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\title{An Extensive Evaluation of the Proposal for "Unified Terrain Categories Exposures and Velocity Profiles" by Choi (2009)}
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             \author[1]{S. A.  Hsu}

             \affil[1]{  Louisiana State University}

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\date{\small \em Received: 8 December 2012 Accepted: 31 December 2012 Published: 15 January 2013}

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\begin{abstract}
        


The proposal for ?unified terrain categories exposures and velocity profiles? by Choi in 2009 has been evaluated extensively. On the basis of 6 articles in open literature (3 papers during Typhoon Muifa in 2011, one during Hurricane Ike in 2008, one during Typhoon Sally in 1996, and one during an atmospheric dispersion experiment in New York City, USA) and nearly simultaneous upper-air measurements when available, it is found that the proposed criteria (except the displacement height) by Choi are evaluated to be useful operationally for engineering applications. An alternative approach using the mean building height (rather than the displacement height)as the input to estimate the power-law exponent and the gradient height is prosed for practical use. 

\end{abstract}


\keywords{Typhoon Sally, Typhoon Muifa, Hurricane Ike, Tall buildings, Power-law exponent, Roughness length, Gradient height, Displacement height, Terrain expos}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
uilding or structural damages by storms, whether they are tropical or extra-tropical cyclones, require an estimation of wind speed. Numerous methodologies have been proposed and used (see, e.g. \hyperref[b19]{Wieringa, 1992}\hyperref[b21]{, Zhou and Kareem, 2002}\hyperref[b12]{, and Irwin, 2006)}. Most recently, \hyperref[b3]{Choi (2009)} has proposed his "Unified Terrain Categories Exposures and Velocity Profiles" as presented in Table \hyperref[tab_0]{1}. The purpose of this study is to evaluate Table \hyperref[tab_0]{1}. II. 
\section[{An Evaluation During Typhoon Muifa in 2011}]{An Evaluation During Typhoon Muifa in 2011}\par
During Typhoon Muifa in 2011 there are 3 studies which can be used for our evaluation. They are: a) Wind Measurements at Two Locations on the Sutong Bridge\par
According to \hyperref[b20]{Xu et al (2013)}, the SutongBridge across the low reaches of the Yangtze River in China is a cable-stayed bridge with its longest span, which is under constant monitoring because of tropical cyclones and other strong winds. During Typhoon Muifa in 2011, there were two anemometers on the bridge. The mean wind speed measured at 76m was 17.08 m/s and at 300.4 m 19.58 m/s, respectively. Using the power-law wind profile formula (see, e.g. \hyperref[b7]{Hsu, 1988)}, we have U2/U1 = (Z2/Z1)\textasciicircum p Note that U2 and U1 are the wind speeds at height Z2 and Z1, respectively. P is the exponent of the power law. Now, compare this over-water p (=0.100) with that in Table \hyperref[tab_0]{1} for open water in Category I in which p = 0.103, we can say that the agreement is excellent. Note that the p (=0.10) value has been measured over the Sicily Strait by \hyperref[b7]{Hsu(1988)}, over the Gulf of Mexico by \hyperref[b8]{Hsu et al. (1994)} under fair weather condition and by \hyperref[b9]{Hsu (2011)} under hurricane condition.Note also that these measurements on the Sutong Bridge are unique in that it was over a large (the Yangtze)river. While the power law has been discussed above, the log law is presented as follows:\par
In the atmospheric boundary layer, vertical distribution of the wind speed (under strong wind conditions so that the thermal effects may be neglected, see \hyperref[b10]{Hsu, 2003)} can be formulated according to the logarithmic wind profile (e.g. \hyperref[b14]{Panofsky and Dutton, 1984)} as:Uz = (U*/k) Ln ((Z-d)/Z 0 ) (3)\par
Where Uz is the wind speed at height Z, U* is the friction velocity, k (=0.4) is the von Karman constant, d is the displacement height, and Z0 is the roughness length.\par
Note that when Z is much larger than d, Eq. (  {\ref 3}) may be reduced toUz = (U*/k) Ln (Z/Z 0 ) (4)\par
Statistically, Eq.(  {\ref 4}) can be written asLn Z = Ln Zo +(k/U*) Uz (5) Y = a 0 + a 1 X\par
