Idealized numerical simulations are presented to investigate the sensitivity of the thermal plateau circulation to the plateau height, width, and the presence of a mountain ridge encompassing the plateau. The study concentrates on plateaus surrounded by land with the same surface properties so that the topography is the only source of differential heating. For low plateaus, it is found that the strength of the plateau circulation increases with the plateau height because the excess heating of the plateau increases with its height. The plateau circulation reaches its maximum strength for plateau heights similar to the mixed-layer depth over the surrounding lowlands. For even higher plateaus, the depth of the circulation decreases whereas the peak intensity exhibits little change. The plateau height also controls the temporal evolution of the plateau circulation. For low plateaus, low-level inflow is primarily found during the night because convection cells forming over the lateral slopes prevent an inward mass flux during the day. With increasing plateau height, the phases of the plateau circulation shift toward earlier times. If the plateau height exceeds the mixed-layer depth over the surrounding lowlands, inflow occurs from afternoon until the late evening. After sunset, the inflow layer tends to assume the characteristics of a density current. The convergence of the density currents propagating from each side of the plateau toward the center helps to fill the heat low formed during the day. Moreover gravity waves are triggered that propagate away from the plateau center and terminate the inflow. The propagation speed of the density currents is found to increase with the plateau height, so that their convergence occurs earlier for high plateaus than for low plateaus. For the parameter range considered in this study, the plateau width is found to have only a minor impact on the mass fluxes associated with the plateau circulation. However, the convergence of the density currents over the plateau center occurs later for a wider plateau, implying that the heat low is more persistent. Substantial changes are obtained when the plateau is surrounded by a mountain ridge. In this case, the inflow toward the plateau gets delayed because a slope wind circulation forms over the mountain ridge. Moreover, the mass fluxes toward the plateau are reduced so that the heat low that formed over the plateau during the day is filled only slowly. As a consequence, the inflow lasts throughout the night in the presence of a high mountain ridge surrounding the plateau.
It has been recognized since the early days of meteorology (e.g., von Hann 1915) that plateaus induce a diurnal circulation on days without significant cloud cover. On a plateau, radiative heating or cooling of the ground and the ensuing turbulent heat fluxes act at a larger height than over the surrounding lowlands. Thus, the overlying atmosphere undergoes a larger diurnal temperature variation than the adjacent atmosphere over the lowlands. During the day, the air over the plateau is warmer than the surrounding free atmosphere so that the pressure decreases with height more slowly over the plateau than around it. This leads to the formation of a thermally direct circulation with inflow at low levels, rising motion over the plateau, and outflow at higher levels. At night, one expects an opposing thermal circulation with downslope winds over the flanks of the plateau.
In the early literature on plateau flows, there has been some debate about the initiation of the plateau circulation. For example, von Hann (1915) argued that the heating of the surrounding lowlands leads to an expansion of the air and thus to a pressure rise at plateau level. This would imply that, for a plateau surrounded by land, the circulation starts with a low-level inflow because the ambient pressure is higher than the pressure at the plateau bottom. On the other hand, Flohn (1953) pointed out that the air expands over the plateau as well, inducing an outward pressure gradient at higher levels. For a plateau surrounded by sea, the circulation should therefore start with an outflow at upper levels. However, numerical experiments by Zängl and Egger (2005) indicated that the low-level inflow and the upper-level outflow evolve together, regardless of whether the initial level of zero pressure gradients is at the plateau bottom or at the top of the heated layer.
The systematic investigation of plateau circulations with numerical simulations started with Sang and Reiter (1982). They considered idealized topography with the dimensions of the Tibetan Plateau and found the expected thermally direct circulation with low-level upslope flow during the day and downslope flow during the night. Due to the influence of the Coriolis force, the daytime (nighttime) flow is cyclonic (anticyclonic) over the plateau. Egger (1987) considered a highly idealized plateau with vertical sidewalls but with valley transects leading from the plains toward the plateau. Upslope flow is absent in this model, but the valleys transport a substantial amount of air mass toward the heated plateau during the day.
The thermal circulation of the Iberian Peninsula was studied, among others, by Gaertner et al. (1993) and Portela and Castro (1996). Gaertner et al. (1993) conducted two-dimensional simulations, considering a north–south cross section from the Bay of Biscay toward the central part of the plateau. They found that the presence of the surrounding sea, the elevation of the landmass, and the (low) soil moisture are important factors in determining the strength of the heat low and the thermal circulation. The combined sea breeze–plateau circulation transforms into a density current after sunset and helps to fill the thermal low during the night. This work was extended by Portela and Castro (1996) to threedimensional simulations. Their experiments revealed that the main river valleys and the passes in the coastal mountain ranges surrounding part of the plateau tend to channel the inflow into the thermal low. Over the plateau, low-level convergence goes along with divergence at higher levels, and the residual between these fluxes determines the evolution of the surface pressure.
A number of further studies considered plateaus surrounded by higher mountain ridges, forming an elevated basin. Such topographic structures are found in several mountainous regions of the world, for example, in Japan (Kimura and Kuwagata 1993), in the Rocky Mountains (Bossert and Cotton 1994a, b), in the Mexico City area (Bossert 1997; Doran and Zhong 2000; Whiteman et al. 2000), and on the Bolivian Altiplano (Zängl and Egger 2005). These intermountain basins have in common that a slope wind system forms over the surrounding mountain ridges during the day, delaying the plateau-scale inflow (also referred to as plain-to-basin wind) until around sunset. However, the presence of a major gap allows for a localized and rather intense inflow already in the afternoon (Doran and Zhong 2000). According to Kimura and Kuwagata (1993), a precondition for the development of a plain-to-basin wind is that the daytime convective boundary layer over the plain exceeds the mountain ridges surrounding the basin. This was doubted by de Wekker et al. (1998, hereafter WZFW) who argued that the presence of a cross-ridge temperature gradient above crest height is sufficient. From their idealized numerical experiments, WZFW also found that a plain-to-basin circulation is even possible when the basin floor is at the same level as the surrounding plain, provided that the surrounding mountain ridges induce an appreciable volume effect (Steinacker 1984). In addition, they reported that, for a narrow basin and a given height of the surrounding mountain ridges, the height of the basin floor has only a minor impact on the strength and depth of the plain-to-basin circulation.
