Effects of different terrain on velocity standard deviations

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1 Atmospheric Science Letters (2001) doi: /asle Effects of different terrain on velocity standard deviations M. H. Al-Jiboori 1,2, Yumao Xu 1 and Yongfu Qian 1 1 Department of Atmospheric Sciences, Nanjing niversity, Nanjing, , P.R. China 2 LAPC, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, , P.R. China Abstract: The standard deviations of wind velocity components are calculated and compared based on the measurements of turbulence uctuations over three underlying surfaces: uniform, inhomogeneous and urban. Statistical analysis shows that there are the differences between them which prove the in uences of surfaces roughness on turbulence. *c 2001 Royal Meteorological Society Keywords: niform, complex and urban terrain, standard deviations. 1. INTRODCTION The standard deviations of wind components over different terrain are important to sign the turbulence characteristics, which are considered of interest in the study of dispersion of pollutants from continuous sources. The major aim of this study is to reveal the effects of various underlying surface types (uniform: land, desert and water; inhomogeneous: varying topography and roughness; and urban city: Beijing City) on turbulence characteristics. According to Monin-Obukhov (M-O) and local similarity theory, dimensionless function of standard deviation of wind components f i ˆ s i /u and j i ˆ s i /u l, i ˆ u, u, w, should be a function of stability parameter z/l for the surface layer and z/l for tower-layer p respectively, where friction velocities u ˆ q j u 0 w 0 j and u l ˆ j ul 0w0 l j are velocity scaling and local velocity scaling, z the height over ground, L ˆ u 3 T=kgw 0 T 0 and L ˆ ul 3 T=kgw l 0T l 0 are M-O length and local M-O length. The tower-layer is an air layer above the surface layer up to about 300±500 m, in which local similarity theory proposed rstly by Nieuwstadt (1984) should be applied and the subscript ``l'' in velocity scaling denotes ``local'' values. There exists considerable uncertainty and less direct study in the literature regarding the scaling of the horizontal velocity standard deviations f u,v and j u,v than that of vertical velocity under unstable and stable boundary layer. Most authors found that s w /u or s w /u l is a function of z/l in either surface-layer similarity (e.g. Panofsky et al., 1977) or function of z/l in local similarity (e.g. Xu et al., 1997). In this paper we focus on the in uences of uniform, inhomogeneous and urban terrain on turbulence intensity in terms of velocity standard deviations under various stability conditions X *c 2001 Royal Meteorological Society

2 2. SITES AND DATA ACQISITION 2.1 Huayin site Huayin is one of the meteorological stations in the Heihe River Basin Field Experiment, which is a Sino±Japanese co-operative investigation program, in Gansu Province, Western China. It is located in the Gobi Desert, is surrounded by a few scattered plants and its surface is composed of sand and gravel. Fluctuation data have been measured by a three-dimensional sonic anemometer±thermometer instrument (Kaijo-Denki Dat-300, path length 20 cm) installed on a mast of height 4.9 m, on 16 August There were many hourly runs, the observation duration for each run was half an hour, and sampled 16 times per second (16 Hz). Total available data analysed were separated into two sectors according to wind direction, as shown in a detailed map of the Huayin Station (Figure 1). One is from direction 180±2308, in which Qilian Mountain is about 40 km south and 10 km south-west from Huayin station. The main peak of the mountain is 5062 m a.s.l., and lies about 65 km west-south-west of Huayin. Thus, under these conditions, the terrain can be considered as being locally uniform. The other is from 310±3608 in which there are natural water areas as oases for producing main crops (wheat and maize). These oases are about 15 km north-west and 2 km north away from the station, therefore an abrupt change in the surface from oasis to desert can be regarded aariable or inhomogeneous. Figure 1. Map of Huayin Station. The numbers represent distances in km.

