Uncertainties in Atlantic Hurricane Characteristics with Application to Coastal Hazard Modeling

Transcription

1 Uncertainties in Atlantic Hurricane Characteristics with Application to Coastal Hazard Modeling Peter J Vickery and Dhiraj Wadhera Applied Research Associates 854 Colonnade Center Drive, Suite 37 Raleigh, NC 7615

2 Hurricane Simulation Modeling Usage Wind Hazard Mapping Building Codes Insurance Risk Modeling PML Estimates, Rate Setting (wind and coastal flood) Estimates of design wave conditions Coastal Flood Modeling Flood Insurance Rates, Building Regulations

3 Background Premise behind hurricane simulation modeling is: If we can characterize the statistics of key hurricane input parameters and use this data in a hurricane wind field model coupled with a rate model, we can artificially create long history records of wind speeds, wave heights, storm surge, etc and develop hazard curves Key wind field input parameters are Central pressure difference Track (lat, long, heading) Translation speed Radius to maximum winds Holland B parameter Major difficulty is there is a short record of historical data and the quality and quantity of data varies over the past 1 years Significant uncertainty in these input variables which propagates to large uncertainties in output hazard estimates which should be considered in decision making 3

4 Holland B Parameter Increase in B yields higher maximum wind speeds and a relatively narrow wind field Decrease in B reduces the maximum wind speed but results in a broader storm Sometimes referred to a tuning or calibration knob Gradient Balance Wind Speed (m/sec) B =.75 B = 1 B = 1.3 B = Distance from Storm Center (r/rmw) Pressure (mbar) Distance from Storm Center (r/rmw) B =.75 B = 1 B = 1.3 B = 1.5 4

5 4 Modeling Input Probability Distributions Approach 15 RMW (km) Holland B Parameter Central Pressure Difference (mbar) y/rmax Storm Surge Elevation w.r.t MSL (ft) 4 Translation Speed (m/s) Heading 8/9//5 (Lat=7., Long=89.1, B=1.4, dp=14mbar, Rmax=4km, Vt=4.7m/s, H=1m) Vmax=5.7m/s (-.3,1) x/rmax Wind Field Model Hazard Curve Return Period (Years) Landfall Distance (km) 4 Hydrodynamic Models e.g. WAVEWATCH, SWAN, ADCIRC, etc Wave Height /17/7 : 9/18/7 : 9/19/7 : 6 #Events/yr 8 1 Distribution of response given hurricane Response 4 (Surge/Waves/Windspeed) 5

6 Simulation Model Validation Examples.18 Texas.18 Louisiana Central Pressure (mb) Central Pressure (mb) TX Return Period (years) SW FL Return Period (years) Central Pressure (mb) Central Pressure (mb) LA Return Period (years) SE FL Return Period (years) P.D.F P.D.F Northwest Florida.18 Southwest Florida Model validated through comparisons of statistical distributions of modeled and observed central pressures, storm heading, translation speed and occurrence rates along the Gulf and Atlantic coasts and in the Caribbean Separate statistical models used to model B and RMW as a function of other hurricane parameters Results in a model that is nominally mean centered Estimates of model uncertainties have to be treated separately 6

7 Objective Given an estimate of the uncertainties in the key model input parameters Δp, RMW, etc we want to know the uncertainty in the output variable such as: 1 year return period wind speed 1 year return period water elevation 475 year return period loss Characterize uncertainties in the inputs and propagate through the simulation model Difficult time consuming process that requires significant simplifications 7

