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Robert L. Grossman
and
Dale R. Durran

Abstract

Seven-year averaged values of percent frequency of occurrence of highly reflective cloud for the months June, July, and August indicate that offshore convection is a major component of the cloudiness of the southwest monsoon. Principal areas of convection occur off of the western coats of India, Burma, Thailand, and the Philippines. This study concentrates on the area upstream of the Western Ghats Mountains of India. Analysis of a special boundary layer mission flown during the WMO/ICSU Summer Monsoon Experiment leads us to believe that partial deceleration of the monsoon flow by upstream blocking effects of the mountains initiates and maintains a vertical and horizontal motion field that could support the observed convection. Data obtained on this mission allow a large-scale momentum budget computation for the subcloud layer, which shows pressure deceleration to be significant. The budget, dominated by advection, predicts an increase of average wind speed which is observed. The pressure deceleration result is further explored by applying an idealized monsoon flow to an analytical, nonliner, two-dimensional mountain-flow interaction model using a smoothed profile of the Western Ghats Mountains. The model qualitatively agrees with aircraft observations taken in the subcloud layer, and predicts large vertical wind shears over the coastal area and mountain crest which would inhibit deep convection. These shears are confirmed by earlier observations.

When the lifting predicted by the model is applied to mean dropwindsonde soundings, well upstream of the coast, for days with and without offshore convection, deep convection is predicted for the mean sounding associated with offshore convection. The mean sounding for days without deep convection shows more offshore lifting is needed to produce convection; even if the lifting were applied, the convection would not be very deep due to a cooler surface layer and a dry layer above the boundary layer which may have originated from the desert areas to the west and/or upper tropospheric downward motion. We conclude that the mountains, though not very high, play an important role in overall monsoon convection for India. It is suggested that, given the climatic character of offshore monsoon convection, interaction of the low-level flow with the western coastal mountains of India, Burma, Thailand, and the Philippines should be considered a factor in monsoon climatology.

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Dale R. Durran
and
Joseph B. Klemp

Abstract

A two-dimensional, nonlinear, nonhydrostatic model is described which allows the calculation of moist airflow in mountainous terrain. The model is compressible, uses a terrain-following coordinate system, and employs lateral and upper boundary conditions which minimize wave reflections.

The model's accuracy and sensitivity are examined. These tests suggest that in numerical simulations of vertically propagating, highly nonlinear mountain waves, a wave absorbing layer does not accurately mimic the effects of wave breakdown and dissipation at high levels in the atmosphere. In order to obtain a correct simulation, the region in which the waves are physically absorbed must generally be included in the computational domain (a nonreflective upper boundary condition should be used as well).

The utility of the model is demonstrated in two examples (linear waves in a uniform atmosphere and the 11 January 1972 Boulder windstorm) which illustrate how the presence of moisture can influence propagating waves. In both cases, the addition of moisture to the upstream flow greatly reduces the wave response.

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Joseph B. Klemp
and
Dale R. Durran

Abstract

A radiative upper boundary condition is proposed for numerical mesoscale models which allows vertically propagating internal gravity waves to pass out of the computational domain with minimal reflection. In this formulation, the pressure along the upper boundary is determined from the Fourier transform of the vertical velocity at that boundary. This boundary condition can easily be incorporated in a wide variety of models and requires little additional computation. The radiation boundary condition is derived from the linear, hydrostatic, Boussinesq equations of motion, neglecting Coriolis effects. However, tests of this radiation boundary condition in the presence of nonhydrostatic, Coriolis, nonlinear and non-Boussinesq effects suggest that it would be effective in many mesoscale modeling applications.

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Johnathan J. Metz
and
Dale R. Durran

Abstract

Strong downslope windstorms can cause extensive property damage and extreme wildfire spread, so their accurate prediction is important. Although some early studies suggested high predictability for downslope windstorms, more recent analyses have found limited predictability for such winds. Nevertheless, there is a theoretical basis for expecting higher downslope wind predictability in cases with a mean-state critical level, and this is supported by one previous effort to forecast actual events. To more thoroughly investigate downslope windstorm predictability, we compare archived simulations from the NCAR ensemble, a 10-member mesoscale ensemble run at 3-km horizontal grid spacing over the entire contiguous United States, to observed events at 15 stations in the western United States susceptible to strong downslope winds. We assess predictability in three contexts: the average ensemble spread, which provides an estimate of potential predictability; a forecast evaluation based upon binary-decision criteria, which is representative of operational hazard warnings; and a probabilistic forecast evaluation using the continuous ranked probability score (CRPS), which is a measure of an ensemble’s ability to generate the proper probability distribution for the events under consideration. We do find better predictive skill for the mean-state critical-level regime in comparison to other downslope windstorm–generating mechanisms. Our downslope windstorm warning performance, calculated using binary-decision criteria from the bias-corrected ensemble forecasts, performed slightly worse for no-critical-level events, and slightly better for critical-level events, than National Weather Service high-wind warnings aggregated over all types of high-wind events throughout the United States and annually averaged for each year between 2008 and 2019.