Where Y = Ln Z, X = Uz, and Zo =Exp(a 0 ) \hyperref[b6]{(6)} Analysis of the log law is presented in Fig.  {\ref 2}. Since approximately 95 per cent of the wind speed variation with height can be explained by this law (because R 2 = 0.95), we can get Zo = 0.223. Figure  {\ref 2} : Verification of logarithmic wind profile during Typhoon Mufia in 2011 on the east coast of Shanghai, China Analysis of power law is provided in Fig.  {\ref 3}, which demonstrates that nearly 96 per cent of the wind speed variation with height can be explained by the power law so that p = 0.194. Note that since R2 is higher for the power law than that for the log law, we can say that the former is as good as the latter for engineering applications. Before the analyses of upper-air data are performed, the concept of virtual potential temperature, v, needs to be discussed briefly, since it can serve as a stability criterion for an atmosphere with a moisture gradient.For more detail, see \hyperref[b17]{Stull (1988)}. For our analyses, we need to know that when vis constant, the atmospheric boundary layer is statically neutral. When it decreases with height, the atmosphere is statically unstable. When it increases with elevation, the atmosphere is statically stable. Since the power-law wind profile is valid within a neutral boundary layer, we need to plot this virtual potential temperature value with height so that the gradient height can be determined.y = 0.2124x -\par
Figs. 4 thru 9 show our results during Typhoon Muifa in 2011 near Shanghai. It can be seen from Figs. 6 and 9 that the average gradient height during these two rawisondings is (677 + 611)/2 = 644 m, which is close to the value of 650 m as proposed in Table \hyperref[tab_0]{1} for Category VI.Note that at 12Z on 06 August 2011, the wind was light and variable near the ground as shown in Figs.  {\ref 4 and 5}, but at 611 m, the wind speed was 17 m/s and direction from 40 degrees. Similar condition was prevailed 12 hours later (Figs.  {\ref 7 and 8}), but the direction was from 315 degrees with a speed of 7.2 m/s near the ground. At 611m, the speed increased to 26.3 m/s and the direction was from 340 degrees.  Height, in meters Virtual potential temperature, in degrees kelvin   {\ref 1}) is presents in Fig. 11, which also indicates that the exponent is determined to be 0.35. This value is close to 0.362 as proposed in Table \hyperref[tab_0]{1} for Category IV.   \hyperref[tab_0]{1}, this value is expected to be the same as that of the wind speed at 650 m over NYC. So, we set U 650m = 10.6 m/s tocompute the wind speeds located at the three rooftops.\par
For the rooftop at 229m, we have These computed values are listed in Table 2 so that they can be compared to the measurements as provided in \hyperref[b6]{Hanna et al (2007)}. Since the margin of error in wind speed measurement is 10 \% as stated above, we can say based on Table \hyperref[tab_5]{2}, that the agreements are excellent and Table \hyperref[tab_0]{1} is evaluated here as useful.  IV. 
\section[{Global Journal of Researches in Engineering}]{Global Journal of Researches in Engineering}\par
An Evaluation using Measurements in Houston, Texas, during Hurricane Ike in 2008\par
When Hurricane Ike passed over the City of Houston, Texas, in September 2008 (see \hyperref[b1]{Berg, 2008)}, there were two wind speed measurements at 20 and 60 meters on a 91 meter communication tower (see \hyperref[b16]{Schade, 2012)}which are useful for our evaluation as follows: a) A Comparison of Boundary-layer Parameters with Table \hyperref[tab_0]{1} According to Schade (2012), several boundarylayer parameters are available for the comparison as shown in Table \hyperref[tab_4]{3}. It can be seen that the Tower in Houston is located in Category V. While both values of roughness parameter and power-law exponent are in excellent agreement, the displacement is not. A recent study of zero-plane displacement height, d, in a highly built-up area of Tokyo shows that the value of d may not be determined from the average building height because ofthe large difference in building heights (see \hyperref[b18]{Tanaka et al., 2011)}. Therefore, values of the displacement height as listed in Table \hyperref[tab_0]{1} needto be further evaluated. But, for now, it is listed only as a general guide. In order to evaluate the tower measurements from Houston, we need to first determine the power-law exponent from nearby Hobby Airport, which was not exactly located in open country but between Categories II and III. This is accomplished as follows:\par
According to Hsu (2013), the power-law exponent, p, can be determined from the 5-second gust over 2 minute (sustained wind speed) period as used in wind speed measurements by the Automated Surface Observing System (ASOS) station at airport worldwide such that,G = 1 + 2.04 P (7)\par
Where G is the gust factor (the ratio of 5-s gust to 2-min sustained wind speed) and p is the power-law exponent. Fig.  {\ref 12} shows that since G = 1.3672 at Houston Hobby Airport, P = 0.180, indicating this location was between Categories II and III. Because there is no further classification, we need to produce the statistical relationships amongst roughness length, power-law exponent and the gradient height. On the basis of Table \hyperref[tab_0]{1}, these relationships are analyzed and presented in Figs.  {\ref 13 through}    
