1
Coupled Model of Statistical Typhoon and Numerical Storm Surge
for Probabilistic Estimation of Surge Height
Sungsu Lee1, Chang Hee Won2, Ga Young Kim2 1School of Civil Engineering, Chungbuk Nat’l Univ, CheongJu, South Korea 2Department of Civil System Eng, Chungbuk Nat’l Univ, CheongJu, South Korea Email : [email protected] , [email protected], [email protected]
ABSTRACT: Storm surge caused by typhoon is one of the natural hazards that give heavy damage to coastal areas, and many studies have been done to estimate the surge height using various numerical models. But due to the random nature of the typhoons, the design sea level for the coastal structure is a very difficult task to determine. In order to resolve this problem, this paper present a coupled method using a numerical model for surge height estimation and a statistical model for typhoon. For the former, SLOSH as a numerical analysis model, developed by NOAA (National Oceanic and Atmospheric Administration) is utilized, while a Monte Carlo Simulation of typhoons is employed for the latter. In particular, different models for the radius of the maximum wind (RMW) for typhoons were tried to analyze the effects of RMW on the maximum storm surge height. The results show that the effects of RMW are essential and estimated surge heights are validated by the measured data, provided by the Korea Hydrographic and Oceanographic Administration. This study is an initial effort for the design water level with probabilistic approach. KEY WORDS: Storm Surge, SLOSH, Monte Carlo Simulation, Radius of the Maximum Wind.
1 INTRODUCTION
Over the past 100 years, the number of typhoons affecting the Korean peninsula is about 300 [1] and coastal areas has been directly or indirectly affected by about three typhoons annually on the average. Storm surge caused by the typhoon is one of the main natural hazards that yield much damage to coastal areas. From 2002 to 2011, about 13.8 trillion won (13.9 billion in USD) damages caused by typhoon reaches 65% of the country natural disaster damage [2]. Recent study on climate change projects the increase of the sea water temperature and the rise of the sea level. In addition, typhoon central pressure is expected to decrease about 4.5hPa and the maximum wind speed will increase by about 2m/s around Korea [3]. All of these will be additional factors for the increased damage from the typhoon in the future. Storm surge is defined as a rise in sea level due to pressure drop and wind shear by typhoon and its height is defined as the difference between the predicted sea level and the observed one which can be measured directly at coastal tide stations. The rising water level will counteract the low atmospheric pressure such that the total pressure at some plane beneath the water surface remains constant. It is well known that the sea level rises about 1cm at the pressure drop of 1hPa in atmospheric pressure. In addition, if a typhoon approaches the coast at high tide, the damage caused by the storm surge is maximized in the coastal lowlands. Typical examples of such coastal damages were those occurred by typhoons SARAH(5914), RUSA(0215) and MAEMI(0314). During those typhoons around Korea, heavy rain with strong winds and storm surge resulted in a large body of casualties and property damage along the coast. Recently, a HAIYAN(1330) with recorded lowest ever central pressure of 895 hPa devastated Southeast Asia, particularly the Philippines, on November 8, 2013. The instantaneous maximum wind speed was about 379km/hour as it passes through the central Philippines, which was the highest level ever recorded by the US Joint Typhoon Warning Center (JTWC). Storm surge height at the islands of Leyte reached about 6~7m, causing deaths more than 6100 and missing persons of 1780, property damages of 12.9 billion USD [4]. Figure 1 shows the devastation of the storm surge damage caused by typhoon MAEMI in Korea and HAIYAN in Philippine. Many countries employ numerical models for storm surge forecasting in their early warning system to mitigate related damages, including Korea Meteorological Administration (KMA) which utilizes a numerical model developed based on POM [5]. In addition to the real time forecasting, the storm surge height along coastal line needs to be estimated in advance for the purposes of the design criteria of coastal structure and the coastal mitigation plan.
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Figure 1. Storm surge damage caused by typhoon (MAEMI(left), HAIYAN(right))
This study proposes the combination of statistical model of climatological features of typhoon and deterministic model of storm surge. A newly developed typhoon model [6-8] is employed to generate the hypothetical typhoons, which provide the location and the intensity. The storm surge corresponding to each of simulated typhoons is computed by SLOSH (Sea, Lake, and Overland Surges from Hurricanes), developed by NOAA (National Oceanic and Atmospheric Administration) [9].
