Overview of Statistical Tropical Cyclone Forecasting

Mark DeMaria, NOAA/NCEP/NHCTemporary Duty Station, Fort Collins, CO

HWRF Tutorial, College Park, MD

January 14, 20141

Outline

• Overview of statistical techniques for tropical cyclone forecasting

• Evolution of track forecast models• Statistical intensity models• Consensus techniques• Statistical prediction of other parameters• Summary

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Weather Forecast Methods1

• Classical statistical models– Use observable parameters to statistical

predict future evolution• Numerical Weather Prediction (NWP)

– Physically based forecast models• Statistical-Dynamical models

– Use NWP forecasts and other input for statistical prediction of desired variables• Station surface temperature, precipitation,

hurricane intensity changes 3

1From Wilks (2006) and Kalnay (2003)

Example of Forecast Technique Evolution: Tropical Cyclone Track Forecasts

• 1954 – NHC begins quantitative track forecasts – Lat, lon to 24 h

• To 48 h in 1961, to 72 h in 1964, to 120 h in 2003– No objective guidance through 1958

• 1959-1996: Barotropic NWP– NMC, SANBAR, VICBAR, LBAR

• 1959-1972: Classical statistical models– MM, T-59/60, NHC64/72, CLIPER, HURRAN

• 1973-1990: Statistical-Dynamical models – NHC73, NHC83, NHC90

• 1976-present: Baroclinic NWP– MFM, QLM, GFDL, HWRF, COAMPS-TC, Global models

• 2006-present: Consensus methods 4

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Barotropic dynamical

Regional dynamical

Global dynamical

Consensus

Purposes of Statistical Models• Deterministic prediction

– Provides quantitative estimate of forecast parameter of interest• e.g., maximum surface wind at 72 hr

• Classification – Assigns data to one of two or more groups

• e.g., Genesis/non-genesis, RI/non-RI

– Probability of group membership usually included

• Forecast uncertainty/difficulty estimation– Baseline models (CLIPER/SHIFOR)– Track GPCE – NHC wind speed probability model 6

Statistical Modeling Philosophy

• Schematic model representation

y = f(x)

y is what you want to predict

x is vector of predictors

f is a function that relates x to y• The x is more important than the f

– Keep f simple unless you have good reason not to

• There is no substitute for testing on truly independent cases 7

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NHC and JTWC Official Intensity Error Time SeriesAtlantic and Western North Pacific

Atlantic 48 hr Intensity Guidance Errors

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Classical statistical

Statistical-dynamical

Consensus

From DeMaria et al 2013, BAMS

NWP

Atlantic Track and Intensity Model Improvement Rates

(1989-2012 for 24-72 hr, 2001-2012 for 96-120 hr)

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Example of a Deterministic Statistical-Dynamical Model

• The Statistical Hurricane Intensity Prediction Scheme (SHIPS)

• Predicts intensity changes out to 120 h using linear regression

• Predictors from GFS forecast fields, SST and ocean heat content analysis, climatology and persistence, IR satellite imagery

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Overview of the SHIPS Model• Multiple linear regression

– y = a0 + a1x1 + … aNxN

• y = intensity change at given forecast time– (V6-V0), (V12-V0), …, (V120-V0)

• xi = predictors of intensity change

• ai = regression coefficients

• Different coefficients for each forecast time• Predictors xi averaged over forecast

period• x,y normalized by subtracting sample

mean, dividing by standard deviation

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Overview of SHIPS

• Five versions – AL, EP/CP, WP, (north) IO, SH

• Developmental sample– Tropical/Subtropical stages– Over water for entire forecast period

• Movement over land treated separately

– AL, EP/CP: 1982-2012– WP, SH 1999-2012– IO 1998-2012

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SHIPS Developmental Sample Sizes

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SHIPS Predictors1. Climatology (days from peak)

2. V0 (Vmax at t= 0 hr)

3. Persistence (V0-V-12)

4. V0 * Per

5. Zonal storm motion

6. Steering layer pressure

7. %IR pixels < -20oC

8. IR pixel standard deviation

9. Max Potential Intensity – V0

10. Square of No. 9

11. Ocean heat content

12. T at 200 hPa

13. T at 250 hPa

14. RH (700-500 hPa)

15. e of sfc parcel - e of env

16. 850-200 hPa env shear

17. Shear * V0

18. Shear direction

19. Shear*sin(lat)

20. Shear from other levels

21. 0-1000 km 850 hPa vorticity

22. 0-1000 km 200 hPa divergence

23. GFS vortex tendency

24. Low-level T advection

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Variance Explained by the Models

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12 hr Regression Coefficients

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96 hr Regression Coefficients

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Impact of Land

• Detect when forecast track crosses land• Replace multiple regression prediction

with

dV/dt = - µ(V-Vb)

