality are highlighted here.

As has been the case over the last 30 years, model resolution will continue to improve.One of the main driving forces is the increased availability of computer memory andprocessing speed. However, resolution improvements will have little impact unless acorresponding increase in data availability at model scales is in existence.

Predictions of tropical cyclones are improving with increased resolution. Forecastsof position, timing and strength of tropical cyclones, during their mature stage, arecrucial to aviation users in the path of the cyclone and for the peripheral dangerarea. It is also important for the general user that NWP models accurately depicttropical cyclones when they become extratropical and get caught up in the mid-latitude flow. When an extratropical cyclone enters the flow, the huge reservoir ofheat and moisture contained in such a small region can cause the flow to buckle anddevelop in a totally different sequence. Such a violent development can change thewhole of the Northern Hemisphere weather systems within three days, even sys-tems on the other side of the globe.

Again primarily as a result of increased resolution, models will continue to improvein their forecasting of meteorological fields impacted by land/sea boundaries. Thisimprovement will be noticed most by aviation forecasts for airports near large bodiesof water.

Land/sea interaction

Tropical cyclone prediction

5.2.2GLOBAL MODELS

Model resolution

5.2.1INTRODUCTION

CHAPTER 5 — FUTURE TRENDS 113

Models will gradually treat hydrological impacts as an explicit event within theirformulation. Surface wetness and evaporation at a grid point, for example, willincrease in response to precipitation forecast by the model at an earlier time step.

Models will increasingly need to know the detailed condition of the underlying sur-face. One type of data which is lacking and which is difficult to model is the soilmoisture content over land grid points. If the soil at a grid point in the model is toowet, then surface exchange processes will all be in error. During a forecast run muchof the wetness may be evaporated off, giving a moist lower atmosphere and lowcloud where there should not be. Dynamic soil moisture models, which run in par-allel with the model, estimating rainfall, run-off, absorption and evaporation areonly partly effective, because for a large part of the globe we have no data to tunethe models by.

The modelling of visibility and cloud needs to improve, particularly for shallow layercloud. Layer cloud is often thinner than the vertical grid scale of the models and so isseldom forecast well. It considerably affects the radiation balance and the surfacetemperatures which are forecast. For general aviation this is important mainly for fore-casting VFR/IFR. Visibility forecasts are improving for higher resolution mesoscalemodels, particularly those which keep track of the advection of aerosols and conden-sation nuclei upon which fog/cloud droplets condense, considerably affecting visibility.

At low to medium levels, models which include cloud liquid water as an intrinsicvariable will show improvements in forecasting aircraft icing. The main problemhere is to tune and verify icing forecasts. There are relatively few reports of theoccurrence of icing to help modellers, and the better the forecasts become, thefewer there might be, because aircraft will divert away from the event!

One of the more significant advances will continue to be the introduction andimprovement of advance data assimilation techniques. With these techniques, datafrom many additional sources can be ingested in NWP models ‘directly’. Radiancemeasurements from satellites, Doppler shifts from radar and wind profilers, forexample, can be ingested into the model without being converted to meteorologi-cal variables. This permits the data to retain their native value and improves theirutility to the model.

Many if not most of the improvements noted above for global models will beapplied to varying degrees to models of higher resolution. In fact, one trend is thatthere will be less and less distinction between global and mesoscale models asNMHSs attempt to reduce the number of separate models running in an NWPcentre. Nested grids make it possible today in some centres to run only a singlemodel with varying resolution.

It is at the surface that most of the energy is put into the atmosphere at low lati-tudes, to be dispersed back to the surface at higher latitudes. The scales of motionare smaller near the surface, and the current resolution of NWP models is leasteffective. However, just increasing the resolution will not be enough because moredata are needed and the physics of the processes needs to be better modelled. Forhigh-resolution mesoscale models going below 10 km, current parameterizations ofconvection and cloud (which average the effects of many clouds in the grid box)start to become inadequate approximations. More sophisticated and detailed mod-elling of convection will be needed. However, in some areas there are more dataavailable than are being used. Frequently, others levels of government or privateindustry operate networks of meteorological data sensors that may be unknown tothe NMHSs. These data may not meet the rigorous data quality checks customarilyapplied to data collected by NMHSs but nevertheless need to be considered fordata assimilation schemes running at high resolution.

Surface data availability

5.2.3REGIONAL MODELS

Variational assimilation

Phases of water

Visibility and cloud

Surface condition

Hydrological cycle


The expected increase in computer power will mean a better depiction of windsnear the jet cores by having a higher resolution in the horizontal and the vertical.On its own this will not solve all problems because many of the more importanterrors which have been reported by aircraft are caused more by a poor initial analysis than by model deficiencies. A general increase in the number, quantity andarea coverage of observations will help here.

