Nguyen, B. M.1*, and Van Gelder, P. H. A. J. M1
1Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands.
*e-mail : b.m.nguyen@tudelft.nl
ABSTRACT
In coastal areas, hurricane, also referred to as typhoon, is one of the costliest and deadliest natural disasters. While hurricanes are unavoidable, their risk can be considerably lessened by numerous approaches, such as an appropriate system of sea defense structures. The reliability of those solutions depends on the accuracy of key typhoon parameters, which are used as inputs for the analysis processes. Currently, all hurricane estimation methods are based on historical records of typhoon tracks and intensities. However, the most crucial limitation relates to the small sample size because hurricanes are both relatively infrequent and small in terms of the length of coastlines affected by these typhoons each year. Therefore, it is difficult to derive accurate key parameter of the strongest typhoons, on which risk analysis and design of coastal defense structures must be relied. The paper presents an advanced technique that can compensate for the lack of reliable hurricane observations and can be utilized for any simulation period. Although only South China Sea region is examined, the approach can be applied to all other locations. This is because of the unchanged theoretical methodology for all case studies and all the required parameters can be searched and extracted from global databases. In this study, the empirical track model is chosen as the theoretical framework for its potential advantages over other techniques. A large database of synthetic tracks is modeled, starting with their initial point and ending with their landfall location or point of final dissipation over the sea. This approach is validated through comparisons between the hurricane statistics derived from the historical data and the simulated ones over the entire research area (i.e. the South China Sea). The results show an acceptable accuracy, even if the input data are short.
Keywords: hurricanes, historical records, empirical track model, risk assessment. INTRODUCTION
Natural hazards, mainly climatic and atmospheric (e.g. blizzards, droughts, cyclonic storms, tornados) and geological hazards (e.g. avalanches, earthquakes, sinkholes, volcanic eruptions), lead to the remarkable human, environmental or financial losses [1]. Moreover, evidences from various sources stress the steady rise in frequency and severity of extreme weather events. For instance, the analysis of data from all 8,498 natural hazards from 1900 through 2008 [2] shows a relentless upward movement in number of reported events, which rose dramatically from nearly 3 per year in the 1900s to 354 per year in the 2000s (see Figure 1).
Figure 1. Average number of extreme weather events per year by decade, 1900–2008. Source: Goklany [2], based on EM-DAT [3]
Hurricane, also referred to as typhoon, or tropical cyclone is the major extreme weather event that have enormous human, economic and social consequences. On average, up to 119 million people are affected by typhoons every year, with 251,384 deaths over the period 1980-2000 [4]. In developing countries, the research showed that the deadliest hurricanes usually happen. For instance, Bangladesh accounts for more than 60 percent of the typhoons’ death toll in the period 1980-2000 [4]. This high fatality rate indicates that in this case high vulnerability coincides with high physical exposure. Follow the same trend as other natural hazards; there have been considerable rises in both typhoons frequency and intensity. From 1958 to 2001, the destructiveness of hurricane has increased by 70% [5]. Over the past 30 years, the wind speed and typhoon duration has increased by 60% in both the Pacific and the Atlantic oceans (Emanuel 2005). Hurricane risk is the estimated degree of threat facing a vulnerable group of people through exposure to hurricanes [6]. While hurricanes are unavoidable, their risk can be considerably lessened by several effective risk reduction approaches (e.g. an effective evacuation program based on an early warning system and the modern building technologies and regulations). The United States is a typical example, in which, loss of life have been significantly reduced, as can be clearly seen from Figure 2.
Figure 2. Deaths and Death Rates due to Hurricanes in the United States, 1900–2006. Source: Goklany [2], based on EM-DAT [3]
LITERATURE REVIEW
The reliability of hurricane risk reduction methods depends on the accuracy of key typhoon parameters, which are used as inputs for the analysis processes. Currently, all current hurricane estimation methods are based on historical records of typhoon tracks and intensities. The typical representations of these compilations are the alleged “best track” records. For each reported hurricane, the catalogues generally give some typhoon-related information such as the center position in geodetic coordinate (i.e. latitude and longitude) together with intensity estimation (i.e. maximum sustained wind speed and/or central pressure) at six-hour intervals along hurricane track since its initiation [7], [8]. These data sets provide a crucial reference in understanding typhoons occurred previously, from which proper risk assessment techniques can be initiated and evolved.
However, the most crucial limitation of those “best track” records relates to the small sample size because hurricanes are both relatively infrequent and small in terms of the length of coastlines affected by these typhoons each year. Therefore, it is difficult to derive accurate key parameter of the strongest typhoons; on which risk analysis and design of coastal defense structures must be relied [9]. Therefore, there is a rising demand for advanced techniques that can compensate for the lack of reliable hurricane observations, in order to step up classical hurricane estimation methods and upgrade cur-rent risk assessment and management.
