Abstract

The Loess Plateau of China consists of dissected flat tablelands with steep gullies. To evaluate the effect of topography on local circulation and cumulus generation over the Loess Plateau, numerical simulations of atmospheric boundary layer (ABL) development were conducted using a cloud-resolving nonhydrostatic model. Two types of numerical simulation were carried out under two sets of bottom boundary conditions: real terrain and flat terrain. The differences in ABL development and cumulus generation between the flat- and real-terrain conditions are described and the local circulation structures induced by ABL development are illustrated. More cumulus clouds were generated over the real terrain than over the flat terrain. In the real-terrain case, large amounts of cumulus cloud were generated on the windward slopes and on the edge of the tableland, with updrafts caused by thermal generation and a local circulation developing with horizontal and vertical scales of several kilometers. Cumulus clouds clearly developed at the top of the ABL because the water vapor is nonhomogeneously lifted by the local circulation on windward slopes and on edge of the tableland. Thus, the topography of the Loess Plateau plays an important role in cumulus generation.

1. Introduction

In daytime, water vapor from the land is transported to the upper part of the atmospheric boundary layer (ABL), often generating cumulus clouds near the ABL top. Cumulus clouds play an important role in the heat and water vapor exchange between the ABL and the free atmosphere. Additionally, cumulus clouds alter the amount and distribution of shortwave and longwave radiative flux divergence in the ABL and are considered important to understanding climate change (Stull 1988).

Studies have suggested that cumulus generation is closely related to local circulation, induced by the topography and heterogeneity of the land surface (e.g., Anthes 1984). Land surface topography and heterogeneity produce spatial heterogeneity of sensible and latent heat fluxes, which drive local circulation. For example, cumulus generation over mountainous regions of the southern Tibetan Plateau has been explained by the thermally induced local circulation process (Kurosaki and Kimura 2002; Fujinami et al. 2005). Moreover, not only natural land cover patterns (Hiyama et al. 2007) but also anthropogenic land cover changes, such as deforestation (Baidya Roy and Avissar 2002) and extensive irrigation in dry areas (Kawase et al. 2008), can modify atmospheric circulations and induce local circulations. This land surface heterogeneity and the induced local circulations have effects on cumulus generation.

In arid and semiarid regions, cumulus clouds are frequently generated in daytime on sunny days in summer, despite low atmospheric water vapor content. In this situation, cumulus clouds might play an important role in regional water cycles. Sato et al. (2007) summarized cloud patterns over arid and semiarid regions of Northeast Asia based on a statistical analysis of satellite observations. Kawase et al. (2008) explained the generation of cumulus clouds around areas of extensively irrigated farmland within Northeast Asia using a mesoscale numerical model. For example, the irrigated farmland of the Hetao Irrigation District is located in the middle reaches of the Yellow River basin. This area is surrounded by the Langshan Mountains to the northwest, the Ulan Buh Desert to the southwest, and the Loess Plateau to the south (Fig. 1a). Kawase et al. (2008) found that the cumulus clouds over the mountains were generated by a mountain–valley circulation that developed between the mountains and the irrigated farmland. They also found that cumulus clouds over the boundary between the desert and the irrigated farmland were generated as a result of a local circulation induced by the land surface heterogeneity. In contrast, the downward flow induced by the two circulations suppressed cloud generation over the irrigated farmland. Sato et al. (2007) showed that cumulus cloud not only generated over these regions but also over the Loess Plateau. However, they did not explain the detailed structure of the cumulus clouds over the Loess Plateau.

Fig. 1.

(a) Map of the Yellow River basin. (b) Topography around the ABL observation site. The star indicates the location of the ABL observation site (35.24°N, 107.68°E).

Fig. 1.

(a) Map of the Yellow River basin. (b) Topography around the ABL observation site. The star indicates the location of the ABL observation site (35.24°N, 107.68°E).

China’s Loess Plateau, located between 34° and 40°N and between 100° and 115°E, corresponds almost exactly with the middle reaches of the Yellow River basin (Fig. 1a). As a semiarid region, the Loess Plateau receives approximately 400 mm of annual precipitation, approximately 70% of which falls in summer (Kimura et al. 2004; Takayama et al. 2004). The Loess Plateau has distinctive topography that consists of dissected flat tablelands with steep gullies (Fig. 1b) and covers a total area of 0.62 × 106 km2 (35% tableland, 65% gully slope; Li et al. 2007). The gullies of the Loess Plateau can reach depths of several hundred meters and widths of several tens of kilometers.