However, there are still several open questions pertaining to the dynamics of plateau or basin circulations. The few existing systematic studies did not clearly separate between the effects of plateau height, excess height of the surrounding mountain ridges, and the volume effect induced by these ridges. Though WZFW conducted some experiments with a small volume factor, these have hardly been reported on. The dynamical impact of the plateau width, controlling whether or when the inflow branches from either side of the plateau converge over the plateau center, is also an unresolved issue. Moreover, the impact of a ridge exceeding the mixed-layer depth over the surrounding plains has only been superficially treated with a couple of sensitivity tests by Kimura and Kuwagata (1993) and WZFW. Even the fairly general issue of the impact of plateau height on the structure and intensity of the thermal circulation still lacks a systematic investigation, particularly for a plateau surrounded by land. So far, there is just evidence that high and low plateaus differ from each other in a fundamental way. Zängl and Egger (2005) found that sea-breeze and plateau circulations are dynamically similar when the plateau height exceeds the mixed-layer depth over the surrounding plains. On the other hand, Reichmann and Smith (2003, hereafter RS03) reported a completely different flow pattern for a low plateau (600 m), with inflow lasting throughout the night even along the flanks of the plateau.
The goal of the present paper is to make a step toward closing these gaps in the understanding of plateau circulations. Using idealized numerical simulations, we will systematically investigate the structure of the plateau circulations for plateau heights between 500 m and 4 km for two different plateau sizes representative for the Bolivian Altiplano and the Tibetan Plateau, respectively. While the former plateau shape allows for a nocturnal flow convergence over the plateau center, the latter does not for most plateau heights. In addition, the effect of a surrounding mountain range with an excess height between 500 m and 1.5 km is examined. Unlike the earlier study by WZFW, the volume factor is kept close to unity in these tests. The remainder of this paper is structured as follows. Section 2 describes the setup of the numerical simulations. The structure of the simulated plateau circulation is discussed in section 3, including an analysis of the average mass fluxes through the lateral boundaries of the plateau. The pressure field over the plateau and its diurnal variation are examined in section 4. Finally, section 5 summarizes the main findings of this study.
2. Model and setup
The numerical simulations presented in this study have been conducted with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5, version 3.3) (Grell et al. 1995). The model solves the nonhydrostatic equations of motion in a terrain-following sigma coordinate system. The experiments with a simple plateau (no surrounding mountain ridge) are conducted on two interactively nested model domains with a horizontal mesh size of 27 and 9 km, respectively. The first (outer) domain has 101 × 101 grid points, and the second one has 79 × 151 points for the narrow plateau and 157 × 151 points for the wide plateau (see Fig. 1). A third model domain with a mesh size of 3 km and 79 × 79 grid points is used in the experiments with a surrounding mountain ridge because the ridge has a gap representing the passes present in real mountain ranges. In the vertical, 44 full-sigma levels are used, corresponding to 43 half-sigma levels where all variables but the vertical wind are computed. The lowermost half-sigma level is located about 15 m above ground, and the vertical distance between the model layers ranges between 40 m near the surface and 800 m near the upper boundary, which is located at 50 hPa.
The shape of the basic plateau is given by
The maximum plateau height h0 ranges between 500 m and 4 km, and the length scales Lx and Ly are set to 250 and 600 km, respectively, for the narrow plateau and to 550 and 600 km, respectively, for the wide plateau. The corresponding shape parameters α and β are 8 and 20 (18 and 20) for the narrow (wide) plateau. This yields plateau sizes similar to the Bolivian Altiplano and to the Tibetan Plateau, respectively. In part of the experiments, a surrounding mountain ridge with an excess height hr of 500 m, 1 km, or 1.5 km and a gap on the eastern side of the plateau is specified. The composed topography is displayed in Fig. 1a for the narrow plateau with h0 = 4 km and a hr = 1.5 km, and the basic wide plateau with h0 = 4 km is shown in Fig. 1b.
The initial and boundary conditions used for our numerical experiments are idealized as well. We assume the absence of large-scale pressure and temperature gradients, implying that atmospheric motion is generated only due to differential heating in the plateau area. For consistency, latitudinal gradients of solar radiation and the dependence of the solar cycle on longitude are disregarded in the model. Solar radiation is computed for a latitude of 15°, 25 days after the winter solstice, and the longitude is specified such that the model time is equal to local time (LT). This setting was also used for the semirealistic simulations presented in Zängl and Egger (2005) so that a direct comparison with the earlier model results is possible. The initial temperature profile corresponds to midnight and starts with a sea level temperature of 305 K. It is composed of an isothermal layer up to a pressure of 950 hPa, an isentropic layer with approximately 310 K between 950 and 750 hPa, a stable tropospheric layer with a vertical temperature gradient of −6.5 K km−1 between 750 and 175 hPa, and an isothermal stratospheric layer higher above. Over the plateau, the surface layer and the isentropic layer are shifted upward by the plateau height, and the surface temperature is given by 305 K − h0(7.5 × 10−3 K m−1). At the lateral boundaries, the initial profile is maintained throughout the simulation except for the surface layer, which follows a diurnal cycle similar to that obtained in the model interior. As will be seen later, this specification is reasonably close to the model’s equilibrium state. After two days of spinup time, there is still a slight drift in part of the simulations (see Fig. 2), but the structural features of the plateau circulation have already reached quasiperiodicity. Moisture is included in the simulations in order to allow for the use of a realistic radiation scheme (see below), but very dry conditions are specified to prevent the formation of clouds. Specifically, the initial relative humidity is set to 25% in the troposphere and to 5% in the stratosphere.
