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Regression analysis of local wind properties with local topographic factors
Journal of Wind Engineering and Industrial Aerodynamics 74—76 (1998) 175—187
Regression analysis of local wind properties with local topographic factors H. Utsunomiya!,*, F. Nagao!, I. Urakami" ! Department of Civil Engineering, The University of Tokushima, Minamijosanjima 2-1, Tokushima 770, Japan " Okayama Prefectural Office, Uchiyamasita 2-4-6, Okayama, Japan
Abstract To improve the accuracy of estimation of local strong wind, new local topographic parameters were introduced in the multiple regression analysis. New azimuthal topographic factors were defined independently of particular radius of fan-shaped area for the estimation of usual topographic factors. In addition to them, some micro-scale local terrain factors were defined from scenery pictures of 16-azimuths around the site. The azimuthal strong wind velocity at a construction site was evaluated through the two-step estimation, in which the representative wind speed at a site was estimated by first regression analysis with the usual topographic factors and second regression analysis with newly defined micro-scale factors was followed to estimate the azimuthal wind speed fluctuation. It was shown that the new topographic factors defined here played an important role in all regression analyses. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Local topographic factors; Regression analysis of local wind properties; Two-stepestimation of azimuthal wind speeds
1. Introduction The exact estimation of strong wind velocity at a construction site is important to evaluate the wind load on a structure and various methods have been proposed in former studies [1—7]. The best method is a long-term observation at a site but it is usually difficult by the restriction of a construction term. The use of a wind map obtained from long-term observations of meteorological stations is a convenient
* Corresponding author. E-mail: [email protected]. 0167-6105/98/$19.00 ( 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 0 1 5 - 4
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method and some design specifications include standardized wind maps combined with some local terrain information. However, they are not always sufficient for exact estimation because of the loose mesh size of the stations and the complexity of terrain like the Japanese Islands. Wind tunnel test with a topographic scaled model is a forceful method for the estimation in spite of including some similarity problems, but it requires a high cost and large scale of the wind tunnel. The regression analysis with topographic factors is a conventional method for the estimation of local wind properties, but a large amount of error was still included in the results of former studies, in which topographic factors took different values corresponding to the particular radius for the evaluation of them. To improve the accuracy of the regression analysis on the azimuthal wind velocities of a site, two different types of new topographic factors such as the micro-scale and azimuthal topographic factors were introduced here. The former was defined from the scenery pictures around the site while the latter was defined uniquely without any restriction of evaluating radius for each azimuthal area. All the data used in this analysis were obtained at the AMeDAS observatories in Shikoku Island described in the following section and these observatories were located at the positions where the wind velocity was heavily influenced by the surrounding local topographies. The regression analysis showed that these new factors had an important role in estimating the local wind properties. The estimation of local strong wind velocity was carried out by the two-stepestimation method. The representative mean wind velocity at a particular site was estimated by the result of first-step regression analysis with ordinary topographic factors and the azimuthal wind velocities fluctuating from the representative wind velocity were obtained by second regression analysis with micro-scale and newly introduced topographic factors. It became clear also that the two-step estimate was very effective to evaluate the azimuthal wind velocities.
2. Observation sites Sample data of wind velocity were obtained from the records of AMeDAS observatories and topographic factors were also obtained corresponding to each observatory sites. There are 1300 observatories of AMeDAS (Automated Meteorological Data Acquisition System) all over the Japanese Islands as a meteorological network system. There are 43 observatories of AMeDAS in Shikoku Island, southwest of Japan, from which typical 29-observatories were chosen for the analysis here as indicated in Fig. 1. Fourteen observatories were eliminated from the analysis by the following reasons: (1) the positions of the observatories were moved during the past 10 years, (2) the positions were located at small islands or on a steep slope, (3) high-rise buildings or structures were there in close vicinity to the observatories and (4) the CCD camera position to evaluate the topographic factors from its scenery pictures was different from the anemometer height.
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Fig. 1. Location of AMeDAS observatories in Shikoku Island.