8 Example Output Hazard Curve 5th Percentile 95th Percentile Mean Return Period (years) 8

9 Return Period (Years) 4 Uncertainty Estimation Approach Sample errors for parameters of each input model/probability distribution (error in mean and standard deviation) Start N year Repeat N year simulation M times y/rmax 15 RMW (km) 4 Translation Speed (m/s) Holland B Parameter Heading 8/9//5 (Lat=7., Long=89.1, B=1.4, dp=14mbar, Rmax=4km, Vt=4.7m/s, H=1m) Vmax=5.7m/s (-.3,1) Storm Surge Elevation w.r.t MSL (ft) 1-1 Wind Field Model x/rmax Hazard Curve Central Pressure Difference (mbar) Landfall Distance (km) 4 Hydrodynamic Models e.g. WAVEWATCH, SWAN, ADCIRC, etc Wave Height /17/7 : 9/18/7 : 9/19/7 : 6 #Events/yr 8 1 Response 4 (Surge/Waves/Windspeed) Modeled Peak Gust Wind Speed (mph) Sample model errors for each storm realization y=.993x Observed Peak Gust Wind Speed (mph) Water Elevation (m) w.r.t Return Period (years) Family of Hazard Curves 9

10 Uncertainties Each input probability distribution (or regression model) is uncertain (i.e. errors in one or more of the mean, variance or even the chosen statistical distribution) Errors will reduce as the record length increases Reduce errors with improved physical models Central Pressure (mb) TX Return Period (years) Radius to Maximum Winds (km) Data Model Median Model +/- Std. Deviations Central Pressure Difference (mb) Physical models have errors associated with lack of understanding of the true physical processes and/or model simplifications and assumptions Errors will reduce as computer power increases and model physics are improved 1

11 Landfall central pressure uncertainty Characterize errors assuming landfall pressure are characterized by a Type I distribution (Error estimate using Cramer-Rao) σ 1/ Δp π σ Δ p ( P) = (.68[ln( ln( P))].514ln( ln( P)) ) n 6 Each, year realization effectively samples from a new distribution of landfall pressures Essentially shifts the landfall pressure hazard curve up and down for an entire, year simulation Error is fully correlated over the, year simulation Landfall Central Pressure GA/SC Landfall Data Model Mean 5th and 95th Percentile Estimate Exceedance Probability 11

12 Pressure Uncertainty 99 GA/SC Landfalling Hurricanes 97 Central Pressure (m Landfall data 19-7 Model Cramer-Rao 9% confidence range 9% confidence derived from ~9 17 Year Simulations Return Period (years) 1

13 Uncertainty in Holland B Parameter y B derived from aircraft pressure data (67 estimates of B from 35 hurricanes) B derived for landfalling storms by matching modeled and measured surface winds and pressures to model results obtained using wind and pressure models defined using central pressure, B, RMW, etc. Estimates for 5 landfalling hurricanes B models published by other researchers Modeled Peak Gust Wind Speed (mph) Holland B Parameter y =.99x R = KBIX KPFN KNEW KMSY KTLH 96 = -.37x R 15 = Radius(km) Hurricane Ivan DPIA1 KNPA FCMP T FCMP T1 KMOB 47 BURL1 GDIL1 SGOF1 KVPS Observed Peak Gust Wind Speed (mph) Peak Gust Wind Speed (mph) 1 Minute Mean Wind Speed (mph) Pressure(mb) SQRT(A) /15/4 1: /15/4 1: DPIA1 Edouard-1996/8/6-1855, B=1.35, Δp=74mb, R max =.5km 9/16/4 : Time DPIA1 9/16/4 : Time 9/16/4 1: 9/16/4 1: Wind Direction Central Pressure (mbar) /15/4 1: 9/15/4 1: DPIA1 9/16/4 : 9/16/4 1: Time DPIA1 9/16/4 : 9/16/4 1: Time 13

14 Example B fits Bret-1999/8/1-11, B=1.7, Δp=5mb, R max =km 13 Bret-1999/8/1-118, B=1.9, Δp=53mb, R max =km Pressure(mb) Pressure(mb) Radius (k m ) Radius(k m ) Edouard-1996/8/6-1855, B=1.35, Δp=74mb, R max =.5km Edouard-1996/8/6-194, B=1.65, Δp=7mb, R max =3km 1 1 Pressure(mb) Pressure(mb) Radius (k m ) Radius(k m ) 14

