Vertical Velocity Variance Measurements from Wind Profiling Radars

Observations of turbulence in the planetary boundary layer are critical for developing and evaluating boundary layer parameterizations in mesoscale numerical weather prediction models. These observations, however, are expensive, and rarely profile the entire boundary layer. Using optimized configurations for 449 MHz and 915 MHz wind profiling radars during the eXperimental Planetary boundary layer Instrumentation Assessment, improvements have been made to the histor5 ical methods of measuring vertical velocity variance through the time series of vertical velocity, as well as the Doppler spectral width. Using six heights of sonic anemometers mounted on a 300-m tower, correlations of up to R = 0.74 are seen in measurements of the large-scale variances from the radar time series, and R = 0.79 in measurements of small-scale variance from radar spectral widths. The total variance, measured as the sum of the smalland large-scales agrees well with sonic 10 anemometers, with R = 0.79. Correlation is higher in daytime, convective boundary layers than nighttime, stable conditions when turbulence levels are smaller. With the good agreement with the in situ measurements, highly-resolved profiles up to 2 km can be accurately observed from the 449 MHz radar, and 1 km from the 915 MHz radar. This optimized configuration will provide unique observations for the verification and improvement to boundary layer parameterizations in mesoscale 15


Introduction
Observations of turbulence quantities in the planetary boundary layer (PBL) are crucial for many applications, and in particular, can be extremely informative for developing and evaluating parameterizations in numerical weather prediction models of the small scales that cannot yet be resolved.20 However, turbulence measurements are predominantly relegated to high-frequency in situ observing instrumentation such as sonic anemometers, limited in their spatial coverage, or are taken by expensive aircraft platforms.Lidar remote sensing instrumentation have demonstrated some potential 1 Atmos.Meas. Tech. Discuss., doi:10.5194/amt-2016-299, 2016 Manuscript under review for journal Atmos.Meas.Tech.Published: 21 September 2016 c Author(s) 2016.CC-BY 3.0 License.
for measuring profiles of turbulence (Eberhard et al., 1989;Frehlich, 1997;O'Connor et al., 2010), but this technology has more commonly focused on mean wind measurements (Menzies and Hardesty, 1989;Grund et al., 2001;Lundquist et al., 2016).Similarly, wind profiling radars (WPRs) have been shown to have capabilities of measuring turbulence, from information contained in the Doppler spectral width of the vertical velocity (Hocking, 1985;Reid, 1987;Angevine et al., 1994;Nastrom and Eaton, 1997), but the adoption of these techniques into routine use has not occurred because of the lack of precision and inability to measure the smallest turbulence values observed by sonic anemometers.
In the full energy spectrum, contributions to the total variance come from large to small scales, the separation of which is determined by different instruments' measurement frequencies and volume sizes.In general, the total variance can be assumed to be the sum of the large and small scales (Angevine et al., 1994): Total Variance = Large Scale Variance + Small Scale Variance (1) For a WPR, the contribution from the large scales can be obtained using the times series of the resolved vertical velocity, and the contribution from unresolved scales that are smaller than the pulse volume can be indirectly estimated through the Doppler spectral width of the vertical velocity.However, conventional WPR configurations are usually not adequate for measuring very small turbulence scales, because accurate measurement of the spectral width contributions due solely to turbulence is not trivial, as other factors, such as the beam-width of the radar antenna, and horizontal and vertical shear of the horizontal winds inside the volume of measurements, act to broaden the spectral widths.
Nevertheless, previous studies have used the Doppler spectral width of vertical velocity with partial success, for calculation of eddy dissipation rates.On the other hand, the typical temporal resolution of time series of first-moment velocities limits the usage of WPRs for direct measurements of the large scale contribution to the total variance.Angevine et al. (1994) used a 915 MHz WPR (Ecklund et al., 1988), to measure vertical velocity variances over both large and small scales by combining the contributions from the time series and spectral widths of the vertical velocity, respectively.
However, the purpose of that study was not the optimization of the radar for variance observations, but the measurement of the vertical heat flux.Furthermore, due to the coarser spectral and temporal resolution of that system, the variances were analyzed over 2-hour periods, and relied on the vertical component of velocity from the oblique beams to increase the resolution for large-scale variance measurements.
This study aims to accurately measure the total variance, as well as the individual contributions from large and small scales, with optimized WPR configurations and post-processing procedures.
Here, we use two WPRs operating in this optimally-defined "turbulence mode" during the eXperimental PBL Instrumentation Assessment, XPIA, to observe profiles of vertical velocity variance, obtaining information on the large scale from the time series of vertical velocity, and information on the small scales from the Doppler spectral widths of the vertical velocity.The confirmation of the poor, or if the difference in the speed of sound between the three non-orthogonal axes was too high (internal instrument quality control).The sonic anemometers recorded three-directional velocities, aligned with u directed into the boom, and v 90-degrees to the left.A planar tilt correction algorithm developed by Wilczak et al. (2001) was applied to the data to first remove any possible vertical tilt of the instrument (which was < 2 • in all cases), and to realign the velocities so that u is coordinated 100 in the 30-minute mean wind direction and v = 0 m s −1 .These aligned velocities were then used in all calculations of vertical velocity variance.