The physics parameterizations used for our idealized simulations comprise a boundary layer parameterization (Shafran et al. 2000) and a sophisticated radiation scheme accounting for moisture (and cloud) effects (Mlawer et al. 1997). We also used a simple cloud microphysics parameterization (Dudhia 1989) because the radiation scheme requires a cloud scheme. The roughness length, soil moisture availability, and surface albedo are set to uniform values of 10 cm, 0.1 and 0.2, respectively. Moreover, we use the modified horizontal diffusion scheme developed by Zängl (2002) that computes the numerical diffusion of temperature and the water vapor mixing ratio truly horizontally rather than along the terrain-following coordinate surfaces. This avoids the generation of spurious motions over steep terrain in the absence of large-scale winds (Zängl 2002). A further reduction of the numerical errors related to steep topography is achieved with the generalized vertical coordinate described by Zängl (2003). This coordinate specification enforces a rapid decay with height of the topographic structures in the coordinate surfaces and thus limits possible numerical errors to low levels. Our integrations are performed with a constant Coriolis parameter of 4 × 10−5 s−1, which was also used in the semirealistic simulations for the Bolivian Altiplano presented by Zängl and Egger (2005). The total integration time is 72 h, the first 48 h of which are considered as spinup time. All results presented in the remainder of this paper are taken from the third day of simulation.
3. Structure of the plateau circulation
a. Narrow plateau
We start our discussion of the model results with the experiments considering the narrow plateau without surrounding mountain ridges. The mass fluxes across the control surface A (see Fig. 1a) are displayed in Fig. 2 for plateau heights ranging between 500 m and 4 km. Inward fluxes are counted positive. Comparing the results for different plateau heights reveals that both the intensity and the timing of the plateau circulation change continuously with the plateau height. The maximum intensity of the plateau circulation increases up to a plateau height of 3 km and stagnates or slightly decreases for even higher plateaus. The depth of the in- and outflow layers starts to decrease for plateau heights larger than 2.5 km, implying that the vertically integrated mass fluxes attain their maximum at plateau heights between 2.5 and 3 km. Moreover, the phases of the plateau circulation continuously shift toward earlier times with increasing plateau height. For shallow plateaus (500 m, Fig. 2a), the direction of the low-level circulation is almost opposite to what one expects from the solar heating cycle. Outward flow prevails from sunrise until sunset, while inward flow prevails throughout the night. With increasing plateau height, the inflow phase gradually shifts to the afternoon and the first half of the night. Correspondingly, low-level outflow is then found in the second half of the night and in the morning. For a plateau height of 4000 m (Fig. 2f), the flow phases are similar to what one typically finds for Alpine valley wind circulations (e.g., Whiteman 1990), whereas the flow phases for intermediate plateau heights (∼2 km) are comparable to those found by RS03 for a shallow plateau surrounded by sea.
To get more insight into the underlying flow dynamics, vertical cross sections of the flow structure are provided in Fig. 3 for plateau heights of 500 m, 2 km, and 4 km. They are taken along line a1–a2 (see Fig. 1a) and are shown for 1500 (Figs. 3a,c,e) and 0000 LT (Figs. 3b,d,f). For the shallow plateau, convection cells form in the afternoon over the upper part of the slope (Fig. 3a). The low-level inflow feeding these cells comes both from the plain side and from the plateau side, explaining the prevalence of outward flow across the control volume. In this context, it needs to be mentioned that the location of the convection cells meanders somewhat along the slopes of the plateau, so the cell structure shown in Fig. 3a does not match the spatial averages referred to in Fig. 2. After sunset, the convection cells decay, and a pronounced circulation develops in response to the spatial pressure gradients built up during the day (Fig. 3b). The leading edge of the inflow still meanders around the plateau (not shown), so its location in Fig. 3b is not the same as for the spatial average. It is interesting to compare these results with those presented by RS03 for a 600-m-high plateau surrounded by land. In agreement with our results, RS03 found maximum inflow around midnight. However, their maximum inflow speed is about twice as large as that found in our study, and inward flow prevails throughout the day. Moreover, a vertical cross section of potential temperature (Fig. 10b in RS03) indicates a nighttime potential temperature difference of 5 K between the plateau and the surrounding land, whereas the difference found in our study does not exceed 1 K. Most of this discrepancy can be traced back to an inconsistent treatment of radiative processes (T. Spengler and R. K. Smith 2005, personal communication). Longwave atmospheric cooling was prescribed over the surrounding landmass but not over the plateau. Moreover, a coding error was discovered afterward in the radiation scheme used by RS03 (T. Spengler and R. K. Smith 2005, personal communication). A small contribution also arises from the larger plateau size considered by RS03 (similar to our “wide plateau”), but it is anticipated from section 3b that the plateau width has only a minor impact on the mass fluxes.
With increasing plateau height, the daytime upslope flow gets faster and more stable (Figs. 3c,e). The higher flow speed arises mainly because the buoyancy forcing of the upslope flow increases with the slope angle. However, the cold-air advection associated with the upslope flow increases as well and prevents further intensification of the upslope flow for plateau heights larger than about 2.5 km. The occurrence of cold-air advection can in turn be explained by the fact that the potential temperature of the mixed layer is higher over the plateau than over the plain, with a difference increasing with plateau height. It is also important to note that the compensating upper-level outflow tends to stabilize the atmosphere over the slope and the adjacent part of the plain so that deep convection in the upslope flow layer is suppressed. Thus, the upslope flow reaches the level part of the plateau earlier for high plateaus than for low plateaus. This explains the time shift of the inflow phase evident in Fig. 2. The decrease of the inflow layer depth for plateau heights larger than 2.5 km is another consequence of the increasing static stability of the ambient atmosphere.
