the Creative Commons Attribution 4.0 License.

the Creative Commons Attribution 4.0 License.

# Spatial and temporal variability of turbulence dissipation rate in complex terrain

### Nicola Bodini

### Julie K. Lundquist

### Raghavendra Krishnamurthy

### Mikhail Pekour

### Larry K. Berg

### Aditya Choukulkar

To improve parameterizations of the turbulence dissipation rate (*ϵ*)
in numerical weather prediction models, the temporal and spatial variability
of *ϵ* must be assessed. In this study, we explore influences on the
variability of *ϵ* at various scales in the Columbia River Gorge
during the WFIP2 field experiment between 2015 and 2017. We calculate
*ϵ* from five sonic anemometers all deployed in a ∼4 km^{2}
area as well as
from two scanning Doppler lidars and four profiling
Doppler lidars, whose locations span a ∼300 km wide region.
We retrieve *ϵ* from the sonic anemometers using the second-order
structure function method, from the scanning lidars with the azimuth
structure function approach, and from the profiling lidars with a novel
technique using the variance of the line-of-sight velocity. The turbulence
dissipation rate shows large spatial variability, even at the microscale,
especially during nighttime stable conditions. Orographic features have a
strong impact on the variability of *ϵ*, with the correlation between
*ϵ* at different stations being highly influenced by terrain.
*ϵ* shows larger values in sites located downwind of complex
orographic structures or in wind farm wakes. A clear diurnal cycle in
*ϵ* is found, with daytime convective conditions determining values
over an order of magnitude higher than nighttime stable conditions.
*ϵ* also shows a distinct seasonal cycle, with differences greater
than an order of magnitude between average *ϵ* values in summer and
winter.

- Article
(7221 KB) -
Supplement
(5183 KB) - BibTeX
- EndNote

Numerical weather prediction models currently assume that the generation of
turbulence within a grid cell is equal to the dissipation of turbulence
*ϵ* within the same grid cell. While this assumption, which is
appropriate for homogeneous and stationary flow (Albertson et al., 1997),
can generally be considered valid when adopting a coarse grid
(Lundquist and Chan, 2007; Mirocha et al., 2010), it breaks down
when using models with finer horizontal resolution
(Nakanishi and Niino, 2006; Krishnamurthy et al., 2011; Hong and Dudhia, 2012), as
turbulence can be advected to a different grid cell before being dissipated.
However, the scales at which the assumption of local equilibrium is no longer valid
are currently not well understood, nor is how different
atmospheric and topographic conditions can impact the development and decay
of turbulent structures.

A more accurate representation of turbulence is crucially needed as it represents the fundamental process to transfer heat, momentum, and moisture in the atmospheric boundary layer (Garratt, 1994). Moreover, turbulence controls a wide range of processes with a direct effect on our socioeconomic activities: turbulence has impacts on forest fire development and propagation (Coen et al., 2013), it affects air traffic control with its influence on aviation meteorology and the dissipation of aircraft vortices (Gerz et al., 2005; Thobois et al., 2015), it determines the characteristics and impacts of pollutant dispersion (Huang et al., 2013), and it affects wind energy production and the lifetime of wind turbines themselves (Kelley et al., 2006). Moreover, the turbulence dissipation rate has been shown to have a primary role in the formation of frontal structures (Piper and Lundquist, 2004), the evolution of cyclones (Bister and Emanuel, 1998), and the development of flows in urban areas and other canopies (Baik and Kim, 1999; Lundquist and Chan, 2007). The precision of wind energy forecasting is also highly impacted by the accuracy of the representation of the turbulence dissipation rate. A recent sensitivity study (Yang et al., 2017; Berg et al., 2018) showed that up to 50 % of the variance in the turbine-height wind speed predicted by the Weather Research and Forecasting model (Skamarock et al., 2005) in complex terrain only depends on the accuracy of the parameterization of the turbulence dissipation rate.

Various techniques have been developed to calculate *ϵ* from different instruments.
In general, all the proposed methods are based on the turbulence theory by Kolmogorov (1941),
which represents the decay of turbulence eddies as an energy cascade in the inertial subrange,
until the length scales are small enough for the turbulence kinetic energy to be dissipated by
molecular diffusion in the viscous subrange. Turbulence dissipation can be calculated from
sonic anemometers on meteorological towers (Champagne et al., 1977; Oncley et al., 1996) and
super-high-frequency hot-wire anemometers suspended on tethered lifting systems
(Frehlich et al., 2006; Lundquist and Bariteau, 2015) or flown on aircraft
(Fairall et al., 1980) or UAVs (Lawrence and Balsley, 2013). Remote sensing instruments
can provide additional insights into our understanding of turbulence dissipation by combining
measurements at greater altitudes with their ease of deployment in complex terrain, despite their
potential drawbacks of limited temporal frequency and inherent volume averaging
(Frehlich and Cornman, 2002; Wang et al., 2016). Wind profiling radars (Shaw and LeMone, 2003; McCaffrey et al., 2017a),
profiling lidars, and scanning lidars have all been successfully used to obtain turbulence measurements.
For lidars, different approaches have been developed to retrieve *ϵ*: width of the Doppler
spectrum (Smalikho, 1995; Banakh et al., 1995), line-of-sight velocity
spectrum (Drobinski et al., 2000; O'Connor et al., 2010; Bodini et al., 2018), structure function
(Frehlich, 1994; Banakh et al., 1996; Banakh and Smalikho, 1997; Smalikho et al., 2005; Frehlich et al., 2006; Wulfmeyer et al., 2016; Smalikho and Banakh, 2017),
and range-gate filtering with a sub-grid-scale parameterization scheme (Krishnamurthy et al., 2010).

Here, we retrieve the turbulence dissipation rate from 11 instruments in a
complex terrain region, thus building one of the widest observational
assessments of *ϵ* to date. We explore how topography triggers the
variability of *ϵ* at various temporal and spatial scales. We describe
the WFIP2 field campaign in Sect. 2, and we define the characteristics of
the sonic anemometers and wind profiling and scanning lidars that we use to
estimate *ϵ*. We also describe the methods used to retrieve *ϵ*
from the different instruments, and we further refine and extend a novel
approach to derive *ϵ* from wind profiling lidars. In Sect. 3 we
present the spatial variability of *ϵ* at both the microscale and
mesoscale by comparing the estimates from multiple instruments in different
locations, with particular attention to the impact that topography has on
the spatial evolution of *ϵ*. In doing so, we also assess the
climatology of turbulence dissipation in terms of both diurnal and seasonal
cycles. Section 4 summarizes our results and suggests future work to further
improve our understanding and representation of the turbulence dissipation rate
in the boundary layer.

## 2.1 The WFIP2 field campaign

The Second Wind Forecast Improvement Project (WFIP2) (Shaw et al., 2019), which involved a field campaign (Wilczak et al., 2019) in the US Pacific Northwest between October 2015 and March 2017, was designed to improve numerical weather prediction model forecasts in complex terrain for wind energy applications. A large number of instruments was deployed in the Columbia River Gorge and basin in a region over 500 km wide. In this study, we focus on the evaluation of turbulence dissipation rate from instruments that span an approximately 300 km wide area. Two profiling lidars were located at the western and eastern edges of this region, at Troutdale (the only site on the western side of the Cascades) and Vansycle Ridge, respectively, with an additional scanning lidar located in Boardman (Fig. 1a). A region with a high density of instruments (HD Site in Fig. 1a), approximately ∼20 km wide, was located in the vicinity of the town of Wasco, from which we will analyze data from two wind profiling lidars, one scanning lidar (Fig. 1b), and the sonic anemometers on five meteorological towers (Fig. 1c). Extensive arrays of wind turbines are located on the northern side of the Columbia River and on the southwestern part of the studied region.

Multiple sonic anemometers were located on several meteorological towers at the Physics Site (Wilczak et al., 2019), which represented the finest array of instruments at WFIP2, aimed at having multiple measurements in an area similar in size to a grid cell of a high-resolution numerical weather prediction model. The site, covered by crop fields, is characterized by a moderately complex topography, with terrain elevation spanning from 405 m to 459 m a.s.l. (the elevations of the locations of the meteorological towers used in this study are reported in Table 1). Several wind turbines are located east of the Physics Site. The sonic anemometers used in this project provide 20 Hz measurements of the three components of the wind and virtual temperature at 10 m a.g.l., and they were operational from late March–early April 2016 to late April–mid-May 2017. To account for tower wake effects, data were excluded when the wind direction was within $\pm \mathrm{30}{}^{\circ}$ from the orientation of the tower boom (McCaffrey et al., 2017b). Less than 10 % of the data was excluded due to tower wake contamination.

