Profiles of variance and skewness: examples for 20 April
Examples of profiles of w variance calculated for four instruments at the
three locations are shown in Fig. . The given times
always indicate the end of the averaging period of 1 h. As described by
or , the variance profiles display a
maximum at a height of about one-third of the convective boundary layer (the
top of the CBL is between 1000 and 1400 m on 20 April,
Fig. ) and a decrease above. The profiles in
Fig. are not normalized so that the diurnal
evolution can be observed: variances are small at 10:00 UTC
(12:00 LT), increase to maximum values at about
12:00–14:00 UTC and decrease subsequently. Above a local minimum
indicating the top of the CBL, an increase of variance can be seen in several
profiles (e.g. 13:00–16:00 UTC profiles of HYB at about 1500 m,
Fig. a). These higher values lie in and above the
capping inversion of the CBL (Fig. b) and may be caused
by gravity waves in the capping inversion and a stable layer above the CBL.
Normalized hourly variance profiles for 18, 20, 22, 24 April and
04 May (11:00–16:00 UTC) with mean profile, standard deviation and
mean normalized statistical error (legend in a), using averaged
(a, b, c) and local scaling (e, f, g, h) for each location;
different energy balance stations were used for scaling the profiles of
Selhausen in (g, h); in (d), the idealized profiles
according to Eq. are given.
As already shown by the comparison of vertical velocity measurements of the
smaller WLS7 and of WTX (Fig. ), the combined variance
profiles fit well at the transition height from one instrument to the other
(Fig. d). The maximum variance is sometimes located
at low heights that are not covered by HYB or WTX (for example, at
11:00 UTC in Fig. c), indicating the
usefulness of the combination of different lidar systems with complementary
ranges. The variance profiles derived from the measurements of HYB and WLS200
(Fig. a and b) do not agree in all details, as
indicated by the calculated cross correlations, but the profiles are much
more similar to each other than to the profiles from the other two sites in
terms of structure, temporal evolution, and absolute values.
Additionally, profiles of skewness (w′3‾/w′2‾3/2) are analyzed (Fig. ).
Positive skewness is usually expected in the CBL and means strong, narrow
updrafts and weaker, broader downdrafts. On 20 April, values of skewness are
positive within the CBL. They confirm the existence of a well-mixed boundary
layer, as they illustrate a net upward transport of variance according
to the variance budget equation of and with this, of turbulent
energy. This means that the turbulent energy is mainly created at the
surface, i.e., by buoyancy.
Scaling of variance profiles
Overview of all scaled variance profiles
Diurnal variability of w variance is obvious on 20 April
(Fig. ). This temporal variability should be
eliminated by scaling with w∗, assuming that the temporal variability
of the w variance depends mainly on the strength of buoyancy. It is
expected that the scaled profiles are similar within the range of uncertainty
indicated by the statistical error. Differences of the Bowen ratio point to a
large spatial heterogeneity (Sect. ). Hence, at an
individual location, the diurnal cycle of the energy input as well as
differences from day to day may be taken into account better by local scaling
than by the averaged one (see Sect. for the
definition of the scaling approaches). Therefore, also the question is
addressed whether the spread of the profiles at each individual location is
smaller for the locally scaled profiles. On 19 May, which is the only day
falling into the wetter period with less surface heterogeneity, lower Bowen
ratio and consequently, lower w∗ is observed at all stations (see
Sect. , Figs. and ).
This day is excluded from the analysis of the scaled profiles.
Correlations of vertical velocity variance averaged over 0.25 to
0.60zi and w∗2, calculated using the weighted-averaged fluxes
(a) and fluxes of nearby stations (b) for all time steps as
in Fig. but for 10:00–17:00 UTC, with lines of
best fit from linear regression, squared correlation coefficients R2 and
confidence interval at the 95 % level.
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. b), which was located in a meadow close to a river.
