b Department of Civil Engineering, Indian Institute of Technology Delhi, India,

Transcription

1 29 Probability Distributions for Cyclone Key Parameters and Cyclonic Wind Speed for the East Coast of Indian Region Pradeep K. Goyal a, T.K. Datta b a Govt. Engineering College, Ajmer,Rajasthan,India,351 pk_goyal23@yahoo.co.in b Department of Civil Engineering, Indian Institute of Technology Delhi, India, tushar_k_datta@yahoo.com Abstract This paper presents a study conducted on the probabilistic distribution of key cyclone parameters and the cyclonic wind speed by analyzing the cyclone track records obtained from India meteorological department for east coast region of India. The dataset of historical landfalling storm tracks in India from with latitude /longitude and landfall locations are used to map the cyclone tracks in a region of study. The statistical tests were performed to find a best fit distribution to the track data for each cyclone parameter. These parameters include central pressure difference, the radius of maximum wind speed, the translation velocity, track angle with site and are used to generate digital simulated cyclones using wind field simulation techniques. For this, different sets of values for all the cyclone key parameters are generated randomly from their probability distributions. Using these simulated values of the cyclone key parameters, the distribution of wind velocity at a particular site is obtained. The same distribution of wind velocity at the site is also obtained from actual track records and using the distributions of the cyclone key parameters as published in the literature. The simulated distribution is compared with the wind speed distributions obtained from actual track records. The findings are useful in cyclone disaster mitigation. Keywords: Tropical cyclones; Bay of Bengal; Simulation; Track; Wind speed 1. INTRODUCTION The Indian subcontinent is one of the six most vulnerable cyclone prone regions in the world. Approximately four to five cyclones and about one to two cyclones occur every year in the Bay of Bengal and in the Arabian Sea, respectively. The coastal states of Tamil Nadu, Andhra Pradesh, Orissa, West Bengal, and Gujarat are severely affected because of the occurrences of cyclonic storms. During the decade of 198 to 199, the estimated average annual loss was around Rs. 2 crores (44 million USD) and that between 1996 to 1999 was around Rs. 8 crores (Lakshmanan et al., 27). Wind and storm surge are the crucial factors in the determination of how much damage occurs in association with any particular tropical cyclone. Among this the damages arising due to strong winds is of particular importance in coastal areas. Thus, cyclone hazard analysis is very crucial in cyclone disaster mitigation system. Along the coastline of India, there are no credible direct measurements of wind speeds. As a result, no statistical analysis could be carried to find return periods of the cyclonic wind speeds from direct measurements. This is a major problem when considering cyclone wind statistics for hazard analysis or risk assessment of a region. The mathematical simulation of hurricanes is the most accepted approach for estimating wind speeds for the design of structures and assessment of hurricane risk. The simulation

