Abstract

Interactions of atmospheric dynamics and cloud microphysics with the Alpine orography are investigated for two north Alpine heavy-precipitation cases (20–22 May 1999 and 22–23 August 2005). Both cases were related to a deep cyclone propagating slowly eastward along the Alps, advecting moist air of Mediterranean origin toward the northern side of the Alps. A validation against high-resolution rain gauge data reveals that the average model bias is below 15% in the region of interest, but there is a tendency to systematically underestimate very heavy precipitation. A scale decomposition of the discrepancies between model and observations reveals that errors on the meso-β-scale contribute at least as much to the total model error as discrepancies on the meso-γ-scale. On the scale of single mountain ridges and valleys, the formation of precipitation maxima at valley locations is investigated, with particular emphasis on a region in which a valley receives systematically more precipitation than the adjacent mountain ridges. It is found that the downstream advection of precipitation hydrometeors generated in an orographic feeder cloud is essential for the development of valley maxima. Strong ambient winds and (due to the fall speed difference between snow/graupel and rain) a low freezing level favor a large distance of the precipitation maximum from the upstream mountain ridge. Under suitable geometrical conditions, downstream advection of hydrometeors can even lead to systematically more precipitation in the valley than over the adjacent ridges. Another mechanism capable of generating a systematic rainfall maximum at valley locations requires a freezing level between valley bottom and crest height and a mountain wave flow penetrating into the valley. Under such conditions, the increase in the fall velocity related to melting of snow or graupel into rain leads to a locally intensified fallout of hydrometeors and thus to a maximum in the precipitation rate.

Abstract

The concept of adaptive vertical coordinates is used to upgrade conventional terrain-following σ coordinates to arbitrary hybrid coordinates. Compared with previous approaches for implementing adaptive coordinates, the method presented here combines unrestricted applicability to nonhydrostatic models with the capability to integrate the atmospheric equations in flux form. The coordinate is based on a three-dimensional field carrying the vertical position of the coordinate surfaces, which is made time dependent by introducing a prognostic equation. As a specific example, the adaptive coordinate is used to emulate a hybrid isentropic system. Idealized tests in which the coordinate surfaces are artificially moved reveal that the ensuing spurious motions are small enough to be negligible in realistic applications. Mountain wave tests demonstrate that the hybrid coordinate remains numerically stable under strong forcing. However, the model layer distribution established with the hybrid isentropic coordinate is not optimal for representing the dynamics of breaking gravity waves because the vertical distance between the model levels tends to be too large in the wave breaking region. On the other hand, real case studies demonstrate that the hybrid coordinate significantly improves the representation of the tropopause because of enhanced vertical resolution in the tropopause region.

Abstract

A set of modifications is presented to reduce the unphysical impact of horizontal diffusion in numerical models with a terrain-following sigma-coordinate system. At model levels sufficiently far away from the ground, vertical interpolation is used to compute diffusion truly horizontally when the coordinate surfaces are sloping. Close to the ground, where truly horizontal computation of diffusion is not everywhere possible without intersecting the topography, a combination of one-sided truly horizontal diffusion and orography-adjusted diffusion along the sigma surfaces is used for most of the variables. The latter means that the diffusion coefficient is reduced strongly when the grid points involved in the computation of horizontal diffusion are located at greatly different heights. For temperature, one-sided horizontal diffusion is not used because it damps the slope wind circulation in an unphysical way. However, a temperature gradient correction is applied to the terrain-following part of the temperature diffusion. Its purpose is to make diffusion neutral with respect to the current vertical temperature gradient. The modifications have been implemented into the Fifth-Generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5). Idealized simulations of the valley wind circulation in the Inn Valley of the Alps are performed to test the modifications. In its original state, the model turns out to be unable to reproduce this valley wind system because of errors related to diffusion along the coordinate surfaces. However, the model captures all essential features of the observed valley wind with the modified diffusion scheme. Both the temporal evolution and the vertical structure of the valley wind are consistent with observations. This result suggests that the model's ability to simulate flow over mountainous topography is greatly improved by use of the modified scheme.

Abstract

A generalized sigma-coordinate system is presented that allows for a rapid vertical decay of small-scale topographic structures in the coordinate surfaces. Its properties are similar to the smooth-level vertical-coordinate system recently introduced by Schär et al., but it is designed for the coordinate definition used in the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5). An idealized advection test demonstrates that the accuracy of the horizontal advection greatly benefits from the reduced slope of the coordinate surfaces at some vertical distance from the topography. Moreover, a test considering an atmosphere at rest in the vicinity of an isolated mountain shows that the new coordinate system strongly reduces the numerical noise appearing in such a configuration. The noise turns out to be related to a local numerical instability triggered by computing the horizontal temperature diffusion along sloping coordinate surfaces. When the temperature diffusion is computed truly horizontally, the noise disappears completely.

