Transcript National Weather Service 3rd Quarter Review 2001

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
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
Probabilistic Storm Surge 2008
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
Probabilistic Storm Surge 2008
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.
Probabilistic Storm Surge 2008
Hurricane Ivan: A case study
Probabilistic Storm Surge 2008
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
Probabilistic Storm Surge 2008
Input Parameters for SLOSH
A single run of SLOSH requires the following
parameters:
• Track (Location and Forward Speed)
• Pressure
• Radius of Maximum Winds (Rmax)
Probabilistic Storm Surge 2008
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
Probabilistic Storm Surge 2008
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:
Probabilistic Storm Surge 2008
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.
Probabilistic Storm Surge 2008
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
Probabilistic Storm Surge 2008
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.
Probabilistic Storm Surge 2008
PDF for Rmax Errors Bin 0-3
Rmax Error Dist Fcst Bin 0 (5..15 sm)
Rmax Error Dist Fcst Bin 1 (15..25 sm)
140
12Hr Fcst
24Hr Fcst
36Hr Fcst
48Hr Fcst
72Hr Fcst
96Hr Fcst
120Hr Fcst
250
12Hr Fcst
24Hr Fcst
36Hr Fcst
48Hr Fcst
72Hr Fcst
96Hr Fcst
120Hr Fcst
120
100
150
Count
Count
80
200
60
100
40
50
20
0
0
-95 -90 -85 -80 -75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5
0
5
10
-90 -85 -80 -75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5
15
10
15
20
25
20
25
30
35
40
45
50
180
45
12Hr Fcst
24Hr Fcst
36Hr Fcst
48Hr Fcst
72Hr Fcst
96Hr Fcst
120Hr Fcst
160
140
120
40
35
30
Count
100
Count
5
Rmax Error Dist Fcst Bin 3 (35..45 sm)
Rmax Error Dist Fcst Bin 2 (25..35 sm)
12Hr Fcst
24Hr Fcst
36Hr Fcst
48Hr Fcst
72Hr Fcst
96Hr Fcst
120Hr Fcst
0
Error (Fcst - Obs) by 5
Error (Fcst - Obs) by 5
25
80
20
60
15
40
10
20
5
0
0
-80 -75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10
Error (Fcst - Obs) by 5
-5
0
5
10
15
20
25
30
35
-70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10
-5
Error (Fcst - Obs) by 5
0
5
10
15
.85 = small size
.50 = medium size
.15 = large size
CDF for Rmax Errors Bin 0-3
Rmax Error Dist Fcst Bin 1 [15..25sm)
Rmax Error Dist Fcst Bin 0 [5..15sm)
0.85
0.85
0.8
12Hr Fcst
24Hr Fcst
36Hr Fcst
48Hr Fcst
72Hr Fcst
96Hr Fcst
120Hr Fcst
0.8
12Hr Fcst
24Hr Fcst
36Hr Fcst
48Hr Fcst
72Hr Fcst
96Hr Fcst
120Hr Fcst
0.75
0.7
0.65
0.6
0.75
0.7
0.65
0.6
0.55
0.55
-54 -52 -50 -48 -46 -44 -42 -40 -38 -36 -34 -32 -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10
-8
-6
-4
0.5
0.5
0.45
0.45
0.4
0.4
0.35
0.35
0.3
0.3
0.25
0.25
0.2
0.2
0.15
-2
0
2
Error (Fcst - Obs)
-30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10
-8
-6
0.15
-2
0
-4
2
4
6
8
26
28
10
Error (Fcst - Obs)
Rmax Error Dist Fcst Bin 3 [35..45)
Rmax Error Dist Fcst Bin 2 [25..35sm)
0.85
12Hr Fcst
24Hr Fcst
36Hr Fcst
48Hr Fcst
0.75
72Hr Fcst
96Hr Fcst
120Hr Fcst
0.65
0.85
0.8
0.8
12Hr Fcst
24Hr Fcst
36Hr Fcst
48Hr Fcst
72Hr Fcst
96Hr Fcst
120Hr Fcst
0.7
0.6
0.75
0.7
0.65
0.6
0.55
0.55
0.5
0.5
0.45
0.45
0.4
0.4
0.35
0.35
0.3
0.3
0.25
0.25
0.2
0.2
0.15
-14
-12
-10
-8
-6
-4
-2
0
2
4
Error (fcst - Obs)
6
8
10
12
14
16
18
-12
-10
-8
-6
-4
0.15
-2
0
2
4
6
8
10
12
Error (Fcst - Obs)
14
16
18
20
22
24
30
Example: Katrina Advisory 23
Probabilistic Storm Surge 2008
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.
Probabilistic Storm Surge 2008
Example: Cross Track Error
Probabilistic Storm Surge 2008
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%)
Probabilistic Storm Surge 2008
Assigning Weights
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%
Along Track Fast 30% 3.729% 6.975% 8.595%
4.972%
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.
