Guidelines for airflow over complex terrain: model developments

INDAER 1308 BALA ROHINI nvs

Journal of Wind Engineering and Industrial Aerodynamics 86 (2000) 169}186

Guidelines for air#ow over complex terrain: model developments Wensong Weng *, Peter A. Taylor , John L. Walmsley
Department of Earth and Atmospheric Science, York University, 4700 Keele Street, Toronto, ON, Canada M3J 1P3
Meteorological Service of Canada, 4905 Duwerin Street, Toronto, ON, Canada M3H 5T4 Received 24 September 1999; accepted 9 November 1999

Abstract The `Guidelinesa for estimating wind speed variations in boundary}layer #ow over hills and other terrain features as well as within internal boundary layers downstream of changes in surface roughness were developed by Taylor and Lee and Walmsley, Taylor and Salmon. We revisit the problem and propose new formulations based on results of our MSFD and NLMSFD calculations of #ow over hills. The e!ects of surface roughness and non-linearity on fractional speed-up are incorporated. Comparisons with experimental data are discussed.  2000 Elsevier Science Ltd. All rights reserved. Keywords: Guidelines; Fractional speed-up ratio; Small-scale topographic features

1. Introduction The `Guidelinesa were originally developed by Taylor and Lee [1] for estimating wind speed variations due to small-scale topographic features. They are based on ideas [2] for #ow over hills and [3] for #ow downwind of a step change in surface roughness. Subsequently, the Guidelines were modi"ed by Walmsley, Taylor and Salmon [4] (referred to as WTS), to allow the wind pro"le at the upwind location to be estimated from a measurement at a separate reference site by using the planetary boundary layer (PBL) resistance laws. The model predictions were improved for twoand three-dimensional rolling terrain and coded as an interactive program for use on

* Corresponding author. E-mail address: [email protected] (W. Weng). 0167-6105/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 0 0 ) 0 0 0 0 9 - X

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IBM-compatible micro-computers. Because of their simplicity and ease of use, the Guidelines have attracted considerable attention and the method is being widely used. For example, the Canadian Climate Centre has used the Guidelines extensively to assist in the estimation of design wind loads for structures, e.g., antenna towers, to be built in complex terrain; the Boundary-Layer Research Division of the Atmospheric Environment Service (AES) has used the Guidelines in a joint study with HydroQueH bec to estimate the wind energy potential of hilltop sites in the I) les-de-la Madeleine [5] and in studies of the representativeness of island wind data for the surrounding waters [6]. Similar models have been developed at Ris+ National Laboratory, Denmark [7] and at University of Western Ontario in Canada [8]. In the LSD model [8] algebraic formulae were proposed for air#ow over topographic features based on wind-tunnel studies and numerical model results obtained with the MS3DJH model [9]. With the LSD model the prediction site can be any location above hillside and escarpment slopes as well as above the hilltop. However, Lemelin et al. [8] treated topography only as 2D or 3D terrain and did not further distinguish whether the terrain was rolling or isolated, which we believe is important, as shown below. In addition, we believe that these simple models or &rules of thumb' give most accurate estimation of wind speed at the hill summit location and it is di$cult to estimate wind speeds at other locations since the detailed shape of the hill will strongly in#uence the spatial variations. Wood [10] also proposes a formula for maximum speed-up based on results of [11]. For detailed wind speed estimates at general locations in complex terrain, physical modelling (wind tunnel) or more sophisticated numerical computation (e.g., MS-Micro [12], WASP [13] or NLMSFD [14]) should be considered.

2. The Guidelines model 2.1. Review of the Guidelines The primary purpose of the Guidelines is to estimate the windspeed, ; , at . a prediction height, Z, above local ground level on a hilltop, P, given a measurement of the wind speed over #at terrain and estimates of some simple topographic parameters; see an idealised situation shown schematically in Fig. 1. The wind speed changes caused by both the topographic feature and a step change in surface roughness were considered. Here we focus only on the e!ects of the small-scale terrain features, as roughness-change e!ects are unchanged from previous versions of the Guidelines. The essential equations of the Guidelines for #ow over topography are as follows: ; can be calculated from . ; "(1#*S); (Z), (1) .  where it has been assumed that *S"*S exp(!AZ/¸ ) with *S "BH/¸ .