15 B vs. RMW, Latitude, SST and Central Pressure Holland B Parameter y = -.x R =.7 Holland B Parameter y = -.7x R = Latitude (Degrees N) RMW (km) Holland B Parameter y =.3x R =.3 Holland B Parameter y =.59x R = Central Pressure Difference (mb) Sea Surface Temperature (Degrees C) 15

16 Estimation of Holland B Parameter Modeled Gust Windspe (mph) y =.99x R = Ivan Observed Gust Wind Speed (mph) 16

17 Estimation of Holland B Parameter Wind Direction /9/5 : 8/9/5 6: FCMP T1 8/9/5 1: 8/9/5 18: 8/3/5 : 8/3/5 6: Pressure (mbar) /9/5 : 8/9/5 6: FCMP T1 8/9/5 1: 8/9/5 18: 8/3/5 : 8/3/5 6: Peak Gust Wind Speed (mph) /9/5 : FCMP T1 - Adjusted for Terrain 8/9/5 6: 8/9/5 1: 8/9/5 18: 8/3/5 : 8/3/5 6: 1 Minute Wind Speed (mph) /9/5 : 8/9/5 6: FCMP T1 - Adjusted for Terrain 8/9/5 1: 8/9/5 18: 8/3/5 : 8/3/5 6: 17

18 Validation Examples Ivan Wind Direction Peak Gust Wind Speed (mph) T1 9/15/4 1: 9/16/4 : 9/16/4 1: 9/17/4 : Time T1 - Adjusted for Terrain 9/15/4 1: 9/16/4 : 9/16/4 1: 9/17/4 : Time Peak Gust Wind Speed (mph) Central Pressure (mbar) /15/4 1: /15/4 1: Peak Gust Wind Speed (mph) /15/4 1: 9/15/4 18: 9/16/4 : 9/15/4 9/16/4 18: : 9/15/4 18: KBIX 9/16/4 6: Time KBIX 9/16/4 : 9/16/4 1: 9/16/4 9/16/4 6: 1: Time DPIA1 Time 9/16/4 6: 9/16/4 18: 9/17/4 : 9/16/4 9/17/4 18: : 9/16/4 1: 9/16/4 18: Central Pressure (mbar) Wind Direction Mean Wind Speed (mph) KBIX /15/4 9/15/4 9/16/4 9/16/4 9/16/4 9/16/4 9/17/4 1: 18: : 6: 1: 18: : /15/4 1: /15/4 1: 9/15/4 18: 9/15/4 18: 9/16/4 : KBIX Time 9/16/4 6: DPIA1 9/16/4 : Time Time 9/16/4 6: 9/16/4 1: 9/16/4 1: 9/16/4 18: 9/17/4 : 9/16/4 18: 1 Minute Mean Wind Speed (mph) /15/4 1: 9/15/4 18: 9/16/4 : DPIA1 Time 9/16/4 6: 9/16/4 1: 9/16/4 18: Wind Direction /15/4 1: 9/15/4 18: DPIA1 9/16/4 : Time 9/16/4 6: 9/16/4 1: 9/16/4 18: 18