After sunset, the upslope flow entering the plateau from the plain transforms into a density current and accelerates. The flow structure at 1800 LT (shortly after sunset) is illustrated in Fig. 4 for plateau heights of 2 and 4 km. For the higher plateau, the density current is already fully developed at that time (Fig. 4b). The characteristic head at the leading edge of a density current, marked by an increased flow depth and an upward bulge in the isentropes, is clearly evident. Near the eastern boundary of the cross section, the density current entering the plateau from the opposite side can be seen. The two density currents collide about 2.5 h later. For the lower plateau, the transition into a density current is still ongoing (Fig. 4a). A head has not yet formed, though the convection cell present at the leading edge of the inflow layer might be misinterpreted as a density-current head. Later on, the propagation speed of the density current remains somewhat lower than for the 4000-m plateau because the related density (or temperature) jump is smaller. In this case, the density currents meet each other shortly before midnight. The ensuing flow pattern is shown in Fig. 3d. The colliding density currents trigger a gravity wave that propagates first vertically and afterward spreads out horizontally. A later stage of the flow evolution can be seen in Fig. 3f, showing the 0000 LT flow field for the 4000-m plateau. After the collision of the density currents, the inflow layers are pushed back to the lateral edges of the plateau, and very little cross-plateau motion remains in the central part of the plateau. The inflow layer also loses its contact to the surface so that the shallow downslope flow layer developing over the slopes shortly after sunset gradually extends toward the level part of the plateau.
It remains to be stressed that the absence of a cross-plateau wind component over the interior of the plateau does not imply the absence of air motion. The horizontal structure of the near-surface flow field (about 250 m AGL) at 0000 LT is displayed in Figs. 5a,b for plateau heights of 2 and 4 km, respectively. Due to the influence of the Coriolis force, a pronounced cyclonic circulation has formed over the plateau in both cases. Over the level part of the plateau, the flow still has a significant inward component for h0 = 2 km but runs almost parallel to the flanks of the plateau for h0 = 4 km. Again, these patterns reflect two subsequent stages of the flow evolution, which proceeds faster for h0 = 4 km than for h0 = 2 km. A similar difference is found over the lateral slopes, where the airflow is still slightly upslope for h0 = 2 km but already downslope for h0 = 4 km. This is in agreement with the h0-dependent shift of the flow phases evident from Fig. 2. After sunrise, the circulation over the level part decays very rapidly due to turbulent vertical mixing of momentum (not shown). This behavior is well known from sea-breeze circulations (e.g., Racz and Smith 1999).
Additional sensitivity experiments, in which the lateral extent of the plateau slopes was doubled, revealed that the slope steepness has only a marginal impact on the structure and propagation speed of the nocturnal density current (not shown). This confirms that the density current is mainly controlled by the temperature contrast between the plateau and the surrounding plain. A more complicated picture arises for the behavior of the daytime upslope winds. For plateau heights up to about 2 km, the average speed of the upslope winds is roughly proportional to the plateau slope. In this parameter range, the upslope motion depends primarily on the buoyancy forcing over the slope because upslope cold-air advection is small. For higher plateaus, the increasing importance of cold-air advection gradually reverses the slope dependence of the upslope wind speed. In particular, the upslope flow speed was found to decrease with slope steepness for a plateau height of 4000 m.
b. Wide plateau
The experiments with the wide plateau have been conducted in order to analyze which aspects of the plateau circulation depend significantly on the plateau width. The mass fluxes across the control surface indicated in Fig. 1b are depicted in Fig. 6. A comparison with the corresponding results for the narrow plateau (Figs. 2b,c,e,f) reveals only minor differences. Most notably, the flow phases of the plateau circulation tend to be delayed compared to the narrow plateau. The delay is about 2 h for low plateau heights (2 km or lower) but becomes small for high plateaus. Moreover, the upper-level return flow is more persistent for the wide plateau than for the narrow one. These differences indicate that a large plateau has a somewhat longer response time than a small plateau. The strength of the lower circulation branch does not depend systematically on the plateau width, but its depth tends to be slightly smaller for the wide plateau. The highest inflow rate happens to be reached at h0 = 4 km for the wide plateau whereas it was attained at h0 = 3 km for the narrow plateau. However, this feature might be affected by the fact that the model results were stored only every 90 minutes. The intensity of the upper-level return flow is similar for both plateau widths during the day, but a notable difference occurs after midnight for high plateaus. Comparing Figs. 2f and 6d reveals that the inward return flow branch is more than twice as strong for the wide plateau than for the narrow one, and the wide plateau even exhibits a well-defined second outflow layer at heights between 1.5 and 3.5 km AGL. As will be clarified below, this difference is related to the fact that the convergence of the inflow branches over the plateau center occurs later for the wide plateau than for the narrow one.
