A comparison of three methods for predicting wind speeds in complex forested terrain

Meteorol. Appl. 6, 329 342 (1999) A comparison of three methods for predicting wind speeds in complex forested terrain Juan C Suárez, Barry A Gardiner and Christopher P Quine, Forestry Commission Research Agency, Northern Research Station, Roslin, Midlothian, EH25 9SY, UK The comparative performance of the WASP and MS-Micro/3 airflow models and of the DAMS scoring system in calculating the wind climate in complex forested terrain has been examined. An analysis was carried out of predicted and observed wind speeds collected over 18 months at six monitoring sites in mountainous country in the Cowal Peninsula, western Scotland. Both airflow models and the DAMS system produced variable results: the airflow models were most accurate on exposed hill tops whereas DAMS tended to be more accurate in valleys and lower slopes. Taken as a whole this study showed that the DAMS scoring system performed as well as the other airflow models considered. 1. Introduction Wind is one of the most important limiting factors for forestry in Britain. Most forestry plantations in this country have been established in upland areas on land marginal for agricultural use. These locations are commonly affected by high winds and poor soil conditions which make windthrow the most serious abiotic hazard in forestry (Miller, 1985). The effect of the wind is directly responsible for important losses of timber every year in Great Britain (NAO, 1993). Forest management options to improve the final crop quality are limited by windiness because it constrains the number of thinning regimes and shortens rotations. In addition, the quality of the timber is also affected by an increase in the proportion of compressed wood, poor stem straightness, repeated loss of leaders, which may developed crooked stems, and important alteration in the relation height diameter. Therefore sites affected by high levels of windiness tend to produce timber less suitable for higher value markets. Consequently, the determination of site vulnerability is important in order to minimise the risk of damage. Aspects influenced by site vulnerability include the choice of species for planting, the selection of silvicultural treatments (thinning and rotation length) and the estimation of the economic return on the investment in plantations (Miller, 1985). 2. Background 2.1. Previous methods to assess the risk of wind damage The Windthrow Hazard Classification (WHC) devised by Booth (1977) and developed by Miller (1985) was designed to predict site vulnerability to strong winds from a combination of four factors, which were individually scored, summed together, and divided into six classes of increasing hazard. The four factors were: the wind zonation of the country, elevation, topographic exposure and soil type. The first three define the windiness of a site, and the soil influences the potential root anchorage and the resistance to overturning. Wind zonation reflects the regional pattern of the British wind climate, which shows an increase in windiness to the north and west of the country, due to the influence of Atlantic depressions. The effect of elevation is well correlated with high mean wind speeds and gales frequency. Topographic exposure (topex) is a measure of the shelter provided by the surrounding terrain and is obtained by summing the angle of inclination to the skyline in the eight main compass directions (Bell et al., 1995). Large values indicate higher ground close to the site while small values reveal an exposed location. To reduce the subjectivity in the evaluation of the wind factors in the WHC, Quine & White (1993, 1994) used multiple regression of the rate of attrition of tatter flags against a group of geographic elements including wind zone, aspect, elevation, topex, valley shape and valley direction. Tatter flags are made with cotton and the rate of loss of this material has been found to be well correlated with mean wind speed over a two-month period (Jack & Savill, 1973). The relative importance of each element was used to create a new scoring system called the Detailed Aspect Method of Scoring (DAMS) (Quine & White, 1993). Bell et al. (1995) developed an application to calculate DAMS at a resolution of 50 m using a raster-based Geographic Information System (IDRISI, Clark University, USA) and elevation data in digital format obtained from the Ordnance Survey. The DAMS scores were calculated for the whole of Scotland, the North of England and Wales and used to update the Windthrow Hazard Classification for substantial forested areas. The calculation of topex was undertaken on a cell-by-cell basis by estimating the 329