We previously carried out temporary continuous ABL observations over the southern Loess Plateau to diagnose the exchange processes of momentum, heat, and water in the land–vegetation–atmosphere system over the Loess Plateau (Hiyama et al. 2005). The ABL observation site (35.24°N, 107.68°E) was located on the edge of the flat tableland, and the nearest gully was located approximately 500 m to the southeast. At the ABL observation site, we frequently observed cumulus clouds on sunny days in early summer. Takahashi et al. (2008) discussed the vertical transport of water vapor as a result of the ABL development and cumulus convection. The cumulus generation might be related not only to the surface wetness but also to the topographical features of the Loess Plateau. Thus, the effect of topography on cumulus generation should also be considered, although the vertical and horizontal scales of the topography are smaller than those in previous studies. Li et al. (2007) demonstrated that the topographic difference between the gully and flat tableland has an effect on the inner surface-layer structure. However, past studies have not investigated the detailed process of cumulus generation over the Loess Plateau.

Recently, several large-eddy simulations of the ABL in the presence of topography have been conducted, and several studies have discussed the effects of topography on ABL developments (e.g., Walko et al. 1992). The height and length scales of idealized terrain, which affect the ABL structure, have also been evaluated (Gopalakrishnan et al. 2000; Zängle and Chico 2006). Furthermore, the effect of background winds on convection within the ABL over idealized hilly terrain has been examined (Tian and Parker 2002). However, most previous studies have used idealized terrain, with only a few conducting numerical simulations of ABL development over real terrain (e.g., Tian et al. 2003). In addition, because of a focus on understanding the basic statistical properties of the ABL, many numerical simulations have been executed without cloud microphysical processes.

Thus, we conducted numerical simulations of ABL development to evaluate the effect of topography on cumulus generation over the Loess Plateau of China. Two types of numerical simulation with cloud microphysical processes were carried out under two sets of bottom boundary condition: real terrain and flat terrain. We describe the differences in ABL development and cumulus generation over the real and flat terrains. We also describe the structure of local circulations induced by ABL development. Finally, possible mechanisms for cumulus generation over the real and flat terrains are discussed.

2. Numerical model and experimental design

We used a cloud-resolving model called the Cloud Resolving Storm Simulator (CReSS; Tsuboki and Sakakibara 2002), which was formulated based on a nonhydrostatic and compressible equation system with terrain-following coordinates. This model uses a 1.5-order turbulence kinetic energy closure scheme, and a bulk method of warm rain is used to explicitly formulate the cloud physics. Because the spatial resolution is high enough to resolve individual convective clouds, CReSS has been used to simulate ABL development and convective cloud generation (e.g., Liu et al. 2006; Yamada 2008). Wang et al. (2005) provide a detailed description of CReSS.

We conducted various numerical simulations (Table 1). The bottom boundary conditions used in the simulations were either real terrain (REAL) or flat terrain (FLAT). In the real-terrain condition, the bottom boundary conditions were based on high-resolution digital elevation data from the Shuttle Radar Topography Mission (Fig. 2). The flat tableland is 1200–1224 m MSL (Fig. 2, gray shading) and extends from northwest to southeast. The northern and southern areas of the tableland have gullies of approximately 200 m in depth. We set the center of the simulation domain as the ABL observation site (35.24°N, 107.68°E), which was located on the tableland. The flat-terrain condition is a flat, homogeneous surface at 1224 m MSL, which corresponds to the altitude of the tableland. CReSS cannot reproduce the difference in shortwave radiation at the surface caused by different slopes of topography. Thus, we consider only the horizontal thermodynamic contrast caused by altitude differences as a result of the presence of topography.

Table 1.

Summary of numerical simulations.

Summary of numerical simulations.
Summary of numerical simulations.
Fig. 2.

Topography of the real terrain that was used as the bottom boundary condition for the REAL runs. The gray area corresponds to flat tableland at 1200–1224 m MSL. The star indicates the location of the ABL observation site. (The digital elevation data were obtained online at http://www2.jpl.nasa.gov/srtm/)

Fig. 2.

Topography of the real terrain that was used as the bottom boundary condition for the REAL runs. The gray area corresponds to flat tableland at 1200–1224 m MSL. The star indicates the location of the ABL observation site. (The digital elevation data were obtained online at http://www2.jpl.nasa.gov/srtm/)

The evaporation efficiency (β) was set to 0.05 for the dry case (DRY) and 0.2 for the relatively wet case (WET). These β values were based on an observational study over the ABL observation site (W. Li 2008, personal communication). Most parts of the tableland were randomly occupied by agricultural fields, including wheat and maize, and apple orchards. Most gullies were occupied by grasslands, sparse woodland, and bare soil. Therefore, most parts of the land surface of the model domain were covered by some type of vegetation. Thus, we assumed that the land cover did not change dramatically between tableland and gully, and the β values were set as uniform for the model domain. Hereinafter, FLAT model runs group the FLAT–DRY and FLAT–WET runs, and the REAL model runs group the REAL–DRY and REAL–WET runs.

