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. Not only the maximum wind speeds registered are needed but also wind direction, time of occurrence, surrounding terrain conditions (roughness), and measurement system characteristics and localization above mean level ground are also needed for an homogenization process and comparison with the reconstructed winds [14, 2, 3].
3 RESULTS
3.1 Historical reconstruction of TC wind speeds Based on the HURDAT database of TC paths and intensities, and using spline functions, the position, speed of travel and intensity for each hour of existence of each cyclone were calculated. Later, with this information the corresponding windfield is evaluated, and speed and direction in sites of interest must be calculated and archived. Maximum wind speeds due to cyclones over the North West Atlantic have been determined. More than 3600 points were studied. Through the application of VELCICT, an algorithm written in FORTRAN, omnidirectional annual maximum wind speeds were calculated as a first step. For each reconstructed and calibrated TC wind speed population over the sites of interest in the CGM region, a probability extreme distribution has been estimated, by an automatic process with RMS error minimization. With these probability distributions, maximum values associated with different risk or probability of exceedence has been calculated.
3.2 Verification To verify the results, we employed the TC-MWS simulated along the coast of the USA [1]. The 48 coastal sites analyzed are separated by 50 nautical miles along the Atlantic coast. For the same coastal sites located in each of distances from 150 up to 2400 nautical miles, wind speeds were historically reconstructed with the hurricane updated model described previously and with the also updated VELCICT algorithm. The verification was applied based on the maximum wind speeds of TCs on these coastal sites for 50, 100 and 200 year return periods. Adjusted probability distributions of extreme value type I, or Gumbel were applied both to simulated and reconstructed TC wind in the U.S. and Mexico. The results of this calibration were displayed in SS88. The quality of calibration is given by the ratio of TC-MWS obtained from simulated and reconstructed wind speeds from along the Atlantic coast. It should be noted that the TC-MWS estimated in this study, for mileposts at 650 and 700 nm, are greater than those of the studies developed in the U.S. The speeds estimated in this study are 24, 18 and 5% higher than the speeds estimated in the U.S. by [1, 21, 24], respectively.
3.3 Maximum TC wind speeds The resulting calibrated maximum TC wind speed maps for the CGM region obtained for the 200-year return period is presented in Figure 2. Its values are hourly averaged at 10 m above a terrain with a type 2 roughness (grassland). Type I probability distribution and a sampling period of three years were applied, resulting in correlation coefficients higher than 0.98 in most cases.
14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015 5
a)
b) Figure 2. Estimated maximum TC wind speeds for 200 yr return period [m/s] in a) the Atlantic, and b) the Pacific coasts of the MXCA2 region. Values are hourly averaged at 10 m above a terrain with a roughness type 2.
Differences and trends for different periods have also been analyzed. Figure 3 displays corridors of increases (decreases) in the southern (northern) CGM region for the TC MWS in the last 50 years (recent period), with respect to the last 150 years. It means that if we have only data after 1950 our estimation over the coastal areas are more conservative than those estimations based on the complete record with data after 1851. It can be justified because during the last decades solar activity shown its multidecadal maximum for the last 8000 years [27].
14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015 6
Figure 3. Comparison ratio of TC MWS in the CGM region for 200-yr return period, of reconstructed winds from the (1950 – 2006) and (1851 – 2006) periods.
This kind of analysis made on the Atlantic winds can be extrapolated to the Pacific winds where the available information is really coming after 1949. It is very important because it can be supporting and justifying the use of the NE Pacific TC MWS based on the 1949-2006 records as conservative wind speeds.
4 SIMPLE PROCEDURE TO CALCULATE WIND-INDUCED PRESSURES ON LOW-RISE SCHOOL BUILDINGS CONSIDERING TC WINDS A simple procedure to design low-rise school buildings was proposed for the new standard of the National Institute for Educational Physical Infrastructure [28]. The simple procedure considers the evaluation of the design pressure by multiplying the dynamic pressure times a local pressure coefficient. To determine the dynamic pressure, the wind velocities obtained from the estimated maximum TC wind speeds are considered as well as geostrophic winds. This procedure can be applied if the structure satisfies the following: • The maximum height of the structure is 15 m, • The footprint of the structure is rectangular or composed by a combination of rectangles, • The relation between the average height to the smaller dimension in plane is less than 4. Since most of the Mexican schools in hurricane-prone areas are built with roof overhangs, as shown in Figure 4, it was decided to include this case for the determination of wind pressures in the simplify procedure. For the determination of wind pressures over low-rise school buildings, sketches were proposed and shown also in Figure 4.
The exterior and interior pressure coefficients suggested in the simplify procedure are summarized in the table 1.
