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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,

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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 2

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Weather Forecast Methods 1 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 1 From 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 : Barotropic NWP –NMC, SANBAR, VICBAR, LBAR : Classical statistical models –MM, T-59/60, NHC64/72, CLIPER, HURRAN : Statistical-Dynamical models –NHC73, NHC83, NHC present: Baroclinic NWP –MFM, QLM, GFDL, HWRF, COAMPS-TC, Global models 2006-present: Consensus methods 4

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5 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 6

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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 7

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

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

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Atlantic Track and Intensity Model Improvement Rates ( for hr, for hr) 10

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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 11

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Overview of the SHIPS Model Multiple linear regression –y = a 0 + a 1 x 1 + … a N x N y = intensity change at given forecast time –(V 6 -V 0 ), (V 12 -V 0 ), …, (V 120 -V 0 ) x i = predictors of intensity change a i = regression coefficients Different coefficients for each forecast time Predictors x i averaged over forecast period x,y normalized by subtracting sample mean, dividing by standard deviation 12

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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: –WP, SH –IO

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SHIPS Developmental Sample Sizes 14

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SHIPS Predictors 15 1.Climatology (days from peak) 2.V 0 (V max at t= 0 hr) 3.Persistence (V 0 -V -12 ) 4.V 0 * Per 5.Zonal storm motion 6.Steering layer pressure 7.%IR pixels < -20 o C 8.IR pixel standard deviation 9.Max Potential Intensity – V 0 10.Square of No Ocean heat content 12.T at 200 hPa 13.T at 250 hPa 14.RH ( hPa) 15. e of sfc parcel - e of env hPa env shear 17.Shear * V 0 18.Shear direction 19.Shear*sin(lat) 20.Shear from other levels km 850 hPa vorticity km 200 hPa divergence 23.GFS vortex tendency 24.Low-level T advection

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Variance Explained by the Models 16

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12 hr Regression Coefficients 17

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96 hr Regression Coefficients 18

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Impact of Land Detect when forecast track crosses land Replace multiple regression prediction with dV/dt = - µ(V-V b ) µ = climatological decay rate ~ 1/10 hr -1 V b = background intensity over land Decay rate reduced if area within 1 deg lat is partially over water 19

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Example of Land Effect 20

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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 21

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Operational LGEM Intensity Model dV/dt = V - (V/V mpi ) n V (A) (B) V mpi = Maximum Potential Intensity estimate = Max wind growth rate (from SHIPS predictors) β, n = empirical constants = 1/24 hr, 2.5 Steady State Solution: V s = V mpi (β/ ) 1/n 22

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LGEM versus SHIPS Advantages –Prediction equation bounds the solution between 0 and V mpi –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 23

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LGEM Improvement over SHIPS AL and EP/CP Operational Runs

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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 25

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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 = a 0 + a 1 x 1 + … a N x N Weights chosen to maximize separation of the classes 26

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Graphical Interpretation of the Discriminant Function 27 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) 28

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RII Predictors 1.Previous 12 h max wind change (persistence) 2.Maximum Potential Intensity – Current intensity 3.Oceanic Heat Content hP shear magnitude (0-500 km) hPa divergence ( km) hPa relative humidity ( km) hPa tangential wind (0-500 km) 8.IR pixels colder than -30 o C 9.Azimuthal standard deviation of IR brightness temperature 29

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RII Discriminant Coefficients 30

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RII Brier Skill Brier Score = ∑ (P i -O i ) 2 –P i = forecasted probability –O i = verifying probability (0 or 100%) For skill, compare with no-skill reference –Brier Score where P i = climatological probability Brier Skill Score = %Reduction in Brier Score compared with climo value 31

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RII Brier Skill Scores 32

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

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Forecast and Predictor Sections 34

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Predictor Contribution Section 35

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RII Section 36

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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 37

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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 38

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1000 Track Realizations 34 kt h Cumulative Probabilities MC Probability Example Hurricane Bill 20 Aug UTC 39

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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 40

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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

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