Larger differences appear over the central part of the plateau where the flow field reacts more directly to the convergence of the inflow branches. This is illustrated in Figs. 5d,e and 7, showing horizontal and vertical cross sections of the flow structure at 0000 LT for plateau heights of 2 and 4 km. In contrast to the corresponding narrow plateau simulations, the inflow currents have not yet reached the plateau center by 0000 LT. However, the differences in the propagation speed of the density currents are similar for both plateau types. Figure 7 shows that the temperature contrast associated with the density current is much higher for h0 = 4 km than for h0 = 2 km, which readily explains the faster propagation speed. Comparing Fig. 7 with the corresponding narrow plateau results (Figs. 3d,f) indicates that the rapid decay of the inflow in the narrow plateau case is due to the convergence of the inflow branches. Not surprisingly, the flow convergence also affects the aforementioned elevated inflow layer over the lateral edges of the plateau (Figs. 2f and 6d). Figure 5d shows that for h0 = 2 km, the upslope wind component over the lateral slopes is stronger for the wide plateau than for the narrow one (Fig. 5a), corroborating the notion of a longer response time. On the other hand, Fig. 5e demonstrates that the development of a nocturnal downslope flow is not linked to the convergence of the inflow branches. This is also true for the lower plateaus (not shown). In all cases, a buoyancy-driven downslope flow develops before the inflow branches meet each other in the plateau center. It is also interesting to note that the flow structure over the plateau shown in Figs. 5d,e is very similar to that obtained for sea-breeze circulations over a large landmass (Racz and Smith 1999; Spengler et al. 2005). This supports the hypothesis that sea-breeze and plateau circulations have substantial dynamical similarities.
c. Plateau surrounded by a mountain ridge
Since real plateaus like the Bolivian Altiplano, the Mexican plateau, or the Tibetan Plateau are at least partly encompassed by higher mountain ranges, we also investigated the dynamical impact of a surrounding mountain ridge. The model topography is still highly idealized as the surrounding ridge has constant height except for one gap that allows for a free airmass exchange between the plateau and the ambient atmosphere. However, this should be sufficient to discover the primary dynamical effects of a surrounding ridge. The mass fluxes across control surface A are displayed in Fig. 8 for plateau heights of 2 and 4 km and ridge heights between 0 m and 1.5 km. This control surface is located near the plateau-side foot of the mountain ridge (see Fig. 1a). In addition, Fig. 9 shows the mass fluxes across control surface B, which is located near the crest line of the mountain ridge.
Before discussing the effects of a mountain ridge encompassing the plateau, we note that the mass fluxes across the control surfaces A and B are quite similar to each other in the absence of a ridge (Figs. 8a,b and 9a,b). The most notable difference is that significant inflow commences earlier for control surface B than for surface A. This is because control surface B is located over the upper part of the slope (if no ridge is present) whereas control surface A is located on top of the plateau over almost level terrain. In the latter case, only a true plateau inflow is counted, whereas control surface B already registers the upslope flow forming in direct response to the solar heating of the ground. On the other hand, control surface B is more directly affected by the katabatic downslope flow forming at night, explaining why the nocturnal outflow is stronger for surface B than for surface A.
The other simulations reveal that the presence of a surrounding mountain ridge greatly changes the structure of the plateau circulation. A low mountain ridge with an excess height of 500 m is already sufficient to induce an upslope flow circulation on the interior side of the ridge (Figs. 8c,d), starting around 0900 LT and reaching its maximum strength in the early afternoon. The upslope flow is stronger and lasts for a longer period of time for h0 = 2 km than for h0 = 4 km. In both cases, the upslope flow is accompanied by an inward return flow at higher levels. As a consequence of the upslope flow, the onset of low-level inward flow is delayed by several hours. On the other hand, the inward flow lasts throughout the night for both plateau heights. It is shallower than for the basic plateau but reaches higher peak flow rates. Inspection of the flow profiles suggests that for h0 = 2 km, a true plateau inflow lasts until the morning, whereas for h0 = 4 km, the plateau inflow turns into a katabatic downslope flow at about 0200 LT. In any case, the nocturnal downslope flow forming over the outer plateau slopes no longer reaches the interior part of the plateau because it is blocked by the mountain ridge encompassing the plateau. The flow profiles over the crest line (Figs. 9c,d) show a weaker response to the presence of the ridge. Compared to the basic plateau, the circulation becomes somewhat weaker and shallower, but the time shift of the flow patterns is not as large as on the interior side of the plateau. In particular, the daytime inward flow starts at approximately the same time as for the basic plateau (Figs. 9a,b) because the slope winds forming on the interior side of the ridge do not reach the crest line. Moreover, there is still a low-level outward flow in the second half of the night, though weaker than for the basic plateau. Comparing Figs. 8d and 9d confirms that the inflow appearing at control surface A between 0200 and 0800 LT is a local katabatic flow forming over the interior side of the mountain ridge.
Similar flow characteristics have also been documented for real plateaus such as the Mexican plateau or the intermountain plateau in the Rocky Mountains (e.g., Bossert and Cotton 1994a, b; Whiteman et al. 2000). Both plateaus are roughly 2 km higher than the surrounding plains, implying that their circulation can be meaningfully compared with the h0 = 2 km case. In agreement with the idealized simulations, upslope flow over the encompassing mountain ridges impedes the plateau inflow during daytime for both plateau regions. Around sunset, the inflow (or plain-to-basin flow) suddenly starts and propagates into the plateau as a density current. However, the observed plain-to-basin flows do not last throughout the night because the Mexican plateau and the intermountain plateau are substantially narrower than our idealized plateau. As a consequence, the inward flow branches take shorter time to converge over the plateau center so that the plain-to-basin pressure difference is equalized more rapidly.
Increasing the height of the encompassing mountain ridge hr to 1000 and 1500 m further enhances the impact on the plateau circulation. On the interior side of the ridge (Figs. 8e–h), the daytime upslope flow toward the crest line becomes deeper, more intense, and more persistent, particularly for the 4-km plateau. For hr = 1500 m, the upslope flow lasts until sunset for both plateau heights. The subsequent plain-to-basin flow persists throughout the night and becomes shallower and stronger with increasing hr. Moreover, the nocturnal inflow is systematically stronger for h0 = 2 km than for h0 = 4 km. Over the crest line (Figs. 9e–h), the circulation becomes weaker and shallower with increasing hr, and the nocturnal outflow disappears. As for control surface A, the plain-to-basin flow is stronger for h0 = 2 km than for h0 = 4 km. The peak inflow rate is reached after sunset for h0 = 2 km but in the afternoon for h0 = 4 km. At night, the vertically integrated inflow is larger for control surface A than for control surface B, indicating that there is some recirculation over the interior side of the mountain ridge. Only part of the inflow rate registered at control surface A constitutes a true plateau inflow.