3 2.2 Beijing site The data were obtained from a 325-m meteorological tower, located straight north of Beijing, 1 km away from the Sanhuan road. The eld around the tower is relatively at with wheat and short grass. Two years ago, many very tall buildings for of ces and departments were set up to the south of this road 100 m away. Instantaneous three-component velocities and temperature with a sampling frequency of 10 times per second (10 Hz) and sampling length of 1 hour, were measured by three dimensional sonic anemometer-thermometers at 47, 140, and 280 m height, from 14 to 23 October The zero-plane displacements required in determining roughness lengths around the tower have been estimated by Yin and Hong (1999), were too large in different wind directions as: 23 m for (0±908), 26 m (90±1808) and 18 m for (270±3608). These values are in accord with that expected for modern cities (Grimmond and Oke, 1999). Roughness length z 0 and other information of both Huayin and Beijing sites can be found in Al-Jiboori et al. (2001a,b). Before standard deviations were calculated using the time series u 0, v 0 and w 0, the data were preprocessed, including coordinate conversion into the mean wind direction as the X-axis direction and second-order polynomial t was applied for detrending. 3. RESLTS AND DISCSSION 3.1 Terrain effect Mean values of variances s u, and s w, friction velocity, and wind speed for three underlying surfaces with their standard deviations (SD) were calculated and are presented in Table 1. Large values of u *l in urban sites compared to other sites as shown in Table 1 is observed as expected for larger roughness lengths. In order to eliminate the effects of height differences on the measurements in this study between Huayin and Beijing sites, the standard deviations, s u, and s w, were normalized with u l for the comparison purposes. The value s u =u over uniform surface iery close to that over variable surface and larger than that of urban, while =u value in inhomogeneous surfaces is larger among other surfaces. This could, however, be stability effect. Lastly, s w =u values is in the same order of magnitudes for all surfaces. This behaviour is also observed Table 1. Average values of turbulence parameters for all runs Terrain u *(l) s u ms 1 s w s u s w s u u * l u * l s w u * l niform* SD Inhomog.{ SD rban SD ±2308 direction. {310±3608 direction.

4 Figure 2. f i ˆ s i /u (i ˆ u(x), v(s), w(n)) for uniform terrain as a function of z/l. The solid, dashed and dash-dotted lines represent similarity relations given by (1) for u-, v- and w-components, respectively. in next subsection and reported by Panofsky and Dutton (1984). The values of s w = are also similar to each other. The values of turbulence intensity s u = appear to be similar in both inhomogeneous and urban sites and larger than that over uniform, while = value over inhomogeneous terrain is larger. Although there are relative differences between the magnitudes of velocity standard deviations for all sites, the order s u 4 4 s w remainalid in Table 1, except for inhomogeneous terrain. An important result can be deduced from the examination of Table 1 that the difference between s u and over uniform and urban terrain are signi cantly larger than that over inhomogeneous, whereas the value of is almost found larger in many studies over coastal areas (e.g. HoÈgstroÈm and Smedman-HoÈstroÈm, 1984). The uctuations of horizontal velocity produced by large eddies can remember the rough conditions of oases upwind and thus yield irregularly excesalues of variances. On the other hand, the ratio =s u, 1.08, over inhomogeneous terrain is larger than unity compared to those over uniform and urban, 0.92 and 0.80, indicating a decreased longitudinal component of turbulence. 3.2 Stability effect In order to clarify the turbulence characteristics over various terrain and under different strati cations, dimensionless function of velocity f i (or j i ) was analysed according to stability parameter, although the data for both uniform and inhomogeneous terrain are little. There were ve runs under unstable conditions for uniform, while seven and three runs under unstable and stable conditions respectively, for inhomogeneous terrain. The values of f i are plotted versus z/l in Figure 2 for uniform and Figure 3 for inhomogeneous terrain, while j i are

