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**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

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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 1From Wilks (2006) and Kalnay (2003)

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**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

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Barotropic dynamical Regional dynamical Global dynamical Consensus

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**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

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**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

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**NHC and JTWC Official Intensity Error Time Series **

Atlantic and Western North Pacific

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**Atlantic 48 hr Intensity Guidance Errors**

Classical statistical NWP Statistical-dynamical Consensus From DeMaria et al 2013, BAMS

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Atlantic Track and Intensity Model Improvement Rates ( for hr, for 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 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

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**SHIPS Developmental Sample Sizes**

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**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

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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

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**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 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

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**LGEM Improvement over SHIPS AL 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 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

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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

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**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

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**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

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**MC Probability Example**

Hurricane Bill 20 Aug UTC 1000 Track Realizations kt h Cumulative Probabilities

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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

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