 

 

(2)

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Fig. 1. Schematic diagram of air#ow over complex terrain situation.

Here ; (Z) is the upstream wind speed at height Z. If it is not available for a location  just upwind of the topographic feature, ; (Z) is calculated from wind data for  a nearby reference site by using PBL Resistance Laws as described in WTS. *S is the fractional speed-up ratio and has been assumed to take its maximum value *S at

 the surface; H is the height of the terrain feature (positive for a hill and negative for a valley or hollow); ¸ is a horizontal length scale de"ned as the distance from the  hilltop or the bottom of the valley to the upstream point where the elevation is 0.5H [2]; A and B are empirical constants; see Table 1 for WTS's recommended values for di!erent terrain features. The upstream wind pro"le is assumed to be logarithmic and thermal strati"cation is taken to be neutral. The appropriate situations are those of moderate-to-high wind speed, maximum slope (0.3 and length scale satisfying ¸ /z '10 and ¸ (2000 m. The applicable height range is z ;Z(150 m.     2.2. The New Formulations In the original Guidelines the parameters A and B were assumed constant for each topography type and independent of z . To "nd a better approximation, we have used 

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W. Weng et al. / J. Wind Eng. Ind. Aerodyn. 86 (2000) 169}186 Table 1 Coe$cients for use with original Guidelines, from WTS Topography type

A

B

2D hills (ridges) 3D hills 2D escarpments 2D rolling terrain 3D rolling terrain Flat terrain

3.0 4.0 2.5 3.5 4.4 0.0

2.0 1.6 0.8 1.55 1.1 0.0

Table 2 Modelled basic terrain shapes Basic terrain type

Hill shape

Analytic form, z Q

Max slope H/¸ 

2D Ridges or 3D Circular hills

Rolling terrain

Bell shaped Gaussian Cosine squared

Sinusoidal

H/[1#(r/¸ )]  Hexp+!(r/¸ )ln 2,  H cos(pr/4¸ ) for "r"(2¸ ;   0 otherwise

0.65 0.71



0.79

H[1#cos(nr/2¸ )]/2 

0.79

r"x for 2D terrain and r"(x#y for 3D terrain.

the mixed spectral "nite di!erence (MSFD) model and its non-linear extension (NLMSFD) to run a series of experiments for di!erent combinations of parameters. We used both E}iz and E}e}q turbulence closures. For MSFD and NLMSFD model details and a discussion of turbulence closure schemes, see Refs. [15,14]. Surface roughness values used in the model calculations are z "0.001, 0.002, 0.005, 0.01,  0.02, 0.05, 0.1, 0.2, 0.5 and 1.0 m and the topographies modelled are given in Table 2. Fig. 2 shows the shapes of some of the isolated hills. Periodic sinusoidal rolling terrains were also used. For the three di!erent shaped isolated hills, even though they have the same values of H/¸ , their local maximum slopes are quite di!erent.  However, we believe that it is more practical to specify H/¸ than to calculate the  maximum slope in applications. The whole computation domain is set as (10¸ ) for  2D isolated terrain and (10¸ ) for 3D isolated topography, while for rolling terrain  they are (4¸ ) and (4¸ ) for 2D and 3D terrain, respectively. The grid points used   are 64 in the horizontal and 41 in the vertical. All the topographies used initially were for low slope (0.08 for rolling terrain and about 0.13}0.157 for isolated hills). We expect that in these cases the linear calculation gives good predictions which non-linear model calculations support; see Fig. 3. Although various turbulence closures can be used in the models (see Ref. [15] for details), it is believed that a relative simple 1-order turbulence closure, such as 

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Fig. 2. Modelled shapes of the various 2D terrain, or the central cross section of 3D terrain.