Both are used for local scaling of the variance profiles from Selhausen. As
Niederzier is a bare-soil station with relatively high sensible heat fluxes
(Fig. b), i.e., a high Bowen ratio, and SE1 is
characterized by a low Bowen ratio, large differences are found between the
two normalizations: the maximum values of mean normalized variance are 0.32
and 0.79, respectively (Fig. g and h). For the averaged
scaling, by contrast, the maximum value of the mean scaled variance at
Selhausen is 0.42 (Fig. c), which is closer to the mean
values of w′2‾/w∗2 at Hambach and Wasserwerk (0.45
and 0.46, respectively, Fig. a and b). This means that in
comparison to the scaled variances at the other locations, the surface
sensible heat flux at Niederzier is too high and SE1 too low with respect to
the observed CBL turbulence at Selhausen. The mean variance profiles at all
locations display a vertical behavior that is similar to the profile of
Fig. d, with a maximum in the lower
half of the CBL, but not exactly at 0.35zi. The difference between
standard deviation of all profiles and the mean normalized statistical error
signifies their temporal variability which is not explained by variability of
buoyancy. At Hambach and Selhausen, the standard deviation is higher than the
statistical error at all heights, most distinctly between 0.2 and 0.6zi.
The mean relative differences between error and standard deviation,
vertically averaged, lie between 5 (Fig. f) and 36 %
(Fig. h). At Wasserwerk, the difference is small,
especially for local scaling (Fig. f). This indicates
either that turbulence at Wasserwerk is strongly influenced by nearby surface
conditions or that the nearby surface conditions represent the larger-scale
upstream conditions very well.
In a similar investigation, found a difference of 10 %
between error and standard deviation. They explained it by dependency on wind
shear or stability, represented by -zi/L. However, a dependency of
w variance on -zi/L cannot be found here, neither on friction
velocity nor on values of wind shear at the CBL top, as derived from
radiosoundings.
Correlation of variance and convective velocity scale
In a next step, correlation coefficients are determined between the
w variance values averaged between 0.25 and 0.60zi
(w′2‾ave) and w∗2. As in
Sect. , values of w∗ for both averaged
(1) and local scaling (2) are applied. By vertical averaging of
w variances, the height dependency of the maximum is eliminated. In case 1,
the squared correlation coefficient R2 is 0.45 for Hambach and 0.50 for
Wasserwerk; in case 2, the correlation is slightly higher than in case 1 for
Hambach (R2=0.49) and considerably higher for Wasserwerk (R2=0.72).
For Selhausen, R2 is 0.46 in case 1 and lower in case 2 when using the
fluxes from Selhausen or Niederzier (R2=0.28 or 0.34, respectively).
This means that the local scaling is not preferable for Selhausen. For
Hambach, local scaling is only slightly better than averaged scaling, but
local scaling is clearly better for Wasserwerk. For the given sample sizes,
the correlations are all significantly higher than zero when considering a
confidence interval on a 95 % level. However, only for Wasserwerk using
local scaling, the explained variance (concerning the temporal evolution of
w′2‾ave, hereafter called “temporal variance” to
avoid ambiguity) is significantly higher than 50 %. In contrast, for
Selhausen using local scaling with SE1, the explained temporal variance is
not significantly higher than 10 %, indicating that this scaling is not
suitable.
and showed that w′2‾(0.35zi)=aw∗2 and found values of a between 0.37 and 0.44,
derived from both numerical experiments and different observations. Here,
R2 is 0.34–0.39 for the averaged w∗2 values and 0.30–0.43 for
the local ones, which agrees tolerably well with values found before. For
Wasserwerk and the local scaling, a is 0.43, i.e., at the upper limit of
values given in literature.
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. ).
Investigation of outliers
The findings show that temporal variability of w variance cannot be
completely eliminated by scaling and that the remaining variability cannot be
explained by wind shear or stability. Therefore, individual profiles with
particularly high values of w′2‾/w∗2 are examined in
detail. The largest outliers from Wasserwerk, which has the smallest portion
of unexplained temporal variance, are selected (Fig. b and
f, respectively). They occur at 12:00 UTC on 20 and 24 April. Each of
the two profiles is compared to a profile from the respective day which is
more similar to the mean (Fig. ). Radiosonde profiles
indicate no strong diurnal change in wind speed or direction on these two
days (not shown). The comparison, including error bars, indicates that
w′2‾/w∗2 is significantly higher for the selected
time periods than usual (Fig. ai and bi). If longer
time periods are chosen, differences decrease, but the statistical error
decreases likewise so that they are still significant.