2 21 Probability Distributions for Cyclone Key Parameters and Cyclonic Wind Speed for the East Coast of Indian Region approach is used in the development of the design wind speed maps in the United States. Russell (1971) first employed mathematical simulation methods to estimate hurricane wind speeds for the Texas coast. Others used the similar mathematical simulation methods to estimate design wind speeds for the US coastlines (Russell and Schueller, 1974; Tryggvason, et al., 1976; Georgiou, et al., 1983; Vickery and Twisdale, 1995a, 1995b). The study of Batts, et al. (198) was a milestone and the first study to examine the entire U.S. coastline, which provided a rational way to determine the design wind speeds of the Gulf and Atlantic coasts of the United States. The basic approach in all these studies is similar in that the site specific statistics of key parameters including central pressure difference, radius of maximum winds, heading, translation speed, and the landfall location or distance of closest approach are obtained. In this paper, the probability distribution functions of cyclone key parameters are obtained from the landfalling track records of Indian coastal region. These probability distributions are compared with those available in the literature. Using these probability distributions, distribution of the cyclonic wind speed for a particular site in the coastal region is obtained and compared with the distribution obtained from actual track records. 2. DATA SOURCES AND CYCLONIC KEY PARAMETERS For the present study, landfalling tropical storms formed over the Bay of Bengal during the period are considered. The hourly latitude/longitude information of cyclone tracks are collected from the Journals of Meteorology and Geophysics, Regional Specialised Meteorological (RSMC) reports, Mausam Journals published by India Meteorological Department (IMD) and database of the Joint Typhoon Warning Centre (JTWC). The latitude/longitude information of cyclone tracks is mapped and landfall locations are assigned. Key cyclone parameters are defined as the parameters which can uniquely determine a wind field. These key parameters are (i) central pressure difference, p (ii) the radius of maximum wind speed, R max, (iii) the translation velocity of cyclone track, V T, and (iv) track angle with site (α). 2.1 Central Pressure Difference The maximum difference between storm central pressure (p o ) and pressure at the storm periphery (p e ) of a cyclone denoted as p, plays a very important role in determining the wind speed. The pressure at the storm periphery (p e ) is assumed as the ambient atmospheric pressure ( hpa). In the absence of central pressure information from track records, the central pressure can be estimated using the pressure-wind relationship, given the sustained wind speed (V m ) of the cyclone. Mishra and Gupta (1976) has developed a regionally based relationship for the Indian seas. The relationship is Vm = ( pe po) (1) where p e is the peripheral pressure and p o is the pressure at the centre of the storm. The central pressure difference can be calculated by using the relation p = p o (2) 2.2 Radius of the Maximum Wind Speed The radius of maximum wind speed, R max, is the radial distance between the vortex and region of maximum wind speeds. Radius of maximum wind is one of the key variable associated with the structure of a cyclone. Unfortunately, database of JTWC and IMD do not include the data of radius of maximum wind of the cyclonic storms. Therefore, the radius of maximum wind for different wind speeds in the Bay of Bengal has been taken from World Meteorological Organisation (WMO) and is shown in Table 1 (WMO, 21). International Journal of Ocean and Climate Systems

3 Pradeep K. Goyal, T.K. Datta 211 Table 1. Radius of maximum wind for different wind speeds Cyclonic Maximum Wind Radius Class Disturbance Speed (km/h) (km) D Depression DD Deep depression CS Cyclonic storm SCS Severe cyclonic storm SCSH Severe cyclonic storm with hurricane intensity SSCS Super cyclonic storm > Translation Velocity V T denotes the translation velocity of cyclone track. It can be obtained by dividing the distance between two points of storm track by the travel time. Distance between two positions (point) of storm track can be calculated by using Haversine formula as given below. lat = lat lat 2 1 long = long2 long1 2 2 a = sin ( lat / 2) + cos( lat1).cos( lat2).sin ( long / 2) c = 2. atan2( a, ( 1 a)) d = Rc. (3) where lat 1 and lat 2 are the latitudes of point 1 and point 2, respectively, long 1 and long 2 are the longitudes of point 1 and point 2, respectively, the two argument function atan2 is a variation of the arctangent function, R is the radius of earth (mean radius = 6,371 km), and d is the distance between point 1 and Heading Direction Cyclone Heading direction (θ ) is determined by using harvesting formula. In this study, the heading direction towards north is defined as zero, while clockwise is positive and counter clockwise negative. θ = atan (sin( long).cos( lat ),cos( lat ).sin( lat ) sin( lat ).cos( lat ).cos( long)) (4) 2.5 Track Angle with Site Track angle with north is calculated as per the procedure followed in heading direction. Track angle with site (α) is determined by using heading direction and track angle with north. 3. METHODOLOGY The first step of cyclone wind hazard exposure analysis is to establish a cyclone recurrence model for the site of interest. Cyclone recurrence rate is derived from the frequency of past cyclones or the occurrence in region of interest. The probabilistic model of recurrence is usually described by homogeneous (uniform) Poisson distribution (Batts et al., 198; Georgiou et al., 1983; Chang, 23), Markov chain process model, and periodic Poisson process (Russell and schueller, 1974). The homogeneous Poisson process has been widely accepted as an appropriate model to describe the annual recurrence rate of cyclonic events. The probability of n cyclones occurring at time t can be expressed as: n ( λt) Pnt (, ) = e n! λt (5) where P(n, t) is the probability function and λ is the average tropical cyclone occurrence rate per year.

