The effects of atmospheric stability on coastal wind climates

Transcription

1 Meteorol. Appl. 6, (1999) The effects of atmospheric stability on coastal wind climates R J Barthelmie, Department of Wind Energy and Atmospheric Physics, Risø National Laboratory, 4000 Roskilde, Denmark (also affiliated to: Climate and Meteorology Program, Department of Geography, Indiana University, Bloomington, USA) A theoretical model of flow over a change in surface roughness shows that given an average geostrophic wind of between 8 and 13 m s 1 and near-neutral conditions the difference in equilibrium wind speed at 50 m height over roughness of 0.1 m and over the sea surface is about 20% or 2 m s 1. However, in nonneutral conditions the difference between on- and off-shore wind speeds is affected by changes in stability conditions. Using data from an off-shore monitoring project it is shown that flow over sea is typically associated with smaller stability corrections to the logarithmic wind speed profile owing to an increase in the number of near-neutral and unstable observations compared to flow over land. The presence of land is still detectable after flow of 1 2 km off-shore but its effect on stability and therefore the wind speed profile is reduced. The differences between stability climates on- and off-shore are not simple to elucidate since a number of factors such as the orientation of the coastline with regard to the prevailing wind direction, water depth and latitude are probably also important. 1. Introduction Atmospheric stability plays an important role in local and meso-scale atmospheric circulation yet relatively little is known about the frequency of different stability conditions in off-shore and coastal areas. As air flows over a coastal discontinuity, two types of change are generally experienced: an abrupt change in roughness, which affects the momentum flux, and a change in the availability of heat and moisture. According to Kaimal & Finnigan (1994) these active scalars influence stability and hence turbulent mixing and momentum transfer. Thus both processes are important in terms of estimating the wind resource (for wind energy applications) and in determining dispersion and deposition to coastal waters. Models that predict meteorological and climate variables at meso- to micro-scales should therefore incorporate effects introduced by the discontinuity at the coast. Development and implementation of suitable parameterizations are currently limited by the lack of information available on temporal and spatial variability of coastal stability conditions. Assuming conditions both on- and off-shore are close to neutral, differences between the wind climate onand off-shore can be ascribed solely to changes in surface roughness. However, data collected at off-shore and coastal platforms suggest that many off-shore areas have stability climates that are frequently non-neutral (Smedman et al., 1997; van Wijk et al., 1990). In stable conditions, off-shore wind speeds may increase very slowly with increasing distance from the coast or even decrease (Bergström et al., 1988), despite the reduction in frictional dissipation caused by the transition to lower roughness off-shore. In unstable conditions, coupling of the surface layer to higher wind speeds aloft and the resulting momentum transfer downward may increase off-shore wind speeds significantly in addition to the acceleration caused by the reduction in roughness. The modification of atmospheric stability occurs onand off-shore on different time scales and coastal regions exhibit larger seasonal temperature variations than areas far off-shore (Joffre, 1985). The seasonal change in sea surface temperature lags changes in land temperature (Korevaar, 1990). Thus in spring, if winds are directed off-shore, the temperature of the air moving over the sea is typically higher than that of the sea surface and conditions are frequently stable. In autumn the converse is true (van Wijk et al., 1990). Diurnal variability in temperature is not significant off-shore, except in shallow water (Barthelmie et al., 1996a). The contrast between on- and off-shore temperature changes and roughness can cause a diurnal cycle of offshore wind speeds that is inverted with respect to that at a typical land site (Barthelmie et al., 1996b). Additionally, the coastal zone is subject to thermally driven effects such as the sea-breeze (Coelingh et al., 1998) and low-level jets (Smedman et al., 1996). Factors affecting wind speeds in coastal region (excluding topography) include: air sea temperature differences, orientation of the coastline, 39