Normalized variance profiles with error bars statistical
error according to; for each (ai) and (bi),
two time steps were selected from Fig. 7b and f, respectively; for each time
step, frequency distributions are given as a function of height
(aii, aiii, bii, and biii, gray shading
with steps proportional to logarithm of relative frequency, higher values for
lighter shadings) and as distributions over a range of heights (aiv, biv).
A hypothesis for high values of w′2‾/w∗2 is the
occurrence of more numerous or stronger thermals.
developed a method for a sub-sampling of thermals from the time series of w
and showed that the variance of thermals is 2–2.5 times
higher than for the environment, depending on the method of calculation (the
ratio is higher when the mean velocity of the sub-samples is subtracted
before calculating the variance). As a sub-sampling would be beyond the scope
of this investigation, the frequency distributions of the respective time
series are investigated (Fig. ). As variance is equal
to the second central moment of a probability distribution, larger variance
signifies a broader and flatter distribution by definition. The frequency
distribution for 20 April, 11:00–12:00 UTC reveals that there is a
higher frequency of w>1 m s-1 than between
14:00–15:00 UTC as well as stronger downdrafts
(Fig. aiv). When the frequency distribution is
considered as a function of height (Fig. aii), it can
be shown that this behavior can be observed between 200 and 900 m, i.e.,
distributed over a large part of the CBL (zi is between 1300 and 1400 m
on this day). On 24 April, the maximum of w′2‾/w∗2 at
12:00 UTC is elevated compared to the one at 10:00 UTC
(Fig. bi), while zi is the same (about 1350 m) for
both periods. In contrast to 20 April, higher variance is caused by a higher
frequency of w>0.5 m s-1 only, not by stronger downdrafts
(Fig. biv). Moreover, the differences between the
frequency distributions occur mainly at heights between 400 and 800 m; i.e.,
they are vertically more confined to the layer where w′2‾/w∗2 is actually higher. The integral time scale, which is on average
56 s on 24 April (Table ), increases to a distinct maximum
of almost 200 s at 800 m (not shown), indicating broader thermals at
12:00 UTC (and at 11:00 UTC when the integral time scale is
about 120 s at 600 m) than on average.
Thus, while high values of normalized variance at Wasserwerk for the profile
at 15:00 UTC on 20 April are caused by strong up- and downdrafts,
they are actually caused by broader thermals on 24 April. This agrees with
the results of that the variance of thermals is higher.
However, it is not possible to explain these thermals by corresponding higher
surface sensible heat fluxes and, thus, why w′2‾/w∗2
is higher than on average.
Due to the elevated maximum, the profile for 12:00 UTC on 24 April
corresponds better to the symmetrical profile of
Fig. d. , e.g., also
discuss the variability of heights of the variance maxima reported by
different authors. The height-dependent frequency distribution shown here
suggests that the elevated maximum is caused by strong thermals rising up to
a certain height. LES of also support the finding
that an elevated maximum of variance is related to particularly strong
plumes.
Vertical velocity variances (hourly profiles averaged over
zmax±250 m) at the three locations with error bars displaying
the statistical error according to for all 6 days
(different panels).
Spatial differences of vertical velocity variances
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 w variance.
Normalized variance profiles with error bars statistical
error according to for three time periods (local scaling); the
black dashed line corresponds to the fit of ,
Eq. ().
One noticeable difference between the hourly variance profiles at the three
locations on 20 April (Fig. ) is the diurnal cycle:
While maximum variance occurs at 12:00 UTC at Wasserwerk and
Selhausen, it occurs at 14:00 UTC at Hambach. To investigate this
spatial difference, the height of maximum variance, zmax, is
determined for all days and all hourly variance profiles. It is encountered
between 0.1 zi and 0.5 zi. A maximum variance
w′2‾max is then calculated by vertical averaging of
each profile over a height range of zmax± 250 m. The
statistical errors are determined for the same height range. The time series
of w′2‾max for the three locations are shown in
Fig. . The difference of
w′2‾max between Wasserwerk and Hambach on 20 April for
the 12:00 UTC period is not significant when considering the
statistical error, but it is significant for the 14:00 UTC period.
