1 A Simple Procedure for the Estimation of Tropical-Cyclone (TC) Wind-Forces on Low-Rise Buildings in Mexico, Central America and the Caribbean (MxCA2) Jorge Sánchez-Sesma1, Alberto López López2, Adrián Pozos-Estrada3 1 Department of Hydrometeorology, Instituto Mexicano de Tecnología del Agua, Jiutepec, Morelos, México 2Department of Civil Engineering, Instituto de Investigaciones Eléctricas, Cuernavaca, Morelos, México 3Department of Applied Mechanics., Instituto de Ingeniería, Universidad Nacional Autónoma de México, México email: [email protected], [email protected], [email protected] ABSTRACT: During the last years, probabilistic definition of maximum wind speeds (MWS) due to tropical cyclones (TCs) in Mexico, Central America and the Caribbean (MxCA2) has been developed and published in technical manuals and papers. However, the increased (population and infrastructure) risks and losses due to TC winds puts forward the need to update and recommend simplified procedures for the application of that knowledge to the majority of structures in the MxCA2. Motivated by previous developments and the International Group for Wind-Related Disaster Risk Reduction (IG-WR-DRR) of IAWE, here, we present: firstly, background information about the historical modeling procedure and their results and secondly, a simple procedure for an assessment of TC wind forces over low-rise buildings (LRB). The possible distribution in internet and audiovisual means of the results is also analyzed and recommended. KEY WORDS: Tropical Cyclone; Maximum wind speed; Simplified design; Mexico, Central America and the Caribbean region 1 INTRODUCTION High winds associated with tropical cyclones are the cause of considerable damage to life and property in coastal areas of MxCA2. In order to reduce this damage without incurring excessive costs, both: designers of buildings and other structures and insurance analysts use probabilistic methods for which statistical information regarding wind speeds is a necessity. A number of studies have been carried out for this purpose. In 1971, Russell [13] obtained the maximum wind speed for Port Aransas, Texas through probabilistic simulation. This method has also been applied to other parts of the U.S., Australia and Asia [1, 5, 23, 24]. This simulation method requires knowledge of the probability distribution of the variables that characterize the phenomenon, and consequently requires a very complete database. These can be found in studies such as the one by Ho et al. [6]. In 1981, 1990 and 2006 the Institute of Electrical Research (Instituto de Investigaciones Electricas, IIE) in Cuernavaca, Mexico, initiated a research program aimed at providing information for the design of electric transmission lines and towers, and for general structures, against the effects of cyclone and other strong winds. Three similar studies were conducted on the information available on extreme wind speeds in Mexico [14, 2, 3], and resulted in isotach maps for different return periods. The last map obtained, and currently in use in Mexico, for a 200-year period is shown in Figure 1. These studies were developed on the basis of an historical reconstruction method proposed by Sánchez-Sesma [15] to estimate the maximum TC wind speeds. Results of this method were published by Sánchez-Sesma et al. [16] (from now SS88), from a study along the coast of the United States, giving results similar to those obtained in two previous research efforts that employed probabilistic simulation of TC wind fields. With respect to the work of Batts et al. [1], the mean deviation for the 100 (2000) year return period is 0.2% (1.8%), and the average of the absolute differences is 7.1% (8.3%). In the case of the results obtained in [5], these kind of differences are -3.2% (-2.6%), 7.5% (7.9%), respectively for the 100 (2000) yr periods. However, the maximum disagreements (with absolute differences near 30%) did appear in places where the greatest TC activity has occurred during the last decade, such as Miami and New Orleans. It should be noted that in the points of maximum disagreement, the historical reconstruction method provided the most conservative values. Taking into account all of these facts, a research project devoted to evaluate the risk level associated with TC wind speeds over the MxCA2 areas based on historical reconstruction of TC wind fields, as proposed by SS88, is described in this paper. In addition, a multi-decadal perspective of TC activity, their maximum winds, and their climatic and meteorological implications are also provided. 14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015 2 Figure 1. Isothac map for a return period of 200 years [3]. 2 DATA AND METHODS A description of the data, fluid dynamics aspects, statistical models and the calibration process are presented in the following subsections. 