\^/ ^~* 'w' BouiderSoradt _U.S. DEPARTMENT OF COMMERCE NGW/ERL\Afeve Propagation Laboratory ju^. AN EVALUATION OF WIND MEASUREMENTS r ' BY FOUR DOPPLER SODARS ■ I II r J II AN EVALUATION OF WIND MEASUREMENTS BY FOUR DOPPLER SODARS J. C. Kaimal J.E. Gaynor P. L. Finkelstein M.E.Graves T. J. Lock hart Report Number Five July 1984 NOAA Boulder Atmospheric Observatory U.S. Department of Commerce National Oceanic and Atmospheric Administration Environmental Research Laboratories A NOAA publication available from NOAA/ERL, Boulder, CO 80303. i c, Danository Copy Digitized by the Internet Archive in 2012 with funding from LYRASIS Members and Sloan Foundation http://archive.org/details/evaluationofwindOOkaim AN EVALUATION OF WIND MEASUREMENTS BY FOUR DOPPLER SODARS by J. C. Kaimal and J. E. Gaynor NOAA/ERL/Wave Propagation Laboratory Boulder, Colorado 80303 P. L. Finkelstein* Environmental Protection Agency Research Triangle Park, North Carolina 27711 M. E. Graves Northrop Services, Inc. Research Triangle Park, North Carolina 27709 T. J. Lockhart** Meteorology Research, Inc. Altadena, California 91001 This study was conducted for U.S. Environmental Protection Agency under Interagency Agreement No. DW1-3F2A059 Wave Propagation Laboratory Environmental Research Laboratory U.S. Department of Commerce Boulder, Colorado 80303 * On assignment from National Oceanic and Atmospheric Administration ** Present Affiliation: Meteorological Standards Institute Fox Island, Washington 98333 NOTICE Acquisition of the information provided in this document was funded in part by the United States Environmental Protection Agency under Interagency Agreement No. DW1- 3F2A059. This study was conducted jointly by NOAA/ Environmental Research Laboratory and the Environmental Protection Agency. Mention of a commercial company or product does not consti- tute an endorsement by NOAA/Envi ronmental Research Labora- tories or the Environmental Protection Agency. IV CONTENTS Abstract vi i Fi gu res vi i i Tabl es xi i Acknowl edgment s xi i i 1. Introduction 1 2. Description of Instrumentation 3 3. Description of Field Program 9 4. Measurement of the Standard Deviation of w 17 5. Measurement of Wind Speed 47 6. Measurement of Wind Direction 65 7. Sodar Rawinsonde Comparisons 81 8. Characteristics of Sodar w Spectra 87 9. Concluding Remarks 97 References 99 Appendix 101 ABSTRACT Measurements of wind speed, wind direction, and the vertical component of turbulence, from four different commercially available Doppler sodars, are compared with similar measurements from in situ sensors on a 300 m instru- mented tower. Results indicate that the four sodars measure wind speed and direction accurately and with reasonably high precision. The sodars tended to overestimate the vertical component of turbulence at night and to underesti- mate it during the day. Precision in those measurements was considerably poorer than for the averaged speeds and directions. Analysis of the vertical wind from the sodars indicates that the measurement inaccuracies arise from a combination of aliasing and spatial averaging. vn FIGURES Number Page 1 Plot plan showing sodar antenna deployment in the BAO test area.... 10 2 Contour map of the immediate BAO terrain showing location of the tower and the sodar test area 11 3 (a) View of the sodar test area looking north from County Road 8... 