Wind Profiling Radars
The The radars measure the backscatter intensity of the atmosphere in quasi-cylindrical volumes of length, ∆R, and with a diameter that increases with distance from the radar.The backscatter time 115 series is then converted into a Doppler spectrum of velocities, S(v), through a fast-Fourier transform (FFT).The distribution of velocities observed in the volume determines the power (0 th moment), mean velocity (1 st moment), and variance or width (2 nd moment), of the Doppler spectrum.The basic method of calculating the moments (standard or single peak-processing, SPP) finds the velocity with the largest power at each height, then gathers the velocities, v 1 and v 2 , on either side of the peak 120 with power greater than a threshold, typically the maximum noise level (Hildebrand and Sekhon, 1974), as the bounds of the integral used to calculate the moments as follows: (2) 125 The 2 nd moment, σ 2 , is output as the spectral width, δ = 2σ.
The length of time between each measurement (dwell time, ∆t) is dependent on the product of several radar parameters including the inter-pulse period (IP P ), the number of coherent integrations (N COH), the number of points used in the fast Fourier transform (N F F T ), and the number of spectral averages (N SP EC): The general post-processing methods for Doppler spectra include a routine to remove the contamination from non-atmospheric signals in the spectra, and then use a peak-processing algorithm to determine the first two moments (radial wind speed and spectral width).It is optional to perform a number of spectral averages (N SP EC) in the post-processing procedure, resulting in lengthened 135 dwell times.The impact generated by using a different number of spectral averages will be included in the analysis of variance measurements (Sect.5).
In the calculation of the Doppler spectrum from the time series of backscatter intensity, wavelet and Gabor post-processing methods are commonly used to filter contamination from birds, radiofrequency interference, ground clutter, and other non-atmospheric signals.The wavelet algorithm 140 acts on the time series of backscatter intensity to reduce the clutter from non-atmospheric frequency signals, and removes them before the FFT is computed (Jordan et al., 1997).Similarly, the Gabor filtering method also works on the time series to identify and remove non-stationary signals from birds and other point targets (Lehmann, 2012).A ground-clutter removal algorithm is also applied, which removes any spectral peaks centered around 0 m s −1 .These processes provide significantly 145 cleaner spectra and have been confirmed to improve estimates of the first moment (Bianco et al., 2013).
Common peak-processing methods include the standard method described above (SPP), as well as the multiple peak-processing (MPP) method of Griesser and Richner (1998).This algorithm identifies the three largest peaks in the spectrum at each height of measurement, then uses continuity 150 in time and space (vertical profiles) to identify the most-likely true peak.MPP was not used in this study because, though it has been shown to calculate more precise mean winds for typical radar setups (Gaffard et al., 2006), the high spectral resolution used in turbulence mode is incompatible with MPP, often identifying multiple peaks within one true peak, leading to greatly under-estimated spectral widths.

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When using SPP, the threshold that determines the spectral width can be set to either the maximum or mean noise level of the spectrum.The common choice is to use the maximum noise level since it is the most conservative for removing noise, providing a better estimation of the first moment of the spectrum, and therefore this threshold was used for all first-moment calculations.However, the choice of the maximum noise level can cause the spectral width to be underestimated.The mean 160 noise level in these cases allows the measured spectral widths to be broader.Figure 2 This threshold was applied to each individual spectrum to determine if the first and second moments 175 are discernible through the noise.A discussion of the accuracy of width measurements based on SNR can be found in the appendix.
During XPIA, the raw time series of backscatter intensity were collected in order for all postprocessing steps to be tested and optimized.The turbulence mode was configured with the goal of capturing the fullest range of scales in the energy spectrum by increasing the number of dwells in 180 each 30-minute interval, and by maximizing the spectral resolution to capture the most accurate spectral widths.This is accomplished by both minimizing ∆t, while maximizing N F F T .Figure 3a shows an example spectrum that has spectral resolution that cannot accurately capture the Doppler width, despite the mean velocity being accurate.On the other hand, Fig. 3b shows how, with a different set-up (more FFT points and fewer spectral averages on the same dwell), smaller spectral widths 185 can be captured.This example contains a ground-clutter peak at 0 m s −1 , but the low resolution cannot distinguish it from the true atmospheric peak, creating one broad peak.The higher spectral resolution can distinguish the ground clutter, and therefore is able to it and accurately measure the narrow width of the true peak.A spectral resolution on the order of 0.01 m s −1 was set, to guarantee that spectral widths down to 0.1 m s −1 could be resolved using several points.Table 1 summarizes 190 the default parameters used in turbulence mode for calculating the Doppler spectra from the two WPRs.The resulting dwell time for the 449 MHz WPR is 13 s, and 17 s for the 915 MHz WPR, with N SP EC = 1 (spectral averaging can be performed in post-processing).
Since the 449 MHz WPR has a larger power-aperture product, and therefore a higher overall SNR, the measured spectra are usually cleaner and the moments more accurate.For this reason our analysis 195 will first be performed on the data from the 449 MHz WPR, and later we will repeat it on the 915 MHz WPR to confirm the applicability to other radar systems.

