A numerical study of moist stratified flow regimes over isolated topography

Transcription

1 Q. J. R. Meteorol. Soc. (2004), 130, pp doi: /qj A numerical study of moist stratified flow regimes over isolated topography By M. M. MIGLIETTA 1 and A. BUZZI 2 1 CNR ISAC, Lecce, Italy 2 CNR ISAC, Bologna, Italy (Received 18 December 2002; revised 16 December 2003) SUMMARY Numerical simulations of moist flows over simply shaped, three-dimensional mountains were undertaken using a mesoscale meteorological model, with the purpose of examining the existence of different flow regimes near obstacles and the transitions among them. Moving the system in parameter space resulted in different solutions for a particular set of parameters. This method was adopted to explore numerically multiple regimes, stable for at least meteorologically interesting time periods. The evolution of the flow was studied in two different experimental set-ups. In the first case, the height of the obstacle was progressively changed over time. In the second case, the effect of an advective change of the humidity content inside the channel was analysed. In both experiments, a dependence on the history of the flow became apparent. A comparison among cases of obstacles with the same aspect ratio and non-dimensional height, but with different horizontal cross-sections, highlighted the importance of the obstacle geometry in perturbing the upstream flow, favouring the persistence of upstream blocked regions in the case of an arc-shaped mountain. The sensitivity of the reversal flow volume to several control parameters was analysed with additional experiments. In particular, the importance of the cooling associated with the evaporation of precipitation was emphasized. KEYWORDS: Mountain shapes Multiple solutions Precipitation 1. INTRODUCTION Several studies have been undertaken to analyse the effect of simply shaped threedimensional (3D) mountains on dry, inviscid, non-rotating flows (see, for example, Smolarkiewicz and Rotunno 1989; Schär and Durran 1993). For mesoscale mountains and simple upstream flows, such studies have shown the flow regime to be governed, in absence of rotation, by the non-dimensional height of the mountain H = h max N/U, where h max is the maximum height of the obstacle, U is a typical upstream wind speed and N is the Brunt Väisälä frequency. Thus U/N is the vertical wavelength of gravity waves. In cases where H is O(1) or larger, the problem can be tackled only with numerical tools. The flow exhibits different regimes (Smith and Grønås 1993; Bauer et al. 2001), associated with the appearance of nonlinear features, such as the formation of upstream blocked areas and the breaking of waves. These features depend not only on H, but also on the geometry of the obstacle. In particular, they depend on a parameter which represents the ratio between the transversal and the longitudinal characteristic lengths of the obstacle (Smith 1989). The problem of humid flows over 3D mesoscale mountains, which we specifically address in this paper, has recently become the focus of increasing interest, especially due to its relevance to the problem of orographic precipitation (see, for example, Medina and Houze 2003). Recent comparative studies of idealized moist and dry flows have revealed a significant reduction in the intensity of mountain-induced wind perturbations, as a consequence of the introduction of humidity. For values of H corresponding to nonlinear flow regimes, associated with the formation of flow splitting and wave breaking, important changes with respect to the dry case appear, depending on the closeness of the atmosphere to saturation. In the moist case, an additional different non-linearity is Corresponding author: CNR ISAC, sezione di Lecce, via per Monteroni, I Lecce, Italy. m.miglietta@isac.cnr.it c Royal Meteorological Society,

2 1750 M. M. MIGLIETTA and A. BUZZI present, related to the condensation threshold. Typically non-linear flow features are either significantly shifted to obstacle heights larger than the corresponding heights in dry cases, or are completely suppressed (Miglietta and Buzzi 2001a, hereafter MB; Jiang 2003). In numerical simulations of real events of orographic precipitation (Buzzi et al. 1998; Ferretti et al. 2000; Rotunno and Ferretti 2003), the presence of moisture can strongly modify the flow characteristics, increasing the flow over and reducing the flow around regimes. These results can be interpreted as an effect of latent heat release; in saturated ascending motion regions, the release can modify the flow response to the orographic forcing. Its effect can be explained, to some extent, in terms of a change in the local value of the effective (moist) Brunt Väisälä frequency in cloudy regions (Durran and Klemp 1982a,b). The effective stratification is strongly reduced in condensed volumes, more efficiently in the lowest part of clouds and less at the top. In the case of precipitation into dry air, evaporative cooling may also have a significant effect on the flow dynamics. Therefore, the flow properties induced by the orography are strongly dependenton the local valueof moist static stability, the moisture content of the impinging flow and, for an unstable atmosphere, on the value of Convective Available Potential Energy (Chu and Lin 2000; Fuhrer and Schär 2002; Gheusi and Stein 2003). The central focus of the said studies was the analysis of the effects of humidity in stationary or nearly stationary conditions. In the present paper, our attention is mainly devoted to the time-evolving properties of orographic moist flows in non-linear regimes, which have not yet been examined in detail. Numerical experiments are undertaken using the hydrostatic Bologna Limited Area Model (BOLAM) in a 3D channel version, with the purpose of analysing the transient development of the wave field and the possible approach to steady-state solutions. The existence of multiple regimes is explored numerically. Due to the difficulty of obtaining strictly stationary solutions (and also because in some cases upstream propagation canalter the inflowboundarycondition), we includein the definition of multiple regimes quasi-stationary solutions that last long enough to be meteorologically significant. Consequently, we intend to verify the hypothesis that such different solutions can be found for the same point in parameter space, but after different histories of evolution. If different solutions occur, the resulting flow regimes may differ significantly from the reference solution, which we heuristically define as the stationary or quasi-stationary solution obtained without changing either the inflow conditions or the external parameters during the simulation. Crook et al. (1990) noticed, for dry atmospheres, a different behaviour depending on the path followed in parameter space, obtained by changing the wind speed. The solutions they found revealed important differences, especially downstream, whether approaching the high-mountain regime from above or below the critical value of H for wave breaking. The existence of multiple solutions in dry flows over obstacles was demonstrated in the study by Smith and Grønås (1993). In particular, the authors demonstrated the existence of bifurcations for H values increasing beyond the threshold for wave breaking. In the present study, we explore different evolutions of internal flow parameters with different obstacle geometries, in the case of moist flows. First, the height of the mountain is modified periodically in the course of the experiment, in a range close to the critical value for the occurrence of wave breaking and flow splitting. Subsequently, the effect of a progressive change of the humidity content inside the channel is analysed and compared with the reference solution. The humidity variation is due to the advection of the moist, almost saturated, air towards the mountain, which is initially embedded in