Data from the sonic anemometers were used to assess atmospheric stability
calculated in terms of the Obukhov length *L*:

where *θ*_{v} is the virtual potential temperature (*K*) calculated from
the virtual temperature measured by the sonic anemometers,
${u}_{*}=({\stackrel{\mathrm{\u203e}}{{u}^{\prime}{w}^{\prime}}}^{\mathrm{2}}+{\stackrel{\mathrm{\u203e}}{{v}^{\prime}{w}^{\prime}}}^{\mathrm{2}}{)}^{\mathrm{1}/\mathrm{4}}$ is the friction velocity
(m s^{−1}), *k*=0.4 is the von Kármán constant, *g*=9.81 m s^{−2}
is the acceleration due to gravity, and
$\stackrel{\mathrm{\u203e}}{{w}^{\prime}{\mathit{\theta}}_{\mathrm{v}}^{\prime}}$ is the kinematic sensible heat flux (m K s^{−1}).
An averaging period of 30 min (De Franceschi and Zardi, 2003; Babić et al., 2012) has been used to apply the
Reynolds decomposition and determine the fluxes. Based on the value of the
Obukhov length, we classify neutral conditions for $L\le -\mathrm{500}$ m
and *L*>500 m, unstable conditions for −500 m < *L*≤0 m, and stable conditions for 0 m $<L\le \mathrm{500}$ m
(Muñoz-Esparza et al., 2012). Neutral conditions were
infrequently recorded (less than 7 % of the time).

A WINDCUBE version 1 (v1) was located in Troutdale (12 m a.s.l.),
about ∼20 km east of Portland, in a relatively flat region at the
Portland–Troutdale Airport at the western edge of the Columbia River Gorge.
The area is semi-urban, with some trees. This type of lidar
(Aitken et al., 2012; Rhodes and Lundquist, 2013) measures line-of-sight
velocity along four cardinal directions with a nominal zenith angle of
28^{∘} and a temporal resolution of about 1 Hz along each
beam direction. The measurements are taken every 20 m from 40 to
220 m a.g.l. The main technical specifications of the instrument are
shown in Table 2.

A second WINDCUBE v1 and a WINDCUBE 200S scanning Doppler lidar were located
at the Wasco Airport (456 m a.s.l.), in an area within the Columbia
basin covered by short grass. The nearby region is characterized by
moderately complex topography in the vicinity of the Columbia River. The
WINDCUBE 200S performed a variety of planned position indicator (PPI),
range-height indicator (RHI), and vertical stare scans within 15 min.
Details on the scan patterns can be found in Choukulkar (2018). For
this instrument we retrieve *ϵ* up to 300 m a.g.l..

A WINDCUBE version 2 (v2) was deployed on a low-grass surface on the top of Gordon Ridge (728 m a.s.l.), on the eastern side of the Cascades. A second v2 was deployed at Vansycle Ridge (542 m a.s.l.), in a site with grazed grass (Yang et al., 2013) about 20 km east of the Wallula Gap, where the Columbia River turns north, thus modifying the main topographic direction of the gorge. Compared to the WINDCUBE version 1, the v2 performs an additional line-of-sight velocity measurement along the vertical, and ∼4 s is required for the beam to complete the five-point scan strategy. The vertical resolution was of 20 m from 40 to 260 m a.g.l. (200 m a.g.l. for the v2 at Vansycle Ridge). Bodini et al. (2018) compared turbulence dissipation retrievals from colocated v1 WINDCUBEs and a WINDCUBE v2 and found a good agreement between the different instruments. Table 2 illustrates the major technical parameters of this lidar.

Finally, a Halo Streamline scanning Doppler lidar was deployed near a
regional airport surrounded by farmland at Boardman (112 m a.s.l.).
The long-range fiber-optic-based scanning Doppler lidar provides 3-D scanning
capabilities and performed a wide range of scans covering the atmospheric
boundary layer over a period of 15 min (Otarola, 2017). In this
analysis, only the 5^{∘} elevation angle scans with a scan rate of 1^{∘} s^{−1}
were used to calculate the turbulence dissipation rate
up to 120 m a.g.l. The other scans within the 15 min time period
were not usable for turbulence calculations due to either fast scan rates
(Frehlich et al., 2006) or low data availability.

For all the instruments, precipitation periods were excluded from the analysis based on measurements at two surface meteorological stations at the Wasco Airport and Troutdale (for the profiling lidar at that location).

## 2.2 Turbulence dissipation rate from sonic anemometer

We estimate the turbulence dissipation rate from the sonic anemometers using the
second-order structure function method, which has been demonstrated
(Muñoz-Esparza et al., 2018) to provide *ϵ* retrievals with a lower
error compared to the commonly used inertial-subrange energy spectrum method.
The second-order structure function *D*_{U} of the horizontal velocity *U* at
the position *x* is defined as a function of the spatial separation *r* as
${D}_{U}\left(r\right)\equiv <\left[U\right(x+r)-U(x){]}^{\mathrm{2}}>$, where $<\cdot >$ denotes an ensemble
average. Within the inertial subrange, Kolmogorov's model
(Kolmogorov, 1941; Frisch, 1995) relates the
second-order structure function with the turbulence dissipation rate
*ϵ*:

where *a* is the Kolmogorov constant, which we set equal to 0.52
(Paquin and Pond, 1971; Sreenivasan, 1995). By invoking
Taylor's frozen turbulence hypothesis (Taylor, 1935), the
spatial separation *r* can be written as temporal separation *τ* so that
*ϵ* can be calculated as

We calculate *ϵ* every 30 s by fitting the Kolmogorov's theoretical
model to the structure function calculated from the sonic anemometer data
using a temporal separation between *τ*=0.1 and *τ*=2 s.
From data inspection, measurements in the chosen time separation
interval lie well within the inertial subrange, and therefore they fulfill
the hypothesis of Kolmogorov's theory. Moreover, the high temporal resolution
of the sonic anemometer suggests an adequate number of data points in this
interval to obtain a robust estimate of the structure function.

## 2.3 Turbulence dissipation rate from wind profiling lidar

Measurements from wind Doppler lidars can extend our understanding of the variability of the turbulence dissipation rate thanks to their relatively easy deployment, even in prohibitive terrain conditions. Moreover, lidars can often provide measurements at higher altitudes compared to most meteorological towers, possibly out of the surface layer.

We follow the approach introduced by O'Connor et al. (2010) and refined by
Bodini et al. (2018) to estimate *ϵ* from the variance of the
line-of-sight velocity measured by the profiling lidars. Assuming locally
homogeneous and isotropic turbulence, the one-dimensional spectrum *S* within
the inertial subrange can be written as a function of the wave number *k* as

where *a*=0.52 is the one-dimensional Kolmogorov constant. By integrating
Eq. (4) over the wavenumber space within the inertial subrange, the
following expression can be found:

where ${\mathit{\sigma}}_{\mathrm{v}}^{\mathrm{2}}$ is the variance (averaged across the different beams) of
the detrended line-of-sight velocity, and *L*_{1} and *L*_{N} are the length
scales that can be used instead of the wavenumbers by invoking Taylor's
frozen turbulence hypothesis (Taylor, 1935). For a single
sample, *L*_{1} can be defined as

where *U* is the horizontal wind speed, *t* is the dwell time, *θ* is
the half-angle divergence of the lidar beam, and *z* the height above ground level. The
second term in Eq. (5) can typically be neglected as Doppler lidars
generally have *θ*<0.1 mrad. For multiple samples, *L*_{N}=*N**L*_{1}, where *N* is the number of samples used in the calculation.

The method relies on the fundamental assumption that the samples used in the
calculation lie within the inertial subrange of turbulence. If longer samples
are used, therefore including contributions from the outer scales, *ϵ*
will be severely underestimated (Bodini et al., 2018). On the other
hand, short samples will undermine the representativeness of the estimation
of the turbulence contribution to variance (Lenschow et al., 1994), and a
higher relative effect of instrumental noise (Lenschow et al., 2000)
will also increase the error. Therefore, the choice of the sampling size *N*
represents a crucial step to obtain accurate estimates of turbulent
quantities, especially in stable conditions (Pichugina et al., 2008).