E!iz, is generally adequate to predict the mean #ow quantities, e.g., wind speed at the hilltop. With the 1-order turbulence closure, the numerical model results show  that *S is almost a constant close to the surface, has its maximum value, *S on the

 surface, and decays monotonically with Z. However, results from higher-order turbulent closure schemes such as E}e}q, predict that *S is slightly larger than that with

 lower-order closures, and is located above the surface, at about half of the height where the velocity perturbation reaches its maximum. It decays towards the surface but is almost identical aloft as that of simple turbulence closures; see Fig. 3. In the Guidelines we have decided to ignore these near surface-variations } which are typically signi"cant only in the lowest few metres of the boundary layer, and use results from our 1-order closure model in determining the coe$cients in Eqs. (3) and  (4), unless otherwise stated. From the MSFD model calculations, we "nd that the predicted fractional speed-up ratio, *S, in fact, varies with surface roughness, z and that Eq. (2) is overly simpli"ed.  The maximum fractional speed-up ratio at the hilltop, *S , can be quite well

 approximated by




*S ¸

 "B #B ln  , (3)   H/¸ z   where B and B are constants to be determined for each terrain type. We also   "nd that the height variation of hilltop fractional speed-up ratio *S can be better modelled as *S(0, Z) ln "A #A (Z/¸ )!A e\ 8* , (4)     *S

 where A (i"1, 2 and 3) are constants to be determined. This formula is intended to G be applied up to Z/¸ "1, since the signi"cant e!ect of the hill on the #ow usually  extends to a height of order ¸ . 

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Fig. 3. Comparison of MSFD and NLMSFD model results with E}iz and E}e}q turbulence closures for #ow over 2D terrain. u is velocity perturbation. (a) and (b) rolling terrain and (c) and (d) for an isolated  hill.

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Table 3 *S /(H/¸ ) for rolling terrain with di!erent ¸ /z

    z (m)  ¸ /z  

0.001 5;10

0.002 2.5;10

0.005 10

0.01 5;10

0.02 2.5;10

0.05 10

0.1 5;10

0.2 2.5;10

0.5 10

1.0 5;10

2D 3D

1.47 1.07

1.49 1.09

1.54 1.12

1.57 1.15

1.60 1.17

1.65 1.21

1.68 1.23

1.72 1.26

1.75 1.29

1.77 1.30

Fig. 4. Variations of *S /(H/¸ ) as a function of ln(¸ /z ) with best "t lines using Eq. (3): (a) rolling

    terrain, (b) isolated hills.

3. Results and discussions 3.1. Rolling terrain Table 3 shows *S varying with z for a "xed ¸ for both the 2D and 3D rolling

   terrain. From the table, we see that *S increases with z for a given ¸ , and that

   *S for 2D terrain is about 35% larger than that for 3D terrain with the same ¸ /z

   and H/¸ . This is what we expected, since air#ow can go around as well as over the  3D terrain. The increased speed-up for rougher hills is a consequence of an increase in the ; (¸ )/; (Z) ratio. Using the least-squares method, we can obtain a good "t to    MSFD model results using Eq. (3) with B "2.07 and B "!0.046 for the 2D   rolling terrain, and with B "1.53 and B "!0.035 for the 3D terrain, see Fig. 4a.   In the original Guidelines, B"1.55 and 1.1 (dashed-lines) were used for 2D and 3D rolling terrain, respectively. They are somewhat lower than most of our model results but appropriate for relatively smooth surfaces (¸ /z +10).  

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Fig. 5. Comparison of the normalised *S decays with height. (a) 2D rolling terrain, (b) 3D rolling terrain, (c) averaged 2D isolated hill shapes, (d) averaged 3D isolated hill shapes. Note that individual data are identi"ed by their ¸/z values. 

The decay of *S with height is rather more complicated. The use of a simple exponential decay in the original Guidelines (Eq. (2)) gives quite a good match to our model results close to the surface in the range 0(Z/¸ )0.3, but decays too fast with  Z for Z/¸ '0.4, see Fig. 5a. In fact, for Z/¸ 3[0.4,1], a straight line (ln*S vs. Z/¸ )    gives a good "t to the model results but does not pass through *S at Z+0. Here

 we "t the MSFD model results with Eq. (4), again by using the least-squares method. Coe$cients are given in Table 4 for a range of values of ¸ /z . We see that A (i"1, 2,   G 3) vary with ¸ /z . Since A and A do not change by very much in the range of ¸ /z      

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Table 4 Constants A (i"1, 2 and 3) for rolling terrain with di!erent z (¸ "500 m) n/a"not applicable and p is G   standard deviation z (m) 

