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 and 915 MHz wind profiling radars during the
eXperimental Planetary boundary layer Instrumentation Assessment (XPIA),
improvements have been made to the historical 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

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.
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 has demonstrated
some potential for measuring profiles of turbulence

In the complete energy spectrum, the total variance is made of contributions from the entire range of scales, from large to small. Furthermore, variances are observed at separate scales 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:

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 ability of the optimized WPR setup and post-processing methods to measure accurate variances at different scales allows the usage of this remote-sensing instrument for a larger variety of applications.

All observations used for this study were gathered at the Boulder Atmospheric
Observatory (BAO), located in Erie, Colorado, and operated by the National
Oceanic and Atmospheric Administration's Earth Systems Research Laboratory

During XPIA, the BAO tower was equipped with 12 Campbell Scientific CSAT3
sonic anemometers (commonly referred to simply as “sonics”), two at each
height every 50 m from 50 to 300 m on southeast- and northwest-facing booms,
at 154 and 334

Wind rose from the 30 min mean winds measured by the sonic
anemometer on the northwest boom at 200 m on the BAO tower. Waked
measurements have been removed and appear as a gap in observations around
154

The two wind profiling radars used during XPIA were a 449 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

The radars measure the backscatter intensity of the atmosphere in
quasi-cylindrical volumes of length,

The length of time between each measurement (dwell time,

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, radio-frequency interference, ground
clutter, and other non-atmospheric signals. The wavelet algorithm 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

Common peak-processing methods include the standard method described above
(SPP), as well as the multiple peak-processing (MPP) method of

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 noise level in these cases
allows the measured spectral widths to be broader.
Figure

Conversely, if the noise power contained in the Doppler spectra is too high
(SNR is too low), identification of the correct atmospheric peak may be
prevented, or the peak may be falsely narrowed (imagine moving the horizontal
noise lines in Fig.

Theoretical Gaussian Doppler spectrum with added random noise, with the mean (dashed line) and maximum (dotted line) noise levels.

During XPIA, the raw time series of backscatter intensity were collected in
order for all post-processing 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 each
30 min interval and by maximizing the spectral resolution to capture the
most accurate spectral widths. This is accomplished by both minimizing

Doppler spectra collected from the 499 MHz WPR during the XPIA
field campaign, with typical spectral resolution

Radar parameters for the 449 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.

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 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.

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 min
variance can be measured, TS

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.

Appropriate averaging timescales must be applied to the sonic anemometer
data for a direct comparison 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,

The complete variance over 30 min of observations includes contributions
from

Each dwell collected by the 449 (915) MHz WPR spans about 13 (17) s,
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 predetermined radar pulses, multiple dwells can be averaged to
span a longer period of fluctuations (dwell time), resulting 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 min period.
Therefore, an analysis was performed to determine the length of time, set by
NSPEC, which produces the most accurate variances from the WPR (TS, SW, and

Since 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 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

Scatter plot of the total sonic anemometer variance versus the sum
of low-passed (LP) and high-passed (HP) variances from sonic anemometers,
with the time-separation interval set to the 449 MHz, un-averaged
(NSPEC

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

Scatter plots of 30 min vertical velocity variance between the
sonic anemometers and the 449 MHz WPR at overlapped heights of 150, 200,
250, and 300 m, for the 2 months of radar measurements:

The correlation between the radar SW variance and the HP variance for NSPEC

The sum of the two portions of the radar's variances is compared to

For the three variables – large scale, small scale, and the total variances –
the lowest height of the WPR performs the poorest, with coefficients of
determination

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
computations) uses multiple beams pointing in different directions to obtain
winds for every 2–5 min 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
timescales, 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 measurements to be used in turbulence
dissipation rates

Figure

However, the correlation and bias improve between the sonic
anemometer HP and the WPR SW variances as more spectral averages are
computed. The MAE does increase with longer averages, but the normalized
bias's behavior shows that the MAE increase occurs at only larger values of
variance, skewing the MAE high, while the normalized behavior shows
improvement. The correlation is at its maximum between NSPEC

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 variance over all timescales,
and this is evident in the correlation (Fig.

