Overview of Statistical Tropical Cyclone Forecasting

1. Overview of Statistical Tropical Cyclone Forecasting Mark DeMaria, NOAA/NCEP/NHC Temporary Duty Station, Fort Collins, CO HWRF Tutorial, College Park, MD January 14, 2014

2. 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

3. 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 1From Wilks (2006) and Kalnay (2003)

4. 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

5. Barotropic dynamical Regional dynamical Global dynamical Consensus

6. 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

7. 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

8. NHC and JTWC Official Intensity Error Time Series Atlantic and Western North Pacific

9. Atlantic 48 hr Intensity Guidance Errors Consensus NWP Classical statistical Statistical-dynamical From DeMaria et al 2013, BAMS

10. Atlantic Track and Intensity Model Improvement Rates (1989-2012 for 24-72 hr, 2001-2012 for 96-120 hr)

11. 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

12. 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

13. 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

14. SHIPS Developmental Sample Sizes

15. SHIPS Predictors • Climatology (days from peak) • V0 (Vmax at t= 0 hr) • Persistence (V0-V-12) • V0 * Per • Zonal storm motion • Steering layer pressure • %IR pixels < -20oC • IR pixel standard deviation • Max Potential Intensity – V0 • Square of No. 9 • Ocean heat content • T at 200 hPa • T at 250 hPa • RH (700-500 hPa) • e of sfc parcel - e of env • 850-200 hPaenv shear • Shear * V0 • Shear direction • Shear*sin(lat) • Shear from other levels • 0-1000 km 850 hPavorticity • 0-1000 km 200 hPa divergence • GFS vortex tendency • Low-level T advection

16. Variance Explained by the Models

17. 12 hr Regression Coefficients

18. 96 hr Regression Coefficients

19. 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 deglat is partially over water

20. Example of Land Effect

21. 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

22. 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

23. 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

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

25. 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

26. 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

27. Graphical Interpretation of the Discriminant Function DF chosen to best separate red and blue points

28. 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)

29. RII Predictors • Previous 12 h max wind change (persistence) • Maximum Potential Intensity – Current intensity • Oceanic Heat Content • 200-850 hP shear magnitude (0-500 km) • 200 hPa divergence (0-1000 km) • 850-700 hPa relative humidity (200-800 km) • 850 hPa tangential wind (0-500 km) • IR pixels colder than -30oC • Azimuthal standard deviation of IR brightness temperature

30. RII Discriminant Coefficients

31. 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

32. RII Brier Skill Scores

33. Forecast Section SHIPS/LGEM Predictor Values SHIPS Forecast Predictor Contributions Rapid Intensification Index

34. Forecast and Predictor Sections

35. Predictor Contribution Section

36. RII Section

37. 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

38. 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

39. MC Probability Example Hurricane Bill 20 Aug 2009 00 UTC 1000 Track Realizations 34 kt 0-120 h Cumulative Probabilities

40. 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

41. 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