\section[{E}]{E}\par
With these methods we can compute the wind speeds at the two heights on the Houston tower as follows:\par
Based on Fig.  {\ref 13}, given p = 0.180 for Houston Hobby Airport, the gradient height is estimated to be 395 m; From Fig.  {\ref 12}, the max sustained 2-min wind speed over Hobby was approximately 34 m/s. Therefore the wind speed at the gradient height of 395 m over Hobby Airport is U 395m = U 10m *(395/10) \textasciicircum  0.18 = 34 * 1.94 = 66 m/s, According to  {\ref Schade (2007)}, the mean turbulence intensity was 0.29 for the tower. According to Hsu (2013), the power-law exponent, p, is numerically equal to the turbulence intensity. We can assign p = 0.29 for this tower location. Thus, from Fig.  {\ref 13}, the gradient height over the tower is 565 m. Now, we can now compute the wind speed at 60 m at the tower to be U 60m = U 565m *(60/565) \textasciicircum  0.29 = 66 * 0.52 = 34 m/s.\par
Similarly, the wind speed at 20 m on the tower is computed asU 20m = U 565m *(20/565) \textasciicircum  0.29 = 66 * 0.38 = 25 m/s.\par
A comparison of these estimations against the measurements is presented in Table \hyperref[tab_7]{4}. It is found that the agreement is excellent, indicating that our methodology as provided above is operational. V. 
\section[{An Evaluation using mean Building Height as Input}]{An Evaluation using mean Building Height as Input}\par
As stated above, the construction of few super tall buildings (building height > 300 m) in several cities makes the estimation of displacement difficult. However, for many urban areas, it is still useful to employ the mean building height as an input to estimate the displacement height. This is done as follows:\par
According to the data as provided in \hyperref[b2]{Burian et al (2005)}, which is listed in Table \hyperref[tab_8]{5}, we can say that the displacement height is approximately 72 per cent of the mean building height in the downtown core areas in the cities as studied. This value is reasonably close to that of 80 \% as suggested by  {\ref Panofsky and Dutton (1984, P.376)}, since the difference is about 10 \%. Zo = 0.2 d\textbf{(8)}\par
Since the coefficient of determination, R 2 =0.97, is very high, Eq. ( \hyperref[formula_6]{8}) should be useful operationally. An Evaluation using Typhoon Sally in 1996 over Hong Kong and Shenzhen, China\par
Full-scale monitoring of typhoon effects on super tall buildings was conducted during the passage of Typhoon Sally in 1996 (see \hyperref[b13]{Li et al., 2005)}. For our evaluation, we employ the measurements at Cheung Chau. From the position provided in \hyperref[b13]{Li et al (2005)}, this station is located in Category I. According to  {\ref Hsu (1988, p. 202}), P = 0.10 and Hsu (1988, pp. 126-127), the gradient height = 250 m. These values are in excellent agreement with Category I as listed in Table \hyperref[tab_0]{1}.\par
Further verification of the gradient height over Hong Kong City is presented in Figures  {\ref 18 and 19}, which show the distinct characteristics of two layer flow with the separation elevation located at 694 m in both wind speed (Fig.  {\ref 18}) and direction (Fig.  {\ref 19}). Since the difference between this measured value of 694 m and the proposed value of 650 m is approximate 6 percent, we may use the proposed value as a first approximation. With the aforementioned verification of the gradient height in mind, we can now comparethe wind speed measurements atop the tall buildingand the wind speed estimates from Table \hyperref[tab_0]{1} in Hong Kong.\par
First, on the basis of the measured max wind speed of 37.5 m/s at 92 m at Cheung Chau, the wind speed at 250 m over that station (Cat. I) is U 250m =U 92m * (250/92) \textasciicircum 0.103 = 37.5 *1.11 =41.6 m/s. This max speed is expected to be the same at U650m over Hong Kong and Shenzhen so that the max wind speeds atop of the Central Plaza Tower at 374 m in Hong Kong and Di Wang Tower at 384 m in Shenzhen are estimated from Table \hyperref[tab_0]{1} for Cat. VI as U 374m = U 650m * (374/650) \textasciicircum  0.362 = 41.6 * 0.82 = 34.1 m/s, and U 384m = U 650m * (384/650) \textasciicircum  0.362 = 41.6 *0.83 = 34.5 m/s, respectively. These results are compared with measurements as shown in Table \hyperref[tab_9]{6}.  Since the average difference is (0.13 + 0.03)/2 = 0.08 or 8 \%, which is within 10 \% for the composite margin of error for wind speed measurements, it is reasonable to say that Table \hyperref[tab_0]{1} is evaluated to be useful operationally. 
\section[{VII.}]{VII.} 
\section[{Conclusions}]{Conclusions}\par
