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Rajul E. Pandya
,
Dale R. Durran
, and
Morris L. Weisman

Abstract

Midlatitude squall lines are typically trailed by a large region of stratiform cloudiness and precipitation with significant mesoscale flow features, including an ascending front to rear flow; a descending rear inflow jet; line-end vortices; and, at later times, mesoscale convective vortices. The present study suggests that the mesoscale circulation in the trailing stratiform region is primarily determined by the time-mean pattern of heating and cooling in the leading convective line. Analysis of the line-normal circulation shows that it develops as thermally generated gravity waves spread away from the leading line. Midlevel line-end vortices are the result of diabatically driven tilting of horizontal vorticity generated by the time-mean thermal forcing. In the presence of the Coriolis force, a symmetric thermal forcing generates an asymmetric stratiform circulation and a pattern of vertical displacement that resembles the comma-shaped stratiform anvil observed in real systems; this suggests that asymmetries in the cloud and circulation behind midlatitude squall lines are not necessarily the result of asymmetries in the convective leading line.

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Chih-Chieh Chen
,
Gregory J. Hakim
, and
Dale R. Durran

Abstract

The impact of transient mountain waves on a large-scale flow is examined through idealized numerical simulations of the passage of a time-evolving synoptic-scale jet over an isolated 3D mountain. Both the global momentum budget and the spatial flow response are examined to illustrate the impact of transient mountain waves on the large-scale flow. Additionally, aspects of the spatial response are quantified by potential vorticity inversion.

Nearly linear cases exhibit a weak loss of domain-averaged absolute momentum despite the absence of wave breaking. This transient effect occurs because, over the time period of the large-scale flow, the momentum flux through the top boundary does not balance the surface pressure drag. Moreover, an adiabatic spatial redistribution of momentum is observed in these cases, which results in an increase (decrease) of zonally averaged zonal momentum south (north) of the mountain.

For highly nonlinear cases, the zonally averaged momentum field shows a region of flow deceleration downstream of the mountain, flanked by broader regions of weak flow acceleration. Cancellation between the accelerating and decelerating regions results in weak fluctuations in the volume-averaged zonal momentum, suggesting that the mountain-induced circulations are primarily redistributing momentum. Potential vorticity anomalies develop in a region of wave breaking near the mountain, and induce local regions of flow acceleration and deceleration that alter the large-scale flow.

A “perfect” conventional gravity wave–drag parameterization is implemented on a coarser domain not having a mountain, forced by the momentum flux distribution from the fully nonlinear simulation. This parameterization scheme produces a much weaker spatial response in the momentum field and it fails to produce enough flow deceleration near the 20 m s−1 jet. These results suggest that the potential vorticity sources attributable to the gravity wave–drag parameterization have a controlling effect on the longtime downstream influence of the mountain.

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Dale R. Durran
,
Patrick A. Reinecke
, and
James D. Doyle

Abstract

The predictability of lowland snow in the Puget Sound region of the Pacific Northwest is explored by analyzing the spread in 100-member ensemble simulations for two events from December 2008. Sensitivities to the microphysical and boundary layer parameterizations in these simulations are minimized by estimating the likely precipitation type from the forecast 850-hPa temperatures and the established rain–snow climatology. Results suggest that the ensemble spread in events such as these, which were triggered by amplifying short waves, may develop a significant fraction of both rain-likely members and snow-likely members at forecast lead times as short as 36 h.

The perturbation kinetic energy of the ensemble members about the ensemble mean ( ) is not maximized at small scales. Instead, the power in the initial spectrum of produced by the authors’ ensemble Kalman filter (EnKF) data assimilation cycle increases with increasing horizontal scale. The power in subsequently grows with time, while maintaining approximately the same spectral shape. There is no evidence of small-scale perturbations developing rapidly and transferring their influence upscale. Instead, the large-scale perturbations appear to grow more rapidly during the first 12 h than those at the smallest resolved scales.

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Chih-Chieh Chen
,
Dale R. Durran
, and
Gregory J. Hakim

Abstract

The evolution of mountain-wave-induced momentum flux is examined through idealized numerical simulations during the passage of a time-evolving synoptic-scale flow over an isolated 3D mountain of height h. The dynamically consistent synoptic-scale flow U accelerates and decelerates with a period of 50 h; the maximum wind arrives over the mountain at 25 h. The synoptic-scale static stability N is constant, so the time dependence of the nonlinearity parameter, ε(t) = Nh/U(t), is symmetric about a minimum value at 25 h.