12 (b) Instrumentation on the BAO 300 m tower 13 4 Comparison of 100 m a values from the AV sodar and the BAO sensor 26 5 Comparison of 100 m a values from the RAD sodar and the BAO sensor 27 6 Comparison of 100 m a values from the REM sodar and the BAO sensor 28 7 Comparison of 100 m a values from the X0N sodar and the BAO sensor 29 8 Comparison of 200 m a values from the AV sodar and the BAO sensor 30 9 Comparison of 200 m a values from the RAD sodar and the BAO sensor 31 10 Comparison of 200 m a values from the REM sodar and the BAO sensor 32 11 Comparison of 200 m values from the XON sodar and the BAO sensor 33 12 Comparison of 300 m a values from the AV sodar and the BAO W OA sensor 34 13 Comparison of 300 m values from the RAD sodar and the BAO sensor 35 14 Comparison of 300 m o w values from the REM sodar and the BAO sensor 36 15 Comparison of 300 m a values from the XON sodar and the BAO sensor 37 vm 16 Comparison of 100 a values from RAD (mode: BI) sodar and the BAO sensor V 38 17 Comparison of 200 m a values from RAD (mode: BI) sodar and the BAO sensor * 39 18 Comparison of 300 m a values from RAD (mode: BI) sodar and the BAO sensor 40 19 Comparison of 100 m a values from RAD (mode: MONO) sodar and the BAO sensor . 41 20 Comparison of 200 m a values from RAD (mode: MONO) sodar and the BAO sensor * 42 21 Comparison of 300 m o values from RAD (mode: MONO) sodar and the BAO sensor 43 22 Comparison of 100 m » 51 Wind speed and wind direction profiles from sodar (AV) rawinsonde, and tower measurements in a convective boundary 1 ayer 85 52 (a) Schematic representation of distortions introduced in the w spectrum from attenuation due to spatial averaging and from aliasing, (b) Shift in spectral behavior with height and its implications for sampling and aliasing errors 89 53 Sodar and sonic anemometer w spectra at (a) 150 m and (b) 200 m compared for morning conditions 91 54 Sodar and sonic anemometer w spectra at 300 m compared for (a) morning and (b) nighttime conditions 92 55 Time series of w corresponding to spectral in the frequency range 0 ^i - i-naD- I T T/R AeroVironment Visitors Area (650 m SSW of BAO tower) ° i CM| oio Figure 1. Plot plan showing sodar antenna deployment in the BAO test area. 10 I05°00' 40°03" — 0.5 1.0 Figure 2. Contour map of the immediate BAO terrain showing location of the tower and the sodar test area. 11 n*» WW ""'■■pj 1 ' Figure 3. (a) View of the sodar test area looking north from County Road 8. (b) Instrumentation on the BAO 300 m tower, 12 13 200, and 300 m. Every morning at 0800 MST the data collected over the pre- vious 24 h period were submitted to EPA personnel directing the experiment in exchange for tower data covering the same period. Concurrent operation of some of the sodars was considered at one time, but quickly ruled out because of cross-contamination, even between systems operating at different frequencies. The sodars were therefore operated in sequence, the switch-over from one system to the other being controlled by a central timer switch. The assigned observing period was one 20 min period each cycle. The experiment took place between 1 and 21 September. On three different occasions, the observing period was extended to 120 min (9 Septem- ber) and to 80 minutes (16/17 and 18/19 September) in order to obtain long enough records for spectrum analysis. The BA0 data were recorded in the raw data mode on these occasions. The three occasions were: 0800-1600, 9 September; 1520-0800, 16/17 September and 1600-0140, 18/19 September. The two 4 h periods, when rawinsonde measurements were made hourly, occurred on 8 September (0400-0800) and 18 September (1200-1600). AV, REM, and RAD computed o , the standard deviation of w (the vertical wind component), from their time series. Missing data points were not filled in by interpolation, but the number of points missed (or accepted) was displayed. REM used four-point block averages instead of the original time series. X0N computed its standard deviation from the width of its 2 min w spectra, estimated for each level. Successive 2 min standard deviations were averaged to obtain the 20 min values. Each spectrum was automatically exa- mined for level and shape of background noise, and steps were taken to remove their effects. 