A proposal based on Choi in 2009 for "unified terrain categories exposures and velocity profiles" has been evaluated extensively in this study. This evaluation includes 3 separate papers published most recently under the conditions of Typhoon Muifa in 2011 over the greater Shanghai, China, region, one study during Hurricane Ike in 2008 over Houston, Texas, USA, one paper for super tall buildings (> 300m) during Typhoon Sally in 1996 over Hong Kong and Shenzhen, China and one study during an atmospheric dispersion experiment in New York City, USA. In addition, in order to support the evaluation of gradient height, upper-air sounding measurements are acquired and analyzed when appropriate. On the basis of these evaluations, it is found that the criteria as shown in Table \hyperref[tab_0]{1} are useful operationally for engineering applications except the designation of the displacement height which requires further investigation. An alternative approach using the mean building height as the input for the power-law exponent is proposed.\par
Year 2013 Volume ( ) E\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}}\end{figure}
           \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.048006644518272426\textwidth}P{0.4927740863787375\textwidth}P{0.05789036544850498\textwidth}P{0.05647840531561462\textwidth}P{0.05083056478405316\textwidth}P{0.04941860465116279\textwidth}P{0.09460132890365448\textwidth}}
\tabcellsep \tabcellsep \tabcellsep B\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep v VI Version I\\
Category\tabcellsep Exposure (description)\tabcellsep Roughness Length, meters\tabcellsep Power-law exponent\tabcellsep Gradient Height,meters\tabcellsep Displacement Height, meters\tabcellsep XIII Issue\\
Cat I\tabcellsep Open water and coastal areas (open sea or lake\tabcellsep 0.002\tabcellsep 0.103\tabcellsep 250\tabcellsep 5\tabcellsep \\
\tabcellsep with few\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep obstructions)\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Cat II Cat III Cat IV\tabcellsep Open country (terrain with scattered obstructions up to 10 m high. Rural areas with a few low rise buildings) Forest/Sub-urban scattered low (3-5 m) buildings (numerous closely spaced 3-5 m obstructions) Urban, large town\tabcellsep 0.04 0.2 0.5\tabcellsep 0.15 0.198 0.241\tabcellsep 350 450 500\tabcellsep 5 10 15\tabcellsep Global Journal of Researches in Engineering\\
\tabcellsep (many medium height (10-50 m)\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep buildings)\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.6039473684210526\textwidth}P{0.08087044534412954\textwidth}P{0.04817813765182186\textwidth}P{0.005161943319838057\textwidth}P{0.013765182186234818\textwidth}P{0.010323886639676113\textwidth}P{0.005161943319838057\textwidth}P{0.013765182186234818\textwidth}P{0.06882591093117409\textwidth}}
\multicolumn{9}{l}{An Extensive Evaluation of the Proposal for "Unified Terrain Categories Exposures and Velocity Profiles"}\\
\tabcellsep \tabcellsep \multicolumn{3}{l}{by Choi (2009)}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
4.00\tabcellsep \tabcellsep \multicolumn{2}{l}{1.5006}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
3.50\tabcellsep \multicolumn{2}{l}{R² = 0.946}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
3.00\tabcellsep \multicolumn{3}{l}{Zo = 0.223}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
2.50\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
2.00\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
1.50\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
1.00\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0.50\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0.00\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0.00\tabcellsep 5.00\tabcellsep \multicolumn{2}{l}{10.00}\tabcellsep 15.00\tabcellsep 20.00\tabcellsep \tabcellsep 25.00\tabcellsep 30.00\\
\multicolumn{3}{l}{(Data Source : Peng et al, 2013)}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0.35\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0.3\tabcellsep \multicolumn{2}{l}{y = 0.194x}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0.25\tabcellsep \multicolumn{2}{l}{R² = 0.957}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0.2\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0.15\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0.1\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0.05\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
0\tabcellsep 0.2\tabcellsep 0.4\tabcellsep 0.6\tabcellsep 0.8\tabcellsep 1\tabcellsep 1.2\tabcellsep 1.4\tabcellsep 1.6\\
\multicolumn{3}{l}{(Data Source : Peng et al, 2013)}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{9}{l}{Figure 3 : Verification of power-law wind profile during Typhoon Mufia in 2011 on the east coas t of Shanghai, China}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep © 2013 Global Journals Inc. (US)\end{longtable} \par
 