3 MOIST STRATIFIED FLOW REGIMES 1751 dry air. The final solution shows significant differences with respect to both the dry and moist reference solutions. To explore the effects of the obstacle shape, we extend the results of the study of Miglietta and Buzzi (2001b) on elliptical and circular mountains to an arc-shaped mountain, with concavity on the upstream side. Previous idealized numerical studies using a simplified topography (Schneidereit and Schär 1999) stressed the role of an arc-shaped mountain in modifying the low-level flow. This shape may favour the convergence of the low-level jet (usually observed in the Alps as a southern pre-frontal jet). Combined with an inhomogeneous humidity distribution (Rotunno and Ferretti 2001), it may promote the formation of rainfall and a flow over regime near the western portion of a mountain. The experiments presented here show that an arc-shaped mountain plays another important role; it favours the persistence of upstream blocked regions, separated from the rest of the flow. The occurrence of upstream blocking may significantly modify the airflow approaching steep terrain, impacting on the intensity of orographic precipitation and extending the influence of the mountain far upstream, as investigated in some Mesoscale Alpine Program (MAP) events (Bougeault et al. 2001; Bousquet and Smull 2003; Rotunno and Ferretti 2003; Steiner et al. 2003). We found that wide upstream flow reversal, due to the concavity and large height of the obstacle, may help in keeping the pre-mountain region separated from the rest of the flow, thus favouring the formation of multiple solutions. For example, even if the system evolves from an initial dry solution (with flow around ) to final moist conditions (normally corresponding to a flow over regime), the solution preserves the characteristics of the initial regime until the end of the simulation. 2. MODEL CHARACTERISTICS AND NUMERICAL SET-UP An updated version of the mesoscale hydrostatic model BOLAM (Buzzi et al. 1994; Buzzi and Foschini 2000; MB) was employed for our simulations. The model was used in a channel version, developed to perform theoretical studies within a limited domain, as used in MB. The applicability of BOLAM in the framework of idealized 3D inviscid simulations over orography is reported in MB; in the same paper the main dynamical and physical characteristics of the model are described. The present version was modified mainly in the advection and the microphysical schemes. The advection scheme is an accurate Weighted Average Flux advection scheme (Billett and Toro 1997), conserving mass with low dispersion properties, and allowing a significant reduction of the horizontal diffusion. Since the main purpose of our study was to analyse the effects of humidity on the flow, an explicit representation of cloud microphysics was dealt with in some detail, with five explicit prognostic variables considered. Recently the microphysical scheme, particularly the fall of precipitation and the treatment of cloud species, has been updated (Drofa 2003). The results of the simulations presented in MB were checked against the newer version of the model; the quantitative results did not change in a significant way, although some noise was reduced. Free-slip conditions were assumed at the surface. The presence of a fourth-order internal diffusion, although reduced in magnitude, made the flow not completely inviscid. Since our aim was mainly to tackle the basic inviscid problem, internal dissipation used to parametrize turbulence was not considered (see MB). As in MB, rotation, surface physics, radiation and boundary layer parametrizations were absent. In the present case, a change of parameters during the integration required a continuous adjustment of the solutions approaching near-equilibrium conditions. This called