14 AV, REM, and RAD reported standard deviations of the wind direction, a D . REM and RAD calculated theirs from the wind direction time series; AV used the relationship a D = a v /U , where U is mean horizontal wind vector. XON reported the standard devia- tions of the longitudinal and lateral wind components. These were obtained through coordinate transformation of horizontal wind components measured by the sodar. No attempt is made in this report to present the results of our a n com- parisons. The azimuth direction standard deviations show very large scatter. The data are withheld pending a better understanding of the reasons for the scatter. Meanwhile, we can only suggest caution in using o n for diffusion predictions. During the experiment, the sodars encountered a wide range of weather conditions: from clear skies to heavy rain, and winds ranging from very light to well over 10 m/s. A summary of daily weather conditions for the duration of the experiment is given in the Appendix. As the manufacturers were asked to submit only data they believed were correct, all submitted data were used in our comparison study. AV, REM, and XON maintained a consistent operating pattern throughout the experiment. However, RAD changed its operating mode every 24 h, switching from multimode to bistatic and monostatic, back to multimode and so on. For the extended observing periods, RAD operated in the monostatic mode on 9 September, in the bistatic mode on 16/17 September, and multimode on 18/19 September. 15 4. MEASUREMENT OF THE STANDARD DEVIATION OF w At the three heights under consideration (100 m, 200 m, 300 m), only AV attained a complete data record. The other three manufacturers had these ranges of completeness at the three heights: RAD, 70% to 95%; REM, 55% to 72%; XON, 77% to 94%. However, wind shadow effects depleted the sonic records so that the final outcome regarding completeness shows composite sonic/sodar percentages of 47% at 100 m, 41% at 200 m, and 47% at 300 m for the sodar ver- sus sonic comparison. 4.1 Sodar Reference Differences Since the sonic measurements of vertical wind speed standard deviation provide reference values, the accuracy and precision of each sodar system can be determined from the collections of 20 mi n average differences. The two input variables for these computations are a for the sodar instruments and /ww for the sonic vertical wind speed. The comparative statistics used to estimate accuracy and precision then become the average difference, or sample bias (b), and the standard deviation of the differences (s). In addition, the root mean square difference, or comparability (c), is computed; this statistic was defined by Hoehne (1971, 1977), and it characterizes the repeatability of a system. Finally, the precision is also represented as a percentage (s 1 ) of the average value of sonic a i.e., a coefficient of variation. 17 Expressions for b, c, s, and s' are given in Eqs. (1) to (4). b = £ I [(o W ) 1 - Mw n .] (1) c = {J-J i [(^ - v^.] 2 } 172 (2) s = (c 2 - b 2 ) 1/2 (3) S' = s/a w x 100. (4) Values of b, c, s, and s' are presented in Table 1 for the combined sodar observations at each of three heights, as well as for the individual vendor data subsets. The sample bias (b) in Table 1 shows a large range of values around nearly constant composite values of 0.08 to 0.09 m/s. At 100 m the spread is greatest, REM having the only negative bias value (i.e., sodar < sonic) and X0N having a sizable 0.23 m/s bias. AV is well below the composite bias amount; RAD is above it. At 200 m the REM value is slightly negative, AV remains small, X0N approximates the composite value, but RAD is in excess of 0.2 m/s. At 300 m the RAD bias continues to be relatively large, but the other vendors are grouped between 0.04 and 0.07 m/s. From Table 1 it is clear that there is much scatter in c and s' about the true value in all systems. There is no statistical difference between s and s' values for AV and REM at any of the levels. The division of Table 1 into daytime and nighttime categories is displayed in Table 2. The bias columns show that all sodar systems tend to overestimate a at night. 