Despite turbulence being a fundamental transport process in the boundary
layer, the capability of current numerical models to represent it is
undermined by the limits of the adopted assumptions, notably that of local
equilibrium. Here we leverage the potential of extensive observations in
determining the variability in turbulence dissipation rate (

Turbulence within the atmospheric boundary layer is critically important to
transfer heat, momentum and moisture between the surface and the upper
atmosphere

The production of turbulence kinetic energy in the boundary layer mainly
takes place at large scales

Hence, improved turbulence parametrizations are crucially needed to refine
the accuracy of model results at fine horizontal scales.

Estimates of turbulence dissipation rate have been calculated from sonic anemometers on meteorological towers

In this study, we prove the capability of wind Doppler lidars to provide
precise estimates of

To analyze the variability in turbulence dissipation rate, we use data from
the meteorological tower and wind Doppler lidars deployed during the XPIA
field campaign, summarized in

Map of the topography of the region where the XPIA field campaign took place. Contours in

During XPIA, the 300 m BAO meteorological tower

We quantify atmospheric stability from the 5 m tower data in terms of the
Obukhov length

At the base of the BAO tower, a tipping-bucket rain gauge was used to measure
precipitation. We have excluded from our analysis the times within 1 h
from precipitation events (

Several vertical profiling and scanning wind Doppler lidars were deployed at
XPIA. In this study, we focus on three vertical profiling lidars and one
scanning lidar mainly used in vertical staring mode. All these instruments
were co-located approximately

A WINDCUBE version 2 (v2) profiling lidar was deployed by the University of
Colorado Boulder from 12 March to 8 June 2015. This lidar samples
line-of-sight velocity in four cardinal directions with a nominal

Two WINDCUBE version 1 (v1) profiling lidars

Finally, a Halo Photonics Stream Line Doppler scanning lidar

Main technical specifications of the lidars at XPIA used in this study.

Sonic anemometer data can be used to calculate turbulence dissipation rate
with two different methods: the inertial subrange energy spectra method and
the second-order structure function method.

According to Kolmogorov's hypothesis, within
the inertial subrange the velocity increments, expressed as second-order
structure function

As already mentioned, data were excluded for wind
directions waked by the tower. When neither of the two anemometers is
affected by tower wakes,

Turbulence energy spectrum according to Kolmogorov's hypothesis.

Wind Doppler lidars can provide a great improvement of our understanding of
the variability in turbulence dissipation thanks to the ease of their
deployment in different locations and the long measurement range allowed by
several commercial models. To do so, robust methods to estimate

Lidar measurements are inherently affected by signal noise as well as
possible variations in the aerosol fall speeds, which provide additional
contributions to the observed variance. By assuming that the contribution of
all atmospheric flows to the observed line-of-sight variance within the
considered short timescales can be regarded to be of a turbulent nature, the
variance

Although promising, the method to calculate

While the high temporal resolution of sonic anemometers facilitates the
identification of sizable samples within the inertial subrange, for lidars,
the length of the samples used to estimate the variance of the line-of-sight
velocity should be accurately chosen. In fact, the shorter the sampling time,
the higher the measurement error in the estimate of the variance of
line-of-sight velocity would be, because of both higher measurement
uncertainty, which impacts its representativeness

Conversely, if the sampling time is too long, the variance will
incorporate undesired contributions from the large-scale processes, which
would cause a severe underestimation of

Example of the dependence of

Moreover, since different atmospheric stability conditions are inherently
characterized by different turbulence scales

Turbulence energy spectrum for a stable case (

To estimate the appropriate timescales which best balance these competing
factors, we calculate

Median absolute error between

To quantify the difference between sonic and lidar estimates of

As the used sample length increases, the average error in

Timescales which minimize the median absolute error (MAE) in the comparison between

As expected, the larger eddies which characterize unstable conditions
determine the need for a longer timescale to capture the influence of all
the scales included in the inertial subrange, while for stable conditions a
shorter timescale is more appropriate. The median error is higher during
stable conditions (average: MAE

Looking at the variability in the results with height, we find that the
optimal timescales increase with height. At those heights

Once the appropriate timescales have been identified at each height,
considerations about how the error in lidar estimates of

