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Brian D. Gross

Abstract

The effect of compressibility on two-dimensional barotropic and baroclinic growth rates is examined by means of a linearized nonhydrostatic compressible model. It is shown that the growth rates are diminished when compressibility is included because perturbation internal energy resents a sink of basic-state kinetic energy when work is done to compress the medium. Nonlinear simulations provided by compressible and incompressible versions of the ZETA model show that the solutions are nearly identical, but the compressible solution develops more slowly than the incompressible one, consistent with the linear analysis.

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Brian D. Gross

Abstract

The interaction of a three-dimensional cold front and an isolated orographic ridge is examined by means of primitive equation model simulations. The front evolves as part of a developing nonlinear baroclinic wave and propagates southward toward the ridge. Many of the features in this interaction, such as the anticyclonic distortion of the front, divergence and frontolysis on the windward slope, convergence and frontogenesis in the lee, and the frontogenetical forcing associated with tilting, have previously been captured by simulations of a passive scalar traversing a ridge.

It is shown that the ridge decelerates the cold postfrontal air and creates a high pressure anomaly on the windward slope. If this anomaly is strong enough, it accelerates air over the ridge peak in a shallow ageostrophic flow that possesses many features found in a gravity current. This current provides relatively strong surface frontogenesis through the convergence term, but cannot transport enough mass across the peak to weaken the anomalous high pressure. The cold air and pressure anomaly propagate eastward in a manner similar to a topographic Rossby wave. When the east ridge end is reached, the anomalous pressure gradient accelerates the flow into the lee, where frontogenesis occurs from shearing. The motion behind the front as it propagates over and around the ridge is distinctly unbalanced.

Blocking, as measured by the ratio of the mass flux around the ridge end to that over the peak, is determined by a Froude number that depends on the propagation speed of the front (i.e., the strength of the baroclinic wave) and the mountain height. Higher mountains or weaker waves tend to produce total blocking of the front, resulting in flow only around the east ridge end. Lower mountains and stronger waves produce frontogenesis patterns and frontal distortions that more closely resemble the passive scalar simulations.

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Brian D. Gross

Abstract

Three-dimensional, adiabatic, inviscid flow over orography is examined by means of a semigeostrophic model expressed in isentropic coordinates. A nondimensional mountain height ε/D ≲ 0.5, based on the deformation depth D ∼ 3 × 103 m, and a Rossby number Ro ≲ 0.3, based on the mountain breadth L ≲ 3.5 × 105 m and a constant Coriolis parameter, f, provide constraints on the flow field.

Vortex tube stretching is evaluated as a mechanism for lee cyclogenesis. It is shown that the convergence of both planetary and geostrophic relative vorticity filaments enhances geostrophic cyclonic vorticity in a semi-geostrophic model. In contrast, ageostrophic cyclonic vorticity is weakened by convergence. These features are illustrated in a numerical simulation of flow over an isentropic isolated mountain. The initial state is characterized by an isolated region of ageostrophic cyclonic vorticity in the lee of the obstacle, accompanied by convergence. A potential vorticity disturbance, associated with an internal cold front and a two-dimensional upper-level jet, is advected over the isolated obstacle. In principle, the coupling of ascending motion ahead of the disturbance with descending motion in the lee provides vortex tube stretching. It is shown that this mechanism does not initiate lee cyclogenesis in either a quasi-geostrophic or semigeostrophic model with isentropic boundaries. In particular, horizontal convergence and vertical stretching are significantly diminished by the intrusion of weakly stratified air into the lee. Additionally, the ageostrophic cyclonic vorticity present in the initial state is not effectively enhanced by vortex tube stretching, according to the ageostrophic vorticity theorem for semigeostrophic flow. The absence of both blocking by the obstacle and potential temperature gradients along the lower boundary is suggested as a possible reason for the failure of vortex tube stretching to initiate lee cyclogenesis in the model presented here.

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Isidoro Orlanski
and
Brian D. Gross

Abstract

The orographic modification of cyclone development is examined by means of primitive equation model simulations. When a mature baroclinic wave impinges on an east—west oriented mountain ridge, a relatively intense cyclone forms on the south side of the ridge. This cyclone extends throughout the depth of the troposphere and possesses relatively small vertical tilts, large velocities, and strong temperature perturbations compared to classical baroclinic eddies. The vorticity growth in the orographic cyclone center is larger than that of baroclinic eddies that grow over flat terrain. However, there is no absolute instability associated with this orographic enhancement. A longer ridge produces a more intense eddy.

The behavior of small-amplitude normal modes on a zonally symmetric mountain ridge shows that baroclinic development is enhanced where the topography slopes in the same direction as the isentropes. This is consistent with earlier studies using uniform slopes that show that the heat flux forced by this terrain enhances the conversion of available potential energy. It is shown that the structure of nonlinear waves is similar to that of linear modes over a mountain ridge with steep slopes, in which the cross-ridge flow and the associated heat flux are partially blocked by the mountain.

Simulations of a stationary cold front interacting with a mountain ridge suggest that orographic cyclogenesis is triggered when the mountain ridge locally modifies the frontal circulation as it impinges on the ridge. Warm southerly flow in the front is diverted westward by the mountain ridge, intensifying the strong hydrostatic pressure gradient between the mountain anticyclone and the developing cyclone to the south. In contrast, cold northerly flow is diverted eastward as it approaches the mountain and effectively broadens the mountain anticyclone toward the north. This produces the characteristic pressure dipole observed in orographic cyclogenesis. It is concluded that mature baroclinic eddies approaching the mountain ridge should have a strong frontal zone with a considerable temperature contrast and strong circulation for an intense response.

