Observations of turbulence dissipation rates in the planetary boundary layer
are crucial for validation of parameterizations in numerical weather
prediction models. However, because dissipation rates are difficult to
obtain, they are infrequently measured through the depth of the boundary
layer. For this reason, demonstrating the ability of commonly used wind
profiling radars (WPRs) to estimate this quantity would be greatly
beneficial. During the XPIA field campaign at the Boulder Atmospheric
Observatory, two WPRs operated in an optimized configuration, using high
spectral resolution for increased accuracy of Doppler spectral width,
specifically chosen to estimate turbulence from a vertically pointing beam.
Multiple post-processing techniques, including different numbers of spectral
averages and peak processing algorithms for calculating spectral moments,
were evaluated to determine the most accurate procedures for estimating
turbulence dissipation rates using the information contained in the Doppler
spectral width, using sonic anemometers mounted on a 300 m tower for
validation. The optimal settings were determined, producing a low bias, which
was later corrected. Resulting estimations of turbulence dissipation rates
correlated well (

In the kinetic energy balance of the atmosphere, the components due to
turbulent motions can be the most difficult to predict and require
parameterizations in numerical models to estimate the contributions at scales
smaller than simulations can resolve. Validation of these parameterizations,
however, requires observations that are often not available or are limited in
time and space. Recent work evaluating the sensitivity of a combined
planetary boundary layer (PBL) and surface layer parameterization scheme within the
Weather Research and Forecasting (WRF) model has shown that the model
forecast skill for boundary layer winds is most sensitive to the
parameterization of the turbulent kinetic energy (TKE) dissipation rate,
contributing to 50 % of the variance in an ensemble of forecast runs

Here, we also use a 915 MHz WPR, set up with higher spectral resolution for
more accurate measurements of small spectral widths. Along with several
parameters and post-processing techniques, we investigate the ability of the
915 MHz WPR, as well as a 449 MHz WPR, run nearby to a highly instrumented
300 m tower, to estimate accurate turbulence dissipation rates throughout
the PBL. With these measurements, comparisons can be made on timescales
appropriate for evaluation of numerical weather prediction models,

This paper is organized as follows: Sect. 2 introduces the observations used, including the sonic anemometers and WPRs. Section 3 discusses the methods of calculating dissipation rates from both sets of instruments. Section 4 describes the different post-processing procedures that will be tested for their impact on dissipation rate estimations in Sect. 5 (449 MHz WPR) and Sect. 6 (915 MHz WPR), respectively. Section 7 discusses a useful bias correction. Section 8 describes the uncertainty quantification applied, and Sect. 9 contains the conclusion.

All observations in this study were gathered at the Boulder Atmospheric
Observatory (BAO), operated by the National Oceanic and Atmospheric
Administration's Earth System Research Laboratory. The site has
gently sloping terrain and is located 20 km east of the foothills of the
Front Range of the Rocky Mountains, about 30 km north of Denver, Colorado. A
300 m meteorological tower instrumented with sonic anemometers and
temperature and humidity sensors is located at the site. During the
eXperimental Planetary boundary layer Inter-comparison Assessment
(XPIA) in March to June of 2015, the tower was instrumented with pairs of
sonic anemometers at six heights up to 300 m. Two WPRs were functioning as
well, from 1 March to 30 April 2015, located 600 m from the tower at the BAO
Visitors' Center. A detailed description of the field campaign and all
instruments included can be found in

A normalized Doppler spectrum collected from the 499 MHz WPR during the XPIA field campaign with high spectral resolution. The vertical red line denotes the first moment (mean velocity) and the horizontal red line denotes the spectral width, using the standard peak processing method.

