Probabilistic Hurricane Storm Surge (P-Surge)

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Probabilistic Hurricane Storm Surge (P-Surge)

• Arthur Taylor
• Meteorological Development Laboratory, National
  Weather Service
• January 20, 2008

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Introduction

• The 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
  planning
• National Hurricane Center (NHC) begins
  operational SLOSH runs 24 hours before forecast
  hurricane landfall

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Introduction

• NHCs 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.

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Hurricane Ivan A case study
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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 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

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Input Parameters for SLOSH

• A single run of SLOSH requires the following
  parameters
• Track (Location and Forward Speed)
• Pressure
• Radius of Maximum Winds (Rmax)

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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

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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

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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.

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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
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Rmax Error Distributions

• For 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
  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.

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PDF for Rmax Errors Bin 0-3
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CDF for Rmax Errors Bin 0-3
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Example Katrina Advisory 23
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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.

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Example Cross Track Error
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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)

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Assigning Weights
Cross Track Weight Cross Track Weight Cross Track Weight Cross Track Weight Cross Track Weight
12.43 23.25 28.65 23.25 12.43
Along Track Slow 30 3.729 6.975 8.595 6.975 3.729
Along Track Medium 40 4.972 9.300 11.460 9.30 4.972
Along Track Fast 30 3.729 6.975 8.595 6.975 3.729

• 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.

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Putting it all together

1. Calculate initial SLOSH input from NHC advisory
2. Determine which size distribution to use, based
   on the size-bin of the storm. Iterate over the
   size
3. 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
4. Iterate over the along tracks, creating slow,
   medium and fast storms
5. Iterate over the intensity, creating weak,
   medium, and strong storms.
6. Assign a weight to the storm (cross track weight
   along track weight intensity weight size
   weight)
7. Perform all SLOSH runs

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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 dont 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

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Katrina Adv 23 Probability gt 5 feet of storm
surge
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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 lt .2
  .4 .1)

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Katrina Adv 23 10 of ensemble storms exceed
this height
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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

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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

OF THE 340 OBSERVATIONS, 2.35 (8/340) ARE lt 2
FEET 16.18 (55/340) ARE lt 5 FEET 35.00
(119/340)ARE lt 7 FEET 61.18 (208/340)ARE lt 10
FEET
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
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gt5 ft Forecasts (Point)
12hr
24hr
48hr
36hr
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gt7 ft Forecasts (Point)
12hr
24hr
48hr
36hr
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gt 10 ft Forecasts (Point)
12hr
24hr
48hr
36hr
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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.

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gt5 ft Forecasts (Gridded)
12hr
24hr
48hr
36hr
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gt7 ft Forecasts (Gridded)
12hr
24hr
48hr
36hr
32
gt10 ft Forecasts (Gridded)
12hr
24hr
48hr
36hr
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Where can you access our product?http//www.weath
er.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.

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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.

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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.