northern component than at height. Thus, due to the modulation of the advected air mass by the upwind surface pattern, a different pattern of vertical motions establishes in the
Ž .
northern than in the southern part of the domain e.g., Fig. 8 . In the northern part, for Ž
. instance, at the WE cross-section at 60 km counted from the south , there is stronger
Ž .
descent over the grass–sand boundary looking from the west . Note that this cross-sec- Ž
. tion is dominated by grass. At the WE cross-section at 30 km counted from the south
Ž .
ascent is stronger over sand–grass boundary looking from the west . This cross-section is dominated by sand. Based on these findings, one may conclude that descent or ascent
depends on the dominant surface type of the cross-section in the northern cross-sections. Ž
. At the WE cross-section at 10 or 20 km counted from the south , however, the vertical
Ž .
motions cannot be assigned to the dominance of the cross-section e.g., Fig. 8 . Several Ž
. small areas of descent and ascent establish Fig. 8 . These facts mean that after the air
mass has passed alternating relatively small patches several times, a less distinct, but still ‘organized’ behavior of vertical motions establishes.
6. Cloudiness
After reaching the condensation level, water vapor condenses and low extended stratus is formed. In all simulations, the domain is totally covered by extended low
stratus during the entire simulation time. The wet adiabatic cooling rates are on the order of 1 Krh. Consequently, radiation and wet adiabatic cooling are approximately equal
contributors to low extended stratus.
At noon, cloud bases are at a height of 250 m and cloud tops are at a height of 450 m. In HOMG and HOMS, the cloud-water mixing ratios of the stratus are horizontally
uniform throughout the entire simulation. At noon, for instance, the cloud-water of HOMG amounts 0.124 and 0.557 grkg at a height of 250 and 450 m, respectively. At
the same time, the cloud-water of HOMS amounts 0.108 and 0.556 grkg at these heights. Obviously, at a height of 450 m, the cloud-water mixing ratios of HOMS and
HOMG hardly differ. In the case of heterogeneous surfaces, deviations from these cloud-water values may be related to the effects of heterogeneity on water vapor supply,
heating, and vertical motions. Secondary differences result from the modified radiative cooling at cloud top caused by the altered cloud-water distribution. For brevity, these
slight effects will not be discussed here.
No apparent response of the low extended stratus to the underlying surface is found for the landscapes with stripes parallel or perpendicular to the wind, no matter of the
Ž .
stripe size SGSR25, GSGR25, SGSP5, GSGP5, SGSR5, GSGR5 . The same is true for Ž
. landscapes with a patch size of 5 km GSGC5, SGSC5 . Therefore, the results of these
simulations are not further discussed. The findings of the following subsection show that the vertical appearance of the low
extended stratus is strongly modulated by the surface characteristics in the case of low degree of heterogeneity. If the low extended stratus is modulated by a landscape, the
cloud-water mixing ratios are greater at higher levels over the ascent areas than over the descent areas or lower layers. For the sake of brevity, in this section, only the most
distinct examples of stratus modulation by surface heterogeneity are discussed for the spatial and temporal development.
6.1. Daily sums of domain-aÕeraged cloud-water When comparing the daily sums of domain-averaged latent heat fluxes with those of
Ž .
cloud-water Table 3 , a correlation is found between the water vapor supply to the atmosphere by turbulent latent heat fluxes and the amount of cloud-water in simulation
SGSX25 and SGSC25. Ž
. Ž
. Although simulations SGSX25
44.4 grass , SGSC25 44.4 grass , SGSP25
Ž .
Ž .
Ž 33.3 grass as well as SGSC5 49.8 grass have less grass than HOMG 100
. grass , their daily sums of domain-averaged cloud-water are higher due to upward
Ž .
moisture transport enhanced by the stronger surface heating of sand Table 3 . On the Ž
. other hand, the counterparts of these simulations, namely, GSGC25 55.6 grass ,
Ž .
Ž .
Ž .
GSGX25 55.6 grass , GSGP25 66.7 grass , and GSGC5 50.2 grass provide Ž
. lower or equal daily amounts of cloud-water than HOMG Table 2 . This finding means
that the combination of heating and evapotranspiring patches may enhance the cloud- water amount of low extended stratus as compared to the case with less surface heating.
