Storm Surge Frequency Analysis using a Modified Joint Probability Method with Optimal Sampling (JPM-OS)

Transcription

1 Storm Surge Frequency Analysis using a Modified Joint Probability Method with Optimal Sampling (JPM-OS) Jay Ratcliff Coastal Hydraulics Lab, of Engineers (USACE) Engineering Research and Development Center (ERDC) Don Resio Senior Scientist Coastal and Hydraulics Lab, USACE ERDC Joannes Westerink University of Notre Dame John Atkinson Arcadis, Inc. JPM-OS Development Team ERDC, NOAA, FEMA, University of Notre Dame, and private agencies

2 Outline of Presentation Brief overview of JPM-OS Motivation, Development and Design JPM-OS Implementation and Results for Louisiana Coast JPM-OS Implementation for Texas Coast Primary TASK Compute Storm Surge Elevations for: 10, 50, 100, 500, and 1000 year return periods

3 Five Parameters Considered in JPM Central Pressure Radius to Maximum Wind Speed Angle of Track Relative to Coast Forward Speed of Storm Distance Between Landfall and a Point of Interest Note: Typically or more storms were simulated for a specific area of interest

4 Older JPM: The estimation of the surge CDF was accomplished by summing the probabilities that exceed a given surge value. The form written below explicitly shows that three terms are involved in this calculation F ( η ) =... p( ΔP, R, v, θ, x) H[ η Φ( ΔP, R, v, θ, x)] δ( ΔP, R, v, θ, x) max p f l max p f l p f l p( ΔP, R, v, θ, x) is the continuous probability density function of 5 parameters p f l Φ( ΔP, R, v, θ, x) is a function (modeling suite) that estimates η p f l for a set of 5 parameters δ( ΔP, R, v, θ, x) is the 5-dimensional volume associated with a single discrete p f l computer run's probability H(z) is the Heaviside function = 1 if z 1, = 0, otherwise. If we simply slice and dice the probabilities we might use something like 6 tracks, 5 angles, 3 forward speeds, 3 pressure-scaling radii, and 3 pressure differentials. This would give 810 computer runs to be made, but we are still ignoring several factors such as tide phase relative to peak surge, Holland B value, variations in decay during approach to coast, model system errors, etc. max

5 How could JPM be modified to permit a minimum number of storms to provide sufficient information to define an estimate of F(S)?

6 Sampling and Numeric's of integration Original JPM used an equivalent to a rectangular or trapezoidal integration method F( S) = Δ P for all Sˆ > S n m k j i ijkmn ijkmn In this method discrete increments of probability are assigned to the value of the simulated surge. In recent years, the concept of a response surface has been developed for many risk applications. In this approach, we assumed that response is a continuous function of the parameters used to discretize the probabilities. For surges it is assumed that we can write S = S( C, R, θ, V, x x ) + ε p max L f max Model result for run ijkmn where xmax is the location of maximum surge for a particular combination of the other parameters.

7 This allows us to move beyond the simple trapezoidal form for quadrature and consider methods more aligned with Gauss Quadrature. This sounds complicated, but all it really amounts to is determining a set of relations between S and the 5-primary probability parameters and using that set of relations to interpolate into a finer integration space without having to simulate each case. F( S) = ΔPi j k m n n' m' k ' j' i' ' ' ' ' ' Where the primes denote smaller increments than the initial ijkmn increments. This used to be done for response to central pressures in the old JPM, but not with the others. NOTE: The probabilities used in this method are assumed to be continuous over the 5-D parameter space.

8 This method potentially offers two advantages: 1. Since probabilities are very nonlinear, the integral should be more accurate than a broad trapezoidal integration 2. The number of computer runs can be minimized. This concept is an attempt to optimize the sampling of the storm set that is simulated. Its accuracy is predicated on the ability to fit the response surface with an accurate set of functional relationships FROM THE ACTUAL SAMPLED STORMS. Response to Cp approximately linear Response to Rmax moves x0 and changes surge levels Response to angle slow variation centered around normal Response to storm speed at coast scales with effect of Vmax inland TBD Response to x-x0 scales with (x-x0)/rmax around x0

9 New JPM: The estimation of the surge CDF includes a random deviation term added to the modeled values. In this way we can retain important aspects of variations that would add too many dimensions to the integral to make it practical. F( η ) =... p( ΔP, R, v, θ, x) H[ η Φ( Δ P, R, v, θ, x) + ε] δ( ΔP, R, v, θ, x) max where p f l max p f l p f l ε is a random deviation due to all the neglected factors This includes both surge-independent terms (tide and model error) and surge-dependent terms (Holland B), etc. After some analyses of different types both Toro and Resio ended up using approximately 150 storms in this sum and similar magnitude epsilon terms.

10 Some Modifications from Original JPM Storm characteristics vary over spatial regions Winds from dynamic (physics-based) PBL model are used Pre-landfall storm variation (Cp, Rmax, B) are implemented Longer tracks defined (need to consider natural patterns) Interdependencies between Cp and Rmax captured EST method applied to estimate dispersion around F(S) Wave effects included Additional parameters included within a secondary set of variables

11 Louisiana Implementation JPM-OS Requires 446 storms for analysis Count == 152 >= Category 2 storms Eastern Louisiana 152 >= Category 2 storms Western Louisiana 71 < Category 2 storms Eastern Louisiana 71 <= Category 2 storms Western Louisiana 4 to 5 Grid (Geometry) Validation Hindcasts Total Louisiana >= 450 storms

12 All storms with Vmax > 125 kts Analyses have shown that intense hurricanes are much more organized than weak hurricanes. Land-falling storms exhibit similar heterogeneity as offshore storms. Northern Entrance To Gulf Southern Entrance To Gulf

13 Eastern and Western LA Work 446 JPM Storms based on 3 track path classifications Western LA track paths shown in red, Eastern LA in blue SW 45 SE 45 Mean Angle

14 Louisiana ADCIRC Mesh > 2 Million Nodes > 4 Million Elements

15 STWAVE Grids

16 ADCIRC + STWAVE HPC Systems Cray XT3 / XT4 IBM P4/P5 Dell Linux Clusters TACC Ranger TACC Lonestar LSU Queenbee Others

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18 JPM-OS Point Stats - Open Marsh Lake Borgne

19 Open Marsh Lake Borgne

20 East and West Louisiana 100 yr surges

21 West Louisiana 100 yr Waves Wave Heights (Feet) Wave Periods (sec)

22 West Louisiana 1000 yr surges

23 Storm 026 Return Periods

24 Katrina Surge Returns

25 Texas JPM-OS Implementation ADCIRC Mesh / Storms Storms 152 High Intensity North Tx 152 High Intensity South Tx 71 Low Intensity North Tx 71 Low Intensity South Tx 4 5 Validation TOTAL 450 Storms

26 Historical Archive of All Tropical Storm/Hurricane Tracks Time Period: All Tropical Storm/Hurricanes Stratified to systems that enter Texas Box 89 Storms Total

27 JPM SW Paths

28 JPM SE Paths

29 JPM Fan Paths

30 Storm 33 Winds

31 Storm 33 Peak Surge

32 Storm 245 Peak Surge Track 245

33 Thank You Forecasting can be very difficult --- particularly when it involves the future. Yogi Berra