\caption{\label{tab_1}Ln Z Wind speed, Uz, in m/s}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.4558529945553539\textwidth}P{0.3262704174228675\textwidth}P{0.06787658802177858\textwidth}}
Now, comparison of theseZo = 0.223 and p = 0.194 values to those in Table 1, we can see that the\tabcellsep speed reaches 32.97 m/s at 494 m on the rooftop. With this data we can evaluate Cat. VI using Table 1 that p =\\
measurement site in Peng et al (2013)was located at Category III. Since values of Zo and p are consistent with those provided in Table 1, we can say that Cat. III is verified.\tabcellsep 0.198 for Cat. III. First, we need to estimate the wind speed at 450 m by applying the power law as follows: U 450m /U 10m = (450/10) \textasciicircum  0.198 = 2.12\\
c) Wind speed measurements at 494 m atop the Shanghai World Financial Center during Typhoon Muifa in 2011 An et al (2012) present their wind mea-surements atop the Shanghai World Financial Center (SWFC) during Muifa. The maximum 10-min mean wind\tabcellsep U 450m = 18.53 * 2.12 = 39.37 m/s This value is expected to be the same at 650 m over SWFC. Now, the wind speed at 494 m atop SWFC is estimated to be\\
\multicolumn{2}{l}{U 494m = U 650m *(494/650) \textasciicircum  0.362 = 39.37*0.91 = 35.65 m/s}\tabcellsep Year 2013\\
\tabcellsep \tabcellsep 3\\
\tabcellsep \tabcellsep v VI Version I\\
\tabcellsep \tabcellsep XIII Issue\\
\tabcellsep \tabcellsep Volume\\
\tabcellsep \tabcellsep ( ) E\\
\tabcellsep \tabcellsep Global Journal of Researches in Engineering\end{longtable} \par
  {\small\itshape [Note: d) Upper-air Measurements from Shanghai during MuifaAs indicated in Table1, the gradient height over measurement at this altitude at present time, we employ the routine upper-air sounding called rawinsonding instead. According to\hyperref[b5]{Geer (1996)}, rawinsonde is a method of upper-air observation consisting of an evaluation of the wind speed and direction, as well as temperature, and humidity aloft by means of a balloonborne radiosonde (instrument package) tracked utilizing position change as determined by directional radio techniques. Note that rawinsonde measurements are routinely available twice per day at many places around the world including Shanghai, China (see www.ncdc.noaa.gov).]} 
\caption{\label{tab_2}Ln (U2/U1) Ln (Z2/Z1)}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.7323076923076923\textwidth}P{0.019615384615384614\textwidth}P{0.019615384615384614\textwidth}P{0.019615384615384614\textwidth}P{0.019615384615384614\textwidth}P{0.019615384615384614\textwidth}P{0.019615384615384614\textwidth}}
305\tabcellsep 306\tabcellsep 307\tabcellsep 308\tabcellsep 309\tabcellsep 310\tabcellsep 311\\
\multicolumn{7}{l}{Figure 6 : Rawinsonding of virtual potential from Shanghai, China, at 12Z on 06 Aug 2011 during Typhoon Muifa}\end{longtable} \par
 