4 1752 M. M. MIGLIETTA and A. BUZZI for longer integration times than in MB, where equilibrium conditions were sought. Preliminary tests were carried out to evaluate the dependence of such solutions on channel extension. A relatively long and wide channel was adopted so as to limit modification of the inflow boundary condition due to upstream propagation and reflections from the lateral boundaries, which might interfere with the internal features. We chose a channel with grid points in the longitudinal and latitudinal directions, respectively; the extension corresponds to km for the horizontal grid distance of 15 km chosen here. In the vertical, the model employs 35 sigma levels. The levels are more closely spaced near the ground; the distance between two adjacent levels is 60 m close to the ground, and more than 5 km at about 30 km height, which is the domain depth. Lateral boundary conditions were prescribed using a relaxation scheme (Davies 1976; Lehmann 1993) to reduce wave reflection. For the inflow and outflow boundaries, the internal fields match the external constant values along a frame of 8 grid points. A second-order divergence diffusion was included, with a sponge layer (MB) designed to damp the reflection from the upper surface. The divergence damping was used with a modulated coefficient slowly increasing with height, in order to minimize any reflection that might occur as a consequence of rapid changes in amplitude. Analytical relationships were employed to define the initial conditions inside the channel, in order to prescribe the values of the parameters on the model grid, adopting pressure as vertical coordinate before interpolating to σ -levels. Dry static stability (N = s 1 in the troposphere and 0.02 s 1 in the stratosphere) and mean sealevel pressure were prescribed uniformly at the beginning. For the advective simulation (H = 2,T s = 18 C, RH = 98%, U 0 = 10 m s 1 ), the surface temperature, T s,was chosen in order to have a convectively stable, though close to neutral, atmosphere both upstream and over the obstacle. Relative humidity, RH, was prescribed uniformly in the vertical direction up to the tropopause (located at 250 hpa), while the air was prescribed to be dry (RH = 1%) in the stratosphere. U 0 was the constant inflow wind component. This condition approximately reflected atmospheric profiles observed during mainly non-convective events of orographic precipitation over the Alps. The obstacle was introduced shock-like at the beginning of the simulations, and its profile was chosen as Gaussian. In the case of an elliptical and circular mountain, its shape is given by: h = h max exp{ (x/l x ) 2 (y/l y ) 2 }. (1) The extension of the transverse axis, L y, was chosen as 150 km. The longitudinal axis, L x, is 150 km for the circular horizontal profile and 50 km for the elliptical mountain. The arc-shaped mountain was defined as: h = { hmax A if (x x 0 )>x crit, h max A exp[ {(x x 0 x crit )/50} 2 ] if (x x 0 )<x crit, (2) where A = exp{ ([{(x x 0 ) (y y 0 ) 2 } ]/39) 2 } and x crit = 8. The mountain was defined in such a way that its maximum altitude was reached along an arc of an ellipse, where x 0 and y 0 are the coordinates of the centre of the ellipse. The wind was defined directly on sigma surfaces, in order to reduce the intensity of perturbations due to the initial unbalance caused by the presence of the obstacle. In simulations with uniform initial conditions, the initial transient perturbation swiftly propagated out of the region of interest and did not affect the long-term evolution of the

5 MOIST STRATIFIED FLOW REGIMES 1753 system. Therefore, the solutions studied here are not sensitive to the starting procedure, as discussed in Smolarkiewicz and Rotunno (1989) and Rotunno and Smolarkiewicz (1991). 3. MOTIVATION OF THE EXPERIMENTS AND REFERENCE SOLUTIONS The purpose of the study was the exploration of the possible existence of different quasi-stationary solutions for the same set of external parameters. Such solutions represent the local flow configurations induced by the obstacle in the region nearby and upstream of the mountain itself. The parameters defining the flow are mountain height, surface temperature, static stability, RH and wind speed, in the entire channel as initial condition, and along the inflow section as boundary conditions. Because the system s parameters can be changed in different ways, the characteristics of the solution may differ significantly. In more theoretical terms, the nature of solutions may differ when fixed points are approached from different directions in parameter space (Guckenheimer and Holmes 1983). The most interesting region of parameter space to be explored is the one characterized by values of H in the vicinity of a bifurcation point between different flow regimes. In this parameter range, small changes in the external parameters may produce dramatic changes in the observed flow patterns. We already know that the appearance of nonlinear features like wave breaking or flow splitting can be triggered by small changes in the controlling parameters, both in the dry (Smith and Grønås 1993) and in the moist case (MB). For a dry flow, the critical values correspond to the region close to the solid curves A and B in Fig. 5 of Smith (1989), which are linear theory estimates of flow stagnation aloft (wave breaking) and near the ground (flow splitting). For a moist flow, condensation displaces the occurrence of wave breaking and flow splitting to higher values of H, more effectively in a moister atmosphere, as shown in MB for a circular mountain. Therefore, moist solutions should not be considered simply as an extension of dry solutions; they are specifically related to the non-linear effects of condensational heating at the saturation threshold, coupled with the dynamical effects due to the presence of the obstacle. The specific properties of moist atmospheres make them worthy of more detailed investigation, aimed at a generalization of the results obtained for a dry atmosphere by Smith and Grønås (1993). A transition between flow regimes is normally achieved through a change in one of the control parameters, of sufficient magnitude to drive the system from one to another of the regions separated by critical curves, as in Smith (1989). As shown below, if a particular path is selected along the parameter space in a moist atmosphere, some features characteristic of the initial set of parameters may still persist at the end of the simulation. Before addressing the more complex problem characterized by multiple solutions and non-trivial geometry, we briefly examine the simpler type of solution, obtained without changing the inflow conditions and external parameters. The results for circular and elliptical mountain geometry are shown in MB and Miglietta and Buzzi (2001b), respectively. For the dry case, flow blocking occurs for values of H larger than about 1.5. The region of upstream blocking is, however, confined to a small area immediately upstream of the mountain top. In the moist case, the reduced stability in cloudy regions prevents the occurrence of flow blocking until H becomes very large. The mountain geometry can enhance the blocking effect in the case of an increase in the cross-wind extension, which favours the flow separation upstream. In regions of closed circulation, the materially conserved properties along the streamlines,

6 1754 M. M. MIGLIETTA and A. BUZZI (a) 800 Y(km) X(km) (b) 500 pressure X(km) Figure 1. Dry reference solution after 36 hours for an arc-shaped mountain: (a) horizontal wind vectors (arrows) and wind speeds (shading, m s 1 ) at 10 m and (b) vertical cross-section of equivalent potential temperature (shading, K) and streamlines along the central axis of the channel. In (a), the horizontal section of the mountain corresponding to h max /3 (see text) is represented by the thick curve near the centre of the domain.

