Design of the study The latent heat fluxes

to the ground to 1 km at the top, which is located in 12-km height. Eight levels are located below the 2-km height and nine are above. Homogeneously flat terrain is assumed for all simulations.

3. Design of the study

Two simulations are performed assuming alternatively a homogeneous cover by sand Ž . and grass grown on loamy soil Fig. 2 . These simulations and their results are denoted as HOMS and HOMG, hereafter. Furthermore, sixteen simulations are performed for Ž . different patterns of sand and grass Fig. 2 . These simulations and their results are addressed according to the coverage by sand, S, and grass, G, their pattern, and the smallest length of patches given in km. The letters SGS, for instance, stand for a dominance by sand, while GSG stands for a dominance by grass. The patches arranged as stripes parallel or perpendicular to the wind, in form of a checkerboard or a cross are Ž . denoted as P, R, C, and X, respectively see Fig. 2 . In the following discussion, simulation results obtained by assuming the aforemen- tioned landscapes are compared with each other. In doing so, the influence of surface pattern on the water vapor supply to the ABL and on cloud formation as well as the interaction between cloudiness and evapotranspiration are elucidated. To examine the influence of surface heterogeneity on latent heat fluxes, vertical motion, and the properties of low extended stratus, the degree of surface heterogeneity is Ž . defined by Molders, 1999 : ¨ d s FrF 1 Ž . max for the inner model domain. This measure considers the total length of boundaries, F , between areas of different surface types in the domain of interest. In the case of a Ž . maximum degree of heterogeneity d s 1 , each grid cell is also the boundary to another surface type. The total length of the boundary equals F . In the case of homogeneity, ma x Ž . there exists only one surface type and no boundary d s 0 . The degree of heterogeneity as obtained by this measure is listed in Table 2 for the various landscapes.

4. The latent heat fluxes

During the day, the entire domain is totally covered by low-level stratus in all simulations. Since clouds reduce insolation, the turbulent moisture and heat fluxes are weak. At noon, the homogeneously grass-covered domain, for instance, provides a latent heat flux of 46.4 Wrm 2 over the entire domain, while, at the same time, the homogeneously sand-covered domain provides a latent heat flux of 39.6 Wrm 2 over the Ž . entire domain Table 2 . The domain-averaged latent heat fluxes of the simulations with Ž . heterogeneous surfaces fall between these values Table 2 . Generally, grass-patches provide greater amounts of water vapor to the ABL than sand-patches. Nevertheless, the daily sum of the latent heat fluxes does not correlate to the coverage by grass or the Ž . degree of heterogeneity Table 2 . Fig. 2. Schematic view of the land-use distributions applied in the numerical experiments. Because of identical initial meteorological conditions, the distribution patterns of latent heat fluxes differ only due to the different land-use distribution. Primary differ- Table 2 Daily sums of domain-averaged latent heat fluxes, ÝL E, domain-averaged latent heat flux at 1300 LT, ÝL E v v Ž . 