Illustrations of the flow pattern are provided in Fig. 10 for hr = 1500 m and both plateau heights. The cross sections follow line a1–a3 (Fig. 1a), crossing the ridge on the western side of the plateau while running along the gap axis on the eastern side. The flow fields at 1500 LT (Figs. 10a,b) clarify the spatial structure of the slope wind circulation in the vicinity of the mountain ridge. As already mentioned, the upslope winds are accompanied by an upper-level return flow on both sides of the ridge, and the convergence line is slightly east (inward) of the crest line. The upslope flow coming from the plain side is substantially stronger for h0 = 2 km than for h0 = 4 km due to differences in the environmental static stability. In the latter case, the stable layer between plateau level and crest level reduces the speed of the upslope flow and limits its vertical extent. This stability effect persists after sunset, explaining why the inflow rates are higher for h0 = 2 km than for h0 = 4 km in the evening (Figs. 8g,h and 9g,h). The flow entering the plateau through the gap has just reached the gap at 1500 LT for h0 = 2 km. For the higher plateau, the gap flow already starts to develop the characteristic structure of a density current. As for the basic plateau discussed in section 3a, the higher environmental static stability helps to accelerate the propagation of the upslope wind toward the plateau. Another factor contributing to the intensity of the gap flow is that the ridge increases the pressure difference between the plateau and the surrounding free atmosphere because it reduces the compensating mass fluxes. This effect is particularly pronounced for h0 = 4 km (see section 4 and Fig. 11). In this context, it needs to be pointed out that the mass fluxes through the gap make only a small contribution to the total mass fluxes considered in Figs. 8 and 9 because the gap is quite narrow.
The flow fields at midnight (Figs. 10c,d) exhibit a pronounced gap flow in both cases that resembles a shooting hydraulic flow. The depth and strength of the gap flow are slightly larger for h0 = 4 km than for h0 = 2 km (note the different vertical extent of the figures), whereas the static stability of the gap flow is much higher for h0 = 4 km. The 250 m AGL wind field displayed in Fig. 5c reveals that the gap flow fans out laterally over the plateau and is quite asymmetric due to the influence of the Coriolis force. Comparing the vertical structure of the gap flow with the average mass fluxes displayed in Figs. 8g,h confirms that the gap flow makes only a minor contribution to the total mass balance. The majority of the air mass enters the plateau via the ridges. The presence of this (very shallow) inflow can be inferred from the structure of the isentropes in Fig. 10c. For h0 = 4 km (Fig. 10d) no inflow via the ridge is present along the central cross section because the gap flow reaches the opposing ridge and piles up cold air along its slope. However, a shallow inflow across the ridge is present outside the influence of the gap flow (Fig. 5c). It is anticipated from the subsequent section that the heat low over the plateau persists throughout the night for hr = 1.5 km because the inward mass fluxes and the local radiative cooling are too weak to offset the layer-integrated heat surplus accumulated during daytime. Thus, the gap flow lasts throughout the night in the presence of a high mountain ridge.
A comparison of the mass fluxes at control surface B with those computed by Zängl and Egger (2005) for the Bolivian Altiplano reveals that the vertically integrated mass fluxes of the real plateau range between those found for the idealized 4-km plateaus with hr = 500 m and hr = 1 km (Figs. 9d,f). This is consistent with the fact that the average excess height of the mountain chains encompassing the Altiplano ranges between 500 m and 1 km. A systematic difference appears for the average vertical flow profiles, showing a deeper inflow layer with a smaller peak flow rate for the real Altiplano than for the idealized topography. This is because the real Altiplano has a large number of individual mountain ridges with embedded passes, implying that the corresponding mass flux profile reflects a smoothed average of various gap flows and ridge flows.
It is also illustrative to compare our results with the simulations conducted by WZFW. They focused on comparatively narrow plateau basins enclosed by a pair of mountain ridges, having a substantial volume effect in most cases. As a consequence, a pronounced plain-to-basin flow occurs even when the basin is at the same elevation as the surrounding plain. Moreover, the inflow phase is comparatively short because the inflow branches converge rapidly over the plateau center. A more interesting difference is that the structure and intensity of the plateau/basin inflow appear to be mainly governed by the height of the ridges in their topographic setting (see their Fig. 9), whereas the height of the plateau bottom plays only a minor role. Our simulations indicate that this behavior is not general. As an example, we compare the experiment with h0 = 2 km and hr = 1 km (Figs. 8e and 9e) with the simple plateau run with h0 = 3 km (Fig. 2e). Evidently, the mass flux profiles differ at all times, particularly at night when an outward flow develops for the simple plateau whereas inflow lasts throughout the night for the elevated basin. Without conducting dedicated sensitivity tests, we hypothesize that the lack of a significant volume effect in our topography contributes to this difference in flow behavior. For a given ridge height and a volume effect increasing with basin depth (as is the case for the topography considered by WZFW), the volume effect partly compensates the influence of basin floor height on the atmospheric heat budget.
