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Statistical analysis of flow characteristics in the coastal zone
Journal of Wind Engineering and Industrial Aerodynamics 90 (2002) 201–221
Statistical analysis of flow characteristics in the coastal zone S.C. Pryora,*, R.J. Barthelmiea,b a
Atmospheric Science Program, Department of Geography, Indiana University, Bloomington, IN 47405, USA b Wind Energy and Atmospheric Physics, Risø National Laboratory, Dk-4000 Roskilde, Denmark Received 3 December 2000; received in revised form 26 November 2001; accepted 26 November 2001
Abstract This paper presents analyses of flow characteristics in the near-shore and offshore environment using data from the Danish wind monitoring network. In this relatively high wind speed environment the temporal auto-correlation of wind speeds measured in the offshore coastal zone at or above a height of 40 m is not significantly higher than that from land masts. However, the persistence of wind speeds above typical wind turbine cut-in speeds is higher at coastal and offshore masts. The parameters of wind speed distributions calculated for the onshore and offshore data indicate that both the mean and form of the distribution is modified during offshore flow. It is shown that in the near-surface layer vertical propagation of the modified momentum flux differentially affects the body and tails of the wind speed distribution. These analyses further indicate that at a height of 50 m under stable stratification the flow has not fully adjusted to the differing fluxes over the sea even after an over water fetch of at least 11–20 km. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Wind energy; Offshore; Wind speed distributions; Persistence; Temporal auto-correlation
1. Introduction Except where topographic forcing enhances flow, wind energy resources offshore are thought to exceed those of onshore regions due principally to (1) greater persistence of flow offshore and (2) higher wind speeds offshore due largely to lower surface roughness [1]. An additional benefit to offshore location of wind farms is *Corresponding author. Tel.: +1-812-855-5155; fax: +1-812-855-1661. E-mail address: [email protected] (S.C. Pryor). 0167-6105/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 0 1 ) 0 0 1 9 5 - 7
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S.C. Pryor, R.J. Barthelmie / J. Wind Eng. Ind. Aerodyn. 90 (2002) 201–221 58.5 58.0
SWEDEN
Latitude (˚N)
57.5 57.0 56.5
DENMARK
56.0 55.5
Omø
Tystofte
55.0 54.5
Gedser Vindeby Rødsand 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0
Longitude (˚E) Fig. 1. Locations of the measurement masts in Denmark from which data are presented here.
reduced turbulence intensity offshore leading to reduced stress on turbine components [2]. However, the magnitude of these benefits has yet to be fully quantified. Because installation and maintenance of wind turbines at great distances from land represent a significant economic burden and presents many technical challenges [3], the first offshore wind turbines are being installed in coastal environments (i.e., typically o10 km from the coast) [1,2] in a region of horizontal inhomogeneity where the flow may not have fully adjusted to the different fluxes from the water surface compared to those from land [4]. Hence, there is a need for more detailed information regarding flow characteristics in coastal and offshore zones. Here we use data collected under the Danish offshore wind monitoring program [5] (see Fig. 1 and Table 1) to quantify differences in the persistence of wind speeds at on and offshore sites. We also address issues regarding how far offshore wind speed distributions exhibit continuing influence from upwind land surfaces and how changes in the wind speed characteristics offshore are manifest in the probability distributions.
2. Persistence of wind speeds at offshore, coastal and land sites 2.1. Background The term persistence has been used within two contexts in the study of atmospheric flow variability. First, to quantify the steadiness of the wind direction
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Table 1 Details of the measurement mast and data Site
Location (offshore/onshore)
Distance to closest coastline
Measurement heights (m) of wind speed data presented
Tystofte Gedser land mast R dsand Vindeby land mast (LM) Vindeby sea mast west (SMW) Om
Onshore Onshore (coastal) Offshore Onshore (coastal) Offshore
3 km 15 m 9 km 15 m 1.8 km
39.6 10, 50 10, 50 10, 30, 48 10, 30, 48
Offshore
12 km
50
(where persistence is defined as the ratio of vector wind speed to scalar wind speed [6]). Second, as in Sigl et al. [7], to indicate the duration of surface wind speeds within specified wind speed classes. In this analysis, we use the term persistence in this latter context. An accurate assessment of the feasibility of wind resource utilization is dependent on the persistence of wind speeds because the reliability and predictability of generated power and duration of time without power generation have implications for network design and meshing of technologies to continuously meet electricity demand [7]. To assess the relative persistence of wind speeds at offshore locations in the Danish monitoring network we present two analyses. First, analysis of the temporal auto-correlation of half-hourly average wind speed measurements and then analysis of the persistence of flow in categories based on cut-in and rated wind speeds for a representative wind turbine. 2.2. Data analysis 2.2.1. Temporal auto-correlation of wind speed time series Data values in discrete time series of atmospheric variables typically exhibit dependence on preceding values of that variable [8]. Temporal auto-correlation is a measure of this dependence. It is the correlation of successive values in the time series at specified lag intervals. An auto-correlation function (the auto-correlation plotted as a function of the lag-time) depicts one measure of the persistence in the time series and may also be used to reveal non-stationarities (such as defined periodicities) in the data. Here we construct auto-correlation functions using data series from 1996–1999 at three meteorological masts in the Danish monitoring network which have semicontinuous half-hourly average wind speed measurements at or above 40 m above the ground or sea-surface. These three sites (Fig. 1) are: *
Tystofte land mast which is located >3 km from the closest coastline and hence is used to represent conditions at a typical land site in Denmark.
204 *
*
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Vindeby land mast (LM) which is located within 15 m of the coast of Lolland and is presumed to represent a mixed sea and land climatology. Vindeby sea mast west (SMW) which has an over water fetch of 2 km from the closest coastline and hence is used to represent a coastal location.
Data are presented for a measurement height of 48 m for the Vindeby masts and 39.6 m at Tystofte. Prior to performing the temporal auto-correlation analysis an unbroken time series for each site was developed in which missing or erroneous data were replaced by the mean of the time series (in each case this resulted in less than 10% replacement of the data series). These modified time series are used to calculate the temporal auto-correlation for lags extending from 30 min to multiple days. As shown in Fig. 2, there is a significant influence of non-stationarities in the Tystofte land data set with clear evidence of a diurnal cycle. However, as described in Barthelmie et al. [9], due to the thermal lag introduced by the water body, in the absence of advection from land, wind speeds in the coastal zone do not exhibit a strong diurnal cycle, and hence a diurnal cycle is not evident in the Vindeby LM and Vindeby SMW data series. As in the study of Brett and Tuller [8] auto-correlation coefficients for lags of less than 12 h are in excess of 0.5. The temporal auto-correlation for lags of 12–36 h is above 0.2 and is slightly higher in the data set from Vindeby SMW than at Vindeby LM or Tystofte for 36–72 h lags. 2.2.2. Persistence analysis Multi-year time series of half-hourly average wind speeds (1996–1999) from four measurement masts; Tystofte, Vindeby LM, Vindeby SMW and R dsand1 (an offshore mast located 9 km southeast of the island of Lolland) are used to generate cumulative frequency distributions of the persistence of wind speeds (U) in four classes: (1) (2) (3) (4)
Uo4 m s1. 4oUo15 m s1. 15oUo25 m s1. U > 25 m s1.
These four classes relate to the performance characteristics for a typical wind turbine which is suitable for deployment offshore; a VESTAS V66 1.65 MW turbine (hub-height=66 m, typical blade diameter E60 m). The classes correspond to; (1) wind speeds below the cut-in speed (i.e., the wind speed at which the turbine commences electricity generation), (2) the transition zone between cut-in and rated speed (i.e., the wind speed at which the power output is equal to the maximum for the turbine), (3) the rated speed to cut-out speed (i.e., the wind speed at which the turbine ceases to generate power) and (4) the wind speeds above the cut-out 1 R dsand is omitted from the temporal auto-correlation analysis presented above because prior to 1999 the data record has data recovery of less than 90% and hence this time series was deemed too highly fractured for that analysis.
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1
0.1 1
Correlation
Correlation
Vindeby SMW Vindeby LM Tystofte
0 0.2 0.4 0.6 0.8
1
Lag (days)
0.01 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Lag (days) Fig. 2. The auto-correlation function for Tystofte, Vindeby LM and Vindeby SMW for half-hour average wind speed data from 1996–1999. The inset shows an enlargement of the figure for lags less than 1 day.
threshold at which electricity ceases to be generated because the turbine is shut down for safety. Analysis of the distribution of missing data points in the time series indicate they are randomly distributed through the data records, and so the persistence analysis is conducted without replacement or interpolation of missing data values. Hence a missing data value is assumed to indicate termination of ‘runs’ of data in a single class. This will tend to lead to an underestimation of actual persistence of wind speeds in the four classes. All quality assured half-hourly average wind speeds from the top measurement height (39.6 m a.g.l. at Tystofte, 48 m at each of the Vindeby masts and 50 m from the R dsand mast) are above 0.2 m s1 and below 25 m s1 (i.e., no observations fall into class (4)). The cumulative probability distributions for persistence in the other three wind speed classes are shown in Fig. 3. In accord with a priori expectations, class (2) which represents wind speeds between the cut-in and rated speed is by the far the most persistent class at all sites. Also as shown, the data collected over the water surfaces indicate greater persistence of wind speeds in classes (2) and (3). For example, the 70th percentile duration of wind speeds in class (2) is 540 min at Tystofte, 660 min at Vindeby LM, 870 min at Vindeby SMW and 900 min at R dsand. Conversely, the persistence of below cut-in wind speeds is higher at the onshore sites. For example, the 90th percentile duration of wind speeds below 4 m s1 (i.e., in class (1)) is 630 min at Tystofte, 420 min at Vindeby LM, 390 min at Vindeby SMW and 330 min at R dsand. It is worthy of note that the analyses presented in Fig. 3 are not only a function of the measurement location (surface type) but also measurement height. To assess the
U < 4 m/s 4 < U < 15 m/s 15 < U < 25 m/s 100
10
1
0
(a)
0.2
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1000 U < 4 m/s 4 < U 15 m/s 15 < U < 25 m/s 100
10
1 0
(c)
0.2 0.4 0.6 0.8 Cumulative probability
1
Number of time intervals (30 minute segments)
Number of time intervals (30 minute segments) Number of time intervals (30 minute segments)
1000
Number of time intervals (30 minute segments)
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1000 U < 4 m/s 4 < U < 15 m/s 15 < U < 25 m/s 100
10
1 0
(b)
0.2
0.4
0.6
0.8
1
Cumulative probability
1000 U < 4 m/s 4 < U < 15 m/s 15 < U < 25 m/s 100
10
1 0
(d)
0.2 0.4 0.6 0.8 Cumulative probability
1
Fig. 3. Cumulative probability distributions of classed wind speeds at (a) Tystofte, 39.6 m; (b) Vindeby LM, 48 m; (c) Vindeby SMW, 48 m and (d) R dsand, 50 m. Data for 1996–1999 at all sites except R dsand where data for 1997–1999 were used. This plot shows the cumulative probability of the specified number of consecutive 30 min average wind speeds in classed wind speed categories (i.e., the probability of observing a wind speed in the given class for a time period equal to or less than the specified duration).
