Probabilistic Hurricane Storm Surge (P-Surge) Arthur Taylor Meteorological Development Laboratory, National Weather Service January 20, 2008

Probabilistic Hurricane Storm Surge (P-Surge)Arthur TaylorMeteorological Development Laboratory, National Weather ServiceJanuary 20, 2008

Probabilistic Storm Surge 2008

IntroductionThe Sea, Lake, and Overland Surges from Hurricanes (SLOSH) model is the NWSs operational hurricane storm surge model.The NWS uses composites of its results to predict potential storm surge flooding for evacuation planningNational Hurricane Center (NHC) begins operational SLOSH runs 24 hours before forecast hurricane landfall


IntroductionNHCs operational SLOSH runs are based on a single NHC forecast track and its associated parameters.When provided accurate input, SLOSH results are within 20% of high water marks.Track and intensity prediction errors cause large errors in SLOSH forecasts and can overwhelm the SLOSH results.


Hurricane Ivan: A case study


Probabilistic Storm Surge MethodologyUse an ensemble of SLOSH runs to create probabilistic storm surge (p-surge) Intended to be used operationally so it is based on NHCs official advisory.P-surges ensemble perturbations are determined by statistics of past performance of the advisories.P-surge uses a representative storm for each portion of the error distribution space rather than a random sampling


Input Parameters for SLOSHA single run of SLOSH requires the following parameters:Track (Location and Forward Speed)PressureRadius of Maximum Winds (Rmax)


Errors used by P-surgeThe ensemble is based on distributions of the following:Cross track error (impacts Location)Along track error (impacts Forward Speed)Intensity error (impacts Pressure)Rmax error


P-surge Error DistributionsThe error distributions for cross track, along track, and intensity are determined by:Calculating the regression of the yearly mean errorAssuming a normal error distributionDetermining the standard deviation (sigma) based on:


Regression of Yearly Mean Error To calculate the yearly mean error:The forecasts from the advisories were compared with observations, represented by the 0 hour information from the corresponding later advisories.The errors were averaged by yearRegression curves were calculated and plotted for each forecast hour (12, 24, 36, )A mean error value was determined from where the regression curve crossed a chosen year.


Example of 24-hour Cross Track Error Regression PlotThe 2004 error regression value 34.8 was chosen as the 24-hour mean cross track error


Rmax Error DistributionsFor Rmax, we cant assume a normal distribution since the error is bounded. To calculate the Rmax error distributions:Group the values in bins according to:

The forecasts from the advisories were matched to the 0 hour estimate, which was treated as an observationThe probability density function (PDF) and cumulative density function (CDF) were plotted for each bin and forecast hour (12, 24, 36, )Since we chose to use 3 storm sizes (small 30%, medium 40%, large 30%) we determined the 0.15, 0.5, and 0.85 values of the CDF for each bin and forecast hour.


PDF for Rmax Errors Bin 0-3

Chart1

0100111

0001001

0101011

0011110

0100011

0010352

0002222

0000401

0111132

0000332

0222234

1243952

1104648

3457977

3711131688

7142122202016

2225262826179

2529363313166

12594584521153

21101710723

5742220

All

0100111

0001001

0101011

0011110

0100011

0010352

0002222

0000401

0111132

0000332

0222234

1243952

1104648

3457977

3711131688

7142122202016

2225262826179

2529363313166

12594584521153

21101710723

5742220

12Hr Fcst

24Hr Fcst

36Hr Fcst

48Hr Fcst

72Hr Fcst

96Hr Fcst

120Hr Fcst

Error (Fcst - Obs) by 5

Count

Rmax Error Dist Fcst Bin 0 (5..15 sm)