Since SLOSH was developed for basins and hurricanes around US territory, all of which are much different from those around Korea, this study simulated the storm surge height during typhoon BOLAVEN (1215), which showed good agreement with the observed data provided by Korea Hydrographic and Oceanographic Administration (KHOA). Based on these approaches, this paper presents the estimation methodology by the probability density distribution of storm surge heights using Monte Carlo simulation.
2 STORM SURGE PREDICTION MODEL 2.1 SLOSH SLOSH model to predict the storm surge heights, has been utilized in the National Hurricane Center (NHC) of NOAA for storm surge forecast with ADCIRC (Advanced Circulation Model for oceanic, coastal, and estuarine waters). SLOSH has shown shortcomings from relatively low grid resolution for coastline and topography and inability to consider the interaction with the astronomical tide. It was reported that the maximum estimation error is about 20% [10]; however SLOSH has shown its computational effectiveness of fast calculation. It has been of great help when even rougher estimation may be needed at the time of present threat by an approaching typhoon. To reduce these errors, NHC in general carries out the storm surge predictions about thousand times by SLOSH with different parameters for a hurricane to establish the maximum envelopes of water (MEOWs) and maximum of MEOWs (MOMs) which play an integral role in emergency management.
2.2 Governing equations and numerical methods Equations (1) and (2) were derived from 3D Navier-Stokes equations and equation, (3) is continuity, which are applicable to rotating fluid at the free surface. Considering relatively low order of spatial dimension in vertical direction compared to the horizontal domain, the physical quantities were integrated through the depth. SLOSH employs finite difference about time, and central difference about space.
U (h h ) (h h ) g(D h)[B 0 B 0 ] f (A V AU) C x C y (1) dt x i y i i
V (h h0 ) (h h0 ) g(D h)[B B ] f (A U AV ) C y C x (2) dt y i x i i h U V (3) t x y
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where U and V are the two components of transport on horizontal plane, g is the gravitational acceleration, D is depth of quiescent water relative to a common datum, h is height of water above datum, h0 is hydrostatic water height, f is Coriolis parameter, xτ and yτ are the two components of surface stress, and AΓ···Ci are the bottom stress terms.
2.3 Wind field model SLOSH wind field model has first been developed in the SPLASH storm model [11] and was supplemented by Jelesnianski et al. [9] and Houston et al [12]. The wind field is assumed stationary with the wind direction of the concentric circles about the eye of a typhoon. The wind speed is modeled as equation (4) for the stationary wind, and equations (5) and (6) represents equations of motion in the tangential direction and the radial direction, respectively [13]. Therefore, if the wind speed V(r) is obtained from equation (4), it is possible to calculate a pressure p and a flow angle φ using equations (5) and (6).
2Rr (4)
V (r) VR 2 2 R r 2 1 dp ksV dV (5) V Pa dr sin dr 2 1 dp V 2 d 2 cos fV cos V sin knV (6) Pa dr r dr
Where V(r) is the maximum wind speed, r is the distance from the storm center, R is the radius of the maximum wind, p(r) is the pressure, φ(r) is the inflow angle across circular isobars toward the storm center, ks is the wind friction coefficient in the tangential direction, kn is the wind friction coefficient in the radial direction, and pa is the atmospheric pressure.
2.4 Radius of the maximum wind (RMW) calculation In computing storm surge height caused by a typhoon, the central pressure and the wind shear are primary driving forces. One of essential parameters determining the effects of typhoon in SLOSH is the radius of maximum wind speed (RMW) which is defined as the distance to the point of the maximum wind speed from the center of the typhoon. There are many different empirical models to relate the central pressure with RMW as listed below.
Table 1 Empirical Model for RMW
Model Description Remark Number
1 RMW 335.18 66.18ln P [14]
2 ln RMW 2.556 0.000050255P2 0.042243032Lat [15]
3 ln RMW 2.06330.0182P 0.00019P2 0.0007336Lat 2 [16]
4 ln RMW 2.377 0.00004825P2 0.0483Lat [17]
where ΔP is (Pn-Pc,) Pn is atmospheric pressure(1013hPa), Pc is central pressure(hPa), Lat is Latitude(degree), and ε is generally use 0.3.