3. Regression analysis 3.1. Wind data Mean wind velocities and wind directions averaged for 10 min in every 1 h obtained at the AMeDAS observatories during ten years from 1983 to 1992 were used to estimate the mean wind velocity and its relative frequency of occurrence of wind direction for 16 azimuths. Wind velocities for a return period of 100 years, » , were 100 estimated from hourly data following the method proposed by Gomes and Vickery [8], where azimuthal Weiblull parameters of wind velocities were obtained with the maximum likelihood method. 3.2. Azimuthal topographic factors Most azimuthal topographic factors were calculated in the usual manner from a fan-shaped field with a particular radius, the center of which was at an observatory site. The altitude data were obtained from Grid Information System Data for Japan where altitude and land information were recorded at an interval of about 250 m. After some preliminary calculations, the radius was chosen as 5 and 60 km for the representative length of close and meso-scale topographies, respectively. Azimuthal topographic factors used here were as follows. The detail of each parameter was described in Ref. [7] except the factors 7 and 8, those were newly introduced in this analysis. (1) Maximum altitude difference (MAD, m): the altitude difference between the highest position inside of the fan-shaped area and the site. (2) Mean altitude difference (AAD, m): the difference between the altitude of the site and that of arithmetic mean of altitudes inside of fan-shaped area.
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(3) Ratio of land (RL, %): the ratio of land area to all fan-shaped area. (4) Ratio of sea (RS, %): the ratio of sea, lake and river area to all fan-shaped area. (5) Minimum distance from sea (MDS, m): the shortest distance from the sea to the site. (6) Minimum distance from obstacle (MDO1, m): obstacle heights were chosen as 50, 100, 200 and 300 m. (7) Minimum distance from obstacle (MDO2, m): distance from the obstacle region given by shaded area shown in Fig. 2, where the minimum distance was defined by MDO2"60 000!r1. r1 was the shortest length from the obstacle region decided by the proper choice of h and r in the figure. In this analysis, some cases of tan h such as 0.05, 0.075, 0.1 and 0.15 rad were examined under fixed r"10 km. (8) Ratio of obstacle (RO, %): ratio of obstacle region shown by shaded area in Fig. 2 (in plan) to the fan-shaped area (in plan) with the radius r2 corresponding to the distance between the highest altitude point and the site. 3.3. Micro-scale topographic factors In addition to the azimuthal topographic factors defined in previous section, the micro-scale topographic factors were necessary to improve the accuracy of estimation
Fig. 2. Definition of obstacle region.
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for wind velocity in complex terrain sites. A CCD video camera which was mounted at the top of a pole besides the anemometer was used to take scenery pictures of 16 azimuths around a site, from which the new micro-scale factors were derived as follows. The efficiency for the use of factors 9 and 11 were already discussed in Ref. [7] where the same factors are evaluated in some different manner. (9) Sheltering effect (EOS1, %): ratio of obstacle area, which was derived from the scenery pictures by the subtraction between obstacle area and the area lower than the site altitude, to the square of mean distance from the site to obstacle (see Ref. [7]). (10) Sheltering effect (EOS2): degree of sheltering effect derived from human judgment with standard scenery pictures, those were ranked from one to five corresponding to the degree of sheltering effect (Fig. 3). Comparing azimuthal pictures of each site with the standard ones, six persons decided the rank of the sheltering effect subjectively for each azimuth of each observatory. (11) Convergence effect (EOC1, %): the counter measure of EOS1 in particular azimuth defined by the subtraction between EOS1 for normal direction to the azimuth (sum of right- and left-hand side EOS1) and EOS1 for coincidence with the particular direction (sum of upstream and downstream EOS1). (12) Convergence effect (EOC2): measure for increasing effect of local terrain wind velocity. For valley-like topography, standard pictures ranked five-steps were prepared for human judgment as for EOS2. Furthermore, the parallel direction to the shoreline observed from the site was given rank 3 uniformly. On the hill and the direction face to sea shore were given rank 1. EOC2"0 if the scenery picture included no increasing effect of local terrain.
3.4. Analytical procedure Two-step analyses were used for the evaluation of the representative and azimuthal wind velocities, respectively. Each multiple regression analysis was carried out by means of the stepwise method that estimated the representative or the azimuthal wind velocity of the objective variable as a linear combination of variables of topographic factors at a site. Local wind velocities were evaluated as a distortion from the representative value corresponding to the azimuthal difference of local terrain. The representative wind velocity was estimated independently in the first step regression analysis with the topographic factors defined by different manner, therefore the factors adopted in the regression equation were different from those of azimuthal wind velocity. All variables used in the second step multiple regression analysis were normalized by the representative value for a site which was obtained expediently by the average of sixteen azimuthal wind velocities and topographic factors respectively. The result of first-step analysis was not used here as the representative wind velocity to reduce the estimation error.