During XPIA, the 300 m tower at the BAO was equipped with twelve Campbell
Scientific CSAT3 sonic anemometers (commonly called sonics), provided by the
Characterizing the Atmospheric Boundary Layer (CABL) program of the National
Center for Atmospheric Research and the University of Colorado. Sonics were
mounted on two booms extending to 154 and 334

Two wind profiling radars, located 600 m southwest of the BAO tower, are
included in the analysis: a 449 MHz radar and a 915 MHz. For each hour, the
systems ran in standard acquisition mode for 25 min for three-dimensional
consensus winds, in radio acoustic sounding system (RASS) mode for 5 min for
measurements of virtual temperature, and in an optimized turbulence mode
(described below) with only a vertically pointed beam for the remaining 30 min. Time series of amplitude and phases (I and Q) were saved during the
30 min of turbulence mode to allow the testing of different post-processing
settings and methods. The radars measure reflectivity in the radial
direction, averaging across a quasi-cylindrical volume with height,

Next, the first and second Doppler spectral moments (mean velocity and
spectral width, respectively) are obtained through peak processing
algorithms, shown in the red vertical and horizontal lines in
Fig.

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.

When modeling the turbulent atmosphere, the budget of the TKE is needed for parameterizing the small-scale processes that
models cannot resolve. The TKE budget can be described as

For all time intervals when

Figure

Velocity spectra for the horizontal (blue) and vertical (red)
velocities with (bright colors with circles) and without (pale colors, dashed
lines) the adjustments, for the northwest sonic anemometer at 150 m on the
BAO tower. A spectral slope of

The method of calculating dissipation rates from WPRs uses the width of the
radar Doppler spectrum (spectral width) rather than the velocity energy
spectrum, like the sonic anemometers' method, since the time resolution of
the velocity moments is insufficient to resolve an inertial range. The
spectral width method is also applied to sodars

Percentage of 2 min dwells (NSPEC

The work by

The dissipation rates were estimated for the 30 min of turbulence mode,
during which the time series of amplitudes and phases (I and Q) were saved,
and different post-processing and moment-calculation methods were
performed. A quantification of the uncertainty in the WPRs' dissipation rates
will be introduced in Sect.

During the calculation process for spectral moments from WPRs, there are several options and parameters to be considered that have the possibility of improving the accuracy of the spectral width measurements. These options include radar setup, time series filtering (of amplitude and phase signal), Doppler spectral processing, and moment calculations, all of which have an effect on the final spectral width used for dissipation rates. Here we will investigate the effect of standard and multiple peak processing methods and noise level thresholds of moment calculations, and spectral averaging on the eddy dissipation rate as determined with the WPRs' spectral width, using the in situ observations from sonic anemometers for comparison.

Once the Doppler spectra are calculated (with wavelet and Gabor filtering
applied) and processed for ground clutter

When using SPP, the noise level threshold that determines the velocity limits in the calculation of the spectral width can be set to either the maximum noise level of the spectrum (SPP max) or the mean noise level (SPP mean). The common choice is the maximum noise level since it is the most conservative for removing noise and produces a more accurate first moment of the spectrum. However, a non-atmospheric signal could create an artificially high maximum noise level, causing the spectral width to be narrowed. The mean noise level in these cases would be more representative of the true noise in the spectrum and potentially allows the measured spectral widths to be more realistic. A comparison of dissipation rates using these three methods (SPP max, SPP mean, and MPP) with the in situ observations from the sonic anemometers will indicate which moment calculation method is most accurate for measuring spectral widths and, consequently, dissipation rates. All other variables in the calculation of dissipation rate are equal across different moment calculation methods, so the accuracy of dissipation rates indicates the accuracy of the spectral width measurements in each method.

Each dwell collected by the 449 MHz WPR spans about 13 s (and the
915 MHz, about 17 s; see Table

With the use of the in situ sonic anemometer observations as the baseline,
the different post-processing techniques presented in
Sect.

Dissipation rates from the sonic anemometer,

Dissipation rates from the sonic anemometer,

When using SPP with either the maximum or mean noise level, averaging over
more than one dwell is immediately an improvement over the shortest dwell
times (Fig.

Scatter plots comparing dissipation rates from the sonic anemometers and WPRs
using the optimized post-processing procedures are shown in
Fig.

Same as Fig.

Same as Fig.