Chart2

0.00469483570.0046948357

0.00469483570.0093896714

0.0140845070.0234741784

0.0140845070.0375586854

0.03286384980.0704225352

0.1032863850.1737089202

0.1173708920.2910798122

0.58685446010.8779342723

0.09859154930.9765258216

0.02347417841


Cumulative distribution


RmaxBinA0

BinErrorFcst0Fcst1Fcst2Fcst3Fcst4Fcst5Fcst6

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0-500111132

0-450000332

0-400222234

0-3512439520.00469483570.0046948357

0-3011046480.00469483570.0093896714

0-2534579770.0140845070.0234741784

0-2037111316880.0140845070.0375586854

0-1571421222020160.03286384980.0704225352

0-1022252628261790.1032863850.1737089202

0-525293633131660.1173708920.2910798122

00125945845211530.58685446010.8779342723

05211017107230.09859154930.9765258216

01057422200.02347417841

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All

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1010001

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4100000

1110000

5423011

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1122534

0200000

12Hr Fcst

24Hr Fcst

36Hr Fcst

48Hr Fcst

72Hr Fcst

96Hr Fcst

120Hr Fcst


Count


RmaxBinA3


3-2000000000

3-1950000000

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3-1850000000

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3-1700000000

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3-1250000000

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3-1050000000

3-1000000000

3-950000000

3-900000000

3-850000000

3-800000000

3-750000000

3-700000000

3-650100001

3-602000110

3-551111000

3-502111000

3-451010000

3-402100010

3-350210000

3-301010001

3-250211100

3-204100000

3-151110000

3-105423011

3-512743211

30403118151455

3543178109413

3102328151013145

31515172920131411

32081314181398

32536957105

33032614767

3351122534

3400200000

3450000000

3500000000

3550000000

3600000000

3650000000

3700000000

3750000000

3800000000

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3900000000

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31000000000

31050000000

31100000000

31150000000

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31300000000

31350000000

31400000000

31450000000

31500000000

31550000000

31600000000

31650000000

31700000000

31750000000

31800000000

31850000000

31900000000

31950000000

32000000000

All

0020010

0312100

0032120

0112020

0110100

0502000

1001101

0001111

0011001

1330100

2540203

6431112

101077655

12191191084

341719201242

1551028159434231

72714345352821

31394544412325

17162625212923

9101112171211

2612131175

0003112

12Hr Fcst

24Hr Fcst

36Hr Fcst

48Hr Fcst

72Hr Fcst

96Hr Fcst

120Hr Fcst


Count


RmaxBinA2


2-2000000000

2-1950000000

2-1900000000

2-1850000000

2-1800000000

2-1750000000

2-1700000000

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2-750020010

2-700312100

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2-550110100

2-500502000

2-451001101

2-400001111

2-350011001

2-301330100

2-252540203

2-206431112

2-15101077655

2-1012191191084

2-5341719201242

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2350000000

2400000000

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2500000000

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2700000000

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21000000000

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21400000000

21450000000

21500000000

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21600000000

21650000000

21700000000

21750000000

21800000000

21850000000

21900000000

21950000000

22000000000

All

0000101

0003022

2021302

0122112

0020021

1022201

0111100

1013120

1210013

0021220

2027333

14611446

5685474

691714795

82112912184

25272730172110

44474934302022

221157122111705439

64535643472130

19352220232415

111519178612

3332330

12Hr Fcst

24Hr Fcst

36Hr Fcst

48Hr Fcst

72Hr Fcst

96Hr Fcst

120Hr Fcst


Count


RmaxBinA1


1-2000000000

1-1950000000

1-1900000000

1-1850000000

1-1800000000

1-1750000000

1-1700000000

1-1650000000

1-1600000000

1-1550000000

1-1500000000

1-1450000000

1-1400000000

1-1350000000

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1-1200000000

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1-1050000000

1-1000000000

1-950000000

1-900000000

1-850000101

1-800003022

1-752021302

1-700122112

1-650020021

1-601022201

1-550111100

1-501013120

1-451210013

1-400021220

1-352027333

1-3014611446

1-255685474

1-20691714795

1-1582112912184

1-1025272730172110

1-544474934302022

10221157122111705439

1564535643472130

11019352220232415

115111519178612

1203332330

1250000000

1300000000

1350000000

1400000000

1450000000

1500000000

1550000000

1600000000

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1700000000

1750000000

1800000000

1850000000

1900000000

1950000000

11000000000

11050000000

11100000000

11150000000

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11250000000

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11350000000

11400000000

11450000000

11500000000

11550000000

11600000000

11650000000

11700000000

11750000000

11800000000

11850000000

11900000000

11950000000

12000000000


CDF for Rmax Errors Bin 0-3

Chart1

0.00469483570.00502512560.00534759360.00571428570.00684931510.00862068970.0126582278