The simulation settings were based on numerical simulations by CReSS of the convective boundary layer over a humid terrestrial area (Endo et al. 2008). The diurnal variation in shortwave radiation was used as the forcing data, and the surface energy balance was considered. The surface process was based on a simple bulk method, with the prediction of soil temperature by thermal diffusion (Louis et al. 1981). The numerical experiments were conducted for 10 h, from initialization at 0800 Beijing standard time (BST). The time step for nonacoustic waves was 0.5 s and for acoustic waves 0.1 s. Results of the numerical simulations were output every 600 s from 0 to 36 000 s (10 h). The initial conditions were set using observational data obtained by microwave radiometer and wind profiler radar at the ABL observation site for below 6724 m MSL and radiosonde data at 00 UTC (0800 BST) at Pingliang (35.55°N, 106.66°E) for above 7520 m MSL (400 hPa). As an example, simulation settings for the REAL–DRY run are summarized in Table 2. Land surface parameters were determined from observations at the ABL observation site and set as uniform. Open (radiation) boundary conditions were set as the lateral boundary for REAL runs. To obtain a wide buffer region, the simulation spanned a domain of 50 000 m × 50 000 m × 11 292 m with a mesh of 500 × 500 × 110 points, and the center domain of 20 000 m × 20 000 m × 11 292 m was used for the REAL runs. The horizontal grid size was 100 m, and the vertical grid size was 50 m less than 4225 m MSL. For the FLAT runs, the lateral boundary was set as periodic boundary conditions. The simulation spanned a domain of 20 000 m × 20 000 m × 12 516 m with a mesh of 200 × 200 × 110 points. The horizontal grid size was 100 m, and the vertical grid size was 62 m less than 5341 m MSL.

Table 2.

Simulation settings for the REAL–DRY run.

Simulation settings for the REAL–DRY run.
Simulation settings for the REAL–DRY run.

We selected 19 June 2005 as the simulation date, when typical cumulus generation was observed in the daytime at the ABL observation site (Takahashi et al. 2008). Observational results for 19 June 2005 have already been reported. The daily mean sensible and latent heat fluxes were 260 and 140 W m−2, respectively, and the maximum height of the ABL top was 2700 m MSL. (Nishikawa et al. 2007). Strong updrafts linked to cumulus convection were frequently observed in the afternoon (Takahashi et al. 2008). The simulation settings for the REAL–DRY run are similar to the case of 19 June 2005. Our intention is to evaluate the effect of topography on cumulus generation, not to reproduce the observational results.

3. Results

In the initial conditions for the simulations, the potential temperature was stably stratified near the surface and neutrally stratified from 2000 to 4500 m MSL, which was probably the residual layer (Fig. 3). The dominant wind directions were southeast up to 2750 m MSL and northeast from 3250 to 5000 m MSL. (Fig. 3). Small-scale cumulus clouds were clearly distributed over the Loess Plateau in the daytime (1400 BST) of 19 June 2005 (Fig. 4).

Fig. 3.

Initial conditions for the simulations. Profiles of (a) potential temperature (θ; solid line with solid circles); (b) the mixing ratio of water vapor (qv; solid line with solid circles) and relative humidity (RH; dotted line with empty circles); and (c) zonal wind speed (u; solid line with solid circles), meridional wind speed (υ; dotted line with empty circles), and wind direction (triangles).

Fig. 3.

Initial conditions for the simulations. Profiles of (a) potential temperature (θ; solid line with solid circles); (b) the mixing ratio of water vapor (qv; solid line with solid circles) and relative humidity (RH; dotted line with empty circles); and (c) zonal wind speed (u; solid line with solid circles), meridional wind speed (υ; dotted line with empty circles), and wind direction (triangles).

Fig. 4.

True-color image of the Loess Plateau observed by Moderate Resolution Imaging Spectroradiometer (MODIS)/Aqua on 19 Jun 2005 (1400 BST). The red star indicates the location of the ABL observation site.

Fig. 4.

