In the spring of 2013, extensive measurements with multiple Doppler lidar systems
were performed. The instruments were arranged in a triangle with edge lengths
of about 3

The vertical velocity variance,

In the part of the CBL where buoyant production dominates over the shear
production of turbulent kinetic energy, turbulent mixing is supposed to be
driven mainly by the heat supply at the Earth's surface.

Different studies addressed the representativeness of point measurements of
turbulent surface fluxes

During the High Definition Clouds and Precipitation for Climate Prediction
(HD(CP)

The length of about 3 km of the three edges had been chosen such that the
lidars at the different sites did not sample the same convective cell at the
same time. Hence, the distance between the lidar sites had to be larger than
the diameter of the convective cells which are assumed to scale with the CBL
depth of 1–2

The aims of this study are to generally analyze the profiles of vertical velocity variance available from HOPE as well as to investigate their spatiotemporal variability. By investigating spatial differences of vertical velocity variance, the representativeness of point measurements of vertical turbulence profiles can be assessed. The paper is structured as follows: in the next section, the observations and the measurement setup are described. Section 3 presents analyses of the vertical velocity measurements and gives an overview of the computation of the vertical velocity variances and considered errors. It also includes considerations regarding the normalization procedure. In Sect. 4, scaled vertical velocity variances are described separately for the different sites as well as compared for the three sites, and possible influencing factors are discussed. Finally, Sect. 5 summarizes the main findings.

The HOPE measurement area was located near Forschungszentrum Jülich, in
the north of a low mountain range (Eifel), with two larger open-pit coal
mines (up to 10

As part of HOPE, the Karlsruhe advanced mobile observation platform KITcube

Overview of lidar instruments at the three sites, with abbreviations
used in the text, measurement range

At Hambach, a 1.6-

Two Doppler lidars (a 2

As all heights used in this study will be in m a.g.l., we will omit the adjunct “a.g.l.” in the following sections.

The energy balance stations measure solar and reflected irradiance, long-wave
incoming and outgoing radiation, soil heat, sensible heat, latent heat, and
momentum fluxes. For the turbulent fluxes, temperature, humidity, and wind
speed are measured with an ultrasonic anemometer/thermometer and a fast
infrared hygrometer at a height of 4 m. All turbulent fluxes used in this
study were calculated for time intervals of 30

To obtain vertical profiles of temperature, humidity, wind speed, and wind
direction, the KITcube radiosonde system (DFM-09, Graw) was operated at
Hambach. On 18 days selected as intensive operation periods (IOPs),
radiosondes were launched every 2 h. On all other days, launches were
done at least at 11:00 and 23:00

Overview of characteristic mean values and scales for all considered
days (spatially averaged for surface measurements and turbulence
characteristics, Hambach for other variables): Diurnal maximum of surface
sensible heat flux

On 6 days with mainly cloud-free CBL conditions, at least one lidar at each
site was configured for

As indicated by microwave radiometer measurements, the IWV was moderately
high on most days and much higher on 24 April. Incoming shortwave radiation,
as measured by a pyranometer network operated by TROPOS (Leipzig), naturally
increased from 18 April to 19 May. At the same time, the spatial standard
deviation of incoming radiation, in combination with ceilometer data and
cloud camera images, revealed the existence of some CBL clouds on 18 April
and of altocumulus clouds at about 5 km on 19 May. Cirrus clouds at about
8 km existed on 24 April, but they did not affect incoming radiation. In
comparison to the other days, the maximum sensible heat flux was reduced on
19 May. The height of the capping inversion of the CBL was also lowest on
19 May, while it was highest on 18 April. As indicated by the temporal
evolution of temperature profiles of the radiosondes for 18 April (not
shown), when the boundary layer grew into this neutral layer, its height
increased abruptly from 700 at 09:00

An overview of the daily averaged Bowen ratios (ratio of sensible heat flux
to latent heat flux, both averaged over 09:00–15:00

The Bowen ratio was below one at Selhausen and Ruraue during all the time so
that spatial heterogeneity within the respective area of about

Vertical velocity as observed by Doppler lidars at three different
locations on 20 April 2013 (11:00–13:00

In order to derive spatially representative values of sensible heat flux, an
average of flux measurements was calculated by weighting each station with
the fraction of the respective land-use class in an area of

As an example, vertical velocity measurements from 11:00–13:00

For a first analysis of the time series, spectra of energy density

In the selected example,

The different values of

The inertial subrange can also be discerned in the given spectra, but the
slope is steeper than the theoretical one of

Moreover,

A steeper slope in the inertial subrange also affects the total variance, as can be seen in the integral spectra: the contribution to the total variance increases up to frequencies of 0.1 Hz only.