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Fig. 3. Example of standard scenery pictures to evaluate EOS2.
4. Analytical result and discussion 4.1. Estimation of representative wind velocity with 100 years return period, » R100 Since it was difficult to obtain the representative wind velocity at the AMeDAS observatory from some published design cords because of their loose mesh size, the averaged value of the records at each observatory was used as a objective variable in regression analysis.
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Representative wind velocity at a site was estimated with two groups of topographic parameters which were the averages of 16-azimuthal values (AAD, RL, RS, EOS-2, EOC-2) and the extremes of individual factors of the site (MAD, MDO, MDS). All the factors except EOS-2 and EOC-2 were used generally in former studies, however, there was no fixed standard to decide the radius of evaluating circle. The anemometer height (HOA), was introduced as an additional factor because the micro-scale factors were derived from the pictures taken at that height. Fig. 4 shows the relation of multiple correlation coefficients of the regression equation to the various radii extracting topographic factors, where the larger or smaller the radius, the more accurate the estimate became. However, in such a case, some partial regression coefficients, which sign corresponded to that of t-value, took wrong signs that meant opposite performances of the corresponding factors. The positive sign of t-value means increasing effect of the variables on the wind velocity. One consistent case for the sign of t-value is shown in Table 1 and Fig. 5, where the extracting radius was 20 km. The asterisk in Table 1 means abandoned factors in the analysis and large t-value means large contribution of the factor to the objective term. Although the topographic factors adopted in this analysis were restricted in several terms, the multiple correlation coefficient became comparatively large as R"0.92. The regression equation was obtained as follows: » (m/s)"0.243 HOA!0.104 RL(20 km)!0.00371 MDO1(H"50 m) R100 !0.000157 MDS#0.605 EOC2#17.75. (1) 4.2. Estimation of azimuthal wind velocity with 100-years return period, » AZ100 The normalized azimuthal wind velocity was defined by the ratio of each azimuthal wind velocity to the representative (averaged) value at a site. The effectiveness of two
Fig. 4. Relation between extracting radius and multiple correlation coefficient.
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H. Utsunomiya et al./J. Wind Eng. Ind. Aerodyn. 74–76 (1998) 175–187 Table 1 Result of multiple regression analysis for representative wind velocity, » (multiple correlation coefficR100 ient R"0.92) Extracting radius (20 km)
t-value
HOA MAD AAD RL RS MDO1 (50 m) MDS’ EOS2 EOC2
2.5 * * !3.0 * 5.0 !1.4 * 1.8
Note: The asterisk * indicates abandoned parameter.
Fig. 5. Scatter diagram for representative wind velocity, » . R100
kinds of micro-scale topographic factors on the accuracy of the estimate was examined as shown in Table 2, which indicates only t-value for the results of two trials with “EOS1, EOC1” and “EOS2, EOC2” in addition to the ordinary topographic factors. The variables with large absolute t-value play an important role in the estimation. It can be seen that the latter micro-scale factors in trial 1 had considerably large t-value and the multiple correlation coefficient become large, but there still remains one problem in trial 1 that three variables had the wrong sign of t-value among the adopted 12 variables. Therefore, other azimuthal factors 7 and 8 explained in the previous section were introduced in the trials. The inclination angle, h, indicated in Fig. 2 was chosen as tan h"0.15 for MDO2 and 0.05 for RO following preliminary regression analyses, in which the multiple correlation coefficients for different four-cases of h values took almost the same value
H. Utsunomiya et al./J. Wind Eng. Ind. Aerodyn. 74–76 (1998) 175–187 Table 2 Effect of micro-scale terrain parameters on » (multiple AZ100 correlation coefficient of 0.91 for trial 1 and 0.85 for trial 2) Trial 1
Trial 2
t-value
t-value
Azimuthal topographic parameter for upstream area (-º) MAD-U
5 km 60 km AAD-U 5 60 RL-U 5 60 RS-D 5 60 MDD1-D 50 100 200 300 m MDS-U
2.5 * * !5.5 * 3 * * * * * * *
* * * !3.9 * 2.3 * * * * !2.9 * !1.6
Azimuthal topographic parameter for downstream area (-D) MAD-D
5 km 60 km AAD-D 5 60 RL-D 5 60 RS-D 5 60 MDD1-D 50 100 200 300 m MDS-D
* * !3 !2.9 3.4 1.5 * 3.7 * * * * !4
* * !1.7 !3.2 3.6 * * * 1.8 * * 1.6 2.2
New micro-scale topographic parameter EOS2U D EOC2U EOS1-U D L, R EOC1