19 Validation Examples - Katrina Peak Gust Wind Speed (mph) Wind Direction /9/5 : /9/5 : 8/9/5 6: 8/9/5 6: KBTR 8/9/5 1: KBTR 8/9/5 1: 8/9/5 18: 8/9/5 18: 8/3/5 : 8/3/5 : 8/3/5 6: 8/3/5 6: Pressure (mbar) 1 Minute Wind Speed (mph) /9/5 : /9/5 : 8/9/5 6: 8/9/5 6: KBTR 8/9/5 1: KBTR 8/9/5 1: 8/9/5 18: 8/9/5 18: 8/3/5 : 8/3/5 : 8/3/5 6: 8/3/5 6: Peak Gust Wind Speed (mph) Wind Direction /9/5 : /9/5 : 8/9/5 6: 8/9/5 6: DPIA1 8/9/5 1: DPIA1 8/9/5 1: 8/9/5 18: 8/9/5 18: 8/3/5 : 8/3/5 : 8/3/5 6: 8/3/5 6: Pressure (mbar) Mean Wind Speed (mph) /9/5 : /9/5 : 8/9/5 6: 8/9/5 6: DPIA1 8/9/5 1: DPIA1 8/9/5 1: 8/9/5 18: 8/9/5 18: 8/3/5 : 8/3/5 : 8/3/5 6: 8/3/5 6: Wind Direction /9/5 : Peak Gust Wind Speed (mph) /9/5 : 8/9/5 6: FCMP T1 8/9/5 1: 8/9/5 18: FCMP T1 - Adjusted for Terrain 8/9/5 6: 8/9/5 1: 8/9/5 18: 8/3/5 : 8/3/5 : 8/3/5 6: 8/3/5 6: Pressure (mbar) Minute Wind Speed (mph) /9/5 : /9/5 : 8/9/5 6: 8/9/5 6: FCMP T1 8/9/5 1: 8/9/5 18: FCMP T1 - Adjusted for Terrain 8/9/5 1: 8/9/5 18: 8/3/5 : 8/3/5 : 8/3/5 6: 8/3/5 6: Wind Direction Peak Gust Wind Speed (mph) /9/5 : /9/5 : 8/9/5 6: 8/9/5 6: FCMP T 8/9/5 1: 8/9/5 18: FCMP T - Terrain Adjusted 8/9/5 1: 8/9/5 18: 8/3/5 : 8/3/5 : 8/3/5 6: 8/3/5 6: Pressure (mbar) Mean Wind Speed (mph) /9/5 : /9/5 : 8/9/5 6: 8/9/5 6: FCMP T 8/9/5 1: 8/9/5 18: FCMP T - Terrain Adjusted 8/9/5 1: 8/9/5 18: 8/3/5 : 8/3/5 : 8/3/5 6: 8/3/5 6: 19

20 Holland B Models Powell, et al (5) B = RMW.197 ψ, r =., σ B =.86 Vickery and Wadhera (8) B = RMW ψ; r =.356, σ B =.1 B = A ; r =.336, σ B =.5 A = RMW f R T d s ln 1+ c Δp pc e Vickery, et al. () B = Δp -.31 RMW; r =.6, σ B =.38 Analysis of Atlantic Ocean Landfalling Hurricanes B = RMW.17 ψ,; r =., σ B =.1 (16 Observations, dependence on latitude not significant) Analysis of Atlantic Ocean and Gulf of Mexico Landfalling Hurricanes B = RMW ψ,; r =-.1, σ B =.6 (5 Observations, latitude and RMW dependence not significant) B = 1.1, σ B =.6

21 B from Landfalling Storms Atlantic and Florida Peninsula Landfalling Hurricanes B North and South Carolina Hurricanes B from wind modeling B From Equation 18 Linear (B from wind modeling) RMW (km) Gulf of Mexico Hurricanes B from wind modeling B from Equation 18 Linear (B from wind modeling) B Florida Peninsula Hurricanes B from wind modeling B from Equation 18 Linear (B from wind modeling) RMW (km) Gulf of Mexico Hurricanes B from wind modeling B from Equation 18 minus.3 Linear (B from wind modeling) Holland B Parameter B Data from landfalling Storms. Model RMW (km) B 1. B RMW (km) RMW (km) 1

22 Comparison of Regression Parameter Estimates with Other Models 1.75 Model Mean Model.5 and 97.5 Limits 1.75 Model Mean Vickery, et al () Model NC/FL landfall Storm Model Linear (NC/FL landfall Storm Model) Holland B ` Holland B ` B Used in Wind Model y =.95x R =.77 Sqrt(A) Andrew Bertha Georges Keys Bob - NC Bonnie Floyd Fran B Derived from Flight Level Data Holland B ` Sqrt(A) Model Mean Vickery, et al () Model Powell et al, 5 Model Linear (Powell et al, 5 Model) Sqrt(A)