4 212 Probability Distributions for Cyclone Key Parameters and Cyclonic Wind Speed for the East Coast of Indian Region The second step consists of finding gradient wind speed as a function of cyclone key parameters. For this purposes, the wind speed distribution in the radial direction is determined from the equilibrium between the centrifugal force of a rotating air mass with the atmospheric pressure gradient and the Coriolis forces. The gradient wind speed (Holmes, 21) can be written as 2 2 rf f r r p V = + + g 2 4 ρ r (6) where f is the Coriolis parameter (= 2Ω sin Φ); Φ is the latitude and Ω is the angular velocity of Earth, p r is the radial distance from the storm centre to the point of interest, ρ is the density of air, and is r the horizontal pressure gradient. Using Eq. (6) a suitable function for pressure gradient can be established (Holland, 198). A p= p + pe p ( )exp B r (7) where p is the pressure of the site of interest, p o is the central pressure of the tropical cyclone, p e is the atmospheric pressure at the edge of storm ( p e is the undisturbed environmental pressure), r is the distance from the storm centre to the point of interest and A and B are scaling parameters. The pressure difference (p e p o ) can be expressed in the form p, and is an indication of the strength of the storm. Differentiating Eq. (7) and substituting in Eq. (6), we have: V 2 2 rf r f p AB A = + + exp 2 4 ρ r r g B B (8) Scale parameters A and B are related with the radius of maximum wind as R A B max = 1/ (9) By using Eq. (8) and Eq. (9) V g 2 2 rf r f = + + B p R 2 4 ρ r max B R exp r max B (1) Hubbert et al. (1991) suggested that B could be empirically determined by ( 98 p B o ) = (11) 12 where p o is the central pressure of a tropical cyclone. After the translation of hurricane is taken into account, the 1-minute average wind speed at 1-meter above the sea surface (Chang and Lindell, 25) can be given by 63. V = 8. V V cosα 1 g T (12) where V 1 denotes the 1-minute average wind speed at 1-meter above the sea surface, V g denotes the gradient wind speed given by Eq. (1), V T denotes translation velocity of the cyclone centre, and α denotes the angle between the hurricane track and surface wind direction in region of interest based on wind field model as shown in Figure 1. The 1-minute average wind velocity can be converted into different time period interval (Durst, 196; Krayer and Marshall, 1992; WMO, 1983). Note that International Journal of Ocean and Climate Systems

5 Pradeep K. Goyal, T.K. Datta 213 N ( p, V T, R max, θ) θ α r Site Coast line Cyclone Track Figure 1. Wind field model 1-minute average wind speed is considered following the norms adopted by the United States National Weather Service (USNWS) which defines sustained winds within tropical cyclones by averaging winds over a period of one-minute (National Weather Service, 28). This is an important distinction between WMO and USNWS is defining the sustained winds within tropical cyclones. The value of 1-minute average sustained wind speed is reported to be 14% greater than a 1 minutes average sustained wind speed as adopted by WMO (Sampson et al., 1995). The third step consists of estimating the probability of cyclonic wind speed exceeding a given threshold speed at a given site in a given time period. The information about wind speeds and occurrences is combined as follows. The wind speed data derived from the cyclones passing through the region of interest are rank ordered and then used to define the wind speed probability distribution conditional on storm being within 25 km of the site, F v [P(V < v)]. The probability that the tropical cyclone wind speed V is exceeded a threshold value v during time period t is PV ( > vt, ) = PV ( > vn) Pnt (, ) n= where PV ( > vn) is the probability of cyclone wind speed V being greater than v given that n storms occur, P(n, t) denotes the probability of n hurricanes occurring during the specified period of time t, n is the number of cyclones occurring during specified time t, and t is the specified period of time. Substituting Eq. (5) into Eq. (13) gives: (13) n t PV ( vt, ) ( Fv ) ( λ > = 1 ) n! n= n e λt (14) Recognizing the summation in Eq. (14) is the series expansion of exponential function, Eq. (14) becomes: PV vt e t F v ( >, ) = λ 1 1 ( ) (15) This is an analytical expression of the cyclone hazard analysis (Chang and Lindell, 25). In order to obtain the wind speed in the region of interest using actual track data, the following procedure is followed: (i) All landfalling storm tracks based on hourly latitude/longitude information are mapped. (ii) A circle of 25 km radius is circumscribed around centre of the site.