As shown in Bodini et al. (2018), the appropriate timescales for the
lidar retrievals can be determined in different ways. When colocated sonic
anemometers are available, the optimal values for *N* can be found by tuning
the lidar method with the *ϵ* values derived from the sonic data.
Another possibility is the use of spectral models
(Kaimal et al., 1972; Panofsky, 1978; Olesen et al., 1984; Kristensen et al., 1989)
to fit the experimental spectra from the lidar measurements and determine the
extension of the inertial subrange from the fit
(Tonttila et al., 2015).

In the WFIP2 case, no sonic anemometers colocated with the profiling lidars
were available. Moreover, all the WINDCUBE lidars at WFIP2 operated in
profiling mode using slant beams rather than in a purely vertical stare mode.
Therefore, modeling the spectra of the line-of-sight velocity measured by
these instruments is not trivial, as most of the spectral models are valid
for either the purely horizontal or vertical components of wind speed, and
projecting these models can lead to variance contamination
(Newman et al., 2016). As a consequence, we further extend this method
and we estimate the optimal sample length *N* to use in the retrieval of
*ϵ* by determining the extension of the inertial subrange as the
maximum in the curve representing a local regression of the spectrum of the
line-of-sight velocity measured by the lidars. In doing so, we do not need to
know the precise functional form for the spectrum of the measured radial
velocity in an arbitrary slant direction. Using the dataset described in
Bodini et al. (2018), with sonic anemometers colocated with lidars,
we tested different local regression techniques, and we select the robust
LOESS technique (Cleveland, 1979), with a span of 15 % of the total
number of data points in each spectrum, which provided the best agreement
(*R*^{2}>0.95) with the *ϵ* values obtained from the fine-tuning with
the estimates from the sonic anemometers. In the determination of the maximum
of the local regression curve, we leave out frequencies greater than 0.05 Hz,
which are most affected by instrumental noise
(Frehlich, 2001). The distribution of sample size values we
obtain is between 20 s (5th percentile) and 300 s
(95th percentile). An example of the local regression of an experimental lidar
spectrum at WFIP2 is shown in Fig. 2.

Finally, the contribution due to instrumental noise needs to be considered. The observed variance ${\mathit{\sigma}}_{\mathrm{v}}^{\mathrm{2}}$ in Eq. (5) can be thought of as a combination of three different contributions, which can be considered as independent of one other (Doviak et al., 1993):

where ${\mathit{\sigma}}_{\mathrm{w}}^{\mathrm{2}}$ is the contribution from atmospheric turbulence at the
scales the lidar can measure (Brugger et al., 2016), ${\mathit{\sigma}}_{\mathrm{e}}^{\mathrm{2}}$ is
due to the instrumental noise, and ${\mathit{\sigma}}_{\mathrm{d}}^{\mathrm{2}}$ is related to the variation
in the aerosol terminal fall velocity within the sampled volume, which can
safely be ignored since the particle fall speed is typically very low (<1 cm s^{−1}). The contribution of instrumental noise ${\mathit{\sigma}}_{\mathrm{e}}^{\mathrm{2}}$
can be written as a function of the signal-to-noise ratio (SNR)
(Pearson et al., 2009):

where Δ*ν* is the signal spectral width, and *α* is the ratio of the
lidar photon count to the speckle count (Rye, 1979), which can be
calculated as a function of the bandwidth *B* as $\mathit{\alpha}=\frac{\mathrm{SNR}}{\sqrt{\mathrm{2}\mathit{\pi}}}\frac{B}{\mathrm{\Delta}\mathit{\nu}}$. The accumulated photon count
*N*_{p} can be calculated as *N*_{p}=SNR*n**M*, with *n* the number of lidar
pulses that are averaged to get a profile and *M* the number of points
sampled within a single range gate. Therefore, *ϵ* can be determined
as

with the accurate choice of the appropriate sample length *N*, as described.

## 2.4 Turbulence dissipation rate from scanning Doppler lidar

The turbulence dissipation rate from the scanning Doppler lidars is estimated using the azimuth structure function method (Frehlich et al., 2006; Krishnamurthy et al., 2011). The structure function from the radial velocity estimates can be used to retrieve the turbulence dissipation rate, the integral length scale, and the velocity variance, assuming a theoretical model for isotropic wind fields. In our approach, corrections for turbulence measurements have been considered to address the complications due to the inherent volumetric averaging of radial velocity over each range gate, the noise of the lidar data, and the assumptions required to estimate the effects of smaller scales of motion on turbulence quantities.

Both the scanning lidars have an azimuth scan rate of 1^{∘} s^{−1};
the Halo Streamline has an accumulation time of 1 s, while the WINDCUBE 200S at Wasco has as a time of 0.5 s.

The structure function ${\widehat{D}}_{\mathrm{wgt}}$ of the mean Doppler lidar velocity perturbations, $\widehat{{v}^{\prime}}$, in the azimuth direction is given by

where ΔΦ is the azimuth angular spacing between adjacent Doppler
velocity estimates, and *N*_{s} is the number of velocity measurements for the
sector scan. The estimation error is uncorrelated with the pulse-weighted
velocity because each estimate is produced with different lidar pulses
(assuming no multi-scattering effects); therefore, the velocity error
variance ${\mathit{\sigma}}_{\mathrm{e}}^{\mathrm{2}}\left(R\right)$ is only a function of the range gate
(Krishnamurthy, 2008).

For homogeneous von Kármán turbulence over a two-dimensional plane, the following model (Hinze, 1959; Frehlich et al., 2006) for the structure function is valid:

where *r* denotes the distance along a fixed laser beam, $s=R({\mathit{\varphi}}_{\mathrm{1}}-{\mathit{\varphi}}_{\mathrm{2}})$ is the transverse coordinate, $p=({r}^{\mathrm{2}}+{s}^{\mathrm{2}}{)}^{\mathrm{1}/\mathrm{2}}$ , *L*_{o} is
the outer scale of turbulence, which is proportional to the integral length
scale *L*_{i}, Λ(*x*) is the universal function, and

Assuming that the averaged radial velocity can be written as a function of the instantaneous radial velocity and an effective spatial filter in terms of the pulse-weighting function and range-gate length of the lidar (Frehlich et al., 2006), the Doppler lidar azimuth structure function can be modeled as

where $s=R({\mathit{\varphi}}_{\mathrm{1}}-{\mathit{\varphi}}_{\mathrm{2}})$, *σ* is the standard deviation of the
transverse velocity fluctuations, and ${G}_{\mathrm{a}}(\mathit{\eta},\mathit{\mu},\mathit{\zeta})$ is the derived
model based on weighted velocity estimates and the von Kármán model, as
provided in Eq. (46) of Frehlich et al. (2006) and fully
derived in Krishnamurthy (2008).

The parameters *σ* and *L*_{o} are estimated by minimizing the error
between the lidar-derived structure function ${\widehat{D}}_{\mathrm{wgt}}(R,kR\mathrm{\Delta}\mathrm{\Phi},\mathit{\theta})$ and the model estimates ${\widehat{D}}_{\mathrm{wgt}}(s,\mathit{\sigma},{L}_{\mathrm{o}})$. The dissipation rate can then be estimated by
(Hinze, 1959)

Although the assumption of homogeneous isotropic turbulence is not valid for
every condition, the effect of anisotropy on the azimuth structure function
is small (Krishnamurthy et al., 2011). Therefore, with an accurate choice of
the scan angle and vertical resolution, the isotropic assumption can be
relaxed in this algorithm for complex terrain applications. Using the
selected scans described in the previous section, we retrieve *ϵ* from
the WINDCUBE 200S and the Halo Streamline lidars every 15 min.

The turbulence dissipation rate has been retrieved from the five sonic
anemometers at the Physics Site, four profiling lidars, and two scanning
lidars. This extensive network of measurements at WFIP2 allows for a unique
assessment of the spatial and temporal variability, at various scales, of
*ϵ* in complex terrain.