J C Suárez, B A Gardiner and P C Quine angle to the skyline within a distance of 10 km. Only positive angles were considered and all the negative angles were rounded to zero; this was necessary to conform to the field measurement practice that supplied values used to formulate DAMS (Bell et al., 1995). DAMS is a practical method to estimate site windiness over large areas and is easy to compute by using GIS. However, it only provides a general representation of the windiness affecting a particular area. The scores are obtained as a function of the rate of attrition against geographic elements close to the tatter flag locations. Therefore, the scores are site dependent, influenced by the availability of tatter flag data, and the results may not be applicable to other locations. In particular, DAMS has no method for representing the effect of changes in the surface roughness elements surrounding the site, which can substantially alter windiness conditions (Hannah, 1993). 2.2 The ForestGALES method Current research is developing a probabilistic model called ForestGALES to replace the WHC. In the new model, the probability of windthrow is calculated as a function of the interaction of wind and tree mechanics (Quine, 1996). The model estimates the threshold wind speed for overturning and breaking trees in a particular stand, the windiness of the area and the probability of critical wind speeds being exceeded (Gardiner & Peltola, 1998). The application of the model requires accurate knowledge of the local wind climate. However, this is limited in upland Britain due to the lack of observations in high ground areas, the lack of an agreed method, and the cost of obtaining data. The number of sites recording wind speed on a regular basis in Britain is 135 with only 14 above 200 m.a.s.l. (Meteorological Office, 1990). 2.3. Methods for the estimation of local wind climate A number of methods have been tried to estimate local wind climate in Britain. These range from statistical models, operating linear regressions against geographic elements (Hannah et al., 1995), to spatial interpolation techniques such as partial thin spline functions (Barrow et al., 1993). These techniques are currently utilised in the calculation of climatic variables such as temperature or rain, which are well correlated to elevation or distance to sea (Barrow et al., 1993). The application of these techniques to the prediction of wind climate is most successful where the reference and the predicted sites are close to each other, and where the local terrain is not very rough. However, the application of geographic elements as covariates in the estimation of wind regime becomes difficult due to the effect of the fluid and thermodynamic processes affecting the lower 330 atmosphere, and the influence of terrain and surface roughness elements. Errors are likely in areas of complex terrain where the wind can be blocked or funnelled in valleys, accelerated downslope or by the tops of hills or momentum is lost by turbulent transfer to rough surfaces. Non-neutral conditions, vertical stratification and diurnal sea breezes all affect flow behaviour and cause serious modifications to the local wind climate (Bowen & Mortensen, 1996). 2.4. Commercial airflow models Over the last 20 years a group of analytic airflow models have been developed based on the original work of Jackson & Hunt (1975), who performed linear, small perturbation analysis of the flow over low hills. The flow field was divided into an outer region in which the flow is inviscid and an inner region in which stress divergence is important. The equations of motion are linearised to allow an analytic solution, and a simple mixing length closure is employed to solve for the turbulence in the inner layer. The original model was extended to three dimensions by Mason & Sykes (1979). Sykes (1980) divided the inner region into an inner surface layer and a sheer stress layer and Hunt et al. (1988) divided the outer region into a middle and an upper layer. These improvements allowed proper matching of velocity perturbations between the layers. The predictions of Jackson and Hunt linear theory have been tested in a number of field experiments (Taylor & Teunissen, 1987; Mason & King, 1985). In general, these were on hills of gentle slope under neutral conditions, but inaccuracies in the model predictions were still found particularly in the lee of hills where flow separation can occur (see review in Finnigan, 1988). Examples of commercially available linear models based on the Jackson and Hunt theory are Flowstar (Carruthers & Hunt, 1990), MS3DJH (Walmsley et al., 1986), MS-Micro/3, a microcomputer-based version of MS3DJH (Walmsley et al., 1986), and WASP (Troen & Petersen, 1989; Mortensen et al., 1993). Beljaars et al. (1987) adapted the linear approach by using a finite difference scheme (MSFD) in the vertical instead of dividing the flow into two regions, which allows higher order turbulence closure to be incorporated. Other airflow modelling schemes include the mass-consistent approach of models such as NOABL (Traci et al., 1977) and fully non-linear models such as RAMS (Pielke et al., 1992). Hannah (1993) and Inglis (1992) investigated how well MS3DJH and Flowstar respectively predicted the mean and turbulent flow in South Kintyre, Scotland. Model computations were compared with ground-based measurements using 10 m masts and airborne measurements obtained with an instrumented light aircraft. In general, the models were conservative in their prediction of wind speed variation, underestimating hill top