The differential in the daily sums of domain-averaged cloud-water between GSGC25
Ž .
and SGSC25 as well as between GSGX25 and SGSX25 exceeds 0.8 grkg Table 3 . These differences may suggest that not the amount of land-use, but the land-use
distribution, i.e., the degree of surface heterogeneity, plays the major role for cloud-water amount. Comparing the daily sums of domain-averaged cloud-water mixing ratios
provided by the simulations with the heterogeneous landscapes, the greatest differences
Ž .
occur for SGSC10 to SGSX25, SGSC25, and SGSP25, respectively Table 3 . The daily sums of the cloud-water mixing ratios of GSGC10 and SGSC10 broadly
Ž agree with those of the simulations that assume nearly the same amounts of grass e.g.,
. GSGC5 50.2, SGSR5 46.7, GSGR5 53.3, GSGP5 53.3, SGSR5 46.7 . Here,
the daily sums of domain-averaged cloud-water differ about 0.3 grkg. The greater importance of the surface distribution than that of the fractional coverage by grass is
also manifested by the daily sums of the domain-averaged cloud-water between HOMG and HOMS, which differ 0.3 grkg, although grass supplies more water vapor to the
Ž .
atmosphere than sand e.g., Tables 2, 3 . 6.2. Horizontal distribution of cloud-water
Ž .
Ž .
In SGSC10 e.g., Fig. 9a , and SGSX25 e.g., Fig. 9b , the distributions of cloud-water clearly reflect the heterogeneity of the underlying surface in both cloud levels. In
Ž .
GSGC10 not shown , a clear relation of the cloud-water amount to surface heterogene- ity exists for the lower part of the low extended stratus. In the upper part, the
relationship is less distinct. Surprisingly, the structures of the cloud-water distribution provided by GSGC25
Ž .
Ž .
e.g., Fig. 9c are similar to those of SGSX25 e.g., Fig. 9b . The opposite is true for Ž
. Ž
. GSGX25 e.g., Fig. 10 and SGSC25 not shown . All other landscapes hardly modulate
Ž the cloud-water distribution e.g., at 12 LT up to 0.01 grkg at a height of 450 m, and up
. to 0.005 grkg at a height of 250 m except SGSP25 and GSGP25. In the case of these
simulations, a slight, but not distinct modulation parallel to the stripes can be detected Ž
. e.g., at 12 LT about 0.03 grkg . Nevertheless, further discussion only focuses on cases
Fig. 9. Distribution of cloud-water mixing-ratio in grkg at 12 LT at a height of 450 m height as simulated by Ž .
Ž . Ž .
a SGSC10, b SGSX25, and c GSGC25, respectively. Grey patches indicate grass and light grey patches indicate sand, respectively.
with a clear modulation of cloud-water by surface heterogeneity, namely, SGSX25, GSGC25, and SGSC10, respectively. Focus is on the level of maximum cloud-water at
12 LT.
6.2.1. SGSX25 Less cloud-water occurs over both the sand- and grass-patches in SGSX25 than in
Ž .
HOMG or HOMS. In SGSX25 Fig. 9b , at a height of 450 m, higher values of cloud-water are found above the WE-oriented sand-stripe in the middle than over the
alternating grass–sand–grass area in the northern and southern part of the domain at 12
Fig. 10. Like Fig. 9, but for the distribution of cloud-water mixing-ratio in grkg at 12 LT for GSGX25 at a Ž .
Ž . height of a 250 m and b 450 m, respectively.
LT. This maximum of cloud-water can be explained as follows: The sand-patches heat Ž
stronger and provide greater sensible heat fluxes than the grass-patches cf. Friedrich .
and Molders, 1998 . Thus, air rises over the sand-patches and is replaced by moist air
¨
from the neighbored upwind grass-patches that evapotranspire at a higher rate than sand-patches. Consequently, upward transport is enhanced over the sand-stripe and leads
to the increased cloud-water mixing ratios. In SGSX25, less cloud-water is formed Ž
above the sand-patches in the northern part in the WE-orientated area between 50–75
. Ž
and 25–50 km counted from the south and the southern part in the WE-orientated area .