Number of storms for Katrina: 369
Weights per storm for Katrina: between 0.038% and 1.14%
Probabilistic Storm Surge 2008
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
Probabilistic Storm Surge 2008
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:
0.1 + 0.2 = 0.3 = 30%
Probabilistic Storm Surge 2008
Katrina Adv 23: Probability > 5 feet of Storm
Surge
Probabilistic Storm Surge 2008
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%.
Probabilistic Storm Surge 2008
Katrina Adv 23: 10% of ensemble storms
exceed this height
Probabilistic Storm Surge 2008
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
Probabilistic Storm Surge 2008
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
Katrina 05
Ivan 04
Isabel 03
Lili 02
Floyd 99
Georges 98
Dennis 05
Wilma 05
Charley 04
Jeanne 04
Frances 04
OBS % OF TOTAL OBS
99
29.12%
50
14.71%
44
12.94%
40
11.76%
37
10.88%
32
9.41%
25
7.35%
5
1.47%
4
1.18%
3
.88%
1
.29%
Probabilistic Storm Surge 2008
OF THE 340 OBSERVATIONS,
2.35%
16.18%
35.00%
61.18%
(8/340) ARE
(55/340) ARE
(119/340)ARE
(208/340)ARE
< 2
< 5
< 7
< 10
FEET
FEET
FEET
FEET
>5 ft Forecasts (Point)
Ratio of Occurence for the 11 Storms To Make Landfall in 12 Hours
12hr
1
19
14
31
0.9
Ratio of Occurence for the 11 Storms To Make Landfall in 24 Hours
24hr
49
1
28
27
20
28
33
25
55
42
0.9
51
19
18
0.8
0.8
54
43
0.7
Ratio of Occurence
Ratio of Occurence
0.7
0.6
47
29
0.5
0.4
0.6
48
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
Probability Forecast(%) > 5 feet
36hr
48hr
Ratio of Occurence for the 11 Storms To Make Landfall in 36 Hours
1
16
45
0.9
4
80
90
100
5
0.9
90
100
56
0.7
32
76
0.8
38
14
33
41
47
34
0.7
Ratio of Occurence
Ratio of Occurence
70
1
51
0.8
60
Ratio of Occurence for the 11 Storms To Make Landfall in 48 Hours
22
61
50
Probability Forecast(%) > 5 feet
0.6
56
0.5
0.4
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
49
0.6
0
0
10
20
30
40
50
60
Probability Forecast(%) > 5 feet
70
80
90
100
0
10
20
30
40
50
60
Probability Forecast(%) > 5 feet
70
80
>7 ft Forecasts (Point)
Ratio of Occurence for the 11 Storms To Make Landfall in 12 Hours
12hr
1
20
Ratio of Occurence for the 11 Storms To Make Landfall in 24 Hours
24hr
21
43
6
1
16
0.9
51
0.9
30
29
41
0.8
28
0.8
16
8
28
0.7
49
0.6
Ratio of Occurence
Ratio of Occurence
0.7
25
0.5
0.4
39
0.6
24
0.5
0.4
22
0.3
92
0.3
92
0.2
0.2
0.1
0.1
0
0
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
Probability Forecast(%) > 7 feet
36hr
80
90
100
90
100
Ratio of Occurence for the 11 Storms To Make Landfall in 48 Hours
16
76
0.8
14
46
43
65
15
41
0.7
Ratio of Occurence
0.7
70
0.9
56
0.8
60
1
15
0.9
Ratio of Occurence
48hr
Ratio of Occurence for the 11 Storms To Make Landfall in 36 Hours
1
50
Probability Forecast(%) > 7 feet
0.6
56
0.5
0.4
0.6
55
0.5
0.4
94
88
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
10
20
30
40
50
60
Probability Forecast(%) > 7 feet
70
80
90
100
0
10
20
30
40
50
60
Probability Forecast(%) > 7 feet
70
80
> 10 ft Forecasts (Point)
Ratio of Occurence for the 11 Storms To Make Landfall in 12 Hours
12hr
39
13
24
1
5
0.9
0.9
0.8
0.8
0.7
0.7
Ratio of Occurence
Ratio of Occurence
1
8
0.6
14
0.5
Ratio of Occurence for the 11 Storms To Make Landfall in 24 Hours
24hr
21
34
0.4
35
65
0.6
40
33
0.5
0.4
8
0.3
0.3
0.2
0.2
46
24
0.1
0.1
128
136
0
0
0
10
20
30
40
50
60
70
80
90
7
0
100
10
20
30
40
19
70
80
90
100
90
100
Ratio of Occurence for the 11 Storms To Make Landfall in 48 Hours
1
0.9
0.9
0.8
0.8
0.7
26
1
0.7
32
Ratio of Occurence
Ratio of Occurence
48hr
Ratio of Occurence for the 11 Storms To Make Landfall in 36 Hours
1
60
Probability Forecast(%) > 10 feet
Probability Forecast(%) > 10 feet
36hr
50
0.6
105
0.5
63
0.4
0.5
66
91
0.4
0.3
0.3
0.2
0.2
0.1
31
0.6
0.1
125
121
0
0
0
10
20
30
40
50
60
Probability Forecast(%) > 10 feet
70
80
90
100
0
10
20
30
40
50
60
Probability Forecast(%) > 10 feet
70
80
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.