For other time periods, as for example for 11:00, 15:00, and
16:00 UTC on 18 April, 11:00 and 12:00 UTC on 24 April,
significant differences between the individual locations are also evident. In
the following sections, different reasons that could cause significant
differences are explored.
Influence of the surface energy balance
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. ). Therefore, it is investigated now whether
the detected spatial differences of w variance are related to the spatial
heterogeneity at the land surface which was described in
Sect. . Even if local scaling could not eliminate spatial
differences on average, it could reduce them for the time periods with
significant spatial differences.
Generally, surface heterogeneity as observed during the drier period
(Fig. ) may be caused by heterogeneous surface
characteristics such as land use and soil moisture, which influence the
partitioning of available energy into sensible and latent heat. On the other
hand, heterogeneity also can result from the available energy itself, which
can be modified strongly by the occurrence of clouds. As shown in
Sect. , clouds actually influenced incoming radiation
on 2 of the 6 selected days.
Net radiation (Q0, upper row) and surface sensible heat flux
(H0) at the five energy balance stations (NIE – Niederzier; RUR –
Ruraue; SE1 – Selhausen; HAM – Hambach; WAS – Wasserwerk; cf.
Fig. ) for 3 days with significant spatial differences of
vertical velocity variances.
Relative deviations between w′2‾max time
series of each two lidars, averaged daily and over all days (a) and
statistical error for each instrument, normalized with the respective
w′2‾max time series (b), given as a function
of the averaging interval used for the calculation of the variance profiles;
absolute values of w′2‾max/w∗2 for the 3-h
averaging interval for HYB, HALO, and WLS200 as a function of
w′2‾max/w∗2 for WTX (c); deviation
normalized with w∗2 for 3-h averaging interval for each day
(d).
Cross correlation functions between w′ time series
(10:30–15:00 UTC) at Hambach and Wasserwerk (WTX and WLS200,
respectively) for all range gates between 380 and 1000 m (upper row) and
w′ time series (±50-s running average) for both lidars at one range
gate (lower row) on 18 April (a) and
24 April 2013 (b).
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 w∗2 (local scaling). For
Selhausen, Niederzier is chosen as it provides better correlations than SE1
(Fig. ).
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. . As the statistical error depends on
the variance itself (Appendix Eqs. and
), it is higher for higher variances. The different
scaling values for the three locations amplify this effect.
For all time periods, at least two profiles still show statistically
significant differences after applying the local scaling. For 18 April,
15:00 UTC (Fig. a), the difference between
Hambach and Wasserwerk becomes even stronger than without scaling. This means
that the spatial differences cannot be explained by the surface
heterogeneity. The reason becomes obvious when looking at the net radiation
and surface sensible heat flux for the three selected time periods
(Fig. ):
On 18 April at 15:00 UTC, the w variance is the highest at
Selhausen and lower at Hambach as well as at Wasserwerk
(Fig. ). If local sensible heat fluxes were
responsible for the spatial differences of CBL turbulence between
14:00–15:00 UTC, the spatial flux differences would be similar.
However, the flux is highest at Hambach (Fig. ) so that
the scaled variance was the lowest. At Niederzier, the flux is slightly lower
and much lower at Wasserwerk. Consequently, the differences of the sensible
heat flux cannot explain the variance differences. Moreover, net radiation
(Fig. ) shows that some clouds occurred on this day and
from cloud camera images, it is known that also boundary-layer clouds were
present between 13:00 and 15:00 UTC. These clouds do not cause
considerable temporal variation in the sensible heat flux data, but they can
certainly influence the variance profiles e.g..
On 20 April, 14:00 UTC, the variance is highest at Hambach and lower
at Wasserwerk and Selhausen (Fig. ). However,
the surface sensible heat flux is equally high at the three locations
(Fig. ). At the same time, the net radiation shows little
spatial variability (<20Wm-2). Thus, the surface forcing
does not display large differences between the three locations, which
explains why a scaling using the fluxes from the nearby stations does not
remove the spatial differences of variances (Fig. b).