Apart from that, the spectra of WLS7 show some artifacts at the highest
frequencies, which were also observed by

Based on the spectra,

In addition to the calculation via the integrated spectrum,

As in

Finally, another error that may have an influence is the missing variance contribution in the higher frequency part of the spectrum due to the vertical averaging of the lidar measurements. This error will be neglected here, as it would lead to higher variances at all stations and not change the spatial differences. Moreover, the missing contributions are small compared to the absolute values of variance.

According to

CBL heights derived from radiosoundings (maximum temperature
gradient = inversion; method 1), from lidar backscatter data (WTX; method 2)
as well as from a variance threshold (method 3) for all considered cloud-free
days; additionally, the convective velocity scale

For

For the 6 days investigated here, the methods agree well for most time
steps around noon (dashed lines and black dots in Fig.

The values of

Vertical profiles of hourly vertical velocity variance and skewness
from lidar measurements at the three locations for 10:00–17:00

Examples of profiles of

Normalized hourly variance profiles for 18, 20, 22, 24 April and
04 May (11:00–16:00

As already shown by the comparison of vertical velocity measurements of the
smaller WLS7 and of WTX (Fig.

Additionally, profiles of skewness

Diurnal variability of

Correlations of vertical velocity variance averaged over 0.25 to

There were two energy balance stations were located near Selhausen: the
energy balance station of Niederzier was about 1 km north of Selhausen, which
may be relatively far away, but the land-use class was the same as at the
lidar location. The station called SE1 was closer, but the land-use class
there differed and the flux was very low, even lower than at Ruraue
(Fig.

In a similar investigation,

In a next step, correlation coefficients are determined between the

The implication of the correlations found here is that it is hard to find the
specific site in a region with heterogeneous surface fluxes which represents
the whole upstream conditions relevant for the turbulence in the CBL.
Therefore, it is preferable to apply a weighted-averaged flux for scaling. A
possible explanation why the correlation for local scaling (Wasserwerk) is
higher than for averaged scaling is the uncertainty of the spatial averaging
procedure and with this, of averaged scaling, due to the combination of
different land-use classes as well as the choice of the considered area
(Sect.

The findings show that temporal variability of

Normalized variance profiles with error bars

A hypothesis for high values of

Thus, while high values of normalized variance at Wasserwerk for the profile
at 15:00

Due to the elevated maximum, the profile for 12:00

Vertical velocity variances (hourly profiles averaged over

The main finding of the investigation of scaled profiles is that averaged
scaling was preferable, i.e., that the same scaling could be used for the
three locations. This implies that also the absolute values of variance
should be similar at the three locations. However, unexplained temporal
variance is found even for the “best” scaling. The question is now if there
is also a spatial variability of

Normalized variance profiles with error bars

One noticeable difference between the hourly variance profiles at the three
locations on 20 April (Fig.

For the days investigated here, positive values of skewness confirm that the
strength of CBL turbulence is dominated by surface-based buoyancy-driven
convection (exemplarily shown for 20 April in
Fig.

Generally, surface heterogeneity as observed during the drier period
(Fig.

Net radiation (

Relative deviations between

Cross correlation functions between

The spatial heterogeneity of the buoyancy flux at the surface, including the
influence of spatially heterogeneous cloud cover, may be considered by
scaling the variance profiles with

For the three selected time periods on 18, 20, and 24 April when spatial
differences were observed, scaled profiles with the corresponding error bars
are given in Fig.