7 MOIST STRATIFIED FLOW REGIMES 1755 (a) 800 Y(km) X(km) 0 (b) 500 pressure X(km) Figure 2. As Fig. 1, but for the moist (RH = 98%) reference solution. e.g. potential vorticity or humidity in absence of condensation, may differ from those in an open flow. Thus, multiple solutions can be obtained if regions of closed circulation remain separated, after the system is driven towards points in parameter space where such flow patterns are normally absent. In our specific case, the initial flow around regime survives after moistening of the air, i.e. after a shift towards a flow over point in parameter space.

8 1756 M. M. MIGLIETTA and A. BUZZI In defining the appropriate experimental strategies, it was found to be impossible to obtain strictly separated regions due to the incompletely inviscid nature of the model flow. In addition, it should be taken into account that the streamlines in the blocked region are actually open, as illustrated in Smolarkiewicz and Rotunno (1990). In fact, the presence of an upstream stagnation and a reversed flow does not imply the presence of strictly closed streamlines. What really distinguishes a typical flow over regime from the blocked case is the time, τ, taken by a parcel to cross the region upstream of the obstacle. In the former case, τ is of the order of τ 0 = L x /U 0, while in the latter case τ τ 0. In order to favour upstream flow separation, we introduced the arbitrary arc-shaped mountain defined in section 2, where the elevation remains nearly constant along the crest for a cross-flow range of about 300 km. A resemblance with the Alps is implied. The solutions shown below are obtained after a suitable integration time (typically 2 days), when the flow has become stationary or quasi-stationary. This is verified at least in the upstream region and for a realistic set of parameters, in the absence of convective instability (see also Smolarkiewicz and Rotunno (1990) for the problem of residual transient aspects). We refer to this solution as the reference solution. Figure 1 shows the reference solution for an arc-shape mountain in the dry case, with a non-dimensional mountain height H = 2.0. The upstream flow blocking is evident, and larger than for the elliptical mountain in Fig. 10(c) of Miglietta and Buzzi (2001b). Note that, although in the latter figure the non-dimensional mountain height is larger (H = 3.0), the extension of the reversal flow upstream is smaller than in our Fig. 1; this is due to the different mountain shape, and in particular to the higher elevations extending in the cross-flow direction. Figure 2 shows the moist solution for the same case as in Fig. 1, with upstream RH equal to 98%, a condition producing condensation upstream and over the mountain. The flow regime differs markedly from the one in Fig. 1, since no upstream blocking is present. The two solutions are also very different downstream; while in the dry case the main vortex with axis across the flow (Fig. 1(b)) does not touch the ground, and the wind downstream remains westerly, in the moist case the flow downstream near the ground is reversed (Fig. 2(b)). 4. EFFECTS OF SLOW CHANGES IN THE NON-DIMENSIONAL MOUNTAIN HEIGHT In this and the following section, the existence of multiple solutions stable at least for time periods of meteorological significance (from a few hours to a few days) is sought by detecting the manifestation of hysteresis cycles and bifurcations when flow parameters are changed slowly. The intensity of the upstream minimum of the u wind component and the volume of the blocked region are the main variables considered for characterizing the different regimes. In this section, we briefly describe results obtained by changing H, as in Miglietta and Buzzi (2001b), but with the arc-shaped mountain described above, as preliminary to the results described in section 5 using a different approach. Control parameters are forced to change during certain stages of the integration at the inflow. The duration of the experiments must be sufficient to allow the adjustment of the solution to the parameter change. In Miglietta and Buzzi (2001b), different ways of changing the control parameters are examined. The effect of a gradual change of H on the flow features is analysed for a circular and an elliptical mountain. The humidity inflow was chosen as constant and close to saturation throughout the troposphere. A solution varying in time was obtained, characterized by upstream blocking for the maximum height reached by the mountain