¸ /z  

2D

3D

A 

A



A 

A 

A

A 



0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.5 1.0

5;10 2.5;10 10 5;10 2.5;10 10 5;10 2.5;10 10 5;10

!0.56 !0.55 !0.56 !0.60 !0.64 !0.62 !0.63 !0.63 !0.62 !0.58

!1.58 !1.63 !1.64 !1.61 !1.58 !1.64 !1.64 !1.65 !1.68 !1.72

9.51 9.35 8.72 7.75 6.83 6.40 5.74 5.09 4.16 3.51

!0.62 !0.59 !0.60 !0.65 !0.71 !0.66 !0.66 !0.66 !0.64 !0.57

!1.91 !1.99 !1.98 !1.92 !1.84 !1.92 !1.89 !1.90 !1.88 !1.93

Mean

n/a

!0.60

!1.64

n/a

!0.63

!1.92

p

n/a

0.034

0.043

n/a

0.041

0.046

7.99 8.10 7.89 6.64 5.76 5.54 4.95 4.42 3.57 2.99 n/a n/a

considered typical, we take average values, AM and AM from Table 4. For A , the    variation with ¸ /z can be well represented by   A "A #A ln(¸ /z ), (5)      where A "!2.03 and A "0.90 for the 2D rolling terrain. For the 3D   rolling terrain, A "!1.67 and A "0.64. By using the mean values for A    and A and calculating A from Eq. (5), expression (4) gives quite good agreement   with model results except for the very rough surface case (¸ /z '10); see Fig. 5a   and b. 3.2. Isolated hills For air#ow over isolated hills (and 2D valleys), we do a similar kind of "tting with the MSFD model data as for the air#ow over rolling terrain. Tables 5 and 6 show *S varying with z for a "xed ¸ (nominally"200 m) for

   various 2D and 3D isolated hills. As for air#ow over rolling terrain, we see from these tables that *S increases with increasing z and that *S for a 2D hill is larger

 

 than that for a 3D hill for given ¸ /z and H/¸ as in Table 3. Note, however, that for    isolated hills the di!erence in *S between a 2D and 3D hill is about 16%, which is

 about half the di!erence between the 2D and 3D rolling terrains. For the isolated hills, the exact values of *S are dependent on the hill-shape details. Therefore, for

 a typical isolated hill, we use the averaged values from the above tables B "2.41 and  B "!0.051 for 2D and B "2.09 and B "!0.049 for 3D isolated hills, see    Fig. 4b. In the "gure, constant B"2 and 1.6 (dashed-lines), as used in the original Guidelines for 2D and 3D isolated hills, respectively, are also shown.

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Table 5 *S /(H/¸ ) for 2D isolated hills with di!erent ¸ /z

    z (m)  ¸ /z  

0.001 2;10

0.002 10

0.005 4;10

0.01 2;10

0.02 0.05 10 4;10

0.1 2;10

0.2 10

Bell-shaped Gaussian Cosine-squared

1.86 1.75 1.72

1.90 1.79 1.76

1.96 1.84 1.81

2.00 1.88 1.85

2.04 2.10 1.92 1.97 1.89 1.94

2.13 2.00 1.98

2.17 2.20 2.04 2.07 2.01 2.04

2.20 2.08 2.06

Averaged value

1.78

1.82

1.87

1.91

1.95 2.00

2.04

2.07 2.10

2.11

1.0 2;10

0.5 4;10

1.0 2;10

Table 6 *S /(H/¸ ) for 3D isolated hills with di!erent ¸ /z

    z (m)  ¸ /z  

0.001 2;10

0.002 10

0.005 4;10

0.01 2;10

0.02 0.05 10 4;10

0.1 2;10

0.2 10

Bell-Shaped Gaussian Cosine-squared

1.56 1.47 1.44

1.60 1.50 1.47

1.65 1.54 1.52

1.69 1.58 1.56

1.72 1.78 1.62 1.67 1.59 1.64

1.81 1.70 1.67

1.84 1.88 1.73 1.77 1.71 1.74

1.89 1.79 1.76

Averaged value

1.49

1.52

1.57

1.61

1.64 1.69

1.73

1.76 1.80

1.81

0.5 4;10

Table 7 Constants A (i"1, 2 and 3) for isolated hills with di!erent z . Averaged values for the di!erent hill shapes G  (¸ "200 m)  z (m) 