## 3.1 Microscale variability of turbulence dissipation rate in complex terrain

The analysis of the retrievals of turbulence dissipation rate from the five
10 m sonic anemometers, all located within a ∼4 km^{2} area at
the Physics Site (Fig. 1c), allows insight into the
microscale variability of *ϵ* in the surface layer in complex terrain.

To gain first insights on the evolution of *ϵ* within the Physics
Site, a portion of the time series of *ϵ* and correspondent wind speed
from the five sonic anemometers can be analyzed (Fig. 3).

The turbulence dissipation rate exhibits variability of at least 3 orders of
magnitude over a diurnal cycle, with higher values generally observed during
daytime conditions and lower values at night. However, the magnitudes
observed in the diurnal cycle of *ϵ* show considerable variability
among different days, with the minimum values during the night of
calendar day 176 when high winds were recorded, similar to the maximum
magnitudes observed during daytime convective conditions on day 178 when the
wind was more quiescent. Moreover, although the five considered towers are
all located within a ∼4 km^{2} area, *ϵ* still shows
considerable variability among the different sonic anemometers. This
variability is particularly accentuated at night (especially for the night
between calendar days 178 and 179), when *ϵ* varies more than
an order of magnitude within the considered microscale region. This
variability can be connected to the intermittent nature of the turbulence
dissipation rate, for which a multifractal theory has been developed
(Frisch, 1995).

Given this distinct variability of *ϵ* at different times of the day,
the impact of atmospheric stability conditions can be additionally
investigated throughout the ∼13 months of measurements at the Physics
Site. To understand whether a systematic difference in the microscale
variability of *ϵ* during different atmospheric stability conditions
can be found, we calculated, at each time, the ratio between *ϵ* from
each sonic anemometer and the average *ϵ* (at that time) from all
five sonic anemometers. We then classified these ratios based on atmospheric
stability, quantified as the median value of the Obukhov length from the five
sonic anemometers. For each sonic anemometer, we estimate the variability of
*ϵ* in different stability conditions in terms of the standard
deviation of the distribution of these *ϵ* ratios, as reported in
Table 3.

For all five sonic anemometers, the standard deviation is higher during
stable conditions compared to unstable conditions, with mean (across the five
anemometers) values of 0.83 and 0.74, respectively. On average, in the
surface layer, at the small spatial scales sampled within the Physics Site,
*ϵ* shows a 12 % larger variability during nighttime stable conditions
compared to daytime convective conditions.

Along with atmospheric stability, topographic features can have an impact on the variability of the turbulence dissipation rate, and the high-density array of meteorological towers at the Physics Site represents an ideal candidate to explore this relation at the microscale. Figure 4 shows the wind rose obtained from the 10 m sonic anemometer on the P03 meteorological tower at the Physics Site (the wind roses from the four other sonic anemometers are qualitatively similar to the one shown here and are reported in the Supplement). The prevailing wind directions at the Physics Site follow the dominant west–east direction of the Columbia River Gorge.

As the wind at the site is almost always slightly southwesterly, it is
interesting to study whether differences in turbulence dissipation rate can
be found as the wind flows from the western to the eastern sides of the
Physics Site. An analysis of the topography of the region reveals two
distinct sets of terrain characteristics. The terrain on the west of the
subgroup of towers on the western side of the Physics Site (towers P03 and
P09) has slopes that reach 60 %, with average slopes larger than 6 %.
In
contrast, the remaining towers east of this cluster, which we will refer to
as “eastern” (towers P04, P05, and P10), are surrounded by a terrain with
more gentle slopes, which are on average less than 6 % and never exceed 25 %.
We note that the far eastern side of the Physics Site includes an 80 m tower
(Wilczak et al., 2019). We can first assess the topographic impact on the
microscale variability of *ϵ* in terms of the distribution of the
ratio between the mean *ϵ* from the groups of sonic anemometers on the
two sides of the Physics Site (Fig. 5e).

A systematic bias is observed in the values of *ϵ* on the two sides of
the Physics Site, with the median value of turbulence dissipation on the
eastern side being only 73 % of the median *ϵ* on the western side.
These differences may be due to the drainage flows and channeling frequently
observed at night at this site. The presence of steep topography increases
the variability of the turbulence dissipation rate, even at small spatial scales
(of the order of 2 km in this case).

To confirm this result, the correlation between *ϵ* retrievals from
all the possible pairs of meteorological towers at the Physics Site can be
studied (Fig. 6a).

Stations that are close by (separation <1 km) and on the same side of the
Physics Site show high correlation coefficients (*R*>0.75). When considering pairs
of stations on opposite sides of the Physics Site (with separations between 1
and 2 km), we find smaller correlations (*R*<0.7) for the turbulence dissipation
rate, as is reasonable since the spatial separation between the towers increases.
However, when looking at the correlation between the retrievals from the two
sonic anemometers on the western side of the Physics Site, which have the
highest separation (∼2.2 km), we still find a relatively high correlation
coefficient (*R*>0.7). Larger separations do not represent the only dominant
factor in determining a progressive reduction of the coefficient of correlation,
as the specific interaction between the atmospheric flow and the topographic
features in complex terrain seems to be capable of modifying the spatial
evolution of correlation between turbulence dissipation at different locations.

The relationship between the correlation coefficient and separation can also
provide confirmation of the larger variability of *ϵ* observed
during stable conditions. When calculating the correlation coefficient
between *ϵ* values classified in stable and unstable conditions,
calculated in terms of the median value of the Obukhov length (Fig. 6b),
we find systematically larger values of *R*
during unstable conditions compared to stable conditions at every spatial
separation. During quiescent stable conditions, the increased variability of
*ϵ* even at the microscale determines a reduced correlation throughout
the site. On the other hand, when considering the evolution of the
correlation coefficient as a function of the elevation difference among the
meteorological towers, no systematic trend can be found (plot shown in the
Supplement).

Finally, the temporal variability of the turbulence dissipation rate at the
microscale can be assessed in terms of the annual cycle of *ϵ*.
Increased daytime convection combined with stronger, on average, winds during
the summer causes larger turbulent mixing, which in turn leads to higher
values of dissipation rates compared to winter months. Figure 7a
quantifies this process by showing how the median value of
*ϵ* varies as a function of the month of the year for each of the
five stations at the Physics Site. The annual cycle of wind speed is shown in
the Supplement.

*ϵ* shows a clear annual cycle in the surface layer, with median
*ϵ* values over an order of magnitude larger in summer than winter at
all five locations considered within the Physics Site. As a consequence,
the interquartile range of *ϵ* also reveals an annual cycle (Fig. 7b),
with a larger range of variability in summer than
winter, again with differences of orders of magnitude.

## 3.2 Mesoscale variability of turbulence dissipation rate in complex terrain

While the analysis of the heavily instrumented Physics Site provides a unique
long-term dataset to explore the microscale variability of the turbulence
dissipation rate in the surface layer, the four wind profiling lidars and the
two scanning lidars allow for an evaluation of the variability of *ϵ*,
at higher altitudes relevant for wind energy, in a region spanning ∼300 km.

The annual cycle in the turbulence dissipation rate found at the Physics Site can
also be detected from the retrievals at higher altitude from the lidars at
the mesoscale. Figure 8 shows the time series of *ϵ* from
the different lidars at 100 m a.g.l., with a low-pass filter (15-day
moving window) applied to filter out the high-frequency and diurnal
fluctuations and focus on the seasonal trend. For the lidars at Gordon Ridge
and at Vansycle Ridge, which were deployed for more than a year, two time
series are plotted for the overlapping calendar days from different years.
The time series of the seasonal cycle of wind speed for the different lidars
is included in the Supplement.

The time series confirm that turbulence dissipation shows a distinct seasonal
variability: *ϵ* is, on average, much higher during the summer, when
strong convection increases turbulence production and consequently
dissipation. Average *ϵ* values during winter are about 1 order of
magnitude lower than what is observed in summer. Measurement records longer
than a single year would be beneficial to filter out possible variations of
*ϵ* linked with specific weather conditions, which, together with snow
melting on the ground, possibly impacted the abrupt increase in average
*ϵ* values at Gordon Ridge in the spring.

Moreover, the smoothed time series also reveals how the turbulence dissipation
rate at Boardman and Gordon Ridge is, except for winter months, much larger
than at the other locations, with the average time series at the other
locations showing, on average, almost 1 order of magnitude lower values of
*ϵ*. To explore why *ϵ* shows much larger values at these
locations, Fig. 9 shows the wind roses and the correspondent
roses of turbulence dissipation rate at 100 m a.g.l. for the
WINDCUBE v2 and the Halo Streamline lidar.