The evolution of the vertical profile of momentum flux shows substantial asymmetry about the midpoint of the cycle even though the nonlinearity parameter is symmetric. Larger downward momentum fluxes are found during the accelerating phase, and the largest momentum fluxes occur in the mid- and upper troposphere before the maximum background flow arrives at the mountain. For a period of roughly 15 h, this vertical distribution of momentum flux accelerates the lower-tropospheric zonal-mean winds due to low-level momentum flux convergence.

Conservation of wave action and Wentzel–Kramers–Brillouin (WKB) ray tracing are used to reconstruct the time–altitude dependence of the mountain-wave momentum flux in a semianalytic procedure that is completely independent of the full numerical simulations. For quasi-linear cases, the reconstructions show good agreement with the numerical simulations, implying that the basic asymmetry obtained in the full numerical simulations may be interpreted using WKB theory. These results demonstrate that even slow variations in the mean flow, with a time scale of 2 days, play a dominant role in regulating the vertical profile of mountain-wave-induced momentum flux.

The time evolution of cross-mountain pressure drag is also examined in this study. For almost-linear cases, the pressure drag is well predicted under steady-state linear theory by using the instantaneous incident flow. Nevertheless, for mountains high enough to preserve a moderate degree of nonlinearity when the synoptic-scale incident flow is strongest, the evolution of cross-mountain pressure drag is no longer symmetric about the time of maximum wind. A higher drag state is found when the cross-mountain flow is accelerating. These results suggest that the local character of the topographically induced disturbance cannot be solely determined by the instantaneous value of the nonlinearity parameter ε.

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Dale R. Durran
,
Tra Dinh
,
Marie Ammerman
, and
Thomas Ackerman

Abstract

Thin cirrus clouds in the tropical tropopause layer (TTL) are warmed through the absorption of infrared radiation. The response of the cloud and the surrounding atmosphere to this thermal forcing is investigated through linear theory and nonlinear numerical simulation. Linear solutions for the circulations forced by a fixed heat source representative of TTL cirrus clouds show ascent in the region of the heating, accompanied by horizontal flow toward the heat source at the base of the heated layer and horizontal outflow at the top of the layer. Gravity waves propagate positive temperature perturbations well beyond the lateral edges of the heated region. Cool layers that also spread horizontally are produced immediately above and below the heated region.

Numerical simulations with a cloud-resolving model allow the radiative heating to change in response to the redistribution of the cloud by the evolving velocity field. The basic atmospheric response in the numerical simulations is nevertheless similar to that generated by the fixed heat source. In the numerical simulations, the advection of ice crystals by the radiatively forced velocity field also lofts the cloud, while horizontally spreading its top and narrowing its base. Ice crystal sedimentation is neglected in these calculations, but it appears that the radiatively induced upward vertical velocities are likely strong enough to maintain clouds consisting of very small crystals (radii less than 4 μm) against sedimentation for many hours.

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Dale R. Durran
,
Matthew O. G. Hills
, and
Peter N. Blossey

Abstract

Leaky trapped mountain lee waves are investigated by examining the structure of individual linear modes in multilayer atmospheres. When the static stability and cross-mountain wind speed are constant in the topmost unbounded layer, modes that decay exponentially downstream also grow exponentially with height. This growth with height occurs because packets containing relatively large-amplitude waves follow ray paths through the stratosphere, placing them above packets entering the stratosphere farther downstream that contain relatively low-amplitude waves. Nevertheless, if the trapped wave train is generated by a compact source, all waves disappear above some line parallel to the group velocity that passes just above the source region.

The rate of downstream decay due to leakage into the stratosphere is strongly dependent on the atmospheric structure. Downstream dissipation is often significant under realistic atmospheric conditions, which typically include elevated inversions and strong upper-tropospheric winds. On the other hand, idealized profiles with constant Scorer parameters throughout each of two tropospheric layers can exhibit a wide range of behaviors when capped by a third stratospheric layer with typical real-world static stability. Assuming the Scorer parameter in the stratosphere is a little larger than the minimum value necessary to allow a particular mode to propagate vertically, the rate of downstream decay is more sensitive to changes in the height of the tropopause than to further increases in the stability of the stratosphere. Downstream decay is minimized when the tropopause is high and the horizontal wavelength is short.

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Matthew O. G. Hills
,
Dale R. Durran
, and
Peter N. Blossey

Abstract

Decaying trapped waves exert a drag on the large-scale flow. The two most studied mechanisms for such decay are boundary layer dissipation and leakage into the stratosphere. If the waves dissipate in the boundary layer, they exert a drag near the surface, whereas, if they leak into the stratosphere, the drag is exerted at the level where the waves dissipate aloft. Although each of these decay mechanisms has been studied in isolation, their relative importance has not been previously assessed.