For cladding, the exterior pressure coefficient should be multiplied by a local factor of 1.5. Near the edges of walls and roofs (dash lines in Figure 4), a local factor of 2 for the design of components to increase the exterior pressure coefficient should be used. The width near the edges of walls and roofs, should be equal to 0.2 of the least horizontal dimension or the total height, whichever is less.
14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015 7
Zones affected by local pressure coefficients
a) b) Figure 4. Mexican schools in hurricane-prone areas with roof overhangs: a) Photograph and b) Zones affected by local pressure coefficients (walls, roofs and overhang roofs)
Table 1. Exterior and interior pressure coefficients.
Location Cpe Openings location Cpi
Windward wall 0.8 Openings in the windward surface 0.75
1 Leeward wall -0.4 Openings in the leeward surface -0.6
Lateral walls -0.8 Openings in the surfaces parallel to the wind -0.5
Flat roofs -0.8 Openings regular distributed in the building envelope -0.3
-1.0 for 0º<≤20º 2 Windward roofs Openings in roofs (close to leeward) -0.7 -1.0<0.05-2.0<0.5 for 20º<0º
Leeward roofs -0.7 Openings in roofs (close to windward) 0.8
Openings in gable or flat roofs3 +/-0.3
Notes: 1) Suction should be considered constant along the height of the windward wall and should be calculated for the average height of the
wall; 2) is the roof slope, in degrees; 3) where two values of Cpi are listed, roof structure shall be designed for the worst condition.
5 CONCLUSIONS A historical reconstruction modeling is applied to update the probabilistic definition of maximum wind speed due to tropical cyclones (TC) on the Mexico, Central America and the Caribbean (MxCA2) coastal areas. Using an updated fluid dynamic model, the history of the tropical cyclone winds is first reconstructed for places distributed over the MxCA2 region from information of paths and intensities. A probabilistic treatment then permits an estimation of the maximum wind speed associated with different return periods, using probability distributions. Previous and recent results from this modeling are similar to those obtained from more elaborated methods in Mexico and USA coastal areas. However, these reconstructed winds show higher speeds for TC prone areas. The modeling has been triple successfully used as part of a large computation scheme to improve coastal wind predictions in Mexico. The TC wind speeds were incorporated into a simple procedure to calculate wind-induced pressures on low-rise school buildings. We are sure that this simple procedure will be very beneficial to designers, since provides an easy to use methodology to consider wind effects on typical MxCA2 low-rise school buildings in high-wind regions. The final version of this work not only will provide several practical examples of common structures in the MxCA2 region, but also will explore possible distribution in internet and audiovisual means.
ACKNOWLEDGMENTS Jorge Sánchez-Sesma acknowledges, as a member of the International Group for Wind-Related Disaster Risk Reduction (IG- WR-DRR) of the IAWE, motivation given by this group challenges about the need for education and technical information in wind related hazards. Adrián Pozos-Estrada would like to thank the support provided by IIUNAM and CONACYT. Also, we thank NOAA for HURDAT database, with the registered TC best track information data. This work was partially carried out
14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015 8
with the aid of MAPFRE and a grant from the Inter-American Institute for Global Change Research (IAI) CRN-II-2050, which is supported by the US National Science Foundation (GEO- 0452325). The information provided by INIFED is gratefully acknowledged.