2 R J Barthelmie prevailing wind speed and direction, water depth, latitude (related to the magnitude of solar radiative forcing), distance from the coastal discontinuity, fetch (fetch is defined here by the surface type over which the wind blows before being measured). The aims of this paper are to assess the magnitude of changes in wind speed caused by roughness and stability changes at the coast using data collected at the Vindeby off-shore wind farm in Denmark and to illustrate the effect of the coastal discontinuity on the stability climate. The analyses are part of an ongoing study to assess the impact of atmospheric stability on wind energy resources in coastal and off-shore areas that are potential locations for the development of wind farms. 2. Theory 2.1. Effects of roughness The relative impact of roughness and stability changes on wind speed can be considered by taking each separately. If there is no change in stability or roughness, friction velocity can be predicted using the geostrophic drag law (e.g. Garratt, 1992): where: U g is the geostrophic wind speed, u * is the friction velocity, k is the von Karman constant, z 0 is the roughness length, f is the Coriolis force, A and B are constants (~1.9 and 4.5; Deacon, 1973). To account for roughness variation with wind speed off-shore, the Charnock equation (Charnock, 1955) can be employed: where: U u g * 1 = κ a is a constant (~0.015), g is acceleration due to gravity. ln u 2 * B A () fz z = a u * 0 ( 2) g In near-neutral conditions, the logarithmic wind profile applies and can be used to determine near-surface wind speed, U z, at height z: 2 U u ln z * 2 = ( 3) κ z 0 Hence for a given geostrophic wind speed, equations (1) and (2) can be solved iteratively to determine values for the friction velocity and roughness off-shore or, assuming a known roughness length (typical land values are in the range 0.01 to 1 m (Wieringa, 1993)), friction velocity can be determined based solely on equation (1). Assuming that latitude and geostrophic wind speed are known, that there is no topographic enhancement of wind speeds and that the wind flow is in equilibrium with the surface, the theoretical difference in near-surface wind speed between a specified roughness (over land) and off-shore wind speeds at a specific height can then be determined (from equation (3)). Figure 1 shows an example of wind speed differences (off-shore minus on-shore) at 50 m height at 55 latitude, where the geostrophic wind speed is varied between 5 and 24 m s 1 and the range of roughness values for land is m to 1 m. Since roughness off-shore increases gradually with the geostrophic wind speed (from about m at 5 m s 1 to m at 24 m s 1 ) the roughness difference (shown on the abscissa) is dominated by the value of roughness length assumed for land. The wind speeds from which the diagram is constructed are theoretically derived and assume equilibrium conditions over both land and sea. However, the inference can be drawn that, given mean geostrophic wind speeds of between 8 and 13 m s 1 over Northern Europe (Troen & Petersen, 1989), the magnitude of the difference between wind speeds over the sea surface and over a land roughness of 0.1 m ascribed solely to roughness change is of the order of 2 m s 1, or 20% Effects of stability Stability corrections can be calculated based on Monin Obukhov similarity theory (see e.g. van Wijk et al., 1990) where the Monin Obukhov length, L, is given by: where: u* L = κ( g/ θ) w θ θ is the potential temperature, w is the vertical velocity. Incorporating a stability correction into the logarithmic wind speed profile, we see that the wind speed U z at height z is calculated by: where Ψ is the stability correction to the wind speed. 3 U u ln z z = z * Ψ κ L ( 4 ) 2 40

