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
: Barotropic NWP
NMC, SANBAR, VICBAR, LBAR
: Classical statistical models
MM, T-59/60, NHC64/72, CLIPER, HURRAN
: 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
Classical statistical
NWP
Statistical-dynamical
Consensus
From DeMaria et al 2013, BAMS

10. Atlantic Track and Intensity Model Improvement Rates ( for hr, for 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 Developmental sample
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:
WP, SH IO

14. SHIPS Developmental Sample Sizes

15. SHIPS Predictors Climatology (days from peak) 850-200 hPa env shear
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 ( hPa)
e of sfc parcel - e of env
hPa env shear
Shear * V0
Shear direction
Shear*sin(lat)
Shear from other levels
km 850 hPa vorticity
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 deg lat 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 Disadvantages
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 SHIPS AL 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
hP shear magnitude (0-500 km)
200 hPa divergence ( km)
hPa relative humidity ( 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 UTC
1000 Track Realizations kt 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