µ = climatological decay rate ~ 1/10 hr-1

Vb = background intensity over land

• Decay rate reduced if area within 1 deg lat is partially over water

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Example of Land Effect

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Limitations of SHIPS

• V predictions can be negative• Most predictors averaged over entire

forecast period– Slow response to changing synoptic

environment• Strong cyclones that move over land and

back over water can have low bias• Logistic Growth Equation Model (LGEM)

relaxes these assumptions

Operational LGEM Intensity Model

dV/dt = V - (V/Vmpi)nV (A) (B)

Vmpi = Maximum Potential Intensity estimate

= Max wind growth rate (from SHIPS predictors)

β, n = empirical constants = 1/24 hr, 2.5

Steady State Solution: Vs = Vmpi(β/)1/n

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LGEM versus SHIPS• Advantages

– Prediction equation bounds the solution between 0 and Vmpi

– Time evolution of predictors (Shear, etc) better accounted for

– Movement between water and land handled better because of time stepping

• Disadvantages– Model fitting more involved– Inclusion of persistence more difficult

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LGEM Improvement over SHIPSAL and EP/CP Operational Runs 2007-2012

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Examples of Classification Models• Storm type classification

– Tropical, Subtropical, Extra-tropical– Based on Atlantic algorithm– Discriminant analysis for classification– Input includes GFS parameters similar to Bob

Hart phase space, SST and IR features• Rapid Intensification Index

– Probability of max wind increase of 30 kt– Discriminant analysis using subset of SHIPS – Separate versions for WP, IO and SH

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Linear Discriminant Analysis• 2 class example

– Objectively determine which of two classes a data sample belongs to• Rapid intensifier or non-rapid intensifier

– Predictors for each data sample provide input to the classification

• Discriminant function (DF) linearly weights the inputs

DF = a0 + a1x1 + … aNxN

• Weights chosen to maximize separation of the classes

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Graphical Interpretation of the Discriminant Function

DF chosen to best separate red and blue points

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The Rapid Intensification Index

• Define RI as 30 kt or greater intensity increase in 24 hr

• Find subset of SHIPS predictors that separate RI and non-RI cases

• Use training sample to convert discriminant function value to a probability of RI

• AL and EP/CP versions include more thresholds (25, 30, 35, 40 kt changes, etc)

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RII Predictors

1. Previous 12 h max wind change (persistence)

2. Maximum Potential Intensity – Current intensity

3. Oceanic Heat Content

4. 200-850 hP shear magnitude (0-500 km)

5. 200 hPa divergence (0-1000 km)

6. 850-700 hPa relative humidity (200-800 km)

7. 850 hPa tangential wind (0-500 km)

8. IR pixels colder than -30oC

9. Azimuthal standard deviation of IR brightness temperature

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RII Discriminant Coefficients

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RII Brier Skill

• Brier Score = ∑ (Pi-Oi)2

– Pi = forecasted probability

– Oi = verifying probability (0 or 100%)

• For skill, compare with no-skill reference– Brier Score where Pi = climatological

probability • Brier Skill Score = %Reduction in Brier

Score compared with climo value

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RII Brier Skill Scores

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Forecast Section

SHIPS/LGEM Predictor Values

SHIPS Forecast Predictor Contributions

Rapid Intensification Index

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Forecast and Predictor Sections

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Predictor Contribution Section

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RII Section

Consensus Models• Special case of statistical-dynamical

models• Simple consensus

– Linear average of from several models• ICON is average of DSHP, LGEM, HWFI, GFDI

• Corrected consensus– Unequally weighted combination of models

• Florida State Super Ensemble• SPICE: SHIPS/LGEM runs with several parent

models• JTWC’s S5XX, S5YY 37

Other Statistical TC Models• NESDIS tropical cyclone genesis model

– Discriminant analysis with SHIPS-type input• Radii-CLIPER model

– Predictions wind radii with parametric model, parameters functions of climatology

• Rainfall CLIPER model– Uses climatological rain rate modified by

shear and topography• NHC wind speed probability model

– Monte Carlo method for sampling track, intensity and radii errors 38

1000 Track Realizations 34 kt 0-120 h Cumulative Probabilities

MC Probability ExampleHurricane Bill 20 Aug 2009 00 UTC

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Upcoming Model Improvements

• Consensus Rapid Intensification Index– Discriminant analysis, Bayesian, Logistic

regression versions• Addition of wind radii prediction to SHIPS

model• TCGI – Tropical Cyclone Genesis Index

– Disturbance following TC genesis model• More physically based version of LGEM

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Long Term Outlook for Statistical Models

• Next 5 years– Incremental improvements in intensity models– Development of wind structure models– Continued role for consensus techniques

• Best intensity forecast will be combination of dynamical and statistical models

– Statistically post-processed TC genesis forecast from dynamical models

• Next 10 years– Dynamical intensity and structure models will

overtake statistical models – Continued role for consensus models and diagnostics

from statistical models 41