Variability in the minimum median absolute error (calculated for the optimized number of samples at each height
for each atmospheric stability condition) between lidar and sonic anemometer estimates of

For the WINDCUBE lidars, the MAE slightly increases with
height, likely because of the severe reduction of the number of acceptable
measurements at higher levels, and it always stays below 50 %. For the Halo
Stream Line lidar, the median error stays almost constant in the considered
portion of the boundary layer. It is reasonable to explain the higher error
(

Time series from 6 April 00:00 UTC to 10 April 2015 00:00 UTC comparing

Possible sources for the discrepancy found between

Correlation between

The good agreement between data from sonic anemometer and lidars is
confirmed, with unstable conditions showing a better performance (

The availability of multiple sonic anemometers co-located with the lidars at
XPIA has allowed for a direct comparison among

When a comparison with sonic anemometer data is not possible, the appropriate
timescale to use in the lidar retrieval of

Example of power spectral density of the vertical component of the wind speed as measured
by the Halo Stream Line lidar on 11 March 2015 18:05 UTC. The red line represents the fit according
to the spectral model from Eq. (

The transition wavelength

To compare the results from this approach with what we obtain from the
comparison with dissipation rates from the sonic anemometer data, we apply
this technique to the data from the Halo Stream Line for the whole period of
XPIA and calculate the average timescales for different stability conditions
at

The use of spectral models to determine the appropriate sample size to use
when retrieving

Time series from 6 April 00:00 UTC to 10 April 2015 00:00 UTC comparing

The use of spectral models to determine the extension of the inertial
subrange in the lidar spectra produces valid estimates of

Once the capability of the method to provide accurate estimates of

The time series of

Daily climatology of turbulence dissipation rate derived from raw
values from the Halo Stream Line

A general good agreement between the climatology from sonic anemometers and
lidars can be observed. A definite diurnal pattern is evident from each
panel. As expected, the mainly quiescent conditions at night determine low
values of turbulence dissipation rate (

Also, the study of the climatology of

Turbulence dissipation rate (raw values) as a function of height for
different instruments. The variability with height is expressed as percentage
change assuming a reference level of

The plot confirms that turbulence dissipation rate shows most of its
variability with height close to the surface, as also found by

The effect of different atmospheric stability conditions on turbulence
dissipation can be investigated in more detail by relating

Turbulence dissipation rate (raw values at

Different stability conditions systematically change the magnitude of
turbulence dissipation rate, with median

Different wind speed regimes can also have a strong impact on the development
and subsequent dissipation of turbulence. Figure

Turbulence dissipation rate (raw values) as a function of the 2 min average wind speed,
as measured at

For both the sonic anemometer and the WINDCUBE v2 lidar data, a strong
dependence of

The accurate numerical representation of nocturnal low-level jets has a
crucial importance. In fact, this sudden increase in wind speed aloft at
night has been shown to have a primary effect on turbulent transport

Nocturnal low-level jet case study.

A considerable increase in wind speed (up to

Turbulence parametrizations currently used in numerical models have been
proven

We have refined an approach to use wind Doppler lidars to quantify

We have tested our methodology by calculating

This analysis reveals that different stability conditions have a considerable
impact on determining the magnitude of

The results from this dataset represent significant progress towards the
full understanding of how turbulence dissipation varies in the boundary
layer. The promising results of the method we propose to retrieve

The data of the sonic anemometers (Bianco, 2018) and wind Doppler lidars
at the XPIA field campaign are publicly available at

The supplement related to this article is available online at:

JKL and RKN designed and carried out the field measurements. NB performed the data analysis and prepared the figures, in close consultation with JKL. NB wrote the paper, with significant contributions from JKL. All co-authors contributed to refining the paper text.

The authors declare that they have no conflict of interest.

The authors thank Matthieu Boquet and Ludovic Thobois at Leosphere for providing the technical parameters of the WINDCUBE v1 and v2 needed for this analysis. We also appreciate Matthieu Boquet's and Evan Osler's (Renewable NRG) efforts to provide version 2 to the XPIA field campaign. Support for Julie K. Lundquist and Nicola Bodini is provided by the National Science Foundation (AGS-1554055) under the CAREER program. Edited by: Laura Bianco Reviewed by: two anonymous referees