True-color image of the Loess Plateau observed by Moderate Resolution Imaging Spectroradiometer (MODIS)/Aqua on 19 Jun 2005 (1400 BST). The red star indicates the location of the ABL observation site.

a. Characteristics of the ABL

The diurnal changes in net radiation, and sensible and latent heat fluxes for all runs are given as mean values for the simulation domain (20 km × 20 km). Diurnal changes in the sensible and latent heat fluxes were similar for the FLAT and REAL runs when β was the same (Fig. 5). The daily maximum sensible and latent heat fluxes were approximately 300 and 250 W m−2, respectively, when β was 0.05 and approximately 150 and 500 W m−2, respectively, when β was 0.2.

Fig. 5.

Diurnal changes in net radiation (solid line), sensible heat (broken line), and latent heat (dotted line) fluxes for the (a) FLAT–DRY run, (b) FLAT–WET run, (c) REAL–DRY run, and (d) REAL–WET run. Net radiation and sensible and latent heat fluxes are the mean values for the simulation domain (20 km × 20 km).

Fig. 5.

Diurnal changes in net radiation (solid line), sensible heat (broken line), and latent heat (dotted line) fluxes for the (a) FLAT–DRY run, (b) FLAT–WET run, (c) REAL–DRY run, and (d) REAL–WET run. Net radiation and sensible and latent heat fluxes are the mean values for the simulation domain (20 km × 20 km).

In the time–height sections of simulated potential temperature with the mixing ratio of water vapor at the center of the simulation domain, the vertical axis represents the height from the tableland (1224 m MSL; Fig. 6). The large gradient in the potential temperature and that in the mixing ratio of water vapor corresponded to the ABL top. We determined the height of the ABL top (ABL height) from the height of the maximum vertical gradient in the potential temperature (δθ/δz)max. The real and flat terrains resulted in different ABL characteristics for each β. The ABL began to develop at around 1000 BST for the FLAT–DRY run, 1030 BST for the REAL–DRY run, 1000 BST for the FLAT–WET run, and 1100 BST for the REAL–WET run. The ABL height matured at around 1300 BST for the DRY runs, 1400 BST for the FLAT–WET run, and 1300 BST for the REAL–WET run. For REAL runs, the ABL began to develop later in the morning. The ABL height matured at around the same time in the afternoon in DRY runs. It matured earlier in the REAL–WET run than in the FLAT–WET run. These results suggest that the ABL developed suddenly in late morning in the REAL runs. The height of the matured ABL top in REAL runs was lower than that in FLAT runs for each β. The values were approximately 2800 m for the FLAT–DRY run, 2400 m for the REAL–DRY run, 2200 m for the FLAT–WET run, and 1800 m for the REAL–WET run. In addition, the potential temperature within the ABL of REAL runs was lower than that of FLAT runs when β was the same. The potential temperature within the ABL at 1200 BST was 313.2 K for the FLAT–DRY run, 312.2 K for the REAL–DRY run, 311.8 K for the FLAT–WET run, and 310.9 K for the REAL–WET run.

Fig. 6.

Time–height sections of simulated potential temperature with the mixing ratio of water vapor (contours every 1 g kg−1) at the center of the simulation domain for the (a) FLAT–DRY run, (b) FLAT–WET run, (c) REAL–DRY run, and (d) REAL–WET run. The black circles denote the ABL height determined from the height of the maximum vertical gradient in the potential temperature (δθ/δz)max. The vertical axis represents the height from the tableland of 1224 m MSL.

Fig. 6.

Time–height sections of simulated potential temperature with the mixing ratio of water vapor (contours every 1 g kg−1) at the center of the simulation domain for the (a) FLAT–DRY run, (b) FLAT–WET run, (c) REAL–DRY run, and (d) REAL–WET run. The black circles denote the ABL height determined from the height of the maximum vertical gradient in the potential temperature (δθ/δz)max. The vertical axis represents the height from the tableland of 1224 m MSL.

Time–height sections of simulated vertical velocity with the mixing ratio of water vapor at the center of the simulation domain indicate that updraft and downdraft occurred repeatedly within the ABL in the daytime (Fig. 7). A thermal is a large column of rising buoyant air in the ABL, and an updraft is caused by thermal generation. Thermal updraft and the associated (compensated) downdraft form a local circulation (Stull 1988). The local circulation was assumed to drift with the mean horizontal wind. The simulated repetition of updraft and downdraft represented the formation of local circulation (Endo et al. 2008). Strong updraft occurred particularly for DRY runs, with a maximum vertical wind speed of approximately 5 m s−1. The maximum vertical velocity did not depend on the bottom boundary conditions for each β. Time–height sections of the simulated mixing ratio of cloud liquid water clearly indicate the locations of cumulus generation (Fig. 8). Particularly in REAL runs, cumulus clouds were generated at the top of the ABL, which corresponds to the top of updrafts (Fig. 7). However, no precipitation occurred in any of the runs.