18 Table 1. Sodar a compared with sonic a, w w Height Vendor b (m/s) c (m/s) s (m/s) s'(%) N 100 m 200 m 300 m All 0.08 0.24 0.22 SO 678 RAD 0.12 0.25 0.21 47 178 REM -0.05 0.18 0.17 38 139 AV 0.01 0.16 0.16 35 190 XON 0.23 0.34 0.24 53 171 All 0.08 0.27 0.26 54 576 RAD 0.22 0.39 0.32 65 144 REM 0.00 0.19 0.19 39 119 AV 0.03 0.20 0.20 43 167 XON 0.08 0.25 0.24 51 146 All 0.09 0.27 0.26 54 665 RAD 0.23 0.38 0.30 62 158 REM 0.07 0.23 0.22 47 136 AV 0.04 0.25 0.25 53 214 XON 0.04 0.19 0.18 38 157 b = bias (accuracy) (sodar-sonic) c = comparability s = standard deviation of differences (precision) s' = s expressed as a percentage of average value of sonic standard deviation N = number of observations AV = Aerovi ronment RAD = Radian REM = Remtech XON = Xontech 19 Table 2. Separation of Table 1 into daytime and nighttime categories Hei ght Vendor b d b n C d c n S d s n S 'd s' n N d N n 100 m All 0.02 0.17 0.21 0.27 0.21 0.21 34 99 389 288 RAD 0.08 0.18 0.23 0.26 0.22 0.20 34 88 100 78 REM -0.10 0.22 0.21 0.24 0.19 0.11 28 58 77 62 AV -0.03 0.08 0.16 0.15 0.16 0.13 27 57 115 75 XON 0.13 0.37 0.25 0.43 0.21 0.22 33 99 97 73 200 m All 0.04 0.14 0.30 0.23 0.30 0.19 43 78 306 269 RAD 0.21 0.23 0.43 0.33 0.38 0.24 54 93 78 66 REM -0.06 0.06 0.21 0.17 0.20 0.16 27 72 62 57 AV -0.02 0.09 0.23 0.18 0.23 0.15 34 62 90 77 XON 0.00 0.17 0.28 0.23 0.28 0.15 42 62 76 69 300 m All 0.06 0.12 0.28 0.27 0.27 0.24 41 89 359 304 RAD 0.21 0.24 0.39 0.36 0.33 0.27 49 98 87 71 REM 0.03 0.11 0.25 0.22 0.25 0.19 36 78 70 66 AV -0.00 0.09 0.23 0.29 0.23 0.27 36 100 121 93 XON 0.03 0.06 0.22 0.15 0.22 0.14 33 52 81 74 Subscript d: Subscript n: daytime (0600-1800 hours) nighttime (0000-0600 and 1800-2400 hours) 20 4.2 Individual 20 Minute Average Values Additional information about the effectiveness of sodar measurements of o can be sought in the scatter plots of their 20 min average values against w the sonic standard deviation of vertical wind speed. Such plots are presented by height and vendor in Figs. 4-15; daytime observations (0600-1800 MST) are distinguished from nighttime observations. Each chart has a broken line at 45° from the origin to represent a slope of 1. The estimates of the correlation coefficient based upon the 20 day sample are given in Table 3. Each chart also has a line for sodar regressed linearly upon reference according to the following model: where Y i ■ b + e 1 x 1 ♦ «, , Y- = ith sodar measurement, X. = ith reference measurement, 8 = Y-intercept, o 8 1 = slope, e. = error term, In all cases, the regression line misses the origin on the upper side and has a slope less than 1. Both characteristics are significant at the 0.05 level . As is readily seen in Figs. 4-15, the sodar systems are all consistently recording too high when a w < 0.5 m/s and too low when a > 1.0 m/s. 21 Table 3. Regression analysis for «. w Height Vendor 100 m 200 m 300 m RAD 0.85 0.28 0.67 178 REM 0.89 0.10 0.68 139 AV 0.89 0.18 0.63 190 XON 0.67 0.46 0.51 171 RAD 0.77 0.39 0.67 144 REM 0.88 0.12 0.75 119 AV 0.84 0.20 0.64 167 XON 0.83 0.26 0.63 146 RAD 0.72 0.39 0.69 158 REM 0.84 0.17 0.79 136 AV 0.70 0.19 0.68 214 XON 0.82 0.13 0.80 157 p = estimate of correlation coefficient 3q = intercept term 3, = slope term N = number of observations 22 4.3 Sodar Modes The sodar systems had two distinct operational modes: monostatic (MONO) and bistatic (BI). AV and REM employed the former mode; XON represented the latter mode; RAD rotated daily among MONO, BI, and a combination of the two modes called multistatic (MULTI). A comparison of RAD modal data with simultaneous sonic standard deviation values yields the b, c, and s results of Table 4. The sample bias (b) is significantly nonzero in all modes at all heights. It is equivalent among modes at each height at a probability level of 0.05, except for a significant difference between MONO and MULTI biases at 200 m. Comparability (c) and standard deviation (s) do not show a