6 214 Probability Distributions for Cyclone Key Parameters and Cyclonic Wind Speed for the East Coast of Indian Region (iii) Cyclone wind speeds at the centre of a site due to storm tracks passing through its circle are calculated using wind field model (Eq. 12). (iv) CDF of the cyclonic wind speed at site is calculated based on the wind speeds derived from the wind field model. (v) Annual mean occurrence rate of cyclones is calculated by dividing total storm tracks passing through the circle by the total number of years. (vi) Probability of exceedance (Hazard curve) can be estimated using Eq. (15). 3.1 Artificial Generation of Distribution of Velocity at a Site using the Published Distribution of the Cyclone Key Parameters The distribution of wind velocity at a particular site is obtained from the storm track data using a methodology described in the previous section for Indian region. The distribution of wind velocity at the site of interest is simulated using the distributions of the cyclone key parameters published in the literature. The distributions of the key parameters include those of the central pressure difference ( P), translation speed (V T ), radius of maximum wind (R max ), heading of cyclone track (θ ), minimum distance between the site of interest and cyclone centre, D min. Once a site of interest has been selected, a circle of influence is circumscribed around the site. The radius of simulation circle is set as 25 km (Georgiou et al., 1983). Several methods exist for locating tropical cyclone paths with respect to any geographical point. Tracks are simulated as straight line paths as shown in Figure 2, defined as θ by their approach angle (θ ), taken as clockwise positive from north, and minimum distance of approach, D min. When a track passes to the left of a site of interest, D min is taken as positive. The first step of wind field simulation is to establish cyclone recurrence model for thesite of interest. The homogeneous Poisson process has been accepted widely as an appropriate model to describe the annual recurrence rate of cyclonic events as described earlier (Eq. 5). After establishing the validity of recurrence model, the probability models of cyclone key parameters are obtained by analyzing the historical cyclonic wind data obtained from the database. Potential probabilistic distributions for these key parameters described from the historical analysis of historical data are shown in Table 2. These parameters are then used to generate simulated cyclones using wind field simulation techniques. Circle of Influence N θ Region of Interest D min Figure 2. Spatial definition of tropical cyclone tracks (Georgiou et al., 1983) International Journal of Ocean and Climate Systems

7 Pradeep K. Goyal, T.K. Datta 215 Table 2. List of distributions of key cyclone parameters Random Variables Key Cyclone Parameters Distribution λ Annual occurrence rate Poisson* p Maximum difference between cyclone central and Lognormal peripheral pressure Weibull* R max The radius of maximum wind speed Lognormal* Normal V T Storm track speed Lognormal* Normal θ Heading of cyclone track Lognormal Normal* Bi-normal Von-Mises D min Minimum distance between the storm and site of interest Uniform* Polynomial Trapezoid *Represents the distributions used for simulating the wind speed A group of cyclone key parameters are generated randomly from the probability distributions. Using these simulated values of the cyclone key parameters, different sets of values for all the cyclone key parameters are generated. Each set represents a particular combination and gives a value of V 1 at a site using Eq. (12). Thus, a set of artificially generated cyclonic wind at the site is obtained and the CDF of the data set calculated. With the help of an assumed value of λ for the Poisson model and the CDF, the hazard curve for the site is determined. 3.2 Proposed Distribution of Cyclone Key Parameters for East Coast of Indian Region The statistical distribution of the key cyclone parameters are derived from actual data of central pressure difference, translation velocity, radius of maximum wind, heading direction of all landfalling tropical cyclones on Indian coastal region formed in Bay of Bengal. The latitude/longitude information for each storm track is mapped and landfall locations are assigned as shown in Figure 3. The key parameters are calculated using the methods as given in section Since each site individually has too few data for the cyclone key parameters, it is difficult to get any good distribution from the data for each site. Therefore, data of the sites located in the eastern side, i.e., Andhra Pradesh, Orissa, Tamil Nadu, West Bengal are grouped together to get the distribution of cyclone key parameters and the same distributions are assumed to hold good for all sites in the eastern region. Standard statistical techniques are employed to determine the best fit distributions. In order to validate this assumption, it is necessary to perform a sensitivity analysis of the distributions of wind speed obtained for different sites of the states (Andhra Pradesh, Orissa, Tamil Nadu, and West Bengal) by using the simulated cyclone key parameters and compare them with those obtained by using actual track records. Such a study is computationally intensive. However, taking one site near the middle of each state, a sensitivity analysis is carried out and results are shown in Figure 4. It is seen from Figure 4 that deviation between the two distributions (actual track record and simulated) for a particular state is insignificant and therefore, the assumption of using the same distributions of cyclone key parameters for entire eastern region seems to be reasonably valid.