Fig. 7.

As in Fig. 6, but for vertical velocity. The vertical axis represents the height from the tableland of 1224 m MSL.

Fig. 7.

As in Fig. 6, but for vertical velocity. The vertical axis represents the height from the tableland of 1224 m MSL.

Fig. 8.

As in Fig. 7, but for the mixing ratio of cloud liquid water.

Fig. 8.

As in Fig. 7, but for the mixing ratio of cloud liquid water.

b. Relationship between the cumulus cloud distribution and topography

To determine the relationship between the distribution of cumulus clouds and the topography, we investigated the positions of cloud generation and the topography (Fig. 9). An area in which cloud liquid water was no less than 1.0 × 10−4 g kg−1 was regarded as cloud (Yamada 2008). Cumulus clouds were generated at the center of the simulation domain in the REAL–DRY run at 1320 BST (Fig. 9c), and the height of the cumulus generation corresponded to the ABL top (Fig. 8c). For FLAT runs, a small amount of cumulus cloud was generated. The amount of cloud, which is defined as the number of grid points of cumulus generation divided by the total number of grid points, was 2.5% for the FLAT–DRY run and 1.6% for the FLAT–WET run. In contrast, large amounts of cumulus cloud were generated in the REAL runs. The amounts of cloud were 20.2% for the REAL–DRY run and 20.7% for the REAL–WET run. The initial dominant wind direction was southeast up to 2750 m MSL (approximately 1500 m from the tableland; Fig. 3c). In all runs, there was a diurnal change of wind direction. This change was particularly remarkable for the REAL–WET run. In the daytime, the dominant wind direction was maintained as southeast for the REAL–DRY run, whereas for the REAL–WET run, the daytime wind direction changed to east-southeast (figure not shown). Interestingly, cumulus clouds tended to be generated at the windward slopes and on the edge of the tableland in both of the REAL runs. For the REAL runs, not only in the center domain but also in the buffer region, cumulus clouds also tended to be generated in the similar topographic areas.

Fig. 9.

The distribution of vertically integrated cloud liquid water at 1320 BST for the (a) FLAT–DRY run, (b) FLAT–WET run, (c) REAL–DRY run, and (d) REAL–WET run. The contour line interval for the REAL runs is 100 m, the thick contour line is the flat tableland at 1200 m MSL, and the red star is the location of the ABL observation site.

Fig. 9.

The distribution of vertically integrated cloud liquid water at 1320 BST for the (a) FLAT–DRY run, (b) FLAT–WET run, (c) REAL–DRY run, and (d) REAL–WET run. The contour line interval for the REAL runs is 100 m, the thick contour line is the flat tableland at 1200 m MSL, and the red star is the location of the ABL observation site.

To compare the amount of cumulus cloud in all runs, cloud liquid water was integrated over the entire time (Fig. 10). The largest amount of cumulus cloud was generated in the REAL–WET run, whereas the smallest amount was generated in the FLAT–DRY run. When β was changed from 0.05 to 0.2 under the same bottom boundary, cloud liquid water increased. If the bottom boundary was changed from flat to real terrain under the same β, cloud liquid water increased dramatically. The increase in cloud liquid water was greater with a change in terrain than with a change in β.

Fig. 10.

As in Fig. 9, but integrated over the entire time (every 600 s from 0 to 36 000 s).

Fig. 10.

As in Fig. 9, but integrated over the entire time (every 600 s from 0 to 36 000 s).

c. Structure of the local circulation induced by ABL development

To investigate the differences in cumulus generation between the flat and real terrains, we examined the vertical structures of the ABL (Fig. 11). The maximum vertical wind speed was similar between the FLAT–DRY and REAL–DRY runs (Fig. 7). In both runs, quasi-two-dimensional structures were simulated. In the lower part of the ABL (Fig. 11, left), updrafts were aligned along the mean horizontal wind. The structures were surface layer streaks (Young et al. 2002). In the middle part of the ABL (Fig. 11, middle), updrafts developed above the surface layer streaks. Some strong updrafts reached and penetrated the capping inversion (Fig. 11, right). However, the horizontal distributions of updrafts and downdrafts differed in the middle part of the ABL (Fig. 11, middle). For the FLAT–DRY run, updrafts had a systematical distribution similar to the Bénard–Rayleigh-type cellular convective structure. Downdrafts appeared widely around the updrafts. In contrast, for the REAL–DRY run, updrafts developed above the surface layer streaks but only at the windward slopes and on the edge of the tableland. The wind directions were southeast (Fig. 11b, left). Compensating downdrafts appeared around the updrafts. Cumulus clouds were clearly generated at the top of strong updrafts. The distribution of the strong updrafts agreed with that of vertically integrated cloud liquid water. The vertical velocity (Fig. 11b, right) and vertically integrated cloud liquid water (Fig. 9c) were positively correlated (r = 0.61; figure not shown). As the height of the vertical velocity approached the ABL height, the number of plots representing updraft and nonzero vertically integrated cloud liquid water increased. Moreover, the correlation coefficient between the two fields also increased.

