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Dale R. Durran

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Numerical simulations are conducted to examine the role played by different amplification mechanisms in the development of large-amplitude mountain waves. It is shown that when the static stability has a two-layer structure, the nonlinear response can differ significantly from the solution to the equivalent linear problem when the parameter Nh/U is as small as 0.3. In the cases where the nonlinear waves are much larger than their linear counterparts, the highest stability is found in the lower layer and the flow resembles a hydraulic jump. Simulations of the 11 January 1972 Boulder windstorm are presented which suggest that the transition to supercritical flow, forced by the presence of a low-level inversion, plays an essential role in triggering the windstorm. The similarities between breaking waves and nonbreaking waves which undergo a transition to supercritical flow are discussed.

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Dale R. Durran

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Expressions are derived for the local pseudomomentum density in two-dimensional compressible stratified flow and are compared with the expressions for pseudomomentum in two-dimensional Boussinesq and anelastic flow derived by Shepherd and by Scinocca and Shepherd. To facilitate this comparison, algebraically simpler expressions for the anelastic and Boussinesq pseudomomentum are also obtained. When the vertical wind shear in the reference-state flow is constant with height, the Boussinesq pseudomomentum is shown to reduce to a particularly simple form in which the pseudomomentum is proportional to the perturbation vorticity times the fluid-parcel displacement. The extension of these compressible pseudomomentum diagnostics to viscous flow and to three-dimensional flows with zero potential vorticity is also discussed.

An expression is derived for the pseudomomentum flux in stratified compressible flow. This flux is shown to simultaneously satisfy the group-velocity condition for both sound waves and gravity waves in an isothermal atmosphere with a constant basic-state wind speed. Consistent with the earlier results of Andrews and McIntyre, it is shown that for inviscid flow over a topographic barrier, the pseudomomentum flux through the lower boundary is identical to the cross-mountain pressure drag—provided that the flow is steady and that the elevation of the topography returns to its upstream value on the downstream side of the mountain.

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Dale R. Durran

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Dale R. Durran

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Dale R. Durran
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Dale R. Durran

Abstract

A new diagnostic equation is presented which exhibits many advantages over the conventional forms of the anelastic continuity equation. Scale analysis suggests that use of this “pseudo-incompressible equation” is justified if the Lagrangian time scale of the disturbance is large compared with the time scale for sound wave propagation and the perturbation pressure is small compared to the vertically varying mean-state pressure. No assumption about the magnitude of the perturbation potential temperature or the strength of the mean-state stratification is required.

In the various anelastic approximations, the influence of the perturbation density field on the mass balance is entirely neglected. In contrast, the mass-balance in the “pseudo-incompressible approximation” accounts for those density perturbations associated (through the equation of state) with perturbations in the temperature field. Density fluctuations associated with perturbations in the pressure field are neglected.

The pseudo-incompressible equation is identical to the anelastic continuity equation when the mean stratification is adiabatic. As the stability increases, the pseudo-incompressible approximation gives a more accurate result. The pseudo-incompressible equation, together with the unapproximated momentum and thermodynamic equations, forms a closed system of governing equations that filters sound waves. The pseudo-incompressible system conserves an energy form that is directly analogous to the total energy conserved by the complete compressible system.

The pseudo-incompressible approximation yields a system of equations suitable for use in nonhydrostatic numerical models. The pseudo-incompressible equation also permits the diagnostic calculation of the vertical velocity in adiabatic flow. The pseudo-incompressible equation might also be used to compute the net heating rate in a diabatic flow from extremely accurate observations of the three-dimensional velocity field and very coarse resolution (single sounding) thermodynamic data.

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Dale R. Durran

Abstract

When extreme weather occurs, the question often arises whether the event was produced by climate change. Two types of errors are possible when attempting to answer this question. One type of error is underestimating the role of climate change, thereby failing to properly alert the public and appropriately stimulate efforts at adaptation and mitigation. The second type of error is overestimating the role of climate change, thereby elevating climate anxiety and potentially derailing important public discussions with false alarms. Long before societal concerns about global warming became widespread, meteorologists were addressing essentially the same trade-off when faced with a binary decision of whether to issue a warning for hazardous weather. Here we review forecast–verification statistics such as the probability of detection (POD) and the false alarm ratio (FAR) for hazardous-weather warnings and examine their potential application to extreme-event attribution in connection with climate change. Empirical and theoretical evidence suggests that adjusting tornado-warning thresholds in an attempt to reduce FAR produces even larger reductions in POD. Similar tradeoffs between improving FAR and degrading POD are shown to apply using a rubric for the attribution of extreme high temperatures to climate change. Although there are obviously significant differences between the issuance of hazardous-weather warnings and the attribution of extreme events to global warming, the experiences of the weather forecasting community can provide qualitative guidance for those attempting to set practical thresholds for extreme-event attribution in a changing climate.

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Dale R. Durran

It is demonstrated that the inertial oscillation is not produced exclusively by “inertial forces,” and that the inertial oscillation appears as oscillatory motion even when viewed from a nonrotating frame of reference. The component of true gravity parallel to the geopotential surfaces plays a central role in forcing the inertial oscillation, and in particular it is the only force driving the oscillation in the nonrotating reference frame.

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Dale R. Durran

Abstract

A simple class of barotropic Rossby waves are shown to propagate westward as the graphically balanced meridional windfield periodically reverses in response to a small meridional pressure gradient arising from the latitudinal variation of the Coriolis parameter.

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