!9.3 !5.4 4.3 * — — — —
— — — — * !2.2 !1.8 *
183
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but the t-value became large for MDO2 of tan h"0.15 and for RO of tan h"0.05. Small h decreased the azimuthal difference of MDO in mountainous area and large h decreased the azimuthal difference of RO in each area. The results with new factors are given in Table 3 and Fig. 6. Though the number of variables adopted in this regression equation were decreased from 12 to 5, the multiple correlation coefficient became slightly larger than that of the previous trial 1 in Table 2 and all variables had correct sign of t-value. The regression equation for azimuthal wind velocity was given
Table 3 t-value of multiple regression analysis with new parameters (multiple correlation coefficient R"0.914) t-value MDS-U -D MDO2-U -D (tan h"0.15) RO-U -D (tan h"0.05) EOS2-U -D EOC2-U -D
* * !5.6 * !1.5 * !7.5 !5.2 !4.5 *
Fig. 6. Scatter diagram of azimuthal wind velocity, » . AZ100
H. Utsunomiya et al./J. Wind Eng. Ind. Aerodyn. 74–76 (1998) 175–187
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as follows: » "!0.0512 MDO2U!0.0179 RO!0.581 EOS2U AZ100 !0.367 EOS2D#0.0504 EOC2U#197.9.
(2)
º and D correspond to upstream and downstream areas, respectively. Fig. 7 indicates the estimated azimuthal wind velocities, » , for 12 observatoAZ100 ries, where comparatively good result can be obtained about the general fitness between the observed and estimated values drawn by solid and broken lines respectively. There is some room for improvement on the evaluation of the convergent effect of topographic factors.
Fig. 7. Comparisons of » between observations (solid line) and estimates (broken line) for 12 AZ100 observatories.
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4.3. Calibration To verify the regression equations (1) and (2), a new observatory having no connection with the series of present analyses was chosen (position O in Fig. 8), where wind velocity observation had been continued for a few years to estimate the effect of large scale earth works. The result of verification is shown in Fig. 9, where the two-step analysis was carried out. The representative wind velocity obtained by Eq. (1) was 14.4 m/s compared to
Fig. 8. Calibration point under the plan of large-scale earth works.
Fig. 9. Result of calibration; solid line for observation and broken line for estimate.
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15.3 m/s observed value. The azimuthal wind velocity was well estimated in average but the accuracy of Eq. (2) was still not satisfactory for strong wind estimation, though there was an open sea in the direction of ENE and it must have some particular effect of convergence in this position.
5. Conclusions (1) The local topography had a direct effect upon the local wind properties at a complex terrain site. (2) Two-step analysis of representative wind velocity and its azimuthal fluctuations was very effective to improve the accuracy of estimations. (3) The introduction of new micro-scale topographic factors was successful for the estimation of local wind velocities though the evaluation process was not objective to some extent. (4) The new azimuthal topographic factors, MDO2 and RO, defined without the particular evaluation radius were also effective for the estimation. (5) The convergence effect of local terrain was not sufficient to understand.
Acknowledgements A part of this study was carried out with the support of Research Grant No. 06555134 of Ministry of Education, Japan.
References [1] N.J. Cook et al., Wind conditions around the rock of Gibraltar, J. Wind Eng. Ind. Aerodyn. 2 (1977/1978) 289—310. [2] ESDU Wind speeds and turbulence, Vol. 1a, b (1986). [3] P.S. Jackson, J.C.R. Hunt, Turbulent wind over a low hill, Quart. J. Roy. Meteor. Soc. 101 (1975) 929—955. [4] T. Miyata et al., Topographical factor analysis of average wind speeds by directional effects, Proc. 9th National Symp. on Wind Eng. 1986, pp. 37—42 (in Japanese). [5] S. Murakami, H. Komine, Prediction method for surface wind velocity distribution by means of regression analysis of topographic effects on local wind speed, J. Wind Eng. Ind. Aerodyn. 15 (1983) 217—230. [6] H. Utsunomiya et al., Estimation of local strong wind around peninsula-like terrain, J. Wind Eng. Ind. Aerodyn. 41 (1992) 405—414. [7] H. Kamiya et al., Estimation of wind properties from local terrain factors, Proc. 9th ICWE. NewDelhi, India, 1995, pp. 2065—2076. [8] L. Gomes, B.J. Vickery, On the prediction of extreme wind speeds from parent distribution, J. Ind. Aerodyn. 2 (1977) 21—36.