0.00938967140.01005025130.01069518720.01142857140.01369863010.01724137930.0253164557

0.0140845070.01507537690.01604278070.01714285710.02054794520.0258620690.0379746835

0.01877934270.02010050250.02139037430.02285714290.02739726030.03448275860.0506329114

0.02347417840.02512562810.02673796790.02857142860.03424657530.04310344830.0632911392

0.02816901410.03015075380.03208556150.03428571430.04109589040.05172413790.0759493671

0.03286384980.03517587940.03743315510.040.04794520550.06896551720.0886075949

0.03755868540.0402010050.04278074870.04571428570.05479452050.07758620690.1012658228

0.04225352110.04522613070.04812834220.05142857140.06164383560.08620689660.1139240506

0.04694835680.05025125630.05347593580.05714285710.06849315070.09482758620.1265822785

0.05164319250.05527638190.05882352940.06285714290.07534246580.10344827590.1392405063

0.05633802820.06030150750.0641711230.06857142860.08219178080.11206896550.1518987342

0.06103286380.06532663320.06951871660.07428571430.08904109590.12068965520.164556962

0.06572769950.07035175880.07486631020.080.0958904110.12931034480.1772151899

0.07042253520.07537688440.08021390370.08571428570.1027397260.13793103450.1898734177

0.07511737090.08040201010.08556149730.09142857140.10958904110.14655172410.2025316456

0.07981220660.08542713570.09090909090.09714285710.11643835620.15517241380.2151898734

0.08450704230.09045226130.09625668450.10285714290.12328767120.16379310340.2278481013

0.08920187790.09547738690.10160427810.10857142860.13013698630.17241379310.2405063291

0.09389671360.10050251260.10695187170.11428571430.13698630140.18103448280.253164557

0.09859154930.10552763820.11229946520.120.14383561640.18965517240.2658227848

0.1032863850.11055276380.11764705880.12571428570.15068493150.19827586210.2784810127

0.10798122070.11557788940.12299465240.13142857140.15753424660.20689655170.2911392405

0.11267605630.12060301510.1283422460.13714285710.16438356160.21551724140.3037974684

0.1173708920.12562814070.13368983960.14285714290.17123287670.2241379310.3164556962

0.12206572770.13065326630.13903743320.14857142860.17808219180.23275862070.3291139241

0.12676056340.1356783920.14438502670.15428571430.18493150680.24137931030.3417721519

0.13145539910.14070351760.14973262030.160.19178082190.250.3544303797

0.13615023470.14572864320.15508021390.16571428570.1986301370.25862068970.3670886076

0.14084507040.15075376880.16042780750.17142857140.20547945210.26724137930.3797468354

0.14553990610.15577889450.16577540110.17714285710.21232876710.2758620690.3924050633

0.15023474180.16080402010.17112299470.18285714290.21917808220.28448275860.4050632911

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0.16901408450.18090452260.1925133690.20571428570.24657534250.31896551720.4556962025

0.17370892020.18592964820.19786096260.21142857140.25342465750.32758620690.4683544304

0.17840375590.19597989950.20320855620.21714285710.26027397260.33620689660.4810126582

0.18309859150.20100502510.20855614970.22285714290.26712328770.34482758620.4936708861

0.18779342720.20603015080.21390374330.22857142860.27397260270.35344827590.5063291139

0.19248826290.21105527640.21925133690.23428571430.28082191780.36206896550.5189873418

0.19718309860.2160804020.22459893050.240.28767123290.37068965520.5316455696

0.20187793430.22110552760.22994652410.24571428570.29452054790.37931034480.5443037975

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0.2347417840.26130653270.27807486630.28571428570.34246575340.43965517240.6329113924

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0.31924882630.34673366830.36898395720.38285714290.45890410960.58620689660.8481012658

0.3239436620.3517587940.37433155080.38857142860.47260273970.59482758620.8607594937

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0.36619718310.39698492460.4224598930.440.54109589040.67241379310.9746835443

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0.52112676060.56281407040.60962566840.62285714290.76027397260.9482758621

