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
1
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
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
3
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
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Barotropic dynamical
Regional dynamical
Global dynamical
Consensus
5
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
9
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)
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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
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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
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SHIPS Developmental Sample Sizes
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SHIPS Predictors
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
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
16.
17.
18.
19.
20.
21.
22.
23.
24.
850-200 hPa env shear
Shear * V0
Shear direction
Shear*sin(lat)
Shear from other levels
0-1000 km 850 hPa vorticity
0-1000 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
– 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
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– 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 of26
the classes
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
1.
2.
3.
4.
5.
6.
7.
8.
9.
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
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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 2009 00 UTC
1000 Track Realizations
34 kt 0-120 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
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from statistical models