Regression analysis of local wind properties with local topographic factors H. Utsunomiya!,*, F. Nagao!, I. Urakami" ! Department of Civil Engineering, The University of Tokushima, Minamijosanjima 2-1, Tokushima 770, Japan " Okayama Prefectural Office, Uchiyamasita 2-4-6, Okayama, Japan
Abstract To improve the accuracy of estimation of local strong wind, new local topographic parameters were introduced in the multiple regression analysis. New azimuthal topographic factors were defined independently of particular radius of fan-shaped area for the estimation of usual topographic factors. In addition to them, some micro-scale local terrain factors were defined from scenery pictures of 16-azimuths around the site. The azimuthal strong wind velocity at a construction site was evaluated through the two-step estimation, in which the representative wind speed at a site was estimated by first regression analysis with the usual topographic factors and second regression analysis with newly defined micro-scale factors was followed to estimate the azimuthal wind speed fluctuation. It was shown that the new topographic factors defined here played an important role in all regression analyses. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Local topographic factors; Regression analysis of local wind properties; Two-stepestimation of azimuthal wind speeds
1. Introduction The exact estimation of strong wind velocity at a construction site is important to evaluate the wind load on a structure and various methods have been proposed in former studies [1—7]. The best method is a long-term observation at a site but it is usually difficult by the restriction of a construction term. The use of a wind map obtained from long-term observations of meteorological stations is a convenient
* Corresponding author. E-mail: [email protected]. 0167-6105/98/$19.00 ( 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 0 1 5 - 4
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H. Utsunomiya et al./J. Wind Eng. Ind. Aerodyn. 74–76 (1998) 175–187
method and some design specifications include standardized wind maps combined with some local terrain information. However, they are not always sufficient for exact estimation because of the loose mesh size of the stations and the complexity of terrain like the Japanese Islands. Wind tunnel test with a topographic scaled model is a forceful method for the estimation in spite of including some similarity problems, but it requires a high cost and large scale of the wind tunnel. The regression analysis with topographic factors is a conventional method for the estimation of local wind properties, but a large amount of error was still included in the results of former studies, in which topographic factors took different values corresponding to the particular radius for the evaluation of them. To improve the accuracy of the regression analysis on the azimuthal wind velocities of a site, two different types of new topographic factors such as the micro-scale and azimuthal topographic factors were introduced here. The former was defined from the scenery pictures around the site while the latter was defined uniquely without any restriction of evaluating radius for each azimuthal area. All the data used in this analysis were obtained at the AMeDAS observatories in Shikoku Island described in the following section and these observatories were located at the positions where the wind velocity was heavily influenced by the surrounding local topographies. The regression analysis showed that these new factors had an important role in estimating the local wind properties. The estimation of local strong wind velocity was carried out by the two-stepestimation method. The representative mean wind velocity at a particular site was estimated by the result of first-step regression analysis with ordinary topographic factors and the azimuthal wind velocities fluctuating from the representative wind velocity were obtained by second regression analysis with micro-scale and newly introduced topographic factors. It became clear also that the two-step estimate was very effective to evaluate the azimuthal wind velocities.
2. Observation sites Sample data of wind velocity were obtained from the records of AMeDAS observatories and topographic factors were also obtained corresponding to each observatory sites. There are 1300 observatories of AMeDAS (Automated Meteorological Data Acquisition System) all over the Japanese Islands as a meteorological network system. There are 43 observatories of AMeDAS in Shikoku Island, southwest of Japan, from which typical 29-observatories were chosen for the analysis here as indicated in Fig. 1. Fourteen observatories were eliminated from the analysis by the following reasons: (1) the positions of the observatories were moved during the past 10 years, (2) the positions were located at small islands or on a steep slope, (3) high-rise buildings or structures were there in close vicinity to the observatories and (4) the CCD camera position to evaluate the topographic factors from its scenery pictures was different from the anemometer height.