Probabilistic Storm Surge 2008
>5 ft Forecasts (Gridded)
Ratio of occurance for the 11 storms forecast to make landfall in 12 hours
12hr
1
21085
17877
21589 1
0.9
0.9
0.8
15064
39439
26042
0.7
Ratio of Occurance
25268
43648
0.6
5010
14340
0.8
0.7
Ratio of Occurance
Ratio of occurance for the 11 storms forecast to make landfall in 24 hours
24hr
28810
0.5
59354
0.4
0.6
64931
42265
0.5
57568
0.4
90598
0.3
71179
0.3
125725
0.2
176494
0.2
246406
0.1
0.1
286559
380314
0
0
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
Probability forecast (%) > 5 feet
Ratio of occurance for the 11 storms forecast to make landfall in 36 hours
36hr
11217
0.9
0.8
90
100
7488
1205
0.8
0.7
45712
Ratio of Occurance
Ratio of Occurance
80
9107
19970.9
229
27574
0.6
69783
0.4
70
1
4195
0.5
60
Ratio of occurance for the 11 storms forecast to make landfall in 48 hours
48hr
1
0.7
50
Probability forecast (%) > 5 feet
90632
0.3
32818
0.6
75688
0.5
20908
0.4
111020
0.3
212597
182758
0.2
0.2
311550
448559
0.1
0.1
476672
545396
0
0
0
10
20
30
40
50
60
Probability forecast (%) > 5 feet
70
80
90
100
0
10
20
30
40
50
60
Probability forecast (%) > 5 feet
70
80
90
100
>7 ft Forecasts (Gridded)
Ratio of occurance for the 11 storms forecast to make landfall in 12 hours
12hr
Ratio of occurance for the 11 storms forecast to make landfall in 24 hours
24hr
1
9761
7096
5975 1
13768
0.9
0.9
12297
0.8
1371
0.8
1247
0.7
Ratio of Occurance
Ratio of Occurance
0.7
17057
0.6
25388
0.5
27049
39130
0.4
0.6
0.5
25013
0.4
34614
55025
0.3
9722
0.3
59475
0.2
0.2
117243
0.1
0.1
263514
0
364482
0
0
10
20
30
40
50
60
70
80
90
100
0
10
Probability forecast (%) > 7 feet
Ratio of occurance for the 11 storms forecast to make landfall in 36 hours
36hr
1
976 0.9
0.8
0.8
341
40
50
60
70
80
90
100
90
100
10180
819
391
0.7
Ratio of Occurance
0.7
Ratio of Occurance
30
1
0.9
9828
0.5
67
43851
0.4
20
Probability forecast (%) > 7 feet
Ratio of occurance for the 11 storms forecast to make landfall in 48 hours
48hr
8935
0.6
75082
91552
204096
0.3
0.6
0.5
10607
35945
0.4
0.3
75407
211
72697
125645
0.2
0.2
0.1
155829
0.1
293160
402053
459210
0
613238
0
0
10
20
30
40
50
60
Probability forecast (%) > 7 feet
70
80
90
100
0
10
20
30
40
50
60
Probability forecast (%) > 7 feet
70
80
>10 ft Forecasts (Gridded)
12hr
24hr
Ratio of occurance for the 11 storms forecast to make landfall in 12 hours
1
8430
4682
1
3213
0.9
Ratio of occurance for the 11 storms forecast to make landfall in 24 hours
0.9
120
0.8
0.8
0.7
4186
0.6
Ratio of Occurance
Ratio of Occurance
0.7
6194
0.5
0.4
0.3
0.6
0.5
23051
0.4
808
0.3
14720
0.2
12793
0.2
41376
0.1
21347
0
10
96889
50651
91280
166709
0
0.1
20
30
40
50
60
70
80
90
100
156700
317212
0
0
10
30
40
Probability forecast (%) > 10 feet
36hr
10870
13474
20
50
60
70
80
90
100
80
90
100
Probability forecast (%) > 10 feet
48hr
Ratio of occurance for the 11 storms forecast to make landfall in 36 hours
1
Ratio of occurance for the 11 storms forecast to make landfall in 48 hours
1
8421
0.9
1537
0.9
271
808
0.8
0.8
0.7
0.7
231
Ratio of Occurance
Ratio of Occurance
12796
0.6
0.5
0.4
0.3
0.6
0.5
352
0.4
0.3
25524
0.2
27362
0.2
0.1
0.1
95239
113622
222183
458804
0
0
10
20
30
40
50
60
Probability forecast (%) > 10 feet
70
80
90
100
269456
672737
0
0
10
20
30
40
50
60
Probability forecast (%) > 10 feet
70
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.
Probabilistic Storm Surge 2008
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.
Probabilistic Storm Surge 2008
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.
Probabilistic Storm Surge 2008
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
Probabilistic Storm Surge 2008