0.52582159620.5678391960.6149732620.62857142860.76712328770.9568965517

0.53051643190.57286432160.62032085560.63428571430.77397260270.9655172414

0.53521126760.57788944720.62566844920.640.78082191780.974137931

0.53990610330.58793969850.63101604280.64571428570.78767123290.9827586207

0.5446009390.59296482410.63636363640.65142857140.79452054790.9913793103

0.54929577460.59798994970.64171122990.65714285710.8013698631

0.55399061030.60301507540.64705882350.66285714290.8082191781

0.5586854460.6080402010.65240641710.66857142860.8150684932

0.56338028170.61306532660.65775401070.67428571430.8219178082

0.56807511740.61809045230.66310160430.680.8287671233

0.57276995310.62311557790.66844919790.68571428570.8356164384

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0.58685446010.63819095480.68449197860.70285714290.8561643836

0.59154929580.64321608040.68983957220.70857142860.8630136986

0.59624413150.6482412060.69518716580.71428571430.8698630137

0.60093896710.65326633170.70053475940.720.8767123288

0.60563380280.65829145730.70588235290.72571428570.8835616438

0.61032863850.66331658290.71122994650.73142857140.8904109589

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0.79812206570.68844221110.73796791440.76571428570.9383561644

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0.80751173710.69849246230.74866310160.77714285710.9520547945

0.81220657280.70351758790.75401069520.78285714290.9589041096

0.81690140850.70854271360.75935828880.78857142860.9657534247

0.82159624410.71356783920.77005347590.79428571430.9726027397

0.82629107980.71859296480.77540106950.80.9794520548

0.83098591550.72361809050.78074866310.80571428570.9863013699

0.83568075120.72864321610.82887700530.81142857140.9931506849

0.84037558690.73366834170.83422459890.81714285711

0.84507042250.73869346730.83957219250.8228571429

0.84976525820.84422110550.84491978610.8285714286

0.85446009390.84924623120.85026737970.8342857143

0.85915492960.85427135680.85561497330.84

0.86384976530.85929648240.86096256680.88

0.86854460090.8643216080.86631016040.8914285714

0.87323943660.86934673370.8716577540.8971428571

0.87793427230.87437185930.87700534760.9028571429

0.8826291080.87939698490.88235294120.9085714286

0.88732394370.88442211060.88770053480.9142857143

0.89201877930.88944723620.89304812830.92

0.8967136150.89447236180.89839572190.9257142857

0.90140845070.89949748740.90374331550.9314285714

0.90610328640.90452261310.90909090910.9371428571

0.91079812210.90954773870.91443850270.9428571429

0.91549295770.91457286430.91978609630.9485714286

0.92018779340.919597990.92513368980.9542857143

0.92488262910.92462311560.93048128340.96

0.92957746480.92964824120.9358288770.9657142857

0.93427230050.93467336680.94117647060.9714285714

0.93896713620.93969849250.94652406420.9771428571

0.94366197180.94472361810.95187165780.9828571429

0.94835680750.94974874370.95721925130.9885714286

0.95305164320.95477386930.96256684490.9942857143

0.95774647890.9597989950.96791443851

0.96244131460.96482412060.9732620321

0.96713615020.96984924620.9786096257

0.97183098590.97487437190.9839572193

0.97652582160.97989949750.9893048128

0.98122065730.98492462310.9946524064

0.9859154930.98994974871

0.99061032860.9949748744

0.99530516431

1

12Hr Fcst

24Hr Fcst

36Hr Fcst

48Hr Fcst

72Hr Fcst

96Hr Fcst

120Hr Fcst

Error (Fcst - Obs)

Cumulative Distribution

Rmax Error Dist Fcst Bin 0 [5..15sm)

Chart2

0.00469483570.00502512560.00534759360.00571428570.00684931510.00862068970.0126582278

0.00938967140.01005025130.01069518720.01142857140.01369863010.01724137930.0253164557

0.0140845070.01507537690.01604278070.01714285710.02054794520.0258620690.0379746835

0.01877934270.02010050250.02139037430.02285714290.02739726030.03448275860.0506329114

0.02347417840.02512562810.02673796790.02857142860.03424657530.04310344830.0632911392

0.02816901410.03015075380.03208556150.03428571430.04109589040.05172413790.0759493671

0.03286384980.03517587940.03743315510.040.04794520550.06896551720.0886075949

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0.04225352110.04522613070.04812834220.05142857140.06164383560.08620689660.1139240506