\caption{\label{tab_3}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.85\textwidth}}
)\end{longtable} \par
 
\caption{\label{tab_4}Table 3}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.3133838383838384\textwidth}P{0.24898989898989898\textwidth}P{0.14166666666666666\textwidth}P{0.14595959595959596\textwidth}}
\multicolumn{4}{l}{measured wind speeds at 3 heights in NYC (Data}\\
\tabcellsep \multicolumn{2}{l}{source: Hanna et al, 2007)}\tabcellsep \\
R Rooftop height, m\tabcellsep Measured Wind speed,m/s\tabcellsep Computed Wind speed, m/s\tabcellsep Difference in Per cent\\
229\tabcellsep 7.3\tabcellsep 7.3\tabcellsep 0 \%\\
153\tabcellsep 5.8\tabcellsep 6.3\tabcellsep 8 \%\\
34\tabcellsep 3.6\tabcellsep 3.6\tabcellsep 0 \%\end{longtable} \par
 
\caption{\label{tab_5}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.4529940119760479\textwidth}P{0.11706586826347305\textwidth}P{0.15269461077844312\textwidth}P{0.1272455089820359\textwidth}}
\tabcellsep \multicolumn{2}{l}{Source Roughness}\tabcellsep \\
\multicolumn{2}{l}{Source Roughness Length, Zo,}\tabcellsep Power-law Exponent, p\tabcellsep Displacement Height, m\\
\tabcellsep m\tabcellsep \tabcellsep \\
Houston\tabcellsep 1.0\tabcellsep 0.29\tabcellsep 8\\
Tower\tabcellsep \tabcellsep \tabcellsep \\
Table 1\tabcellsep 1.0\tabcellsep 0.289\tabcellsep 20\\
\multicolumn{4}{l}{b) A Comparison of Wind Speed Measurements}\end{longtable} \par
 
\caption{\label{tab_6}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.09132231404958678\textwidth}P{0.3512396694214876\textwidth}P{0.19669421487603306\textwidth}P{0.21074380165289255\textwidth}}
\tabcellsep \multicolumn{2}{l}{Hurricane Ike in 2008}\tabcellsep \\
Height, m\tabcellsep Estimated wind Speed, m/s\tabcellsep Measured Speed, m/s wind\tabcellsep Difference In per cent\\
60\tabcellsep 34\tabcellsep 33\tabcellsep 3 \%\\
20\tabcellsep 25\tabcellsep 25\tabcellsep 0 \%\end{longtable} \par
 
\caption{\label{tab_7}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.6806311881188118\textwidth}P{0.06206683168316831\textwidth}P{0.012623762376237623\textwidth}P{0.059962871287128704\textwidth}P{0.03471534653465347\textwidth}}
\tabcellsep \multicolumn{3}{l}{Burian et al, 2005)}\tabcellsep \\
City\tabcellsep Mean\tabcellsep building\tabcellsep Displacement\tabcellsep Ratio\\
\tabcellsep \multicolumn{2}{l}{Height in}\tabcellsep Height, d, m\tabcellsep \\
\tabcellsep \multicolumn{2}{l}{Downtown, m}\tabcellsep \tabcellsep \\
Los Angeles\tabcellsep \tabcellsep 45\tabcellsep 27.38\tabcellsep 0.61\\
Houston\tabcellsep \multicolumn{2}{l}{22.8}\tabcellsep 19.87\tabcellsep 0.87\\
Oklahoma\tabcellsep \multicolumn{2}{l}{19.4}\tabcellsep 13.14\tabcellsep 0.68\\
City\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Albuquerque\tabcellsep \tabcellsep 14\tabcellsep 12.93\tabcellsep 0.92\\
Phoenix\tabcellsep \multicolumn{2}{l}{16.2}\tabcellsep 11.55\tabcellsep 0.71\\
Portland\tabcellsep \multicolumn{2}{l}{18.1}\tabcellsep 9.97\tabcellsep 0.55\\
\tabcellsep \tabcellsep \tabcellsep mean\tabcellsep 0.72\\
\multicolumn{5}{l}{Using Table 5, we can now analyze and plot the}\\
\multicolumn{5}{l}{relationship between the mean building height and}\\
\multicolumn{5}{l}{the displacement height. Since there are only 6}\\
\multicolumn{5}{l}{cities, this R 2 = 0.76 is considered to be useful as}\\
\multicolumn{5}{l}{a first approximation. This is needed since there are many cities in the hurricane or typhoon prone areas,}\\
\multicolumn{5}{l}{which does not have the survey of the displacement}\\
\multicolumn{5}{l}{height as those shown in Table 5, but the mean}\\
\multicolumn{5}{l}{building heights in many downtown areas are}\\
\multicolumn{5}{l}{known as published in the National Building Statistics Database: Version 2 by the Los Alamos}\\
\multicolumn{5}{l}{National Laboratory (Publication Number LA-UR-08-}\\
1921).\tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_8}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6} \par 
\begin{longtable}{P{0.85\textwidth}}
Sally in 1996\end{longtable} \par
 
\caption{\label{tab_9}Table 6 :}\end{figure}
 			\footnote{© 2013 Global Journals Inc. (US)An Extensive Evaluation of the Proposal for "Unified Terrain Categories Exposures and Velocity Profiles" by\hyperref[b3]{Choi (2009)} } 			\footnote{© 2013 Global Journals Inc. (US)} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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\end{document}