Ž .
between 0–25 and 25–50 km counted from the south than over grass Fig. 9b . Especially at the northern and southern edges of the domain, there exist higher values
above grass-patches than sand-patches. The effect of the different water vapor supply from grass and sand is visible at a
Ž .
height of 450 m behind the grass–sand boundary Fig. 9b . In the northern part as well as in the southern part, cloud-water decreases behind the grass-patch with 0.005–0.020
grkg and increases after passing the sand with up to 0.010 grkg.
6.2.2. GSGC25 Ž
. In GSGC25, at a height of 450 m, Fig. 9c , the structures in the cloud-water
Ž .
distribution are similar to those of SGSX25 Fig. 9b . Despite of the grass-patch in the center of the domain, in GSGC25, there exists no response to this patch in the
distribution of cloud-water. On the contrary, in GSGC25 like in SGSX25, distinct responses in the cloud-water mixing ratio exist at the northern and southern WE-orien-
Ž .
tated stripe 0–25 and 50–75 km counted from the south , providing different values over grass than sand.
6.2.3. SGSC10 Ž
. In SGSC10 Fig. 9a , less cloud-water is formed than in HOMG or HOMS. In the
northern most WE-directed stripes, a distinct response to the underlying surface is found with an increase and a decrease of cloud-water after passing either a grass- or a
Ž sand-patch. In the middle WE-orientated part of the domain between 25 and 50 km
. Ž
counted from the south , maximum cloud-water mixing ratios exceed 0.56 grkg Fig. .
9a . The clear differences found for the latent heat fluxes over grass and sand are not Ž
. reflected in the cloud-water distribution Fig. 9a . Seemingly between 20 and 50 km
counted from the southern edge of the inner model domain, the cloud-water distribution behaves more like that of a WE-orientated, homogeneously covered surface than that of
Ž .
a heterogeneous surface Fig. 9a . Although, a response is visible, the types of surface do not provide a distinct assignable response in cloud-water mixing ratios.
6.3. Vertical distribution of cloud-water As aforementioned, on average, the amount of cloud-water increases from cloud-base
Ž .
Ž .
to cloud-top e.g., up to 0.4 grkg at noon for all simulations e.g., Fig. 10 . Since there is no relationship between the distributions of the surface and cloud-water for the
landscapes with patch lengths of 5 km as well as those with stripes of 25 km width perpendicular to the geostrophic wind direction, the vertical distribution of cloud-water
in these landscapes is not further discussed, here.
If the cloud-water distribution clearly shows structures at a height of 250 m, these Ž
structures will disappear at the 450-m level and new structures will build up e.g., Fig. .
10 . As pointed out already, in GSGC10, a clear relation between the cloud-water distribution and surface heterogeneity exists only for the lower part of the low extended
Ž .
stratus. In our study, the greatest and most distinct changes of cloud-water distribution Ž
. Ž
. with height are found for GSGX25 e.g., Fig. 10 and GSGC25 not shown at noon, for
which these cases are exemplary discussed in detail. For landscapes with large patches Ž
. i.e., low degree of heterogeneity , cloud-water is at a minimum in lower levels in the
Ž ascent areas, while at higher levels, maximum values of cloud-water are found e.g., Fig.
. 10 .
6.3.1. GSGX25 In GSGX25, for example, the maximum of cloud-water is found in the middle
Ž .
WE-orientated stripe between 25 and 50 km counted from the south at a height of 250 Ž
. m Fig. 10a . Here, the specific cloud-water values exceed those at the edges by more
than 0.020 grkg. Obviously, this middle grass-stripe governs the cloud-water distribu- tion at the southern edges. The lower values of cloud-water occurring over sand-patches
Ž .
at the corners Fig. 10a , may be explained by, on average, lower relative humidity and slightly warmer air occurring over sand than grass. As mentioned before, more water
Ž evapotranspires over the grass-cross. The steady lifting without disturbance by a change
. in the underlying surface; Fig. 7 supports the formation of the cloud-water maximum.
At a height of 450 m, the cloud-water mixing ratio exceeds 0.560 grkg in the southern Ž
. part of the domain Fig. 10b . Minimum values of cloud-water mixing ratios amount
Ž .
0.515 grkg at the interface sand–grass at 50 km counted from the south and at the Ž
. interface grass–sand at 50 km in WE-direction counted from the south; Fig. 10b . Note
that the behavior of SGSC25 is similar. 6.3.2. GSGC25
Ž .
