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## Overview of Statistical Tropical Cyclone Forecasting

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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**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**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)**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**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**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**NHC and JTWC Official Intensity Error Time Series**Atlantic and Western North Pacific**Atlantic 48 hr Intensity Guidance Errors**Consensus NWP Classical statistical Statistical-dynamical From DeMaria et al 2013, BAMS**Atlantic Track and Intensity Model Improvement Rates**(1989-2012 for 24-72 hr, 2001-2012 for 96-120 hr)**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**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**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**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**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**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**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**LGEM Improvement over SHIPSAL and EP/CP Operational Runs**2007-2012**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**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**Graphical Interpretation of the Discriminant Function**DF chosen to best separate red and blue points**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)**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**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**Forecast Section**SHIPS/LGEM Predictor Values SHIPS Forecast Predictor Contributions Rapid Intensification Index**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**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**MC Probability Example**Hurricane Bill 20 Aug 2009 00 UTC 1000 Track Realizations 34 kt 0-120 h Cumulative Probabilities**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**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