Vertical Velocity Variance Calculations
When comparing vertical velocity variance from sonic anemometers, which measure velocity at very high frequency, and WPRs, which measure a Doppler spectrum at lower temporal resolution, multiple calculation methods must be applied for the resolved and unresolved scales.From the time series of the first moments of WPR Doppler spectra, the resolved, large-scale, 30-minute variance can be measured, T S = w 2 r 30 , while the small-scale variance can be measured from the Doppler spectral width (second spectral moment), SW = ( 1 2 δ) 2 .Equation 1 can be specified for the WPR, and the total WPR variance be computed as Since the WPR observes a volume, the finite beam-width of the radar antenna as well as the wind shear across the measurement volume will contribute to the broadening of the spectrum, generating larger spectral widths.Nastrom and Eaton (1997) have determined the shear and beam-broadening contributions, σ 2 s , on the observed width (in terms of spectral variance) to depend on both the mean 210 wind transverse to the beam axis, V T , as well as the antenna properties as In the case of a vertical pointing beam (θ = 0 o ), this simplifies to where ν is the half-width to the half-power point in the antenna pattern, and du/dz is the vertical mean wind shear.In our analysis, these effects have been subtracted from each dwell's observed spectral width, since the total variance is a sum of these independent contributions.In the cases when σ 2 s is larger than the measured spectral width, the dwell was discarded.Though this may produce a high bias in the 30-minute WPR average, as seen by Dehghan et al. (2014), all other solutions 220 (replacing the value with 0, allowing a negative spectral width, or substituting a small value) are not physically realistic, or are artificially created, causing statistical inaccuracies.Furthermore, fewer than 10% of the 449 MHz dwells had a situation of σ 2 s larger that the measured spectral width (the 915 MHz is more impacted).
Appropriate averaging time scales must be applied to the sonic anemometer data for a direct com- The total variance from the sonic anemometers, with time-scale separation that matches the WPR 235 resolution, is then obtained by (in the form of Eq. 1): Total Variance sonic = LP + HP. (10) Though instrument noise, n, is sometimes subtracted from the observed variance (Thomson et al., 2010), n is negligible in relation to the velocity fluctuations, and will, therefore, be ignored in the variance calculations herein.The agreement between the WPR and sonic anemometer measurements 240 will be quantified using the mean difference or absolute error, normalized bias, and the coefficient of determination, R 2 .Since the results are best presented on logarithmic scales, the log 10 of all values is used for computing these variances.
The complete variance over 30-minutes of observations includes contributions from all time scales, and thus the most accurate total variance can be obtained from the 20-Hz sonic anemometer 245 data: tot = w 2 20Hz 30 .It is therefore possible, from the sonic anemometer data, to determine if Eq. 10 is valid.If so, and if the WPR TS and sonic LP variances, and WPR SW and sonic HP variances are equal, then it can also be assumed that the sum of TS and SW variances will equal the total variance measured by the sonic anemometer.Each pair of sonic-WPR scales and their totals will be compared in Sect. 4.

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Each dwell collected by the 449 (915) MHz WPR spans about 13 (17) seconds, capturing only a short period of the atmosphere's motions.This leaves a large portion of the variance to the large scale, and the small scale variance by itself will not be representative of the turbulent flow, as it is missing a large portion of the energy spectrum.In the case of Doppler spectra from pre-determined radar pulses, multiple dwells can be averaged to span a longer period of fluctuations (dwell time) resulting 255 in more representative turbulence statistics.However, averaging over periods that are too long, and therefore non-stationary, will result in broadening the spectral peak due to a shifting mean velocity, rather than true fluctuations from turbulence.In this case, the SW variance will be unrealistically large, and the TS variance will lack resolution over the 30-minute period.Therefore, an analysis was performed to determine the length of time, set by N SP EC, which produces the most accurate With the confidence that the sum of sonic anemometers' LP and HP variance accurately calculates the full variance, the partitioned sonic's contributions can be compared to the WPR's.Figure 5 shows the comparisons between each scale's contribution: a) and b) the LP variance from the sonic is strong, with a slope of the best fit line of 0.724 (Fig. 5a).The largest errors occur for radar 280 TS variances that are significantly higher than the sonic anemometers' LP variance.The average overestimation of the WPR by three (or more) times the sonic anemometers comes mostly from the small variance values, but at the highest values, the agreement is much better (see the departure of the red-dashed best fit line from the black-dashed one-to-one line).
The correlation between the radar SW variances and the HP variance for N SP EC = 1 (Fig. 5c),