9 MOIST STRATIFIED FLOW REGIMES 1757 (H = 4.0) during the integration, and by a flow over regime, though very close to upstream stagnation, for the initial and final values of H (= 2.0). For a mountain with a circular horizontal cross-section, no significant differences from the reference solution were found. For an elliptical mountain, the change in H decreased the final upstream minimum of the zonal wind component by about 10% of the upstream value, U 0, with respect to its reference solution. We repeated similar experiments for the arc-shaped mountain. The results reported briefly below are without figures, since we consider them as physically less significant than those discussed in section 5. The upstream RH is still set at 98%. The value of H is increased from 2.0 to 4.0 in the range from 20 to 40 hours, and then back to 2.0 from 50 to 70 hours, as in Fig. 1 of Miglietta and Buzzi (2001b). The final (after 110 hours) upstream minimum of the u-component of the wind is 1.4 ms 1, significantly less than 2.3 m s 1, which is the value of the upstream minimum observed in the moist reference solution. The differences are associated with the gradual change of the initial flow over regime (H = 2.0) into a partly blocked regime (H = 4.0), with an upstream reversed-flow region. This induces a reduction in the upstream vertical motion and, consequently, in the latent heat release, as no condensation occurs at low levels upstream of the mountain, where a relatively low amount of humidity is present, associated with weak downward motions typical of blocked flows. A small vortex with horizontal axis upstream of the mountain top is generated in the concavity of the obstacle when H increases, persisting until the end of the simulation. This explains, to some extent, the reduced value of the u wind component, observed immediately upstream, which persists in the final state for H = 2.0. In conclusion, the simulations provide some evidence of the existence of memory in the solution when transitions between different regimes occur. This property of the moist flow will emerge more clearly in the experiments described in the next section. 5. MOIST ADVECTION EXPERIMENTS We consider here the experimental set-up that produced the most interesting results, and was more realistic from a meteorological point of view. We chose to induce a transition from dry to humid conditions by advecting moist air from the entrance of the channel towards the obstacle, which is initially embedded in dry air. The advancing transitional zone, separating pre-existing dry air from the incoming moist air, appears as a sort of humidity front. The results obtained allow greater insight into the transition properties among different orographic flow regimes. We refer to this case as the advective solution. At the beginning of the simulations, an inhomogeneous humidity distribution is chosen and allowed to be advected along the channel. The atmosphere is divided into two different volumes, a moist region (RH = 98% in the troposphere), occupying about one third of the distance between the entrance of the channel and the obstacle, and a dry region (RH = 1%) in the rest of the channel. The transition between the two regions is smoothed by defining a constant humidity gradient in a region 75 km wide. This definition introduces horizontal density gradients, which impose a solenoidalforcing on the atmosphere, altering the flow dynamics with respect to the case of uniform humidity. In order to avoid the appearance of such density gradients, the temperature distribution at the initial time is defined so that the virtual temperature is constant at each vertical level. Thus, the humidity front can preserve its coherent structure before its arrival near the obstacle. The temperature field in this case exhibits a weak horizontal gradient, with the dry air slightly warmer than the incoming moist air.

10 1758 M. M. MIGLIETTA and A. BUZZI The case of the arc-shaped mountain, which turned out to be the most significant, is illustrated in detail in subsection 5(a). The advective solution obtained by following this particular flow evolution is compared with the reference solution for the same mountain shape. In subsection 5(b), similar experiments, but with a circular and an elliptical mountain, are contrasted with the experiment with the arc-shaped mountain. (a) Advective experiment with an arc-shaped mountain The initial patterns close to the mountain are the typical dry solution features, similar to those shown in Fig. 1 for the dry reference case, since the moist air is still confined to a limited portion of the channel on the entrance side. This means that, for the selected set of parameters at the initial time, the solution corresponds to a flow around regime, associated with an upstream reversal. We expect that the arrival of moisture near the obstacle will modify the solution, as a consequence of the change in the local value of the Froude number (see MB). We first examine the time evolution of the flow during the entire course of the simulation. Figure 3(a) shows how the values of the upstream minimum remain negative throughout the experiment. A reduction in the absolute value of the reversed flow can be observed in the interval between about 10 and 20 hours, coinciding with the arrival of moisture close to the mountain top. However, immediately afterwards, the generation of a low-level density current, whose edge moves slowly upstream away from the mountain, is reflected in the reinvigorated reversed flow, which by 28 hours reaches a speed maximum in excess of 10 m s 1. Subsequently, the intensity decreases slowly, reaching by 50 hours an almost stationary value of about 8 ms 1. Figure 3(b) shows the time evolution of another significant parameter, the volume of the region affected by flow reversal. This parameter gradually tends towards an almost stationary value, after reaching a maximum of about km 3 (corresponding to 1454 grid points) at 24 hours. We focus here on the solution patterns at 36 hours, a few hours after the transient reversal maximum was observed, and at 60 hours, representative of the quasi-stationary state attained in the final part of the simulation. However, in order to understand the flow features observed at 36 hours, one must briefly consider the previous transient phase. Figure 4 depicts the situation at 16 hours, when the humidity front arrives close to the obstacle. At this time, the differential advection, due to the vertical shear induced by the mountain, strongly modifies the shape of the humidity front, as shown by the equivalent potential temperature contours (in agreement with the theoretical calculations of Smith (1982)). While the presence of the obstacle delays the arrival of the humidity in the pre-mountain region near the ground, at upper levels the moist air moves more rapidly. Furthermore, on the two sides of the mountain the moist air advances more quickly than along the central axis. In the transient phase, therefore, the deformation of the front leaves a region of residual dry air in the concavity of the mountain. The gradient of equivalent potential temperature intensifies upstream of this region (see again Fig. 4). The equivalent isentropes tilt downstream with height and, near the ground, start propagating backwards upstream of the mountain in the counter-flow region. Figure 5 depicts the situation at 36 hours. The intensity of the upstream minimum is 8.8 ms 1 and the volumetric extension of the reversed flow is about km 3. The upstream region is still dry, surrounded by a significant humidity gradient. The low-level dry air, close to the upwind mountain slope, does not escape by flowing over the mountain, probably because the local value of the non-dimensional height H in the dry region corresponds to a flow around regime (see also MB). In fact, the