¸ /z  

2D hill

3D hill

A 

A



A 

A 

A

A 



0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.5 1.0

2;10 10 4;10 2;10 10 4;10 2;10 10 4;10 2;10

!0.64 !0.64 !0.66 !0.67 !0.68 !0.65 !0.66 !0.68 !0.53 !0.47

!1.28 !1.30 !1.31 !1.31 !1.30 !1.36 !1.36 !1.32 !1.52 !1.54

7.65 7.46 6.79 6.37 5.87 5.34 4.72 4.07 3.61 3.02

!0.67 !0.67 !0.68 !0.69 !0.70 !0.66 !0.67 !0.69 !0.52 !0.47

!1.46 !1.46 !1.47 !1.46 !1.44 !1.49 !1.48 !1.42 !1.61 !1.60

Mean

n/a

!0.63

!1.36

n/a

!0.64

!1.49

p

n/a

0.070

0.092

n/a

0.080

0.064

7.26 7.11 6.49 6.10 5.61 5.14 4.55 3.93 3.52 2.98 n/a n/a

The decay of *S with height is similar to that for rolling terrain. We "rst take the averaged values of *S from our three di!erent hill shapes and then calculate those coe$cients from Eq. (4) by using the least-squares method. The results are listed in Table 7. From the table, we see that the exact values of these A (i"1, 2, 3) are G

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sensitive to ¸ /z , especially for A . Again, for simplicity, we shall ignore the    dependence of A and A on ¸ /z and use averaged values of A and A from the       last line of Table 7. Eq. (5) gives a good "t for A with A "!0.55 and A "0.69    for a 2D isolated hill and A "!0.34 and A "0.64 for a 3D isolated hill. Fig. 5c,   and d show the comparisons of the model results with the approximation (4), in which the mean values, AM and AM are used and A is calculated from Eq. (5), for 2D and 3D    isolated hills, respectively. The agreement is good, again with the largest discrepancies for very rough surfaces (¸ /z '10).   For the terrain shapes used here, the LSD model [8] gives B"2.3 for 2D and B"1.64 for the 3D terrains (for both rolling and isolated hills). If we were to plot these values in Fig. 4, it is obvious that B"2.3 is too large even for 2D isolated hills. For 3D topographies, B"1.64 is better for isolated hills, but the value is far too large for rolling terrain. 3.3. Ewects of nonlinearity The above results are deduced from the linear MSFD model which is, in general, only a good approximation for terrain with small slope or H/¸ . As H/¸ increases,   nonlinear e!ects become important [14]. To incorporate these e!ects, we have conducted some NLMSFD model runs by varying H. The largest value of H/¸ used  in the calculation is 0.7 (slope+0.5). For 3D terrain, a "xed roughness z "0.05 m is  used. By considering Eq. (3), we assume that *S can be modelled as

 *S ¸

 " B #B ln  G(H/¸ ), (6)    H/¸ z   where G is a function of H/¸ to be determined.  From the results of NLMSFD model calculations for 2D terrain, we "rst take average values of *S over di!erent z for a given value of H/¸ and then do a least

   squares "t. (For the isolated hills, averages have been done for three di!erent hill shapes as well.) The results show that G can be well approximated by a second-degree polynomial in H/¸ . The resulting constants are rearranged so that the proposed new  formula for *S to be used in the Guidelines is in the form of

 *S ¸ H H 

 " B #B ln  1#B #B . (7)   ¸  ¸ H/¸ z     The new constants are listed in Table 8. Fig. 6 shows the plot of the function G(H/¸ )  vs. H/¸ for various terrain shapes. It is interesting to note that the behaviour of  G(H/¸ ) for 3D topographies is quite di!erent than that of 2D terrain. For 3D hills,  G(H/¸ ) increases initially, reaches its maximum at about H/¸ "0.3 and then   decreases there after. For 2D ridges G(H/¸ ) decreases monotonically with H/¸ ,   while with 2D rolling terrain, it decreases almost linearly. Note that one should be cautious in applying Eq. (7) to topography with large values of H/¸ . For the NLMSFD calculations, we encounter convergence di$culties  for slopes larger than about 0.5. The formula is not applicable for G(H/¸ ))0. 