Fig. 11.

Horizontal sections of vertical and horizontal wind velocity at 1320 BST for the (a) FLAT–DRY run at (left) 243 (z/zi ∼ 0.1, where zi is the ABL height), (middle) 1367 (z/zi ∼ 0.5), and (right) 2804 m height (z/zi ∼ 1) and (b) REAL–DRY run at (left) 251 (z/zi ∼ 0.1), (middle) 1401 (z/zi ∼ 0.5), and (right) 2851 m height (z/zi ∼ 1; right). These heights are from the tableland (1224 MSL). The colors indicate vertical wind and the vectors horizontal wind.

Fig. 11.

Horizontal sections of vertical and horizontal wind velocity at 1320 BST for the (a) FLAT–DRY run at (left) 243 (z/zi ∼ 0.1, where zi is the ABL height), (middle) 1367 (z/zi ∼ 0.5), and (right) 2804 m height (z/zi ∼ 1) and (b) REAL–DRY run at (left) 251 (z/zi ∼ 0.1), (middle) 1401 (z/zi ∼ 0.5), and (right) 2851 m height (z/zi ∼ 1; right). These heights are from the tableland (1224 MSL). The colors indicate vertical wind and the vectors horizontal wind.

To investigate the detailed structure of the ABL, we examined a cross section centered on an updraft (Fig. 12). At 1320 BST in the REAL–DRY run, an updraft developed on the windward slope at 30 km and extended to the upper part of the ABL but changed to downdrafts at the upwind and downwind sides of the updraft (Fig. 12a). At 3-km height at the upwind side of the updraft at 31–32 km, weak reverse flow developed (Fig. 12b). This indicates the development of local circulation. The updraft transported water vapor from the surface to the upper part of the ABL, which induced cumulus generation at the ABL top. Compensating downdrafts entrained dry air from the free atmosphere. Therefore, local circulation played an important role in water vapor exchange between the ABL and the free atmosphere. The horizontal and vertical scales of the local circulation were approximately 3 and 2 km, respectively; the aspect ratio is approximately 1.5. The vertical scale was within the range of the ABL. In the FLAT–DRY run, a local circulation induced by a thermal generation also developed. Updrafts tend to take the form of walls, arranged in an irregular polygon pattern (Garratt 1992); therefore, the systematical distribution, which was similar to Bénard–Rayleigh-type cellular convective structure (Fig. 11a, middle), could have resulted from the arrangement of local circulations. The horizontal and vertical scales of the local circulation were several kilometers (data not shown). The horizontal and vertical scales of the local circulation in the FLAT–DRY run were consistent with those in the REAL–DRY run.

Fig. 12.

(a) Cross section of vertical and horizontal wind velocity from 28 to 33 km (x axis) and 26 km (y axis) at 1320 BST for the REAL–DRY run. (b) Cross section of the altitude. The colors indicate vertical wind and the vectors indicate horizontal wind. The contour line indicates the mixing ratio of water vapor for every 2 g kg−1. The thick dotted line indicates the cloud edge, defined as a mixing ratio of cloud liquid water of 1.0 × 10−4 g kg−1.

Fig. 12.

(a) Cross section of vertical and horizontal wind velocity from 28 to 33 km (x axis) and 26 km (y axis) at 1320 BST for the REAL–DRY run. (b) Cross section of the altitude. The colors indicate vertical wind and the vectors indicate horizontal wind. The contour line indicates the mixing ratio of water vapor for every 2 g kg−1. The thick dotted line indicates the cloud edge, defined as a mixing ratio of cloud liquid water of 1.0 × 10−4 g kg−1.