It is likely that, for the busier airfield where there are copious ascent and descentobservations and high-resolution surface observing networks, locally run very high-resolution models may help to forecast short-term wind conditions including thepersistence of wake vortices.

It is expected that there will be an increase in models developed to be run at asingle grid point such as an airport. Linked to larger scale models, these pointmodels will be able to explicitly depict the detailed interactions between the sur-face and the atmosphere at the location in question. These may use “multiple tiles”,each of which may represent a type of land use in the region near the site. Each tile(effectively 1 km square) has a separate boundary layer and soil layer model.Resultant forecast is a weighted average of the tile forecast. This can help to pro-duce very detailed local forecasts and may help with TAFs.

With increased computer power and variational data assimilation it may prove possible to provide skilled automated guidance for short-term forecasts atairports.

With the improvements noted above, particularly enhanced regional models orsingle point models, TAF forecasts of specific weather elements will continue toimprove. Forecasters will need to remain very aware of the detailed formulation andperformance of their numerical models to be able to use this product to itsmaximum.

Winds at airports may be one of the first direct model output products available toforecasters. Particularly in areas where data assimilation techniques include theingest of wind profiler or Doppler radar data, useful local wind forecasts to allowplanning for events including runway changes may be available.

Forecasters may soon be receiving forecasts of weather elements with a probabilityor confidence level attached. These can be created by a number of means, but themost promising is by ensemble techniques. In ensemble forecasting, either anumber of different models are run on the same initial conditions, or a single modelis run with a range of initial conditions representative of the uncertainty in theobservational system. Simply put, if all models or runs of the same model producesimilar outputs for the area of concern, the confidence level will be high that theevents will occur. Conversely, if the outputs diverge, confidence will be lower.Results so far have been positive for global models in the medium range. For short-range, high-resolution models, results so far have been poor.

The power of supercomputers continues to increase at a rapid rate. Existingcomputer power is still a limitation on the types of models and resolutions that couldbe run. Other limitations are beginning to become noticeable. Top among theseother factors is data availability. It does little good to run models at very highresolution without the corresponding data density. This does not necessarily implythat the increased resolutions made possible by increased computing power willrequire denser surface or upper-air data networks. Work into data assimilationtechniques will ensure that the maximum use of existing data sets will be made.

Increasing at an even faster rate, this will allow the transmission of more detailedand comprehensive data sets. This could allow small NMHSs in the developing

Communications band width

5.2.5COMPUTING POWER AND

COMMUNICATIONS

Computing power

Probabilistic forecasts

Local winds

5.2.4PRODUCTS

Short-term forecasts

Semi-automated TAF forecasts

Single point models

Wake vortex modelling

Wind speed and direction forecasts

CHAPTER 5 — FUTURE TRENDS 115

world to have nearly a full range of model output. The training implications of thisoccuring are large and clear.

Aviation global models will continue to be restricted to a few centres. However thisis to ensure consistency of aviation forecasts and operational backup. For mesoscalemodels, however, there will be no such limitation and these will proliferate. It maybe, however, that these regional models may be driven by only a few global analy-ses and forecasts.

Not only does lack of data in a region affect model forecast accuracy everywhere,but in the nature of things, such areas tend to be ignored. Modellers tend not tofocus on the quality of forecasts for areas for which they get no feedback. A crucialpart of the modelling process is tuning the NWP model to correct biases of prob-lems reported by users. For global models, North America, the Atlantic and Europe(and to a lesser extent the Pacific) are heavily studied because modellers receiveregular reports from users of the perceived quality of the forecasts. Areas for whichthe modellers seldom receive critical reports will go unchecked. Most of theSouthern Hemisphere and most of Africa fall in this category, because even if thedata reach users in those regions, few critical appraisals of the forecast are everreceived by the modellers. Regular reports are most useful, because the tuningprocess is lengthy and needs regular feedback. The advantages of improving fore-casts for particular regions tend to improve the general quality of forecasts foreveryone.

5.2.6USER FEEDBACK

Stewardship


REFERENCES AND RECOMMENDED READING

Altherr, J.D., M. Dupanloup, Y. Ganter and E. Junet, 1982: Prévision objective des hauteurs de précipitations et de l’ensoleillementrelatif au moyen de l’analyse discriminante. Swiss Meteorological Institute, No. 44, 43 pp.

Becker, B.D., et al., 1996: A simulated future atmospheric observation database including ATOVS, ASCAT, and DWL.Bulletin of the American Meteorological Society, Vol. 77, No. 10, pp. 2279-2294.

Beljaars, A.C.M. and A.K. Betts, 1992: Validation of the boundary layer representation in the ECMWF model. Validationof models over Europe, ECMWF Seminar Proceedings, September 1992.

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