5 Figure 3. f i ˆ s i /u*(i ˆ u(x), v(s), w(n)) for inhomogeneous terrain as a function of z/l. The solid, dashed and dash-dotted lines represent similarity relations given by (1) for u-, v- and w-components, respectively. plotted versus z/l in Figure 4 for urban terrain. In Figure 3, two points of the f u and f v in the stable side have been excluded, because their values are suspiciously large. In these gures the data points of f u and j u, f v and j v, and f w and j w symbolized as ``x'', and ``s'' and ``n'', respectively. We tted data under unstable for all sites, and only under stable conditions for urban site since no data and a few data in uniform and inhomogeneous terrain respectively, by a general function s i z z 1=3 ˆ a i 1 b i or 1 u * l L L where a i and b i are empirical constants, which are presented in Table 2. We can see from Table 2 that a u,v and j b u,v j for both uniform and inhomogeneous terrain under unstable conditions are signi cantly larger than those of urban. The reason is mainly attributed to the relative large values of u *l over urban site, as shown in Table 1. Near neutral conditions, a u,v values over inhomogeneous terrain are largest among all sites and a w values are roughly similar to each other for all sites. The large spread of value j b w j under unstable air is evident for uniform and inhomogeneous sites compared to that of urban, which iery close to that in stable air for urban surface. Figures 2±4 show that dimensionless quantities of horizontal velocity, s u,v, for all sites have more scatter than the s w /u *. nder unstable conditions for all gures, the functions f i and j i increase with increasing instability. For stable air, the result from Figures 3 and 4 shows that f i and j i also increase with stability, which are in agreement with well-known observations over coastal (e.g. HoÈgstroÈm and Smedman-HoÈgstroÈm, 1984) and urban terrain (e.g. Xu et al., 1997).

6 Figure 4. j i ˆ s i /u *l (i ˆ u(x), v(s), w(n)) for uniform terrain as a function of z/l over urban terrain. The solid, dashed and dash-dotted lines represent similarity relations given by (1) for u-, v- and w-components, respectively. 4. CONCLSIONS As demonstrated in the introduction, the main purpose of this work is to add some evidence on the turbulence characteristics over various underlying surfaces; uniform, inhomogeneous and urban. The effects of these surfaces are revealed by comparing of mean values of velocity variances and their analyses under different stability conditions. Mean values of dimensionless quantities of horizontal velocity standard deviation over inhomogeneous terrain were found to be larger than those over uniform and urban terrain, while those of vertical velocity values are similar for all terrain. It means that f u,v are sensitive to local terrain. The difference between mean values of horizontal velocity standard deviations s u and for both uniform and urban terrain is larger than that of inhomogeneous terrain. Table 2. Empirical constants a i and b i in eqn (1) Terrain parameters/constants niform ( z/l) Inhomog. ( z/l) rban ( z/l) rban (z/l) a i j a i j a i j a i j s s V s W

7 Acknowledgements Supported by the National Sciences Foundation of China under Grant No and References Al-Jiboori, M. H., Xu, Y. and Qian, Y., 2001a. Turbulence characteristics over complex terrain in West China. Bound.-Layer Meteorol. (in press). Al-Jiboori, M. H., Xu, Y. and Qian, Y., 2001b. Vertical structure of second-moment turbulent variables. ACTA Meteorologica Sinica, 15, 218±232. Grimmond, C. S. B. and Oke, T. R., Aerodynamic properties of urban areas derived from analysis of surface form. J. Appl. Meteorol., 38, 1262±1292. HoÈgstroÈm,. and Smedman-HoÈgstroÈm, A., The wind regime in coastal areas with special reference to results obtained from the Swedish wind energy program. Bound.-Layer Meteorol., 30, 351±373. Nieuwstadt, F. T. M., The turbulent structure of the stable nocturnal boundary layer. J. Atmos. Sci., 41, 2202±2216. Panofsky, H. A., Tennekes, H., Lenschow, D. H. and Wyngaard, J. C., The characteristics of turbulent velocity components in the surface layer under convective conditions. Bound.-Layer Meteorol., 1355±1361. Xu, Y., Zhou, C., Li, Z. and Zhang, W., Turbulent structure and local similarity in the tower-layer over the Nanjing area. Bound.-Layer Meteorol., 82, 1±21. Yin, D. and Hong, Z., Study on the boundary layer structure and parameter under heavy pollution conditions in Beijing. Clim. Envi. Rea., 4, 303±307.

October 1991 J. Wang and Y. Mitsuta 587 NOTES AND CORRESPONDENCE. Turbulence Structure and Transfer Characteristics

October 1991 J. Wang and Y. Mitsuta 587 NOTES AND CORRESPONDENCE Turbulence Structure and Transfer Characteristics in the Surface Layer of the HEIFE Gobi Area By Jiemin Wang Lanzhou Institute of Plateau