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W. Weng et al. / J. Wind Eng. Ind. Aerodyn. 86 (2000) 169}186 Table 8 Constants B for 2D and 3D rolling terrain and isolated hills G Constant

B 

B 

B 

B 

2D 3D 2D 3D 2D

2.20 1.58 2.40 2.05 2.57

!0.049 !0.036 !0.051 !0.048 !0.054

!0.64 0.069 0.029 0.24 !0.65

!0.19 !0.85 !0.51 !0.40 !0.80

rolling terrain rolling terrain isolated hill isolated hill valley

Fig. 6. Function G(H/¸ ) vs H/¸ .  

4. Comparison with experimental data 4.1. Comparison with Field Observations There are several "eld experiments [1] which can be used for comparison. However, the topographic features involved were not ideal, as used in our calculations, and only rough comparisons are possible. Although the general conclusion reached in Ref. [1] when the original Guidelines were compared with experimental data does not change, the new formulations have slightly improved some results. Table 9 shows observed fractional speed-up for selected 2 h runs together with wind directions, estimated corresponding values of ¸ (from Ref. [1]) and Guidelines 

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Table 9 Measured and estimated *S for Askervein hill from the 1982 experiment Run no

1.22 1.23a 1.23b 2.25 2.27 2.29b 2.01a 2.01b 2.02

Wind direction (deg)

180 230 245 120 165 235 165 155 200

*S measured at Z"10 m

0.61 0.78 0.61 0.34 0.62 0.65 0.53 0.40 0.82

L (m) 

280 220 240 650 380 220 380 530 210

*S Estimates at Z"10 m Original Guidelines 2D, 3D

New Guidelines 2D, 3D

0.74, 0.92, 0.85, 0.34, 0.56, 0.92, 0.56, 0.41, 0.96,

0.63, 0.74, 0.70, 0.31, 0.50, 0.74, 0.50, 0.38, 0.76,

0.58 0.70 0.65 0.27 0.44 0.70 0.44 0.32 0.73

0.60 0.72 0.67 0.27 0.46 0.72 0.46 0.33 0.74

In the Guidelines calculations, H"116 m and z "0.03 m are used. 

estimates for *S. Since Askervein hill is neither axisymmetric nor two-dimensional and is essentially elliptical in plan with a 1 km minor axis and a 2 km major axis, the results of both 2D and 3D isolated hill formulations are listed in Table 9. In general, 2D results of the original Guidelines are always larger than that of new Guidelines and observed values while the reverse is true for the 3D results. If one takes the average of 2D and 3D model results, both the original and the new Guidelines estimates seem reasonable. Observations of the wind speed over the summit of an isolated, roughly circular, hill were reported in Ref. [16]. The height of Nyland hill is 70 m and the base diameter is about 500 m which leads to ¸ +125 m. A surface roughness length z "0.1 m is   suggested by Mason. Fig. 7a shows comparison of the Guidelines with these "eld experimental data. Although the new Guidelines improve the comparison slightly, the observed values are still about 30% larger than our estimates. We have no real explanations for this anomaly, but do note that the observed *S value (&1.3) are

 rather higher than found elsewhere. Wood's formula [10] predicts *S +1.65,

 which is too large even at Z"1 m. A series of measurements from a 100 m tower at the crest of a wooded 170 m hill } Black Mountain are reported in Ref. [17]. The hill is slightly asymmetric with ¸ +275 m. The surface roughness was estimated as z K1 m. The estimation from   the Guidelines and experimental data are shown in Fig. 7b. For individual runs, the experimental data are rather scattered. In the "gure, mean values of 10 di!erent runs are plotted. Apart from the discrepancy close to the surface, the agreement between the original Guidelines and data is quite good; the new Guidelines appear to underestimate *S slightly in comparison with these data. Using Wood's formula [10], we obtain *S +1.9 which is far too large comparing with the data.