8 216 Probability Distributions for Cyclone Key Parameters and Cyclonic Wind Speed for the East Coast of Indian Region Figure 3. Historical storm tracks in Bay of Bengal CDF Actaul Track Data (A.P.) Using Indian Distributions (A.P.) Actual Track Data (Orissa) Using Indian Distributions (Orissa) Acuual Track Data (W.B.) Using Indian Distributions (W.B.) Actaul Track Data (T.N.) Using Indian Distributions (T.N.) Wind Speed (m/s) Figure 4. Comparison of CDFs between those obtained by simulated and actual track record International Journal of Ocean and Climate Systems

9 Pradeep K. Goyal, T.K. Datta NUMERICAL STUDY The state of Andhra Pradesh is the most disaster prone state in the Indian Union. Therefore, a particular site near the coastal regions of Andhra Pradesh is taken as the example problem for the numerical study. The location of the site A is shown in Figure Proposed Distribution of Cyclone Key Parameters for Indian Coastal Region The distributions of the cyclone key parameters are obtained from the track records for the site using the method describe before. They are compared with the distributions of key cyclone parameters reported in the literature (given in Table 2). The distributions are shown in Figures 6-9. In Figure 6, the histograms obtained for the central pressure difference are shown. Two standard distributions, namely Weibull and lognormal, are fitted to the histograms as shown in the same figure. From the Chi-square and K-S tests, it was observed that lognormal distribution fits best to the histograms. From Table 2, it is seen that one of the reported distributions in the literature is the lognormal distribution (Batts et al., 198). In Figure 7, histograms of radius of maximum wind (RMW) are shown. Three distributions, namely lognormal, normal, and logistic are fitted to the histograms and shown in the same figure. From the Chisquare and K-S test, lognormal distribution is found to be the best fit for the radius of maximum wind. Table 2 shows that the distribution as obtained from Indian data is the same as that observed elsewhere (Georgiou et al., 1983; Vickery and Twisdale, 1995a; Huang et al., 21). Figure 5. Cyclone Tracks passing through the radius of influence

10 218 Probability Distributions for Cyclone Key Parameters and Cyclonic Wind Speed for the East Coast of Indian Region.6.5 Data Longnormal Distribution Weibulll Distribution.4 PDF Central pressure Difference (hpa) Figure 6. Probability density function of central pressure data PDF Data Lognormal Distribution Normal Distribution Logistic Distribution Radius of maximum wind (km) Figure 7. Probability density function of radius of maximum wind.1.8 Data Normal distribution PDF Heading Direction (degs) Figure 8. Probability density function of storm heading data International Journal of Ocean and Climate Systems

