NUMERICAL WEATHER PREDICTION

K. Lagouvardos-V. KotroniInstitute of Environmental Research

National Observatory of Athens

 

WHAT IS THE NUMERICAL WEATHER PREDICTION?

A method to forecast weather conditions based on:

o Equations describing the flow within the atmosphere as well as many physical processes

o Translation into code executed on computerso Application on a specific geographic domain (grid)o Integration in time, based on initial and boundary

conditionso Provision of final products (forecasts of wind, temperature,

humidity, rain/snow, etc)

o1922: L. Richardson, forecast using human calculatorso1950: ΕNIAC forecast for three specific weather eventso1966: world coverage (USA)

o 1970: Foundation of the European Center for Medium-range Weather Forecasts (ECMWF)

1979 : first weather forecast issued by the ECMWFtoday: 10 days forecast, horizontal resolution~15 km

o 1990: first weather forecasts issued by universities, research centers and private companies.

HISTORY

EQUATIONS

Conservation of momentum (Newton’s law)3 equations for accelerations of wind (F = Ma)

Conservation of massequation for conservation of air (mass continuity)equation for conservation of water

Conservation of energy

equation for the first law of thermodynamics Relationship among p, V, and T

equation of state (ideal gas law)

NUMERICAL METHODS

Write the governing equations in form of spatial and temporal derivatives and transform them into algebraic equations

Computers can solve these equations, usually using finite difference schemes (expansion in Taylor series) on a grid

All terms are defined and computed on a fixed grid.Example: 1-D advection equation ∂u / ∂t = -u (∂u / ∂x)

x x+1x-1

∆x ∆x

tuu

tu

xuu

xu

xx

x

xxx

tt

2

2

11

11

GRID

All atmospheric processes are described

within a grid

Need for a large number of calculations

3-D GRID

Physical processes-parameterizations

Parameterizations are necessary for the representationof physical processes that are small in size or short in life, complex

or poorly known to be explicitly represented

Physical processes-parameterizations

Parameterizations are necessary for the representationof physical processes that are small in size or short in life, complex

or poorly known to be explicitly represented

What happens inside the clouds

WITHIN THE GRID

Constructing the initial conditions

Initial conditions: surface obs

Initial conditions: buoys

Initial conditions: soundings

Initial conditions: airplanes

Initial conditions: satellites

Global model (Source: USA)

Limited area- Region 1

Region 2

Weather forecasts at NOA

Limited area model: area 1

Limited area model: area 2

Final forecast product

Final forecast product

Forecast errors

Limited knowledge of initial conditions

Limited knowledge of physical processes

(parameterizations!!!)

Result:

Forecast errors grow in time

Ensemble forecasting

It is known that neither the models nor the initial conditions are perfect

Problem: deterministic forecasts have limited predictability

Possible solution: base the final forecast not only on the predictions of one model

(deterministic forecast) but on an ensemble of weather model outputs

ENSEMBLE FORECASTING

Based on perturbing the initial conditions (20-50 perturbed members) provided to

individual models, depending on a realistic spectrum of initial errors

Ensemble forecasting

OTHER APPLICATIONS

Model outputs can be used as an input to:

o Wave modeling and ocean circulationo Hydrological modeling for flood forecastingo Fire expansion modelso Air-quality models

ATMOSPHERIC RESEARCHTHEORY

OBSERVATIONS MODELS