relative importance of the difference in measurement height between the onshore site at Tystofte and the coastal and offshore masts (39.6 versus 48/50 m), the analysis of persistence is repeated for the 38 m measurement height at Vindeby SMW. The results of this analysis (Fig. 4) indicate the difference between the persistence of cutin to rated wind speeds at the two measurements heights at Vindeby is smaller than the difference between Tystofte and the Vindeby data. A similar result is found for the other wind speed classes and indicates the differences shown in Fig. 3 are largely the result of differences in surface type not measurement height. Similar analyses of the classed wind speed persistence are conducted for higher resolution data sets using continuous records of 10 min average wind speeds collected at a mast located over the sea (11 km from the coast) at Om and at the Tystofte land mast (Table 1) during March–November 1999. The distributions are less robust than those shown in Fig. 3 due to the smaller data sets used to construct
Number of time intervals (30 minute segments)
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1000 Tystofte 39.6m Vindeby SMW 38m Vindeby SMW 48m 100
10
1 0
0.2
0.4 0.6 0.8 Cumulative probability
1
Fig. 4. Cumulative probability distributions of wind speeds between 4 and 15 m s1 at Tystofte (39.6 m), and Vindeby SMW at 38 and 48 m height. This plot shows the probability of observing a wind speed of between 4 and 15 m s1 for a time period equal to or less than the specified duration (i.e., the 50th percentile indicates the median run duration for wind speeds in this class at Vindeby SMW at 48 m is 5 h).
the statistics and so only data for the wind speed class (2) are shown in Fig. 5. However, this plot confirms that above the 40th percentile the persistence of wind speeds in this class is higher at the sea mast (Om ). 2.3. Discussion Although Fig. 2 presents some evidence of slightly higher temporal autocorrelation at Vindeby SMW than Vindeby LM and Tystofte, the differences in correlation coefficients are generally small. This finding may seem to be at odds with expectations of greater persistence over water surfaces and analyses presented in Figs. 3 and 5. However, recall that the temporal auto-correlation is insensitive to the magnitude of observations. These analyses suggest, therefore, that the major difference in the consistency of wind speeds over land versus water surfaces is not the temporal auto-correlation (i.e., direct correlation between sequences of observations), but rather that low winds speeds are less frequent and persist for shorter periods over water surfaces and higher wind speeds are more frequent and persist for longer periods over water surfaces. Hence, the synthesis of these analyses represents a subtle but important distinction. Winds are not necessarily more persistent over water surfaces per se but rather calm conditions are less frequent and moderate to high wind speeds are more frequent over water surfaces. A further inference from Fig. 3 is that, during the measurement period, the maximum duration of nonelectricity producing wind speeds (Uo4 m s1) at the sea masts is less than one day,
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Number of time intervals (10minute segments)
1000
100
10 Tystofte Omoe 1 0
0.2 0.4 0.6 Cumulative probability
0.8
1
Fig. 5. Cumulative probability distribution of winds in class (2) i.e., 4oUo15 m s1 at Om (50 m) and Tystofte (39.6 m) calculated using 10 min average wind speeds. As in Fig. 4 this plot shows the probability of observing a wind speed of between 4 and 15 m s1 for a time period equal to or less than the specified duration.
while onshore measurement data indicate maximum persistence of low wind speeds of over two days. Hence, in the context of the Danish climate (i.e., a maritime, midlatitude, high wind speed regime) the duration of wind speeds below the threshold for electricity generation is substantially reduced in the offshore locations relative to a topographically homogeneous onshore site.
3. Flow in the coastal zone: wind speed distributions 3.1. Background The difference between winds measured over land and adjacent water bodies is non-linearly related to the strength of the wind, atmospheric stability, fetch (distance from the coastline along the prevailing wind direction), and contrasts in heat, water vapor and momentum fluxes [10]. To ensure correct assessment of the offshore wind resource it is necessary to fully characterize the entire wind speed probability distribution. Smedman-Hogstrom and Hogstrom [10] developed a technique for determining wind speed frequency distributions within a layer extending approximately 200 m from the surface from measured data at a reference height (10 m). The technique requires knowledge of the upstream roughness length ðz0 Þ and is based on the rate of growth of internal boundary layers (IBL) from surface discontinuities and assumptions regarding the
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shape of the wind profile. They assumed the vertical wind profile is comprised of N internal boundary layers associated with terrain discontinuities upstream of the measurement location. Within each layer they used the power law to describe the wind profile [11], and the growth of the IBL was described using a simple formulation where the height of the IBL is a function of z0 and stability. This model is applied to data from R dsand (where z0 ; stability and fetch are calculated as discussed in Section 3.2) assuming a single IBL propagates downwind from the coastline. The exponent of the power law is calculated using coefficients from Smedman-Hogstrom and Hogstrom [10] and z0 calculated from the Charnock equation [12]. The results are shown in Fig. 6 for the entire data set (frame a) and for the data conditionally sampled by stability class (frames b–d). This figure indicates that, in this application, the model overestimates the magnitude of wind speeds at 50 m across the entire probability distribution, largely due to overestimation of wind speeds under stable stratification. The cause of this overestimation may be the simple parameterization of the IBL growth used (where the factors a and b from SmedmanHogstrom and Hogstrom [10] are based on IBL growth over a surface with z0 o0:06 14
Predicted Measured
Wind speed (m/s)
Wind speed (m/s)
16
12
8
4 20
(a)
40
60
80
8
100
0
20
(b)
Percentile 16
40
60
80
100
80
100
Percentile 10
14
Wind speed (m/s)
Wind speed (m/s)
10
6 0
12 10 8 6
8 6 4 2
0
(c)
12
20
40
60
Percentile
80
100
0
(d)
20
40
60
Percentile
Fig. 6. Wind speed at R dsand as measured at 50 m and as predicted based on the model of SmedmanHogstrom and Hogstrom [10] using data measured at 10 m. The data are shown for (a) the entire data set (with an offshore fetch of o20 km), (b) near-neutral stratification and an offshore fetch of o20 km, (c) unstable conditions and an offshore fetch of o20 km and (d) stable stratification and an offshore fetch of o20 km. Note the changing scale between the frames.
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Wind speed (m/s)
12 10 8 6 38 m SM 38 m LM 20 m SM 20m LM
4 2 0 0
20
40
60
80
100
Percentile Fig. 7. Wind speed distributions at 20 and 38 m from Vindeby (land mast (LM) versus sea mast south (SM)) for near-neutral stability and flow moving offshore. Data from 1994.
and hence over-estimates IBL growth over the sea), or the height dependence of the power law exponent [13]. A more subtle inference drawn from Fig. 6 is that the form of the modelled wind speed distribution under near-neutral and unstable conditions is different from that derived from the measurements. This may reflect the influence of conditioning of the model by Smedman-Hogstrom and Hogstrom [10] using land based data sets while wind speed distributions offshore exhibit different characteristics. Below we examine wind speed distributions from onshore locations and relative to those from coastal and offshore data sets to examine these possible differences in detail. Pryor and Barthelmie [14] used 1994 data from the Vindeby offshore wind farm to examine the effect of fetch, stability and surface roughness on wind speeds in the coastal zone. They found that with offshore flow at 1.2–1.7 km from the coast the wind speed distributions up to a height of 20 m under all stability conditions were significantly different from those measured at a mast on the coastline. This implies that adjustment of the flow to the new surface conditions had propagated vertically to 20 m height during over water flow of 1.2–1.7 km. However, the form of the wind speed distributions above 20 m height was not statistically different at the sea masts indicating that some of the statistical properties of flow at this height had not significantly changed as a result of the modified surface conditions (Fig. 7). Here we extend this research to further examine the fetch dependence of the vertical propagation of the adjustment of the flow under differing stability conditions and to provide a more detailed analysis of the descriptive parameters of the wind speed distributions. 3.2. Data analysis To extend the analysis of Pryor and Barthelmie [14] we present data from two sets of onshore and offshore masts with varying fetch; (1) Gedser land mast and R dsand
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offshore mast, and (2) on a south–north transect from the island of Lolland; at Vindeby LM, Vindeby SMW and Om offshore mast (see Fig. 1). In the following analyses stability is characterized using the Monin-Obukhov length, L; determined using parameterizations given in Beljaars et al. [15] and applied in Pryor and Barthelmie [14] where: L¼
Tu2 *
T* gk
ð1Þ
T is the absolute temperature (K), u * is friction velocity (m s1), g is gravity (9.81 m s2), k is the von Ka! rma! n constant (0.4), and T* is the temperature scale (K) parameterized using: H T* ¼ ð2Þ rCp u * r is the air density (1.225 kg m3), Cp is the specific heat for air (1004.67 J kg1 K1), H is the heat flux (W m2) and is parameterized as a function of vertical temperature gradient ðDTÞ: For the land masts the Monin–Obukhov lengths are calculated using wind speed at 11 m height at Gedser and 8 m height at Vindeby, temperature difference ðDTÞ (17–8 m at Vindeby and 47–10 m at Gedser) and absolute temperature at 10 m at Gedser and 8 m at Vindeby. Monin-Obukhov lengths at the sea masts were calculated using wind speed at 8 m height, the sea surface temperature and DT (45– 8 m at Om , 45–10 m at Vindeby SMW, 48–8 m at R dsand). These measurement heights indicate the distance from the mast base located approximately 2.5 m above mean sea level. Using these parameterizations the sign of the Monin–Obukhov length is determined by the temperature profile and the magnitude is determined iteratively where an initial value is estimated assuming that the wind speed profile is close to neutral and determining the friction velocity based on wind speed and roughness length (assigned for land as 0.05 m) and calculated for sea according to the Charnock equation [12]). Stability classes used herein are defined as in Pryor and Barthelmie [14] where jLj > 1000 m indicates near-neutral conditions,1000 m oLo0 m indicates unstable conditions and 1000 m>L>0 m indicates stable conditions. Two statistical techniques are employed to examine the differences in wind speed distributions at the on and offshore masts by stability class and wind direction; Wilcoxon Matched-Pairs Signed Ranks test and the Kolmogorov–Smirnov equality of distributions test [16]. The Wilcoxon Matched-Pairs Signed Ranks test is used to quantitatively compare the magnitude of the observations underlying the distribution and the Kolmogorov–Smirnov test [17] is used to quantitatively compare the form of the distributions. Both tests have previously been applied to the study of wind speed distributions (e.g., [18,19,14]). In the Wilcoxon Matched-Pairs Signed Ranks test the difference score for each matched pair (coincident wind speed observations) is calculated ranked by absolute magnitude. The rank scores for all positive values are summed and compared to the summed rank scores for the negative differences. If the two wind speed data sets are drawn from the same