 Note that the measured fractional speed-up from Nyland hill and Black Mountain experiments both show *S increasing from small Z and reaching its maximum value

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Fig. 7. Comparison of Guidelines estimates with experimental data at the summit of (a) Nyland hill, (b) Black Mountain.

then decreasing with height. The location of *S is away from the surface, as in the

 results of the MSFD and NLMSFD models with higher-order turbulence closure, see Fig. 3. 4.2. Comparison with wind tunnel experimental data We "rst consider wind tunnel experimental data taken from Ref. [18]. Detailed #ow and turbulence measurements were made over a 2D ridge and a 3D circular hill, both having cosine-squared cross-sections (see Table 2) and H/¸ +, in the wind tunnel at   the Department of Agriculture, Reading University. The simulated neutrally strati"ed boundary layer is about 0.3 m deep. The mean wind speed is adequately represented by a logarithmic law with the friction velocity u "0.055; and the surface roughH  ness z "0.17 mm (; "8 m s\ is the free-stream wind speed) over a #at #oor. The   characteristic scales for the 2D ridge are H"31 mm and ¸ "100 mm, and for the  3D circular hill, H"35 mm and ¸ "100 mm. Fig. 8 shows the comparison of the  Guidelines formulation and the Lemelin et al. LSD model [8] with the wind tunnel experimental data. There are large discrepancies very close to the surface, all model approximations apparently over-predicting *S . However, the di$culty of making

 accurate measurements very close to the surface may also contribute the di!erence. Overall, the new formulation of the Guidelines agrees well with the data.

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Fig. 8. Comparison of Guidelines and the Lemelin et al. LSD estimates with Gong's wind tunnel data: (a) 2D ridge, (b) 3D circular hill.

A second set of wind tunnel data are those of the EPA experiments, RUSHIL and RUSVAL [19,20]. The EPA (Environmental Protection Agency) wind tunnel experiments simulated a neutral atmospheric boundary layer with a 2D underlying surface. The velocity pro"le in the absence of the hill/valley is well described by a logarithmic law with u "0.178 m s\ and z "0.157 mm. It reaches the free-stream wind speed H  ; "3.9 m s\ at a height of 1 m. The shape of the underlying surface is given  parametrically, i.e.,



a x" m 1#  m#m(a!m)





a z" m(a!m 1!  m#m(a!m) z"0





if "m")a,

if "x"'a,

(8)

where m"H/a#((H/a)#1, H is the maximum height/depth of the hill/valley and a its half-width. The topographies described by Eq. (8) have smooth forms that are symmetric about the origin x"0 and smoothly merge into a #at plane at x"$a. For the RUSHIL, three model hills, all with H"0.117 m are used in the experiments. Their aspect ratios, de"ned as a/H, were 8, 5 and 3, corresponding to maximum slopes of 0.176, 0.287 and 0.488, respectively. These numbers are used as hill identi"ers for RUSHIL: H8, H5 and H3. For RUSVAL, H"!0.117 m and z is negative in Eq. (8). The identi"ers become V8, V5 and V3.

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Fig. 9. Comparison of Guidelines and the Lemelin et al. LSD estimates with EPA wind tunnel data. At the top of RUSHIL: (a) H8, (b) H5, (c) H3. At the bottom of RUSVAL: (d) V8, (e) V5, (f) V3.

The Guidelines and the Lemelin et al.'s LSD estimates, together with the wind tunnel experimental data, are shown for the hills in Fig. 9a}c. Surprisingly, the agreement between the estimates and data is better for H5 and H3 than for H8, especially close to the surface } where large di!erences exist for H8. Overall, the new Guidelines perform slightly better than the other models. Fig. 9d}f show the comparison of the Guidelines estimates with the wind tunnel observations for RUSVAL: V8, V5 and V3. There is little di!erence between the estimates of the original and new Guidelines except that high up the predictions of the original Guidelines decay too quickly. The Guidelines give a good estimates for V8 but under-predict the wind speed reduction close to the surface of V5 and V3.

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5. Concluding remarks The Guidelines are a useful and practical tool for roughly estimating wind speed variations due to small-scale topographic features and step changes in roughness. Based on numerical model results from MSFD and NLMSFD, new formulations are presented. The dependence of the fractional speed-up on surface roughness and a nonlinear e!ect are included. Although the comparison with experimental data is not conclusive, we believe that the new formulation is now better in re#ecting the numerical model results and can be expected to improve the Guidelines performance in practice. There is a Windows 95 version of the original Guidelines available, from Jim Salmon at Zephyr North (personal communication).

Acknowledgements This work has been funded in part by the Canadian Climate Research Network under a research agreement with York University and in part through a Collaborative Research Agreement with the Canadian Atmospheric Environment Service.