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2.5 Application to typhoon BOLAVEN In order to examine the applicability of SLOSH to the basin around Korea and the different models for RMW, the storm surge heights were computed for the case of typhoon BOLAVEN whose track is shown in Figure 2. The grid system to resolve the coastal region of Korea is also depicted in Figure 3. About 28 000 nodes were employed for hyperbolic grid with a minimum grid size of 1km. Climatological information and different RMWs of typhoon BOLAVEN are listed in Table 2, and bathymetry was from NGDC (National Geophysical Data Center). Figure 4 shows the comparisons of storm surge heights between computational results with different RMW models and observations made at two tide stations, INCHEON and DAESAN, both of which are located at the western coast of Korea. Since the western coastline is located on the right side of the advancing typhoon, the storm surge height reaches more than 1m high. Most of the simulated heights are in reasonable agreements with the observation, in particular, at the time of peak height. The results also show that RMW model using Fujii’s study [14] is the most appropriate one for the basin around Korea.
Figure 2. Path of typhoon BOLAVEN(1215)
Figure 3. SLOSH grid system
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Table 2 Information of typhoon BOLAVEN(1215)
RWM (mile) Pressure TIME(UTC) GRADE Lat(˚N) Long(˚E) Delta-P (hPa) MODEL 1 MODEL 2 MODEL 3 MODEL 4
2012082618 5 275 1274 940 73 31.81 19.57 29.21 19.54
2012082700 5 284 1269 955 58 41.27 22.44 33.51 22.43
2012082706 5 299 1260 960 53 44.98 24.58 36.25 24.77
2012082712 5 313 1256 960 53 44.98 26.08 38.60 26.51
2012082718 5 330 1255 960 53 44.98 28.02 41.83 28.78
2012082800 5 348 1251 960 53 44.98 30.24 45.74 31.39
2012082806 4 366 1248 965 48 49.05 33.46 50.52 35.09
2012082812 4 387 1245 975 38 58.66 38.18 55.68 40.48
2012082818 3 416 1258 980 33 64.46 43.94 64.52 47.37
2012082900 3 443 1283 980 33 64.46 49.25 76.49 53.96
2012082906 6 460 1300 982 31 67.04 53.25 84.58 58.94
2012082912 6 477 1324 984 29 69.78 57.56 93.78 64.36
2012082918 6 500 1344 986 27 72.72 63.80 108.92 72.31
Figure 4. Comparison of storm surge height (Tide excluded)
3 COUPLED MODEL FOR MONTE CARLO SIMULATION 3.1 Coupled model for Monte Carlo Simulation Monte Carlo Simulation (MCS) is a numerical approach to predict future values of the random variable. The typhoon simulation using MCS consists of statistical models for climatological parameters and physical models for wind field. A newly
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developed typhoon model was proposed and described in detail in references [6-8]. In general, MCS is composed of four models, as shown in Figure 5; initial condition model, tracking models, intensity model and wind field model. This study proposes the iterative coupling of MCS with SLOSH as shown in Figure 6
3.2 Estimation of design water level Based on the past history of the typhoon landed in Korean peninsula, MCS lists hypothetical typhoons with their meteorological features including central pressure. In the first place, the probabilistic approach of step 2 to 4 in Figure 6 is repeatedly conducted for the hypothetical typhoons. Once the maximum surge heights are obtained for every typhoons and at locations of interest, a series of statistical analysis in step 5 to 8 is followed for obtained the best probabilistic distributions of extreme values. Once the optimal probability distribution is selected in step 9, the design storm surge height can be estimated for the return period of interest. In step 10, superimposition of the tide and the estimated storm surge height leads to the design water level.
Figure 5. Component diagram of the MCS
Figure 6. Probabilistic estimation process of the storm surge height
4 CONCLUSION This study presents a model for estimation of probabilistic storm surge height using coupled computation of statistical typhoon and deterministic storm surge. The statistical model for typhoon consists of probabilistic estimations of typhoon genesis location, randomness of track and intensity affected by sea surface temperature. The deterministic estimation of the storm surge height is numerically computed using SLOSH developed by NOAA. In order to validate the applicability of SLOSH to Korean basin, a
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computation is carried out for a historical typhoon, BOLAVEN, which showed the effectiveness. Due to climatological and oceanographic differences between US basins and Korea, different models for RMW were tried and the model proposed by Fujii[14] produces the best results. The proposed coupled model will be applied to estimate storm surge height along coast in the sense of probability in order to establish the mitigation plan.