uniform ranking of modes with height. The large c-value for MONO at 200 m is partly due to the large bias and the presence of two a values slightly greater than 2 m/s in the subset. The s-values are inconsistent in their equivalence from height to height, possibly because of the sparseness of the data. Scatter diagrams of individual 20 min average values of sodar a versus J 3 w sonic a are shown by height and by mode in Figs. 16-24. The BI mode has the w largest departures from the 1:1 line. Figures 16-18 do not include sonic a > 1.0 m/s. Thus the plots involving BI mode are not strictly comparable with the others. In summary, there is a consistent tendency in all sodar systems to overestimate o at low sonic readings (in stable conditions). Conversely, the w sodar systems underestimated o when the true value was higher (unstable conditions). In all cases the regression lines had positive y-intercepts and slopes less than unity. 23 On average, sample biases were generally significantly positive, but AV did not show a significant bias at 100 m and was marginally biased at 200 m and 300 m. REM was the only vendor with a negative bias at 100 m, but at 300 m, REM had a positive bias, as did all the others. REM performed very well with respect to c and s at 200 m, but results for these statistics were not consistent with height. In fact, a different vendor emerged with the lowest, i.e., best, values of c and s at each level. Mode switching in the RAD system revealed a significant amount of bias in each mode (BI, MONO, MULTI) at 100 m, 200 m, and 300 m. However, as Table 4 indicates, there was little difference among modes. 24 Table 4. Radian modal a compared with sonic a. w w Height Mode b (m/s) c (m/s) s (m/s) 100 m 200 m 300 m MONO 0.14 0.28 0.24 68 BI 0.14 0.24 0.19 44 MULTI 0.10 0.22 0.20 66 MONO 0.30 0.50 0.40 58 BI 0.19 0.35 0.29 30 MULTI 0.15 0.26 0.21 56 MONO 0.25 0.36 0.25 57 BI 0.23 0.40 0.32 48 MULTI 0.19 0.39 0.34 53 b = bias (accuracy) c = comparability s = standard deviation of differences (precision) N = number of observations 25 in E o o i - IT ^T -i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r Ift <5> CO 1 o "c o CO ® a r a. 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I- Ui O t~ a. x uj O I- -« r o CO C a> o o o CV1 o on Cx. o o cvj OJ fi- rs 45 E o o CO Q < DC 00 vo * oj - in CO 1 o "c o CD s, in ® "i — r— i — r ' i i — i — i — i — i — i — i — i — i — i — r— i — i — i — i — i — i — r— r * if> fU if) (s/w) J^pos UI z> z. a <-i UI -J as r o o ►-! UI u a oc a ui J o r a o tn o- V) ** r • O UI •- a »- o Z> V) a ui a r oo a o 9 ui • E K •-« a I- UI o X UJ o t- *-> r o cr O o CO <+- O o CO It) CL o <3- CO a> 13 CD 46 5. MEASUREMENT OF WIND SPEED Measurements of wind speed (S) were obtained at sampling rates of 1 datum/15 s (REM, RAD, XON) and 1 datum/24 s (AV), and average S was computed in the field over 20 min intervals. The four sodars cycled in sequence, so that a maximum of about 1440/4, or 360, values could be obtained by each ven- dor in the 20 days of the experiment. At the three heights under con- sideration (100 m, 200 m, 300 m), AV had complete data and the other manufacturers ranged in completeness as follows: RAD, 60% to 96%, REM, 55% to 72%; XON, 91% to 92%, depending on the variable. To examine the accuracy and precision of the sodars, simultaneous obser- vations of wind speed were recorded from sonic anemometers at the same three heights on a tower that was about 600 m from the sodar systems. The sonic systems had a sampling rate of 10 Hz, and they are regarded as the reference instruments in the evaluation. However, owing to a wind shadow zone created by the tower, extending ±40° from north for the sonic instruments, reference data in this sector were obtained by the propeller-vane at the BA0 tower. A comparison of sonic and propeller wind speed measurements on the tower showed that the instruments were approximately equivalent. The resulting sonic and propeller data sets are about equal in size at 200 m, but the sonic set has one-third more data at 100 m and four-thirds more data at 300 m. Considering omissions in the reference data, these completeness percentages resulted: AV, 83% to 91%; RAD, 55% to 88%; REM, 51% to 66%; XON, 75% to 84%. 