At Gordon Ridge, westerly winds are the prevailing pattern, with some
northeasterly winds being the second most common situation. The highest
values for *ϵ* are measured during westerly wind conditions, while
cases with easterly winds rarely have $\mathit{\u03f5}>{\mathrm{10}}^{-\mathrm{3}}$ m^{2} s^{−3}.
When the wind flows from the west, the location of the WINDCUBE v2
lidar is at the easternmost edge of an area (∼6 km wide) with
a particularly complex topography, where the Deschutes River (tributary of
the Columbia) shapes a steep valley, with terrain slopes that locally exceed
70 % (see map in the Supplement).

With the dominant southwesterly wind, the lidar at Boardman turns out to be
located downwind (about 15 km) of a large wind farm. Wind farm
wakes are associated with reduced wind speed and increased turbulence
(Tennekes and Lumley, 1972), which can have important impacts on wind energy
production downwind (Lissaman, 1979; Nygaard, 2014). Wind speed deficits
from wind farm wakes have been observed using SAR
(Christiansen and Hasager, 2005; Hasager et al., 2006), radars
(Hirth et al., 2015), and aircraft measurements (Platis et al., 2018)
up to 25 km downwind of the plants. Systematic turbulence
measurements that far downwind of wind farms have not yet been made. However,
turbulence dissipation measurements 2–3 rotor diameters in the wake of a
single turbine (Lundquist and Bariteau, 2015) showed an elevated level of
*ϵ*. Therefore, the increased dissipation aloft observed at Boardman
is likely due to the increased turbulence aloft in the wind farm wake. Wind
roses and turbulence dissipation roses for the other lidars are included in
the Supplement.

The seasonal variability of turbulence dissipation can be additionally
investigated by considering the differences in the average daily conditions
of *ϵ* throughout the year. Figures 10 and
11 show the average diurnal climatology of the turbulence
dissipation rate at the various locations of the four profiling lidars and
the two scanning lidars, respectively. The left column shows the average
climatology for the summer, calculated as average conditions from 1 June to
31 August. For the profiling lidars at Gordon Ridge and Vansycle Ridge and
the scanning lidar at Wasco, which were also deployed during winter months,
the panels on the right show the average daily cycle for the winter
using *ϵ* retrievals from 1 December to the end of February.

For all the lidars, we neglect the heights at which less than 15 % of data
within the considered season are available (the complete data availability is
shown in the Supplement). In all the locations, turbulence dissipation rate
shows a clear diurnal cycle, with higher values during daytime convective
conditions and lower values at night, with differences greater than
1 order of magnitude, especially in summer. The intercomparison between the
plots from the different lidars also confirms the impact of topography in
determining much higher average values of *ϵ* at Gordon Ridge compared
to what is recorded at the other locations. In particular, daytime summer
values are about 1 order of magnitude higher than what is found from the
other lidars. At Boardman, large average values of dissipation are found
aloft at night. In fact, the increased turbulence in the wind farm wake can
be further advected during nighttime stable periods, when stronger
stratification is found in the boundary layer. The comparison between the
summer climatologies (left panels) with the winter ones (right panels)
reveals how larger values of *ϵ* are found during the summer compared
to what is found in the wintertime diurnal climatology, when daytime
*ϵ* values are about 2 to 3 orders of magnitude lower, and with
a much weaker difference between daytime and nighttime average conditions. It
is reasonable to expect that the increased diurnal convection during the
summer months determines much stronger turbulent mixing, which in turn
causes higher values of turbulence dissipation.

Although turbulence is a fundamental transport mechanism in the atmospheric
boundary layer, current numerical weather prediction models are limited in
their representation of turbulence, for which a local equilibrium between
the production and dissipation (*ϵ*) of turbulence is assumed. The error
introduced by the parameterization of *ϵ* has been shown to be
responsible for up to 50 % of the variance of hub-height wind speed predicted
by models. Detailed study of observations in the surface layer has
great potential for reducing the uncertainty in our understanding of
the turbulence dissipation rate. Although methods to retrieve *ϵ*, at
least from in situ measurements, have been known for decades, comprehensive
analysis of the spatial and temporal variability of *ϵ* using data
from instruments covering wide regions had not been fully explored to date.
In this study we have presented an extensive assessment of the variability,
both in space and time, of the turbulence dissipation rate in complex terrain at
both the microscale and mesoscale using measurements from both in situ and
remote sensing instruments. The impact of topography and other forcings, like
large wind farms, on the variability of *ϵ* has been captured at the
different sampled scales.

The turbulence dissipation rate has been calculated from five 10 m sonic
anemometers, four wind profiling lidars, and two scanning lidars deployed at
the WFIP2 field campaign in the Columbia River Gorge and basin from fall 2015
to spring 2017. The sonic anemometers were all located in an area with an
extension of approximately 2 km × 2 km, and they
therefore allow for an assessment of the variability of *ϵ* in the
surface layer at the microscale. More homogeneous turbulence across the
investigated region is caused by convective mixing during the day. On the
other hand, considerable differences (up to 1 order of magnitude) in
*ϵ* are found at night when comparing retrievals of *ϵ* from
the different meteorological towers. On average, *ϵ* is 12 % more
variable during nighttime stable conditions than during unstable convective
conditions. Systematic differences emerged from *ϵ* measured on the
western and eastern sides of the Physics Site, the former being located
downwind of terrain with larger slopes compared to the latter, thus
suggesting the possible impact of terrain slope in triggering the variability
of *ϵ*. The change in correlation between *ϵ* in different
locations is not fully determined purely by spatial separation, as
topographic features maintain an importance in influencing it. Therefore, the
representation of the turbulence dissipation rate in complex terrain, especially
during nighttime stable conditions, needs to be extremely localized to fully
capture the turbulence variability in the surface layer.

The variability of *ϵ* at the mesoscale can be analyzed from the 100 m
altitude retrievals from the four wind profiling lidars and the two scanning
lidars, which were deployed over a region ∼300 km wide. For
the profiling lidars, the retrieval approach proposed in
Bodini et al. (2018) has been further refined here and tested to
derive *ϵ* without the need for in situ measurements colocated with
the lidars. The profiling lidar located at the topographically complex Gordon
Ridge site systematically detected *ϵ* values which, on average, were
over 1 order of magnitude higher than what was measured by the profiling
lidar deployed in the gentler Troutdale, Wasco Airport, and Vansycle Ridge
sites. The dominant westerly winds at the site resulted in the location of
this lidar being on the downwind edge of an orographic complex, therefore
experiencing a strong increase in turbulence production and consequently
dissipation. Similarly, the scanning lidar located at Boardman showed higher
values of *ϵ* due to increased turbulence in the wake of a wind
farm.

The extensive duration of the WFIP2 field campaign has allowed for the
evaluation of the annual cycle of *ϵ*: the increased convective mixing
in summer determines higher values of *ϵ* compared to the typically
more quiescent winter conditions, with an average difference that can reach
1 order of magnitude, both at the microscale and at the mesoscale, in the
surface layer and above. We have determined the impact of this seasonal cycle
on the average diurnal climatology of *ϵ*. Overall, *ϵ* is, on
average, up to 3 orders of magnitude higher in summer compared to winter.
The diurnal cycle, with higher values of *ϵ* during daytime convective
conditions and lower values at night, is much stronger during the summer
when diurnal differences in *ϵ* values are about 2 orders of
magnitude, while the reduced daytime convection during wintertime leads to a
more uniform average daily climatology, with less than 1 order of magnitude
of difference between daytime and nighttime values of *ϵ*.

Future work can explore and compare the variability of *ϵ* from other
datasets in different topographic conditions, as well as in the offshore
environment
(Peña et al., 2009; Canadillas et al., 2010; Türk and Emeis, 2010).
Assessing the spatial and temporal variability of *ϵ* within a typical
grid cell of a mesoscale model will provide further insights into the
validity of sub-grid-scale *ϵ* parameterization schemes during various
atmospheric stability conditions. As this variability appears to be dependent
on several different atmospheric and topographic factors, complex techniques
are likely needed to provide accurate spatial representations of *ϵ*
over a mesoscale grid. Sophisticated tools such as physics-driven machine-learning techniques
(Sharma et al., 2011; Xingjian et al., 2015; Alemany et al., 2018; Gentine et al., 2018)
are paving the path to accurately capture the microscale variability of *ϵ* in
mesoscale models.