REFERENCES [1] K.H. Choi, G.Y. Choi and Y.M. Kim, Salty Wind Damages in Windbreak Forests of Jeju Island by Typhoon Bolaven, Journal of the Korean Geographic Society, Vol.49 No.1 pp.18-31, 2014. [2] National Emergency Management Agency, Disaster Annals, 2012. [3] K.H. Jang, J.Y. Kim, W.S. Yun, K.Y. Byeon, K.S. Choi, W.J. Lee and J.H. Lee, Korea's typhoon Forecast and Analysis Status, Journal of the Korean Society of Hazard Mitigation, Vol.13 No.4 pp.6-16, 2013. [4] J.S. Kim, C.Y. SON and Y.I. Moon, Super typhoon ' HAIYAN ' and future typhoon prospects, Journal of Korea Water Resources Association, Vol. 47, No. 2, pp. 46-54, 2014. [5] G.L. Mellor, USERS GUIDE for A THREE-DIMENSIONAL, PRIMITIVE EQUATION, NUMERICAL OCEAN MODEL, Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ 08544-0710, 1998. [6] Y.K. Lee, S. Lee and C.W. Park, Analysis on Radii of Maximum Sustained Winds of Typhoons around Korean Peninsula, Journal of the wind engineering institute of Korea, Vol. 11, No. 2, 203-210, 2007. [7] G.Y. Kim, Empirical Models for Intensity and Track of Typhoons around Korean Peninsula. Master’s thesis, Chungbuk National University, CheongJu, South Korea, 2012. [8] S. Lee and G.Y. Kim, Development of Empirical Typhoon Tracking Model around Korean Peninsula, Journal of the wind engineering institute of Korea, Vol. 16, No. 2, 57-64, 2012. [9] C.P. Jelesnianski, J. Chen and W.A. Shaffer, SLOSH : Sea, lake and overland surges from hurricanes, NOAA Technical Report NWS 48. Silver Spring, MD: Dept. of Comm. NOAA, 1992. [10] B. Glahn, A. Taylor, N. Kurkowski and W.A. Shaffer, The Role of the SLOSH Model in National Weather Service Storm Surge Forecasting, National Weather Digest, Vol. 33, No. 1, pp. 3-14, 2009. [11] C.P. Jelesnianski and A.D. Taylor, A preliminary view of storm surges before and after storm modifications, NOAA Technical Memorandum ERL WMPO- 3, National Oceanic and Atmospheric Administration, U.S. Department of Commerce, pp. 33, 1973. [12] S.H. Houston and M.D. Powell, Observed and modeled wind and water-level response from Tropical Storm Marco(1990), Weather and Forecasting, Vol. 9, pp. 427-439, 1994. [13] V.A. Myers and W. Malkin, Some properties of hurricane wind fields as deduced from trajectories, National Hurricane Research Project Report No. 49, National Oceanic and Atmospheric Administration, U.S. Department of Commerce, pp. 43, 1961. [14] T. Fujii, Statistical Analysis of the Characteristics of Severe Typhoons Hitting the Japanese Main Islands, Monthly Weather Reviews, Vol. 126, No. 4, pp. 1091-1097, 1998. [15] S.H. Houston, W.A. Shaffer, M.D. Powell, and J. Chen, Comparisons of HRD and SLOSH Surface Wind Fields in Hurricanes: Implications for Storm Surge Modeling, Wea. Forecasting, 14, 671–686. 1999. [16] M. Powell, G. Soukup, S. Cocke, S. Gulati, N. Morisseau-Leroy, S. Hamid, N. Dorst and L. Axe, State of Florida hurricane loss projection model: Atmospheric science component, J. Wind Eng. Ind. Aerodynamic, Vol.93, pp.651-674, 2005. [17] P.J. Vickery and D. Wadhera, Statistical Models of Holland Pressure Profile Parameter and Radius to Maximum Winds of Hurricanes from Flight-Level Pressure and H*Wind Data, Journal of Applied Meteorology and Climatology, Vol.47, pp.2497-2517, 2008.
ACKNOWLEDGEMENT The work described in this paper was supported by the grant (NEMA-JAYEON-2012-52) from Natural Hazard Mitigation Research Group funded by National Emergency Management Agency, Korea.
14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015