In appreciation of the above, it is important to review existing methods and the manner in which these approaches are being applied to specific circumstances. Currently, numerical modeling is the most accepted technique for estimating hurricane wind speed, which is widely used to design coastal structures and to assess the risks associated with typhoon winds. According to Resio et al. [10], at least five techniques have been utilized to investigate hurricane parameters in past studies. These methodologies include the formulation of design storm events, the Peaks Over Threshold (POT) approach, Empirical Simulation
Technique (EST), Joint Probability Method (JPM), and empirical track model. Among them, the empirical track model, which was introduced by Vickery et al. [11], is one of the most recent techniques. The authors successfully generated typhoons over a very long period (i.e. 20,000 years) using available track observations and local climatological variables [12]. According to Ravela & Emanuel [13], the most important improvement of this method over conventional techniques is that it removes the need to specify a parametric form for the distributions of key hurricane parameters in the critical range of values. Therefore, this approach provides an excellent source for validating the statistical characteristics of the typhoon [10].
METHODOLOGY
3.1. Theoretical framework
Taking into account the above-mentioned situation, the main objective of this research is to develop a suitable method for the simulation of hurricanes on the basis of the available historical record. In this study, the empirical track model is chosen as the theoretical framework because of its potential advantages over other techniques. The track of a typhoon is modeled, starting with its initial point and ending with its landfall location or point of final dissipation over the sea. Using this approach, a user can compute 6-h changes in hurricane heading, translation speed, and wind speed along this track as linear functions of previous values of those parameters as well as typhoon center location and Sea Surface Temperature (SST). Thus, a large database of synthetic tracks is generated that is based on a limited observed track compilation and a local climatological variable (i.e. SST). Vietnam is chosen as the case study for this research. The method is validated through comparisons between the hurricane statistics derived from the historical data and the simulated ones over the whole South China Sea region.
3.2. Data sources
The most important input for an empirical track model is the observed track record. For the Vietnamese case study, the RSMC Best Track Data [14] is used. This compilation is one of the most complete and recent databases, which includes the historical track for every single hurricane that occurred within the South China Sea area from 1951 to 2011. Another data collection used is the NOAA NCDC ERSST version 3b [15], which contains the global extended reconstructed monthly SST values. Finally, the digital coastline map of the South China Sea is provided by the NOAA National Geophysical Data Center (NGDC) Marine Geology & Geophysics Division and collocated by World Data Center for Marine Geology & Geophysics, Boulder [16]. 3.3. Empirical track modeling
The number of typhoons, which have to be simulated each year, is sampled from a negative binomial distribution with a mean value of 10.05 (hurricanes/year) and a standard deviation of 3.61 (hurricanes/year). This distribution is estimated using the observed annual number of hurricanes in the research area (i.e. the South China Sea). The starting position of typhoon center and all relevant parameters including the month of occurrence, heading, translation speed, and wind speed are sampled from a set of hurricane initiations. This series is derived from the surveyed track database by selecting the first location of each historical typhoon, which was inside the research area. The significance of this sampling method is to retain all the climatology data combined with any seasonal preferences for the point of hurricane initiation [11].
Given these original conditions, the new position, translation speed, heading, and wind speed are estimated based on the changes in these parameters over the current 6-h period using Equations 1, 2, and 3. They are written in a general form, which can be used for any time period (i.e. between the time steps i and i + 1):
Δlnci = lnci+1 − lnci = a1 + a2 Ψi + a3 λi + a4 lnci + a5 θi + a6 θi−1 + εi1 (1)
Δθi = θi+1 − θi = b1 + b2 Ψi + b3 λi + b4 ci + b5 θi + b6 θi−1 + εi2 (2)
ln(Ii+1) = c1 + c2 ln(Ii) + c3 ln(Ii−1) + c4 ln(Ii−2) + c5 Ti + c6 (Ti+1 - Ti) + εi3
(3) where Ψ and λ = latitude and longitude of typhoon center, respectively; c = translation speed; θ = heading; T = sea surface temperature; I = relative intensity; ε = random error.
The symbol Δ situated before each parameter de-notes the change of this quantity over the current period; the subscripts i and i + 1 specified for each parameter express the value at the corresponding time step; and a1, a2, etc. is a set of constants for each rectangular grid cell within the research area. When the hurricane travels from one grid cell to another, these values are changed accordingly. The constants are computed using a multiple linear regression solution. Because this process is repeated until the synthetic typhoon makes landfall or final dissipation over the sea, a full track is created, along with all main parameters, at each time step.
In order to improve the conventional empirical track approach by Vickery et al. [11], various model alternatives are also considered. By using the adjusted R2 statistics, one can determine the options, which are best suited to the specific conditions of the South China Sea (see Table 1, 2 and 3)
Table 1. All tracks vs Westerly/Easterly headed tracks.