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Dale R. Durran
and
Joseph B. Klemp

Abstract

Expressions are derived for the Brunt- Väisälä frequency Nm , in a saturated atmosphere, which are analogous to commonly-used formulas for the dry Brunt- Väisälä frequency. These formulas are compared with others which have appeared in the literature, and the derivation by Lalas and Einaudi (1974) is found to be correct. The simplifying assumptions, implicit in derivations by Dudis (1972) and Fraser et al. (1973) are clarified. Numerical examples are presented which suggest that these incomplete formulations for Nm are reasonably accurate approximations, except when the saturated static stability is small. A new formula expressing Nm in terms of moist conservative variables is presented, and an accurate approximation is also given which may be useful when evaluating Nm .

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Dale R. Durran
and
Joseph B. Klemp

Abstract

The effects of latent heat release on the dynamics of mountain lee waves are examined with the aid of two-dimensional numerical simulations, for several situations in which the Scorer parameter has a nearly two-layer vertical structure. Changes in the moisture in the lowest layer are found to produce three fundamentally different behaviors: 1) resonant waves in an absolutely stable environment are distorted and untrapped by an increase in moisture; 2) resonant waves in a conditionally unstable layer are destroyed by an increase in moisture; and 3) resonant waves in a moist environment are detuned by a decrease in moisture. Changes in the humidity in the upper layer are found to amplify or damp the wave response, depending on the depth of the lower layer. In most situations, the wave response is significantly more complicated than that predicted by simply replacing the dry stability with an equivalent moist stability in the saturated layer.

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Louisa B. Nance
and
Dale R. Durran

Abstract

The accuracy of three anelastic systems (Ogura and Phillips; Wilhelmson and Ogura; Lipps and Hemler) and the pseudo-incompressible system is investigated for small-amplitude and finite-amplitude disturbances. Based on analytic solutions to the linearized, hydrostatic mountain wave problem, the accuracy of the Lipps and Hemler and pseudo-incompressible systems is distinctly superior to that of the other two systems. The linear dispersion relations indicate the accuracy of the pseudo-incompressible system should improve and the accuracy of the Lipps and Hemler system should decrease as the waves become more nonhydrostatic.

Since analytic solutions are not available for finite-amplitude disturbances, five nonlinear, nonhydrostatic numerical models based on these four systems and the complete compressible equations are constructed to determine the ability of each “sound proof” system to describe finite-amplitude disturbances. A comparison between the analytic solutions and numerical simulations of the linear mountain wave problem indicate the overall quality of the simulations is good, but the numerical errors are significantly larger than those associated with the pseudo-incompressible and Lipps and Hemler approximations. Numerical simulations of flow past a steady finite-amplitude heat source for an isothermal atmosphere and an atmosphere with an elevated inversion indicate the Lipps and Hemler and pseudo-incompressible systems also produce the most accurate approximations to the compressible solutions for finite-amplitude disturbances.

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Rajul E. Pandya
and
Dale R. Durran

Abstract

The dynamical processes that determine the kinematic and thermodynamic structure of the mesoscale region around 2D squall lines are examined using a series of numerical simulations. The features that develop in a realistic reference simulation of a squall line with trailing stratiform precipitation are compared to the features generated by a steady thermal forcing in a “dry” simulation with no microphysical parameterization. The thermal forcing in the dry simulation is a scaled and smoothed time average of the latent heat released and absorbed in and near the leading convective line in the reference simulation. The mesoscale circulation in the dry simulation resembles the mesoscale circulation in the reference simulation and around real squall lines; it includes an ascending front-to-rear flow, a midlevel rear inflow, a mesoscale up- and downdraft, an upper-level rear-to-front flow ahead of the thermal forcing, and an upper-level cold anomaly to the rear of the thermal forcing. It is also shown that a steady thermal forcing with a magnitude characteristic of real squall lines can produce a cellular vertical velocity field as the result of the nonlinear governing dynamics. An additional dry simulation using a more horizontally compact thermal forcing demonstrates that the time-mean thermal forcing from the convective leading line alone can generate a mesoscale circulation that resembles the circulation in the reference simulation and around real squall lines.