11 MOIST STRATIFIED FLOW REGIMES a) arc-shaped elliptical circular u (m/s) reversal extension (grid points) b) arc-shaped elliptical circular time (h) Figure 3. Time evolution of advective solution showing (a) the intensity of the upstream wind minimum (m s 1 ) and (b) the extension of the upstream flow reversal (number of grid points) for the circular, elliptical and arc-shaped mountains. general characteristics of the flow shown in Fig. 5 are much closer to those of Fig. 1 ( flow around ) than those of Fig. 2 ( flow over ). Figure 5(a) shows that the lowlevel reversed flow converges with the incoming flow in a narrow arc-shaped belt (with opposite curvature to that of the mountain) upstream of the obstacle. This upstream structure (see also Fig. 5(b)) appears similar to the secondary gravity wave described by Smolarkiewicz and Rotunno (1990) that appears for a relatively large across-/alongstream length aspect ratio. Near the two lateral wings of the mountain, large diffluence is associated with strong cross-channel motion away from the central axis, similar to, but more pronounced than, the corresponding flow shown in Fig. 1(a). The low-level descending motion just upstream of the obstacle (see Fig. 5(b)) reduces the RH and, consequently, also the extension of the condensed volume in the region immediately upstream. Because the streamlines are not closed in the blocked region, the gradual inflow of moist air produces a slow increase in the amount of

12 1760 M. M. MIGLIETTA and A. BUZZI pressure X(km) Figure 4. Advective solution for an arc-shaped mountain: vertical cross-section of equivalent potential temperature (contours and shading, K) and combined u and w wind components along the central axis of the channel after 16 hours. humidity also in this region. Therefore, near the end of the simulation, the upstream region presents an intermediate humidity content between that of the moist air and that of the pre-existing dry air. The upstream blocked region corresponds to the lower branch of a shallow vortex with a horizontal axis that appears in the vertical cross-section (Fig. 5(b)) along the centre of the channel. It should be noted, however, that the flow is far from being 2D, so that the vortex in the vertical plane represents only a projection of the 3D flow. The upwind portion of the vortex, characterized by ascending motion, is associated with condensation. Thus, alongside the more common low-level orographic cloud, located immediately upstream of the mountain top, an additional cloud is present in the solution, produced by the lifting above the upstream convergence region. As indicated in Fig. 3, at 60 hours the solution retains a memory of the dry flow regime existing before the arrival of the humid air (Fig. 6). The extension of the reversal remains almost constant with time: it is still wide (about km 3 ), and the upstream minimum wind ( 7.5 ms 1 ) is still stronger than in the case of the dry solution (Figs. 6(a) and 3). The residual drier air upstream of the obstacle is reduced to a shallow tongue. The horizontal-axis vortex becomes progressively elongated in the longitudinal direction, extending far from the mountain, corresponding to the backward propagation of the density current (Fig. 6(b)). The volume of the far upstream cloud is reduced, as the depth of the counter-flow also decreases. Figure 7 shows that accumulated precipitation appears in two distinct bands, one over the upstream flank of the mountain (orographic precipitation), the other over the upstream convergence belt, just above the head of the density current (see also Grossman and Durran 1984). The two precipitation regions remain separate, as shown in Fig. 7,

13 MOIST STRATIFIED FLOW REGIMES 1761 (a) 800 Y(km) X(km) (b) 500 pressure X(km) Figure 5. As Fig. 1, but for the advective solution for an arc-shaped mountain after 36 hours.

14 1762 M. M. MIGLIETTA and A. BUZZI (a) 800 Y(km) X(km) (b) 500 pressure X(km) K Figure 6. As Fig. 1, but for the advective solution for an arc-shaped mountain after 60 hours.

15 MOIST STRATIFIED FLOW REGIMES Y(km) X(km) Figure 7. Advective solution for an arc-shaped mountain: accumulated total precipitation (mm h 1 )after 60 hours Y(km) X(km) Figure 8. Advective solution for an arc-shaped mountain: air temperature at 2 m ( C) after 60 hours.

16 1764 M. M. MIGLIETTA and A. BUZZI Figure 9. Surface streamlines for an arc-shaped mountain after 60 hours from (a) the reference dry simulation, (b) the reference moist simulation and (c) the advective simulation. until the end of the simulation. The orographic precipitation rate near the mountain increases up to 0.6 mm h 1, remaining almost constant after about 48 hours. Even though the intensity of the precipitation reaching the ground in the upstream band is about 0.1 mm h 1 at around 60 hours, and the extension of the affected region is just 60 km in the longitudinal direction, the cumulative effect of evaporation of precipitation is sufficient to cause a significant cooling of the air close to the ground. In Fig. 8, the 2 m temperature field exhibits a maximum immediately upstream of the mountain, about 2 degc warmer than in the upstream region affected by precipitation. Finally, Fig. 9 presents a comparison among the time-constant ( reference ) dry solution, the reference moist solution and the advective moist solution described in the quasi-stationary phase. In the moist reference case a flow over regime can be observed, while the advective solution described here still reveals a wide portion of reversed flow. It is interesting to note that, at all times after the adjustment stage, the intensity and area of reversed flow is even larger in the advective case than in the dry reference case. Therefore, long after the passage of the front over the obstacle, the upstream solution still presents specific features that cannot be obtained in the case of an initially uniform humidity distribution.