23 Upper and Lower Bound B Uncertainty Models Lower Bound Estimate Standard Error in mean =.4 Standard Error in slope =.8 Upper Bound Estimate Standard Error in mean =.8 Standard Error in slope =.5 Holland B Holland B Model Mean Linear (NC/FL landfall Storm Model) Linear (Powell, et al. (5) Model) ` Sqrt(A) ` Model Mean Linear (Vickery, et al () Model) Sqrt(A) 3

24 RMW Uncertainty Example Models derived using aircraft data (35 hurricanes) and landfall data (17 hurricanes) Landfall data has limited intense hurricane data (minimum pressure 99 mbar) In Gulf landfall data shows no RMW-Δp relationship. Rejected this model, but it should be considered in uncertainty analysis Used basic regression error analysis to propagate RMW errors for both Gulf and Atlantic hurricanes Radius to Maximum Wi Radius to Maximum Wi Data Model Median Model +/- Std Dev Central Pressure Difference (mbar) Model Median from Aircraft Data Model +/- Std Dev, Central Pressure Difference (mbar) 4

25 Propagation of Uncertainties Example Storm surge study for location on Kiawah Island, SC Straight Monte Carlo, year simulation using empirical track modeling technique coupled with a nested grid finite difference storms model. Finest grid resolution m Waves not modeled Single point site specific example 5

26 Return Period (Years) 4 Uncertainty Estimation Approach Sample errors for parameters of each input model/probability distribution (error in mean and standard deviation) Start N year Repeat N year simulation M times y/rmax 15 RMW (km) 4 Translation Speed (m/s) Holland B Parameter Heading 8/9//5 (Lat=7., Long=89.1, B=1.4, dp=14mbar, Rmax=4km, Vt=4.7m/s, H=1m) Vmax=5.7m/s (-.3,1) Storm Surge Elevation w.r.t MSL (ft) 1-1 Wind Field Model x/rmax Hazard Curve Central Pressure Difference (mbar) Landfall Distance (km) 4 Hydrodynamic Models e.g. WAVEWATCH, SWAN, ADCIRC, etc Wave Height /17/7 : 9/18/7 : 9/19/7 : 6 #Events/yr 8 1 Response 4 (Surge/Waves/Windspeed) Modeled Peak Gust Wind Speed (mph) Sample model errors for each storm realization y=.993x Observed Peak Gust Wind Speed (mph) Water Elevation (m) w.r.t Return Period (years) Family of Hazard Curves 6

27 Approach Relatively low risk location on the Southern SC coast Basic simulation is, years Estimate errors input statistical distribution parameters and models Compute model sensitivity coefficients (i.e. changes in water elevation caused by change in hurricane parameter) Repeat, simulation N times, with each, year repetition associated with a different potential realization of the statistics of the key input variables Generate N different hazard curves 7

28 Storm Surge Example Propagate uncertainty due to Holland B, central pressure and RMW at site. Compute sensitivity coefficients: η η dη, and B Δp drmw Sensitivity coefficient obtained by selecting ~3 simulated hurricanes at random and varying B, RMW and Δp one-at-a-time and computing the change in the water elevation at the site. Each storm re-modeled using mean ±.5,1. and. standard deviations (6*3*3 simulations) Sensitivity coefficients are then used to change the computed surge values from the base case, year simulation. Base case storms perturbed so each simulated storm, and storm effect, is from a new underlying distribution 8

29 Example Results Estimates of CoV Parameter 1 Year 5 Year Δp 14% 14% B 13% 1% RMW 1% 1% Occurrence Rate 15% 6% Total 5% % Water Elevation (m) th Percentile 95th Percentile Mean Return Period (years) 9

30 Summary Uncertainty Estimates Estimate of 1 year coastal storm surge elevation CoV ~%-3%. Uncertainty due to Hurricane modeling only. Estimates will vary with site Developing uncertainties of model inputs is somewhat subjective Uncertainty estimates are not usually provided, and if provided, users often not sure what do with them Estimates of uncertainty should be considered in any economic decision making 3