3 Effects of atmospheric stability on coastal wind climates are stable or unstable (the absolute value of the stability correction is larger if conditions are stable) and by how much conditions deviate from near-neutral (as defined by the Monin Obukhov length). As conditions approach neutral, the Monin Obukhov length increases; conversely as conditions become more unstable or more stable, the Monin Obukhov length tends towards zero. Note that corrections are subtracted from the near-neutral wind speed; hence the net impact is that near-surface wind speeds are increased relative to a logarithmic prediction in stable conditions and decreased in unstable conditions. The wind speed also depends on the ratio u * /κ, and u * is typically lower when conditions are non-neutral. The combined effect of roughness and stability changes is also influenced by the distance from the surface discontinuity and is typically modelled using internal boundary layer (IBL) theory (Garratt, 1990). The difficulties in applying IBL theory in coastal locations appear to stem from absence of data regarding stability off-shore and regarding the heights of the two parts of the IBL (the lower equilibrium layer and the upper adjustment layer; Deaves, 1981) under different stability conditions. In the following section, the magnitude of stability correction to wind speed profiles is calculated from observations taken at one coastal and one off-shore mast and examined to determine the impact of fetch on stability. 3. The Vindeby project Meteorological monitoring at the Vindeby wind farm (located off the north-western coast of the island of Lolland, Denmark; Dyre, 1992) has been conducted since April 1993 using instruments on three 45 m mete- Figure 1. The difference between equilibrium off-shore and on-shore wind speeds (m s 1 ) for varying geostrophic wind speed and roughness difference (z 0(land) varies from m to 0.1 m; z 0(sea) given by equation (2)). For stable conditions (L > 0): For unstable conditions (L < 0): where: Ψ= 5 z L + Ψ= x x 1 2ln ln 1+ 2tan x π 2 z x = 1 16 L 1 4 Thus the magnitude and sign of stability corrections to near-neutral wind speed profiles (Ψ(z/L)) (shown in Figure 2 for 50 m height) depend on whether conditions Figure 2. Magnitude of the stability correction to wind speeds (m s 1 ) at 50 m height according to the Monin-Obukhov length (m). 41

4 R J Barthelmie orological masts, one on land (LM) and two off-shore (SMS and SMW) (Figure 3). The site and instrumentation are described in Barthelmie et al. (1994) and a general description of the wind climate is given in Barthelmie et al. (1996a). No topographic enhancement of the wind speed is expected since Lolland is nearly flat and lies close to sea level. Around the off-shore masts and the wind farm the water depths are shallow (2 5 m) and the sea is relatively sheltered. Data used in all the analyses presented herein are from the period January December 1994 inclusive. There is generally little difference between observations at SMS and SMW, so data from SMS are used here to represent offshore conditions Stability correction at Vindeby The Monin Obukhov length at LM and SMS is determined using parameterizations given in Beljaars et al. (1989). All calculations are based on wind speed measured at 20 m height and the temperature difference between 7 and 44 m. The definition of stability classes (a) is as given in van Wijk et al. (1990) based on the Monin Obukhov length, L, where very stable: 0 < L < 200 m, stable: 200 < L < 1000 m, near-neutral: 1000 < L < 1000 m, unstable: 1000 < L < 200 m, very unstable: 200 < L < 0 m. The observations are dominated by stable (48 and 36% at LM and SMS, respectively) and near-neutral (33 and 53%) conditions with fewer observations in the unstable classes (19 and 11%). Analysis of Vindeby data undertaken in Barthelmie et al. (1996a) suggests that for the period January to December 1994 inclusive, assuming near-neutral conditions with a constant roughness length ( m offshore and 0.05 m for land) gives reasonable predictions of the wind speed profile to 48 m height (within ±0.25 m s 1 or ±5%). However, application of the stability correction is shown to improve the average wind speed profile prediction (Figure 4) and reduces the root mean square error (from 0.64 to 0.46 at LM and from 0.57 to 0.43 at SMS) and may also be important at seasonal or shorter time scales Temporal variability (b) Figure 3. (a) Location of the Vindeby site and (b) position of the masts ( ) and wind farm (the position of each wind turbine is marked with ). 