17 MOIST STRATIFIED FLOW REGIMES 1765 (a) (b) (c) Figure 10. Advective solution: surface streamlines after 60 hours for (a) a circular mountain, (b) an elliptical mountain and (c) an arc-shaped mountain. (b) Effects of mountain shape and sensitivity experiments The effects of mountain geometry on orographic flows were investigated by adopting different mountain shapes. A comparison among cases of obstacles with the same aspect ratio and maximum height (see also sections 2 and 3) as the arc-shaped mountain, but with different horizontal cross-sections, stresses the role of obstacle geometry in assuring the persistence of upstream blocking. In the case of a circular mountain, the passage of the front modifies the flow features significantly,althoughonly in an initial transient stage (see Fig. 3), which occurs earlier than for the other mountains, due to the greater longitudinal extension of the obstacle. Perturbations pass quickly beyond the mountain; the solution evolves rapidly from the initial flow around towards the flow over moist solution. Such behaviour appears to be associated with the mountain shape, which does not favour the separation of the upstream region. A transient wide region of diffluence is observed along the central axis, immediately upstream of the mountain. After about 40 hours, the flow blocking disappears (Fig. 10(a)).

18 1766 M. M. MIGLIETTA and A. BUZZI In the elliptical case, the solution shows intermediate features compared to those observed for the other two shapes. The persistence of flow reversal is longer than for the circular mountain. The extension of the region affected by flow reversal, limited in the longitudinal direction, is initially smaller than in the case of the circular mountain, but decreases more slowly with time (see again Fig. 3). However, the comparison with the arc-shaped mountain (compare Figs. 10(b) and (c)) indicates the stagnation point to be much closer to the mountain crest. In addition, the intense diffluent flow advects the upstream dry air around the obstacle more quickly than for the arc-shaped mountain. As a result, the reversal almost disappears after about 60 hours. Comparing the different mountain shape solutions shown in Fig. 10, it is interesting to note that a substantial reversed flow is present only for the arc-shaped mountain. The upstream reversed flow, simulated in the standard experiment described earlier, can be interpreted as a density current (see, for example, Simpson 1987; Houze 1993). It is well known that the propagation speed of the density current edge depends on the intensity of the incoming main flow. A change in the value of U 0 affects the propagation of the current and, consequently, the extension of the region of the reversed flow. In the present study, an evaluation of the sensitivity to the upstream flow speed was attempted. Some results were derived from simulations performed with different values of U 0, bearing in mind that changes in the velocity at the entrance imply modifications in the non-dimensional parameter H and, possibly, in the flow regime of the solution. A higher value of U 0 (e.g. 12 m s 1 ) reduces the extension of the upstream blocking with respect to the reference value (10 m s 1 ). Conversely, for a weaker mean flow (8 m s 1 ), the intensity of the upstream reversal is not simply proportional to the decrease of U 0.This result is not surprising, since a different H introduces some changes in the solution that do not depend only on U 0. Precipitation is another variable that plays an important role in the modification of the upstream features. Its maximum over the mountain top changes with U 0 from about 0.25 mm h 1 (with U 0 = 8ms 1 )to1mmh 1 (with U 0 = 12 m s 1 )atthe final time of the experiment. However, the intensity of the precipitation in the area located far upstream of the mountain is more significant. As already observed, the deformation of the front induced by the mountain generates an upward motion in this region, which is strong enough to generate a large amount of liquid-water content and to shift precipitation upstream (see Peterson et al. 1991). The amount and persistence of this not-strictly-orographic precipitation can significantly modify the observed flow features, as a consequence of the role played by evaporation. For a better analysis of this role, further simulations were performed, excluding the release of latent heat of evaporation. In the advective experiment, the appearance of a cold belt upstream and alongside the obstacle, like the one shown in Fig. 8, is due to the cooling produced by evaporation of precipitation in the convergence region. The absence of evaporative cooling can significantly change the upstream temperature and the flow near the ground; there is no longer a cold area in front of the dry region, and the extension of flow reversal is confined closer to the obstacle. In fact, after 36 hours the reversed flow volume is about 30% less than in the advective simulation described in subsection 5(a); after 60 hours it undergoes a reduction of about 20%. A number of additional simulations were carried out, changing other external parameters. The sensitivity to the value of RH near saturation (95% < RH < 100%) was tested without encountering large differences in the results. Sensitivity to the basic atmospheric stability underwent preliminary investigation, using the upstream surface temperature as a control parameter. A slightly higher temperature (20 C) induces a higher liquid-water content and a significant increase in the upstream precipitation and

