1. Storm Surge Forecasting Practices, Tools for Emergency Managers, A Probabilistic Storm Surge Model Based on Ensembles and Past Error Distributions
Arthur Taylor
Meteorological Development Laboratory, National Weather Service
January 20, 2008

2. Hurricane Storm Surge Damage
“The greatest potential for loss of life related to a hurricane is from the storm surge.”
Aerial Photo overlay of Katrina 2005 storm surge over Hancock County, Mississippi

3. 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

4. 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.

5. Hurricane Ivan: A case study

6. 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

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

8. 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

9. 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:

10. 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.

11. 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

12. 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.

13. PDF for Rmax Errors Bin 0-3

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

15. Example: Katrina Advisory 23

16. 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 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.

17. Example: Cross Track Error

18. 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%)

19. Assigning Weights
Cross Track Weight
12.43%
23.25%
28.65%
Along Track Slow 30%
3.729%
6.975%
8.595%
Along Track Medium 40%
4.972%
9.300%
11.460%
9.30%
Along Track Fast 30%
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.
Number of storms for Katrina: 369
Weights per storm for Katrina: between 0.038% and 1.14%

20. 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 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

21. Probability of Exceeding X feet
To calculate the probability of exceeding X feet:
For each cell, add the associated weights of the hypothetical storms whose maximum surge values are greater than X feet.
Example:
Five hypothetical storms have weights of 0.1, 0.2, 0.4, 0.2, and 0.1
Assume that the first two exceeded X feet in a given cell.
Then the probability of exceeding X feet in that cell is: = 0.3 = 30%

22. Katrina Adv 23: Probability > 5 feet of Storm Surge

23. Height Exceeded by X percent of the Ensemble of Storms
Determine what height to choose in a cell so that there is a specified probability of exceeding it:
For each cell, find the surge value where the weights of the surge values which are higher add up to a value < X.
Example:
Five hypothetical storms have maximum surge values of 6, 5, 4, 3, 2 feet and respective weights of 0.2, 0.4, 0.1, 0.1, 0.2.
The height exceeded by 60% of the ensemble is 4 feet, since the 6 foot value represents the top 20% of the storms, and the 5 foot value represents the next 40%.

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

25. 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

26. 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 %
Ivan %
Isabel %
Lili %
Floyd %
Georges %
Dennis %
Wilma %
Charley %
Jeanne %
Frances %
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

27. >5 ft Forecasts (Point)
12hr
24hr
36hr
48hr

28. >7 ft Forecasts (Point)
12hr
24hr
36hr
48hr

29. > 10 ft Forecasts (Point)
12hr
24hr
36hr
48hr

30. 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.

31. >5 ft Forecasts (Gridded)
12hr
24hr
36hr
48hr

32. >7 ft Forecasts (Gridded)
12hr
24hr
36hr
48hr

33. >10 ft Forecasts (Gridded)
12hr
24hr
36hr
48hr

34. 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.

35. 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.

36. 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.

37. Summary We’ve discussed: A new set of storm surge guidance
An ensemble method whose perturbations are based on historic error statistics
An ensemble method which uses representative members which are weighted based on those error statistics
A way to estimate improvements in those error statistics
A method to deal with the paucity of hurricane storm surge observations when dealing with possible calibration