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Tomislav Marić
and
Dale R. Durran

Abstract

Using extensive observations collected from various platforms around the Brenner Pass in the Austrian Alps during the Mesoscale Alpine Programme, a detailed description of the kinematic and thermodynamic structure of the shallow-foehn event that occurred on 20 October 1999 in the Wipp Valley is constructed. Downstream of the gap the flow develops a well-mixed surface layer capped by a relatively strong temperature inversion of 5–6 K. Such inversions are often assumed to be kinematically similar to the free surface at the top of a liquid; however, the data suggest the presence of strong subsidence through the mean position of the inversion layer capping the flow. Such subsidence is supported by in situ aircraft observations and Doppler lidar measurements but is not consistent with the observed turbulent heat fluxes, which are too small to account for the diabatic heating required by the isentrope-relative downward velocities. The 1-Hz time resolution of the P3 data may, however, be too coarse to correctly capture the full turbulent heat flux.

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Patrick A. Reinecke
and
Dale R. Durran

Abstract

The sensitivity of downslope wind forecasts to small changes in initial conditions is explored by using 70-member ensemble simulations of two prototypical windstorms observed during the Terrain-Induced Rotor Experiment (T-REX). The 10 weakest and 10 strongest ensemble members are composited and compared for each event.

In the first case, the 6-h ensemble-mean forecast shows a large-amplitude breaking mountain wave and severe downslope winds. Nevertheless, the forecasts are very sensitive to the initial conditions because the difference in the downslope wind speeds predicted by the strong- and weak-member composites grows to larger than 28 m s−1 over the 6-h forecast. The structure of the synoptic-scale flow one hour prior to the windstorm and during the windstorm is very similar in both the weak- and strong-member composites.

Wave breaking is not a significant factor in the second case, in which the strong winds are generated by a layer of high static stability flowing beneath a layer of weaker mid- and upper-tropospheric stability. In this case, the sensitivity to initial conditions is weaker but still significant. The difference in downslope wind speeds between the weak- and strong-member composites grows to 22 m s−1 over 12 h. During and one hour before the windstorm, the synoptic-scale flow exhibits appreciable differences between the strong- and weak-member composites. Although this case appears to be more predictable than the wave-breaking event, neither case suggests that much confidence should be placed in the intensity of downslope winds forecast 12 or more hours in advance.

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Saša Gaberšek
and
Dale R. Durran

Abstract

Gap winds produced by a uniform airstream flowing over an isolated flat-top ridge cut by a straight narrow gap are investigated by numerical simulation. On the scale of the entire barrier, the proportion of the oncoming flow that passes through the gap is relatively independent of the nondimensional mountain height ϵ, even over that range of ϵ for which there is the previously documented transition from a “flow over the ridge” regime to a “flow around” regime.

The kinematics and dynamics of the gap flow itself were investigated by examining mass and momentum budgets for control volumes at the entrance, central, and exit regions of the gap. These analyses suggest three basic behaviors: the linear regime (small ϵ) in which there is essentially no enhancement of the gap flow; the mountain wave regime (ϵ ∼ 1.5) in which vertical mass and momentum fluxes play a crucial role in creating very strong winds near the exit of the gap; and the upstream-blocking regime (ϵ ∼ 5) in which lateral convergence generates the strongest winds near the entrance of the gap.

Trajectory analysis of the flow in the strongest events, the mountain wave events, confirms the importance of net subsidence in creating high wind speeds. Neglect of vertical motion in applications of Bernoulli's equation to gap flows is shown to lead to unreasonable wind speed predictions whenever the temperature at the gap exit exceeds that at the gap entrance. The distribution of the Bernoulli function on an isentropic surface shows a correspondence between regions of high Bernoulli function and high wind speeds in the gap-exit jet similar to that previously documented for shallow-water flow.