Here, numerical simulations are conducted showing that the relative strength of these two mechanisms depends on the details of the environment supporting the waves. During actual trapped-wave events, the environment often includes elevated inversions and strong winds aloft. Such conditions tend to favor leakage into the stratosphere, although boundary layer dissipation becomes nonnegligible in cases with shorter resonant wavelengths and higher tropopause heights. In contrast, idealized two-layer profiles with constant wind speeds and high static stability beneath a less stable upper troposphere support lee waves that are much more susceptible to boundary dissipation and relatively unaffected by the presence of a stratosphere. One reason that trapped waves in the two-layer case do not leak much energy upward is that the resonant wavelength is greatly reduced in the presence of surface friction. This reduction in wavelength is well predicted by the linear inviscid equations if the basic-state profile is modified a posteriori to include the shallow ground-based shear layer generated by surface friction.

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Daniel J. Lloveras
,
Dale R. Durran
, and
James D. Doyle

Abstract

We use convection-permitting idealized simulations of moist midlatitude cyclones to compare the growth of synoptic-scale perturbations derived from an adjoint model with the growth of equal-energy-norm, monochromatic-wavelength perturbations at the smallest resolved scale. For initial magnitudes comparable to those of initial-condition uncertainties in present-day data assimilation systems, the adjoint perturbations produce a “forecast bust,” significantly changing the intensity and location of the cyclone and its accompanying precipitation. In contrast, the small-scale-wave perturbations project strongly onto the moist convection, but the upscale growth from the random displacement of individual convective cells does not significantly alter the cyclone’s development nor its accompanying precipitation through 2–4-day lead times. Instead, the differences in convection generated at early times become negligible because the development of subsequent convection is driven by the mostly unchanged synoptic-scale flow. Reducing the perturbation magnitudes by factors of 10 and 100 demonstrates that nonlinear dynamics play an important role in the displacement of the cyclone by the full-magnitude adjoint perturbations, and that the upscale growth of small-magnitude, small-scale perturbations is too slow to significantly change the cyclone. These results suggest that a sensitive dependence on the synoptic-scale initial conditions, analogous to that of the Lorenz (1963) system, may be more relevant to 2–4-day midlatitude-cyclone forecast busts than the upscale error growth in the Lorenz (1969) model.

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Johnathan J. Metz
,
Dale R. Durran
, and
Peter N. Blossey

Abstract

Simulations of the weather over the South Island of New Zealand on 28 July 2014 reveal unusual wave activity in the stratosphere. A series of short-wavelength perturbations resembling trapped lee waves were located downstream of the topography, but these waves were in the stratosphere, and their crests were oriented north–south, in contrast to both the northeast–southwest orientation of the spine of the Southern Alps and the crests of trapped waves present in the lower troposphere. Vertical cross sections through these waves show a nodal structure consistent with that of a higher-order trapped-wave mode. Eigenmode solutions to the vertical structure equation for two-dimensional, linear, Boussinesq waves were obtained for a horizontally homogeneous sounding representative of the 28 July case. These solutions include higher-order modes having large amplitude in the stratosphere that are supported by just the zonal wind component. Two of these higher-order modes correspond to trapped waves that develop in an idealized numerical simulation of the 28 July 2014 case. These higher-order modes are trapped by very strong westerly winds in the midstratosphere and are triggered by north–south-oriented features in the subrange-scale topography. In contrast, the stratospheric cross-mountain wind component is too weak to trap similar high-order modes with crest-parallel orientation.

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Alison M. Anders
,
Gerard H. Roe
,
Dale R. Durran
, and
Justin R. Minder

Abstract

Persistent, 10-km-scale gradients in climatological precipitation tied to topography are documented with a finescale rain and snow gauge network in the Matheny Ridge area of the Olympic Mountains of Washington State. Precipitation totals are 50% higher on top of an ∼800-m-high ridge relative to valleys on either side, 10 km distant. Operational fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) runs on a 4-km grid produce similar precipitation patterns with enhanced precipitation over high topography for 6 water years.

The performance of the MM5 is compared to the gauge data for 3 wet seasons and for 10 large precipitation events. The cumulative MM5 precipitation forecasts for all seasons and for the sum of all 10 large events compare well with the precipitation measured by the gauges, although some of the individual events are significantly over- or underforecast. This suggests that the MM5 is reproducing the precipitation climatology in the vicinity of the gauges, but that errors for individual events may arise due to inaccurate specification of the incident flow.

A computationally simple model of orographic precipitation is shown to reproduce the major features of the event precipitation pattern on the windward side of the range. This simple model can be coupled to landscape evolution models to examine the impact of long-term spatial variability in precipitation on the evolution of topography over thousands to millions of years.

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