REFERENCES [1] Batts, M.E., Cordes, M.R., Russell, L.R., Shaver, J.R., and Simiu, E. "Hurricane wind speeds in the U.S.A.", NBS Building Science Series 124, Department of Commerce, National Bureau of Standards, Washington, D.C., 1980. [2] CFE (Comisión Federal de Electricidad), Manual de Diseño de Obras Civiles, Cap. C-1-4, Diseño por Viento, 1993. [3] CFE (Comisión Federal de Electricidad), Manual de Diseño de Obras Civiles, Diseño por Viento, Mexico, 2008. [4] Davenport, A.G., "Wind structure and wind climate", Proceedings, the International Research Seminar on Safety of Structures Under Dynamic Loading, Norwegian Institute of Technology, Throndheim, 209-256, 1978. [5] Georgiou, P.N., Davenport, A.G. and Vickery, B.J., "Design wind speeds in regions dominated by tropical cyclones," J. Wind Engng. and Ind. Aerodyn., Vol. 13, 139-152, 1983. [6] Ho, F.P., Schwerdt, R.W. and Goodyear, H.V., "Some climatological characteristics of hurricane and tropical storms, Gulf and East Coasts of the United States", NOAA Tech. Rep. NWS 15, Washington, D.C., 1975. [7] Ishizaki, H., "Wind damage and wind load problems in Japan," Proc. U.S.A.- Japan Res. Seminar: Wind Loads on Structures, Hawaii, 1-12, 1970. [8] Jarvinen, B.R., C.J. Neumann, and M.A.S. Davis, A tropical cyclone data tape for the North Atlantic basin, 1886–1983, NOAA Tech. Memo., NWS NHC 22, 21 pp. (Available at http://www.nhc.noaa. gov/pdf/NWS-NHC-1988-22.pdf), 1984. [9] Landsea, C.W., C. Anderson, N. Charles, G. Clark, J. Dunion, J. Fernandez-Partagas, P. Hungerford, C. Neumann, and M. Zimmer, "The Atlantic hurricane database re-analysis project: Documentation for the 1851–1910 alterations and additions to the HURDAT database, in Hurricanes and Typhoons: Past, Present and Future", edited by R.J. Murname and K.-B. Liu, pp. 177–221, Columbia Univ. Press, New York, 2004. [10] Landsea, C.W., D.A. Glenn, W. Bredemeyer, M. Chenoweth, R. Ellis, J. Gamache, L. Hufstetler, C. Mock, R. Perez, R. Prieto, J. Sanchez-Sesma, D. Thomas, and L. Woolcock, "A Reanalysis of the 1911-20 Atlantic Hurricane Database". Journal of Climate, 21, p.2138-2168, 2008. [11] Landsea, C.W., "A Reanalysis of the 1911-20 Atlantic Hurricane Database". Nature, 21, p.2138-2168, 2006. [12] Graham, G.E. and Nunn, D.E., "National Hurricane Research Project", Report No 33, Weather Bureau, U.S. Dept. of Commerce, Washington, D.C. [13] Russell, L.R., "Probability distributions for Hurricane effects", J. Waterways, Harbors and Coastal Engng. Div., Proc. ASCE, Vol. 97, No. WW1, 139-154, 1959, 1971. [14] Sánchez-Sesma, J., Aguirre, R.J. and Villegas, V.A., ”Maximum wind speeds in México for structural design purposes," IV Congreso Nacional de Ingenier'ia Estructural, Leon, Guanajuato, Mexico, G110-G119 (in Spanish), 1984. [15] Sánchez Sesma, J., "Vientos máximos debidos a ciclones tropicales," Master’s thesis, Facultad de Ingeniería, UNAM, Mexico. 1985. [16] Sánchez-Sesma, J. et al., “Simple Modeling Procedure for Estimation of Cyclonic Wind Speeds”, Journal of Structural Engineering, 144, 2, 353-370, 1988. [17] Scholoemer, R.N., "Analysis and synthesis of hurricane wind patterns over Lake Okeechobee", Florida, U.S. Weather Bureau Hydrometeor. Rep. No. 31, 1954. [18] Simiu, E. and Scanlan, R.H., "Wind effects on structures: An introduction to wind engineering", 2nd ed., John Wiley and Sons, New York, 1986. [19] Springall, R.G., "Study and statistical analysis of waves produced by hurricanes in the Southeast Gulf of Mexico," Instituto de Ingeniería, U.N.A.M, Mexico City, Rep. No. 361 (in Spanish), 1980. [20] Holland, G.J., "An analytic model of the wind and pressure profiles in hurricanes", Mon. Wea. Rev., 108, 1212–1218, 1980. [21] Vickery, P.J., and Twisdale, L.A., "Wind-field and filling models for hurricane wind-speed predictions". J. Struct. Engrg., ASCE, 121 (11), 1700-1709, 1995a. [22] Vickery, P.J, Skerlj, P.F., Steckley, A.C., and Twisdale, L.A., "Hurricane wind field model for use in hurricane simulations", J. Strct. Engrg., ASCE, 126 (10), 1203-1221, 2000a. [23] Vickery, P.J, and Twisdale, L.A., "Prediction of hurricane wind speeds in the risk in the United States", J. Struct. Engrg., ASCE, 121 (11), 1691-1699, 1995b. [24] Vickery, P.J, Skerlj, P.F., Steckley, A.C., and Twisdale, L.A., "Simulation of hurricane risk in the U.S. using empirical track model", J. Strct. Engrg., ASCE, 126 (10), 1222-1237, 2000b. [25] Yevjevich, V., "Probability and statistics in hydrology," Water Resources Publ., Ft. Collins, Colorado, 1972. [26] Russell, L.R. and Schueller, G.I., "Probabilistic models for the Texas Gulf Coast Hurricane occurrences," J. Petroleum Tech., 279-288, 1974. [27] Solanki, S. K., I. G. Usoskin, B. Kromer, M. Schüssler, and J. Beer, "Unusual activity of the Sun during recent decades compared to the previous 11,000 years", Nature, Vol. 431, No. 7012, 1084–1087, 2004. [28] INIFED, "Escuelas-seguridad estructural de la infraestructura física educativa-requisitos", in Spanish, Mexico, 2015.
14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015