19 MOIST STRATIFIED FLOW REGIMES 1767 evaporation, which, together with a stronger upward motion far upstream, favours the upstream movement of the density current. Since the transition to an unstable profile is likely to introduce large variability into the solution (Chu and Lin 2000), the problem is out of the scope of the present study. Further experiments with different mountain heights (H = 1.0, 1.5, 2.5, 3.0) showed that the widest extension of the reversal is obtained for the highest obstacle (H = 3.0). This result is not surprising since also the reference solution in uniform moist conditions exhibits a flow reversal for the same mountain height value (see MB). For the lowest obstacles (H = 1.0, 1.5), more air is involved in the flow over and the extension of the reversal is limited. It is interesting to notice that, for H = 1.5, the horizontal extension near the ground remains quasi-stationary in the second half of the simulation, even though the blocked volume decreases rapidly and is eventually reduced to a shallow layer. Thus, for a short time, the mean flow almost counterbalances the speed of the density current. The sensitivity of the blocking to physical parametrizations and other model settings was analysed in other tests. Doubling the numerical diffusion coefficient has only a limited effect, since the reversed flow intensity remains almost the same and the affected volume is reduced by just 10 20%. Similarly, the effect of the microphysics does not appear significant: turning off the autoconversion and the collection processes does not appreciably modify the reversed flow. In a further experiment with a higher vertical resolution (60 levels), the blocking persists until the end of the simulation, and is enhanced with respect to the standard advective experiment. Finally, two experiments were performed with the purpose of checking the general set-up of the numerical strategy. The first simulation was carried out in order to force the system to change in the opposite direction in parameter space. The initial positions of the moist and dry air were interchanged with respect to the advective experiment. As expected, the flow regime tends towards the dry reference solution, moving from flow over to flow around. However, it is worth noting that a small bubble of moist air remains temporarily blocked by the mountain near the ground. In the advective experiment, a constant value of virtual temperature at each level was chosen in order to avoid unwanted baroclinic effects across the humidity front. As a consequence, the dry air was warmer than the moist air at the same level. In order to avoid this problem, we tested an alternative, less physicalapproach;the model definition of virtual temperature was altered by simply setting it as equal to the temperature. In this way, dry and moist air maintain the same temperature and density. In this case, although the transient solution evolves rather differently with respect to the advective experiment in the vicinity of the mountain, the two solutions are similar after 60 hours. 6. SUMMARY AND CONCLUSIONS The purpose of this work was to generalize the results of previous studies on moist flows over simply-shaped mountains in idealized conditions. In particular, the possible existence of multiple solutions was investigated in a moist atmosphere, attempting to extend some of the results obtained in dry conditions by Smith and Grønås (1993). Our study was based on model simulations, and was driven by working assumptions on the effects of moisture on the properties of flow regimes past obstacles. Different solutions were obtained with the same set of parameters for different paths and obstacle geometries, suggesting that the history of the system is important in determining the evolution of the flow. For example, experiments performed by modifying the height of the obstacle in the course of the simulation indicate that the solution retains a memory

20 1768 M. M. MIGLIETTA and A. BUZZI (hysteresis) of the transient blocked flow. In particular, a flow over type of (moist) solution, established as a result of a transition from a blocked flow regime, turns out to be different from a solution for the same parameters, established in the absence of a previous blocked flow. Changes in the evolution of the system can be attributed to the non-reversible processes associated with condensation. However, such solutions are not strictly speaking steady-state solutions, but stable enough for meteorological time scales. In this sense, these solutions have similar characteristics to those found by Smith and Grønås (1993). The presence of a quasi-stationary non-trivial solution of the type described above is distinguished in the main experiment described in this work. Moist air is advected from the entrance of the channel towards the obstacle, which is initially embedded in dry air. A wide region of reversed flow remains confined upstream of the obstacle, even after moisture has filled most of the domain. In addition, the intensity of the blocking is enhanced with respect to the initial dry flow regime, and the reversal persists until the end of the simulation. This occurs for regions of the parameter space that correspond to flow over, in simulations where the inflow conditions and the external parameters do not change in time. The maintenance of the region of reversed flow depends on a dynamic balance between the upstream propagation of the dry region and the incoming main flow. This balance depends in turn on the obstacle geometry. The above solutions do not appear simply as an extension of those found in the dry case. They are specifically related to the effects of condensation and evaporation, coupled with those associated with the dynamical properties of flow past an obstacle. Such diabatic effects are responsible for the non-trivial, time-dependent, but long-lasting solutions described here. Theoretical and modelling studies of an air stream incident upon mesoscale orography have addressed a wide range of factors (stratification, vertical structure, frictional and diabatic effects, rotation). Special attention was devoted here to the sensitivity of solutions to obstacle shape, with experiments performed for a particular arc-shaped mountain. The results indicate that the shape of the mountain is important, suggesting that the extent of the blocked and/or reversed upstream flow is one of the main factors that favours the existence of multiple solutions. The effect of mountain geometry was evaluated by comparing solutions obtained for obstacles of different shape. Unlike the case of the arc-shaped mountain, with circular and elliptical mountains the system swiftly evolved towards the flow solutions obtained without adjusting the inflow conditions or external parameters. Sensitivity to different parameters was tested. The evaporation of precipitation turns out to be important; the portion of observed flow reversal is reduced in simulations where the contribution of cooling due to evaporation of precipitation is suppressed. Hill (1978) inferred the role of precipitation in flows over mountains from radiosonde ascents upwind of a mountain barrier in almost neutral conditions. Rotor-type blocked flows can be induced via precipitation drag and evaporation; downward vertical motions appear on the windward side. More recently, observations during the field phase of MAP showed a down-valley drainage flow developing below a flow of moist air moving in an opposite direction over the topographic barrier; the lowest air remains constrained upstream, and only air from the layers above 1 2 km rises over the mountain (Steiner et al. 2003). In conclusion, the study of particular non-stationary solutions may serve as a basis for interpreting features observed in real events. Appropriate field observations may represent a valid test for the verification of the results obtained. The significant