4. Discussion

The ABL had different characteristics over real and flat terrains for each β. The ABL began to develop later in the morning in REAL runs than in FLAT runs and developed suddenly in late morning. In addition, the potential temperature within the ABL was lower in REAL runs than in FLAT runs. We extrapolated the variables within the gullies at the beginning of the simulation, because no observational data were available for these areas. This linear extrapolation used the lowest two data points (Fig. 3a). Hence, the potential temperature within the gullies was smaller than that over the tableland because of the positive potential temperature gradient of the lowest two data points. In a mountainous region, radiative cooling causes surface air to sink, resulting in cold downward winds. The chilled air flows into the valleys and collects as cold pools (Stull 1988). Through the night from 18 to 19 June, the weather was fine and the winds near the surface were calm. This condition was favorable for radiative cooling to occur, and we speculate that cold air pooled in the gullies. Thus, the potential temperature within the gullies is plausibly lower than that over the tableland in the morning. The sensible heat flux was used to heat the air within the gullies before it was used to heat the air over the tableland. Therefore, the characteristics of the ABL differed for real and flat terrains. The sudden development of the ABL is qualitatively consistent with observational results (Nishikawa et al. 2007). Additionally, a one-dimensional energy budget calculation reproduced a lower potential temperature over the real terrain than over the flat terrain.

The height of the matured ABL top in REAL runs was lower than that in FLAT runs for each β. This was because the sensible heat flux was used to heat the air within the gullies. Time–height sections (Fig. 6) were depicted from the height of the tableland (1224 m MSL). It should be noted that the height difference of the matured ABL between the FLAT and REAL runs included the height difference between the tableland and the gullies in the REAL runs (1146 m, which is the average height of the center domain). In addition, a one-dimensional energy budget calculation also reproduced the lower height of the matured ABL top over the real terrain relative to the flat terrain.

The FLAT runs generated small amounts of cumulus cloud. In contrast, the REAL runs generated large amounts of cumulus cloud at the windward slopes and on the edge of the tableland as a result of updrafts and thermal generation (Figs. 9, 10). The distributions of cumulus clouds differed between the REAL–DRY run (Figs. 9c, 10c) and the REAL–WET run (Figs. 9d, 10d). The initial dominant wind direction was southeast in both cases. In the REAL–DRY run, the dominant wind direction remained southeast up to 1320 BST (Fig. 11b, left). However, in the REAL–WET run, it changed from southeast to east-southeast in the daytime (figure not shown). Although the wind speeds were so weak that the dominant wind direction was variable, the diurnal change of the wind direction affected the cumulus cloud distribution. Tian et al. (2003) investigated convective rolls and ABL structure over real terrain representing the south of England using a large-eddy simulation and found that hilly areas and windward slopes of high ridges were marked by more clouds, whereas there were relatively fewer clouds on the lee sides of these ridges. They pointed out that persistent ascents and descents forced by topography have mechanical effects on the convective activity and speculated that smaller-scale convective updrafts were enhanced at the windward slope of the topography, whereas convective clouds were suppressed at the leeward side.

Walko et al. (1992) investigated the effects of idealized hilly terrain on ABL development using a large-eddy simulation and showed that updrafts tended to be located above the top ridges. This means that the hilly terrain disrupted the systematical distribution of updrafts. Focusing on the distribution of updrafts and downdrafts, in the FLAT–DRY run, updrafts showed a systematic distribution that had Bénard–Rayleigh–type cellular convective structure, and downdrafts appeared around the updrafts (Fig. 11a). In contrast, in the REAL–DRY run, updrafts developed above the surface layer streaks, developing only at the windward slopes and on the edge of the tableland. (Fig. 11b). Therefore, the systematic distribution of updrafts in the FLAT–DRY run was disrupted as a result of the topography of the Loess Plateau in the REAL–DRY run.

In the FLAT–DRY run, updrafts tended to develop throughout the simulation domain. Water vapor was transported from the surface to the upper part of the ABL homogeneously, leading to relatively homogeneous horizontal distribution of water vapor near the top of the ABL. In the REAL–DRY run, updrafts tended to develop at the slopes and on the edge of the tableland. Water vapor was nonhomogeneously lifted from the surface to the upper part of the ABL, which induced the generation of cumulus clouds at the ABL top.