Fractional biases in dissipation rate from all 6 heights of the
915 MHz WPR:

The 915 MHz WPR operating during XPIA was set up to have similar temporal
and spectral resolution as the 449 MHz, but the different systems produce
spectra with different noise levels and slightly different resolutions (see
Table

The overall biases in dissipation rates seen in Figs.

Figure

The second method uses a bias correction dependent on the WPR values, rather
than the sonic, as in the first method. The WPR-dependent bias
(Fig.

The two bias correction methods, with their definitions and
equations of corrections to the observed

Fractional bias in dissipation rate, defined as

Same as Fig.

To determine the dissipation rates that are most impacted by the bias
corrections, Fig.

Fractional bias in dissipation rate (defined as

Observed dissipation rates,

Analyzing the average biases as a function of the WPR-estimated dissipation
rate gives insight into the accuracy of those measurements
(Fig.

Though the two corrections, based on each instrument, are not mathematically
identical, their constant corrections are nearly the reciprocal of one
another. This creates bias corrections that are nearly equal, but since the
corrections are defined by an average, and applied to individual points
before further averaging in Fig.

Applying the same correction methods to the 449 MHz WPR results in similarly
improved dissipation rates, using

Box-and-whisker plots of observed dissipation rates,

These bias corrections were created based on 1 month of data (March) and
show large improvements. However, the applicability of the corrections can be
seen by applying the respective bias corrections for each radar to the
observations taken during April. Figure

Two different methods were used to quantify the uncertainty in the
dissipation rates from the sonic anemometers and the WPRs. For the sonic
anemometers, the error analysis method of

Dissipation rate,

Dissipation rate,

When investigating the accuracy of the bias-corrected WPR measurements,
box-and-whisker plots were made from dissipation rates at all heights
(Fig.

We also note that the lower

An example time series of bias-corrected dissipation rates near 200 m from
both WPRs and sonic anemometers is shown in Fig.

Using an optimized setup of two WPRs during the XPIA field
campaign in March and April 2015, turbulence dissipation rates were
calculated and compared to in situ observations from sonic
anemometers on the 300 m tower at the BAO. Using only the vertically pointing
beam and a large number of FFT points to obtain the Doppler spectra with high
spectral resolution, post-processing methods were compared to determined the
optimal method of estimating dissipation rates from the WPRs. The MPP method of calculating spectral moments showed
inaccurate results, often measuring spectral widths that were far too small,
most likely due to MPP only selecting part of the total atmospheric peak at
high spectral resolution. Using the maximum or mean noise level with the
SPP method showed small differences, but
ultimately the mean noise level was chosen since it produced lower biases in
dissipation rates than the maximum noise level. Analysis of the dwell time,
dependent on the number of spectral averages, showed that, for both the
915 and 449 MHz WPRs, dwell times of approximately 2 min (NSPEC

A simple bias correction was applied to the WPR dissipation rates, based on
the fractional bias between the radar-estimated and sonic-estimated
dissipation rates. A slightly smaller correction was needed for the 915 MHz
WPR, and the constant correction produced improved dissipation rates above
values of

High-vertical-resolution profiles of dissipation rates up to 2 km are
obtainable from the 449 MHz WPR and often up to 1 km from the 915 MHz WPR.
These observations will be very useful for the validation of boundary layer
parameterizations in numerical weather prediction models and reduce the
uncertainty due to these parameters as seen in

Data are available at the A2E Data Archive and Portal at

KM completed the primary analysis with the aid of LB and JW. KM prepared the manuscript with contributions from all co-authors.

This article is part of the special issue “Pushing the limits: The eXperimental Planetary boundary layer Instrumentation Assessment (XPIA) campaign”. It is not associated with a conference.

Thanks are due to Timothy Coleman, Daniel Gottas, Paul Johnston, and Dave Carter for their role in data acquisition and post-processing. Katherine McCaffrey was funded by the NRC 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's CABL project, sponsored by the National Science Foundation. Edited by: Julie Lundquist Reviewed by: two anonymous referees