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  • Author or Editor: W. C. Skamarock x
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J. B. Klemp
and
W. C. Skamarock

Abstract

For the numerical simulation of atmospheric flows that extend as high as the thermosphere, it is more appropriate to represent the upper boundary of the model domain as a material surface at constant pressure rather than one characterized by a rigid lid. Consequently, in adapting the Model for Prediction Across Scales (MPAS) for geospace applications, a modification of the height-based vertical coordinate is presented that permits the coordinate surfaces at upper levels to transition toward a constant pressure surface at the model’s upper boundary. This modification is conceptually similar to a terrain-following coordinate at low levels, but now modifies the coordinate surfaces at upper levels to conform to a constant pressure surface at the model top. Since this surface is evolving in time, the height of the upper boundary is adaptively adjusted to follow a designated constant pressure upper surface. This is accomplished by applying the hydrostatic equation to estimate the change in height along the boundary that is consistent with the vertical pressure gradient at the model top. This alteration in the vertical coordinate requires only minor modifications and little additional computational expense to the original height-based time-invariant terrain-following vertical coordinate employed in MPAS. The viability of this modified vertical coordinate formulation has been verified in a 2D prototype of MPAS for an idealized case of upper-level diurnal heating.

Significance Statement

Most atmospheric numerical models that use a height-based vertical coordinate employ a rigid lid at the top of the model domain. While a rigid lid works well for applications in the troposphere and stratosphere, it is not well suited for applications extending into the thermosphere where significant vertical expansion/contraction occurs due to deep heating/cooling of the atmosphere. This paper develops and tests a simple modification to the height-based coordinate formulation that allows the height of the upper boundary to adaptively follow a constant pressure surface. This added flexibility in the treatment of the upper domain boundary for height-based models may be particularly beneficial in facilitating their transition to a deep atmosphere configuration without significant retooling of the model numerics.

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S. B. Trier
,
C. A. Davis
, and
W. C. Skamarock

Abstract

Idealized numerical simulations are used to quantify the effect of quasi-balanced lifting arising from the interaction of the ambient vertical shear with midtropospheric cyclonic vortices (MCVs) generated by mesoscale convective systems on thermodynamic destabilization over a range of ambient vertical shear strengths and vortex characteristics observed in Part I. Maximum upward displacements occur beneath the midtropospheric potential vorticity anomaly, near the radius of maximum tangential vortex winds. The location of the region of upward displacements relative to the ambient vertical shear vector depends on the relative strength of the vortex tangential flow and the ambient vertical shear, and ranges from downshear for vortices of moderate strength in strong ambient vertical shear to 90° to the left of downshear for strong vortices in weak ambient vertical shear. Although significant upward displacements occur most rapidly with small vortices in strong ambient vertical shear, maximum upward displacements are associated with large vortices and occur in approximately average vertical shear for MCV environments.

The simulations suggest that in larger and stronger than average MCVs, the lifting that results from the MCV being embedded in a weakly baroclinic environment is, alone, sufficient to saturate initially moist and conditionally unstable layers immediately above the boundary layer. The horizontal location of the resulting thermodynamic instability is approximately coincident with the maximum lower-tropospheric upward displacements. Since in the absence of sustained deep convection the vortices develop substantial vertical tilt, the destabilized region in the lower troposphere lies nearly underneath the vortex center at its level of maximum strength, consistent with observations that redevelopment of organized, long-lived (e.g., t ≥ 6 h) deep convection is most often found near the midtropospheric MCV center. This location for convectively induced stretching of preexisting vertical vorticity is optimal for maintaining the vortex against the deleterious effect of differential advection by the ambient shear.

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J. B. Klemp
,
W. C. Skamarock
, and
J. Dudhia

Abstract

Historically, time-split schemes for numerically integrating the nonhydrostatic compressible equations of motion have not formally conserved mass and other first-order flux quantities. In this paper, split-explicit integration techniques are developed that numerically conserve these properties by integrating prognostic equations for conserved quantities represented in flux form. These procedures are presented for both terrain-following height and hydrostatic pressure (mass) vertical coordinates, two potentially attractive frameworks for which the equation sets and integration techniques differ significantly. For each set of equations, the linear dispersion equation for acoustic/gravity waves is derived and analyzed to determine which terms must be solved in the small (acoustic) time steps and how these terms are represented in the time integration to achieve stability. Efficient techniques for including numerical filters for acoustic and external modes are also presented. Simulations for several idealized test cases in both the height and mass coordinates are presented to demonstrate that these integration techniques appear robust over a wide range of scales, from subcloud to synoptic.

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S. B. Trier
,
W. C. Skamarock
,
M. A. LeMone
,
D. B. Parsons
, and
D. P. Jorgensen

Abstract

In this study a numerical cloud model is used to simulate the three-dimensional evolution of an oceanic tropical squall line observed during the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment and investigate the impact of small-scale physical processes including surface fluxes and ice microphysics on its structure and evolution. The observed squall line was oriented perpendicular to a moderately strong low-level jet. Salient features that are replicated by the model include an upshear-tilted leading convective region with multiple updraft maxima during its linear stage and the development of a 30-km scale midlevel vortex and associated transition of the line to a pronounced bow-shaped structure.

In this modeling approach, only surface flukes and stresses that differ from those of the undisturbed environment are included. This precludes an unrealistically large modification to the idealized quasi-steady base state and thus allows us to more easily isolate effects of internally generated surface fluxes and stresses on squall line evolution. Neither surface fluxes and stresses nor ice microphysics are necessary to simulate the salient features of the squall line. Their inclusion, however, results in differences in the timing of squall line evolution and greater realism of certain structural characteristics. Significant differences in the convectively induced cold pool strength occur between the early stages of simulations that included ice microphysics and a simulation that contained only warm-rain microphysical processes. The more realistic strength and depth of the cold pool in the simulations that contained ice processes is consistent with an updraft tilt that more closely resembles observations. The squall-line-induced surface fluxes also influence the strength but, more dramatically, the areal extent of the surface cold pool. For the majority of the 6-h simulation, this influence on the cold pool strength is felt only within several hundred meters of the surface. Significant impact of squall-line-induced surface, fluxes on the evolving deep convection at the leading edge of the cold pool is restricted to the later stages (t ≥ 4 h) of simulations and is most substantial in regions where the ground-relative winds are strong and the convectively induced cold pool is initially weak and shallow.

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