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with R 2 = 0.53, has a different behavior, with a large over-estimation of small variances, and frequent under-estimations at large variances, as highlighted by the slope of the best fit line much less than 1.At this short time-separation scale, the variance from WPR spectral widths is inaccurate at almost all variance levels.It is also noteworthy that the magnitude of variance is larger overall at the large scale (TS and LP) than the small scale (SW and HP).

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The sum of the two portions of the radar's variances is compared to Total Variance sonic in Fig. 5e.
Though dominated in magnitude by the large scales, the spread of values is more condensed than the large-scale values in Fig. 5a, and remains closer to the one-to-one line than the small-scale variances in Fig. 5c.With an R 2 value of 0.78, the agreement is overall better than either of the apportioned contributions.This agreement is very encouraging, showing that it is possible to measure vertical surements to be used in turbulence dissipation rates (Hocking, 1985) will call for a different time scale than variances using the time series of resolved vertical velocities from a WPR.Averaging over longer dwells moves more variance contributions into the spectral width, at scales smaller than the dwell time, and out of the time series, increasing the spectral widths, and reducing the contribution of the variance from the resolved-scale measurements.For a sonic anemometer, averaging over 310 longer time scales simply moves LP variance into the HP variance, until, averaging up to 30 minutes, HP would equal the total variance.However, for a WPR, it is unrealistic for the spectral width of a 30-minute dwell to accurately capture the total variance.It remains to be seen if the radar and sonic anemometers measure the same variances as the information is moved from one set of scales to the other; the spectral averaging of the WPR and the time series averaging of the sonic anemometers 315 deal with the additional information differently, so the final variances may vary as well.How each scale of WPR observations, as well as the sum of the two, compares to the equivalent variance from the sonic anemometers as the separation time scale lengthens is unknown.ability between the two instruments will be reduced.As the averaging time increases, there is also an overall increase in the magnitude of the variances from SW, but there is no apparent decrease in the magnitude of the TS variance, as the energy is moved from one scale to the other.Again, the average 340 overestimation of the WPR SW by three times the sonic HP occurs mostly from the small variance values (the larger difference between the red-dashed best fit line and the black-dashed one-to-one line), but at the highest values, the agreement is much better.
With the improved small-scale SW variance but worsened large-scale TS variances with longer spectral averaging, it is reasonable that the sum would remain equally correlated with the total sonic 345 variance over all time scales, and this is evident in the correlation (Fig. 6c, purple).While R 2 between Total Variance sonic and the sum of the WPR variances remains fairly constant at 0.78 − 0.79 over all N SP EC, the MAE (Fig. 6a) and biases (Fig. 6b) both increase with larger N SP EC.The MAE increases at nearly the same rate as the MAE in SW, but the bias increases more slowly than the bias in TS.The MAE increase in the WPR sum is due to the fact that the magnitude of the SW 350 variance increases with longer dwells (as discussed above), but the TS variance does not decrease to keep the total equal.Since this behavior occurs at all variance levels, the normalized bias increases slower than the bias in TS, which increases drastically with averaging.The main difference between Figs. 5e and f is the slightly larger magnitude of all points, due to the increase in SW values.
With confidence in the agreement between the corresponding sonic anemometer and WPR mea-355 surements at 13-s and 2-min scales, and the agreement between the sum of the sonic LP + HP versus Total Variance sonic at 13-s, the agreement between the two sums (sonic LP+HP and WPR TS+SW) was also investigated.The correlation, MAE and bias between the two sums is virtually equal to those of Total Variance sonic vs. WPR TS+SW for all N SP EC, indicating the strong correlation between the sum of the LP and HP and Total Variance sonic that is independent of the separation time 360 scale.The comparison between these with varying N SP EC (using the 449 MHz WPR dwell times) is performed in Fig. 7: a) the mean bias as the sum minus the total variance normalized by the total; b) and the coefficient of determination.As expected, the R 2 values are close to 1, and the bias is low for all N SP EC.As the time scale of separation changes, the variance contributions shift from the LP portion to the HP portion, and their sum overestimates the total variance slightly.This positive 365 bias in the sum comes from the remaining low-frequency trends in the HP variance, which decrease with longer averages.Overall, however, the agreement between the Total Variance sonic and the sum of HP and LP is quite good, confirming the accuracy of Eq. 10 for all N SP EC.