47 5.1 Sodar Reference Differences Values of sample bias (b), comparability (c), and standard deviation (s) and coefficient of variation (s 1 ) for the differences between sodar and reference values are presented in Table 5 for combined sodar observations at each height as well as for the sodar record of each vendor. Propeller wind speeds were excluded when the wind speed was less than 1 m/s. The estimates of bias in Table 5 show mostly negative values at 100 m and a composite value near -0.4 m/s. Since the difference is taken as (sodar - reference), this means that the sodar systems tend to register too low. An exception is RAD, which does not have a significant bias at 100 m. At 200 m, the vendors all record too high, and at 300 m, RAD and X0N again record too high whereas AV is slightly negative and REM unbiased. Biases were computed for day (0600-1800 hours) and night (1800-0600 hours) values. Most differences between day and night are insignificant. The comparability (c) of sodar wind speeds with reference values is also given in Table 5. Precision is represented by standard deviation (s) and per- centage deviation (s 1 ). The s' values range from about 15% to 35% around com- posite values near 25%. 5.2 Individual 20 Minute Average Values Additional information about the characteristics of sodar measurements of S can be sought in the scatter diagrams of sodar 20 mi n average values plotted against reference values. Such plots are presented by height and by vendor in Figs. 25-36. Each chart has a broken line at 45° from the origin representing a slope 48 of 1. The estimates of the correlation coefficient, slope, and intercept are given in Table 6. The agreement between sodar and tower wind speed measurements is obviously quite good. Differences between manufacturers can be deduced by the reader. 5.3 Sodar Modes A comparison between RAD modal data and corresponding 20 min reference averages yields the b, c, and s results of Table 7. The monostatic mode had significantly higher bias than the other two modes at all heights. The comparability and standard deviation show a distinct advantage to the bistatic mode; MONO has the greatest magnitudes of c at 200 m and 300 m, and MULTI has the greatest magnitudes of s at 100 m and 300 m. 49 Table 5. Sodar wind speed compared with reference wind speed Height Vendor b (m/s) c (m/s) s (m/s) s'(%) N 100 m 200 m 300 m All -0.42 1.28 1.21 28 1179 AV -0.50 1.03 0.90 21 327 RAD 0.02 1.18 1.18 28 315 REM -0.12 0.62 0.60 14 236 XON -1.04 1.88 1.56 37 301 All 0.14 0.98 0.96 23 1019 AV 0.05 0.72 0.72 17 298 RAD 0.31 1.00 1.47 35 258 REM 0.12 0.73 0.72 17 194 XON 0.09 0.71 0.70 17 269 All 0.16 1.24 1.23 27 1005 AV -0.10 1.15 1.15 25 328 RAD 0.29 1.71 1.69 37 198 REM 0.02 0.74 0.74 17 183 XON 0.44 1.20 1.12 25 296 b = bias (accuracy) c = comparability s = standard deviation of differences (precision) s' = s expressed as a percentage of average value of reference wind speed N = number of observations AV = Aerovi ronment RAD = Radian REM = Remtech XON = Xontech 50 Table 6. Regression analysis for wind speed Height Vendor 100 m 200 m 300 m AV 0.94 -0.03 0.89 327 RAD 0.90 0.41 0.91 315 REM 0.97 -0.22 1.02 236 XON 0.82 -0.07 0.77 301 AV 0.96 -0.02 1.02 298 RAD 0.87 0.04 1.07 258 REM 0.96 0.34 0.95 194 XON 0.96 0.02 1.01 269 AV 0.93 0.45 0.88 328 RAD 0.85 1.02 0.84 198 REM 0.96 0.18 0.96 183 XON 0.93 0.46 0.97 296 p = *0 = h = N = estimate of correlation coefficient intercept term slope term number of observations 51 Table 7. Sodar Radian modes: Accuracy and precision for wind speed Height Mode b (m/s) c (m/s) s (m/s) 100 m 200 m 300 m BI MULTI MONO -0.15 -0.10 0.31 0.56 1.54 1.18 0.54 1.53 1.04 90 128 97 BI MULTI MONO -0.01 0.27 0.74 0.90 1.64 1.79 0.90 1.62 1.63 78 110 70 BI MULTI MONO 0.08 0.12 1.01 1.26 1.89 1.96 1.26 1.88 1.68 66 92 40 b = bias (accuracy) c = comparability s = standard deviation of differences (precision) N = number of observations 52 ;;:■; 40 » E c CO > O c 2 O CO ® (s/uj) j^pos u z -J o z o *- in « z ■ O UJ r -' a. 