H. Utsunomiya et al./J. Wind Eng. Ind. Aerodyn. 74–76 (1998) 175–187
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Fig. 1. Location of AMeDAS observatories in Shikoku Island.
3. Regression analysis 3.1. Wind data Mean wind velocities and wind directions averaged for 10 min in every 1 h obtained at the AMeDAS observatories during ten years from 1983 to 1992 were used to estimate the mean wind velocity and its relative frequency of occurrence of wind direction for 16 azimuths. Wind velocities for a return period of 100 years, » , were 100 estimated from hourly data following the method proposed by Gomes and Vickery [8], where azimuthal Weiblull parameters of wind velocities were obtained with the maximum likelihood method. 3.2. Azimuthal topographic factors Most azimuthal topographic factors were calculated in the usual manner from a fan-shaped field with a particular radius, the center of which was at an observatory site. The altitude data were obtained from Grid Information System Data for Japan where altitude and land information were recorded at an interval of about 250 m. After some preliminary calculations, the radius was chosen as 5 and 60 km for the representative length of close and meso-scale topographies, respectively. Azimuthal topographic factors used here were as follows. The detail of each parameter was described in Ref. [7] except the factors 7 and 8, those were newly introduced in this analysis. (1) Maximum altitude difference (MAD, m): the altitude difference between the highest position inside of the fan-shaped area and the site. (2) Mean altitude difference (AAD, m): the difference between the altitude of the site and that of arithmetic mean of altitudes inside of fan-shaped area.
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(3) Ratio of land (RL, %): the ratio of land area to all fan-shaped area. (4) Ratio of sea (RS, %): the ratio of sea, lake and river area to all fan-shaped area. (5) Minimum distance from sea (MDS, m): the shortest distance from the sea to the site. (6) Minimum distance from obstacle (MDO1, m): obstacle heights were chosen as 50, 100, 200 and 300 m. (7) Minimum distance from obstacle (MDO2, m): distance from the obstacle region given by shaded area shown in Fig. 2, where the minimum distance was defined by MDO2"60 000!r1. r1 was the shortest length from the obstacle region decided by the proper choice of h and r in the figure. In this analysis, some cases of tan h such as 0.05, 0.075, 0.1 and 0.15 rad were examined under fixed r"10 km. (8) Ratio of obstacle (RO, %): ratio of obstacle region shown by shaded area in Fig. 2 (in plan) to the fan-shaped area (in plan) with the radius r2 corresponding to the distance between the highest altitude point and the site. 3.3. Micro-scale topographic factors In addition to the azimuthal topographic factors defined in previous section, the micro-scale topographic factors were necessary to improve the accuracy of estimation
Fig. 2. Definition of obstacle region.
H. Utsunomiya et al./J. Wind Eng. Ind. Aerodyn. 74–76 (1998) 175–187
179
for wind velocity in complex terrain sites. A CCD video camera which was mounted at the top of a pole besides the anemometer was used to take scenery pictures of 16 azimuths around a site, from which the new micro-scale factors were derived as follows. The efficiency for the use of factors 9 and 11 were already discussed in Ref. [7] where the same factors are evaluated in some different manner. (9) Sheltering effect (EOS1, %): ratio of obstacle area, which was derived from the scenery pictures by the subtraction between obstacle area and the area lower than the site altitude, to the square of mean distance from the site to obstacle (see Ref. [7]). (10) Sheltering effect (EOS2): degree of sheltering effect derived from human judgment with standard scenery pictures, those were ranked from one to five corresponding to the degree of sheltering effect (Fig. 3). Comparing azimuthal pictures of each site with the standard ones, six persons decided the rank of the sheltering effect subjectively for each azimuth of each observatory. (11) Convergence effect (EOC1, %): the counter measure of EOS1 in particular azimuth defined by the subtraction between EOS1 for normal direction to the azimuth (sum of right- and left-hand side EOS1) and EOS1 for coincidence with the particular direction (sum of upstream and downstream EOS1). (12) Convergence effect (EOC2): measure for increasing effect of local terrain wind velocity. For valley-like topography, standard pictures ranked five-steps were prepared for human judgment as for EOS2. Furthermore, the parallel direction to the shoreline observed from the site was given rank 3 uniformly. On the hill and the direction face to sea shore were given rank 1. EOC2"0 if the scenery picture included no increasing effect of local terrain.