For all time periods, at least two profiles still show statistically
significant differences after applying the local scaling. For 18 April,
15:00

On 18 April at 15:00

On 20 April, 14:00

On 24 April, 12:00

Therefore, it must be concluded that the heterogeneous surface conditions
cannot explain the statistically significant spatial differences of the

The variance profiles considered so far were determined using hourly
averaging periods. We now want to investigate how strongly the spatial
differences are dependent on the length of the applied averaging periods. For
this reason, the differences between

The daily mean relative deviation for HYB and WLS200 is less than 0.1 for

As the absolute difference does not provide any evidence of possible biases
between the instrument measurements, absolute values of

The comparison reveals that on 3 days (18, 20, and 22 April), the
deviations are largest between HALO and WTX and on 1 day between HALO and
HYB (24 April). On 4 May, which is closest to a perfectly cloud-free day, the
differences are smallest and on 19 May, which is a day with several mid-level
clouds, they are largest. 19 May is the only day that falls into the wetter
period with the Bowen ratio being low for all stations. Therefore, scaling
with

We finally conclude that the spatial differences on average are as large as the statistical error derived from theory, independent of the averaging period. The instrument uncertainty can be estimated to about 2 % and the mean error is about 10 % for an averaging period of 3 h.

For two of the three time periods investigated in
Sect.

As the convective time scale

On 24 April, the mean wind direction again is southwest, but weaker than on
18 April. A maximum of the cross correlation function between WLS200 and WTX
can also be discerned (Fig.

In contrast to 18 and 24 April, the mean wind direction on 20 April is
northeast. On this day, large differences of

The mean wind direction may thus be one explanation why differences between
the variances at Wasserwerk and Hambach are small on 18 and 24 April, but
significant on 20 April (Fig.

Mean vertical velocity (running average of 60

Vertical velocity at 600 m on 24 April 2013 from LES model output:

On 20 April, mean wind comes from the northeast, so that thermals traveling from
Hambach to Selhausen may be observed. However, this is not the case, and

During the HOPE campaign, multiple Doppler lidars were operated simultaneously at three different sites in the vertical stare mode to retrieve temporally high-resolved vertical velocity measurements. For this study, profiles of vertical velocity variance were derived for the three sites to investigate the spatiotemporal heterogeneity of turbulence in the cloud-free CBL. The aims were to analyze temporal variability as well as scaling of variance profiles and to compare the variance profiles for the different sites. It was investigated if spatial differences were statistically significant and if they depended on surface conditions, atmospheric conditions or on the averaging intervals.

The investigated area was characterized by patchy agricultural land use. The
typical size of the crop fields was of the order of 100 m. The 8 weeks
of the measurement period were divided into a drier period (mid-April to
6 May) and a wetter one (starting on 7 May). The Bowen ratio varied between
0.5 and 4 during the drier period, while it was

Boundary-layer mixing was strong on all of the selected days and the height
of the CBL was between 1.2 and 2 km. Different methods to derive

The combination of smaller and larger Doppler lidars with complementary
measurements at different heights proved to be beneficial for the
investigations. For the calculation of higher-order moments of

For the scaling of the

Evaluating the correlations between

Thus, time series of

Statistically significant spatial differences were found by comparing vertically averaged values of vertical velocity variance at the three sites. They also occurred on days with westerly to southwesterly wind, when the influence of a large open-pit coal mine in the surroundings was presumably low. To investigate whether these differences were generated by heterogeneous surface conditions, local scaling was applied. The results implied that the heterogeneity of the surface conditions could not be the main reason.

Secondly, the influence of different averaging intervals on the spatial
differences of

Finally, a detailed analysis of periods with significant spatial differences
of

Based on these findings, the following conclusions can be drawn: (1) the
representativeness of single-column turbulence characteristics as observed by
Doppler lidars is not necessarily given, even if long time periods are
available (with the maximum possible length of the time period being the
whole part of day with an existing CBL); (2) local scaling with

The so-called “uncorrelated noise” defined by

According to

The random or sampling error takes into account that the length of the
measured time series is not unlimited and that “random” time slots may
differ.

Going back to

This work was funded by the Federal Ministry of Education and Research in
Germany (BMBF) under the research program “High Definition Clouds and
Precipitation for Climate Prediction “HD(CP)