Looking at the cloud-water distribution of GSGC25 at 450 m height Fig. 9c , for instance, low cloud-water mixing ratios are found over the northern and southern part
where more grass exists than over the middle part and descent occurs. The opposite is Ž
. true for 250 m not shown . Here, namely, low cloud-water mixing ratios are found over
Ž .
the strong ascent zones at 30–40 km counted from the south at the 250-m level. Greater mixing ratios of cloud-water are found over the decent zones of the grass-
Ž dominated WE-cross-section between 5–20 and 55–75 km both counted from the
. south; Fig. 8 left . Note that the behavior of SGSX25 is similar.
6.4. Temporal deÕelopment of cloud-water distribution In the diurnal course, the amount of cloud-water is related to the magnitude of the
sensible and latent heat fluxes with a delay of about 3 h. Increasing latent heat fluxes Ž
. enhance cloud formation positive feedback . Thus, the liquid-water content of the low
extended stratus is maximal at about 15 LT for all simulations. Later on, this enhanced Ž
cloudiness reduces insolation and, hence, the fluxes of sensible and latent heat negative .
feedback , which again slightly diminishes cloud-water. At about 18 LT, cloud base starts to sink for most of the simulations.
As pointed out before, only SGSX25, GSGX25, SGSC25, GSGC25, SGSC10, and GSGC10, provide a clear response in cloud-water distribution to the underlying surface.
Moreover, GSGC25 and SGSX25 as well as GSGX25 and SGSC25 provide a similar behavior concerning the distribution pattern of cloud-water and the former pair behaves
opposite to the latter pair. For these reasons, the discussion of the temporal development of cloud-water distribution can be exemplary limited to that of SGSX25 and SGSC10,
respectively.
6.4.1. SGSX25 Ž
. As mentioned already, at 12 LT Fig. 9b , areas of low cloud-water mixing ratios are
Ž .
found in the northern and southern parts above the sand-patches Fig. 9b . The
maximum in the amount of cloud-water occurring over the middle sand-stripe resembles Ž
a maximum in sensible heat flux at 12 LT above the sand-stripe not shown; for a .
discussion of the sensible heat fluxes see Friedrich and Molders, 1998 and a maximum
¨
Ž .
in latent heat flux above the grass-corners Fig. 3 . Note that in the northern and
Fig. 11. Like Fig. 9, but for the distribution of cloud-water mixing-ratio in grkg for SGSX25 at a height of Ž .
Ž . 450 m at a 15 LT and b 18 LT, respectively.
southern sand-patches, the latent heat fluxes increase slightly behind 40 km in WE-direc- Ž
. tion see Fig. 3 .
Ž The extension of the area of high cloud-water mixing ratios increases until 15 LT cf.
. Figs. 9b, 11a . This increase agrees with the maximum of the domain-averaged latent
heat flux at 13 LT. The cloud-water maximum that at 12 LT occurs above the Ž
sand-stripe in WE-direction at the interface grass–sand at 40–60 km counted from the .
Ž .
south , shifts northwards with progressing time cf. Figs. 9b, 11a,b . The same is true for Ž
. the minimum of cloud-water 0.545–0.540grkg . The distinct upward motion occurring
Ž .
Ž .
over sand Fig. 6 breaks down in the late afternoon not shown . Accordingly, the Ž
. highest values of cloud-water occur at 18 LT in the grass-covered parts Fig. 11b , while
over the sandy parts the cloud-water amount decreases rapidly. In the northern and southern parts, the sand-patches do not influence cloud-water amount at the height of
450 m. These findings suggest that surface heterogeneity may not only affect the spatial, but also the temporal development of low extended stratus.
6.4.2. SGSC10 In SGSC10, the cloud-water distribution shows a similar behavior with time than
Ž .
Ž .
SGSX25 Figs. 9b, 11 . In SGSC10 Fig. 9a , at a height of 450 m, however, a clear response of cloud-water to surface heterogeneity only exists at 12 LT. The maximum
Ž .
values achieved in the mixing ratios of cloud-water more than 0.560 grkg are found in the WE-orientated area between 25–40 km at 12 LT, 35–55 km at 15 LT, and 40–60
Ž .
Ž .
km all counted from the south at 18 LT not shown . Between 15 and 18 LT, the amount of cloud-water decreases agreeing with the decrease of the domain-averaged
latent heat flux.
7. Conclusions and outlook