11 Pradeep K. Goyal, T.K. Datta 219 PDF Data Weibull Distribution Normal Distribution Lognormal Distribution Translation wind speed (m/s) Figure 9. Probability density function of forward motion PDF of storm heading direction is shown in Figure 8. Normal distribution is found to be the best fit from Chi-square and K-S tests. Table 2 shows that the distribution as obtained from Indian data is the same as that observed elsewhere (Huang et al., 21). Histograms of translation velocity are shown in Figure 9. Three distributions, namely Weibull, lognormal and normal are fitted to the histograms of translation wind velocity. A Weibull distribution ranks first as the best fit for the translation speed. Lognormal distribution ranks second. It is seen from Table 2 that the distribution of translation velocity (found elsewhere) is given as either lognormal/ normal. Thus, there is some variation in the distribution of the key parameter of translation velocity (for Indian condition) compared to those in the literature. This kind of deviation is expected because characteristics of the cyclonic wind speed are likely to vary from region to region and from country to country. Distributions of other key parameters (for Indian condition) confirm to the distributions reported in the literature. 4.2 Distributions of Wind Velocity The distributions of wind velocity at the particular site is obtained from (i) actual track records (procedure given in section 3), (ii) procedure outlined in section 3.1 using the distributions of the key parameters given in Table 2, and (iii) procedure given in section 3.1 using the distributions of key parameters for Indian region as shown in section 4.1. Note that in (ii) and (iii), the wind velocities are artificially generated. They are not the actual measured wind velocities. For generating the wind velocities for the case (ii), the distributions with asteric mark in Table 2 are used, while for the case (iii), the distributions as observed in section 4.1 are used. For both the cases, the mean and standard deviation of the key parameters like, p, V T, etc. required for generating the data for a particular site are obtained from the track record data are shown in Table 3. The distribution obtained for the case (iii) is termed as Indian distribution. Figure 1 compares the distributions of wind velocity at the site obtained from the three cases. It is seen from the figure that the Indian distribution is very close to that obtained directly from the track records. This validates both the simulation procedure and distributions for cyclone key parameter for Indian region. Further, it is seen from Figure 1 that the results of simulation procedure using the distribution of key parameters published in the literature also compare well with the other two distributions. This shows that distributions of cyclone key parameters given in the literature are applicable in general and, therefore, can be used for places where enough statistical data are not available. The hazard curves for the site obtained using the three distributions are compared in Figure 11. It is seen from the figure that three hazard curves also compare very well. In order to examine the applicability of the above validation over the entire spatial domain considered in the study, three more

12 22 Probability Distributions for Cyclone Key Parameters and Cyclonic Wind Speed for the East Coast of Indian Region Table 3: Statistical distributions and distribution parameters Parameter Mean COV Distribution Distribution Parameters Annual occurrence.625 Poisson* λ =.625 rate, λ Heading angle, Normal* µ = σ = θ (degrees) Central pressure Lognormal* µ = σ =.5936 difference, Weibull a = b = p(hpa) Radius of maximum Lognormal* µ = σ =.174 winds, R max (km) Translation velocity, Weibull* a = b = 2.34 V T (m/s) Lognormal µ = σ =.438 D min (km) Uniform* a =.2; R x R * Represents the distributions of cyclonic key parameters for Indian region CDF.4 Actual Track Data.2 Using Indian Distributions Using Distributions from Literature Wind Speed (m/s) Figure 1. Comparison of CDF of the cyclonic wind speed (site A; Figure 5) Annual Probability of Exceedance Actual Track Data Using Indian Distributions Using Distributions from Literature Wind Speed (m/s) Figure 11. Comparison of annual probability of exceedance of the cyclonic wind speed (site A; Figure 5) International Journal of Ocean and Climate Systems

13 Pradeep K. Goyal, T.K. Datta 221 sites B, C, D as shown in Figure 4 are selected. Distributions of wind speed obtained from the actual track data and simulation procedure for these three sites also compared well as shown in Figures CD F Actual Track Data Using Indian Distributions Using Distributions from Literature Wind Speed (m/s) Figure 12. Comparison of CDF of the cyclonic wind speed (site B; Figure 5) CDF.4 Actual Track Data.2 Using Indian Distributions Using Distributions from Literature Wind Speed (m/s) Figure 13. Comparison of CDF of the cyclonic wind speed (site C; Figure 5) CD F.4.2 Actual Track Data Using Indian Distribution Using Distributions from Literature Wind Speed (m/s) Figure 14. Comparison of CDF of the cyclonic wind speed (site D; Figure 5)

