Probabilistic Hurricane Storm Surge (P-Surge)

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

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

3. Introduction • NHC’s 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.

4. Hurricane Ivan: A case study

5. Probabilistic Storm Surge Methodology • Use an ensemble of SLOSH runs to create probabilistic storm surge (p-surge) • Intended to be used operationally so it is based on NHC’s official advisory. • P-surge’s 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

6. Input Parameters for SLOSH • A single run of SLOSH requires the following parameters: • Track (Location and Forward Speed) • Pressure • Radius of Maximum Winds (Rmax)

7. Errors used by P-surge • The 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

8. P-surge Error Distributions • The error distributions for cross track, along track, and intensity are determined by: • Calculating the regression of the yearly mean error • Assuming a normal error distribution • Determining the standard deviation (sigma) based on:

9. 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 year • Regression 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.

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

11. Rmax Error Distributions • For Rmax, we can’t 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 observation • The 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.

12. PDF for Rmax Errors Bin 0-3

13. .85 = small size .50 = medium size .15 = large size CDF for Rmax Errors Bin 0-3

14. Example: Katrina Advisory 23

15. Cross Track Variations • To vary the cross track storms, we consider the coverage and the spacing. • Chose to cover 90% of the area under the normal distribution. • This was 1.645 standard deviations to the left and right of the central track • Chose to space the storms Rmax apart at the 48 hour forecast. • Storm surge is typically highest one Rmax to the right of the landfall point. So for proper coverage, we wanted the storms within Rmax of each other.

16. Example: Cross Track Error

17. Varying the Other Parameters: • Size: Small (30%), Medium (40%), Large (30%) • Forward Speed: Fast (30%), Medium (40%), Slow (30%) • Intensity: Strong (30%), Medium (40%), Weak (30%)

18. Assigning Weights • This is repeated for other two dimensions (Rmax weights, Intensity weights) • A representative storm is run for each cell in the 4 dimensional (Cross, Along, Rmax, Intensity) error space. • Actual number of Cross Track weights depends on Rmax.

19. Putting it all together • Calculate initial SLOSH input from NHC advisory • Determine which size distribution to use, based on the size-bin of the storm. Iterate over the size • Calculate the cross track spacing, a function of the size. Iterate over the cross tracks, stepping by the spacing and covering 1.645 standard deviations to left and right • Iterate over the along tracks, creating slow, medium and fast storms • Iterate over the intensity, creating weak, medium, and strong storms. • Assign a weight to the storm (cross track weight * along track weight * intensity weight * size weight) • Perform all SLOSH runs

20. Product 1: Probability of exceeding X feet • To calculate the probability of exceeding X feet, we look at the maximum each cell in each SLOSH run attained. • If that value exceeds X, we add the weight associated with that SLOSH run to the total. • Otherwise we don’t increase the total. • The total weight is considered the probability of exceeding X feet. • Example: 5 storms have weights of 0.1, 0.2, 0.4, 0.2, 0.1, and the first 2 exceeded X feet in a given cell. The probability of exceeding X feet in that cell is: • 0.1 + 0.2 = 30%

21. Katrina Adv 23: Probability >= 5 feet of storm surge

22. Product 2: Height exceeded by X percent of the ensemble storms. • Determine what height to choose in a cell so that there is a specified probability of exceeding it. • For each cell, sort the heights of each SLOSH run. • From the tallest height downward, add up the weights associated with each SLOSH run until the given probability is exceeded. • The answer is the height associated with the last weight added . • Example: 5 storms have surge values of 3, 6, 5, 2, 4 feet and respective weights of .1, .2, .4, .2, .1. • Make ordered pairs of the numbers: (3, .1), (6, .2), (5, .4), (2, .2), (4, .1) • Sort by surge height: (6, .2), (5, .4), (4, .1), (3, .1), (2, .2) • Height exceeded by 60% of storms = 4 (.6 < .2 + .4 + .1)

23. Katrina Adv 23: 10% of ensemble storms exceed this height

24. Is it Statistically Reliable? • If we forecast 20% chance of storm surge exceeding 5 feet, does surge exceed 5 feet 20% of the time? • Create forecasts for various projections and thresholds • Get a matching storm surge observation • Problem: Insufficient observations • Observations are made where there has been surge, so there is a bias toward higher values. • Storm surge observations contaminated by waves and astronomical tide issues. • Number of hurricanes making landfall is relatively small. • Result: 340 observations for 11 Storms from 1998-2005

25. Point Observations • 11 Storms (340 Observations): • Dennis 05, Katrina 05, Wilma 05, Charley 04, Frances 04, Ivan 04, Jeanne 04, Isabel 03, Lili 02, Floyd 99, Georges 98 STORM OBS % OF TOTAL OBS Katrina 05 99 29.12% Ivan 04 50 14.71% Isabel 03 44 12.94% Lili 02 40 11.76% Floyd 99 37 10.88% Georges 98 32 9.41% Dennis 05 25 7.35% Wilma 05 5 1.47% Charley 04 4 1.18% Jeanne 04 3 .88% Frances 04 1 .29% OF THE 340 OBSERVATIONS, 2.35% (8/340) ARE < 2 FEET 16.18% (55/340) ARE < 5 FEET 35.00% (119/340)ARE < 7 FEET 61.18% (208/340)ARE < 10 FEET

26. >5 ft Forecasts (Point) 12hr 24hr 36hr 48hr

27. >7 ft Forecasts (Point) 12hr 24hr 36hr 48hr

28. > 10 ft Forecasts (Point) 12hr 24hr 36hr 48hr

29. Gridded Analysis • In order to deal with the paucity of observations, we wanted to use an analysis field as observations. Used SLOSH hindcast runs. • NHC used best historical information for input • Given accurate input, model results are within 20% of high water marks. • Advantage: • Observation at every grid point (on the order of 106) • Observations are made where there is little surge. • Disadvantage: • Used same model in analysis as we did in p-surge method.

30. >5 ft Forecasts (Gridded) 12hr 24hr 36hr 48hr

31. >7 ft Forecasts (Gridded) 12hr 24hr 36hr 48hr

32. >10 ft Forecasts (Gridded) 12hr 24hr 36hr 48hr

33. Where can you access our product?http://www.weather.gov/mdl/psurge • When is it available? • Beginning when the NHC issues a hurricane watch or warning for the continental US • Available approx. 1-2 hours after the advisory release time.

34. Current Development • We were “experimental” in 2007, and plan on becoming “operational” in 2008. • We have added the data to the NDGD (National Digital Guidance Database), and are now working on delivering the data to AWIPS. • We are developing more training material. • We are updating the error statistics used in our calculations based on the 2007 storm season, and will continue to investigate the reliability diagrams.

35. Future Development • We would like to: • Include probability over a time range, both incremental and cumulative. • Allow interaction with the data in a manner similar to the SLOSH Display program. • Investigate its applicability to Tropical storms. • Add gridded astronomical tides to forecast probabilistic total water levels.