On 24 April, 12:00 UTC, the variance at Selhausen is significantly
lower than at Hambach and Wasserwerk (Fig. ) but
again, the spatial differences between the fluxes cannot explain this
difference (Fig. ). The flux is highest at Niederzier so
that the scaled variance profile for Selhausen becomes very low compared to
the scaled profiles at the other two locations
(Fig. c).
Therefore, it must be concluded that the heterogeneous surface conditions
cannot explain the statistically significant spatial differences of the
w variances. This is consistent with the finding from
Sect. that significantly increased values of the
w variance within the diurnal cycle cannot be eliminated by scaling,
either.
Influence of averaging periods and measurement uncertainties
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 w′2‾max values at
different locations are calculated for different averaging periods Δt. For the computation of variances for Δt>1 h, the
non-stationarity of the CBL, especially due to increasing zi in the
morning, has to be considered. For this, w′2‾max
values are first determined for the hourly averaging periods and then
averaged to retrieve w′2‾max for longer averaging
periods. In contrast, the statistical error (Fig. b) is
taken from variance calculations for explicitly larger time periods. After
that, relative deviations (absolute difference normalized by the mean value)
are calculated for each time step and each instrument combination. The
resulting mean relative differences are given as an average of all considered
6 days (Fig. a). For the 3 days when simultaneous
w measurements by HYB and WLS200 at Wasserwerk are available (20, 22, and
24 April), the relative difference between these two measurements at the same
site is calculated as well. This gives a good estimate for the uncertainty
that exists due to the comparison of measurements by instruments that are
based on different technologies or made by different manufacturers
(instrument uncertainty).
The daily mean relative deviation for HYB and WLS200 is less than 0.1 for
Δt=1 h and about 0.05 for longer averaging periods. For the other
instrument combinations, it is about 0.5 for Δt=10 min and
decreases to about 0.2 for Δt=3 h. For Δt>3 h, it does
not clearly decrease further. The mean normalized statistical error for
Δt=3 h is about 0.1 (Fig. b), so that the
relative deviation is about twice the error. This means that the spatial
differences between the variances are not statistically significant on average, at least if the instrument-to-instrument uncertainty is considered.
However, this does not exclude the possibility of individual periods with
significant spatial differences existing; the diurnal time series of
w′2‾max with the corresponding error bars are also
compared for larger Δt and the significant differences for the
periods concerned remain (not shown). At the same time, a mean relative
deviation of about 0.2 for Δt=3 h means that the mean error that
has to be expected when calculating variances from point measurements is
about 10 % minus the instrument uncertainty of about 2 % (a factor of 0.5
is taken into account to derive the uncertainty of a single instrument from
the calculated deviation); in other words, a point measurement is – on average – spatially representative with an uncertainty of less than 10 %
when a measurement period of 3 h is covered. This agrees with the
statistical error of that was derived by theoretical
considerations.
As the absolute difference does not provide any evidence of possible biases
between the instrument measurements, absolute values of
w′2‾max/w∗2 are compared in
Fig. c. The variances are normalized by w∗2
(averaged scaling) to retrieve comparable values for the different days.
While on average they are as high at Wasserwerk (HYB and WLS200) as at
Hambach, most values are below the 1-1 diagonal for HALO. This explains
why the relative difference is higher between HALO and both other instruments
than between HYB and WTX (Fig. a). Nevertheless, there
is no clear explanation why the variance is systematically smaller at
Selhausen than 3 km north of this location. The sensible heat flux of SE1 is
quite low most of the time, but as shown in Sect. ,
it is not representative of the surroundings of the HALO site. Finally, to
compare the daily differences, the absolute differences between the lidars
are normalized by w∗2 (Fig. d).
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 w∗2 (using a small sensible heat flux) results in higher values
than for the other days. The variation of the differences from day to day
can, hence, partly be explained by the occurrence of clouds and by the
resulting differences of the incoming radiation (Table ).
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.