References [1] P.A. Taylor, R.J. Lee, Simple Guidelines for estimating wind speed variations due to small scale topographic features, Climatological Bull. 18 (2) (1984) 3}22. [2] J.C.R. Hunt, Wind over hills, in: J.C. Wyngaard (Ed.), Workshop on the Planetary Boundary-layer, American Meteorological Society, Boston, 1980, pp. 107}144. [3] W.P. Elliott, The growth of the atmospheric internal boundary layer, Transactions of the American Geophysical Union 39 (1958) 1048}1054. [4] J.L. Walmsley, P.A. Taylor, J.R. Salmon, Simple guidelines for estimating wind speed variations due to small-scale topographic features } an update, Climatological Bulletin 23 (1) (1989) 3}14. [5] P.A. Taylor, J.L. Walmsley, J.R. Salmon, Guidelines and models for estimating wind speeds at WECS sites in complex terrain, INTERSOL85 Proceedings, 9th Biennial Congress of the International Solar Energy Society, Montreal, Canada, 23}29 June, 1985, Pergamon Press, New York, 1986, pp. 2009}2014. [6] J.L. Walmsley, P.A. Taylor, J.R. Salmon, 1985, Boundary-layer studies of winds over islands with applications to surface wind data from Grindstone Island (I) les-de-la-Madeleine) and Sable Island, in: T.A. Agnew, V.R. Swail (Eds.), Proceedings, International Workshop on O!shore Winds and Icing, Halifax, Nova Scotia, Canada, 7}11 October, 1985, pp. 165}174. [7] N.O. Jensen, E.L. Petersen, I. Troen, Extrapolation of Mean Wind Statistics with Special Regard to Wind Energy Applications, WMO Publication, WCP-86, 1984, 85 pp. [8] D.R. Lemelin, D. Surry, A.G. Davenport, Simple approximations for wind speed-up over hills, J. Wind Engineering and Industrial Aerodynamics 28 (1988) 117}127. [9] J.L. Walmsley, J.R. Salmon, P.A. Taylor, On the application of a model of boundary-layer #ow over low hills to real terrain, Boundary-Layer Meteorol. 23 (1982) 17}46. [10] N. Wood, The onset of separation in neutral, turbulent #ow over hills, Boundary-Layer Meteorol. 76 (1995) 137}164. [11] S.E. Belcher, Turbulent boundary layer #ow over undulating surface, Ph.D dissertation, Cambridge University (1990).

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[12] J.L. Walmsley, D. Woolridge, J.R. Salmon, MS-Micro/3 User's Guide', Report ARD-90-008, Atmospheric Environment Service, Downsview, Ontario, Canada, 1990, 88 pp. [13] I. Troen, N.G. Mortensen, E.L. Petersen, WASP Wind Atlas Analysis and Application Program user's Guide', Ris+ National Laboratory, Roskilde, Denmark, 1988, 32 pp. [14] D. Xu, K.W. Ayotte, P.A. Taylor, Development of a non-linear mixed spectral "nite di!erence model for turbulent boundary-layer #ow over topography, Boundary-Layer Meteorol. 70 (1994) 341}367. [15] K.W. Ayotte, D. Xu, P.A. Taylor, The impact of turbulence closure schemes on predictions of the mixed spectral "nite-di!erence model for #ow over topography, Boundary-layer meteorol. 68 (1994) 1}33. [16] P.J. Mason, Flow over the summit of an isolated hill, Boundary-layer meteorol. 37 (1986) 385}405. [17] E.F. Bradley, An experimental study of the pro"les of wind speed, shearing stress and turbulence at the crest of large hill, Quart. J.Roy. Meteorol. Soc. 106 (1980) 101}123. [18] W. Gong, A. Ibbetson, A wind tunnel study of turbulent #ow over model hills, Boundary-Layer Meteorol. 49 (1989) 113}148. [19] L.H. Khurshudyan, W.H. Snyder, I.V. Nekrasov, Flow and dispersion of pollutants over twodimensional hills, U.S. EPA Report No.EPA-6000/4-81-067. Research Triangle Park, NC 27711, 1981. [20] L.H. Khurshudyan, W.H. Snyder, I.V. Nekrasov, R.E. Lawson Jr, R.S. Thompson, F.A. Schiermeier, Flow and dispersion of pollutants within two-dimensional valleys, U.S. EPA Report No.EPA-600/390-025. Research Triangle Park, NC 27711 1990.