Thus, in the REAL-DRY run, local circulation caused by thermal generation played an important role in cumulus generation. The horizontal and vertical scales of the local circulation were approximately 3 and 2 km, respectively. However, the gullies on the Loess Plateau are several hundred meters deep and several tens of kilometers wide. The horizontal scale of the local circulation did not follow the horizontal length scale of the gullies. Previous studies have shown that meso-β-scale (50–150 km) topography induces local circulation. For example, Sato et al. (2007) found that local circulation (mountain–valley circulation) formed over the mountains of southern Mongolia (the Gorban–Saikhan mountain range) in an analysis of diurnal variation in cloud frequency. The horizontal range of the Gorban–Saikhan mountain range is approximately 50 km, with a height difference of 1000 m. The horizontal scale of the local circulation corresponded to the horizontal range of the mountain. A numerical study by Lee and Kimura (2001) also showed that topography-induced circulation is the dominant cause of convergence over mountaintops in a mountainous area having a height difference of 1000 m and width of 50–150 km. Over such relatively small-scale topography as the Loess Plateau, local circulation caused by thermal generation is more dominant than the local circulation following the horizontal length scale.

The series of numerical simulations also showed that topography is more critical than surface wetness for cumulus generation. The source of cumulus clouds is mainly water vapor within the gullies. Therefore, the topography of dissected flat tablelands with steep gullies over the Loess Plateau plays an important role in small-scale cumulus generation and has a strong effect on heat and water vapor exchange over the Loess Plateau. The results of numerical simulations imply that cumulus clouds are generated wherever the topography consists of dissected flat tablelands with steep gullies, such as the Loess Plateau. Numerical simulations with low resolution cannot identify small-scale topography and thus treat it as flat terrain. The effects of small-scale topography on heat and water vapor exchange need to be accounted for in the subgrid-scale parameterization.

We conducted numerical simulations under just one initial condition. Wind speeds within the ABL were calm; the dominant wind direction within the ABL was initially southeast, which followed the shape of the tableland. The responses of the tableland to local circulation and cumulus generation under various wind speeds and directions remain unknown. Future studies should clarify the detailed structure of the ABL under various wind speeds and directions.

5. Conclusions

To evaluate the effect of topography on local circulation and cumulus generation over the Loess Plateau of China, numerical simulations of ABL development were conducted using the CReSS model. Two types of numerical simulation were carried out under two sets of bottom boundary conditions: real terrain and flat terrain. In addition, two β values were used: one for a dry case and the other for a relatively wet case. The differences in ABL development and cumulus generation over the real and flat terrains were described. The simulations also represented the structures of local circulations induced by the ABL development.

ABL development began later in the morning over the real terrain than over the flat terrain; the ABL development occurred rapidly over the real terrain in late morning. The potential temperature within the ABL was lower over the real terrain than over the flat terrain, because the sensible heat flux was used to heat the cooler air within the gullies before it was used to heat the air over the tableland.

Although a small amount of cumulus cloud was generated over the flat terrain, large amounts of cumulus cloud were generated over the real terrain. In the latter case, updrafts caused by thermal generation were clearly represented at the windward slopes and on the edge of the tableland. In terms of the detailed structure of the ABL, over the flat terrain, updrafts were systematically distributed and had Bénard–Rayleigh–type cellular convective structures, and downdrafts appeared around the updrafts. In contrast, over the real terrain, updrafts developed above the surface layer streaks, and they developed only at the windward slopes and at the edge of the tableland. Local circulation developed with horizontal and vertical scales of several kilometers. Therefore, water vapor was transported nonhomogeneously from the surface to the upper part of the ABL, inducing cumulus cloud generation at the top of the ABL.

The results of a series of numerical simulations also indicated that the topography was more critical for cumulus generation than was for surface wetness. Thus, the topography of the Loess Plateau plays an important role in cumulus generation and has a strong effect on heat and water vapor exchange over the Loess Plateau.

Acknowledgments

This study was supported by the Recent Rapid Change of Water Circulation in the Yellow River and its Effects on the Environment research project of the Research Institute for Humanity and Nature, Japan. This research was partly supported by the Grants-in-Aid for Scientific Research (KAKENHI) No. 20360406 from the Japan Society for the Promotion of Science (JSPS) and was also supported by the research program of the Hydrospheric Atmospheric Research Center (HyARC), Nagoya University. We are grateful to Dr. Wenzhao Liu of the Institute of Soil and Water Conservation of the Chinese Academy of Sciences and Dr. Shuangjiang Li of Hubei University of Science and Technology for their collaboration in the field experiment. We thank Mr. Atsushi Sakakibara of Chuden CTI, Ltd., for developing the CReSS model and the Information Technology Center of the University of Tokyo for performing the simulations. We also thank Prof. Atsushi Higuchi of Chiba University for providing the satellite image.

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Footnotes

* Current affiliation: Tottori University of Environmental Studies, Tottori, Japan

Corresponding author address: Masanori Nishikawa, Graduate School of Environmental Studies, Nagoya University, Nagoya 464-8601, Japan. Email: nishikawa.masanori@nagoya-u.jp