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Daniel J. Kirshbaum
and
Dale R. Durran

Abstract

The development of shallow cellular convection in warm orographic clouds is investigated through idealized numerical simulations of moist flow over topography using a cloud-resolving numerical model. Buoyant instability, a necessary element for moist convection, is found to be diagnosed most accurately through analysis of the moist Brunt–Väisälä frequency (N m ) rather than the vertical profile of θ e . In statically unstable orographic clouds ( N 2 m < 0), additional environmental and terrain-related factors are shown to have major effects on the amount of cellularity that occurs in 2D simulations. One of these factors, the basic-state wind shear, may suppress convection in 2D yet allow for longitudinal convective roll circulations in 3D. The presence of convective structures within an orographic cloud substantially enhanced the maximum rainfall rates, precipitation efficiencies, and precipitation accumulations in all simulations.

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Dale R. Durran
and
Mark Gingrich

Abstract

The spectral turbulence model of Lorenz, as modified for surface quasigeostrophic dynamics by Rotunno and Snyder, is further modified to more smoothly approach nonlinear saturation. This model is used to investigate error growth starting from different distributions of the initial error. Consistent with an often overlooked finding by Lorenz, the loss of predictability generated by initial errors of small but fixed absolute magnitude is essentially independent of their spatial scale when the background saturation kinetic energy spectrum is proportional to the −5/3 power of the wavenumber. Thus, because the background kinetic energy increases with scale, very small relative errors at long wavelengths have similar impacts on perturbation error growth as large relative errors at short wavelengths. To the extent that this model applies to practical meteorological forecasts, the influence of initial perturbations generated by butterflies would be swamped by unavoidable tiny relative errors in the large scales.

The rough applicability of the authors’ modified spectral turbulence model to the atmosphere over scales ranging between 10 and 1000 km is supported by the good estimate that it provides for the ensemble error growth in state-of-the-art ensemble mesoscale model simulations of two winter storms. The initial-error spectrum for the ensemble perturbations in these cases has maximum power at the longest wavelengths. The dominance of large-scale errors in the ensemble suggests that mesoscale weather forecasts may often be limited by errors arising from the large scales instead of being produced solely through an upscale cascade from the smallest scales.

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Jonathan A. Weyn
and
Dale R. Durran

Abstract

Idealized ensemble simulations of mesoscale convective systems (MCSs) with horizontal grid spacings of 1, 1.4, and 2 km are used to analyze the influence of numerical resolution on the rate of growth of ensemble spread in convection-resolving numerical models. The ensembles are initialized with random phases of 91-km-wavelength moisture perturbations that are captured with essentially identical accuracy at all resolutions. The rate of growth of ensemble variance is shown to systematically increase at higher resolution. The largest horizontal wavelength at which the perturbation kinetic energy (KE′) grows to at least 50% of the background kinetic energy spectrum is also shown to grow more rapidly at higher resolution. The mechanism by which the presence of smaller scales accelerates the upscale growth of KE′ is clear-cut in the smooth-saturation Lorenz–Rotunno–Snyder (ssLRS) model of homogeneous surface quasigeostrophic turbulence. Comparing the growth of KE′ from the MCS ensemble simulations to that in the ssLRS model suggests interactions between perturbations at small scales, where KE′ is not yet completely saturated, and somewhat larger scales, where KE′ is clearly unsaturated, are responsible for the faster growth rate of ensemble variance at finer resolution. These results provide some empirical justification for the use of deep-convection-related stochastic parameterization schemes to reduce the problem of underdispersion in coarser-resolution ensemble prediction systems.

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Xiaoming Shi
and
Dale R. Durran

Abstract

The sensitivity of stratiform midlatitude orographic precipitation to global mean temperature is investigated through numerical simulations. As a step toward understanding the relative influence of thermodynamic and dynamical processes on orographic precipitation, simple idealizations of Earth’s major north–south mountain chains are considered. The individual terrain elements occupy four islands equally spaced around the Northern Hemisphere of a planet otherwise covered by ocean. Although these mountains have very little influence on the sensitivity of the zonally averaged precipitation to changes in global mean surface temperature, the precipitation on the windward slopes of the ridges is highly sensitive to such changes. When the ridges run between 40° and 60°N, the windward-slope hydrological sensitivity exceeds the Clausius–Clapeyron scaling of about 7% K−1 over the northern half of the barrier, leading to substantial precipitation changes. The annual accumulated orographic precipitation is modified by changes in both the mean precipitation intensity and the changes in the number of hours during which precipitation occurs. The changes in the number of hours with significant precipitation largely results from modifications in synoptic-scale storminess associated with changes in the midlatitude storm tracks. A simple diagnostic model reveals the primary factors modifying the mean orographic precipitation intensity are variations in 1) the moist adiabatic lapse rate of saturation specific humidity, 2) the wind speed perpendicular to the mountain, and 3) the vertical displacement of saturated air parcels above the windward slope. The strong dependence of 2 and 3 on latitude further confirms that changes in midlatitude storminess are a major factor determining the response of orographic precipitation to global warming.