42 The percentage of observations in each of the stability classes by hour of the day is shown in Figure 5(a) for LM and in Figure 6(a) for SMS. As expected the frequency of unstable classes increases during the day at LM followed by increasing stability. At SMS, there is little diurnal variability except for an increase in the number of near-neutral conditions during the day. The distribution of the stability classes by month (Figures 5(b) and 6(b)) is difficult to interpret since the frequency of different direction and wind speed classes both vary by month. However, it appears that the number of observations in the unstable classes increases during the summer while the number of observations in the stable classes increases during the winter Spatial variability The influence of wind direction on stability can be seen in Figures 5(d) and 6(d). At LM the presence of land in the fetch (between 110 and 270 ) is linked to an increase in the number of very stable and stable observations, while the off-shore fetch over north contains more near-neutral and unstable observations. Note that the longest land fetch (between 120 and 190 ) produces the highest frequency of observations in the very stable class. At SMS the longest sea fetch (over north) produces the highest frequency of unstable observations while the land fetch to the south produces only a small increase in the frequency of stable classes. Highest wind speeds are found in the south west sector

5 Effects of atmospheric stability on coastal wind climates Figure 4. Average observed and predicted wind speed profiles at SMS and LM (m s 1 ). (Figure 7) and are associated with an increase in the number of near-neutral observations at SMS Variability with wind speed The percentage of observations of each of the stability classes according to wind speed is shown in Figure 5(c) for LM and in Figure 6(c) for SMS. The Monin Obukhov length is proportional to the cube of the friction velocity; high wind speeds are typically associated with near-neutral conditions. Below approximately 4 m s 1, observations are evenly divided between unstable and stable classes. At wind speeds in excess of 12 m s 1 most observations at SMS and more than 60% of observations at LM are in the near-neutral class Linking stability and fetch conditions The above analysis suggests that the fetch description has a strong influence on the frequency of different stability classes with the presence of land being linked with a higher frequency of stable conditions and the presence of sea being linked with a higher frequency of unstable and near-neutral conditions. Stability climates are therefore influenced by the orientation of the coastline. The prevailing wind direction (here south-westerly) will also be linked to a relatively high frequency of near-neutral conditions if this direction is also associated with high wind speeds (Figure 7). To examine the correction to the logarithmic wind speed profile due to stability, equation (4) can be rearranged and the stability correction calculated for each observation: U u in z u z = z * * ( ) κ κ Ψ L 5 o logarithmic profile stability correction Figure 8 shows the distribution of the stability correction at 48 m at LM and SMS. As shown, this correction is typically small (less than 1 m s 1 ). Stability corrections cluster around zero for SMS while at LM there is a higher frequency of larger stability corrections. Plotting the median correction by direction (Figure 9) shows that the stability correction is similar for the offshore fetch to both LM and SMS but that the presence of land in the fetch affects the stability correction substantially (between direction at LM and at SMS). The effect of land in the fetch is evident at SMS (with an off-shore fetch of 1 2 km) but smaller than the effect at LM. Thus the differences in stability introduced by the fetch type are likely to be an important factor in predicting the modification of offshore wind speeds in the coastal zone. 43

6 R J Barthelmie (a) (b) (c) (d) Figure 5. Frequency (%) of different stability conditions at LM by (a) hour of the day, (b) month, (c) wind speed class and (d) direction. Stability classes are defined based on the Monin-Obukhov length, L Ratios of off- to on-shore wind speeds Examining wind speeds at SMS and LM (given as a percentage differences in Table 1) shows that differences decrease with height, which is to be expected since they are primarily caused by changes in surface characteristics. Since mean ratios are complicated by different fetches, roughness changes and the presence of the wind farm, differences have also been calculated using only southerly wind directions such that the flow is over land to LM and over a short sea fetch (~1.3 km) to SMS. On average, the largest differences occur in autumn at Vindeby, when conditions off-shore should theoretically be more unstable (van Wijk et al., 1990), and the smallest median difference occurs in spring, which might be expected if stable conditions off-shore are impeding the increase of wind speed owing to lower