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The increase in scatter above 4 m/s suggests that the larger spatial separation introduced between sensing volumes at the larger wind speeds (with the rawin- sonde drifting farther away from the release point) is a factor to be recognized when rawinsondes are used for evaluating sodar performance. Another factor to be recognized (but not obvious in Fig. 49) is the possibi- lity of large wind direction differences in sodar rawinsonde comparison under light wind conditions. Wind directions under such conditions tend to be highly variable both spatially and temporally. These conditions occur fre- quently at the BAO when the winds are from E to SE. One cannot expect good agreement between the near-instantaneous and the time-average measurements from the two systems during periods of light winds. This point is brought home very clearly in the speed and direction profiles of Figs. 50 and 51. When wind speeds drop below 2 m/s, wind direction differences become large regardless of stability. When the wind speeds are larger, the agreement be- tween the rawinsonde and sodar profiles is good. The two cases presented here are perhaps more spectacular in terms of the wind speed effect on the com- parison than most of the other cases examined. Over more complicated terrain, differences in speed and directions between sodars and rawinsondes could be much larger. Caution must be exercised, therefore, in interpreting data that compare sodars with rawinsondes. Nonetheless, this evaluation does indicate that, under proper conditions, reasonable agreement can be expected between the two sets of measurements as though both techniques measured bulk proper- ties of the wind with reasonable accuracy. 86 8. CHARACTERISTICS OF SODAR w SPECTRA The spectra of the vertical wind speed derived from sodar Doppler measure- ments should, in principle, correspond to spectra from the sonic anemometers, subject to the effects of spatial averaging and aliasing. Spatial averaging attenuates fluctuations with scales smaller than the dimensions of the sampling volume. Aliasing folds energy left over at frequencies above n , the Nyquist frequency (= 1/2 sampling rate), back into the available spectral bandwidth (0 < n < n ). In the presence of spatial averaging, the energy folded back is reduced by the amount lost through averaging. A schematic representation of the distortions introduced on a typical w spectrum for two different sampling rates is given in Fig. 52(a). In this example, the atten- uation from spatial averaging is assumed to commence at frequency n, = 0.02 Hz. The wavelength a, corresponding to this frequency (a, * U/n. , where U is the mean horizontal wind component) is roughly 2tt times the longest dimension in the sampling volume. (A sampling volume 40 m diam x 40 m long is assumed here with U = 5 m/s.) Because of the sharp spectral attenuation above 0.02 Hz, aliasing is confined primarily to the first fold, which merely raises the energy near n by a factor of 2. For typical beamwidths used in most sodar operations, n * n, * 0.02 Hz at 100 < z < 300 m for moderate wind speeds. In the convective boundary layer the percentage of spectral energy con- tained in frequencies above n increases as height, Z, decreases. Conse- quently the uncertainties in the observed spectral forms and in the measured 87 variances also increase as the height decreases. Figure 52(b) shows the progression of the spectrum on a typical day. The frequency at the n S (n) spectral maximum, n , is nearly constant above 0.25 Z^ , (where Z. is the boundary layer depth) and varies inversely with height below that. Within the height range of most sodar systems, the wavelength at the spectral peak can be approximated by \n = U/n r 6Z, (Z < 0.25 Z.) L 1.5Z i , (Z > 0.25 Z.) (5) Spectral energy in the observed bandwidth also drops with decreasing Z. The attendant decrease in signal-to-noise ratio in the sodar measurements serves to increase further the uncertainty in the spectral and variance (a ) estimates . In the stable nocturnal atmosphere, the w spectral scales and intensities are more strongly controlled by stratification than by Z. Over flat terrain, within the stable boundary layer (Kaimal et al., 1972) one can approximate x using m 3 -l ^ . Z(0.55 + Z/L) x , « L, for L « Z , (6) where L is the Monin-Obukhov length. Within the height range of our com- parisons, \ would be roughly an order of magnitude smaller than under unstable conditions. There is proportionally less energy within the spectral bandwidth, so one can expect to find larger uncertainties and errors in the nighttime spectra than in the daytime spectra. This may account for the increased scatter in the nighttime — 4 E 1 ( Si < o \ \ \ True y spectrum in" 3 Spectrum attenuated by / \ \ spatial averaging m- 4 l i _L 1 Figure 52. (a) Schematic representation of distortions introduced in the w spectrum from attenuation due to spatial averaging and from aliasing, (b) Shift in spectral behavior with height and its implica- tions for sampling and aliasing errors. 89 accuracy is possible in the presence of strong gravity waves because of its large contribution to variance at frequencies below n . The spectra presented in Figs. 53 and 54 were computed from time series provided by AV. No significance is attached to the choice of AV. The outputs are treated as generic signals from a Doppler sodar. The absence of liftup at the high end implies extensive influence of spatial averaging at frequencies below n . o The sonic spectra in Fig. 54(a) and (b) illustrate the effect of stability on spectral wavelengths and intensities at the 300 m level. The sodar spectrum shows poor agreement with the sonic spectrum at night; spectral levels are greatly enhanced. The high a levels at night in Sec. 4 can now be traced back to this distortion. To determine how much of this distortion comes from aliasing, the sonic time series was converted to grab samples every 24 s. The resulting spectrum, also shown in Fig. 54(b), has the same shape as the sodar spectrum, but one-half the energy. More precise estimates of the contributions from aliasing and other fac- tors, such as spatial averaging and noise, can be made from the variances listed in Table 12. Sonic anemometer variances estimated over two bandwidths, 0-5 Hz and 0-0.02 Hz, are listed alongside the sodar variances. Sodar vari- ances appear to be 10% - 15% lower than the full range (5 Hz) sonic variances during the day but 15% - 20% higher than the sonic variances integrated to 0.02 Hz (see Table 12). From Table 13 (last column) we find the sonic anemom- eter variance in the band 0.02 < n < 5 Hz to be between 20% and 25% of the total variance (0 < n < 5 Hz) under convective conditions. If all that variance were to be aliased back into the frequency range < n < 0.02 Hz, the rati0 (a w\odar/(° w 2 ) S on(0 10" 10 10" -3 (b) 0800-1000 MST Z = 200m — — Sonic • • Sodar io~ 4 io~ 3 io~ 2 io" 1 10° io 1 n (Hz) Figure 53. Sodar and sonic anemometer w spectra at (a) 150 m and (b) 200 m compared for morning conditions. 91 10 10 v "5 1 > 10 E 5 -2 GO 10 10 10 (a) 0800-1000 MST Z = 300m J L 10 10 v "g 10 U> 10" 10 10 3 10 (b) 2220-2340 MST Z=300m Sonic • • Sodar Sonic (sample/24s) J L 10 -3 10 10 n (Hz) 10 10' Figure 54. Sodar and sonic anemometer w spectra at 300 m compared for (a) morning and (b) nighttime conditions. 92 Table 12. 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