The data from the sonic anemometers and wind Doppler lidars at the WFIP2 field campaign are publicly available at https://a2e.energy.gov/data (last access: 27 March 2017).

The supplement related to this article is available online at: https://doi.org/10.5194/acp-19-4367-2019-supplement.

JKL, LKB, MP, and AC helped design and carry out the field measurements. NB analyzed the data from the sonic anemometers and the profiling lidars and made the figures, in close consultation with JKL. RK analyzed the data from the scanning lidars. NB wrote the paper, with significant contributions from JKL and RK. All the coauthors contributed to refining the paper text.

The authors declare that they have no conflict of interest.

The authors thank Josh Aikins, Joseph Lee, Clara St. Martin, Jessica Tomaszewski, and Rochelle Worsnop for helping with the deployment of the profiling lidars at Troutdale, Wasco, and Gordon Ridge. The authors thank David Cook for deploying some of the 10 m meteorological towers whose data have been used in this work. The authors also thank Chris Hocut from the Army Research Laboratory and Harindra J. Fernando from the University of Notre Dame for providing the scanning lidar data at Boardman. The authors thank Alan Brewer, Scott Sandberg, and Ann Weickmann for deploying the NOAA WINDCUBE 200S scanning lidar at Wasco. The authors also thank Sonia Wharton at the Lawrence Livermore National Laboratory for providing data from the lidar at Vansycle Ridge. LLNL funding came from A2e Mesoscale Physics and Inflow: WFIP2 (project no. 01.03.1.302), U.S. DOE Office of Energy Efficiency and Renewable Energy Wind Energy Technologies. The authors appreciate Matthieu Boquet's and Ludovic Thobois' efforts to provide some of the technical specifications of the WINDCUBE v1 and v2 used in our analysis. Julie K. Lundquist and NB are supported by the National Science Foundation (AGS-1554055) under the CAREER program. Raghavendra Krishnamurthy is supported by internal funds from the University of Notre Dame for contributions to this paper. Larry K. Berg and Mikhail Pekour were supported by the Department of Energy, Office of Energy Efficiency and Renewable Energy Wind Power Program. The Pacific Northwest National Laboratory is operated for the DOE by the Battelle Memorial Institute under contract DE-A06-76RLO1830. This work was authored (in part) by NREL, operated by the Alliance for Sustainable Energy, LLC, for the U.S. DOE under contract no. DE-AC36-08GO28308, with funding provided by the U.S. DOE Office of Energy Efficiency and Renewable Energy Wind Energy Technologies.

This paper was edited by Ken Carslaw and reviewed by three anonymous referees.

Aitken, M. L., Rhodes, M. E., and Lundquist, J. K.: Performance of a wind-profiling lidar in the region of wind turbine rotor disks, J. Atmos. Ocean. Tech., 29, 347–355, https://doi.org/10.1175/JTECH-D-11-00033.1, 2012. a

Albertson, J. D., Parlange, M. B., Kiely, G., and Eichinger, W. E.: The average dissipation rate of turbulent kinetic energy in the neutral and unstable atmospheric surface layer, J. Geophys. Res.-Atmos., 102, 13423–13432, 1997. a

Alemany, S., Beltran, J., Perez, A., and Ganzfried, S.: Predicting Hurricane Trajectories using a Recurrent Neural Network, arXiv preprint, arXiv 1802.02548, 2018. a

Babić, K., Bencetić Klaić, Z., and Večenaj, Ž.: Determining a turbulence averaging time scale by Fourier analysis for the nocturnal boundary layer, Geofizika, 29, 35–51, 2012. a

Baik, J.-J. and Kim, J.-J.: A numerical study of flow and pollutant dispersion characteristics in urban street canyons, J. Appl. Meteorol., 38, 1576–1589, 1999. a

Banakh, V. and Smalikho, I.: Determination of the turbulent energy dissipation rate from lidar sensing data, Atmospheric and Oceanic Optics c/c of Optika Atmosfery I Okeana, 10, 295–302, 1997. a

Banakh, V., Werner, C., Köpp, F., and Smalikho, I.: Measurement of the turbulent energy dissipation rate with a scanning Doppler lidar, Atmospheric and Oceanic Optics c/c of Optika Atmosfery I Okeana, 9, 849–853, 1996. a

Banakh, V. A., Smalikho, I. N., Köpp, F., and Werner, C.: Representativeness of wind measurements with a CW Doppler lidar in the atmospheric boundary layer, Appl. Opt., 34, 2055–2067, 1995. a

Berg, L. K., Liu, Y., Yang, B., Qian, Y., Olson, J., Pekour, M., Ma, P.-L., and Hou, Z.: Sensitivity of Turbine-Height Wind Speeds to Parameters in the Planetary Boundary-Layer Parametrization Used in the Weather Research and Forecasting Model: Extension to Wintertime Conditions, Bound.-Lay. Meteorol., 170, 1–12, 2018. a

Bister, M. and Emanuel, K. A.: Dissipative heating and hurricane intensity, Meteorol. Atmos. Phys., 65, 233–240, 1998. a

Bodini, N., Lundquist, J. K., and Newsom, R. K.: Estimation of turbulence dissipation rate and its variability from sonic anemometer and wind Doppler lidar during the XPIA field campaign, Atmos. Meas. Tech., 11, 4291–4308, https://doi.org/10.5194/amt-11-4291-2018, 2018. a, b, c, d, e, f, g

Brugger, P., Träumner, K., and Jung, C.: Evaluation of a procedure to correct spatial averaging in turbulence statistics from a Doppler lidar by comparing time series with an ultrasonic anemometer, J. Atmos. Ocean. Tech., 33, 2135–2144, 2016. a

Canadillas, B., Bégué, A., and Neumann, T.: Comparison of turbulence spectra derived from LiDAR and sonic measurements at the offshore platform FINO1, in: Proceedings of the 10th German Wind Energy Conference, DEWEK, 2010. a

Champagne, F., Friehe, C., LaRue, J., and Wynagaard, J.: Flux measurements, flux estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land, J. Atmos. Sci., 34, 515–530, 1977. a

Choukulkar, A.: Lidar-ESRL WindCube 200S, Wasco Airport-Reviewed Data, Tech. rep., Atmosphere to Electrons (A2e) Data Archive and Portal, Pacific Northwest National Laboratory, PNNL, available at: https://a2e.energy.gov/data (last access: 27 March 2019), 2018. a

Christiansen, M. B. and Hasager, C. B.: Wake effects of large offshore wind farms identified from satellite SAR, Remote Sens. Environ., 98, 251–268, 2005. a

Cleveland, W. S.: Robust locally weighted regression and smoothing scatterplots, J. Am. Stat. Assoc., 74, 829–836, 1979. a

Coen, J. L., Cameron, M., Michalakes, J., Patton, E. G., Riggan, P. J., and Yedinak, K. M.: WRF-Fire: coupled weather-wildland fire modeling with the weather research and forecasting model, J. Appl. Meteorol. Clim., 52, 16–38, 2013. a

De Franceschi, M. and Zardi, D.: Evaluation of cut-off frequency and correction of filter-induced phase lag and attenuation in eddy covariance analysis of turbulence data, Bound.-Lay. Meteorol., 108, 289–303, 2003. a

Doviak, Richard J.: Doppler radar and weather observations, Courier Corporation, 2006. a

Drobinski, P., Dabas, A. M., and Flamant, P. H.: Remote measurement of turbulent wind spectra by heterodyne dopplerlidar technique, J. Appl. Meteorol., 39, 2434–2451, 2000. a

Fairall, C., Markson, R., Schacher, G., and Davidson, K.: An aircraft study of turbulence dissipation rate and temperature structure function in the unstable marine atmospheric boundary layer, Bound.-Lay. Meteorol., 19, 453–469, 1980. a

Frehlich, R.: Coherent Doppler lidar signal covariance including wind shear and wind turbulence, Appl. Opt., 33, 6472–6481, 1994. a