Predicting wind speeds in complex forested terrain wind speeds and overestimating wind speeds in the wake of the hills. Some improvement was obtained in the predictions, particularly in the outer region, when the atmospheric stability was incorporated in Flowstar (Inglis et al., 1995). Walmsley et al. (1990) compared three linear models (Mason-King Model D, MS3DJH, and WASP) and a mass-consistent model (NOABL) against field data obtained from Blashaval, North Uist. The models all performed similarly, with the greatest agreement, as expected, between the three linear models. Barnard (1991) performed a similar comparison between MS3DJH, WASP and NOABL using data from the Askervein project (Taylor & Teunissen, 1987). In this paper the predictions of two linear airflow models, WASP and MS-Micro/3, and the DAMS scoring system are compared with wind speed measurements in an area of extremely complex terrain. These two airflow models were selected for this experiment because they are being extensively used in the wind industry, they are linear models, and they are PC based, which makes them more affordable and simple to operate. This experiment was designed to test the models close to their theoretical limits on their ability to predict wind speeds in the wide range of terrain conditions in which forests are found. Previous comparisons have tested models on a case study basis by contrasting predictions against data obtained over a few hours (Barnard, 1991; Hannah, 1993; Inglis, 1992; Inglis et al., 1995; Moore et al., 1998, Walmsley et al., 1990). In this study the ability of the methods to predict the general wind climate of an area was examined by testing them against data obtained over a period of nearly two years. 3. Methods 3.1. The study site The study area was a rugged forested terrain located in the Glenbranter forest in the Cowal Peninsula (56 06 N, 5 02 W), Scotland (Figure 1). The forest consists mainly of Sitka spruce (Picea sitchensis) and lodgepole pine (Pinus contorta). The forest was severely damaged during a storm in 1968 and since 1987 it has been monitored for the onset and progression of wind damage. The topography is extremely complex with elevations ranging from 741 m at the top of Beinn Mhor to 25 m above sea level at Loch Eck within less than 3 km, and with a combination of valleys crossing north south (Glenshellish, Glen Branter of Caol Ghleann) and west east (Bernice Glen). Mean slope gradients are around 20 % and more than a quarter of the slopes are above 45 %. 3.2. Data collection The input data for testing the models were obtained for a 10 10 km area and provide information about the terrain, the roughness length of the surface elements and time-series of wind speed and direction from six locations. The terrain data were obtained from the Ordnance Survey 1:50000 Digital Terrain Model (DTM). The information was originally in tiles of 20 20 km with a 50 m resolution. However, only an area 10 10 km was analysed in order to keep a balance between computing effort and output resolution of the airflow models. A roughness length map was obtained from a reclassification of the Macaulay Land Use Research Institute (MLURI) 1988 land cover maps of Scotland (MLURI, 1993). The original land cover codes were grouped into five roughness classes according to the definitions of the European Wind Atlas (Troen & Petersen, 1989). The number of classes was dictated by the number of roughness lengths accepted by WASP (Mortensen et al., 1993) (Table 1). Time series of wind speed and direction were collected at six anemometer sites. Their locations were chosen according to the different configuration of the nearby terrain to ensure a wide variety of situations such as top of the hills, bottom of the valleys and mid-slope positions (Figure 1). A three-cup anemometer and wind vane (A100R and W200G Vector Instruments, North Wales) were mounted at the top of 10 m guyed masts. A detailed description of the anemometer sites is given in Table 2. Wind speed and direction values were logged every eight seconds and stored as frequency distributions every half hour on removable ramcards (Holtech Associates, Harwood-in-Teesdale, County Durham), which were collected on a monthly basis. The period of measurement extended from September 1990 to April 1992. 