13 , coverage by grass, C, size of the largest grass-covered patch, A, and degree of heterogeneity, d , for all simulations 2 2 2 Ž . Ž . Ž . Ž . Ž . Simulation ÝL E Wrm ÝL E 13 Wrm C A km d v v HOMG 404.6 46.4 100.0 5625 0.00 SGSX25 396.9 41.7 44.4 625 0.16 SGSC25 386.1 43.2 44.4 625 0.20 GSGP25 379.3 43.7 66.7 1875 0.13 SGSP25 378.5 42.8 33.3 1875 0.13 GSGR25 373.6 43.7 66.7 1875 0.13 SGSR5 370.1 43.3 46.7 375 0.53 GSGP5 368.9 43.1 53.3 375 0.53 GSGC25 368.6 42.6 55.6 625 0.20 SGSP5 368.4 43.1 46.7 375 0.53 GSGC5 366.1 42.7 50.2 25 1.00 SGSC10 366.0 42.5 48.0 150 0.47 GSGC10 361.8 42.8 52.0 150 0.47 GSGX25 358.9 44.4 55.6 3125 0.16 SGSC5 353.0 42.2 49.8 25 1.00 SGSR25 345.3 41.8 33.3 1875 0.13 GSGR5 343.9 41.7 53.3 375 0.53 HOMS 316.6 39.6 0.0 0.00 ences in water-vapor supply result from the different surface characteristics of grass and Ž . Ž . sand Tables 1, 2 and different surface arrangements Fig. 2 . Here, the different albedo, for instance, leads to differences in net radiation. Hence, incoming energy is differently partitioned into the fluxes of sensible and latent heat. Secondary differences result from the modified micrometeorological condition that again affects the heat fluxes. Thus, water supply and moisture transport into the ABL differ too. Therefore, with progressing integration time, further differences may arise from the altered thermal stratification, cloudiness, net radiation reaching the surface and, hence, modified evapo- transpiration, as well as due to differences in the advection of momentum, heat, and moisture. Moreover, at cloud top, the different cloud-water amount leads to changes in Ž . long-wave radiative cooling that again slightly affect the microphysics of the stratus. Although at the tops of low extended stratus, the impact of surface heterogeneity on radiative cooling may be of some importance, for brevity, this article is limited to the discussion of the influence of surface heterogeneity on latent heat fluxes, vertical motions, and cloud-water amount. 4.1. Distribution pattern of latent heat fluxes Surface heterogeneity influences the near-surface atmosphere and flow by the altered Ž surface characteristics e.g., albedo, roughness length, emissivity, evaporative conductiv- . ity, etc. . Since the atmospheric moisture and temperature states try to achieve an equilibrium with the respective underlying surface, the micrometeorological conditions Ž . e.g., near-surface wind, near-surface temperature and humidity, etc. are modified by fluxes when ever a parcel passes a change in the underlying surface. Thus, after passing several alternating patches of grass and sand, the micrometeorological condition over a grass-patch located in the western part of the domain, for instance, slightly differ from those over grass in the eastern part of the domain because of the frequent modulation of the air mass when ever passing a discontinuity. These differences grow with time and with increasing distance from the first change in the underlying surface. The altered micrometeorological properties again modify the sensible and latent heat fluxes. The magnitude to which a surface may coin the air mass depends on the time it rests above the patch and, hence, on the patch size. Thus, if the patch size falls below 10 = 10 km 2 like for SGSR5, GSGR5, SGSP5, GSGP5, SGSC5, and GSGC5, respectively, the flux distribution shows hardly an organized response to the underlying surface. Therefore, the results of these studies are not discussed explicitly. For patch sizes larger than 10-km side-length, for instance, in GSGC25, each patch evokes a discernible and assignable Ž . own response. These findings broadly agree with Shuttleworth’s 1988 theoretical considerations. 4.1.1. SGSX25 and GSGX25 Ž . Rotation of crops may cause differences in surface distribution like SGSX25 Fig. 3 Ž . Ž and GSGX25 Fig. 4 , for instance. Juxtaposing the results obtained for 12 LT local . time by simulations with same degree of surface heterogeneity, and patch arrangement, Ž . but inverted distribution of grass and sand e.g., SGSX25 and GSGX25, Figs. 3, 4 Ž shows that landscapes with large connected grass-patches in this example the cross, Fig. . Ž . 