Frehlich, R.: Estimation of velocity error for Doppler lidar measurements, J. Atmos. Ocean. Tech., 18, 1628–1639, 2001. a

Frehlich, R. and Cornman, L.: Estimating spatial velocity statistics with coherent Doppler lidar, J. Atmos. Ocean. Tech., 19, 355–366, 2002. a

Frehlich, R., Meillier, Y., Jensen, M. L., Balsley, B., and Sharman, R.: Measurements of boundary layer profiles in an urban environment, J. Appl. Meteorol. Clim., 45, 821–837, 2006. a, b, c, d, e, f, g

Frisch, U.: Turbulence: the legacy of A. N. Kolmogorov, Cambridge University Press, 298 pp., 1995. a, b

Garratt, J. R.: The atmospheric boundary layer, Earth-Sci. Rev., 37, 89–134, 1994. a

Gentine, P., Pritchard, M., Rasp, S., Reinaudi, G., and Yacalis, G.: Could machine learning break the convection parameterization deadlock?, Geophys. Res. Lett., 45, 5742–5751, 2018. a

Gerz, T., Holzäpfel, F., Bryant, W., Köpp, F., Frech, M., Tafferner, A., and Winckelmans, G.: Research towards a wake-vortex advisory system for optimal aircraft spacing, C. R. Phys., 6, 501–523, 2005. a

Hasager, C. B., Barthelmie, R. J., Christiansen, M. B., Nielsen, M., and Pryor, S.: Quantifying offshore wind resources from satellite wind maps: study area the North Sea, Wind Energy, 9, 63–74, 2006. a

Hinze, J.: Turbulence: An introduction to its mechanisms and theory, Mech. Eng., Mcgraw-Hill, 1st Edition, 586 pp., 1959. a, b

Hirth, B. D., Schroeder, J. L., Gunter, W. S., and Guynes, J. G.: Coupling Doppler radar-derived wind maps with operational turbine data to document wind farm complex flows, Wind Energy, 18, 529–540, 2015. a

Hong, S.-Y. and Dudhia, J.: Next-generation numerical weather prediction: Bridging parameterization, explicit clouds, and large eddies, B. Am. Meteorol. Soc., 93, ES6–ES9, 2012. a

Huang, K., Fu, J. S., Hsu, N. C., Gao, Y., Dong, X., Tsay, S.-C., and Lam, Y. F.: Impact assessment of biomass burning on air quality in Southeast and East Asia during BASE-ASIA, Atmos. Environ., 78, 291–302, 2013. a

Kaimal, J. C., Wyngaard, J., Izumi, Y., and Coté, O.: Spectral characteristics of surface-layer turbulence, Q. J. Roy. Meteor. Soc., 98, 563–589, 1972. a

Kelley, N. D., Jonkman, B., and Scott, G.: Great Plains Turbulence Environment: Its Origins, Impact, and Simulation, Tech. Rep., National Renewable Energy Laboratory (NREL), Golden, CO, available at: https://www.nrel.gov/docs/fy07osti/40176.pdf (last access: 27 March 2019), 2006. a

Kolmogorov, A. N.: Dissipation of energy in locally isotropic turbulence, in: Dokl. Akad. Nauk SSSR, 32, 16–18, 1941. a, b

Krishnamurthy, R.: Retrieval of the dissipation of turbulent kinetic energy from coherent Doppler lidar data, Master's thesis, Arizona State University, 102 pp., 2008. a, b

Krishnamurthy, R., Calhoun, R., and Fernando, H.: Large-Eddy simulation-based retrieval of dissipation from coherent Doppler Lidar data, Bound.-Lay. Meteorol., 136, 45–57, 2010. a

Krishnamurthy, R., Calhoun, R., Billings, B., and Doyle, J.: Wind turbulence estimates in a valley by coherent Doppler lidar, Meteorol. Appl., 18, 361–371, 2011. a, b, c

Kristensen, L., Lenschow, D., Kirkegaard, P., and Courtney, M.: The spectral velocity tensor for homogeneous boundary-layer turbulence, Boundary Layer Studies and Applications, Springer, 149–193, 1989. a

Lawrence, D. A. and Balsley, B. B.: High-resolution atmospheric sensing of multiple atmospheric variables using the DataHawk small airborne measurement system, J. Atmos. Ocean. Tech., 30, 2352–2366, 2013. a

Lenschow, D., Mann, J., and Kristensen, L.: How long is long enough when measuring fluxes and other turbulence statistics?, J. Atmos. Ocean. Tech., 11, 661–673, 1994. a

Lenschow, D. H., Wulfmeyer, V., and Senff, C.: Measuring second-through fourth-order moments in noisy data, J. Atmos. Ocean. Tech., 17, 1330–1347, 2000. a

Lundquist, J. K. and Bariteau, L.: Dissipation of Turbulence in the Wake of a Wind Turbine, Bound.-Lay. Meteorol., 154, 229–241, 2015. a, b

Lundquist, J. K. and Chan, S. T.: Consequences of urban stability conditions for computational fluid dynamics simulations of urban dispersion, J. Appl. Meteorol. Clim., 46, 1080–1097, 2007. a, b

McCaffrey, K., Bianco, L., and Wilczak, J. M.: Improved observations of turbulence dissipation rates from wind profiling radars, Atmos. Meas. Tech., 10, 2595–2611, https://doi.org/10.5194/amt-10-2595-2017, 2017a. a

McCaffrey, K., Quelet, P. T., Choukulkar, A., Wilczak, J. M., Wolfe, D. E., Oncley, S. P., Brewer, W. A., Debnath, M., Ashton, R., Iungo, G. V., and Lundquist, J. K.: Identification of tower-wake distortions using sonic anemometer and lidar measurements, Atmos. Meas. Tech., 10, 393–407, https://doi.org/10.5194/amt-10-393-2017, 2017b. a

Mirocha, J., Lundquist, J., and Kosović, B.: Implementation of a nonlinear subfilter turbulence stress model for large-eddy simulation in the Advanced Research WRF model, Mon. Weather Rev., 138, 4212–4228, 2010. a

Muñoz-Esparza, D., Cañadillas, B., Neumann, T., and van Beeck, J.: Turbulent fluxes, stability and shear in the offshore environment: Mesoscale modelling and field observations at FINO1, J. Renew. Sustain. Ener., 4, 063136, https://doi.org/10.1063/1.4769201, 2012. a

Muñoz-Esparza, D., Sharman, R. D., and Lundquist, J. K.: Turbulence dissipation rate in the atmospheric boundary layer: Observations and WRF mesoscale modeling during the XPIA field campaign, Mon. Weather Rev., 146, 351–371, 2018. a

Nakanishi, M. and Niino, H.: An improved Mellor–Yamada level-3 model: Its numerical stability and application to a regional prediction of advection fog, Bound.-Lay. Meteorol., 119, 397–407, 2006. a

Newman, J. F., Klein, P. M., Wharton, S., Sathe, A., Bonin, T. A., Chilson, P. B., and Muschinski, A.: Evaluation of three lidar scanning strategies for turbulence measurements, Atmos. Meas. Tech., 9, 1993–2013, https://doi.org/10.5194/amt-9-1993-2016, 2016. a

Nygaard, N. G.: Wakes in very large wind farms and the effect of neighbouring wind farms, Journal of Physics, Conference Series, IOP Publishing, 524, p. 012162, 2014. a

O'Connor, E. J., Illingworth, A. J., Brooks, I. M., Westbrook, C. D., Hogan, R. J., Davies, F., and Brooks, B. J.: A method for estimating the turbulent kinetic energy dissipation rate from a vertically pointing Doppler lidar, and independent evaluation from balloon-borne in situ measurements, J. Atmos. Ocean. Tech., 27, 1652–1664, 2010. a, b

Olesen, H. R., Larsen, S. E., and Højstrup, J.: Modelling velocity spectra in the lower part of the planetary boundary layer, Bound.-Lay. Meteorol., 29, 285–312, 1984. a

Oncley, S. P., Friehe, C. A., Larue, J. C., Businger, J. A., Itsweire, E. C., and Chang, S. S.: Surface-layer fluxes, profiles, and turbulence measurements over uniform terrain under near-neutral conditions, J. Atmos. Sci., 53, 1029–1044, 1996. a