3.3. Data preparation Mean hourly values of wind speed and direction were obtained from the half-hour frequency distributions. Directional information for wind speeds less than 2 ms 1 was omitted because it is unreliable. The data were checked for dubious or missing information due to equipment failure, lightning, resetting the data loggers and icing of the instruments. The two periods with the greatest amount of missing data were May 1991 and December 1991 January 1992. To ensure that the period of the study was still representative and that the missing data did not have an important effect on the estimation of wind speed and direction, the values for the 18-month study period in Strathlachlan (1990 1992) were compared to a seven year data set (1986 1992) for the same location. Data from both periods were passed through the same checks and input into WASP to calculate frequencies of wind direction. The resulting wind roses (Figure 2) 331

J C Suárez, B A Gardiner and P C Quine Figure 1. The location of the study area. Table 1. Reclassification of roughness length classes for WASP Roughness (m) showed broad agreement between the two periods, and consequently the 18-month data used in this study were taken to be representative of the wind climate of the area. 3.4. The models (a) WASP The WASP airflow model uses the BZ model of Troen (1990) and a map analysis routine in order to calculate the flow perturbation profile at an observation point. The model makes use of a polar computational grid, 332 Surface 0.0004 Water surfaces 0.03 Grasslands 0.15 Newly planted trees, annuals, crops 0.5 Trees up to 15 20 years old, open landscapes, bushes 1 Fully grown trees, woodlands and urban areas expanding from the centre, in place of the usual rectangular grid. The input data are time series records of wind speed and direction limited to eight azimuth sectors to conform with the eight topex directions calculated for DAMS. The data are corrected upstream for the effect of surface roughness changes, the effect of obstacles and variations in terrain. The program then creates what is called a Wind Atlas for the region, which consists of Weibull distributions showing the probability density functions of wind speed for the eight azimuth sectors, a group of five heights above ground level and five different roughness lengths. Predictions are made using a speed-up factor calculated as a function of roughness and terrain heights between the reference site and the predicted locations (Mortensen et al., 1993). Geographic features like roughness length and terrain are kept in WASP in a vector data structure. The roughness data defines a topological structure with roughness lines with values to the left and to the right. In contrast, the terrain data only needs to store a unique value to define the changes in elevation. Time series data for wind speed and direction recorded at Strathlachlan were used as the anemometer reference to calculate the wind climate of the area. Strathlachlan

Predicting wind speeds in complex forested terrain Table 2. Anemometer sites used in the study area Site East North Elevation (m) Site description Strathlachlan 205201 696201 317 Located at the top of a 300 m high north facing ridge. No important orographic obstacles interrupt the winds from the west. This anemometer site was selected as the reference site in the WASP and MS-Micro/3 simulations. Cruich Buidhe 212500 694700 568 Situated at the top of a bell-shaped hill of 550 m. This exposed site is open to winds from all directions. Bernice Gap 211600 692200 370 In the middle of a saddle open to the north-west and south-east and with high ground to north-east and south-west Garrachra 210000 692600 275 Situated in a narrow valley open to the south-west and north-east. Glenshellish RS 211700 693500 270 On the west-facing slope of a valley open to the north. The anemometer site is surrounded by higher ground. Glenshellish Lower 210900 694400 90 At the bottom of a valley open to the north. Figure 2. Wind rose representations for frequencies of wind direction in Strathlachlan. was chosen as the reference site because of its good exposure and because it was the most western of the anemometer sites. A version of WASP (BIGWASP) which allows 16000 points was used to calculate the wind climate within the area of interest. Because WASP performs calculations for only one point at a time the model was run in batch mode and calculations were undertaken for a 100 m resolution grid over a 10 10 km area. The 100 m resolution was a restriction imposed by computational limitation. Following calculation, the results were re-gridded in SURFER (Golden Software, Golden, Colorado) using the nearest neighbour spatial interpolation method to create a 256 256 grid with 78 m resolution, to obtain the same resolution as MS-Micro/3. Problems that might occur at the edges of the calculation domain were avoided by using input data over a 20 20 km area but calculating solutions only within the central 10 10 km area. (b) MS-Micro/3 MS-Micro/3 is based on the theory of Jackson & Hunt (1975) as improved by Sykes (1980), which divides the 333

