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Dale R. Durran
and
Maximo Q. Menchaca

Abstract

The influence of vertical shear on the evolution of mountain-wave momentum fluxes in time-varying cross-mountain flows is investigated by numerical simulation and analyzed using ray tracing and the WKB approximation. The previously documented tendency of momentum fluxes to be strongest during periods of large-scale cross-mountain flow acceleration can be eliminated when the cross-mountain wind increases strongly with height. In particular, the wave packet accumulation mechanism responsible for the enhancement of the momentum flux during periods of cross-mountain flow acceleration is eliminated by the tendency of the vertical group velocity to increase with height in a mean flow with strong forward shear, thereby promoting vertical separation rather than concentration of vertically propagating wave packets.

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Maximo Q. Menchaca
and
Dale R. Durran

Abstract

The feedback of mountain waves and low-level blocking on an idealized baroclinically unstable wave passing over an isolated ridge is examined through numerical simulation. Theoretical analysis implies that the volume-integrated perturbation momentum budget is dominated by mean-flow deceleration, the divergence of vertical fluxes of horizontal momentum, and the Coriolis force acting on the perturbation ageostrophic wind. These do indeed appear as the dominant balances in numerically computed budgets averaged over layers containing 1) wave breaking in the lower stratosphere, 2) flow blocking with wave breaking near the surface, and 3) a region of pronounced horizontally averaged mean-flow deceleration in the upper troposphere where there is no wave breaking. The local impact of wave breaking on the jet in the lower stratosphere is dramatic, with winds in the jet core reduced by almost 50% relative to the no-mountain case. Although it is the layer with the strongest average deceleration, the local patches of decelerated flow are weakest in the upper troposphere. The cross-mountain pressure drag over a 2-km-high ridge greatly exceeds the vertical momentum flux at mountain-top level because of low-level wave breaking, blocking, and lateral flow diversion. These pressure drags and the low-level momentum fluxes are significantly different from corresponding values computed for simulations with steady forcing matching the instantaneous conditions over the mountain in the evolving large-scale flow.

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Maximo Q. Menchaca
and
Dale R. Durran

Abstract

The influence of gravity waves generated by surface stress and by topography on the atmospheric kinetic energy (KE) spectrum is examined using idealized simulations of a cyclone growing in baroclinically unstable shear flow. Even in the absence of topography, surface stress greatly enhances the generation of gravity waves in the vicinity of the cold front, and vertical energy fluxes associated with these waves produce a pronounced shallowing of the KE spectrum at mesoscale wavelengths relative to the corresponding free-slip case. The impact of a single isolated ridge is, however, much more pronounced than that of surface stress. When the mountain waves are well developed, they produce a wavenumber to the −5/3 spectrum in the lower stratosphere over a broad range of mesoscale wavelengths. In the midtroposphere, a smaller range of wavelengths also exhibits a −5/3 spectrum. When the mountain is 500 m high, the waves do not break, and their KE is entirely associated with the divergent component of the velocity field, which is almost constant with height. When the mountain is 2 km high, wave breaking creates potential vorticity, and the rotational component of the KE spectrum is also strongly energized by the waves. Analysis of the spectral KE budgets shows that the actual spectrum is the result of continually shifting balances of direct forcing from vertical energy flux divergence, conservative advective transport, and buoyancy flux. Nevertheless, there is one interesting example where the −5/3-sloped lower-stratospheric energy spectrum appears to be associated with a gravity-wave-induced upscale inertial cascade.

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Dale R. Durran
and
Jonathan A. Weyn

Abstract

One important limitation on the accuracy of weather forecasts is imposed by unavoidable errors in the specification of the atmosphere’s initial state. Much theoretical concern has been focused on the limits to predictability imposed by small-scale errors, potentially even those on the scale of a butterfly. Very modest errors at much larger scales may nevertheless pose a more important practical limitation. We demonstrate the importance of large-scale uncertainty by analyzing ensembles of idealized squall-line simulations. Our results imply that minimizing initial errors on scales around 100 km is more likely to extend the accuracy of forecasts at lead times longer than 3–4 h than efforts to minimize initial errors on much smaller scales. These simulations also demonstrate that squall lines, triggered in a horizontally homogeneous environment with no initial background circulations, can generate a background mesoscale kinetic energy spectrum roughly similar to that observed in the atmosphere.