The collection of comparisons in Figs. 6 and 7 shows that the WPR and sonic anemometers do not respond to changes in the averaging time scale in the same manner.The optimal time scale for the to- The 449 and 915 MHz WPRs were set up to have very similar spectral and temporal resolution, but have different parameter sets that produce these desired values (see Table 1).The filtering methods with longer dwells, but also has increasing MAE.However, the normalized bias is constant with increasing N SP EC (Fig. 10b).The sum of the WPR TS and SW correlates to Total Variance sonic nearly equally at all time scales as well.The main difference between the 915 MHZ and 449 MHz is that the variance from TS vs. LP remains better correlated than SW vs. HP up to 5-min dwells.Therefore, the optimal dwell time for SW variance from the 915 MHz may be longer than the 449 MHz, up the SW variance increases.In the full energy spectrum, the variance is being transferred from the large scale portion to the small scale portion.However, Fig. 5 shows that the SW variance grows 445 more (panels c to d) than the TS variance decreases (panels a to b) with longer averaging, causing an overall increase in the total or summed variance (panels e to f), and overall higher bias in the summed variance (Fig. 6b).
Having assessed the correlations with the in situ observations from the sonic anemometers on the 300-m tower, shown in the figures above, full vertical profiles of vertical velocity variance can .Spectral methods of estimating velocity variance from the Fourier transform of a velocity times series allows the separation of turbulence and noise through subtraction of the random signal from the power density spectrum (Moyal, 1952).When calculating variance from spectral density curves using spatially-averaged measurements (like sonic anemometers and WPRs), corrections must also be applied to account for path-averaging as well as inaccuracies in using the 520 assumption of Taylor's hypothesis across the measurement volume (Kaimal et al., 1968;Wyngaard and Clifford, 1977).
In the current study, the noise contributions to the variance measured by each instrument must be addressed.In the case of the high-frequency point measurement of the sonic anemometers, the manufacturer-prescribed noise level is n = 0.1 cm s −1 , which can be 3 orders of magnitude less than 525 the fluctuations in velocity due to turbulence, so n 2 is typically negligible.For the WPR, however, there does not exist an inherent n, but rather each dwell has an independent noise level, observed in the signal-to-noise ratio, SNR.
Though the effects of beam-broadening and shear-broadening are removed from the WPR spectral width, there is no equivalent method of removal of noise from variance measurements calculated 530 from the time series of velocities, nor any adjustment for errors in spectral widths due to noise.
However, expanding upon the work of Riddle et al. (2012) on the minimum threshold of usability for WPRs based on SNR, the accuracy of spectral width measurements can be determined.Riddle et al. (2012) determined the lowest possible SNR needed to recognize a signal in the spectrum, and adopting his method can identify the true spectral width using an additional SNR, P R, above the 535 base level needed.To begin, we assume that the true signal, as a function of velocity, S(v), has a Gaussian distribution with mean velocity, V 0 , and variance, σ 2 : The moments are defined as Eqs.2-4, integrating symmetrically based on the velocity at which the noise level is reached, B. Integrating Eq.A.1 from V 0 −B to V 0 +B (in Eq. 4) produces the estimator 540 of the width, W 2 obs : The value of W 2 obs will be the most accurate measure of σ 2 when the SNR is high, since B will be large.The fractional error in the width, F W 2 , is thus 545 two wind profiling radars used during XPIA were a 449 MHz and a 915 MHz WPR, both located near the BAO visitor's center (the 915 MHz to the west, the 449 MHz just to the south), about 600 m 105 to the southwest of the 300-m tower.The profilers collected data from 1 March until 30 April 2015 in a rotation of three modes each hour: for the first 25 minutes of each hour in "normal acquisition mode," with collection of Doppler spectra for consensus winds from 3 beams (one vertical and two oblique); for 30 minutes in "turbulence mode," with collection of time series of backscatter intensity from only the vertical-pointing beam; and for the last 5 minutes of each hour in Radio Acoustic 110 Sounding System (RASS) mode.Backscatter intensity time series and Doppler spectra files were post-processed to obtain raw data files containing radial velocity, spectral width, and signal-to-noise ratio (SNR) for analysis.