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population then each matched pair has the same probability of being positive or negative. If not the value of the actual rank score differences can be used to determine the confidence with which one can assert the data sets are different. The Kolmogorov–Smirnov equality of distributions test is used here to examine whether the form of the wind speed distributions at each measurement height (sampled by stability class and fetch) are statistically different at the land and sea masts. The two distributions are compared by assuming one conforms to an idealized distribution and evaluating whether the other distribution shows similar form. Probability distributions may be described using a number of descriptive parameters including the mean, standard deviation, skewness and kurtosis. The standard deviation represents the dispersion of the data set. Skewness reports the asymmetric nature of the distribution and kurtosis represents the peakedness of the distribution both relative to a Gaussian distribution. Wind speed probability distributions are typically positively skewed and hence are characterized by skewness values greater than 0. A number of statistical distributions have been fitted to, or used to represent wind speed data (e.g., log-normal and bi-variate Gaussian, Weibull [20]). However, the most commonly used is the two parameter Weibull distribution (e.g., [21,22,18]), and so this distribution is also used here. The Weibull distribution has been shown to give a good fit to observed wind speed distributions [20,23] particularly over water surfaces [19]. The actual goodness of fit of the Weibull distribution to observed wind speed distributions is station dependent. It is generally poorest under conditions with high topographic forcing of the flow or other influences (e.g., frontal passages) which result in a highly asymmetric pattern of wind speed with direction [23]. The Weibull distribution is described by two parameters; k; the dimensionless shape parameter, and c; the scale parameter. The Weibull probability density function (where f ðUÞ is the frequency of occurrence of wind speed U) is given by ( ) k U k1 U k f ðUÞ ¼ : ð3Þ exp c c c The shape parameter ðkÞ is inversely related to the variance of wind speed around the mean value. For ko1; (3) exhibits monotonic decay. If k ¼ 2:0; (3) gives the Rayleigh distribution and for k ¼ 3:6; the function approximates a Gaussian distribution. The scale parameter (c) is related to the mean of the time series and has units of wind speed (i.e., m s1 in the analysis presented here). Eq. (3) may be integrated for U ¼ 0 to an upper limit of U to give the Weibull cumulative distribution: ( ) U k PðUÞ ¼ 1 exp : ð4Þ c In terms of the terminology used above, the Wilcoxon Matched-Pairs Signed Ranks test is most sensitive to changes in c; and the Kolmogorov–Smirnov test is most sensitive to changes in the form of the distribution which is represented in the Weibull distribution by k:
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3.2.1. Wind speed distributions at Gedser and R dsand As shown in Fig. 1 the Gedser land mast is located on the tip of the island of Falster (a north–south oriented island), while the R dsand mast is approximately 22 km offshore to the west. Using conditional sampling the half-hourly average wind speed data from R dsand and Gedser from 1997–1999 were classified based on stability and fetch characteristics (i.e., distance to the coastline along the prevailing wind direction). For the analysis presented here we focus on periods when the stability at both masts was commonly defined as near-neutral, stable and unstable and when the flow to the Gedser land mast was over a land surface and the flow to the R dsand sea mast was in one of two fetch categories; over sea fetch of o20 km and over sea fetch of >20 km. The number of observations in each combined conditionally sampled group is shown in Table 2. Fig. 8 shows wind speed distributions from the two masts at 10 and 50 m height sampled by fetch and stability class. As shown, acceleration of the flow due to the lower roughness of the sea surface is most marked at 10 m height under all stability conditions and is much less pronounced at 50 m. As expected, wind speed distributions at all heights and in all stability classes indicated significantly higher wind speeds at the sea mast (i.e., significant Wilcoxon matched pair results) (Table 2). The results of the statistical analyses also indicate that, except at the 50 m height, the wind speed distributions exhibit a different form at the Gedser and R dsand masts. It is hypothesized that this is due to a change in momentum exchange with the surface which causes a modification of the wind speed profile. At 50 m height, however, the adjustment to the modified surface fluxes has not significantly altered the form of the wind speed distribution even after a fetch of over 20 km. This suggests that, at this height, the flow characteristics are still heavily influenced by the land surface over which the wind had previously blown. The exception to this result is found under stable conditions with short fetch. This anomaly is the subject of further analysis, but may reflect acceleration of the flow near to or above the internal boundary layer possibly associated with the position of maximum temperature contrast [24]. Table 2 Wind speed data availability by fetch and stability class (N=near-neutral, US=unstable, S=stable) at R dsand (off-shore mast) and Gedser (land mast). Also shown are the results of significance tests. The first symbol shows results of the Wilcoxon matched-pairs signed ranks test and the second the Kolmogorov– Smirnov test Height
10 m
Fetch to R dsand mast
o20 km
>20 km
o20 km
>20 km
o20 km
>20 km
*/* */* */*
*/* / */*
*/* */* */*
*/* / */*
*/+ */+ */*
*/+ / */+
No. obs.
o20 km
>20 km
N US S
499 93 537
336 25 490
30 m
*=Significantly different at 99.9% confidence level. =Not tested due to low n: +=Not significantly different at 99.9% confidence level.
50 m
16
16
14
14
14
12
12
12
10
10
10
8
8
8
6
6
6
4
4
4
2
2
2
0
0 0
40
60
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100
0 0
20
Near-neutral
16
Wind speed (m/s)
20
40
60
80
Unstable
12
0
20
10
80
100
80
100
80
100
80
100
12 10 8
insufficient data
6
6
4
4 2
10 m height
0 0
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16
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12 10 8 6 4 2 0
20
40
60
80
Unstable Roedsand Gedser
14 12 10
0
100
20
40
60
Stable
16 14
Fetch > 20 km
0
40
Percentile
Fetch < 20 km
Percentile
Wind speed (m/s)
60
14
8
2
Wind speed (m/s)
40
Stable
16
Roedsand Gedser
14
100
Fetch > 20 km
Wind speed (m/s)
16
Fetch < 20 km
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214
12 10
8
8
insufficient data
6 4
6 4
50 m height
2 0
2 0
0
20
40
60
Percentile
80
100
0
20
40
60
Percentile
Fig. 8. Wind speed distributions from Gedser land mast and R dsand sea mast at 10 m (above) and 50 m (below) for flow over land to the Gedser mast and over sea at the R dsand mast under different stability conditions. Fetch refers to the oversea fetch distance to the R dsand mast.
3.2.2. Wind speed distributions at Vindeby LM, Vindeby SMW and Omø Data from the three masts on a south–north transect from the island of Lolland were also classified based on stability and fetch. Wind speed distributions for southerly flow moving offshore from Vindeby LM to Vindeby SMW and Om were
10 8 6 4 2 0 0
20
12 10 8 6 4 2 0 0
(b)
80
20
40 60 Percentile
80
10 8 6 4 2 0 0
100
Wind speed (m/s) 30 m height
Wind speed (m/s) 10 m height
(a)
40 60 Percentile
12
100
Wind speed (m/s) 48/50 m height
OMOE SMW LM
20
40 60 Percentile
80
12 10 8 6 4 2 0 0
20
40 60 Percentile
80
100
215
12 10 8 6 4 2 0
100
Wind speed (m/s) 48/50 m height
12
Wind speed (m/s) 30 m height
Wind speed (m/s) 10 m height
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0
20
40 60 Percentile
80
100
0
20
40 60 Percentile
80
100
12 10 8 6 4 2 0
Fig. 9. Wind speed distributions at Vindeby LM, Vindeby SMW and Om for (a) stable conditions and (b) unstable for southerly (offshore) flow. The individual panels show the different measurement heights; 10, 30 and 48 m at LM and SMW and 50 m at Om . The fetch to the LM is over at least 10 km of land, the fetch to the SMW is 2–5 km over water and the fetch to Om is at least over 12 km of sea. Data are presented only for periods when the stability was in the same class (i.e., stable, 0oLo1000 m) at the Vindeby LM and Om masts.
calculated by stability for the period of continuous overlapping records; March– December 1999. Due to the relatively short data set, sufficient data are only available for calculating distributions when the stability at Vindeby LM and Om is commonly defined as stable or unstable. Fig. 9 shows the resulting distributions graphically and the results of significance testing are given in Table 3. 3.3. Discussion Before discussing the implications of the analyses presented above it is important to reiterate that stability was held constant in the comparison of onshore and offshore data and hence that these results do not describe the evolution of stability with over water flow. Analyses presented here indicate that at the lowest measurement height (10 m) for offshore flow the majority of the wind speed adjustment under stable stratification occurs within 2 km of the coastline. However, for offshore flow the wind speed distribution at 48 m has not responded to the change in surface characteristics within 2 km of the shoreline and under stable stratification there is no difference in the form
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Table 3 Data availability and results of significance tests for wind speed data from Vindeby LM, Vindeby SMW and Om for flow moving offshore. The first symbol shows results of the Wilcoxon test and the second shows the results of the Kolmogorov–Smirnov test Height
10 m SMW
No. obs.: US=231. S=404 LM US */* LM S */* SMW US SMW S
30 m
48/50 m
OMØ
SMW
OMØ
SMW
OMØ
*/* */* */* */+
*/* */*
*/* */* */* */*
*/+ */+
*/* */+ */* */+
*=Significantly different at 99.9% confidence level. =Not tested due to low n: +=Not significantly different at 99.9% confidence level. US=unstable. S=stable.
of the distribution even after a further over sea fetch of 9 km. It is also shown that wind speed distributions over 20 km from the coast continue to exhibit the influence of land surfaces upwind of the measurement location particularly under stable conditions which may prevail in coastal and offshore environments in the middle and high latitudes (e.g., [1,25]). Information presented in Figs. 7 and 8 and Table 3 also may be used to infer that the adjustment of flow moving offshore is manifest as a change in the statistical properties of the distribution. Wind speed distributions offshore indicate higher mean values (e.g., mean wind speed during March–November 1999 was 6.03 m s1 at Vindeby LM, 6.37 m s1 at SMW and was and 7.54 m s1 at Om ), and that the low tail of the distribution is moved towards the mean and the upper tail is shifted towards higher wind speed values relative to distributions from onshore sites. There is evidence in Figs. 7 and 8 and Table 3 that the mean of the distribution begins to shift towards higher values more quickly (i.e., in a shorter over water distance) than the form of the distribution changes (as a response to lower probability of extremely low wind speeds and increased probability of high wind speeds). This inference is also supported by analysis of the Weibull parameters shown in Table 4. Although these statistics should be treated with care due to the relatively small number of coincident observations used to develop these parameters (number of observations =6871), they indicate that the shape parameter (k) shows greater similarity between Vindeby LM and Vindeby SMW than the scale parameter (c) from Vindeby SMW which exhibits greater similarity to those calculated for data from Om . Hence the postulate may be offered that there is some degree of decoupling between the descriptive parameters of the wind speed distribution. Specifically, changes in skewness and kurtosis of the distribution between land and offshore sites appear to develop more slowly with over water flow than the acceleration of the flow. In other words, the mean wind speed adjusts more quickly (or over shorter distances) than the higher moments of the distribution.
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Table 4 Weibull parameters for wind speed data collected between March 1999 and November 1999 at Vindeby LM, Vindeby SMW and Om LM Height
10 m
c k
6.3 2.65
SMW
OMØ
LM
SMW
OMØ
30 m 7.2 2.69
7.8 2.81
7.3 2.61
LM
SMW
OMØ
8.3 2.57
8.6 2.65
48/50 m 7.9 2.57
8.2 2.62
7.4 2.52
Justus et al. [20,26] report analyses which indicate the Weibull scale factor (c) and Weibull shape parameter (k) vary with height (z; in m) according to: n c z ð5Þ ¼ cA zA
k kA
¼
1 0:88 lnðz=10Þ ; 1 ¼ 0:88 lnðzA =10Þ
ð6Þ
where A indicates the anemometer height, and the power law exponent, n; may be found from: n¼
0:37 0:88 ln cA 1 0:088 lnðzA =10Þ
ð7Þ
k was found to increase with height to 60 m in data from land sites by Justus et al. [20]. However, as shown in Table 4, the k parameter calculated from the time series data from Vindeby LM, SMW and Om indicate decreasing values with height. Also, c and k derived for 10 m height using the 30 m data from LM, SMW and Om show poor agreement with c and k derived from the time series. The discrepancy between k and c calculated from the time series and using Eqs. (5)–(7) are in excess of 10% and so are larger than those derived in the analysis of Justus et al. [20]. While the k and c parameters derived here are subject to uncertainties due to the short data series, these findings and those presented in Section 3.1 are indicative of some degree of decoupling of the flow statistics in the vertical at these coastal sites. To further develop this thesis, Table 5 summarizes descriptive parameters of wind speeds distributions at Vindeby LM and SMW and Om under southerly flow. As shown, the distributions of wind speeds at all sites are more peaked and positively skewed under stable conditions. This may be the result of truncation of high wind speeds under unstable conditions when the conditions become near-neutral according to the definitions of stability classes described above. However, it may also be hypothesized that regardless of the stability class definitions, wind speed distributions in unstable conditions are neutrally or negatively skewed because unstable conditions can not be supported in high wind speeds in temperate offshore environments. Buoyant forcing of turbulence in these environments has a limited practical range defined by vertical temperature gradients (of approximately one order of magnitude) while mechanical forcing of turbulence can vary over a much
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Table 5 Mean (M) (m s1), standard deviation (s) (m s1), skewness (S) and kurtosis (K) for wind speed data collected between March 1999 and November 1999 at Vindeby LM, Vindeby SMW and Om with southerly (offshore) flow LM Height
SMW
OMØ
10 m
All data No. obs. 2614 2614 2614 M 4.40 5.82 6.56 s 1.95 2.39 2.78 S 0.66 0.45 0.44 K 3.30 2.96 2.77
LM
SMW
OMØ
LM
30 m
48/50 m
1571 2610 2614 6.03 6.37 7.54 2.39 2.49 3.07 0.28 0.42 0.37 3.13 3.19 2.94
2609 6.47 2.27 0.20 3.30
SMW
OMØ
2614 2614 6.78 7.99 2.54 3.20 0.24 0.31 3.31 2.97
Stable No. obs. M s S K
632 3.82 1.62 1.08 4.22
632 5.23 2.05 0.70 3.37
632 5.68 2.37 0.78 3.50
305 5.38 1.96 0.42 3.96
632 5.93 2.21 0.54 3.40
632 6.92 2.57 0.51 3.38
630 6.36 2.03 0.19 3.22
632 6.58 2.31 0.23 3.39
632 7.60 2.79 0.33 3.18
Unstable No. obs. M s S K
322 4.67 1.81 0.09 2.73
322 6.17 2.17 0.14 2.77
322 7.04 2.28 0.31 2.70
227 6.22 2.27 0.22 3.24
322 6.48 2.32 0.06 2.83
322 7.76 2.60 0.31 2.62
322 6.25 2.23 0.01 3.02
322 6.59 2.34 0.02 2.88
322 7.97 2.70 0.28 2.74
larger range as friction velocity can reasonably span at least two orders of magnitude due to variations in surface roughness due to wind-wave coupling [27]. Under stable conditions at 50 m the skewness and kurtosis exhibit considerable evidence of the significant influence of land upwind while at lower heights the kurtosis is lower offshore representing modification of the distribution to include higher wind speeds.
4. Summary and conclusions This paper documents analyses of flow characteristics in the near-shore and offshore environment using data from the Danish wind monitoring network. The principal findings of the analyses presented herein may be summarized as follows: *
In this relatively high wind speed environment (a maritime climate in the Northern Hemisphere mid-latitudes), the temporal auto-correlation of wind speeds measured at, or above, 40 m in the near-coastal zone is not significantly higher than that from land sites. However, the persistence of wind speeds above typical turbine cut-in speeds is higher at sites over water surfaces. At the sites considered here, in over three years, the maximum duration of winds below
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*
*
219
4 m s1 at approximately 40 m height at the offshore sites was less than one day, while at a land site it exceeded two days. Conversely, the persistence of wind speeds in excess of 15 m s1 is substantially higher at the offshore sites. Under offshore flow, flow above 30 m height is not fully adjusted to reduced surface roughness even after over water distances of 20 km. This is in accord with analyses presented in Smith and MacPherson [4] and indicates the maximum change in wind speed is not fully realized at this distance from the coastline. However, there is substantial acceleration of the flow even within 2 km of the coastline. Observations are presented which indicate that for offshore flow the mean wind speeds 2 and 11 km offshore are approximately 30% and 50% higher than those from an onshore coastal site at 10 m, 6% and 25% higher at 30 m and 5% and 24% higher at approximately 50 m. As flow moves offshore the mean of the wind speed moves to higher wind speeds, the low end tail moves towards the mean and the upper tail extends to higher wind speeds. There is evidence that the mean (scale) and variance or form (shape) of the wind speed distribution are modified at different rates as flow moves offshore.
It has been suggested that differences in the wind speed distributions at the sites used here may reflect the influence of differential synoptic forcing. However, the distances under consideration are much smaller than those which characterize the synoptic scale and half-hourly average wind speeds from even the two most distant sites considered here (R dsand and Tystofte) exhibit a Spearman correlation coefficient of 0.97 for the data record from 1996–1999. The major implications of this research for harnessing the offshore wind resource are as follows: *
*
*
The frequency and duration of wind speeds below typical wind turbine cut-in speeds is markedly decreased in offshore environments relative to comparable land sites. Also the frequency and duration of wind speeds above rated values for wind turbines is markedly increased in offshore environments. This indicates that the power generation from wind turbines located offshore should be more stable (consistent) than that from land based turbines. The maximum change in wind speed due to reduced surface roughness is not fully realized after an over water fetch of 20 km. This indicates the importance of accurate modelling of flow in the coastal zone for wind resource estimation and assessment of the relative costs of power transmission versus the benefits of increased wind speeds (and hence power production) with increasing distance from the coast. Under offshore flow, wind speed data indicate frequent decoupling of flow above approximately 30 m from the very near surface flow. The implication is wind turbines located within a few kilometers of the coastline may frequently be subject to considerable vertical shear across the turbine blades and different turbulence regimes above and below the internal boundary layer.
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Acknowledgements This research was partly supported by the ‘Predicting Offshore Wind Energy Resources’ project (contract JOR3-CT98-0286). The authors also gratefully acknowledge SEAS A.m.b.A. for their financial support. The technical support staff at Ris are acknowledged for their work in operating the offshore network and Scott M. Robeson is acknowledged for his helpful suggestions on an earlier draft of this manuscript.
References [1] J.P. Coelingh, A.J.M. van Wijk, A.A.M. Holtslag, Analysis of wind speed observations over the North Sea coast, J. Wind Eng. Ind. Aerodynam. 73 (1998) 125–144. [2] R.J. Barthelmie, I. Bryden, J. Coelingh, S.C. Pryor, Energy from the oceans: wind, wave and tidal, in: C. Sheppard (Ed.), Seas at the Millennium, Elsevier: Amsterdam, 2000, pp. 303–321. [3] R.J. Barthelmie, A brief review of offshore wind energy activity in the 1990s, Wind Eng. 22 (1999) 265–274. [4] P.C. Smith, J.I. MacPherson, Cross-shore variations of near-surface wind velocity and atmospheric turbulence at the land-sea boundary during CASP, Atmos. Ocean 25 (1987) 279–303. [5] R.J. Barthelmie, M. Courtney, B. Lange, M. Nielsen, A.M. Sempreviva, J. Svenson, F. Olsen, T. Christensen, Offshore wind resources at Danish measurement sites, In Proceedings of the 1999 European Wind Energy Conference and Exhibition. James and James Scientific Publishers Ltd, Nice 1999, pp. 1101–1104. [6] D.Y.C. Leung, C.H. Liu, Improved estimators for the standard deviations of horizontal wind fluctuations, Atmos. Environ. 30 (1996) 2457–2461. [7] A.B. Sigl, R.B. Corotis, D.J. Won, Run duration analysis of surface wind speeds for wind energy applications, J. Appl. Meteorol. 18 (1979) 156–166. [8] A.C. Brett, S.E. Tuller, The autocorrelation of hourly wind speed observations, J. Appl. Meteorol. 30 (1991) 823–833. [9] R.J. Barthelmie, B. Grisogono, S.C. Pryor, Observations and simulations of diurnal cycles of nearsurface wind speeds over land and sea, J. Geophys. Res. (Atmospheres) 101 (1996) 21327–21337. [10] A.-S. Smedman-Hogstrom, U. Hogstrom, A practical method for determining wind frequency distributions for the lowest 200 m from routine meteorological data, J. Appl. Meteorol. 17 (1978) 942–954. [11] S.A. Hsu, Determining the Power-law wind-profile exponent under near-neutral stability conditions at sea, J. Appl. Meteorol. 33 (1994) 757–765. [12] H. Charnock, Wind stress on a water surface, Q. J. R. Meteorol. Soc. 81 (1955) 639–640. [13] T. Hanafusa, C.B. Lee, A.K. Lo, Dependence of the exponent in power law profiles on stability and height interval, Atmos. Environ. 20 (1986) 2059–2066. [14] S.C. Pryor, R.J. Barthelmie, Analysis of the effect of the coastal discontinuity on near-surface flow, Ann. Geophys. 16 (1998) 882–888. [15] A.C.M. Beljaars, A.A.M. Holtslag, R.M. van Westrhenen, Description of a Software Library for the Calculation of Surface Fluxes, KNMI, De Bilt, Netherlands, 1989. [16] J.B. Kennedy, A.M. Neville, Basic Statistical Methods for Engineers, Scientists, Harper and Row, New York, 1986. [17] W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes in FORTRANFThe Art of Scientific Computing, Second Edition, Cambridge University Press, Cambridge, 1989, 963pp. [18] D.J. Erickson, J.A. Taylor, Non-Weibull behavior observed in a model-generated global surface wind field frequency distribution, J. Geophys. Res. (Oceans) 94 (1989) 12 693–12 698.
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[19] E.G. Pavia, J.J. O’Brien, Weibull statistics of wind speed over the ocean, J. Climate Appl. Meteorol. 25 (1986) 1324–1332. [20] C.G. Justus, W.R. Hargraves, A. Yalcin, Nationwide assessment of potential power output from wind-powered generators, J. Appl. Meteorol. 15 (1976) 673–678. [21] I. Troen, E.L. Petersen, European Wind Atlas. Roskilde, Ris National Laboratory, Denmark, 1989, 656pp. [22] K. Conradsen, L.B. Nielsen, L.P. Prahm, Review of Weibull statistics for estimation of wind speed distributions, J. Climate Appl. Meteorol. 23 (1984) 1173–1183. [23] S.E. Tuller, A.C. Brett, The characteristics of wind velocity that favor the fitting of a Weibull distribution in wind speed analysis, J. Climate Appl. Meteorol. 23 (1984) 124–134. [24] P.A. Taylor, A model of airflow above changes in surface heat flux, temperature and roughness for neutral and unstable conditions, Boundary-Layer Meteorol. 1 (1970) 18–39. [25] H.J. Erbrink, R.D.A. Scholten, Atmospheric turbulence above coastal waters: determination of stability classes and a simple model for offshore flow including advection and dissipation, J. Appl. Meteorol. 34 (1995) 2278–2293. [26] C.G. Justus, W.R. Hargraves, A. Mikhail, D. Graber, Methods for estimating wind speed frequency distributions, J. Appl. Meteorol. 17 (1978) 350–353. [27] H.K. Johnson, J. H jstrup, J. Vested, S.E. Larsen, On the dependence of sea surface roughness on wind waves, J. Phys. Oceanograph. 28 (1997) 1702–1716.
Statistical analysis of flow characteristics in the coastal zone S.C. Pryora,*, R.J. Barthelmiea,b a
Atmospheric Science Program, Department of Geography, Indiana University, Bloomington, IN 47405, USA b Wind Energy and Atmospheric Physics, Risø National Laboratory, Dk-4000 Roskilde, Denmark Received 3 December 2000; received in revised form 26 November 2001; accepted 26 November 2001
Abstract This paper presents analyses of flow characteristics in the near-shore and offshore environment using data from the Danish wind monitoring network. In this relatively high wind speed environment the temporal auto-correlation of wind speeds measured in the offshore coastal zone at or above a height of 40 m is not significantly higher than that from land masts. However, the persistence of wind speeds above typical wind turbine cut-in speeds is higher at coastal and offshore masts. The parameters of wind speed distributions calculated for the onshore and offshore data indicate that both the mean and form of the distribution is modified during offshore flow. It is shown that in the near-surface layer vertical propagation of the modified momentum flux differentially affects the body and tails of the wind speed distribution. These analyses further indicate that at a height of 50 m under stable stratification the flow has not fully adjusted to the differing fluxes over the sea even after an over water fetch of at least 11–20 km. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Wind energy; Offshore; Wind speed distributions; Persistence; Temporal auto-correlation
1. Introduction Except where topographic forcing enhances flow, wind energy resources offshore are thought to exceed those of onshore regions due principally to (1) greater persistence of flow offshore and (2) higher wind speeds offshore due largely to lower surface roughness [1]. An additional benefit to offshore location of wind farms is *Corresponding author. Tel.: +1-812-855-5155; fax: +1-812-855-1661. E-mail address: [email protected] (S.C. Pryor). 0167-6105/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 0 1 ) 0 0 1 9 5 - 7
202
S.C. Pryor, R.J. Barthelmie / J. Wind Eng. Ind. Aerodyn. 90 (2002) 201–221 58.5 58.0
SWEDEN
Latitude (˚N)
57.5 57.0 56.5
DENMARK
56.0 55.5
Omø
Tystofte
55.0 54.5
Gedser Vindeby Rødsand 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0
Longitude (˚E) Fig. 1. Locations of the measurement masts in Denmark from which data are presented here.
reduced turbulence intensity offshore leading to reduced stress on turbine components [2]. However, the magnitude of these benefits has yet to be fully quantified. Because installation and maintenance of wind turbines at great distances from land represent a significant economic burden and presents many technical challenges [3], the first offshore wind turbines are being installed in coastal environments (i.e., typically o10 km from the coast) [1,2] in a region of horizontal inhomogeneity where the flow may not have fully adjusted to the different fluxes from the water surface compared to those from land [4]. Hence, there is a need for more detailed information regarding flow characteristics in coastal and offshore zones. Here we use data collected under the Danish offshore wind monitoring program [5] (see Fig. 1 and Table 1) to quantify differences in the persistence of wind speeds at on and offshore sites. We also address issues regarding how far offshore wind speed distributions exhibit continuing influence from upwind land surfaces and how changes in the wind speed characteristics offshore are manifest in the probability distributions.
2. Persistence of wind speeds at offshore, coastal and land sites 2.1. Background The term persistence has been used within two contexts in the study of atmospheric flow variability. First, to quantify the steadiness of the wind direction
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Table 1 Details of the measurement mast and data Site
Location (offshore/onshore)
Distance to closest coastline
Measurement heights (m) of wind speed data presented
Tystofte Gedser land mast R dsand Vindeby land mast (LM) Vindeby sea mast west (SMW) Om
Onshore Onshore (coastal) Offshore Onshore (coastal) Offshore
3 km 15 m 9 km 15 m 1.8 km
39.6 10, 50 10, 50 10, 30, 48 10, 30, 48
Offshore
12 km
50
(where persistence is defined as the ratio of vector wind speed to scalar wind speed [6]). Second, as in Sigl et al. [7], to indicate the duration of surface wind speeds within specified wind speed classes. In this analysis, we use the term persistence in this latter context. An accurate assessment of the feasibility of wind resource utilization is dependent on the persistence of wind speeds because the reliability and predictability of generated power and duration of time without power generation have implications for network design and meshing of technologies to continuously meet electricity demand [7]. To assess the relative persistence of wind speeds at offshore locations in the Danish monitoring network we present two analyses. First, analysis of the temporal auto-correlation of half-hourly average wind speed measurements and then analysis of the persistence of flow in categories based on cut-in and rated wind speeds for a representative wind turbine. 2.2. Data analysis 2.2.1. Temporal auto-correlation of wind speed time series Data values in discrete time series of atmospheric variables typically exhibit dependence on preceding values of that variable [8]. Temporal auto-correlation is a measure of this dependence. It is the correlation of successive values in the time series at specified lag intervals. An auto-correlation function (the auto-correlation plotted as a function of the lag-time) depicts one measure of the persistence in the time series and may also be used to reveal non-stationarities (such as defined periodicities) in the data. Here we construct auto-correlation functions using data series from 1996–1999 at three meteorological masts in the Danish monitoring network which have semicontinuous half-hourly average wind speed measurements at or above 40 m above the ground or sea-surface. These three sites (Fig. 1) are: *
Tystofte land mast which is located >3 km from the closest coastline and hence is used to represent conditions at a typical land site in Denmark.
204 *
*
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Vindeby land mast (LM) which is located within 15 m of the coast of Lolland and is presumed to represent a mixed sea and land climatology. Vindeby sea mast west (SMW) which has an over water fetch of 2 km from the closest coastline and hence is used to represent a coastal location.
Data are presented for a measurement height of 48 m for the Vindeby masts and 39.6 m at Tystofte. Prior to performing the temporal auto-correlation analysis an unbroken time series for each site was developed in which missing or erroneous data were replaced by the mean of the time series (in each case this resulted in less than 10% replacement of the data series). These modified time series are used to calculate the temporal auto-correlation for lags extending from 30 min to multiple days. As shown in Fig. 2, there is a significant influence of non-stationarities in the Tystofte land data set with clear evidence of a diurnal cycle. However, as described in Barthelmie et al. [9], due to the thermal lag introduced by the water body, in the absence of advection from land, wind speeds in the coastal zone do not exhibit a strong diurnal cycle, and hence a diurnal cycle is not evident in the Vindeby LM and Vindeby SMW data series. As in the study of Brett and Tuller [8] auto-correlation coefficients for lags of less than 12 h are in excess of 0.5. The temporal auto-correlation for lags of 12–36 h is above 0.2 and is slightly higher in the data set from Vindeby SMW than at Vindeby LM or Tystofte for 36–72 h lags. 2.2.2. Persistence analysis Multi-year time series of half-hourly average wind speeds (1996–1999) from four measurement masts; Tystofte, Vindeby LM, Vindeby SMW and R dsand1 (an offshore mast located 9 km southeast of the island of Lolland) are used to generate cumulative frequency distributions of the persistence of wind speeds (U) in four classes: (1) (2) (3) (4)
Uo4 m s1. 4oUo15 m s1. 15oUo25 m s1. U > 25 m s1.
These four classes relate to the performance characteristics for a typical wind turbine which is suitable for deployment offshore; a VESTAS V66 1.65 MW turbine (hub-height=66 m, typical blade diameter E60 m). The classes correspond to; (1) wind speeds below the cut-in speed (i.e., the wind speed at which the turbine commences electricity generation), (2) the transition zone between cut-in and rated speed (i.e., the wind speed at which the power output is equal to the maximum for the turbine), (3) the rated speed to cut-out speed (i.e., the wind speed at which the turbine ceases to generate power) and (4) the wind speeds above the cut-out 1 R dsand is omitted from the temporal auto-correlation analysis presented above because prior to 1999 the data record has data recovery of less than 90% and hence this time series was deemed too highly fractured for that analysis.
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1
0.1 1
Correlation
Correlation
Vindeby SMW Vindeby LM Tystofte
0 0.2 0.4 0.6 0.8
1
Lag (days)
0.01 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Lag (days) Fig. 2. The auto-correlation function for Tystofte, Vindeby LM and Vindeby SMW for half-hour average wind speed data from 1996–1999. The inset shows an enlargement of the figure for lags less than 1 day.
threshold at which electricity ceases to be generated because the turbine is shut down for safety. Analysis of the distribution of missing data points in the time series indicate they are randomly distributed through the data records, and so the persistence analysis is conducted without replacement or interpolation of missing data values. Hence a missing data value is assumed to indicate termination of ‘runs’ of data in a single class. This will tend to lead to an underestimation of actual persistence of wind speeds in the four classes. All quality assured half-hourly average wind speeds from the top measurement height (39.6 m a.g.l. at Tystofte, 48 m at each of the Vindeby masts and 50 m from the R dsand mast) are above 0.2 m s1 and below 25 m s1 (i.e., no observations fall into class (4)). The cumulative probability distributions for persistence in the other three wind speed classes are shown in Fig. 3. In accord with a priori expectations, class (2) which represents wind speeds between the cut-in and rated speed is by the far the most persistent class at all sites. Also as shown, the data collected over the water surfaces indicate greater persistence of wind speeds in classes (2) and (3). For example, the 70th percentile duration of wind speeds in class (2) is 540 min at Tystofte, 660 min at Vindeby LM, 870 min at Vindeby SMW and 900 min at R dsand. Conversely, the persistence of below cut-in wind speeds is higher at the onshore sites. For example, the 90th percentile duration of wind speeds below 4 m s1 (i.e., in class (1)) is 630 min at Tystofte, 420 min at Vindeby LM, 390 min at Vindeby SMW and 330 min at R dsand. It is worthy of note that the analyses presented in Fig. 3 are not only a function of the measurement location (surface type) but also measurement height. To assess the
U < 4 m/s 4 < U < 15 m/s 15 < U < 25 m/s 100
10
1
0
(a)
0.2
0.4
0.6
0.8
1
Cumulative probability
1000 U < 4 m/s 4 < U 15 m/s 15 < U < 25 m/s 100
10
1 0
(c)
0.2 0.4 0.6 0.8 Cumulative probability
1
Number of time intervals (30 minute segments)
Number of time intervals (30 minute segments) Number of time intervals (30 minute segments)
1000
Number of time intervals (30 minute segments)
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1000 U < 4 m/s 4 < U < 15 m/s 15 < U < 25 m/s 100
10
1 0
(b)
0.2
0.4
0.6
0.8
1
Cumulative probability
1000 U < 4 m/s 4 < U < 15 m/s 15 < U < 25 m/s 100
10
1 0
(d)
0.2 0.4 0.6 0.8 Cumulative probability
1
Fig. 3. Cumulative probability distributions of classed wind speeds at (a) Tystofte, 39.6 m; (b) Vindeby LM, 48 m; (c) Vindeby SMW, 48 m and (d) R dsand, 50 m. Data for 1996–1999 at all sites except R dsand where data for 1997–1999 were used. This plot shows the cumulative probability of the specified number of consecutive 30 min average wind speeds in classed wind speed categories (i.e., the probability of observing a wind speed in the given class for a time period equal to or less than the specified duration).
relative importance of the difference in measurement height between the onshore site at Tystofte and the coastal and offshore masts (39.6 versus 48/50 m), the analysis of persistence is repeated for the 38 m measurement height at Vindeby SMW. The results of this analysis (Fig. 4) indicate the difference between the persistence of cutin to rated wind speeds at the two measurements heights at Vindeby is smaller than the difference between Tystofte and the Vindeby data. A similar result is found for the other wind speed classes and indicates the differences shown in Fig. 3 are largely the result of differences in surface type not measurement height. Similar analyses of the classed wind speed persistence are conducted for higher resolution data sets using continuous records of 10 min average wind speeds collected at a mast located over the sea (11 km from the coast) at Om and at the Tystofte land mast (Table 1) during March–November 1999. The distributions are less robust than those shown in Fig. 3 due to the smaller data sets used to construct
Number of time intervals (30 minute segments)
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1000 Tystofte 39.6m Vindeby SMW 38m Vindeby SMW 48m 100
10
1 0
0.2
0.4 0.6 0.8 Cumulative probability
1
Fig. 4. Cumulative probability distributions of wind speeds between 4 and 15 m s1 at Tystofte (39.6 m), and Vindeby SMW at 38 and 48 m height. This plot shows the probability of observing a wind speed of between 4 and 15 m s1 for a time period equal to or less than the specified duration (i.e., the 50th percentile indicates the median run duration for wind speeds in this class at Vindeby SMW at 48 m is 5 h).
the statistics and so only data for the wind speed class (2) are shown in Fig. 5. However, this plot confirms that above the 40th percentile the persistence of wind speeds in this class is higher at the sea mast (Om ). 2.3. Discussion Although Fig. 2 presents some evidence of slightly higher temporal autocorrelation at Vindeby SMW than Vindeby LM and Tystofte, the differences in correlation coefficients are generally small. This finding may seem to be at odds with expectations of greater persistence over water surfaces and analyses presented in Figs. 3 and 5. However, recall that the temporal auto-correlation is insensitive to the magnitude of observations. These analyses suggest, therefore, that the major difference in the consistency of wind speeds over land versus water surfaces is not the temporal auto-correlation (i.e., direct correlation between sequences of observations), but rather that low winds speeds are less frequent and persist for shorter periods over water surfaces and higher wind speeds are more frequent and persist for longer periods over water surfaces. Hence, the synthesis of these analyses represents a subtle but important distinction. Winds are not necessarily more persistent over water surfaces per se but rather calm conditions are less frequent and moderate to high wind speeds are more frequent over water surfaces. A further inference from Fig. 3 is that, during the measurement period, the maximum duration of nonelectricity producing wind speeds (Uo4 m s1) at the sea masts is less than one day,
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Number of time intervals (10minute segments)
1000
100
10 Tystofte Omoe 1 0
0.2 0.4 0.6 Cumulative probability
0.8
1
Fig. 5. Cumulative probability distribution of winds in class (2) i.e., 4oUo15 m s1 at Om (50 m) and Tystofte (39.6 m) calculated using 10 min average wind speeds. As in Fig. 4 this plot shows the probability of observing a wind speed of between 4 and 15 m s1 for a time period equal to or less than the specified duration.
while onshore measurement data indicate maximum persistence of low wind speeds of over two days. Hence, in the context of the Danish climate (i.e., a maritime, midlatitude, high wind speed regime) the duration of wind speeds below the threshold for electricity generation is substantially reduced in the offshore locations relative to a topographically homogeneous onshore site.
3. Flow in the coastal zone: wind speed distributions 3.1. Background The difference between winds measured over land and adjacent water bodies is non-linearly related to the strength of the wind, atmospheric stability, fetch (distance from the coastline along the prevailing wind direction), and contrasts in heat, water vapor and momentum fluxes [10]. To ensure correct assessment of the offshore wind resource it is necessary to fully characterize the entire wind speed probability distribution. Smedman-Hogstrom and Hogstrom [10] developed a technique for determining wind speed frequency distributions within a layer extending approximately 200 m from the surface from measured data at a reference height (10 m). The technique requires knowledge of the upstream roughness length ðz0 Þ and is based on the rate of growth of internal boundary layers (IBL) from surface discontinuities and assumptions regarding the
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shape of the wind profile. They assumed the vertical wind profile is comprised of N internal boundary layers associated with terrain discontinuities upstream of the measurement location. Within each layer they used the power law to describe the wind profile [11], and the growth of the IBL was described using a simple formulation where the height of the IBL is a function of z0 and stability. This model is applied to data from R dsand (where z0 ; stability and fetch are calculated as discussed in Section 3.2) assuming a single IBL propagates downwind from the coastline. The exponent of the power law is calculated using coefficients from Smedman-Hogstrom and Hogstrom [10] and z0 calculated from the Charnock equation [12]. The results are shown in Fig. 6 for the entire data set (frame a) and for the data conditionally sampled by stability class (frames b–d). This figure indicates that, in this application, the model overestimates the magnitude of wind speeds at 50 m across the entire probability distribution, largely due to overestimation of wind speeds under stable stratification. The cause of this overestimation may be the simple parameterization of the IBL growth used (where the factors a and b from SmedmanHogstrom and Hogstrom [10] are based on IBL growth over a surface with z0 o0:06 14
Predicted Measured
Wind speed (m/s)
Wind speed (m/s)
16
12
8
4 20
(a)
40
60
80
8
100
0
20
(b)
Percentile 16
40
60
80
100
80
100
Percentile 10
14
Wind speed (m/s)
Wind speed (m/s)
10
6 0
12 10 8 6
8 6 4 2
0
(c)
12
20
40
60
Percentile
80
100
0
(d)
20
40
60
Percentile
Fig. 6. Wind speed at R dsand as measured at 50 m and as predicted based on the model of SmedmanHogstrom and Hogstrom [10] using data measured at 10 m. The data are shown for (a) the entire data set (with an offshore fetch of o20 km), (b) near-neutral stratification and an offshore fetch of o20 km, (c) unstable conditions and an offshore fetch of o20 km and (d) stable stratification and an offshore fetch of o20 km. Note the changing scale between the frames.
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Wind speed (m/s)
12 10 8 6 38 m SM 38 m LM 20 m SM 20m LM
4 2 0 0
20
40
60
80
100
Percentile Fig. 7. Wind speed distributions at 20 and 38 m from Vindeby (land mast (LM) versus sea mast south (SM)) for near-neutral stability and flow moving offshore. Data from 1994.
and hence over-estimates IBL growth over the sea), or the height dependence of the power law exponent [13]. A more subtle inference drawn from Fig. 6 is that the form of the modelled wind speed distribution under near-neutral and unstable conditions is different from that derived from the measurements. This may reflect the influence of conditioning of the model by Smedman-Hogstrom and Hogstrom [10] using land based data sets while wind speed distributions offshore exhibit different characteristics. Below we examine wind speed distributions from onshore locations and relative to those from coastal and offshore data sets to examine these possible differences in detail. Pryor and Barthelmie [14] used 1994 data from the Vindeby offshore wind farm to examine the effect of fetch, stability and surface roughness on wind speeds in the coastal zone. They found that with offshore flow at 1.2–1.7 km from the coast the wind speed distributions up to a height of 20 m under all stability conditions were significantly different from those measured at a mast on the coastline. This implies that adjustment of the flow to the new surface conditions had propagated vertically to 20 m height during over water flow of 1.2–1.7 km. However, the form of the wind speed distributions above 20 m height was not statistically different at the sea masts indicating that some of the statistical properties of flow at this height had not significantly changed as a result of the modified surface conditions (Fig. 7). Here we extend this research to further examine the fetch dependence of the vertical propagation of the adjustment of the flow under differing stability conditions and to provide a more detailed analysis of the descriptive parameters of the wind speed distributions. 3.2. Data analysis To extend the analysis of Pryor and Barthelmie [14] we present data from two sets of onshore and offshore masts with varying fetch; (1) Gedser land mast and R dsand
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offshore mast, and (2) on a south–north transect from the island of Lolland; at Vindeby LM, Vindeby SMW and Om offshore mast (see Fig. 1). In the following analyses stability is characterized using the Monin-Obukhov length, L; determined using parameterizations given in Beljaars et al. [15] and applied in Pryor and Barthelmie [14] where: L¼
Tu2 *
T* gk
ð1Þ
T is the absolute temperature (K), u * is friction velocity (m s1), g is gravity (9.81 m s2), k is the von Ka! rma! n constant (0.4), and T* is the temperature scale (K) parameterized using: H T* ¼ ð2Þ rCp u * r is the air density (1.225 kg m3), Cp is the specific heat for air (1004.67 J kg1 K1), H is the heat flux (W m2) and is parameterized as a function of vertical temperature gradient ðDTÞ: For the land masts the Monin–Obukhov lengths are calculated using wind speed at 11 m height at Gedser and 8 m height at Vindeby, temperature difference ðDTÞ (17–8 m at Vindeby and 47–10 m at Gedser) and absolute temperature at 10 m at Gedser and 8 m at Vindeby. Monin-Obukhov lengths at the sea masts were calculated using wind speed at 8 m height, the sea surface temperature and DT (45– 8 m at Om , 45–10 m at Vindeby SMW, 48–8 m at R dsand). These measurement heights indicate the distance from the mast base located approximately 2.5 m above mean sea level. Using these parameterizations the sign of the Monin–Obukhov length is determined by the temperature profile and the magnitude is determined iteratively where an initial value is estimated assuming that the wind speed profile is close to neutral and determining the friction velocity based on wind speed and roughness length (assigned for land as 0.05 m) and calculated for sea according to the Charnock equation [12]). Stability classes used herein are defined as in Pryor and Barthelmie [14] where jLj > 1000 m indicates near-neutral conditions,1000 m oLo0 m indicates unstable conditions and 1000 m>L>0 m indicates stable conditions. Two statistical techniques are employed to examine the differences in wind speed distributions at the on and offshore masts by stability class and wind direction; Wilcoxon Matched-Pairs Signed Ranks test and the Kolmogorov–Smirnov equality of distributions test [16]. The Wilcoxon Matched-Pairs Signed Ranks test is used to quantitatively compare the magnitude of the observations underlying the distribution and the Kolmogorov–Smirnov test [17] is used to quantitatively compare the form of the distributions. Both tests have previously been applied to the study of wind speed distributions (e.g., [18,19,14]). In the Wilcoxon Matched-Pairs Signed Ranks test the difference score for each matched pair (coincident wind speed observations) is calculated ranked by absolute magnitude. The rank scores for all positive values are summed and compared to the summed rank scores for the negative differences. If the two wind speed data sets are drawn from the same
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population then each matched pair has the same probability of being positive or negative. If not the value of the actual rank score differences can be used to determine the confidence with which one can assert the data sets are different. The Kolmogorov–Smirnov equality of distributions test is used here to examine whether the form of the wind speed distributions at each measurement height (sampled by stability class and fetch) are statistically different at the land and sea masts. The two distributions are compared by assuming one conforms to an idealized distribution and evaluating whether the other distribution shows similar form. Probability distributions may be described using a number of descriptive parameters including the mean, standard deviation, skewness and kurtosis. The standard deviation represents the dispersion of the data set. Skewness reports the asymmetric nature of the distribution and kurtosis represents the peakedness of the distribution both relative to a Gaussian distribution. Wind speed probability distributions are typically positively skewed and hence are characterized by skewness values greater than 0. A number of statistical distributions have been fitted to, or used to represent wind speed data (e.g., log-normal and bi-variate Gaussian, Weibull [20]). However, the most commonly used is the two parameter Weibull distribution (e.g., [21,22,18]), and so this distribution is also used here. The Weibull distribution has been shown to give a good fit to observed wind speed distributions [20,23] particularly over water surfaces [19]. The actual goodness of fit of the Weibull distribution to observed wind speed distributions is station dependent. It is generally poorest under conditions with high topographic forcing of the flow or other influences (e.g., frontal passages) which result in a highly asymmetric pattern of wind speed with direction [23]. The Weibull distribution is described by two parameters; k; the dimensionless shape parameter, and c; the scale parameter. The Weibull probability density function (where f ðUÞ is the frequency of occurrence of wind speed U) is given by ( ) k U k1 U k f ðUÞ ¼ : ð3Þ exp c c c The shape parameter ðkÞ is inversely related to the variance of wind speed around the mean value. For ko1; (3) exhibits monotonic decay. If k ¼ 2:0; (3) gives the Rayleigh distribution and for k ¼ 3:6; the function approximates a Gaussian distribution. The scale parameter (c) is related to the mean of the time series and has units of wind speed (i.e., m s1 in the analysis presented here). Eq. (3) may be integrated for U ¼ 0 to an upper limit of U to give the Weibull cumulative distribution: ( ) U k PðUÞ ¼ 1 exp : ð4Þ c In terms of the terminology used above, the Wilcoxon Matched-Pairs Signed Ranks test is most sensitive to changes in c; and the Kolmogorov–Smirnov test is most sensitive to changes in the form of the distribution which is represented in the Weibull distribution by k:
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3.2.1. Wind speed distributions at Gedser and R dsand As shown in Fig. 1 the Gedser land mast is located on the tip of the island of Falster (a north–south oriented island), while the R dsand mast is approximately 22 km offshore to the west. Using conditional sampling the half-hourly average wind speed data from R dsand and Gedser from 1997–1999 were classified based on stability and fetch characteristics (i.e., distance to the coastline along the prevailing wind direction). For the analysis presented here we focus on periods when the stability at both masts was commonly defined as near-neutral, stable and unstable and when the flow to the Gedser land mast was over a land surface and the flow to the R dsand sea mast was in one of two fetch categories; over sea fetch of o20 km and over sea fetch of >20 km. The number of observations in each combined conditionally sampled group is shown in Table 2. Fig. 8 shows wind speed distributions from the two masts at 10 and 50 m height sampled by fetch and stability class. As shown, acceleration of the flow due to the lower roughness of the sea surface is most marked at 10 m height under all stability conditions and is much less pronounced at 50 m. As expected, wind speed distributions at all heights and in all stability classes indicated significantly higher wind speeds at the sea mast (i.e., significant Wilcoxon matched pair results) (Table 2). The results of the statistical analyses also indicate that, except at the 50 m height, the wind speed distributions exhibit a different form at the Gedser and R dsand masts. It is hypothesized that this is due to a change in momentum exchange with the surface which causes a modification of the wind speed profile. At 50 m height, however, the adjustment to the modified surface fluxes has not significantly altered the form of the wind speed distribution even after a fetch of over 20 km. This suggests that, at this height, the flow characteristics are still heavily influenced by the land surface over which the wind had previously blown. The exception to this result is found under stable conditions with short fetch. This anomaly is the subject of further analysis, but may reflect acceleration of the flow near to or above the internal boundary layer possibly associated with the position of maximum temperature contrast [24]. Table 2 Wind speed data availability by fetch and stability class (N=near-neutral, US=unstable, S=stable) at R dsand (off-shore mast) and Gedser (land mast). Also shown are the results of significance tests. The first symbol shows results of the Wilcoxon matched-pairs signed ranks test and the second the Kolmogorov– Smirnov test Height
10 m
Fetch to R dsand mast
o20 km
>20 km
o20 km
>20 km
o20 km
>20 km
*/* */* */*
*/* / */*
*/* */* */*
*/* / */*
*/+ */+ */*
*/+ / */+
No. obs.
o20 km
>20 km
N US S
499 93 537
336 25 490
30 m
*=Significantly different at 99.9% confidence level. =Not tested due to low n: +=Not significantly different at 99.9% confidence level.
50 m
16
16
14
14
14
12
12
12
10
10
10
8
8
8
6
6
6
4
4
4
2
2
2
0
0 0
40
60
80
100
0 0
20
Near-neutral
16
Wind speed (m/s)
20
40
60
80
Unstable
12
0
20
10
80
100
80
100
80
100
80
100
12 10 8
insufficient data
6
6
4
4 2
10 m height
0 0
20
40
60
80
0 0
100
20
16
16
16
14
14
14
12
12
10
10
8
8
6
6
4
4
2
2
0
0 20
40
60
80
100
Near-neutral
16
60
12 10 8 6 4 2 0
20
40
60
80
Unstable Roedsand Gedser
14 12 10
0
100
20
40
60
Stable
16 14
Fetch > 20 km
0
40
Percentile
Fetch < 20 km
Percentile
Wind speed (m/s)
60
14
8
2
Wind speed (m/s)
40
Stable
16
Roedsand Gedser
14
100
Fetch > 20 km
Wind speed (m/s)
16
Fetch < 20 km
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12 10
8
8
insufficient data
6 4
6 4
50 m height
2 0
2 0
0
20
40
60
Percentile
80
100
0
20
40
60
Percentile
Fig. 8. Wind speed distributions from Gedser land mast and R dsand sea mast at 10 m (above) and 50 m (below) for flow over land to the Gedser mast and over sea at the R dsand mast under different stability conditions. Fetch refers to the oversea fetch distance to the R dsand mast.
3.2.2. Wind speed distributions at Vindeby LM, Vindeby SMW and Omø Data from the three masts on a south–north transect from the island of Lolland were also classified based on stability and fetch. Wind speed distributions for southerly flow moving offshore from Vindeby LM to Vindeby SMW and Om were
10 8 6 4 2 0 0
20
12 10 8 6 4 2 0 0
(b)
80
20
40 60 Percentile
80
10 8 6 4 2 0 0
100
Wind speed (m/s) 30 m height
Wind speed (m/s) 10 m height
(a)
40 60 Percentile
12
100
Wind speed (m/s) 48/50 m height
OMOE SMW LM
20
40 60 Percentile
80
12 10 8 6 4 2 0 0
20
40 60 Percentile
80
100
215
12 10 8 6 4 2 0
100
Wind speed (m/s) 48/50 m height
12
Wind speed (m/s) 30 m height
Wind speed (m/s) 10 m height
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0
20
40 60 Percentile
80
100
0
20
40 60 Percentile
80
100
12 10 8 6 4 2 0
Fig. 9. Wind speed distributions at Vindeby LM, Vindeby SMW and Om for (a) stable conditions and (b) unstable for southerly (offshore) flow. The individual panels show the different measurement heights; 10, 30 and 48 m at LM and SMW and 50 m at Om . The fetch to the LM is over at least 10 km of land, the fetch to the SMW is 2–5 km over water and the fetch to Om is at least over 12 km of sea. Data are presented only for periods when the stability was in the same class (i.e., stable, 0oLo1000 m) at the Vindeby LM and Om masts.
calculated by stability for the period of continuous overlapping records; March– December 1999. Due to the relatively short data set, sufficient data are only available for calculating distributions when the stability at Vindeby LM and Om is commonly defined as stable or unstable. Fig. 9 shows the resulting distributions graphically and the results of significance testing are given in Table 3. 3.3. Discussion Before discussing the implications of the analyses presented above it is important to reiterate that stability was held constant in the comparison of onshore and offshore data and hence that these results do not describe the evolution of stability with over water flow. Analyses presented here indicate that at the lowest measurement height (10 m) for offshore flow the majority of the wind speed adjustment under stable stratification occurs within 2 km of the coastline. However, for offshore flow the wind speed distribution at 48 m has not responded to the change in surface characteristics within 2 km of the shoreline and under stable stratification there is no difference in the form
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Table 3 Data availability and results of significance tests for wind speed data from Vindeby LM, Vindeby SMW and Om for flow moving offshore. The first symbol shows results of the Wilcoxon test and the second shows the results of the Kolmogorov–Smirnov test Height
10 m SMW
No. obs.: US=231. S=404 LM US */* LM S */* SMW US SMW S
30 m
48/50 m
OMØ
SMW
OMØ
SMW
OMØ
*/* */* */* */+
*/* */*
*/* */* */* */*
*/+ */+
*/* */+ */* */+
*=Significantly different at 99.9% confidence level. =Not tested due to low n: +=Not significantly different at 99.9% confidence level. US=unstable. S=stable.
of the distribution even after a further over sea fetch of 9 km. It is also shown that wind speed distributions over 20 km from the coast continue to exhibit the influence of land surfaces upwind of the measurement location particularly under stable conditions which may prevail in coastal and offshore environments in the middle and high latitudes (e.g., [1,25]). Information presented in Figs. 7 and 8 and Table 3 also may be used to infer that the adjustment of flow moving offshore is manifest as a change in the statistical properties of the distribution. Wind speed distributions offshore indicate higher mean values (e.g., mean wind speed during March–November 1999 was 6.03 m s1 at Vindeby LM, 6.37 m s1 at SMW and was and 7.54 m s1 at Om ), and that the low tail of the distribution is moved towards the mean and the upper tail is shifted towards higher wind speed values relative to distributions from onshore sites. There is evidence in Figs. 7 and 8 and Table 3 that the mean of the distribution begins to shift towards higher values more quickly (i.e., in a shorter over water distance) than the form of the distribution changes (as a response to lower probability of extremely low wind speeds and increased probability of high wind speeds). This inference is also supported by analysis of the Weibull parameters shown in Table 4. Although these statistics should be treated with care due to the relatively small number of coincident observations used to develop these parameters (number of observations =6871), they indicate that the shape parameter (k) shows greater similarity between Vindeby LM and Vindeby SMW than the scale parameter (c) from Vindeby SMW which exhibits greater similarity to those calculated for data from Om . Hence the postulate may be offered that there is some degree of decoupling between the descriptive parameters of the wind speed distribution. Specifically, changes in skewness and kurtosis of the distribution between land and offshore sites appear to develop more slowly with over water flow than the acceleration of the flow. In other words, the mean wind speed adjusts more quickly (or over shorter distances) than the higher moments of the distribution.
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Table 4 Weibull parameters for wind speed data collected between March 1999 and November 1999 at Vindeby LM, Vindeby SMW and Om LM Height
10 m
c k
6.3 2.65
SMW
OMØ
LM
SMW
OMØ
30 m 7.2 2.69
7.8 2.81
7.3 2.61
LM
SMW
OMØ
8.3 2.57
8.6 2.65
48/50 m 7.9 2.57
8.2 2.62
7.4 2.52
Justus et al. [20,26] report analyses which indicate the Weibull scale factor (c) and Weibull shape parameter (k) vary with height (z; in m) according to: n c z ð5Þ ¼ cA zA
k kA
¼
1 0:88 lnðz=10Þ ; 1 ¼ 0:88 lnðzA =10Þ
ð6Þ
where A indicates the anemometer height, and the power law exponent, n; may be found from: n¼
0:37 0:88 ln cA 1 0:088 lnðzA =10Þ
ð7Þ
k was found to increase with height to 60 m in data from land sites by Justus et al. [20]. However, as shown in Table 4, the k parameter calculated from the time series data from Vindeby LM, SMW and Om indicate decreasing values with height. Also, c and k derived for 10 m height using the 30 m data from LM, SMW and Om show poor agreement with c and k derived from the time series. The discrepancy between k and c calculated from the time series and using Eqs. (5)–(7) are in excess of 10% and so are larger than those derived in the analysis of Justus et al. [20]. While the k and c parameters derived here are subject to uncertainties due to the short data series, these findings and those presented in Section 3.1 are indicative of some degree of decoupling of the flow statistics in the vertical at these coastal sites. To further develop this thesis, Table 5 summarizes descriptive parameters of wind speeds distributions at Vindeby LM and SMW and Om under southerly flow. As shown, the distributions of wind speeds at all sites are more peaked and positively skewed under stable conditions. This may be the result of truncation of high wind speeds under unstable conditions when the conditions become near-neutral according to the definitions of stability classes described above. However, it may also be hypothesized that regardless of the stability class definitions, wind speed distributions in unstable conditions are neutrally or negatively skewed because unstable conditions can not be supported in high wind speeds in temperate offshore environments. Buoyant forcing of turbulence in these environments has a limited practical range defined by vertical temperature gradients (of approximately one order of magnitude) while mechanical forcing of turbulence can vary over a much
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Table 5 Mean (M) (m s1), standard deviation (s) (m s1), skewness (S) and kurtosis (K) for wind speed data collected between March 1999 and November 1999 at Vindeby LM, Vindeby SMW and Om with southerly (offshore) flow LM Height
SMW
OMØ
10 m
All data No. obs. 2614 2614 2614 M 4.40 5.82 6.56 s 1.95 2.39 2.78 S 0.66 0.45 0.44 K 3.30 2.96 2.77
LM
SMW
OMØ
LM
30 m
48/50 m
1571 2610 2614 6.03 6.37 7.54 2.39 2.49 3.07 0.28 0.42 0.37 3.13 3.19 2.94
2609 6.47 2.27 0.20 3.30
SMW
OMØ
2614 2614 6.78 7.99 2.54 3.20 0.24 0.31 3.31 2.97
Stable No. obs. M s S K
632 3.82 1.62 1.08 4.22
632 5.23 2.05 0.70 3.37
632 5.68 2.37 0.78 3.50
305 5.38 1.96 0.42 3.96
632 5.93 2.21 0.54 3.40
632 6.92 2.57 0.51 3.38
630 6.36 2.03 0.19 3.22
632 6.58 2.31 0.23 3.39
632 7.60 2.79 0.33 3.18
Unstable No. obs. M s S K
322 4.67 1.81 0.09 2.73
322 6.17 2.17 0.14 2.77
322 7.04 2.28 0.31 2.70
227 6.22 2.27 0.22 3.24
322 6.48 2.32 0.06 2.83
322 7.76 2.60 0.31 2.62
322 6.25 2.23 0.01 3.02
322 6.59 2.34 0.02 2.88
322 7.97 2.70 0.28 2.74
larger range as friction velocity can reasonably span at least two orders of magnitude due to variations in surface roughness due to wind-wave coupling [27]. Under stable conditions at 50 m the skewness and kurtosis exhibit considerable evidence of the significant influence of land upwind while at lower heights the kurtosis is lower offshore representing modification of the distribution to include higher wind speeds.
4. Summary and conclusions This paper documents analyses of flow characteristics in the near-shore and offshore environment using data from the Danish wind monitoring network. The principal findings of the analyses presented herein may be summarized as follows: *
In this relatively high wind speed environment (a maritime climate in the Northern Hemisphere mid-latitudes), the temporal auto-correlation of wind speeds measured at, or above, 40 m in the near-coastal zone is not significantly higher than that from land sites. However, the persistence of wind speeds above typical turbine cut-in speeds is higher at sites over water surfaces. At the sites considered here, in over three years, the maximum duration of winds below
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*
*
219
4 m s1 at approximately 40 m height at the offshore sites was less than one day, while at a land site it exceeded two days. Conversely, the persistence of wind speeds in excess of 15 m s1 is substantially higher at the offshore sites. Under offshore flow, flow above 30 m height is not fully adjusted to reduced surface roughness even after over water distances of 20 km. This is in accord with analyses presented in Smith and MacPherson [4] and indicates the maximum change in wind speed is not fully realized at this distance from the coastline. However, there is substantial acceleration of the flow even within 2 km of the coastline. Observations are presented which indicate that for offshore flow the mean wind speeds 2 and 11 km offshore are approximately 30% and 50% higher than those from an onshore coastal site at 10 m, 6% and 25% higher at 30 m and 5% and 24% higher at approximately 50 m. As flow moves offshore the mean of the wind speed moves to higher wind speeds, the low end tail moves towards the mean and the upper tail extends to higher wind speeds. There is evidence that the mean (scale) and variance or form (shape) of the wind speed distribution are modified at different rates as flow moves offshore.
It has been suggested that differences in the wind speed distributions at the sites used here may reflect the influence of differential synoptic forcing. However, the distances under consideration are much smaller than those which characterize the synoptic scale and half-hourly average wind speeds from even the two most distant sites considered here (R dsand and Tystofte) exhibit a Spearman correlation coefficient of 0.97 for the data record from 1996–1999. The major implications of this research for harnessing the offshore wind resource are as follows: *
*
*
The frequency and duration of wind speeds below typical wind turbine cut-in speeds is markedly decreased in offshore environments relative to comparable land sites. Also the frequency and duration of wind speeds above rated values for wind turbines is markedly increased in offshore environments. This indicates that the power generation from wind turbines located offshore should be more stable (consistent) than that from land based turbines. The maximum change in wind speed due to reduced surface roughness is not fully realized after an over water fetch of 20 km. This indicates the importance of accurate modelling of flow in the coastal zone for wind resource estimation and assessment of the relative costs of power transmission versus the benefits of increased wind speeds (and hence power production) with increasing distance from the coast. Under offshore flow, wind speed data indicate frequent decoupling of flow above approximately 30 m from the very near surface flow. The implication is wind turbines located within a few kilometers of the coastline may frequently be subject to considerable vertical shear across the turbine blades and different turbulence regimes above and below the internal boundary layer.
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Acknowledgements This research was partly supported by the ‘Predicting Offshore Wind Energy Resources’ project (contract JOR3-CT98-0286). The authors also gratefully acknowledge SEAS A.m.b.A. for their financial support. The technical support staff at Ris are acknowledged for their work in operating the offshore network and Scott M. Robeson is acknowledged for his helpful suggestions on an earlier draft of this manuscript.
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