3.4. Analytical procedure Two-step analyses were used for the evaluation of the representative and azimuthal wind velocities, respectively. Each multiple regression analysis was carried out by means of the stepwise method that estimated the representative or the azimuthal wind velocity of the objective variable as a linear combination of variables of topographic factors at a site. Local wind velocities were evaluated as a distortion from the representative value corresponding to the azimuthal difference of local terrain. The representative wind velocity was estimated independently in the first step regression analysis with the topographic factors defined by different manner, therefore the factors adopted in the regression equation were different from those of azimuthal wind velocity. All variables used in the second step multiple regression analysis were normalized by the representative value for a site which was obtained expediently by the average of sixteen azimuthal wind velocities and topographic factors respectively. The result of first-step analysis was not used here as the representative wind velocity to reduce the estimation error.
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Fig. 3. Example of standard scenery pictures to evaluate EOS2.
4. Analytical result and discussion 4.1. Estimation of representative wind velocity with 100 years return period, » R100 Since it was difficult to obtain the representative wind velocity at the AMeDAS observatory from some published design cords because of their loose mesh size, the averaged value of the records at each observatory was used as a objective variable in regression analysis.
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Representative wind velocity at a site was estimated with two groups of topographic parameters which were the averages of 16-azimuthal values (AAD, RL, RS, EOS-2, EOC-2) and the extremes of individual factors of the site (MAD, MDO, MDS). All the factors except EOS-2 and EOC-2 were used generally in former studies, however, there was no fixed standard to decide the radius of evaluating circle. The anemometer height (HOA), was introduced as an additional factor because the micro-scale factors were derived from the pictures taken at that height. Fig. 4 shows the relation of multiple correlation coefficients of the regression equation to the various radii extracting topographic factors, where the larger or smaller the radius, the more accurate the estimate became. However, in such a case, some partial regression coefficients, which sign corresponded to that of t-value, took wrong signs that meant opposite performances of the corresponding factors. The positive sign of t-value means increasing effect of the variables on the wind velocity. One consistent case for the sign of t-value is shown in Table 1 and Fig. 5, where the extracting radius was 20 km. The asterisk in Table 1 means abandoned factors in the analysis and large t-value means large contribution of the factor to the objective term. Although the topographic factors adopted in this analysis were restricted in several terms, the multiple correlation coefficient became comparatively large as R"0.92. The regression equation was obtained as follows: » (m/s)"0.243 HOA!0.104 RL(20 km)!0.00371 MDO1(H"50 m) R100 !0.000157 MDS#0.605 EOC2#17.75. (1) 4.2. Estimation of azimuthal wind velocity with 100-years return period, » AZ100 The normalized azimuthal wind velocity was defined by the ratio of each azimuthal wind velocity to the representative (averaged) value at a site. The effectiveness of two
Fig. 4. Relation between extracting radius and multiple correlation coefficient.
182
H. Utsunomiya et al./J. Wind Eng. Ind. Aerodyn. 74–76 (1998) 175–187 Table 1 Result of multiple regression analysis for representative wind velocity, » (multiple correlation coefficR100 ient R"0.92) Extracting radius (20 km)
t-value
HOA MAD AAD RL RS MDO1 (50 m) MDS’ EOS2 EOC2
2.5 * * !3.0 * 5.0 !1.4 * 1.8
Note: The asterisk * indicates abandoned parameter.
