for the same degrees of surface heterogeneity. However, no correlation of the daily sums of domain-averaged latent heat fluxes to patch size and arrangement is found in
Ž .
simulations with stripes perpendicular to the wind GSGR25, SGSR25, GSGR5, SGSR5 . SGSC25 and SGSX25 have the same fractional coverage by grass, but different
degree of surface heterogeneity. Thus, in this case, the different sums of domain-aver- Ž
aged latent heat flux result from the different degrees of surface heterogeneity Tables 2, .
3 . All these findings suggest that the orientation of the pattern to the wind and the patch
size cause differences in the daily sums of the domain-averaged latent heat fluxes. This Ž
. broadly agrees with the Molders’ 1999 findings who investigated the sensitivity of the
¨
impact of land-use changes to the direction of wind. Moreover, the results suggest that both the fractional coverage and the degree of heterogeneity concurrently affect the
latent heat fluxes.
5. Vertical motions
As discussed before, different surface characteristics and discontinuities may lead to different moistening of low-level atmosphere through transpiration and different air
heating. Induced by surface thermal heterogeneity, the ascending motions differ. Note that since the vertical velocities are volume averages representing volumes of the
thickness of the model layer times 5 = 5 km
2
, the magnitude of vertical velocity depends on grid size. Generally, the inclusion of a finer grid increases ability of
meteorological models to produce larger vertical motions because small-scale horizontal temperature gradients and velocities can be resolved. To avoid differences resulting from
grid size, in our study, all simulations are performed with the same grid size of 5 = 5 km
2
as pointed out already in Section 2. In all simulations, vertical velocities do not exceed 0.05 mrs. As mean vertical
velocities are small, turbulence, in principle, is an important contributor to vertical transport processes, energetics and physics of low extended stratus. In absolute magni-
tude, however, the turbulence level is low in low extended stratus. The pattern of vertical motions depends on patch distribution, patch size, and
modulation of the air mass by upwind surface heterogeneity. Water vapor is transported to higher levels by upward motions. In the ABL, a distinct pattern of ascent and descent
only develops for some patch arrangements, namely, SGSX25, GSGC25, SGSC10, and GSGX25. In the following, the vertical motions at 12 LT will be exemplary examined
for these simulations.
5.1. SGSX25 In Fig. 6, the vertical wind distribution of SGSX25 is exemplary shown at two
Ž representative WE cross-sections. In the cross-section at 35 km counted from the
. Ž
. south , sand exists only while, in the cross-section at 60 km counted from the south ,
Ž .
grass dominates Fig. 6 . As pointed out before, sand heats more strongly, but supplies less water vapor to the ABL than grass. Due to the stronger heating upward motions
Ž .
develop over sand at the 35-km cross-section Fig. 6b . Descent occurs over the northern
Ž . Ž .
Ž .
Fig. 6. WE cross-section at a 60 km and b 35 km both counted from the south of vertical wind distribution in cmrs as simulated by SGSX25. At 60 km, maximum and minimum values are 0.2 and y1.1
cmrs, respectively. At 35 km, maximum value is 0.9 cmrs. The black underlined parts represent grass.
Ž .
and southern grass-dominated part cf. Fig. 6a . Here, however, over sand, the down- Ž
. ward motions exceed those occurring over grass Fig. 6a .
5.2. GSGX25 Ž
. Despite of the same degree of heterogeneity like SGSX25 Table 2 , in GSGX25, a
Ž .
totally different pattern of vertical motion establishes Figs. 6, 7 . In GSGX25, namely, Ž
. Ž
. ascent occurs in the WE cross-sections at 25 Fig. 7c and 15 km Fig. 7d , while
Ž .
Ž descent is found for the WE cross-sections at 35 Fig. 7b and 60 km Fig. 7a; always
. counted from the south . In contrast to its inverse counterpart SGSX25, in GSGX25,
descent or ascent cannot be related to the surface type dominant in the WE cross-section
Ž . Ž .
Ž . Ž .
Ž .
Fig. 7. WE cross-section at a 60 km, b 35 km, c 25 km, and d 15 km all counted from the south of vertical wind distribution in cmrs as simulated by GSGX25. At 15 km, maximum and minimum values are
1.2 and y0.1 cmrs. At 25 km, maximum and minimum values are 1.3 and y0.1 cmrs. At 35 km, maximum and minimum values are 0.3 and y0.7 cmrs. At 60 km, maximum and minimum values are 0.2 and y1.6
cmrs. The black underlined parts represent grass. The dashes stand for the grass-sand boundary.
Ž .
Ž .
Ž .
cf. Fig. 7 . The WE cross-sections at 60 descent and 15 km ascent , for instance, are both dominated by sand. In the WE cross-sections at 35 km, the descent enhances
Ž .
toward the east Fig. 7 . This different behavior results from the altered heating and evapotranspiring, which modifies thermal stratification and vertical motions. This find-
ing means that the surface distribution and patch size, i.e., the degree of heterogeneity, are not the only factor that determines the atmospheric response. Additionally, the kind
of surface characteristics plays an important role. The effects of heterogeneity and surface characteristics are juxtaposed in the atmospheric response. The effects may even
enhance each other in their impact.
5.3. GSGC25 Ž
. In the case of GSGC25 not shown , the vertical motions are similar to those of
SGSX25 for the WE cross-section at 35 and 60 km, because of the same patch Ž
. distribution here see Fig. 2 . In the area of ascent located between 25 and 50 km
Ž .
counted from the south , however, ascent is less continuously in GSGC25 than in SGSX25 due to the grass-patch in the middle of the domain in GSGC25. Perturbations
occur above the borders of different surface types, i.e., the additional grass-patch only slightly modifies the vertical motions.
5.4. SGSC10 For a patch size of 10 = 10 km
2
, the pattern of vertical motion is quite complicate Ž
. Fig. 8 . Since the wind turns to the left when approaching the surface, it has a more
Ž . Ž .
Ž . Ž .
Ž .
Fig. 8. WE cross-section at a 60 km, b 30 km, c 20 km, and d 10 km all counted from the south of vertical wind distribution in cmrs as simulated by SGSC10. At 10 km, maximum and minimum values are 0.3
and y0.3 cmrs. At 20 km, maximum and minimum values are 0.3 and y0.2 cmrs. At 30 km, maximum and minimum values are 0.7 and y0.1 cmrs. At 60 km, maximum and minimum values are 0.1 and y1.3 cmrs.
The black underlined parts represent grass.
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