With confidence in the agreement between the corresponding sonic anemometer
and WPR measurements at 13 s and 2 min scales, and the agreement between the
sum of the sonic LP

The collection of comparisons in Figs.

Since the timescales of turbulence are impacted by convection in the
PBL, an analysis was completed to understand if the timescale 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. Figure

Same as in Fig.

Same as in Fig.

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. 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

Same as Fig.

Same as Fig.

With 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. Figure

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 now be observed by the
two WPR systems. As seen in Figs.

Mean percent contribution of the WPR time series (TS; blue) and
spectral width (SW; red) variances to the sum of the TS and SW variances
binned by the total variance of the sonic anemometers. Solid lines use
NSPEC

Time–height cross sections of

Same as Fig.

Profiles created using the optimal settings for the different variances show
the relative contributions from each, supporting the results of
Fig.

With the goal of improving methods of measuring vertical velocity variance
from wind profiling radars, two WPRs were run alongside the

In an analysis of the contributions that the large and small scales make to the total variance, there are differences that depend on the total variance, and the timescale of separation (set by the number of spectral averages) between scales. Using a larger number of spectral averages move a greater portion of the variance into the small scales, and vice versa. At large total variance levels, the small scales decrease in relative contribution, and the large scales increase. Understanding the scales and levels of variance measured by each method (WPR TS or SW) indicates the best setup for the WPR, depending on the application.

With these results, wind profiling radars have been shown to reasonably
accurately measure vertical velocity variance over the full range of
turbulence scales and magnitudes observed by sonic anemometers. This allows
profiles to be collected with these systems through the PBL without being
limited to the locations of the in situ observations. The 449 MHz system
observes reliable vertical velocity variance profiles up to 2 km in the
setup used in XPIA, and the 915 MHz WPR measures consistently up to 1 km.
With the ability to observe profiles of variance throughout the PBL from
WPRs, progress can be made in many areas including improving PBL
parameterizations in numerical weather prediction models. The evolution of
the PBL can be analyzed in more detail with the use of turbulence profiles
from WPRs. Verification of subgrid-scale parameterizations of large-eddy
simulations (LES) is possible using the small-scale variances measured in the
WPR spectral widths, while the resolved scales of the LES can be verified by
the WPR variance from the time series of vertical velocities. Furthermore,
improved spectral width measurements will allow for more accurate
observations of turbulence dissipation rates from WPRs, as performed in a
companion paper

All data are publicly accessible at the DOE Atmosphere to Electrons Data
Archive and Portal, found at

In observations of turbulence, the inherent fluctuations and noise that an
instrument introduces to the true measurements must be accounted for. Even in
perfectly laminar flow, instrument noise would result in non-zero variance
observations, whether due to the limited accuracy of the measurements or
assumptions made to extract velocity from other raw data, as in the case of
WPRs. The removal of the noise contribution to turbulence observations is
completed in many different ways, depending on the instrument type and its
level of accuracy. For example, since the noise in measurements is
uncorrelated from turbulence,

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

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 from the time series of velocities, nor
any adjustment for errors in spectral widths due to noise. However, expanding
upon the work of

To relate this value to SNR, we use the ratio of power at the peak of the
signal and the power at the integration limits (noise level).

Left blue axis: fractional error of variance from
Eq. (

Katherine McCaffrey completed the primary analysis with the aid of Laura Bianco and James M. Wilczak. Paul Johnston contributed in radar setups and post-processing. Katherine McCaffrey prepared the manuscript with contributions from all co-authors.

The authors declare that they have no conflict of interest.

Thanks are due to Timothy Coleman and Dan Gottas for their roles in data acquisition and processing, to Dave Carter for his help with data processing in POPN4, and to Chris Fairall for many conversations and much wisdom. Katherine McCaffrey was funded by the NRC Research Associateship Postdoctoral Fellowship. The XPIA field program was funded under the US Department of Energy's Atmospheres to Electrons (A2e) program and by NOAA/ESRL. We would like to acknowledge operational, technical, and scientific support for the sonic anemometry provided by NCAR's Earth Observing Laboratory, sponsored by the National Science Foundation. Edited by: A. Clifton Reviewed by: S. Jacoby-Koaly and S. Emeis