J C Suárez, B A Gardiner and P C Quine atmosphere into inner, middle and outer layers and assumes a neutrally stratified flow. The model uses a mixing-length closure scheme for turbulent stresses (Walmsley et al., 1986) and Fast Fourier Transformations (FFTs) to calculate the velocity and pressure perturbations in wave number space. Inverse FFTs convert these perturbations back into wind speed variations in normal space. The limitations imposed by this method are described in Walmsley et al. (1986). In order to run MS-Micro/3 it was necessary to set a parameter file with information on: wind directions, percentage of time from each direction, wind speed from each direction, roughness classes in metres, upstream roughness class, and upstream terrain height. The 18-month wind rose in Figure 2 was used to define the wind information in the parameters file for these simulations. The same roughness classes were used as in the WASP simulation. MS-Micro/3 assumes that the wind is always from the negative X direction (270 ), so SURFER was used to create eight rotated terrain and roughness grids to represent each azimuth direction. Grids consisted of 256 256 points representing an area of 20 20 km. The results of the calculations included wind speeds and direction deviations for each of the eight input wind directions. Outputs were presented as a grid of 128 128 points covering an area of 10 10 km at a resolution of 78 m. The eight wind speeds were averaged together to provide the climatic mean wind speed for comparison with the other models. (c) Model output normalisation Discrepancies between the input and the predicted mean wind speed at the reference site occurred because the measured wind speeds at Strathlachlan were used as surrogates for the incident undisturbed upstream wind speeds for each direction. This was not ideal even though Strathlachlan is well exposed in all directions. However, we were primarily interested in how well the models predicted relative differences in wind speed at different sites. Because the models are linear it is possible to multiply the output data by the ratio of the measured wind speed at Strathlachlan in order to obtain agreement at the reference site without affecting the relative differences between the sites. All output data from WASP and MS-Micro/3 have been normalised in this way. (d) DAMS The original digital maps of DAMS were calculated at 50 m resolution and in tiles of 20 20 km with boundaries identical to the Ordnance Survey DTM (Bell et al., 1995). In order to compare the DAMS scores with the airflow models, data were aggregated to the same resolution (78 m) and the scores transformed into wind speeds. This was achieved by multiplying the DAMS 334 grid by the ratio of the measured mean wind speed to the DAMS score at Strathlachlan. 4. Results 4.1. Summary results of the wind roses obtained in the monitoring areas Time series of wind speed and direction for each anemometer site were processed by WASP and the results plotted as wind roses showing the frequencies of wind direction in eight azimuth sectors (Figure 3). The wind roses indicated a strong dependency of the frequencies on the terrain. Sites like Strathlachlan and Cruich Buidhe were most exposed to the prevailing winds that come from the west and south. In sheltered sites like Bernice Gap, in the middle of a narrow valley that goes north-west to south-east, and Garrachra, in a location only exposed to the south-west, the valley orientation defined the prevailing wind directions. Glenshellish Lower received a high frequency of winds from the north and south with the predominance of south-east winds being due to the funnelling effect of the Glenshellish valley (Figure 1). At Glenshellish Restock the situation was similar to Glenshellish Lower. However, its position in the middle of a slope facing west left it slightly more exposed to westerly winds. 4.2. Linear regression One of the principal assumptions of the linear airflow models used in this study is that the different sites are subject to the same neutrally stable weather regime (Bowen & Mortensen, 1996) and that there is a unique speed-up factor between sites for each wind direction sector, independent of the weather conditions so long as they remain neutral. A high correlation between the actual wind speed and directions at different sites suggests that the models will perform accurately. The wind climate at Strathlachlan was compared with that recorded at the other sites by performing a series of linear regressions of wind speed and direction for each wind direction sector and for the combined data. The use of multiple regression techniques has already been used in the past (Hannah et al., 1995). Equations were forced to a second- or third-order polynomial to obtain the best possible correlation (R 2 value). The resulting R 2 values for each regression are presented in Table 3. The highest direction independent correlation of wind speed occurred between Strathlachlan and Cruach Buidhe. Cruach Buidhe is at the top of a 568 m hill which is exposed from all directions similar to Strathlachlan. The distance from Strathlachlan to Cruach Buidhe is 7.5 km with no high ground in