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Lucas M. Harris
and
Dale R. Durran

Abstract

Most mesoscale models can be run with either one-way (parasitic) or two-way (interactive) grid nesting. This paper presents results from a linear 1D shallow-water model to determine whether the choice of nesting method can have a significant impact on the solution. Two-way nesting was found to be generally superior to one-way nesting. The only situation in which one-way nesting performs better than two-way is when very poorly resolved waves strike the nest boundary. A simple filter is proposed for use exclusively on the coarse-grid values within the sponge zone of an otherwise conventional sponge boundary condition (BC). The two-way filtered sponge BC gives better results than any of the other methods considered in these tests. Results for all wavelengths were found to be robust to other changes in the formulation of the sponge boundary, particularly with the width of the sponge layer. The increased reflection for longer-wavelength disturbances in the one-way case is due to a phase difference between the coarse- and nested-grid solutions at the nested-grid boundary that accumulates because of the difference in numerical phase speeds between the grids. Reflections for two-way nesting may be estimated from the difference in numerical group velocities between the coarse and nested grids, which only becomes large for waves that are poorly resolved on the coarse grid.

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Dale R. Durran
and
Peter N. Blossey

Abstract

Implicit–explicit (IMEX) linear multistep methods are examined with respect to their suitability for the integration of fast-wave–slow-wave problems in which the fast wave has relatively low amplitude and need not be accurately simulated. The widely used combination of trapezoidal implicit and leapfrog explicit differencing is compared to schemes based on Adams methods or on backward differencing. Two new families of methods are proposed that have good stability properties in fast-wave–slow-wave problems: one family is based on Adams methods and the other on backward schemes. Here the focus is primarily on four specific schemes drawn from these two families: a pair of Adams methods and a pair of backward methods that are either (i) optimized for third-order accuracy in the explicit component of the full IMEX scheme, or (ii) employ particularly good schemes for the implicit component. These new schemes are superior, in many respects, to the linear multistep IMEX schemes currently in use.

The behavior of these schemes is compared theoretically in the context of the simple oscillation equation and also for the linearized equations governing stratified compressible flow. Several schemes are also tested in fully nonlinear simulations of gravity waves generated by a localized source in a shear flow.

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Dale R. Durran
and
Leonard W. Snellman

Abstract

The physical reason for quasi-geostrophic vertical motion is reviewed. Various techniques for estimating synoptic-scale vertical motion are examined, and their utility (or lack thereof) is illustrated by a case study. The Q-vector approach appears to provide the best means of calculating vertical motions numerically. The vertical motion can be estimated by eye with reasonable accuracy by examining the advection of vorticity by the thermal wind or by examining the relative wind and the isobar field on an isentropic chart. The traditional form of the omega equation is not well suited for practical calculation.

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Dale R. Durran
and
Leonard W. Snellman

Abstract

No abstract available

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Matthew O. G. Hills
and
Dale R. Durran

Abstract

The behavior of nonstationary trapped lee waves in a nonsteady background flow is studied using idealized three-dimensional (3D) numerical simulations. Trapped waves are forced by the passage of an isolated, synoptic-scale barotropic jet over a mountain ridge of finite length. Trapped waves generated within this environment differ significantly in their behavior compared with waves in the more commonly studied two-dimensional (2D) steady flow. After the peak zonal flow has crossed the terrain, two disparate regions form within the mature wave train: 1) upwind of the jet maximum, trapped waves increase their wavelength and tend to untrap and decay, whereas 2) downwind of the jet maximum, wavelengths shorten and waves remain trapped. Waves start to untrap approximately 100 km downwind of the ridge top, and the region of untrapping expands downwind with time as the jet progresses, while waves downstream of the jet maximum persist. Wentzel–Kramers–Brillouin (WKB) ray tracing shows that spatial gradients in the mean flow are the key factor responsible for these behaviors. An example of real-world waves evolving similarly to the modeled waves is presented.

As expected, trapped waves forced by steady 2D and horizontally uniform unsteady 3D flows decay downstream because of leakage of wave energy into the stratosphere. Surprisingly, the downstream decay of lee waves is inhibited by the presence of a stratosphere in the isolated-jet simulations. Also unexpected is that the initial trapped wavelength increases quasi-linearly throughout the event, despite the large-scale forcing at the ridge crest being symmetric in time about the midpoint of the isolated-jet simulation.

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Justin R. Minder
,
Dale R. Durran
, and
Gerard H. Roe

Abstract

Observations show that on a mountainside the boundary between snow and rain, the snow line, is often located at an elevation hundreds of meters below its elevation in the free air upwind. The processes responsible for this mesoscale lowering of the snow line are examined in semi-idealized simulations with a mesoscale numerical model and in simpler theoretical models. Spatial variations in latent cooling from melting precipitation, in adiabatic cooling from vertical motion, and in the melting distance of frozen hydrometeors are all shown to make important contributions. The magnitude of the snow line drop, and the relative importance of the responsible processes, depends on properties of the incoming flow and terrain geometry. Results suggest that the depression of the snow line increases with increasing temperature, a relationship that, if present in nature, could act to buffer mountain hydroclimates against the impacts of climate warming. The simulated melting distance, and hence the snow line, depends substantially on the choice of microphysical parameterization, pointing to an important source of uncertainty in simulations of mountain snowfall.

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