The ability of this steady thermal forcing to generate the mesoscale circulation accompanying squall lines suggests that this circulation is the result of gravity waves forced primarily by the low-frequency components of the latent heating and cooling in the leading line. The gravity waves in the dry and reference simulation produce a perturbed flow that advects diabatically lifted air from the leading line outward. In the reference simulation, this leads to the development of leading and trailing anvils, while in the dry simulation this produces a pattern of vertically displaced air that is similar to the distribution of cloud in the reference simulation. Additional numerical simulations, in which either the thermal forcing or large-scale environmental conditions were varied, reveal that the circulation generated by the thermal forcing shows a greater sensitivity to variations in the thermal forcing than to variations in the large-scale environment. Finally, it is demonstrated that the depth of the thermal forcing in the leading convective line, not the height of the tropopause, is the primary factor determining the height of the trailing anvil cloud.

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Peter P. Miller
and
Dale R. Durran

Abstract

The influence of terrain asymmetry on the development and strength of downslope windstorms was examined through the numerical simulation of three basic atmospheric configurations: 1) flow beneath a mean-state critical layer, 2) flow in the presence of breaking waves and 3) flow in a two-layer atmosphere without wave breaking or a mean-state critical layer. When a mean-state critical layer was present in the flow and the wind speed and stability beneath that critical layer were essentially constant, the maximum downslope wind speed was nearly independent of mountain asymmetry. Such insensitivity to mountain shape is consistent with hydraulic theory and supports the idea that there is a close mathematical analog between stratified flow beneath a mean-state critical layer and conventional shallow-water hydraulic theory. When downslope winds were generated by breaking waves, and the upstream stability and wind speed were constant with height, the dependence of lee-slope velocities on terrain asymmetry remained weak. When downslope winds were produced in a two-layer atmosphere without wave breaking or a mean-state critical layer, the flow exhibited a noticeable, but not dominating, sensitivity to mountain asymmetry.

The preceding results were obtained from simulations without surface friction. When a surface friction parameterization was included in the numerical model, the sensitivity of the downslope wind speed to mountain asymmetry was significantly enhanced. It appears that in the surface friction simulations, the most significant shape parameter is not mountain asymmetry per se, but simply the steepness of the lee slope, with steep lee slopes being most favorable for strong winds.

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Louisa B. Nance
and
Dale R. Durran

Abstract

The impact of mean-flow variability on finite-amplitude trapped mountain lee waves is investigated by conducting two-dimensional mountain wave simulations for a set of idealized, time-dependent background flows. The lee-wave patterns generated by these time-dependent flows depend on two factors: 1) the degree to which the transition in the background flow changes the amplitude of the stationary trapped lee wave and 2) the difference between the group velocities of the trapped waves generated before and after the transition. When the transition in the background flow significantly reduces the amplitude of the stationary lee wave, the lee-wave pattern generated prior to the transition gradually drifts downstream away from the mountain or back over the mountain, depending on the sign of this wave packet’s group velocity after the transition. When the transition in the background flow changes the resonant wavelength while leaving the lee-wave amplitude relatively unchanged, the lee-wave train develops either 1) a smooth transition in horizontal wavelength or 2) a region of irregular variations in wavelength and amplitude, depending on the difference between the group velocities of the waves generated before and after the transition. Although linear theory is able to predict how changes in the background flow will affect the group velocities of the trapped waves, it is not able to predict whether the temporal variations in the large-scale environmental flow will amplify or dampen the resonant waves when the waves are no longer linear.

Regions of irregular variations in wavelength and amplitude may develop when stationary trapped waves generated after a transition in the background flow overtake the trapped waves generated before the transition. The fluctuations in the vertical velocities associated with such numerically simulated lee waves are compared with wind profiler observations. Estimates of the time required for the trapped waves generated after the transition to overtake those generated before the transition suggest that the temporal changes in the background flow required to qualitatively reproduce the observed vertical velocity variations are not likely to occur on a realistic timescale. In addition, the observed temporal variations in lee-wave vertical velocities appear to be the superposition of at least two distinct frequencies, whereas the temporal variations in the simulated waves are dominated by one distinct frequency.

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