Predicting wind speeds in complex forested terrain Figure 3. Wind roses obtained from the time series period. Table 3. Linear Regression coefficients of wind speed and direction with respect to Strathlachlan (direction sectors defined at Strathlachlan) Sites Wind Direction Direction dependent independent N NE E SE S SW W NW 337.5 22.5 67.5 112.5 157.5 202.5 247.5 292.5 22.5 67.5 112.5 157.5 202.5 247.5 292.5 337.5 Cruach Buidhe Speed 0.65 0.57 0.48 0.55 0.48 0.73 0.72 0.78 0.72 Direction 0.45 0.16 0.05 0.13 0.04 0.06 0.07 0.01 0.00 Bernice Gap Speed 0.31 0.17 0.05 0.10 0.54 0.44 0.39 0.50 0.67 Direction 0.46 0.00 0.36 0.05 0.00 0.09 0.13 0.00 0.00 Garrachra Speed 0.33 0.70 0.52 0.37 0.30 0.61 0.80 0.25 0.11 Direction 0.65 0.12 0.00 0.13 0.09 0.33 0.00 0.20 0.08 Glenshellish RS Speed 0.41 0.47 0.01 0.16 0.20 0.62 0.52 0.53 0.48 Direction 0.43 0.05 0.00 0.08 0.02 0.18 0.33 0.10 0.13 Glenshellish Lower Speed 0.34 0.62 0.29 0.14 0.51 0.71 0.60 0.26 0.32 Direction 0.03 0.04 0.06 0.15 0.00 0.15 0.07 0.09 0.24 between. The reduction in correlation when the wind has an easterly component may be due to the fact that generally winds will be stronger from the west and the atmosphere better mixed and more neutral. In easterly winds greater thermal stratification of the atmosphere occurs, which will significantly affect the flow patterns, a phenomenon that is not included in the models used (Moore et al., 1998; Inglis et al., 1995). Some airflow models such as Flowstar (Carruthers & Hunt, 1990) do incorporate atmospheric stratification, but adding this 335

J C Suárez, B A Gardiner and P C Quine as a climatic variable presents enormous difficulties. In particular, the joint probability distributions between wind speed and stratification would need to be obtained for the whole of Britain. Poorer overall correlations were found between Strathlachlan and lower elevation sites indicating the extreme influence of topography on local wind speeds. There were much more marked differences in the correlations for different wind sectors than was the case for Cruach Buidhe. For example, Garrachra showed the best correlation when the wind at Strathlachlan was blowing from the north, north-east, south or southwest; Bernice Gap when the wind was from the northwest or south-east; Glenshellish RS when the wind was from the south, south-west, west or north-west; and Glenshellish Lower when the wind was from the north, south-east, south or south-west. Examination of Figure 1 shows that these are the directions from which these sites are most exposed to the wind, and for Garrachra and Bernice Gap is in good agreement with the valley orientation. 4.3. Model performance The performance of each model (WASP, MS-Micro/3 and DAMS) against the measured data from each site is shown in Table 4. In addition, the predicted wind speeds along a transect from the north-west to the south-east of the study area (Transect 1) and from the south-west to the north-east (Transect 2) are plotted in Figures 4(a) and 4(b) respectively. All models are relative to Strathlachlan because the results have been normalised to the measured wind speed at this site. However, at the other sites discrepancies of up to 56% were found between the observed wind speeds and those predicted by each model. Plotting the predicted wind speeds against the observed wind speeds for each model (Figure 5) shows more clearly how each model performs. Perfect agreement of the results would align the points on the 1:1 line which is also shown. The results were quite similar with each model overpredicting wind speeds at some sites and underestimating at others. The two linear airflow models gave similar results for the exposed summit of Cruach Buidhe. This is consistent with previous observations (Hannah et al., 1995), which found the best predictions for these types of model were between hill top sites. DAMS, on the other hand, underpredicted the wind speed at Cruach Buidhe, which is possibly because the scoring system in DAMS does not allow for negative skyline angles. This results in an underprediction of the exposure of the tops of steep hills or ridges (Hannah, 1993). All models overpredicted the wind speed at Glenshellish Lower. This suggests that flow separation is prevalent at this site. All models assume much closer coupling between the flow at Strathlachlan and