roughness. However, ratios calculated according to stability conditions at SMS do not reflect these patterns (Table 1), typically being larger in near-neutral/stable conditions and smaller in unstable conditions. This and 44 the small or negative ratios at 38 and 48 m are thought to reflect: the small number of observations in the unstable classes from the south (see Figure 6); differences in the shape of wind speed profiles in stable and unstable conditions with a smaller vertical gradient in unstable conditions; independent variations of stability conditions onand off-shore; the dependence of the ratios on wind speed, highest wind speeds typically being associated with near-neutral conditions; the growth of the IBL and the position of the measurements at 38 and 48 m at SMS either within the IBL, the transition zone or above the IBL. Given the range of possible wind speed ratios and their dependence on a number of factors such as fetch type and distance and wind speed, the best approach to predicting off-shore wind speeds from on-shore data

7 Effects of atmospheric stability on coastal wind climates (a) (b) (c) (d) Figure 6. Frequency (%) of different stability conditions at SMS by (a) hour of the day, (b) month, (c) wind speed class and (d) direction. Stability classes are defined based on the Monin-Obukhov length, L. appears to be a physically based model that can account for stability differences. 4. Discussion The effects of both roughness changes and stability on equilibrium wind speeds can be modelled successfully and have been shown to impact wind speeds at typical turbine hub-heights (around 50m). Measurements from the Vindeby campaign have been analysed to show that there are differences in stability climates on- and offshore (Pryor & Barthelmie, 1998) that lead to differences in wind speed profiles. Wind turbines typically do not operate ( cut-in ) below 4 m s 1 and achieve rated power at about 12 m s 1. Impacts of stability on wind speeds are greatest at low wind speeds while above 12 m s 1 the majority of observations both on- and off-shore at Vindeby are nearneutral. Therefore stability corrections are most important for resource assessment between typical cut-in and rated wind speeds. Fetch type appears to be a major causal factor of the differences between the wind climates at LM and SMS. At both sites at Vindeby, flow from the south (land fetch to LM and short off-shore fetch of 1 2 km to SMS) is associated with a greater frequency of stable conditions, while flow from the north (off-shore fetch) is associated with greater frequency of unstable conditions. This is in accord with observations in Coelingh et al. (1996) and Barthelmie et al. (1991). Coelingh et al. (1996) examined wind climates from sites that have a prevailing wind direction giving an off-shore fetch and found predominantly unstable conditions while the analysis presented in Barthelmie et al. (1991) focused on a site off the east coast of the UK at which stable conditions were most common. The position of an offshore wind farm with respect to the nearest land will 45

8 R J Barthelmie Figure 8. Distribution of the stability correction (m s 1 ) to the logarithmic profile (see equation (5)) at 48 m at SMS and LM. Figure 7. Wind roses at (a) LM and (b) SMS. Wind speeds, U, are plotted in four bins: 0 U < 3, 3 U < 6, 6 U < 9, 9 U m s 1 in 30 sectors. Circles mark 5% intervals (Mortensen et al., 1995). Figure 9. Median stability correction to the logarithmic profile (m s 1 ) (see equation (5)) at 48 m at SMS and LM plotted by 10 directional bin. Table 1. Normalised median wind speed ratios (U SM U LM )/U LM at various heights expressed as a percentage calculated using all observations and calculated using observations with wind flow over direct land fetch to LM and approximately 1.3 km sea fetch to SMS (south sector) Category Normalised wind speed difference (%) 46 All Height (m) South Height (m) Average Winter (DJF) Spring (MAM) Summer (JJA) Autumn (SON) Near-neutral Stable Unstable