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parison to WPR variances at small and large scale.For the resolved, large-scale variance, low-passed sonic anemometer variance (labeled "LP" on figures) is calculated from an averaged time series that matches the resolution of the WPR time series (dwell time, ∆t).The variance is therefore calculated by first averaging the 20-Hz data to the dwell time of the WPR, w ∆t , and then computing the 30minute variance as LP = w 2 ∆t 30 .The small-scale, high-passed variance from the sonic anemometers 230 7 Atmos.Meas.Tech.Discuss., doi:10.5194/amt-2016-299,2016 Manuscript under review for journal Atmos.Meas.Tech.Published: 21 September 2016 c Author(s) 2016.CC-BY 3.0 License.(labeled"HP"), which contains all of the high-frequency information lost in the averaging in LP, is calculated computing the variance of the 20-Hz sonic data over the same dwell time of the WPR, as HP = w 2 20Hz ∆t .The high-frequency information contained in HP is thus equivalent to that of the spectral width of the WPR Doppler spectrum, and 30-minute averages of each can be compared.
260variances from the WPR (TS, SW, and Total Variance WPR ) compared to the in situ observations from the sonic anemometers.4Results from the 449 MHz WPRSince the WPR is unable to resolve all scales of variance directly, its various contributions must be compared to the equivalent contributions in the sonic anemometers' variance.This requires the Atmos.Meas.Tech.Discuss., doi:10.5194/amt-2016-299,2016   Manuscript under review for journal Atmos.Meas.Tech.Published: 21 September 2016 c Author(s) 2016.CC-BY 3.0 License.assumption, however, that the sum of the small-and large-scale contributions (sonic anemometers LP and HP variance and the equivalent WPR TS and SW contributions) is equal to the total variance over all scales, as calculated by the sonic anemometers.To confirm this, the sum of sonic LP and HP and Total Variance sonic are compared in Fig.4.Though all data in this figure are from the sonic anemometers, the time scale of separation between LP and HP is determined by the un-averaged 270 (N SP EC = 1) dwell time of the 449 MHz WPR of 13 s.The agreement is very good, with an R 2 value of 0.97 and a mean difference of −0.01 m 2 s −2 .
275anemometers is compared to the TS variance from the 449 MHz WPR; c) and d) the sonic HP variance is compared to the WPR SW variance; and e) and f) Total Variance sonic is compared to the sum of the variances from the WPR TS and SW (Figs.5b, d, and f with N SP EC = 8 will be discussed in Sect.5).With an R 2 value of 0.74, the agreement between TS and LP at N SP EC = 1

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velocity variance with reasonable accuracy from the volume-measurements of the WPRs. 5 Spectral Averaging Effects on Variance Measurements Averaging multiple Doppler spectra in time can reduce the noise level in the radar measurements, and has implications for the scales of turbulence observed in either the spectral width or the time series of vertical velocity.The typical WPR setup optimized for wind measurements (first moment 300 9 Atmos.Meas.Tech.Discuss., doi:10.5194/amt-2016-299,2016 Manuscript under review for journal Atmos.Meas.Tech.Published: 21 September 2016 c Author(s) 2016.CC-BY 3.0 License.computations) uses multiple beams pointing in different directions to obtain winds for every 2-5 minutes in order to capture a representative sample of atmospheric motions, while still observing a relatively stationary atmosphere.When analyzing the variance measured by a WPR on two different time scales, it becomes a relevant question of how much averaging should be performed to get the most accurate measurement for each scale.For example, an optimization of spectral width mea-305

Figure 6
Figure6shows the mean absolute error (a), normalized bias (WPR minus sonic divided by sonic, b) and coefficient of determination, R 2 (c), for each set of variances compared in Fig.5as a function 320

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tal variance as the sum of WPR variances is the shortest dwell time, with no spectral averaging.The WPR's measurements vary as well; the TS variance correlates best with the sonic anemometers' LP variance at short time scales, while the WPR's SW variance correlates best with the sonic anemometers' HP at slightly longer, 2-5 minute time scales.Based on these results, if Total Variance WPR is theAtmos.Meas.Tech.Discuss., doi:10.5194/amt-2016-299,2016   Manuscript under review for journal Atmos.Meas.Tech.Published: 21 September 2016 c Author(s) 2016.CC-BY 3.0 License.desired quantity, then no spectral averaging should be performed (N SP EC = 1), gaining the high-375 est correlation with the lowest biases.However, if variance from the spectral widths is the desired quantity (for calculation of dissipation rates, for example), then the highest correlation and lowest biases occur at N SP EC = 5 − 10.For further analysis herein, we use N SP EC = 8.6 Effect of StabilitySince the time scales of turbulence are impacted by convection in the planetary boundary layer, an 380 analysis was completed to understand if the time scale at which the WPRs measure the most accurate resolved and unresolved variances is affected by the stability of the atmosphere.Data were separated into daytime (convective) and nighttime (stable) sets, and the same comparisons were made.Figure8shows the a) MAE, b) normalized bias (sonic minus WPR divided by sonic), and c) coefficient of determination, R 2 , for each pair of variances in the daytime and nighttime, with 385 increasing N SP EC.The overall result is that the daytime, convective variance (solid lines) is better measured by the WPRs in all methods, following the same behavior as the entire dataset in the preceding sections.In the nighttime stable boundary layer, when turbulence is suppressed, the WPR is not as accurate (dashed lines).The magnitudes of the MAE are smaller at night because the overall amplitude of the variance is smaller, but the normalized bias shows the larger error at night.Even 390 at night, we see the correlation decrease with increasing N SP EC for the TS vs. LP variances, but increase between WPR SW and sonic HP.In both night and day, the sum of WPR stays equally correlated at larger N SP EC, but with increasing MAE, again supporting the use N SP EC = 1 for Total Variance WPR .Figure9shows the daytime (left column) and nighttime (right column) scatterplots of variances, using the optimum N SP EC for each method (N SP EC = 1 for TS vs. LP and 395 TS+SW vs.Total Variance sonic , and N SP EC = 8 for SW vs. HP).Beside the increased number of observations of small variances at night, the scatter is increased at both large and small scales, and ultimately the sum as well.The low variances that occur at night are inherently more difficult for the WPR to measure, since the remaining noise in the Doppler spectrum can dominate the small turbulent contributions to the measured spectral widths.400Results from the 915 MHz WPR The 915 MHz WPR was situated within 20 m of the 449 MHz WPR for the extent of XPIA, so it provides another opportunity to test the ability of WPR systems to calculate vertical velocity variance.