4. Analysis of the pressure field
Another important aspect of plateau and sea-breeze circulations is the pressure field. On the one hand, temporal changes in the surface pressure reflect the vertically integrated mass balance of the circulation. On the other hand, horizontal pressure gradients drive the plateau circulation and thus indicate where significant wind is blowing. We start our discussion with time series of the average pressure difference between the interior of the plateau and the adjacent plain (Fig. 11). Negative values indicate that the pressure is lower over the plateau. The pressure difference is evaluated at 50 m above plateau level in order to avoid pressure reduction, which is known to induce spurious effects over high plateaus (e.g., Hoinka and Castro 2003). Horizontal averaging is done over 15 × 41 grid points around the plateau center and over 10 × 41 grid points on the western side of the plateau, respectively.
The results for the basic narrow plateau (Fig. 11a) show that the largest pressure difference is attained in the afternoon or early evening for all plateau heights. The peak difference is significantly larger for h0 = 4 km than for the lower plateaus. This can be explained by the fact that the plateau height exceeds the mixed-layer depth over the plain in this case (see Fig. 3e) so that the vertically integrated temperature difference between the plateau and the adjacent free atmosphere becomes particularly large. After sunset, the pressure difference decreases again. The pressure difference reaches approximately zero or even becomes slightly reversed when the density currents propagating into the plateau (see Figs. 3 –5) collide in the plateau center. This stage occurs earliest for h0 = 4 km (2200 LT) and latest for h0 = 1 km (0300 LT) because the propagation speed of the density currents depends on the associated temperature jump, which increases with the plateau height. For h0 = 1 km, and to a weaker extent for h0 = 2 km, a separate drop of the pressure difference is seen around sunset. The interpretation of this feature is not fully clear, and it seems also surprising that the maximum pressure difference for h0 = 1 km is almost as large as for h0 = 2 km and h0 = 3 km. A possible explanation could be that the plateau circulation sets in only after sunset for low plateaus because convection cells persist over the slope during daytime (see Figs. 2a,b and 3a). Thus, the weak outflow at high levels (outside the plotting range of Fig. 2) forming in response to the air expansion over the heated plateau is not opposed by a low-level inflow, leading to a slightly increased pressure over the adjacent plain. In the late afternoon, this feature starts to decay as the plateau circulation develops.
The presence of surrounding mountain ranges delays and reduces the mass fluxes toward the plateau so that the heat low is filled more slowly than for the basic plateau (Figs. 11b,c). This is consistent with the fact that the inflow across the ridges and through the gap lasts throughout the night in the presence of high mountain ridges (see Fig. 8). However, the development of a high pressure anomaly over the plateau in the late night and early morning is reinforced by the surrounding ridge except for the case h0 = 4 km and hr = 1.5 km. This can be explained by the fact that the ridges prevent the outflow of stably stratified air from the interior part of the plateau, which forms due to the combination of cold-air advection (density current) and radiative cooling (see Fig. 8). The exceptional case arises because the cold-air advection does not suffice to fill the heat low for h0 = 4 km and hr = 1.5 km. Recall that the inward mass fluxes are generally weaker for h0 = 4 km than for h0 = 2 km because the environmental air is more stably stratified (Figs. 8 –10).
The primary difference between the wide and narrow plateaus is that the propagation of the density currents toward the plateau center takes more time for the wide plateau. The convergence of the density currents is not reached at all for h0 = 1 km (Fig. 11d) and occurs between 0500 and 0900 LT for the other plateau heights. For h0 = 1 km and h0 = 2 km, the pressure increase around sunset, which is not related to the density currents, is even more pronounced than for the narrow plateau. The presence of surrounding mountain ridges again delays the inflow of cold and stable air from the environment. In contrast to the narrow plateau cases, no positive pressure anomaly forms over the plateau. This is probably because the convergence of the density currents occurs too late, implying that the ensuing adiabatic cooling cannot become reinforced by downward sensible heat fluxes related to local radiative cooling of the ground.
Additional information on the spatial structure of the pressure field is provided by east–west cross sections of the perturbation pressure displayed in Figs. 12 and 13. The perturbation pressure is the difference between the actual pressure and a reference pressure field on which the vertical coordinate of the MM5 is based. Horizontal gradients of the perturbation pressure are true pressure gradients, but vertical gradients reflect a difference between the actual and reference temperatures and have no direct physical meaning. The pressure profiles shown in Figs. 12 and 13 are averaged in the y direction over five grid points centered around the plateau center and are evaluated at 50 m above plateau level.
Figures 12a,b displays the pressure profiles at 1630 LT, representing the time of maximum pressure difference in the majority of cases. Over the plateau, the pressure field exhibits a lot of small-scale structures at that time. These are related to resolved convection cells that develop between 1500 LT and 1630 LT in response to the superadiabatic vertical temperature gradient (Fig. 3). In reality and in simulations using realistic topography, such convection cells develop much earlier (see Zängl and Egger 2005), but the perfectly flat plateau surface used in our idealized simulations delays the formation of the convection cells. The convection cells also appear to break the east–west symmetry of the simulated flow, which might be related to an asymmetry in the numerical truncation of positive and negative numbers. For h0 ≤ 3 km, the main pressure drop occurs near the lateral edges of the plateau (about x = ±200 km and ±450 km for the narrow and wide plateau, respectively). However, the density current and the associated pressure jump is already on top of the plateau for h0 = 4 km. In the central part of the plateau, the pressure field does not exhibit a systematic spatial gradient except for the wide plateau with h0 = 4 km for which a persistent heat low is maintained in the plateau center.