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Xiaoming Shi
and
Dale R. Durran

Abstract

Global warming–induced changes in extreme orographic precipitation are investigated using a hierarchy of models: a global climate model, a limited-area weather forecast model, and a linear mountain wave model. The authors consider precipitation changes over an idealized north–south midlatitude mountain barrier at the western margin of an otherwise flat continent. The intensities of the extreme events on the western slopes increase by approximately 4% K−1 of surface warming, close to the “thermodynamic” sensitivity of vertically integrated condensation in those events due to temperature variations when vertical motions stay constant. In contrast, the intensities of extreme events on the eastern mountain slopes increase at about 6% K−1. This higher sensitivity is due to enhanced ascent during the eastern-slope events, which can be explained in terms of linear mountain wave theory as arising from global warming–induced changes in the upper-tropospheric static stability and the tropopause level. Similar changes to these two parameters also occur for the western-slope events, but the cross-mountain flow is much stronger in those events; as a consequence, linear theory predicts no increase in the western-slope vertical velocities. Extreme western-slope events tend to occur in winter, whereas those on the eastern side are most common in summer. Doubling CO2 not only increases the precipitation, but during extreme western slope events it shifts much of the precipitation from snow to rain, potentially increasing the risk of heavy runoff and flooding.

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Maximo Q. Menchaca
and
Dale R. Durran

Abstract

The interaction of a midlatitude cyclone with an isolated north–south mountain barrier is examined using numerical simulation. A prototypical cyclone develops from an isolated disturbance in a baroclinically unstable shear flow upstream of the ridge, producing a cold front that interacts strongly with the topography. The structure and evolution of the lee waves launched by the topography are analyzed, including their temporal and their north–south variation along the ridge. Typical mountain wave patterns are generated by a 500-m-high mountain, but these waves often exhibit significant differences from the waves produced in 2D or 3D simulations with steady large-scale-flow structures corresponding to the instantaneous conditions over the mountain in the evolving flow. When the mountain height is 2 km, substantial wave breaking occurs, both at low levels in the lee and in the lower stratosphere. Despite the north–south uniformity of the terrain profile, large north–south variations are apparent in wave structure and downslope winds. In particular, for a 24-h period beginning after the cold front passes the upstream side of the ridge toward the south, strong downslope winds occur only in the northern half of the lee of the ridge. Just prior to this period, the movement of the cold front across the northern lee slopes is complex and accompanied by a burst of strong downslope winds and intense vertical velocities.

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Jonathan A. Weyn
and
Dale R. Durran

Abstract

Recent work has suggested that modest initial relative errors on scales of O(100) km in a numerical weather forecast may exert more control on the predictability of mesoscale convective systems at lead times beyond about 5 h than 100% relative errors at smaller scales. Using an idealized model, the predictability of deep convection organized by several different profiles of environmental vertical wind shear is investigated as a function of the horizontal scale and amplitude of initial errors in the low-level moisture field. Small- and large-scale initial errors are found to have virtually identical impacts on predictability at lead times of 4–5 h for all wind shear profiles. Both small- and large-scale errors grow primarily up in amplitude at all scales rather than through an upscale cascade between adjacent scales. Reducing the amplitude of the initial errors improves predictability lead times, but this improvement diminishes with further reductions in the error amplitude, suggesting a limit to the intrinsic predictability in these simulations of slightly more than 6 h at scales less than 20 km. Additionally, all the simulated convective systems produce a k −5/3 spectrum of kinetic energy, providing evidence of the importance of the unbalanced, divergent gravity wave component of the flow produced by thunderstorms in generating the observed atmospheric kinetic energy spectrum.

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