405
and moments' calculation methods are independent of the WPR parameters, but the number of spectral averages, which impacts the SNR and depends on the exact temporal resolution of each WPR system, must be tested for the 915 MHz WPR independently from the 449 MHz results.Using the Atmos.Meas.Tech.Discuss., doi:10.5194/amt-2016-299,2016 Manuscript under review for journal Atmos.Meas.Tech.Published: 21 September 2016 c Author(s) 2016.CC-BY 3.0 License.same post-processing techniques, the a) MAE, b) bias, and c) coefficient of determination between variance from the WPR TS and SW and sonic LP and HP variances are shown in Fig. 10, with vary-410ing N SP EC.Though the overall error is higher, and correlation is lower due to the inherently noisier 915 MHz system, the behavior is consistent with the results from the 449 MHz WPR.The WPR TS and sonic anemometer LP become less correlated and more biased with longer dwells, due to the smaller number of velocity observations that contribute to each variance measurement, but with relatively constant MAE.The correlation between the WPR SW and sonic anemometer HP increases 415 420to N SP EC = 35, or 10-min dwell time.Figure11shows the distributions of variance observations at each scale (a -d), and Total Variance sonic (e and f), using no spectral averaging (N SP EC = 1, left column), and N SP EC = 35 (right column).Again, the improvement in agreement in variance from WPR SW and sonic anemometer HP can be seen from the left column to the right (c to d), but a digression is seen in the variance from WPR TS and sonic anemometer LP (a to b).At these longer 425 time scales, only 3 points contribute to creating the 30-minute variance, so the large scale variance is not expected to be accurate.The agreement between the WPR sum and Total Variance sonic (e to f) also increases at N SP EC = 35, dominated by the contributions at the small scale in the SW and HP variances.8Contributions of Measurements to Total Variance 430With two different scales of measurements contributing to the total variance in the atmosphere, the relative contributions of each can be analyzed.Over the range of variances observed by the 449 MHz radar, the ratio of WPR TS and SW to the sum can illustrate where each scale contributes to the total variance.Figure12shows the ratios of the average observed WPR TS (blue) and SW (red) to the sum of TS+SW in bins of Total Variance sonic .At large variance values, the contribution from 435 the large scale, TS, variances increases, as the portion from the SW decreases.At smaller values, however, the contributions remain constant, with more equal portions from TS and SW.The difference between the solid (N SP EC = 1) and dashed (N SP EC = 8) lines shows that the fraction from the SW is larger with longer averages.In fact, the increase leads to a greater contribution to the summed variance than the TS until the TS begins its increase at larger variances.It isn't until 440 Total Variance sonic = 10 −1 m 2 s −2 that the TS contributes more variance than the SW.This occurs because more spectral averaging acts to widen the spectral peak.The resolution of the time series of vertical velocity also decreases with longer dwell times, and the TS variance thus decreases asAtmos.Meas.Tech.Discuss., doi:10.5194/amt-2016-299,2016   Manuscript under review for journal Atmos.Meas.Tech.Published: 21 September 2016 c Author(s) 2016.CC-BY 3.0 License.
450now be observed by the two WPR systems.As seen in Figs.13 and 14, the 449 MHz WPR can nearly continuously measure the variance up to 2 km, and the 915 MHz often measures to 1 km or higher.Variance levels as high as 10 m 2 s −2 near the surface, and down to 10 −4 m 2 s −2 aloft are observed by both WPRs.Throughout the days shown, the growth and decay of the boundary layer is visible in increasing variance levels in diurnal cycles.The 499 MHz has a narrow-enough beam that 455 the broadening term does not surpass the measured widths, but the 915 MHz WPR's wider beams require a large broadening term to be removed, often larger than the observed spectral width, and thus small variance values are generally not measured at heights above the boundary layer.As the daytime boundary layer grows, however, the measurement height of the 915 MHz profiler increases, as the convection generates stronger velocities, and larger widths become more decipherable despite 460 the large beam-broadening term for that WPR.With observations every 25 m in the vertical, both WPR systems provide highly-resolved profiles of vertical velocity variance within the PBL.Profiles created using the optimal settings for the different variances show the relative contributions from each, supporting the results of Fig.12.In the left columns of Figs. 13 and 14 with no spectral averages, the magnitude of the SW variance is much less than that of the TS variance, and 465 in the right columns, with longer time separations, the magnitude of the SW variance is larger.For observations of the variance from the time series of WPR vertical velocity alone, Figs.13a and 14aare optimal; for variance from WPR spectral widths alone, Figs.13d and 14d are optimal, and for the total variance, using the sum of TS and SW, Figs.13e and 14e are optimal.9 Conclusions 470 With the goal of improving methods of measuring vertical velocity variance from wind profiling radars, two WPRs were run alongside the 300-m BAO tower with 6 heights of sonic anemometers for two months of the XPIA field campaign.The WPRs were set-up with high N F F T and low N SP EC to optimize both the temporal and spectral resolution, allowing measurement of the highest frequencies possible in the energy spectrum, and also allowing flexibility in post-processing 475 through spectral averaging.The spectral resolution of the obtained Doppler spectra was also set to be much higher than in usual operations, in order to get very accurate spectral widths, and to capture the smallest variances possible.Using the in situ observations of vertical velocity variance Atmos.Meas.Tech.Discuss., doi:10.5194/amt-2016-299,2016 Manuscript under review for journal Atmos.Meas.Tech.Published: 21 September 2016 c Author(s) 2016.CC-BY 3.0 License.noise variance, n 2 , from oceanic acoustic Doppler current profilers and velocimeters can simply be subtracted from the observed variance, u 2 , to obtain the true variance used in calculating turbulence 515 intensity, I = √ u 2 −n 2 u