Method All tracks Westerly/Easterly headed tracks
Formula 1 2 1 2
Tracks All All Westerly Easterly Westerly Easterly
Grid number No Obs Adj R2 No Obs Adj R2 No Obs Adj R2 No Obs Adj R2 No Obs Adj R2 No Obs Adj R2 1 117 0.0854 117 0.1656 6 0.5375 111 0.1072 6 0.2911 111 0.2652 2 230 0.1200 230 0.1921 25 0.5375 205 0.0910 25 0.2911 205 0.1597 3 293 0.1297 293 0.2571 48 0.1807 245 0.1159 48 0.3892 245 0.1189 4 144 0.1525 144 0.3673 2 0.0886 142 0.1169 2 0.3137 142 0.0748 5 663 0.1393 663 0.1090 47 0.0886 616 0.1327 47 0.3137 616 0.0560 6 1136 0.1799 1136 0.1482 199 0.3224 937 0.1363 199 0.2174 937 0.0410 7 447 0.1084 447 0.1473 8 0.0653 439 0.0940 8 -0.4853 439 0.1057 8 1253 0.1450 1253 0.1251 186 0.1399 1067 0.1431 186 0.1332 1067 0.0963 9 1585 0.1408 1585 0.1478 365 0.1086 1220 0.1548 365 0.1090 1220 0.1042 10 134 0.1200 134 0.2791 2 0.0987 132 0.1142 2 0.1232 132 0.1718 11 237 0.0828 237 0.1472 30 0.0987 207 0.0520 30 0.1232 207 0.1742 12 424 0.1070 424 0.2422 129 0.0904 295 0.1085 129 0.1631 295 0.1544 Total no Obs 6663 6663 1047 5616 1047 5616 6663 6663 Average adj R2 0.1394 0.1597 0.1351 0.1092
Table 2. Ordinary Least Squares (OLS) vs Robust multiple linear regression solutions.
Method OLS Robust ('talwar')
Formula 1 2 1 2
Grid number No Obs Adjusted R2 Adjusted R2 Adjusted R2 Adjusted R2
1 117 0.0854 0.1656 0.1446 0.1151 2 230 0.1200 0.1921 0.1301 -0.0003 3 293 0.1297 0.2571 0.1629 0.0234 4 144 0.1525 0.3673 0.1378 0.0032 5 663 0.1393 0.1090 0.1598 0.0539 6 1136 0.1799 0.1482 0.1830 0.0111 7 447 0.1084 0.1473 0.1261 0.2851 8 1253 0.1450 0.1251 0.1715 0.1306 9 1585 0.1408 0.1478 0.1526 0.0342 10 134 0.1200 0.2791 0.1130 0.1612 11 237 0.0828 0.1472 0.0753 0.1814 12 424 0.1070 0.2422 0.1555 0.1816 Average adjusted R2 0.1394 0.1597 0.1561 0.0834
Table 3. Different grid sizes.
Grid size (degrees) Lack-data grids Formula 1 Formula 2 Average
5.5 x 5.5 0 0.1526 0.1603 0.1564
5.0 x 5.0 0 0.1561 0.1597 0.1579
4.5 x 4.5 0 0.1535 0.1590 0.1563
4.0 x 4.0 0 0.1582 0.1566 0.1574
3.5 x 3.5 1 - - -
RESULTS AND DISCUSSIONS
The above methodology is validated through comparisons between historical and modeled statistics, which are obtained from a 10,000-year simulation over the entire South China Sea. Because the evaluation is given within the whole region, all typhoons are taken into account, even if they end at the ocean or only pass
through the research area. This is an improvement over the research by Vickery et al. [11]. In that pioneering study, only hurricanes that enter the sub-regions around certain Points Of Interest (POIs) are taken into account. Because those POIs are normally situated at the coastline, typhoons that do not make landfall were ignored, although they are still very important for various sectors. Synthetic hurricanes are initiated using available historical track records and propagated over water using Equations 1, 2, and 3 to estimate their locations and parameters. In terms of qualitative evaluation, the mean and standard deviation of translation speed, heading, and wind speed of both observed and simulated typhoons are computed and plotted in the same figures as shown in Figure 3. As one can clearly see in the figures, the modeled data are very close to the historical ones.
Figure 3. Qualitative comparison of the observed and simulated key parameters.
Figure 4. Quantitative comparison of the observed and simulated key parameters.
Quantitative assessment is also carried out by plotting the Probability Density Function (PDF) of both observed and simulated main statistics and computing the correlation coefficients between those values. The correlation coefficients are always between −1 and 1. When these quantities are close to 1, the historical and modeled data are highly (positively) correlated. Furthermore, a comparison between these PDFs can also be made with a chi-square statistic. When it is smaller than the critical value, the observed and simulated key parameters are considered to have the same distribution shape. With degree of freedom of 1 and
significance level of 0.05, the critical chi-square value is 3.84 [17]. Figure 4 gives these comparisons for translation speed, heading, and wind speed. In this figure, all the correlation coefficients are close to 1. The chi-square statistics are much smaller than 3.84. Therefore, one can conclude that the main statistics derived from simulation can describe observed hurricanes remarkably well.
CONCLUSION
A new modeling technique to simulate the entire track of a hurricane in the South China Sea region has been presented. Some crucial enhancements are proposed by using the empirical track framework to compensate for conditions in which there are data shortages. The model validation is executed over the entire research area and shows a very close correlation between observed and modeled data. There is persuasive evidence that indicates that this model has many improved features compared to other models. Moreover, all the required data can be searched and extracted from global databases. Thus, the methodology mentioned in this study can be applied to other research at different locations.
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