Fig. 5. Scatter diagram for representative wind velocity, » . R100
kinds of micro-scale topographic factors on the accuracy of the estimate was examined as shown in Table 2, which indicates only t-value for the results of two trials with “EOS1, EOC1” and “EOS2, EOC2” in addition to the ordinary topographic factors. The variables with large absolute t-value play an important role in the estimation. It can be seen that the latter micro-scale factors in trial 1 had considerably large t-value and the multiple correlation coefficient become large, but there still remains one problem in trial 1 that three variables had the wrong sign of t-value among the adopted 12 variables. Therefore, other azimuthal factors 7 and 8 explained in the previous section were introduced in the trials. The inclination angle, h, indicated in Fig. 2 was chosen as tan h"0.15 for MDO2 and 0.05 for RO following preliminary regression analyses, in which the multiple correlation coefficients for different four-cases of h values took almost the same value
H. Utsunomiya et al./J. Wind Eng. Ind. Aerodyn. 74–76 (1998) 175–187 Table 2 Effect of micro-scale terrain parameters on » (multiple AZ100 correlation coefficient of 0.91 for trial 1 and 0.85 for trial 2) Trial 1
Trial 2
t-value
t-value
Azimuthal topographic parameter for upstream area (-º) MAD-U
5 km 60 km AAD-U 5 60 RL-U 5 60 RS-D 5 60 MDD1-D 50 100 200 300 m MDS-U
2.5 * * !5.5 * 3 * * * * * * *
* * * !3.9 * 2.3 * * * * !2.9 * !1.6
Azimuthal topographic parameter for downstream area (-D) MAD-D
5 km 60 km AAD-D 5 60 RL-D 5 60 RS-D 5 60 MDD1-D 50 100 200 300 m MDS-D
* * !3 !2.9 3.4 1.5 * 3.7 * * * * !4
* * !1.7 !3.2 3.6 * * * 1.8 * * 1.6 2.2
New micro-scale topographic parameter EOS2U D EOC2U EOS1-U D L, R EOC1
!9.3 !5.4 4.3 * — — — —
— — — — * !2.2 !1.8 *
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but the t-value became large for MDO2 of tan h"0.15 and for RO of tan h"0.05. Small h decreased the azimuthal difference of MDO in mountainous area and large h decreased the azimuthal difference of RO in each area. The results with new factors are given in Table 3 and Fig. 6. Though the number of variables adopted in this regression equation were decreased from 12 to 5, the multiple correlation coefficient became slightly larger than that of the previous trial 1 in Table 2 and all variables had correct sign of t-value. The regression equation for azimuthal wind velocity was given
Table 3 t-value of multiple regression analysis with new parameters (multiple correlation coefficient R"0.914) t-value MDS-U -D MDO2-U -D (tan h"0.15) RO-U -D (tan h"0.05) EOS2-U -D EOC2-U -D
* * !5.6 * !1.5 * !7.5 !5.2 !4.5 *
Fig. 6. Scatter diagram of azimuthal wind velocity, » . AZ100
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as follows: » "!0.0512 MDO2U!0.0179 RO!0.581 EOS2U AZ100 !0.367 EOS2D#0.0504 EOC2U#197.9.
(2)
º and D correspond to upstream and downstream areas, respectively. Fig. 7 indicates the estimated azimuthal wind velocities, » , for 12 observatoAZ100 ries, where comparatively good result can be obtained about the general fitness between the observed and estimated values drawn by solid and broken lines respectively. There is some room for improvement on the evaluation of the convergent effect of topographic factors.
Fig. 7. Comparisons of » between observations (solid line) and estimates (broken line) for 12 AZ100 observatories.
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4.3. Calibration To verify the regression equations (1) and (2), a new observatory having no connection with the series of present analyses was chosen (position O in Fig. 8), where wind velocity observation had been continued for a few years to estimate the effect of large scale earth works. The result of verification is shown in Fig. 9, where the two-step analysis was carried out. The representative wind velocity obtained by Eq. (1) was 14.4 m/s compared to
Fig. 8. Calibration point under the plan of large-scale earth works.
Fig. 9. Result of calibration; solid line for observation and broken line for estimate.
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15.3 m/s observed value. The azimuthal wind velocity was well estimated in average but the accuracy of Eq. (2) was still not satisfactory for strong wind estimation, though there was an open sea in the direction of ENE and it must have some particular effect of convergence in this position.
5. Conclusions (1) The local topography had a direct effect upon the local wind properties at a complex terrain site. (2) Two-step analysis of representative wind velocity and its azimuthal fluctuations was very effective to improve the accuracy of estimations. (3) The introduction of new micro-scale topographic factors was successful for the estimation of local wind velocities though the evaluation process was not objective to some extent. (4) The new azimuthal topographic factors, MDO2 and RO, defined without the particular evaluation radius were also effective for the estimation. (5) The convergence effect of local terrain was not sufficient to understand.
Acknowledgements A part of this study was carried out with the support of Research Grant No. 06555134 of Ministry of Education, Japan.
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