2.1 Historical TC tracks and intensities The National Hurricane Center of the National Oceanic and Atmospheric Administration (NHC/NOAA) has maintained a computer file on North Atlantic and NE Pacific TCs since the 1980s. This file, named HURDAT and EastPAC (Hurricane Database), contains dates, tracks, wind speeds and central pressure values (if available) for all TCs occurring since 1851 and 1949, respectively [9]. One important aspect to be taken into account is that the amount of records of the NE Pacific is smaller than that of the North Atlantic. The NE Pacific record has only 65 years, in contrast the HURDAT record has 100 years more. This temporal length is important because climatological information from more than 85 years is desirable, since a significant energy content associated with such periods has been observed in cyclonic wind spectra in previous studies [7, 26]. 2.2 Fluid dynamic models The fluid dynamic model that has been developed on the basis of previous studies [12, 17, 19, 20] can be described as follows: Using the radial balance of pressure and centrifugal forces, 2 Vg Vt sen 1 P ( f )Vg 0 (1) r r r an expression for the gradient wind is obtained, 1 kr kr 2 V [( )2 V ]2 (2) g 2 2 c where: 14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015 3 V sen k f t (3) r 2 1 D Vc (Pn P0 )rn exp(rn ) (4) where is a measured angle, from the hurricane center in anticyclonic gyre, of the site of interest with respect to the hurricane movement. At the point of maximum wind, this value is equal to: (5) 2 The radius at which the maximum wind speed occurs and the exponent D are given by the following relations which are obtained from the work of Vickery and Twisdale [21] and Vickery et al. [22]. 2 Rmax=exp{2.636-0.00005086.(dP) +0.0394899.L} (6) D= 1.38 + 0.00184dP - 0.00309Rmax (7) where Rmax is expressed in kilometers, D is adimensional, dP is pressure difference (inside/outside) in millibar, and L is the geographic latitude. The ratio of the gradient wind outside the surface boundary layer to the wind speed at the surface is given by the following relation [17]: Vs 0.56 H 0.64 exp(rn ) (8) Vg rn 2.3 Probabilistic models The Type I Extreme Value, or Gumbel probability distribution was considered for the present study [18, 25], defined as, V PVV ˆ exp expI (9) I where P represents the probability that the maximum wind speed V is less than the calculated value. For the purpose of statistical analysis these probability distributions are reduced to linear expressions through suitable transformations. A least square technique is used to adjust a straight line represented by y(x) to available data. Values of the parameters are found for a best fit. A correlation coefficient is also determined to estimate the quality of the straight line fit. 2.4 Historical reconstruction procedure Two main steps are involved in the calculation: 1) From individual recorded histories of over-sea cyclones, an evaluation is made of the maximum surface wind speeds at the coastal points of interest, 2) The proposed probability distribution is then adjusted to the evaluated information. First, the position, speed of travel and intensity for each hour of existence of each cyclone are calculated from recorded data, with interpolation using spline functions. The maximum gradient wind is then calculated from equation (1), based on information regarding the translation speed and latitude of the cyclone. Equations (2), (4) and (5) form a set, which can be solved iteratively for three unknowns R, p0 and Vg at the maximum wind point. The cyclostrophic wind velocity at any radius can now be calculated using equation (4) again, and the gradient and surface winds from equations (2) and (1). The maximum surface wind obtained is over sea for an averaging time of 60 seconds. The direction of the surface wind is calculated from equation (6). To evaluate its equivalent over grassland, and for an averaging time of one hour, a multiplication factor of 0.675 is used. This factor has been deduced based on the work of [4, 18]. Based on the results described, the values of the annual maximum surface wind speeds for different directions can be obtained and stored. 14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015 4 2.5 Calibration The fluid dynamic model reproduces at a specific coastal point the winds resulting from each one of the hurricanes that have affected it with acceptable precision. Further, after statistical and calibration based on observations and other simulations, the results of the predictions of trends and overall values are reasonably close to the actual observations and other estimations. Observations are coming from the coastal first class meteorological stations which are maintained by the national meteorological services in the CGM region.