4 and small isolated sand-patches here the edges of the inner domain may supply more water vapor to the ABL than those of opposite arrangement of grass and sand. In Fig. 3. Distribution of latent heat-fluxes in Wrm 2 at 12 LT as simulated by SGSX25. Grey patches indicate grass and light grey patches indicate sand, respectively. Fig. 4. Like Fig. 3, but for GSGX25. GSGX25 and SGSX25, the surface characteristics of the cross-area govern the distribu- tion and magnitude of heat and moisture exchange. At noon, for instance, the maximum 2 Ž . latent heat flux of SGSX25 amounts more than 46 Wrm over grass Fig. 3 compared 2 Ž . with more than 50 Wrm over grass in GSGX25 Fig. 4 . 4.1.2. GSGC25 and GSGX25 Comparing the results of simulations with different patch sizes and degree of heterogeneity, but same fractional coverage of grass shows that large connected grass- Ž patches may provide higher latent heat fluxes than isolated grass-patches e.g., compare . GSGX25 and GSGC25, Figs. 4, 5 . The latent heat fluxes of the grass-patch located in Ž . 2 the center in GSGC25 Fig. 5 , for instance, amounts less than 46 Wrm , while, in GSGX25, here, locally more than 50 Wm 2 are achieved. Thus, one may conclude that the mean water vapor supply to the ABL by one patch, among others, depends on its size. These findings mean that the surface characteristic of the largest connected part, in the case of GSGX25, the grass-cross, does not only dominate the latent heat-flux distribution, but also affects the fluxes of the downwind neighbored patches. Note that in the checkerboard arrangement of GSGC25, the grass-patches provide Ž . similar fluxes than those in SGSX25 compare Figs. 3, 5 . 4.1.3. GSGC25 and SGSC10 GSGC25 and SGSC10 are landscapes of different degrees of surface heterogeneity, Ž . and different coverage by grass, but similar patch pattern Table 2, Fig. 2 . At noon, for instance, the latent heat fluxes of GSGC25 and SGSC10 range from 32 Wrm 2 to 48 2 Ž . Wrm in both simulations e.g., Fig. 5 . Like in GSGC25, in SGSC10, the latent heat Ž . flux distribution reflects the surface patches not shown . Consequently, in SGSC10, the latent heat-flux distribution is more heterogeneous than in GSGC25. Fig. 5. Like Fig. 3, but for GSGC25. 4.2. Daily domain aÕerages The largest differentials in the daily sums of the domain-averaged latent heat fluxes Ž 2 . Ž . 88 Wrm occur between the results of HOMG and HOMS Table 3 . The domain- averaged latent heat fluxes of all simulations assuming heterogeneous surfaces range Ž . between these two values see also Table 2 . The greatest differential between simula- tions with heterogeneous surface-cover amounts 53 Wrm 2 for SGSX25 and GSGR5. On the contrary, the daily sums of domain-averaged latent heat fluxes hardly differ for the following pairs: GSGP5 and GSGC25, GSGP25 and SGSP25, as well as GSGC5 Ž . and SGSC10 Table 3 . The daily sums of the domain-averaged latent heat fluxes do not always grow with increasing coverage by grass, size of the grass-covered patches or Ž . degree of heterogeneity Tables 2, 3 . Ž The greatest deviations arise between HOMS and nearly all other simulations Table . 3 . In this homogeneously dry and warm, sandy domain, the incoming energy is partitioned toward higher sensible and lower latent heat fluxes than in the partly grass-covered domains or than in the totally grass-covered domain. Even for small fractional coverage by grass, the latent heat flux increases rapidly as compared to Ž . HOMS Table 3 . Out of all the simulations assuming heterogeneous landscapes, SGSX25 provides the greatest daily sums of the domain-averaged latent heat fluxes Ž 2 . Ž . 