Abstract

High-resolution numerical simulations with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) are presented to investigate the processes leading to the formation of extreme cold-air pools in elevated sinkholes. The simulations are idealized in the sense that they are conducted with idealized model topography and with idealized large-scale conditions representing an undisturbed wintertime high pressure situation. After a number of model modifications, the temperature fields, radiative cooling rates, and sensible heat fluxes simulated by the model were in good agreement with the available observations, giving confidence that the model is suitable for this process study.

The model results indicate a number of necessary preconditions for the formation of an extreme cold-air pool in a sinkhole. Apart from undisturbed clear weather, a small heat conductivity of the ground and an effective mechanism drying the low-level air during the cooling process are required. The importance of the heat conductivity results from the fact that the net cooling of the ground is only a small residual between the net radiative heat loss and the ground heat flux. As a consequence, extreme cooling events are strongly favored by the presence of freshly fallen powder snow. The necessity of a drying mechanism is related to the strong temperature dependence of the saturation vapor pressure, decreasing by a factor of about 2.5 per 10 K temperature decrease at temperatures below −20°C. Except in cases of very dry ambient air, a nocturnal cooling by 25 or 30 K (as observed in extreme cases) must be accompanied by an order-of-magnitude reduction of the water vapor mixing ratio to prevent the formation of fog. According to the simulations, the most effective drying mechanism is provided by the formation of ice clouds and the subsequent sedimentation of the ice particles. Near the surface, direct deposition of water vapor at the ground also seems to play a significant role.

Abstract

This study presents high-resolution numerical simulations in order to examine the dynamical mechanisms controlling the persistence of wintertime cold-air pools in an Alpine valley system. First, a case study of a cold-pool episode is conducted, the formation of which was related to the passage of a warm front north of the Alps. While the preexisting cold air was rapidly advected away in the Alpine foreland, a persistent cold pool was maintained in the inner-Alpine part of the valley system, associated with sustained horizontal temperature differences of up to 10 K over a distance of 30 km. The case study is complemented by a series of semi-idealized simulations, combining realistic topography with idealized large-scale flow conditions. These simulations consider a range of different ambient wind directions in order to investigate their impact on the cold-pool persistence.

The results indicate that the most important dynamical mechanism controlling the persistence of cold-air pools in deep Alpine valleys is cold-air drainage toward the Alpine foreland. The preferred direction for such a drainage flow is down the pressure gradient imposed by the (geostrophically balanced) ambient flow. Thus, for a given valley geometry and a given strength of the ambient flow, the probability for persistent cold-air pools mainly depends on the ambient wind direction. If the direction of the imposed pressure gradient matches a sufficiently wide connection to the foreland (a valley or a low pass), then a drainage flow will lead to a rapid removal of the cold air. However, the presence of pronounced lateral constrictions in the connecting valley may strongly reduce the drainage efficiency. Cold-pool erosion by turbulent vertical mixing seems to play a comparatively minor role in deep valley systems as considered in this study.

Abstract

Orographic gravity waves excited by a narrow mountain ridge are investigated with the aid of numerical simulations. When the nondimensional mountain half-width Na/U is around 1—N, a, and U being the Brunt–Väisälä frequency, the dimensional half-width, and the ambient wind speed, respectively—only part of the gravity wave spectrum excited by the mountain is able to propagate vertically. In this case, linear theory, as well as numerical simulations with low mountains, show two wind maxima: one at the mountain crest and one in the lee of the mountain. As Na/U is reduced below 1, the wind maximum in the lee weakens and moves farther downstream, and the maximum at the crest intensifies rapidly with decreasing Na/U. Simulations in which a gap with a level axis is embedded in the mountain ridge demonstrate that the wind perturbations along the gap axis are qualitatively similar to those over the adjacent mountain ridge. However, their magnitude is substantially lower, and the tendency to form a wind maximum at the gap center (corresponding to a maximum at the mountaintop) is rather weak.

When the mountain is high enough for nonlinear effects to become important, the flow structure changes substantially. Provided that Na/U is not below 1, there is a range of nondimensional mountain heights where gravity wave breaking establishes a flow structure very similar to that typical for wider mountains, including strong downslope winds in the lee of the mountain and a pressure drag well above the linear value. The results indicate that nonlinearity can shift the primary wind maximum from the mountain crest into the lee. For Na/U ≈ 0.75, gravity wave breaking no longer occurs, and the wind maximum is reached at the top of the mountain regardless of its height. Along a gap axis, however, there is a tendency for a pronounced wind maximum on the lee side even for narrow mountain ridges. In agreement with the results known for wider mountains, surface friction is found to reduce the wind speed close to the ground, to promote flow separation from the ground over the lee slope of the mountain and to reduce the tendency toward gravity wave breaking. For Na/U ≈ 1 and moderate surface friction, the formation of rotors becomes possible even for uniform large-scale flow.