Figure 1 .Figure 2 .
Figure 1.Windrose from the 30-minute mean winds measured by the sonic anemometer on the northwest boom at 200m on the BAO tower.Waked measurements have been removed and appear as a gap in observations around 154 • .

Figure 3 .Figure 4 .
Figure 3. Doppler spectra collected from the 499 MHz WPR during the XPIA field campaign, with typical spectral resolution (a) and higher spectral resolution (b), accomplished through computing fewer spectral averages on the same dwell.The vertical red lines denote the first moments (mean velocity) and the horizontal red lines denote the spectral widths, using the standard peak processing method.

Figure 5 .Figure 6 Figure 7 Figure 8 .
Figure 5. Scatter plots of 30-minute vertical velocity variance between the sonic anemometers and the 449 MHz WPR at overlapped heights of 150, 200, 250, and 300-m, for the two months of radar measurements: a) and b) low-passed variance from sonic anemometers (LP) versus WPR time series of vertical velocity (TS); c) and d) high-passed variance from sonic anemometers (HP) versus variance from WPR spectral widths (SW); e) and f) total variance from sonic anemometers versus the sum of TS and SW from the WPR.In panels a), c) and e), no averaging was performed on the WPR spectra, producing a dwell time of 13 s, and in panels b), d), and f) N SP EC = 8, generating a dwell time of approximately 2 minutes.The slopes of the best fit lines (red dashed lines), mean absolute errors, R 2 values, and number of points, N, are shown for each plot.

Figure 9 .Figure 10 .
Figure 9. Same as in Fig. 5 but separated by daytime (a, c, e) and night time (b, d, f), with the respective N SP ECs shown.

Figure 11 .Figure 12 .
Figure 11.Same as Fig. 5, but for the 915 MHz WPR, with N SP EC = 1 on the left column, and N SP EC = 35 on the right.Data from all six overlapping heights and all available days are included.

Figure 13 .
Figure 13.Time-height cross-sections of: a) and b) time series vertical velocity variance; c) and d) spectral width variance; and e) and f) total variance as measured by the 449 MHz WPR at the BAO, using N SP EC = 1 (a, c, e) and N SP EC = 8 (b, d, f), from 13 to 20 March 2015.

Figure 15 .
Figure15.Left blue axis: Fractional error of variance from Eq. A.4 as a function of B/σ.Right red axis: Ratio of observed power to power at noise level integration limits, P R from Eq. A.6, as a function of B/σ.
and the maximum noise level (dotted line) will occur at narrower velocity values than the intersection with the mean noise level (dashed line).As a consequence, the use of the maximum 165 noise level will generate smaller spectral widths than those obtained using the mean noise level. spectrum

Table 1 .
Radar parameters for the 449 MHz and 915 MHz wind profiling radars, running in "turbulence mode" for minutes 25 − 55 of each hour during XPIA from 1 March to 30 April 2015.