Glenshellish Lower than is the case. The largest discrepancy occurred for Glenshellish RS where the wind speed was overpredicted 16% by WASP, 56% by MS-Micro/3 and 46% by DAMS (see Table 4). This was the only site which had a mid-slope position and indicates the difficulties for modelling due to the steepness of the terrain in this area. At Glenshellish RS the slope was approximately 44%, which is well outside the range over which the linear airflow models are expected to work (0 17%). For the five sites evaluated, there was relatively little difference between the predictions of the three models (see Figure 5), although WASP was the most and MS-Micro/3 the least accurate. However, the results from the transects (Figures 4(a) and 4(b)) and the output maps (Figure 6) showed substantial spatial variations in the predictions of each model. The spatial variation in the predictions for the cells around each anemometer site was obtained by comparing the value calculated for the cell at each anemometer site and the eight surrounding cells. The standard deviations from the mean of the estimated values in the cells around each site demonstrated that WASP was the most variable (σ = 2.13 ms 1 ), DAMS the least variable (σ = 1.01 ms 1 ), with MS-Micro/3 in between (σ = 1.46 ms 1 ). Some of these discrepancies are due to the coarseness of the solution grid (78 m) with the result that the measurement location may be up to 55.15 m from the nearest grid point. Nevertheless, these variations are due also to differences in the calculation method of the models. DAMS is a purely empirical model whereas the other models attempt to solve the flow equations over complex terrain. The topographic shelter value used in DAMS does not account for very localised variations in topography Table 4. General performance of the models at each anemometer site. Model output was normalised to give agreement at Strathlachlan (wind speed = 7.1 ms 1 ) which acted as the model input site Site Measured wind WASP MS-Micro/3 DAMS speed (ms 1 ) Wind (ms 1 ) Diff (%) Wind (ms 1 ) Diff (%) Wind (ms 1 ) Diff (%) Cruich Buidhe 10.6 10.6 0 10.9 3 9.3 13 Bernice Gap 6.7 8.1 19 6.9 3 6.6 2 Garrachra 5.0 4.2 16 4.0 20 5.7 13 Genshellish RS 3.9 4.5 16 6.1 56 5.7 46 Glenshellish Lower 4.7 4.0 14 3.9 16 4.3 8 336

Predicting wind speeds in complex forested terrain Figure 4. Mean wind speed predictions along (a) transect 1 and (b) transect 2 compared with measured wind speeds. and so DAMS will tend to smooth out variations in wind speed. There are also important differences between the two linear models. For example, MS- Micro/3 uses a regular grid to solve for all points simultaneously, whereas WASP is calculated on a cell by cell basis for each point using a grid which has finer resolution as one approaches the solution point. According to Monteith (1973) this is the most likely situation in the real world because the wind flow is normally affected by variations in roughness length elements over very short distances. Therefore, although the physics is the same, differences in the gridding methods may account for the differences found between the two linear models. In particular changes in topography close to the solution point will be better accounted for in WASP than MS-Micro/3 and could account for the greater 337

J C Suárez, B A Gardiner and P C Quine Figure 5. Predicted versus observed wind speed calculated by each model (straight line is 1:1 relationship between predicted and observed wind speeds). variability in the WASP solution. More anemometer sites would be necessary to fully check that the variations shown by WASP are realistic. At the moment, the limited number of sample sites in our experiment does not allow discrimination between the models and does not provide a reliable estimate of differences in model performance. 338 5. Conclusions Poor correspondence were obtained between the mean wind speeds measured at a reference hill top site (Strathlachlan) and five other sites on the Cowal peninsula, Scotland. The correlations between the measured wind directions were even worse and this was reflected

Predicting wind speeds in complex forested terrain Figure 6. Spatial variations of wind speed values calculated by each model. 339