Abstract

This paper investigates wintertime cold-air pools in a basinlike part of the Danube Valley, located in the German state of Bavaria. Specifically, the focus is on cold-pool events restricted to the basin area, that is, not extending to the more elevated parts of the Alpine foreland. An analysis of observational data indicates that the delay of warm-air advection in the basin area relative to the Alpine foreland plays a major role in these events. However, the relationship between warming in the Alpine foreland and a temperature deficit in the northeast–southwest-oriented basin appears to depend sensitively on the ambient wind direction. A statistically significant correlation is found only for westerly and southerly wind directions but not for easterly directions. To examine the dynamical reasons for this phenomenon, idealized numerical simulations have been conducted. They are initialized with a pronounced cold pool in the basin area and examine the response of the cold pool to the dynamical forcing imposed by a geostrophically balanced large-scale wind field of various directions and strengths. Sensitivity tests consider the effects of the surrounding mountain ranges and of turbulent vertical mixing. The model results indicate that the most important dynamical processes capable of dissolving cold-air pools in a large basin are (i) ageostrophic advection of the cold air toward lower ambient pressure and (ii) downstream advection by the ambient flow. The former might also be interpreted as an adjustment of the cold air to the external pressure gradient, which can be balanced by the development of a spatial gradient in cold-pool depth. In principle, both advection processes are most effective in the along-basin direction because the advected air does not have to surmount significant topographic obstacles. However, a combination of several effects induced by the surrounding mountain ranges—for example, upstream flow deceleration and wake formation—modifies the dependence of the cold-pool persistence on the ambient wind direction. In agreement with observational data, the simulations with full topography predict a higher tendency for cold-pool persistence in the Danube basin for westerly and southerly flow than for easterly flow. Turbulent vertical mixing is found to make a significant contribution to the erosion of cold pools, but its effect is smaller than the sensitivity to the ambient wind direction.

Abstract

To extend the numerical stability limit over steep slopes, a truly horizontal pressure-gradient discretization based on the ideas formulated by Mahrer in the 1980s has been developed. Conventionally, the pressure gradient is evaluated in the terrain-following coordinate system, which necessitates a metric correction term that is prone to numerical instability if the height difference between adjacent grid points is much larger than the vertical layer spacing. The alternative way pursued here is to reconstruct the pressure gradient at auxiliary points lying at the same height as the target point on which the velocity is defined. This is accomplished via a second-order Taylor-series expansion in this work, using the hydrostatic approximation to transform the second derivatives into first derivatives to facilitate second-order accurate discretization in the presence of strong vertical grid stretching. Moreover, a reformulated lower boundary condition is used that avoids the extrapolation of vertical derivatives evaluated in potentially very thin layers. A sequence of tests at varying degrees of idealization reveals that the truly horizontal pressure-gradient discretization improves numerical stability over steep slopes for a wide range of horizontal mesh sizes, ranging from a few hundreds of meters to tens of kilometers. In addition, tests initialized with an atmosphere at rest reveal that the spurious circulations developing over steep mountains are usually smaller than for the conventional discretization even in configurations for which the latter does not suffer from stability problems.

Abstract

The first step in the evolution of the diurnal circulation of grand plateaus is the matutinal buildup of inflow through mountain passes connecting the lowlands with the plateau proper. Maximum inward transport is attained in the afternoon. Corresponding observations at the Bolivian Altiplano are described in the first part of this paper. Here, both a linear model and the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) are used to better understand the dynamics of this process. First discussed is the solution to the linear sea-breeze problem where a heated fluid layer is restricted to the half plane x ≤ 0. Rapidly moving barotropic modes lead to surface pressure fall in the heated half plane and to pressure rise for x ≥ 0. Slow baroclinic modes describe the horizontally expanding inflow toward the heated layer near the ground with return flow aloft. This basic structure of the response carries over to more complicated topographies where a heated plateau with vertical sidewalls is separated from the lowlands by a barrier and a pass. The baroclinic modes are fanning out from the pass into the plateau’s interior in linear numerical calculations. These flow patterns hardly change when additional slopes connect the plains and the plateau.

The restrictions imposed by the linear approach are removed step by step in simulations with MM5 in which an idealized plateau with an optional pass is prescribed. There is good agreement with respect to the basic flow pattern, but the linear theory is found to overestimate inflow velocities because of its neglect of momentum and perturbation temperature advection. Moreover, a front moves from the pass into the plateau’s interior where the stratification is neutral or even unstable, a situation that is beyond the scope of the linear theory. The upslope winds evolving at the slope connecting the plateau with the lowlands are unimportant for the thermal circulation of the plateau, a result also suggested by the linear theory. Finally, simulations of the diurnal cycle are performed for the real topography of the Altiplano. The presentation of results concentrates on the observation sites. It is demonstrated that the idealized calculations help to better understand the resulting flows as well as the observations reported in Part I. The total inflow to the Altiplano is discussed as well.