Nocturnal pressure profiles (0000 LT) are shown in Figs. 12c,d. The results reflect again the different propagation speeds of the density currents. At the same time, they represent different stages of the temporal evolution of a specific simulation. For h0 = 1 km, the density currents have not yet reached the plateau center. Consequently, the pressure field exhibits a minimum in the central part of the plateau. In contrast, the simulation with h0 = 2 km exhibits a local pressure maximum in the plateau center. This is related to the fact that the density currents have just met each other. As illustrated in Fig. 3d, this triggers a vertically propagating gravity wave, the pressure signal of which is seen in Fig. 12c. This gravity wave also constitutes a superposition of eastward and westward propagating waves that interfere constructively at that time. Subsequently, the partial waves propagate away from the plateau center so that a new local pressure minimum appears there. This stage is seen in Fig. 12c for h0 = 3 km and h0 = 4 km. The flow field for the latter case (Fig. 3f) demonstrates that the pressure maxima are related to a bulge in the isentropes. Moreover, it is evident that the retreat of the inward flow component is linked to the outward-propagating gravity wave.
For the wide plateau, the pressure profiles at 0000 LT (Fig. 12d) just reflect the different propagation speeds of the density current. However, a similar evolution takes place later on. This is illustrated in Fig. 13, showing the temporal evolution between 0000 and 1030 LT for h0 = 2 km and h0 = 4 km. In the first case, the pressure waves gradually approach each other between 0000 and 0730 LT. By 0900 LT, the collision of the density currents has induced a pronounced pressure peak at the plateau center with an amplitude of almost 1 hPa. Afterward, the pressure wave spreads out laterally and decreases in amplitude. The further evolution is not shown because it is disturbed by solar heating. For h0 = 4 km, the evolution proceeds faster, and the flow stage at 0600 LT approximately corresponds to that obtained for the lower plateau at 1030 LT. The subsequent evolution confirms that a new pressure minimum forms in the center whereas the pressure maxima propagate away.
Idealized numerical simulations have been performed to deepen our dynamical understanding of plateau circulations, focusing on plateaus surrounded by land with the same surface properties as on the plateau. Specifically, we investigated the impact of the plateau height, plateau width, and of the presence of a mountain ridge encompassing the plateau. Generally, a plateau circulation forms because the solar heating acts at a larger height over a plateau than over the surrounding lowlands. During the day, the atmosphere over the plateau is heated more strongly than the surrounding atmosphere that is farther away from the ground, so a thermally direct circulation with low-level inflow toward the plateau is expected. At night, the situation is reversed since radiative cooling acts primarily at the surface.
Regarding the influence of the plateau height, our results reveal that the strength of the plateau circulation increases with the plateau height for low plateaus because the temperature contrast between the atmosphere over the plateau and the environmental atmosphere increases with the plateau height. The mass fluxes related to the plateau circulation reach a maximum for plateau heights comparable to the boundary layer depth over the surrounding plain. For even higher plateaus, the maximum strength of the plateau circulation stagnates but its depth decreases. This can be explained by an increasingly stable stratification of the surrounding atmosphere, which limits the upward mass fluxes over the slopes of the plateau. In this context, it is also important to note that the plateau circulation itself has an impact on the mixed-layer depth over the surrounding plain. During the inflow period, the upper-level return flow involves subsidence over the plain, leading to downward advection of potentially warm air and thus to a slight reduction of the ambient mixed-layer depth.
The plateau height is also found to have a fundamental impact on the timing of the plateau circulation. For plateau heights much smaller than the mixed-layer depth, a reversed diurnal cycle with outward mass fluxes during the day and inward fluxes during the night is encountered at the lateral edges of the plateau top. With increasing plateau height, the phases of the plateau circulation shift toward earlier times. If the plateau height exceeds the mixed-layer depth over the surrounding lowlands, the inflow phase lasts from afternoon until the late evening. The reversed cycle found for very low plateaus can be explained by the fact that convection cells form during the day over the slopes of the plateau, receiving their inflow both from the plain side and from the plateau side. In this case, an inflow is established only after sunset when the convection decays. With increasing plateau height, the upslope flow becomes more stable and reaches the plateau already during the day. Around sunset, the plateau inflow generally transforms into a density current that propagates toward the plateau center. The static stability and the propagation speed of the density current increases with the plateau height, consistent with the height dependence of the environmental static stability. The convergence of the density currents in the plateau center fills the heat low that forms over the plateau during the day.
The primary effect of doubling the plateau width is that the convergence of the density currents in the plateau center gets delayed. The heat low over the plateau is no longer completely filled until the morning. However, the mass fluxes across the lateral boundaries of the plateau top undergo only minor changes for the plateau widths investigated here. Compared to the narrow plateau, the phase of the low-level circulation branch gets somewhat delayed, particularly for low plateaus, but the flow speed remains almost unchanged. The strength of the upper-level return flow branch changes little during the day but increases at night for high plateaus. More pronounced changes are found when the central plain of the plateau is encompassed by a mountain ridge. Since a separate slope wind circulation forms over the mountain ridge, the onset of the inflow toward the plateau gets substantially delayed. For a ridge height of 1.5 km, the inflow starts only after sunset. The mass fluxes toward the plateau are substantially reduced in the presence of a high mountain ridge so that the heat low that formed over the plateau during the day is filled only slowly. Thus, the inflow lasts throughout the night in the presence of a high mountain ridge.
An analysis of the pressure field revealed that the maximum pressure difference between the plateau center and the environment is reached in the afternoon. This difference is significantly larger when the plateau height exceeds the mixed-layer depth over the adjacent lowlands than if it does not. Surrounding mountain ridges also tend to increase the pressure difference because the compensating mass fluxes are reduced. The nocturnal convergence of the density currents is found to trigger gravity waves that propagate away from the plateau center afterward. These gravity waves appear in the pressure field as pronounced local maxima and tend to terminate the mass inflow toward the plateau.
The authors would like to express their gratitude to Dave Whiteman and an anonymous reviewer for their constructive comments that led to a significant improvement of the paper.
Corresponding author address: Dr. Günther Zängl, Meteorologisches Institut der Universität München, Theresienstraße 37, D-80333 Munich, Germany. Email: email@example.com