Correlations of vertical velocity at different locations
For two of the three time periods investigated in
Sect. (on 18 and 24 April), the mean wind direction
is west to southwest. On both days, it is noticeable that the diurnal time
series of w′2‾max at Wasserwerk and Hambach are very
similar, while the time series is different at Selhausen
(Fig. ). As the variances are similar, it can be
expected that also the time series of w at Wasserwerk and Hambach exhibit a
certain similarity. To investigate this, the cross correlation function of
the two time series of w is determined (Fig. ).
As the convective time scale t∗ is of the order of 10 min and
the travel time for the given distances between the lidar locations of about
3 km is between 4 and 12 min, convective cells can be preserved
between two locations at least on days with relatively strong mean wind. The
day with the highest mean wind speed is 18 April; in the westerly flow, the
WTX at Hambach is located downstream of WLS200 at Wasserwerk. The cross
correlation function between WLS200 and WTX in fact reveals a distinct
maximum of correlation at a time lag of 200 s
(Fig. a). The maximum correlation of 0.44 is found
at heights between 500 and 900 m. When shifting the time series of w′ at
600 m for WTX backwards by 200 s compared to that of WLS200, the two time
series agree very well (Fig. a). That means that
the larger convective cells are advected from Wasserwerk to the Hambach site
without substantial changing (Taylor's hypothesis), which explains the
similarity of the time series at the two locations for both w and
w′2‾max.
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. b), but it is only
0.27. Nevertheless, the two time series (WTX shifted by 400 s) at 700 m
agree very well, at least after 11:45 UTC. At the same time, the
cross correlation mainly gives negative values, if it is calculated between
the time series of vertical velocity for Selhausen and Hambach or between
Selhausen and Wasserwerk (not shown).
In contrast to 18 and 24 April, the mean wind direction on 20 April is
northeast. On this day, large differences of w′2‾max
are observed between Hambach and Wasserwerk in the afternoon. The cross
correlation function also shows very low correlations (<0.1; not shown).
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. ), although
similar surface conditions exist on all of these days: the diurnal cycles of
variances are similar at the two sites when the mean wind is parallel to
their connecting axis, but different otherwise. For the time periods when the
correlation between the two sites is high, the correlation between the third
site and each of the two is low. It is remarkable that on 24 April, when
convective cells are advected past Wasserwerk and Hambach without substantial
changing, the mean vertical velocity (Fig. ) is positive
at Wasserwerk between 11:00–12:00 UTC (more than 1 m s-1) and
negative at Selhausen (11:00–13:00 UTC, i.e., even for 2 h). We
hypothesize that, while many cells are observed on the northern axis, less
occur about 3 km further south due to the subsidence in the surroundings of
the cells. This assumption is confirmed by model simulations for 24 April
with the Consortium for Small-scale Modeling (COSMO) model in LES mode. They
were performed on a grid with 100 m horizontal resolution using a
3-D-turbulence parameterization by . Model analyses of the
operational model COSMO-DE provided atmospheric initial and
boundary conditions. The vertical velocity as calculated by the model is
shown on a horizontal cross section at 600 m (Fig. ). The
instantaneous as well as the field averaged over 1 h is given. About
1–1.5 km south and north of the regions where the mean vertical velocity is
positive on the hourly average, which is caused by convective cells advected
with the mean wind, subsidence prevails. As shown by , the
mean w within thermals is positive and nearly 2 times higher than in the
environment, where it is negative. This agrees very well with the mean w
observed at the different locations on 24 April (Fig. ).
The spatial variance differences on 18 and 24 April can therefore be
explained by the occurrence of organized structures of turbulence: while more
convective cells travel past the Wasserwerk as well as past Hambach,
subsidence in the surroundings of these cells prevails at Selhausen. This
structure is presumably the signature of horizontal rolls that develop during
conditions of combined surface heating and strong winds Ch.
11.2, as was observed by or .
Mean vertical velocity (running average of 60 min) at 700 m
(±1 range gate) at Wasserwerk and Selhausen on
24 April.
Vertical velocity at 600 m on 24 April 2013 from LES model output:
(a) instantaneous, (b) averaged field.
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
w variance at both other sites differs from the one at Hambach
(Fig. ). One possible explanation is that, on
days with easterly wind, the strongest influence of the open-pit coal mine on
w variance occurs at Hambach.