0.04694835680.05025125630.05347593580.05714285710.06849315070.09482758620.1265822785

0.05164319250.05527638190.05882352940.06285714290.07534246580.10344827590.1392405063

0.05633802820.06030150750.0641711230.06857142860.08219178080.11206896550.1518987342

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0.13145539910.14070351760.14973262030.160.19178082190.250.3544303797

0.13615023470.14572864320.15508021390.16571428570.1986301370.25862068970.3670886076

0.14084507040.15075376880.16042780750.17142857140.20547945210.26724137930.3797468354

0.14553990610.15577889450.16577540110.17714285710.21232876710.2758620690.3924050633

0.15023474180.16080402010.17112299470.18285714290.21917808220.28448275860.4050632911

0.15492957750.16582914570.17647058820.18857142860.22602739730.29310344830.417721519

0.15962441310.17085427140.18181818180.19428571430.23287671230.30172413790.4303797468

0.16431924880.1758793970.18716577540.20.23972602740.31034482760.4430379747

0.16901408450.18090452260.1925133690.20571428570.24657534250.31896551720.4556962025

0.17370892020.18592964820.19786096260.21142857140.25342465750.32758620690.4683544304

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0.18779342720.20603015080.21390374330.22857142860.27397260270.35344827590.5063291139

0.19248826290.21105527640.21925133690.23428571430.28082191780.36206896550.5189873418

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0.20187793430.22110552760.22994652410.24571428570.29452054790.37931034480.5443037975

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0.21596244130.24120603020.25133689840.26285714290.31506849320.40517241380.582278481

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0.27699530520.30653266330.32620320860.33714285710.4041095890.51724137930.746835443

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0.30516431920.33668341710.35828877010.37142857140.44520547950.56896551720.8227848101

0.31455399060.34170854270.36363636360.37714285710.45205479450.57758620690.835443038

0.31924882630.34673366830.36898395720.38285714290.45890410960.58620689660.8481012658

0.3239436620.3517587940.37433155080.38857142860.47260273970.59482758620.8607594937

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0.33333333330.36180904520.3850267380.40.49315068490.61206896550.8860759494

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0.96713615020.96984924620.9786096257

0.97183098590.97487437190.9839572193

0.97652582160.97989949750.9893048128

0.98122065730.98492462310.9946524064

0.9859154930.98994974871

0.99061032860.9949748744

0.99530516431

1

12Hr Fcst

24Hr Fcst

36Hr Fcst

48Hr Fcst

72Hr Fcst

96Hr Fcst

120Hr Fcst

Error (Fcst - Obs)


simp

X-12Y-12X-24Y-24X-36Y-36X-48Y-48X-72Y-72X-96Y-96X-120Y-120

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1

12Hr Fcst

24Hr Fcst

36Hr Fcst

48Hr Fcst

72Hr Fcst

96Hr Fcst

120Hr Fcst

Error (Fcst - Obs)

Cumulative Distribution


Chart2

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0.06280193240.06561679790.07022471910.0822784810.10460251050.1350.1543209877

0.06521739130.06824146980.07303370790.0854430380.10878661090.140.1604938272

0.06763285020.07086614170.07584269660.08860759490.11297071130.1450.1666666667

0.07004830920.07611548560.07865168540.09177215190.11715481170.150.1728395062

0.07246376810.07874015750.08146067420.09493670890.12133891210.1550.1790123457

0.07487922710.08136482940.08426966290.09810126580.12552301260.160.1851851852

0.0772946860.08398950130.08707865170.10126582280.13389121340.1650.1913580247

0.07971014490.08661417320.08988764040.10443037970.13807531380.170.1975308642

0.08212560390.08923884510.09269662920.10759493670.14225941420.1750.2037037037

0.08454106280.09186351710.0955056180.11075949370.14644351460.180.2098765432

0.08695652170.0944881890.09831460670.11392405060.15062761510.1850.2160493827

0.08937198070.09711286090.10112359550.11708860760.15481171550.190.2222222222

0.09178743960.09973753280.10393258430.12025316460.15899581590.1950.22839

Documents

Probabilistic Hurricane Storm Surge (P-Surge) Arthur Taylor Meteorological Development Laboratory, National Weather Service January 20, 2008