J C Suárez, B A Gardiner and P C Quine in the fact that sector-dependent correlations between wind speeds were often much worse than the directionindependent wind speed correlations. The only consistent correlation across all direction sectors was between Strathlachlan and the other hill top at Cruach Buidhe. The directionality of the flow can be clearly observed in the wind roses for each site (Figure 3) and illustrates the strong directional influence of the terrain. Good correspondence, therefore, is only obtained when the general direction of the wind provides relatively uninterrupted flow onto both sites. When either site is in the lee of steep terrain the correlations fall to very low values (< 0.3). The reason is that the flow in such circumstances probably becomes separated and detached from the surface so that each site is in a different flow regime although the anemometer sites are too scattered to be absolutely certain that this did occur. Linear regressions provide an unreliable method of interpolation under such circumstances. Furthermore, the underlying assumption of linear airflow models that all points in the terrain are subject to the same flow regime (Bowen & Mortensen, 1996) is no longer valid and the performance of the models may be adversely affected. Three methods for predicting wind speed in complex terrain were tested including two linear airflow models (WASP and MS-Micro/3) and a method using geographic predictors (DAMS). All three methods performed better than was expected based on the results from previous tests carried out on individual case studies (periods of one to three hours) using data gathered on the Kintyre peninsula (Inglis, 1992; Inglis et al., 1995; Hannah, 1993) and the Cowal peninsula (Moore et al., 1998). Unlike these case studies, the two computer models (WASP and MS-Micro/3) do not have a consistent tendency to overestimate the wind speeds in the lee of the hills and in valleys. A tentative explanation is that the comparisons in this study take all wind directions into account. So overpredictions, when a location is in the lee of a hill, are compensated for by underpredictions when the wind is from other directions. This also suggests that errors in prediction for short term periods tend to cancel out over the longer term (1 2 years) so that, although wind speed predictions for an individual storm may be poor, climatic wind speed predictions will be better. All three methods gave similar results when predictions were compared against the five test sites (normalised to the reference site at Strathlachlan). The major difference was the variability in the predictions over the test areas. WASP shows the largest variations, DAMS the least with MS-Micro/3 in between. The result is that the predictions from WASP vary by a large amount over small distances. For example, at Cruach Buidhe in the maps illustrated in Figure 6 a change in a single grid point used to make the comparisons at Cruach Buidhe has a larger impact with WASP (18.5%), than MS3 (16%) or DAMS (8%). 340 There are a number of ways which the model predictions might be improved. An increase in the resolution of the gridded data for the linear airflow model simulations would help as this is known to be the most important factor in controlling the model predictions (Walmsley & Taylor, 1996). Unfortunately, a doubling of the resolution would reduce the area covered to a quarter otherwise the corresponding computational cost would be enormous. An improved DAMS could be developed by allowing negative skyline angles in the calculation of topex and restricting the distance over which topex is calculated to less than 3 km (Hannah, 1995). Another possibility is to produce a combined model which uses a geographic predictor system similar to DAMS to correct the output of the linear airflow models in areas where these are known to have difficulties (Bowen & Mortensen, 1996). This has the advantage over just using geographic predictors because it allows the calculation of the directional variation at each site, which is yet not possible with DAMS. Such information would be valuable in predicting the forest edges most vulnerable to damage because of the direction they face. To determine exactly which method is most accurate at predicting wind speeds in complex terrain will require data from a much greater number of anemometer sites. However, at present there appears to be little justification for replacing DAMS with linear airflow models in our evaluation method for predicting damage risk to British forests. The major weakness of DAMS is that it does not account for variations in surface roughness, which will affect the results obtained, particularly close to the ground. This means that any changes in roughness brought about by thinning or felling parts of the forests will not affect the DAMS predictions. The major advantage of DAMS is its ease of use and its wide applicability. The 1300 tatter flags that have already been monitored throughout Britain have allowed the DAMS model to be developed to incorporate national location as well as local effects. The windiness scores have subsequently been calculated for the whole country. The computing time was low and calculations at 50 m resolution for the whole of Britain took less than 24 hours using a PC486 running at 33 MHz. The task of calculating windiness at a similar resolution using the linear airflow models is daunting, even with more powerful computers. 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