396.9 Wrm , although it has not the largest amount of grass Table 2 . This behavior may be explained by the oasis effect. The slightly warmer air, due to the stronger heating of sand than of grass, enhances evapotranspiration. In contrast to SGSX25, the daily sum of domain-averaged latent heat fluxes is smaller for the ‘‘inverse landscape’’ Ž . GSGX25 which is dominated by grass because the greater grass-coverage of GSGX25 leads to a slightly cooler lower ABL than for SGSX25. Table 3 Ž . Ž Daily sums of the domain-averaged latent heat flux upper values and cloud-water mixing ratio lower values . Ž . in brackets . Deviations values vertical minus horizontal line are given in the upper and lower triangle of the table for latent heat fluxes and cloud-water, respectively. Note that fluxes and mixing ratios are rounded for clarity of table 2 Wrm HOMG SGSX25 SGSC25 GSGP25 SGSP25 GSGR25 SGSR5 GSGP5 grkg HOMG 405 y8 y19 y26 y26 y31 y35 y36 Ž . 12.6 SGSX25 y0.7 397 y11 y18 y19 y23 y27 y28 Ž . 13.3 SGSC25 y0.7 386 y7 y7 y12 y16 y17 Ž . 13.3 GSGP25 0.1 0.8 0.8 379 y5 y9 y10 Ž . 12.5 SGSP25 y0.7 y0.8 379 y5 y8 y10 Ž . 13.3 GSGR25 0.7 0.7 y0.1 0.7 374 y4 y5 Ž . 12.6 SGSR5 0.7 0.7 y0.1 0.7 370 y1 Ž . 12.6 GSGP5 0.7 0.7 y0.1 0.7 369 Ž . 12.6 GSGC25 0.1 0.8 0.8 0.8 0.1 0.1 0.1 SGSP5 0.7 0.7 y0.1 0.7 GSGC5 0.7 0.7 y0.1 0.7 SGSC10 0.3 1 1 0.2 1 0.3 0.3 0.3 GSGC10 0.7 0.7 y0.1 0.7 GSGX25 0.1 0.8 0.8 0.8 0.1 0.1 0.1 SGSC5 y0.1 0.6 0.6 y0.2 0.6 y0.1 y0.1 y0.1 SGSR25 0.1 0.8 0.8 0.8 0.1 0.1 0.1 GSGR5 0.7 0.7 y0.1 0.7 HOMS 0.3 1 1 0.2 1 0.3 0.3 0.3 Looking at the simulations with checkerboard-like landscapes, in the sand-majorized Ž . landscapes with large patch sizes e.g., SGSC25, SGSC10 , the daily sums of domain- averaged latent heat fluxes exceed those of their grass-majorized counter-pairs like in Ž . SGSX25 e.g., GSGC25, GSGC10 . Here, SGSC10 and GSGC5 provide the same sum Ž 2 . 366 Wrm ; Table 3 . Out of the checkerboard-arranged landscapes, SGSC5 provides Ž 2 . the smallest daily sum of domain-averaged latent heat fluxes 353 Wrm ; Table 3 . In GSGC25 SGSP5 GSGC5 SGSC10 GSGC10 GSGX25 SGSC5 SGSR25 GSGR5 HOMS y36 y37 y39 y39 y43 y46 y52 y60 y61 y88 y28 y29 y31 y31 y35 y38 y44 y52 y53 y80 y17 y18 y20 y20 y24 y27 y33 y41 y42 y69 y10 y11 y13 y13 y17 y20 y26 y34 y35 y62 y10 y11 y13 y13 y17 y20 y26 y34 y35 y62 y5 y6 y8 y8 y12 y15 y21 y29 y30 y57 y1 y2 y4 y4 y8 y11 y17 y25 y26 y53 y1 y3 y3 y7 y10 y16 y24 y25 y52 369 y1 y3 y3 y7 y10 y16 y24 y25 y52 Ž . 12.5 y0.1 368 y2 y2 y6 y9 y15 y23 y24 y51 Ž . 12.6 y0.1 366 y4 y7 y13 y21 y22 y49 Ž . 12.6 0.2 0.3 0.3 366 y4 y7 y13 y21 y22 y49 Ž . 12.3 y0.1 y0.3 362 y3 y9 y17 y18 y45 Ž . 12.6 0.1 0.1 y0.2 0.1 359 y6 y14 y15 y42 Ž . 12.5 y0.2 y0.1 y0.1 y0.4 y0.1 y0.2 353 y8 y9 y36 Ž . 12.7 0.1 0.1 y0.2 0.1 0.2 345 y1.4 y28 Ž . 12.5 y0.1 y0.3 y0.1 0.1 y0.1 344 y27 Ž . 12.6 0.2 0.3 0.3 0.3 0.2 0.4 0.2 0.3 317 Ž . 12.3 the sand-dominated checkerboard landscapes, the daily domain-averaged latent heat fluxes are arranged according to the patch size. Ž In simulations with stripes orientated parallel to the wind GSGP25, SGSP25, . GSGP5, SGSP5 , the daily sums of domain-averaged latent heat fluxes increase with the patch sizes and fractional coverage by grass in the domain. Here, for the same patch sizes, the degree of surface heterogeneity is the same and the fluxes differ only slightly 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