9 Effects of atmospheric stability on coastal wind climates influence the stability climate at that site and thus the mean wind profile, turbulence conditions and possibly the wake effects within the wind farm. If off-shore wind energy is to develop successfully, good predictions of off-shore and coastal wind climates are required. Despite the development of wind models that can predict both off-shore and on-shore wind speeds reasonably well, it is difficult to predict the modification of wind speed in the coastal zone because of the effects of roughness and stability, which influence both spatial and temporal variability of wind climates. Placing wind turbines at the maximum distance from the coast gives the largest average increase in wind speed. However, after an initial wind speed increase which may occur within a few kilometres of the coast, winds may thereafter increase relatively slowly, depending on wind speed, the air sea temperature difference and the orientation of the coastline which influence stability changes. Thus there is a need for both observational and modelling studies to increase understanding of stability climates off-shore and how these affect wind climates, particularly in the coastal zone. Acknowledgements I gratefully acknowledge my colleagues at Risø National Laboratory for their work on the Vindeby project. I would also like to thank two anonymous reviewers for their comments on this paper. References Barthelmie, R. J., Courtney, M. S., Højstrup, J. & Larsen, S. E. (1996a). Meteorological aspects of off-shore wind energy observations from the Vindeby wind farm. J. Wind. Eng. Indust. Aerodyn., 62: Barthelmie, R. J., Courtney, M. S., Højstrup, J. & Sanderhoff, P. (1994). The Vindeby Project: a description. Risø-R- 741(EN), Risø National Laboratory, Denmark. Barthelmie, R. J., Grisogono, B. & Pryor, S. C. (1996b). Observations and simulations of diurnal cycles of near-surface wind speeds over land and sea. J. Geophys. Res., 101(D16): Barthelmie, R. J., Palutikof, J. P. & Davies, T. D. (1991). Predicting UK off-shore wind speeds. Annales Geophysicae, 9: Beljaars, A. C. M., Holtslag, A. A. M. & van Westrhenen, R. M. (1989). Description of a software library for the calculation of surface fluxes. Technical Report TR-112, KNMI, De Bilt, Netherlands. Bergström, H., Johansson, P.-E. & Smedman, A.-S. (1988). A study of wind speed modification and internal boundarylayer heights in a coastal region. Boundary-Layer Meteorol., 42: Charnock, H. (1955). Wind stress on a water surface. Q. J. R. Meteorol. Soc., 81: 639. Coelingh, J. P., van Wijk, A. J. M. & Holtslag, A. A. M. (1996). Analysis of wind speed observations over the North Sea. J. Wind. Eng. Indust. Aerodyn., 61: Coelingh, J. P., van Wijk, A. J. M. & Holtslag, A. A. M. (1998). Analysis of wind speed observations over the North Sea coast. J. Wind. Eng. Indust. Aerodyn., 73: Deacon, E. L. (1973). Geostrophic drag coefficients. Boundary-Layer Meteorol., 5: Deaves, D. M. (1981). Computation of wind flow over changes in surface roughness. J. Wind. Eng. Indust. Aerodyn., 7: Dyre, K. (1992). Vindeby off-shore wind farm the first experiences. In The Potential of Wind Farm, ed Madsen,.P. H. & Lundsager, P.), EWEA Special Topic Conference 92, September 1992, Herning, Denmark, Paper B7. Garratt, J. R. (1990). The internal boundary layer a review. Boundary-Layer Meteorol., 50: Garratt, J. R. (1992). The Atmospheric Boundary Layer. Cambridge Atmospheric and Space Science Series. Cambridge University Press, Cambridge, 316 pp. Joffre, S. M. (1985). The structure of the marine atmospheric boundary layer: a review from the point of view of diffusivity, transport and deposition processes. Technical Report No. 29, Finnish Meteorological Institute, Helsinki. Kaimal, J. C. & Finnigan, J. J. (1994). Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, New York, 289 pp. Korevaar, C. G. (1990). North Sea Climate. Kluwer, 152 pp. Mortensen, N. G., Landberg, L., Troen, I. & Petersen, E. L. (1995). Wind Analysis and Application Program (WASP) Vol. 3. Utility Programs. Risø-I-666 (EN) (v.3), Risø National Laboratory, Roskilde, Denmark. Pryor, S. C. & Barthelmie, R. J. (1998). Analysis of the effect of the coastal discontinuity on near-surface flow. Annales Geophysicae, 16: Smedman, A. S., Hogstrom, U. & Bergstrom, H. (1996). Low level jets a decisive factor for off-shore wind energy siting in the Baltic Sea. Wind Eng., 20: Smedman, A.-S., Bergstrom, H. & Grisogono, B. (1997). Evolution of stable internal boundary layers over a cold sea. J. Geophys. Res., 102(C1): Troen, I. & Petersen, E. L., (1989). European Wind Atlas. Risø National Laboratory, Roskilde, Denmark, 656 pp. van Wijk, A. J. M., Beljaars, A. C. M., Holtslag, A. A. M. & Turkenburg, W. C. (1990). Evaluation of stability corrections in wind speed profiles over the North Sea. J. Wind. Eng. Indust. Aerodyn., 33: Wieringa, J. (1993). Representative roughness parameters for homogeneous terrain. Boundary-Layer Meteorol., 63: