2 Sites Correlation Models

Journal of Wind Engineeringand Industrial Aerodynamics 79 (1999) 233—268

A two-site correlation model for wind speed, directionand energy estimates

James R. Salmon!,*, John L. Walmsley",1

! Zephyr North, 4034 Mainway, Burlington, Ont., Canada L7M 4B9" Atmospheric Environment Service, 4905 Dufferin Street, Downsview, Ont., Canada M3H 5T4

Received 20 September 1997; accepted 2 April 1998

Abstract

A two-site wind correlation model was first modified and then tested on long-term data fromfive pairs of Canadian weather stations. The stations were chosen to cover a variety oftopographic situations and surface cover types. A preliminary analysis of data from each of the10 stations concluded that an absolute minimum of 12 months of monitoring is needed toestimate the long-term wind speed distribution. Increasing this short-term monitoring period to24 months causes noticeable improvements; thereafter, the improvement is more gradual. It wasalso found that a short-term monitoring period between 12 and 24 months might produceworse estimates than for a 12-month period. For the two-site tests, one station from each of thefive pairs was designated as a reference station; the other was designated as a target station. Itwas found that the model results derived from 1 yr of short-term simultaneous monitoring atthe two stations and long-term data at the reference station outperform the estimates basedsolely on 2 yr of monitoring at the target station. The model results are further improved byusing 2 yr of short-term monitoring. The conclusions from this study have implications for windenergy and air pollution studies where long-term estimates of the wind speed and directiondistribution are needed and must be based on a relatively short-term period of monitor-ing. ( 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Two-site correlation; Wind energy estimates; Wind correlation model

1. Introduction

Walmsley and Bagg [1] developed a two-station wind correlation scheme andapplied it to data from Fort McMurray and Mildred Lake, Alberta. Simultaneoushourly data from the period 1974—75 were used to produce a matrix of correlation

*Corresponding author. E-mail: [email protected].

0167-6105/99/$ — see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 1 1 9 - 6

coefficients, which were multiplied by longer-term (1963—75) data from the FortMcMurray Airport weather station to generate an estimate of the wind climatology atMildred Lake. (For a summary of the method, see Appendix A.) Walmsley and Bagg[2] employed these synthetic data, comprising a joint relative frequency distributionof wind speed, wind direction and atmospheric stability, in an application with theclimatological dispersion model (CDM) [3] to estimate surface concentrations ofsulphur dioxide.

The Walmsley-Bagg wind correlation model was developed to be compatible withlong-term, joint relative frequency data produced by the Day—Night version of theS¹AR program developed by the National Climatic Center at Asheville, NorthCarolina. It was subsequently modified to accept a user-specified number of stabilityclasses and user-defined wind speed and direction classes, but until now it has notbeen tested with independent data.

In addition to air pollution studies, the Walmsley—Bagg model may also be appliedto the assessment of the potential long-term wind resource at a proposed wind-turbinesite. The wind-energy potential in the US Great Plains and Canadian Prairies isenormous. In exploiting this potential, important questions that need to be answeredare: is a short-term dataset at a candidate turbine site representative of the long-termclimatology, and what is the best estimate of the long-term wind resource andavailable wind energy.

The goal of the present study, therefore, was to test the Walmsley—Bagg model onindependent data sets and to answer two specific questions: (i) What length ofshort-term dataset at a candidate wind-turbine site is required to be representative ofthe long-term climatology? and (ii) Can the model be used to improve the long-termestimates of the wind resource at a candidate wind-turbine site?

2. Previous studies

A search of the literature failed to uncover any statistical correlation methods thatare closely related to the Walmsley—Bagg method, although Walmsley [4] includeda short section on measure—correlate—predict (MCP) methods. Of the methodstabulated, only the Walmsley—Bagg model had been published in the open literature.The other [5] had been introduced in an internal report. Walmsley [4] also referred toa formula given by AWEA [6] that may be used for estimating long-term mean windspeeds at a potential wind turbine site. While an estimate of the mean may be useful ina preliminary evaluation, information on the frequency distribution of wind speeds isneeded for a proper evaluation of the wind resource.

Kau et al. [7] introduced a statistical model for predicting surface wind speed anddirection. The former was found to depend primarily upon the slope wind, cross-isobaric angle, surface thermal stability, and geostrophic wind; the latter dependedprimarily upon the geostrophic wind direction, aspect angle of the topography,up-canyon direction, and cross-isobaric angle in the boundary layer.

Hanna and Chang [8] derived an empirical formula (their Eq. (12)) for the spatialcorrelation between wind speeds observed at two stations, as a function of spatial

234 J.R. Salmon, J.L. Walmsley/J. Wind Eng. Ind. Aerodyn. 79 (1999) 233–268

separation and averaging time. It was found that their observations of spatialcorrelations were best fit if two independent integral distance scales were used:a boundary-layer distance scale of about 300 m for small station separations anda mesoscale distance scale of about 10 km for larger station separations. This formulamay be useful in determining whether a weather station’s data applies at a nearbyprediction site. The formula, however, gives no estimate of the wind speed or directionat the prediction site.

Palomino and Martı́n [9] modified the interpolation scheme of Goodwin et al. [10]by changing the weighting from an inverse-distance-squared formulation to thedifference in topographic elevation between a grid node and an observation point.This change tended to improve the spatial interpolation of wind fields in a complexterrain. The method, however, was applied in a single valley and the maximumhorizontal distance between grid nodes and observation points was less than 2 km.

Finally, an abbreviated account of the present study appeared in Ref. [11].

3. Modifications to the Walmsley—Bagg model

For this study, the Walmsley—Bagg model was modified slightly in order toincorporate variable numbers and sizes of wind speed and wind direction classes orbins. The number of stability classes (6) was unchanged and corresponds to thestandard distribution of Day—Night S¹AR stability categories. Thirty-two wind speedclasses with a bin size of 0.5 m s~1 ranging from 0 to 16 m s~1 were chosen. Sixteenequally-sized wind direction bins of width 22.5° were selected, with the first bincentred on north. The total number of bins in the joint distribution was therefore6]32]16, requiring a correlation matrix of size 30722 or 9.44]106, which wassuccessfully handled by our personal computer (PC) with 16 Mbytes of RAM. Latertests showed a very weak dependence on atmospheric stability; therefore, it waspossible to eliminate stability while increasing the number of speed bins to 64 (i.e.,ranging from 0 to 32 m s~1), making 64]16 bins and a correlation matrix of size10242 or 1.05]106.

Wind speed bin widths of 0.5 m s~1 correspond approximately to the size of binsused for reporting and verification of wind-turbine power curves. The 16 winddirection classes of width 22.5° correspond to the maximum allowed for use in theMS-Micro wind flow model of Ref. [12]. They are also roughly the same size as the 12classes of width 30° suggested for use in the WA4P wind flow modelling program ofRef. [13]. The software corresponding to the present model is designed so that theuser can specify the number (and hence the width) of speed bins, as well as the numberof direction bins, up to the limits discussed above.

4. Testing procedures

Five pairs of stations were examined. One station in each pair was designated as thereference station and the other as the target station. In normal applications of the

J.R. Salmon, J.L. Walmsley/J. Wind Eng. Ind. Aerodyn. 79 (1999) 233–268 235

Walmsley—Bagg model, the reference station would be the one with long-term,high-quality hourly wind data. (In this study, however, either station of the pair couldhave been designated as the reference station, as all stations met the data require-ments.) Atmospheric stability can usually be determined at the reference station fromother meteorological parameters using the Day—Night S¹AR program. Air densitycan be calculated from temperature and barometric pressure.

For these tests, a relatively short period of time is selected during which simulta-neous hourly data are processed from both the target and reference stations. Innormal applications, wind data would be needed at the target station, temperatureand pressure may also be available, and parameters needed to calculate atmo-spheric stability would likely not be available. Thus an assumption would bemade that atmospheric stability at the target station is the same as at the referencestation. If temperature is not measured at the target station, it would be estimated byassuming a temperature lapse rate, which may be stability-dependent. If pressure isnot measured at the target station, it would be estimated from the reference stationconditions, using the hydrostatic approximation to adjust for any difference inelevation.

In normal applications, one would use the short-term data at the target andreference stations together with the long-term data available at the reference stationand apply the Walmsley—Bagg model to estimate the long-term wind climatology asa function of stability at the target station. (By incorporating a calculation of airdensity, an estimate of the long-term available wind power can also be determined.) Inthe present case, because of the availability of long-term data at both stations, theprocess was taken one step further: verification of the estimated wind climatology andwind power with long-term data at the target station.

In summary, in the present study, we applied the modified Walmsley—Bagg modelto pairs of stations for which the long-term data sets were available at both stationsand designated one station as the reference and the other as the target. The estimatedlong-term wind climatology at the target was then compared with the observedclimatology.

5. Stations and periods for testing

Five pairs of stations were chosen for testing. They are shown in Fig. 1 and listed inTable 1. (Hereafter the “A” in each station name, used to identify the airport site, willbe dropped for brevity, as will the “International” following “Vancouver”.) Thecriteria for choosing the station pairs were: proximity, geographical distribution,variety of terrain and surface cover, and data quality and stability. The focus wasrestricted to Canada because quality-controlled data were readily available, but thedecision to consider a variety of conditions implies that the results will have widerapplicability.

Fig. 1 and Table 1 show that the stations in each pair are reasonably close to eachother (within 100 km, with one exception), increasing the likelihood that both thereference and target stations were within the same air mass and therefore had similar


Fig. 1. Map of Canada showing the five pairs of weather stations. Inset maps are, respectively, from east towest, Regions A—E of Table 1.

Table 1List of stations with period, location, elevation and distance between each pair. The first station listed ineach region was used as the reference station; the second is the target station. All data periods ended on 31December 1989

Region Description Station Start ofPeriod

Lat.(°N)

Long.(°W)

Elev.(m MSL)

Dist.(km)

A Northumberland Moncton A 1968 46.12 64.68 71Strait Summerside A 1968 46.43 63.83 24 74

B St. Lawrence Mont Joli A 1969 48.60 68.20 52Estuary Baie Comeau A 1967 49.13 68.20 22 59

C Great Lakes Wiarton A 1972 44.75 81.10 222Gore Bay A 1972 45.88 82.57 193 170

D Prairies Moose Jaw A 1965 50.33 105.55 577Regina A 1969 50.43 104.67 577 64

E Lower Fraser Vancouver Int. A 1964 49.18 123.17 3Valley Abbotsford A 1972 49.03 122.37 58 61


atmospheric stability characteristics and that their wind regimes were probablycorrelated. It is evident that the five station pairs represent five well-defined geo-graphical regions (designated A—E) of Canada. (The middle and far north, however,lack representation.) The terrain types range from maritime and flat (Region A) tocontinental and rolling (Regions C and D) and from prairie grassland (Region D) tolakeside forest (Region C). The wind flow may be strongly influenced by the presenceof larger-scale topography: mountains along either side of the estuary in Region B andthe river delta bordered by mountains on the north and southeast sides in Region E.By considering this variety of conditions, it is expected that the results will haveapplicability elsewhere, both within Canada and in other countries.

Regarding data quality, an attempt was made to choose stations that had noobvious data flaws. Treatment of the data to eliminate potential problems is describedbelow.

6. Input data processing

Data sets for this study were available in the Canadian Weather Energy andEngineering Data Sets (CWEEDS) compiled by the Atmospheric Environment Ser-vice (AES) in 1993. This large compilation of Canadian weather data at 143 stations isavailable on CD-ROM in compressed WYEC2 (Weather Year for Energy Calcu-lation, Version 2) format. A companion diskette to the CD-ROM provides anemom-eter-height history data.

The data required for the present study were wind speed, wind direction and theparameters required to calculate atmospheric stability (see below). Temperature andstation barometric pressure were also extracted from the CWEEDS data sets asauxiliary data.

6.1. Wind speed and wind direction

Wind speed and direction data were extracted directly from the CWEEDS WYEC2files. Both required further processing, however, to minimize the discretization prob-lems associated with the use of integer values in recording, converting and storing thedata.

In past years, wind speed measurements were recorded as values (in eithermiles h~1, kt or, more recently, in km h~1) to the nearest integer. A conversion wasoften made, e.g., from miles h~1 to kt and the integer nearest to the converted valuewas stored. All processed data in the AES archive have since been converted to integervalues in units of km h~1. For the CWEEDS data sets, they were further converted tom s~1 and stored as integer values in dm s~1. These recording, conversion andstorage procedures could potentially have caused problems for data analysis, as gapsappeared in the continuum of wind speeds. In converting between integer values fromkt to km h~1, for example, the only possible resultant wind speeds are 0, 2, 4, 6, 7, 9,11, 13, 15, 17,2 km h~1. A problem arises, therefore, when the distribution of windspeeds is examined. If, for example, the data are placed in wind speed bins of width


1 km h~1, there would be no data at all in bins representing 1, 3, 5, 8, 10, 12, 14, 16,2km h~1, and the representation of the distribution of the wind speeds would beunrealistic.

To avoid the problem of empty wind-speed bins, we treated the data as follows.Each wind speed datum was converted back from its CWEEDS value in dm s~1 to itsAES archive value in km h~1 and thence to an integer value in the units (miles h~1 orkt) originally used for recording. Since the corresponding forward conversion proced-ures went from lower to higher resolution, thus creating empty bins, it was alwayspossible to recover the originally recorded integer from this reversal process. To thisoriginal value was added a random offset so that the modified values ranged over theappropriate integer-bin width. The modified number was then subjected to theoriginal conversion process but without rounding to the nearest integer values at anystage. The result of this procedure was a continuum of wind speeds in the archivedunits.

The wind direction data were subjected to a similar procedure. Each value wasconverted from its archive storage value (i.e., to the nearest 10° value) back to its valuein the original measurement system, either 8 or 16 sectors. This was done using aconversion table supplied by AES: Documentation for the Digital Archive of CanadianClimatological Data (Surface) Identified by Element. The resulting original data hadrandom offsets introduced to spread them evenly within their (8 or 16) sectors. Theseconverted data were then used for the analysis.

Temperature and barometric pressure data were copied from the CWEEDS datasets unchanged.

6.2. Atmospheric stability

As atmospheric stability data are not recorded explicitly in the CWEEDS data sets,they were calculated using a set of AES customized programs modified to run on PCs.First, the annual data files were extracted from the CD-ROM and uncompressed(using PKUNZIP) to the PC hard drive. The files for the period under study (whichvaries by station; see Table 1) were then concatenated into a large ASCII file in WYEC2format. This file was subsequently converted to a proprietary format readable by theAES customized program GRP115S as modified for use on a PC. GRP115S calculateshourly atmospheric stability from station location, date and time, cloud ceiling height,wind direction, wind speed and amount of cloud cover. All of these, except for thelocation data, are included in the CWEEDS data sets. GRP115S uses the S¹ARalgorithm to determine which one of six stability classes should be assigned to thedata hour in question. The six stability classes were introduced by Pasquill [14] andare known as the Pasquill—Gifford stability categories.

6.3. Further data processing

The two data sets, one with the atmospheric stabilities and the other with the windspeed, wind direction, temperature and barometric pressure were merged into onedata set of hourly values of these parameters.


Fig. 2. Autocorrelation results obtained by using short-term data for varying lengths of time at a singlestation to estimate the long-term climatology at the same location. (a) Worst-case estimates, X

TS/»

TLand

NTS

/»TL

. (b) Standard deviations of estimates, 1$pTS

/»TL

.

The data were then checked for continuity (no significant gaps) and completeness(24 h coverage). Also checked were the anemometer histories of the stations to ensurethat the anemometers had not been moved (horizontally or vertically) during the dataperiods of the study.

The above procedures resulted in acceptably clean data sets for the statisticalstudies to be described below.

7. Autocorrelation results

The first set of tests was carried out on each of the 10 station data sets in Table 1,i.e., there was no segregation into reference and target locations. The purpose was to


Fig. 2. Continued.

determine the sensitivity of the long-term average wind speed estimate based on thelength of the short-term observation period. These results were then used to judge theaccuracy of the correlation method.

The following parameters were defined: »TL

and »TS

are the average windspeeds over the long- and short-term data records, respectively, at the target station;pTS

, NTS

and XTS

are the standard deviation, minimum and maximum, respectively,of »

TSbased on a series of calculations over the short-term record. In these auto-

correlation tests, »TL

was based on at least 18 and up to 26 yr of data. For »TS

,the period ranged from 1 to 60 months. Since there are a number of contiguousshort-term periods within a long-term period (e.g., 216 one-month periods in an 18 yrrecord), »

TSwas calculated for each of these. (Note that all possible contiguous


short-term periods were used, resulting in an overlap in the case of short-term periodsof greater than one month in length. Thus, for example, there were 205 contiguous12-month periods in 18 yr.) The outcome of this test was a series of estimates of»

TLbased on values of »

TSdetermined from short-term data periods of varying

length.The results of the autocorrelation calculations are presented in Fig. 2. Fig. 2a

shows the ratios of XTS

/»TL

and NTS

/»TL

and Fig. 2b shows values of 1$pTS

/»TL

, allas functions of the number of months in the short-term period. All values arepresented as percentages.

Fig. 2a provides worst-case estimates of the long-term wind speed as a function ofthe length of the short-term monitoring period. As would be expected, the worst-caseestimates improve, i.e., approach 100%, as the short-term period increases. Theimprovement is dramatic up to 1 yr and then gradual thereafter. The worst worst-caseestimates at one month are 35% (Abbotsford) and 180% (Wiarton). These improve to76% (Baie Comeau) and 126% (Abbotsford) after 1 yr and to 84% and 120% (MontJoli) after 2 yr. The best worst-case estimates at one month are 65% and 133%(Moncton), which improve to 87% and 114% (Moncton) after 1 yr and to 91% (GoreBay) and 107% (Wiarton, Moncton) after 2 yr. In all cases there is a gradual, butsteady improvement in the worst-case estimates after the second year of short-termmonitoring.

Fig. 2b shows the behaviour of the standard deviation of the estimates. The plotsshow a behaviour similar to the worst-case curves of Fig. 2a. Values of p

TS/»

TLranged

between 13% (Regina) and 26% (Abbotsford) at one month, between 5% (Moncton)and 13% (Abbotsford) at 1 yr and between 3% (Wiarton) and 12% (Abbotsford) at2 yr. For comparison purposes, Table 2 shows percentage uncertainties in estimates oflong-term mean wind speeds from other studies. At the 95% confidence interval, theseare 11—13% after 1 yr of monitoring and 8—9% after 2 yr, i.e., in the upper half of theranges shown in Fig. 2.

The curves for Moncton are reproduced in Fig. 3 at higher resolution as anexample to show that the estimates are worse in the 13—22 month monitoring periodthan they are at 12 months. This is attributed to seasonal variations and the use ofa non-integral number of years to estimate the long-term annual average from theshort-term calculations.

The results of the autocorrelation tests suggest the following procedures forestimating the long-term wind regime at a given site. A minimum of 12 months ofmonitoring is recommended. Even with 12 months of monitoring, there is stillsignificant uncertainty in the estimates of the long-term average speed (p

TS/»

TLranging from 5—13%; worst errors ranging from 13—26%). If these uncertaintiesare considered unacceptable, 24 months of monitoring would reduce the stan-dard deviations slightly (p

TS/»

TLto the 4—12% range) and the worst errors more

significantly (to 7—20%). After 24 months, the improvement is more gradual. Adecision to monitor for a period between 12 and 24 months could produceworse estimates than for the 12-month period. The same is true for the 24—36,36—48 and 48—60 month periods, though this effect of seasonal variability diminisheswith increasing length of record. Nevertheless, it is important to monitor for an


Table 2Percentage uncertainties in estimates of long-term mean wind speed asa function of monitoring period (source: Ref. [4])

Confidence Source Period (months)interval (%)

1 12 24 60

80 WR83 24 7 5 390 C80 37 11 8 595 WR83 37 11 8 595 C80 44 13 9 6

WR83 from Ref. [16].C80 from Ref. [17]. See also Ref. [18].

Fig. 3. Autocorrelation results for Moncton. Worst-case and standard deviations of estimates, plotted athigher resolution than the curves labelled ‘‘T’’ in Fig. 2.


Fig. 4. Cross-correlation results obtained by using simultaneous short-term data for varying lengths oftime at both the reference and target stations and long-term data at the reference station to estimate thelong-term climatology at the target station using the modified Walmsley—Bagg model. Plotted are values of1$p

TS/»

TL. The station names at the top of each diagram indicate the reference and target locations,

respectively. (a) Northumberland Strait. (b) St. Lawrence Estuary. (c) Great Lakes. (d) Prairies. (e) LowerFraser Valley.


Fig. 4. Continued.

integral number of years to get the best estimate of thelong-term wind climatology.These results also suggest that at least 12 months, and preferably 24 months ofshort-term data are required for the two-site correlation application to be described inthe next section.

8. Two-site correlation results

8.1. Standard deviation of estimates

The wind-speed results from application of the modified Walmsley—Bagg model toeach of the two-site reference-target pairs are presented in Fig. 4. Only the standarddeviations of estimates are shown, as values of 1$ p

TS/»

TL, corresponding to the

autocorrelation results of Fig. 2b, which displays similar looking curves.Use of the modified Walmsley—Bagg correlation model (solid curves in Fig. 4)

reduced the standard deviations compared with what would be obtained bymonitoring alone (dashed curves), i.e., inferring wind climatology from short-termmonitoring without the use of a model. The improvement is significant for monitoringperiods of less than 1 yr in all regions except the Prairies (Fig. 4d), where it is justnoticeable.

Standard deviations after 12 months or more of monitoring without model ap-plication (dashed curves) are in the range 4—10% in Fig. 4a—4d and 10—13% inFig. 4e. For monitoring periods of 12 months or more, application of the model


caused reductions of 0—1 percentage points in Fig. 4a and 4d, 1 percentage point inFig. 4c and 2—3 percentage points in Fig. 4b and 4e. These translate to reductions instandard deviation of 0—20% in Fig. 4a, 20—35% in Fig. 4b and 10—20% in Fig. 4cand 4e. Even though the model-enhanced results in Fig. 4e are still consistently poorerthan those of Fig. 4a—4d, they are significantly improved over the monitoring-onlyscenario. The correlation model gave little improvement over 12 months or more ofmonitoring in Fig. 4d.

As noted, even after application of the correlation model, the results in Fig. 4e areconsistently poorer than those of the other four reference-target pairs. This suggeststhat wind data from the Abbotsford and Vancouver stations are the most poorlycorrelated of the five pairs of station data selected for this study.

Fig. 5 presents, as an example, both the worst-case and the standard devia-tions of estimates for the pair of stations in the Northumberland Strait area (seeFig. 4a). As with the standard deviations (Fig. 4), the worst-case estimates wereimproved most significantly by application of the model in the first 12 months ofmonitoring.

There was very little difference amongst the three methods of estimating long-termaverage wind speed: using the model to correlate (i) wind speed alone; (ii) wind speedand direction; and (iii) wind speed, wind direction and thermal stability. This is shownby solid curves in Fig. 4 for the first two of these methods. Not shown but equally trueare the results of correlating speed, direction and stability.

8.2. Correlation matrices

Tables 3—5 present sample long-term correlation matrices for stability, windspeed and wind direction, respectively, using Moose Jaw and Regina as the reference-target pair. For display purposes, the 32 wind-speed bins of width 0.5 m s~1 werereduced to five of width 4 m s~1 and the number of wind direction classes was reducedfrom 16 to 8. The results presented here, however, are very similar to those producedwith greater resolution. Summing the values in the cells along the central diagonalgives the percentage of time that the same class occurred at both stations. Thefootnote at the bottom of each table indicates that the same class was observed45—59% of the time. The frequency of classes that differed by no more than one wasobtained by summing values along the three central diagonals. (Recalling that thewind direction is a circular distribution, Class 8 is adjacent to Class 1, so the top-rightand bottom-left cells are included in the summation.) These frequencies ranged from80—98%.

Table 6 summarizes the two-site correlation matrices and presents additionalstatistics for the individual regions. Table 6a shows that the same stability class occursat the reference and target stations 50—70% of the time. The same or next adjacentclass occurs 80—95% of the time. The highest values are found in Region A; the lowestin Region D. The differences found in Region D, the least geographically complex ofthe five regions, were not expected.

Table 6b shows that the same wind speed class occurs at the reference and targetstations 52—68% of the time. The same or next adjacent class occurs 95—98% of the


Fig. 5. Cross-correlation results for Northumberland Strait (see Fig. 4a). The six inner curves show valuesof 1$p

TS/»

TL; the six outer curves show worst-case estimates, X

TS/»

TL(upper three curves) and N

TS/»

TL(lower three curves).

time. Significant differences in these frequencies between regions are not apparent.Also shown are mean wind speeds at both reference and target stations for theshort-term (2 yr) and long-term (full dataset) periods and the correlation coefficientbetween reference and target datasets for both short- and long-term periods. Themean wind speeds range between 2.6 and 5.5 m s~1, with the highest values tending tobe in Regions A and D (and at the reference station in Region B) and the lowest inRegion E. The correlation coefficients are highest (&70%) in Regions A and D andlowest (&35%) in Region E.

Table 6c shows that the same wind direction sector occurs at the reference andtarget stations 16—49% of the time. (With eight sectors and random distributions, the


Table 3Sample reference-target thermal stability correlation matrix for Region D. The period is 1969—90. SixPasquill—Gifford stability categories, ranging from unstable (1) to stable (6), are shown. The referencestation (columns) is Moose Jaw; the target station (rows) is Regina. N"182 990. Row, column anddiagonal totals are subject to round-off errors

Class 1 2 3 4 5 6 Total

1 0.000 0.001 0.001 0.002 0.000 0.000 0.0032 0.001 0.006 0.008 0.024 0.000 0.000 0.0393 0.001 0.010 0.016 0.056 0.002 0.002 0.0874 0.002 0.024 0.049 0.437 0.052 0.055 0.6215 0.000 0.000 0.002 0.087 0.020 0.021 0.1316 0.000 0.000 0.002 0.079 0.019 0.020 0.120Total 0.004 0.041 0.078 0.685 0.093 0.098 1.000

Sum on diagonal"0.499; sum on three central diagonals"0.805.

Table 4Sample reference-target wind speed correlation matrix for Region D. The period is 1969—90. Five windspeed classes with bin widths of 4 m s~1 are shown. The reference station (columns) is Moose Jaw; the targetstation (rows) is Regina. N"182 990. Row, column and diagonal totals are subject to round-off errors

Class 1 2 3 4 5 Total

1 0.266 0.108 0.009 0.000 0.000 0.3842 0.135 0.250 0.047 0.003 0.000 0.4353 0.009 0.070 0.068 0.008 0.000 0.1554 0.000 0.003 0.012 0.008 0.001 0.0245 0.000 0.000 0.000 0.001 0.001 0.003Total 0.410 0.431 0.136 0.020 0.003 1.000

Sum on diagonal"0.593; sum on three central diagonals"0.975.

Table 5Sample reference-target wind direction correlation matrix for Region D. The period is 1969—90. Eight winddirection classes with bin widths of 45° are shown. Class 1 is centered on N, Class 2 on NE, etc. Thereference station (columns) is Moose Jaw; the target station (rows) is Regina. N"182 990. Row, columnand diagonal totals are subject to round-off errors

Class 1 2 3 4 5 6 7 8 Total

1 0.032 0.010 0.003 0.002 0.002 0.003 0.010 0.027 0.0892 0.010 0.015 0.008 0.003 0.002 0.002 0.003 0.005 0.0483 0.004 0.011 0.039 0.024 0.007 0.006 0.005 0.005 0.1004 0.004 0.004 0.036 0.101 0.051 0.030 0.014 0.007 0.2475 0.001 0.001 0.003 0.012 0.028 0.025 0.009 0.003 0.0846 0.001 0.001 0.001 0.002 0.009 0.036 0.021 0.004 0.0767 0.003 0.001 0.002 0.002 0.004 0.026 0.095 0.029 0.1618 0.018 0.003 0.002 0.002 0.002 0.006 0.059 0.102 0.196Total 0.073 0.047 0.094 0.148 0.105 0.134 0.217 0.182 1.000

Sum on diagonal"0.448; sum on three central diagonals#two corner cells"0.823.


Table 6

a. Summary of thermal stability correlation in Regions A—E

Variable Source Region

A B C D E

&1

Table 3 0.707 0.649 0.635 0.499 0.603&3

Table 3 0.945 0.901 0.888 0.805 0.851

&1"Sum on central diagonal.

&3"Sum on three central diagonals.

b. Summary of wind speed (m s~1) correlation in Regions A—E

&1

Table 4 0.589 0.521 0.594 0.593 0.676&3

Table 4 0.977 0.954 0.976 0.975 0.976»

RSFig. 7a 4.5 5.1 4.1 5.3 3.8

»TS

Fig. 7a 5.2 4.1 4.9 5.5 2.8»

RLFig. 7b, Fig. 9 4.7 5.2 3.9 5.0 3.2

»TL

Fig. 7b, Fig. 9 5.5 4.4 4.6 5.3 2.6rS

— 0.73 0.55 0.56 0.69 0.33rL

— 0.72 0.55 0.56 0.68 0.37


&3"Sum on three central diagonals.

»"Mean wind speed.R"Reference; T"target.S"Short-term (2 yr); L"long-term.r"Correlation coefficient, R and ¹ observations.

c. Summary of wind direction (°) correlation in Regions A—E

&1

Table 5 0.492 0.320 0.357 0.448 0.161&3

Table 5 0.879 0.708 0.737 0.823 0.4980RS$d

RS248$92 224$96 239$112 271$105 127$99

0TS$d

TS241$102 286$99 269$120 264$137 189$143

0RL$d

RL241$88 235$92 239$103 253$98 123$99

0TL$d

TL240$95 289$97 265$110 231$129 218$122

0TS~RS

$d !3$36 12$64 !3$52 !4$42 !24$870TL~RL

$d 4$35 9$62 1$52 !2$43 !15$89


&3"Sum on three central diagonals#corner cells.

0"Circular mean wind direction.d"Circular standard deviation of wind direction.R"Reference; T"target; S"short term (2 yr); L"long term.TS—RS, TL—RL"statistics based on wind direction differences.


Fig. 6. Sample wind speed and direction distributions for the Northumberland Strait region. Modelestimates use wind speed and direction correlation. (a) 1 yr period of simultaneous hourly data at thereference (Moncton) and target (Summerside) stations. Differences between target and reference distribu-tions appear in the bottom pair of plots. (b) 22 yr period of data at the reference site and a comparison ofestimates and data for the same long-term period at the target site. Differences between estimates and datadistributions at the target site appear in the bottom pair of plots.

sum along the central diagonal would be 12.5%.) The same or next adjacentsector occurs 50—88% of the time (compared with 37.5% for random distributions).The highest values are found in Region A; the lowest in Region E. Values of thecircular mean wind direction and their respective circular standard deviations [15]


Fig. 6. Continued.


(see Appendix B) are also presented in Table 6c for the reference and targetstations over both short- and long-term periods. Circular means and standarddeviations were computed for the difference in wind directions (target — reference) forboth periods and appear in Table 6c. The nonlinear nature of these data is evident, asthe differences in mean wind direction are not the same as the means of the differences.Mean direction differences are )12° in Regions A—D but are significantly larger(&20°) in Region E.

9. Estimated wind speed and direction distributions

9.1. Sample distributions. Region A: 1 yr short-term period

Fig. 6 presents another method of displaying the results, using Region A as anexample. The top pair of plots in Fig. 6a shows the wind direction and wind speeddistributions at the reference station (Moncton), based on hourly data for a 1 yrperiod (1968). The middle pair of plots displays the target station (Summerside) datafor the same period. The bottom pair gives the differences between the target and thereference station data. Wind direction and speed bins are 22.5° and 0.5 m s~1 wide,respectively. The low frequency in the second speed bin (0.5—1.0 m s~1) compared withthe first and third bins is possibly related to the anemometer start-up speed, ratherthan to a physical phenomenon. This “gap” would be significantly reduced if bins ofwidth 1.0 m s~1 were used. There is also a spike in the 6.5—7.0 m s~1 bin in theMoncton data. This persists out to 8 yr of observations (1968—75) and is probablyrelated to observer bias, 7 m s~1 being close to both 15 miles h~1 and 25 km h~1.This bias probably does not have much impact on the present calculations, as nothingsignificant shows up in the “target estimate minus actual” plots in Fig. 6b.

The top pair of plots in Fig. 6b displays the long-term (22 yr) data at the referencestation (Moncton). The wind rose is somewhat different from the correspondingshort-term period (Fig. 6a), the maximum frequency at W having been shifted toWSW. In the wind speed distribution, the main difference from the short-term isa broadening and lowering of the peak frequencies and elimination of the spike near7 m s~1. The third pair of plots in Fig. 6b shows the observed long-term data at thetarget station (Summerside). Here, the wind speed distribution is very similar to theshort-term, except for a drop in frequency of the lowest speed bin from 10—4%. Theshort-term and long-term wind roses at Summerside look rather similar, except fora decrease in frequency of westerly winds from 14—9%.

The wind rose at Moncton is significantly different from that at Summerside, bothfor the short- and the long-term periods (Fig. 6a and 6b, respectively). Monitoring thewind direction at one station would not give a good estimate of the wind rose at theother station without use of the wind correlation model.

Examining the plots in the second row from the top of Fig. 6b, it can be seen thatthe model-produced “target station estimate” of both wind speed and directiondistributions more closely resemble the corresponding “target station actual” thanthey do the reference station, i.e., the wind climatology at Summerside cannot be


inferred from wind monitoring at Moncton. In fact, monitoring at Moncton for 22 yrwithout the application of the model gives a poorer estimate of the long-term windclimatology at Summerside than does 1 yr of simultaneous data with the windcorrelation model.

The differences between estimated and observed distributions at Summerside aredisplayed in the bottom pair of plots in Fig. 6b. Differences in wind directionfrequencies do not exceed 2.5 percentage points for any of the 16 sectors. Differencesin wind speed frequencies are less than 1.4 percentage points in magnitude, except forthe lowest wind speed bin where the difference is 5 percentage points.

Fig. 6a and 6b also give observed and estimated values of the average windspeed and the kinetic power density, defined in the same way as wind powerdensity but with air density held fixed at 1 kg m~3. At Moncton, the short-termvalues of these parameters agree quite closely with the long-term values (4.7 m s~1

and 103 W m~2, respectively). At Summerside, however, both the short-term dataand the long-term model estimate underpredict the observed long-term averagespeed (5.5 m s~1) and kinetic energy density (173 W m~2) by 5—7% and 8—13%,respectively.


Fig. 7 portrays the same information as Fig. 6, except that the short-term period istwo years instead of one. The main differences found in the 2 yr data (Fig. 7a)compared with the 1 yr data (Fig. 6a) are a reduction in the frequency of westerlywinds at both stations and a reduction in frequency of the lowest wind speed bin atSummerside. The “target station estimate” wind rose in Fig. 7b is very similar to thecorresponding one in Fig. 6b. The most obvious improvement in the wind speeddistribution is the reduction of frequency in the lowest bin, cutting the deviation fromthe observed frequency from 5.2 to 2.6 percentage points. The underprediction of windspeed is reduced from 5% to 2% and the underprediction of kinetic energy density isreduced from 13% to 6%.


Fig. 8 is the same as Figs. 6 and 7, except that the short-term period is now 4 yr.The wind rose in Fig. 8a remains much the same as it was in Fig. 7a, while thewind speed distribution shows a further small reduction in frequency of thelowest wind speed bin at Summerside. The “target station estimate” wind rose inFig. 8b is somewhat better than the corresponding ones in Fig. 6b and Fig. 7b,especially in the frequency of southerly winds. There is a further improvementin the lowest wind-speed bin, the deviation from the observed frequency being reducedto 1.6 percentage points. The underprediction of wind speed remains at the same levelas in Fig. 7b (2%), whereas the underprediction of kinetic energy density is furtherreduced to 5%. Increasing the short-term period of simultaneous observations be-yond 4 yr did not yield significant improvement over the 22 yr estimates shown inFig. 8b.


Fig. 7. Same as Fig. 6 except that the short-term period is 2 yr. (a) Short-term data and differences betweentarget and reference distributions. (b) Long-term data, estimates and differences.

9.4. Distributions for Regions B—E: 2 yr short-term period

Fig. 9 shows long-term wind speed and direction distributions for the remainingfour regions. The short-term period is 2 yr, so these figures should be compared withFig. 7b. Examining Fig. 7b and Fig. 9 reveals several interesting facts. First, theobserved wind roses at the reference and target stations are very different from oneanother. Even in the Prairies (Fig. 9c), where the closest resemblance is found, the


Fig. 7. Continued.


Fig. 8. Same as Fig. 7 except that the short-term period is 4 yr. (a) Short-term data and differences betweentarget and reference distributions. (b) Long-term data, estimates and differences.

frequency of SE winds at Regina is double what it is at Moose Jaw. It is clear thatmonitoring wind direction at the reference site, even for a long period of time, wouldnot give a good estimate of the wind rose at the target site and vice versa. Second,except in the Prairies, the observed wind speed distributions at the reference andtarget sites are significantly different. This is also reflected in the values of averagewind speed and kinetic power density. Again, long-term monitoring of wind speed atthe reference site would give a poor estimate of the wind speed distribution, average


Fig. 8. Continued.


Fig. 9. Wind speed and direction distributions for all regions except Northumberland Strait. Short-termperiod is 2 yr. Long-term data, estimates and differences are displayed. Model estimates use wind speed anddirection correlation. (a) St. Lawrence Estuary. (b) Great Lakes. (c) Prairies. (d) Lower Fraser Valley.


Fig. 9. Continued.


Fig. 9. Continued.


Fig. 9. Continued.


wind speed and kinetic power density at the target site and vice versa. Third, use ofthe wind correlation model gives a much better estimate of the long-term windclimatology at the target station, even with only 2 yr of short-term data, comparedwith monitoring at the reference station alone. Differences between estimated andobserved frequencies at the target site were within 3.9 percentage points for alldirection sectors and speed bins; in the great majority of cases, they were within 1.8percentage points.

9.5. Summary

Table 7 summarizes the results of estimating long-term average wind speed andkinetic power density at the five target stations based on model calculations thatused 1, 2 and 4 yr of short-term data. Table 7a gives the values, while Table 7bpresents the percentage differences from the long-term observed values. Several factsemerge from an examination of Table 7. First, errors are reduced by the applica-tion of the model to two years of short-term data. Second, the model applied to 1 yr ofshort-term data tends to perform at least as well as estimates based on 2 yr of datawithout modelling (with the exception of kinetic power density estimates at Summer-side and Gore Bay). Third, the model estimates using 4 yr of short-term data are notsignificantly better than those made with 2 yr of monitoring, and are sometimesmarginally worse.

Finally, by considering the five regions together, the RMS errors confirm that, ingeneral, the model results derived from 1 yr of short-term monitoring outperform theestimates based on 2 yr of monitoring alone and that the model results are furtherimproved by using 2 yr of monitoring. At this point the RMS errors are down to lessthan 4% for average wind speed estimates and less than 10% for kinetic energydensity. Additional years of monitoring do not yield further improvement in themodel estimates.

Table 8a summarizes the results of estimating long-term average wind direction atthe five target stations based on model calculations that used 1, 2 and 4 yr ofshort-term data. Comparing the last three columns in Table 8a with the long-term observations, it was found that, except for Region E, the largest error was 15°and the next largest was 9° (see Table 8b). There was no consistent pattern ofimprovement with increasing length of the monitoring period; however, theerrors in the mean directions were small enough for this not to be a concern.Using 2 yr of observations without model application yielded estimates of thelong-term mean direction that were only in error by 1—4° in Regions A to C, where-as a 33° error was obtained in Region D. Application of the model with only 1 yrof monitoring did significantly better (3° error) than 2 yr of monitoring alone inRegion D.

The 2 yr wind rose at Abbotsford (Region E) is highly bi-modal (see Fig. 9d), i.e.,there is almost an equal probability that the average direction could be NNE—NEor SSW—SW. The fact that these two opposite directions almost balance in fre-quency, accounts for the large errors of 140° and 147° for the model estimates based


Table 7

a. Long-term estimates of average wind speed SM (m s~1) and kinetic energy density oN (W m~2) at targetstation compared with long- and short-term observed values. Model estimates are made for threeshort-term monitoring periods

Region Observations Model estimates with monitoring period

Long term 2 yr 1 yr 2 yr 4 yr

Years SM oN SM oN SM oN SM oN SM oN

A 22 5.5 173 5.2 156 5.2 151 5.4 162 5.4 164B 21 4.4 101 4.1 82 4.5 113 4.2 93 4.2 92C 18 4.6 104 4.9 114 4.3 83 4.7 102 4.8 108D 21 5.3 153 5.5 169 5.1 140 5.1 142 5.5 162E 18 2.6 32 2.8 42 2.6 38 2.7 37 2.8 38

b. Percentage errors in long-term estimates of average wind speed *SM and kinetic energy density *oN attarget station. Observed long-term values SM (m s~1) and oN (W m~2), respectively, are copied from Table 7a.Monitoring estimate is made from 2 yr of observations. Model estimates are made for three short-termmonitoring periods. Also shown is the RMS error

Region Years SM oN *SM *oN *SM *oN *SM *oN *SM *oN

A 22 5.5 173 !5.5 !9.8 !5.5 !12.7 !1.8 !6.4 !1.8 !5.2B 21 4.4 101 !6.8 !18.8 2.3 11.9 !4.5 !7.9 !4.5 !8.9C 18 4.6 104 6.5 9.6 !6.5 !20.2 2.2 !1.9 4.3 3.8D 21 5.3 153 3.8 10.5 !3.8 !8.5 !3.8 !7.2 3.8 5.9E 18 2.6 32 7.7 31.3 0.0 18.8 3.8 15.6 7.7 18.8

RMSE 6.2 18.0 4.3 15.1 3.4 9.0 4.8 10.1

on 1- and 2 yr monitoring, respectively. For this region, therefore, it appears thatmodel estimates based on more than 2 yr of monitoring is needed to reduce thedirection error to an acceptable level. (With 4 yr of monitoring, for example, the erroris only 12°.)

The difficulty with predicting the wind direction in Region E is reflected in the A—Eaverage error and RMSE rows in Table 8b. Those values are large (approximately 30°and 60°, respectively) for model estimates based on 1 or 2 yr of monitoring. ForRegions A—D, on the other hand, model estimates based on only 1 yr of monitoringtend to be more accurate than estimates based on 2 yr of monitoring without use ofthe model.

The above calculations were all repeated with the incorporation of the thermalstability class together with wind speed and direction; however, this method producedresults that were only marginally different from the above results using speed anddirection alone.


Table 8

a. Long-term estimates of circular average wind direction 0M (°) at target stationcompared with long- and short-term observed values. Model estimates are made forthree short-term monitoring periods. Errors are with respect to the long-term ob-served values

Region Observations Model estimates withmonitoring period

Long term 2 yr 1 yr 2 yr 4 yr

Years 0M 0M 0M 0M 0M

A 22 240 241 232 234 234B 21 289 286 292 287 286C 18 265 269 268 250 264D 21 231 264 234 231 222E 18 218 189 358 071 230

b. Errors in long-term estimates of circular average wind direction *0M (°) at targetstation

Region Years 0M *0M *0M *0M *0M

A 22 240 #1 !8 !6 !6B 21 289 !3 #3 !2 !3C 18 265 #4 #3 !15 !1D 21 231 #33 #3 0 !9E 18 218 !29 #140 !147 #12

A—E AVE — 14 31 34 6A—D AVE — 10 4 6 5A—E RMSE — 20 63 66 7A—D RMSE — 17 5 8 6

AVE"Average error.RMSE"Root mean square error.

10. Summary and conclusions

The two-site correlation model of Ref. [1] has been modified to allow greaterflexibility in the choice of wind speed bins and wind direction sectors.The revised model was then tested on long-term data from five pairs ofCanadian weather stations. The stations were chosen to cover a variety of terrainsituations.

A preliminary analysis was performed on data from each of the 10 stations todetermine the length of a short-term period of data required to estimate the long-term


wind climatology at the same location. It was concluded that an absolute minimum of12 months of monitoring is needed; even so, there is still significant uncertainty in theestimates of the long-term average speed. Increasing the short-term monitoring periodto 24 months reduces the standard deviations slightly and the worst errors moresignificantly. After 24 months, the improvement is more gradual. A short-termmonitoring period between 12 and 24 months might produce worse estimates than forthe 12-month period.

For the two-site tests, one station from each of the five pairs was designated asa reference station; the other was designated as a target station. Three methods oftesting were used to estimate the long-term wind speed distribution. It was found,however, that there was very little difference whether the correlations were based on(i) wind speed alone; (ii) wind speed and direction; or (iii) wind speed, wind directionand thermal stability. Similarly, method (iii) showed little difference from method (ii)for estimating the long-term wind direction distributions. Including the wind directionin the correlation, however, was essential in estimating the long-term wind directiondistributions.

In general, it was found that, first, the model results derived from 1 yr of short-term monitoring outperform the estimates based on 2 yr of monitoring alone.Secondly, the model results are further improved by using 2 yr of monitoring, butadditional years of monitoring do not yield further improvement in the modelestimates. The only exception to this finding was for wind direction estimates inRegion E where the target-station wind rose was highly bimodal. In that case modelestimates using more than 2 yr of monitoring were required to reduce the directionerror to acceptable levels.

Therefore, to respond to the questions raised in the Introduction: (i) a short-termdataset at a candidate wind-turbine site must be at least 1 yr and preferably 2 yr inlength to be representative of the long-term climatology; and (ii) model results basedon 1 yr of monitoring data usually produce better long-term estimates of the windresource at a candidate wind-turbine site than does 1 yr of monitoring alone. Theexception to (ii) may be for wind direction estimates when the wind rose is highlybi-modal.

For wind-energy applications, the wind speed distribution estimates produced bythe model are the most crucial results. Wind direction distribution estimates areusually less important, but may be relevant for wind-turbine siting (e.g., avoidingundesirable upwind roughness or turbulence generators). The wind direction esti-mates are also important for air pollution studies.

Acknowledgements

James Salmon was supported by a contract from Atmospheric Environment Ser-vice. John Walmsley was partially supported by the Government of Canada’s Panelon Energy Research and Development. We thank Dr. Wanmin Gong for her reviewand comments on the manuscript.


Appendix A

Let A and B be two sites having simultaneous short-term wind data, where A isa reference site (e.g., a weather station) with a long-term period of wind data and B isa site at which climatological wind estimates are required. Defining d

ijas the relative

frequency of simultaneous occurrence of wind categories i at A and j at B, then let

Fi,

J+j/1

dij

(A.1a)

Gj,

I+i/1

dij

(A.1b)

be the relative frequencies of occurrence of category i at A and category j at B,respectively. The wind categories may be, for example, those of a joint distribution ofwind speed classes and wind direction bins. (For 6 classes and 16 bins, I"J"96.)

Calculate a coefficient matrix cij

from:

cij"

dij

Fi

(A.2)

with no summation on i. It can then be shown that

Gj"c

ijFi, (A.3)

where the summation convention is in effect. The coefficient matrix cij

derived fromshort-term simultaneous data is then used to estimate g

j, the long-term climatology at

B from:

gj"c

ijfi, (A.4)

where the summation convention is in effect. Here firepresents the long-term data at

A. Verification of the accuracy of the method can be obtained by applying Eq. (A.4) toan independent period for which the g

jdata are available.

Walmsley and Bagg [1] presented details of the proper way to distribute cases ofcalm winds amongst the wind direction bins when calculating the matrix d

ijfrom the

raw data.

Appendix B

Formulae for means and standard deviations of directional data were given byMardia [15] and are summarized here. If 0

1, 0

2,2, 0

nare a set of directions and P

iis

a point on the circumference of the unit circle corresponding to 0i, then the centre of

gravity of the n points is (CM , SM ), where

CM "1

n

n+i/1

ficos 0

i, SM "

1

n

n+i/1

fisin 0

i. (B.1)


Here fiis the frequency associated with direction 0

iin the case of grouped data; f

i"1

for individual data points. The mean direction is

0M "tan~1 (SM /CM ), (B.2)

which is conveniently calculated by Fortran code as 0M "A¹AN2(SM ,CM ) in the range(!p, p) radians.

The mean resultant length of the vectors from the origin of the unit circle to thepoints P

iis

RM "(CM 2#SM 2)1@2 (B.3)

and the circular variance is

S0"1!RM , (B.4)

values of which lie in the range (0, 1). Finally, the circular standard deviation is

d"[!2 ln(1!S0)]1@2, (B.5)

values of which lie in the range (0, R) radians.

References

[1] J.L. Walmsley, D.L. Bagg, A method of correlating wind data between two stations with applicationto the Alberta Oil Sands, Atmos.-Ocean. 16 (1978) 333—347.

[2] J.L. Walmsley, D.L. Bagg, Calculations of annual averaged sulphur dioxide concentrations at groundlevel in the AOSERP study area, Alberta Oil Sands Environmental Research Program, Edmonton,1977.

[3] A.D. Busse, J.R. Zimmerman, User’s Guide for the Climatological Dispersion Model, Rep., EPA-R4-73-024, US Environmental Protection Agency, Research Triangle Park, NC, 1973, pp. 131.

[4] J.L. Walmsley, Assessing the Wind Resource, in: Wind-Diesel Systems, Cambridge University Press,Cambridge, 1994, pp. 54—94.

[5] S. Kunz, M. Baumgartner, Evaluation von Extrapolationsmodellen der Windgeschwindigkeit,OFEN, Bern, Switzerland, 1986.

[6] AWEA, Standard Procedures for Meteorological Measurements at a Potential Wind Turbine Site,Publ. AWEA 8.1-1986. Amer. Wind Energy Assoc., Alexandria, VA, 1986, pp. 18.

[7] W.S. Kau, H.N. Lee, S.K. Kao, Statistical model for wind prediction at a mountain and valley stationnear Anderson Creek, California, J. Appl. Meteorol. 21 (1982) 18—21.

[8] S.R. Hanna, J.C. Chang, Representativeness of wind measurements on a mesoscale grid with stationseparations of 312 m to 10 km, Boundary-Layer Meteorol. 60 (1992) 309—324.

[9] I. Palomino, F. Martı́n, A simple method for spatial interpolation of the wind in complex terrain,J. Appl. Meteorol. 34 (1995) 1678—1693.

[10] W.R. Goodwin, G.J. McRae, J.H. Seinfeld, A comparison of interpolation methods for sparse data:application to wind and concentration fields, J. Appl. Meteorol. 18 (1979) 761—771.

[11] J.R. Salmon, J.L. Walmsley, Testing a correlation model for wind speed and direction estimates,Proc. 2nd European and African Conf. on Wind Engineering, 22—26 June 1997, Genoa, Italy,pp. 189—196.

[12] J.L. Walmsley, D. Woolridge, J.R. Salmon, MS-Micro/3 User’s Guide, Rep. ARD-90-008, Atmo-spheric Environment Service, Downsview, Ontario, Canada, 1990, 88 pp.


[13] I. Troen, N.G. Mortensen, E.L. Petersen, WASP Wind Atlas Analysis and Application ProgrammeUser’s Guide, Ris+ National Laboratory, Roskilde, Denmark, 1988.

[14] F. Pasquill, The estimation of the dispersion of windborne material, Meteorol. Mag. 90 (1961) 33—49.[15] K.V. Mardia, Statistics of Directional Data, Academic Press, London, 1972.[16] J. Wieringa, P.J. Rijkoort, Windklimaat van Nederland, Staatsuitgeverij, Den Haag, 1983.[17] N.J. Cherry, Wind energy resource survey methodology, J. Indust. Aerodyn. 5 (1980) 247—280.[18] J. Wieringa, Roughness-dependent geographical interpolation of surface wind speed averages, Quart.

J. Roy. Meteorol. Soc. 112 (1986) 867—889.


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