Otarola, S.: Lidar-ND Halo Scanning Doppler, Boardman-Reviewed Data, Tech. rep., Atmosphere to Electrons (A2e) Data Archive and Portal, Pacific Northwest National Laboratory; PNNL, available at: https://http://a2e.energy.gov/data (last access: 27 March 2019), 2017. a

Panofsky, H. A.: Matching in the convective planetary boundary layer, J. Atmos. Sci., 35, 272–276, 1978. a

Paquin, J. and Pond, S.: The determination of the Kolmogoroff constants for velocity, temperature and humidity fluctuations from second-and third-order structure functions, J. Fluid Mech., 50, 257–269, 1971. a

Pearson, G., Davies, F., and Collier, C.: An analysis of the performance of the UFAM pulsed Doppler lidar for observing the boundary layer, J. Atmos. Ocean. Tech., 26, 240–250, 2009. a

Peña, A., Hasager, C. B., Gryning, S.-E., Courtney, M., Antoniou, I., and Mikkelsen, T.: Offshore wind profiling using light detection and ranging measurements, Wind Energy, 12, 105–124, 2009. a

Pichugina, Y. L., Tucker, S. C., Banta, R. M., Brewer, W. A., Kelley, N. D., Jonkman, B. J., and Newsom, R. K.: Horizontal-velocity and variance measurements in the stable boundary layer using Doppler lidar: Sensitivity to averaging procedures, J. Atmos. Ocean. Tech., 25, 1307–1327, 2008. a

Piper, M. and Lundquist, J. K.: Surface layer turbulence measurements during a frontal passage, J. Atmos. Sci., 61, 1768–1780, 2004. a

Platis, A., Siedersleben, S. K., Bange, J., Lampert, A., Bärfuss, K., Hankers, R., Cañadillas, B., Foreman, R., Schulz-Stellenfleth, J., Djath, B., et al.: First in situ evidence of wakes in the far field behind offshore wind farms, Sci Rep.-UK, 8, 2163, https://doi.org/10.1038/s41598-018-20389-y, 2018. a

Rhodes, M. E. and Lundquist, J. K.: The Effect of Wind-Turbine Wakes on Summertime US Midwest Atmospheric Wind Profiles as Observed with Ground-Based Doppler Lidar, Bound.-Lay. Meteorol., 149, 85–103, https://doi.org/10.1007/s10546-013-9834-x, 2013. a

Rye, B.: Antenna parameters for incoherent backscatter heterodyne lidar, Appl. Opt., 18, 1390–1398, 1979. a

S. Lissaman, P. B: Energy effectiveness of arbitrary arrays of wind turbines, J. Energy, 3, 323–328, 1979. a

Sharma, N., Sharma, P., Irwin, D., and Shenoy, P.: Predicting solar generation from weather forecasts using machine learning, in: 2011 IEEE International Conference on Smart Grid Communications, IEEE, 528–533, 2011. a

Shaw, W. J. and LeMone, M. A.: Turbulence dissipation rate measured by 915 MHz wind profiling radars compared with in-situ tower and aircraft data, in: 12th Symposium on Meteorological Observations and Instrumentation, available at: https://ams.confex.com/ams/pdfpapers/58647.pdf (last access: 27 March 2019), 2003. a

Shaw, W. J., Berg, L. K., Cline, J., Draxl, C., Grimit, E., Lundquist, J. K., Marquis, M., McCaa, J., Olson, J., Sivaraman, C., Sharp, J., and Wilczak, J. M.: The Second Wind Forecast Improvement Project (WFIP 2): General Overview, Bull. Amer. Meteor. Soc., in review, 2019. a

Skamarock, W. C., Klemp, J. B., Dudhia, J., Gill, D. O., Barker, D. M., Wang, W., and Powers, J. G.: A description of the advanced research WRF version 2, Tech. Rep., National Center For Atmospheric Research, Boulder CO, 101 pp., 2005. a

Smalikho, I.: On measurement of the dissipation rate of the turbulent energy with a cw Doppler lidar, Atmospheric and Oceanic Optics c/c of Optika Atmosfery I Okeana, 8, 788–793, 1995. a

Smalikho, I., Köpp, F., and Rahm, S.: Measurement of atmospheric turbulence by 2 µm Doppler lidar, J. Atmos. Ocean. Tech., 22, 1733–1747, 2005. a

Smalikho, I. N. and Banakh, V. A.: Measurements of wind turbulence parameters by a conically scanning coherent Doppler lidar in the atmospheric boundary layer, Atmos. Meas. Tech., 10, 4191–4208, https://doi.org/10.5194/amt-10-4191-2017, 2017. a

Sreenivasan, K. R.: On the universality of the Kolmogorov constant, Phys. Fluids, 7, 2778–2784, 1995. a

Taylor, G. I.: Statistical theory of turbulence, P. Roy Soc. A-Math. Phy., 151, 421–444, 1935. a, b

Tennekes, H. and Lumley, J. L.: A first course in turbulence, MIT press, Cambridge, MA, 300 pp., 1972. a

Thobois, L. P., Krishnamurthy, R., Loaec, S., Cariou, J. P., Dolfi-Bouteyre, A., and Valla, M.: Wind and EDR measurements with scanning doppler LIDARs for preparing future weather dependent separation concepts, in: 7th AIAA Atmospheric and Space Environments Conference, p. 3317, 2015. a

Tonttila, J., O'Connor, E. J., Hellsten, A., Hirsikko, A., O'Dowd, C., Järvinen, H., and Räisänen, P.: Turbulent structure and scaling of the inertial subrange in a stratocumulus-topped boundary layer observed by a Doppler lidar, Atmos. Chem. Phys., 15, 5873–5885, https://doi.org/10.5194/acp-15-5873-2015, 2015. a

Türk, M. and Emeis, S.: The dependence of offshore turbulence intensity on wind speed, J. Wind Eng. Ind. Aerod., 98, 466–471, 2010. a

Wang, H., Barthelmie, R. J., Pryor, S. C., and Brown, Gareth.: Lidar arc scan uncertainty reduction through scanning geometry optimization, Atmos. Meas. Tech., 9, 1653–1669, https://doi.org/10.5194/amt-9-1653-2016, 2016 a

Wilczak, J. M., Stoelinga, M., Berg, L., Sharp, J., Draxl, C., McCaffrey, K., Banta, R., Bianco, L., Djalalova, I., Lundquist, J. K., Muradyan, P., Choukulkar, A., Leo, L., Bonin, T., Eckman, R., Long, C., Worsnop, R., Bickford, J., Bodini, N., Chand, D., Clifton, A., Cline, J., Cook, D., Fernando, H. J., Friedrich, K., Krishnamurthy, R., Lantz, K., Marquis, M., McCaa, J., Olson, J., Otarola-Bustos, S., Pichugina, Y., Scott, G., Shaw, W. J., Wharton, S., and White, A. B.: The Second Wind Forecast Improvement Project (WFIP2): Observational Field Campaign, B. Am. Meteorol. Soc., in review, 2019. a, b, c

Wulfmeyer, V., Muppa, S. K., Behrendt, A., Hammann, E., Späth, F., Sorbjan, Z., Turner, D. D., and Hardesty, R. M.: Determination of convective boundary layer entrainment fluxes, dissipation rates, and the molecular destruction of variances: Theoretical description and a strategy for its confirmation with a novel lidar system synergy, J. Atmos. Sci., 73, 667–692, 2016. a

Xingjian, S., Chen, Z., Wang, H., Yeung, D.-Y., Wong, W.-K., and Woo, W.-C.: Convolutional LSTM network: A machine learning approach for precipitation nowcasting, Adv. Neur. In., 802–810, 2015. a

Yang, B., Qian, Y., Berg, L. K., Ma, P.-L., Wharton, S., Bulaevskaya, V., Yan, H., Hou, Z., and Shaw, W. J.: Sensitivity of turbine-height wind speeds to parameters in planetary boundary-layer and surface-layer schemes in the weather research and forecasting model, Bound.-Lay. Meteorol., 162, 117–142, 2017. a

Yang, Q., Berg, L. K., Pekour, M., Fast, J. D., Newsom, R. K., Stoelinga, M., and Finley, C.: Evaluation of WRF-predicted near-hub-height winds and ramp events over a Pacific Northwest site with complex terrain, J. Appl. Meteorol. Clim., 52, 1753–1763, 2013. a