14 222 Probability Distributions for Cyclone Key Parameters and Cyclonic Wind Speed for the East Coast of Indian Region 5. CONCLUSIONS A method for obtaining the distribution of cyclonic wind speed for a region of interest using cyclone track record data is presented. Further, the distributions of cyclone key parameters for the Indian coastal region are also obtained from the track records and are compared with those available in the literature. For selected sites, cyclonic wind speed distribution and the hazard curves are obtained directly from the track records and are compared with those obtained from the simulation procedure. Results of the study lead to the following conclusions: (i) The distributions of Indian cyclone key parameters namely, central pressure difference, radius of maximum wind speed and storm heading direction are the same as reported in literature. Only the key parameter, translation velocity has marginally different distribution than that reported in the literature. (ii) The distribution of the wind speed and the hazard curve obtained from simulation procedure compare extremely well with those obtain directly from track records. (iii) The distributions of the cyclone key parameters as given in the literature can be used for simulating cyclone wind speeds in areas where enough track record data is not available. 6. REFERENCES Batts, M.E., Russell, L.R. and Simiu, E. (198). Hurricane Wind Speeds in the United States. Journal of the Structural Division, ASCE, 16(ST1), pp Chang, L. (23). Typhoon Risk Analysis and GIS Applications for China s Southeast Coast. Master Thesis, School of Civil Engineering, Harbin Institute of Technology, Harbin, China. Chang, L. and Lindell, M.K. (25). Hurricane Wind Risk Assessment for Miami-Dade Country, Florida: A Consequence Based Engineering (CBE) Methodology. CBE Report for the Mid- America Earthquake (MAE) Center. Durst, C.S. (196). Wind Speeds over Short Periods of Time. The Meteorological Magazine, 89, pp Georgiou, P.N., Davenport, A.G. and Vickery, B.J. (1983). Design Wind Speeds in Regions Dominated by Tropical Cyclones. Journal of Wind Engineering and Industrial Aerodynamics, 13(1-3), pp Huang, Z., Rosowsky, D.V. and Sparks, P.R. (21). Long-term Hurricane Risk Assessment and Expected Damage to Residential Structures. Reliability Engineering and System Safety, 74(3), pp Holland, G.J. (198). An Analytic Model of the Wind and Pressure Profiles in Hurricanes. Monthly Weather Review, 18(8), pp Holmes, J.D. (21). Wind Loading of Structures, Spon Press, New York. Hubbert, G.D., Holland, G.J., Leslie, L.M., and Manton, M.J. (1991). A Real Time System for Forecasting Tropical Cyclone Storm Surges. Weather and. Forecasting, American Meteorological Society, 6(1), pp Krayer, W.R. and Marshall, R.D. (1992). Gust Factors Applied to Hurricane Winds. Bulletin of American Meteorological Society, 73 (5), pp Lakshmanan, N., Arunachalam, S., Gomathinayagam, S. and Rajan, S.S. (27). Cyclone and Wind disaster mitigation An Overview of R&D Contributions of Structural Engineering Research Centre. Journal of Structural Engineering, 34(1), pp.1-13 Mishra, D.K. and Gupta, G.R. (1976). Estimation of Maximum Wind Speeds in Tropical Cyclones Occurring in Indian Seas. Indian Journal of Meteorology, Hydrology and Geophysics, 27(3), pp National Weather Service (28). Tropical Cyclone Definitions. Tropical Cyclone Weather Services Program, NWSPD 1-6. National Oceanic & Atmospheric Administration, Silver Spring, MD, USA. International Journal of Ocean and Climate Systems

15 Pradeep K. Goyal, T.K. Datta 223 Russell, L.R. (1971). Probability Distributions for Hurricane Effects. Journal of Waterways, Harbors, and Coastal Engineering Division, ASCE, 97(1), pp Russell, L.R. and Schueller, G.F. (1974). Probabilistic Models for Texas Gulf Coast Hurricane Occurrences. Journal Petroleum Technology, pp Sampson, C. R., Jeffries, R. A., Neumann, C. J., and Chu, J-H. (1995). Tropical Cyclone Intensity. Tropical Cyclone Forecasters Reference Guide, NRL Rep. NRL/PU/ Tryggvason, B.V., Surry, D., and Davenport, A.G. (1976). Predicting Wind-Induced Response in Hurricane Zones. Journal of Structural Division, ASCE, 12(12), pp Vickery, P.J. and Twisdale, L.A. (1995a). Prediction of Hurricane Wind Speeds in the United States. Journal of Structural Engineering, ASCE, 121(11), pp Vickery, P.J. and Twisdale, L.A. (1995b). Wind-field and Filling Models for Hurricane Wind Speed Prediction. Journal of Structural Engineering, ASCE, 121(11), pp WMO (1983). Global Guide to Tropical Cyclone Forecasting. World Meteorological Organization, Report No. TCP-31, TD-No.56, Geneva, Switzerland. WMO (21). Tropical Cyclone. Operational Plan for the Bay of Bengal and the Arabian Sea, Tropical Cyclone Programme, Report No. TCP-21,WMO/TD-No.84, World Meteorological Organization, Geneva, Switzerland.