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Brian D. Gross
and
William Blumen

Abstract

Steady, three-dimensional, inviscid flow over orography is examined by means of a semi-geostrophic model. A nonuniform basic current, represented by a deformation flow, is employed. A constant Coriolis parameters ƒ and uniform potential vorticity (constant Brunt-Väisälä frequency N) characteristic this model. A nondimensional mountain height ε/D ≲ 0.5, based on the deformation depth D ∼ 3 × 103 m, and a Rossby number Ro ≲ 0.3, based on the mountain breadth L ≳ 3.5 × 105 m, provide constraints on the flow field. Analytic solutions are represented in geostrophic coordinate space as the sum of the deformation flow and an anticyclonic mountain vortex. Although the two solutions are independent in geostrophic coordinate space, these flows are coupled nonlinearly in the transformation to physical coordinate space.

A solution is presented for flow over an isolated mountain. The decomposition of the physical space solution into fields of translation, rotation, divergence, and deformation forms the basis of the present analysis. The principal features associated with the solution are a region of relatively strong cyclonic vorticity in the lee of the mountain, accompanied by a region of convergence, and a region of weaker cyclonic vorticity on the windward slope, accompanied by a region of divergence. It is the ageostrophic component of the vorticity that provides these cyclonic centers, which are associated with enhanced deformation upstream and downstream of the peak. Further, the lee-side cyclonic vorticity enhancement is associated with the advection of geostrophic deformation, a feature of semi-geostrophic models that is absent in quasi-geostrophic models. By displacing the basic current's axis of dilatation into the lee of the obstacle, a deformation advection pattern is established that enhances the lee-side cyclonic vorticity center. The uniform flow solution is characterized by a single band of cyclonic vorticity north of the peak. This pattern is also established by the advection of geostrophic deformation. The possible relevance of the present model results to physical mechanisms that promote the initiation of lee cyclogenesis is discussed.

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William Blumen
and
Brian D. Gross

Abstract

A basic uniform current flows over a two-dimensional finite-amplitude ridge of characteristic male L and amplitude ε. The disturbance field is constrained by the geostrophic momentum approximation, by uniform potential vorticity (uniform Brunt-Väisälä frequency N) and by the constant Coriolis parameter f. Solutions are represented as the sum of a steady disturbance, recently found by Blumen and Gross, and a relatively weak translating disturbance. The translating disturbance is a passive scalar that is advected by the steady mountain circulation. The propagation speed over a ridge in an unbounded atmosphere is shown to increase with the parameter ε/D, where D=fL/N is the deformation depth. The steady mountain circulation produces frontolysis in the disturbance field on the windward slope and frontogenesis on the leeward slope. These frontogenetical features are primarily controlled by the steady horizontal velocity, which is divergent on the windward side and convergent in the Ice. The steady mountain circulation also disrupts the initial state of thermal wind balance imposed on the disturbance potential temperature and cross-stream velocity fields. An approximate evaluation of the ageostrophic circulation required to restore thermal wind balance is provided. This circulation, which may be direct or indirect, is related to the spatial structure of the initial disturbance and to its relative position on the ridge. Comparison with a related study by Bannon, and an evaluation of the principal limitations of both models complete the study.

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William Blumen
and
Brian D. Gross

Abstract

Three-dimensional, steady and inviscid flow over orography is examined by means of a semigeostrophic model. A constant Coriolis parameter f, uniform potential vorticity and a uniform basic flow characterize this model, first used by Merkine and Kálnay-Rivas. It is demonstrated that the neglect of ageostrophic accelerations, which characterize a semigeostrophic model, essentially requires low Rosssby number flow Ro≲0.3, and relatively small values of the nondimensional mountain height ε/D ≲ 0.5, where D ∼3 × 103 m is the deformation depth. In this parameter range the disturbance potential is a solution of Laplace's equation; the atmosphere is semi-infinite and the finite-amplitude lower boundary is an isentropic surface.

The basic solution, expressed in prolate spheroidal coordinates, provides disturbance flows over an isolated mountain, finite ridges, and the limiting flow over a two-dimensional ridge. A comparison between the quasi-geostrophic and semigeostrophic responses to flow over the isolated mountain shows that (i) a rotational gradient wind correction to quasi-geostrophic flow that is independent of the basic current is introduced; (ii) the ageostrophic response associated with the basic current is an irrotational flow; and (iii) transformation of the semigeostrophic solution from geostrophic coordinate space to physical space displaces the circulation features on level, surfaces radially outward from the vertical axis, and the displacement is proportional to the mountain height.

An anticyclonic bound vortex, representing the sum of the quasi-geostrophic solution and the rotational wind correction, occurs over an isolated circular mountain (mountain parameter a = 0) and over long ridges (a > 0). However, these circulations are not typically Taylor columns, since they are not two-dimensional: vertical motions occur for 0 < a < . The existence of a closed circulation when a basic current is considered is dependent upon Ro, ε/D and a. In general, relatively larger values of Ro (or smaller ε/D) inhibit the formation of a closed circulation, but there is slight dependence on a. In agreement with Merkine and Kálnay-Rivas, it is shown that a closed circulation will occur around a mountain at a larger value of Ro when the ridge line is aligned with the basic current than when the ridge fine is normal to the current. The difference is relatively small, and probably unobservable in real flows.

A passive scalar disturbance is advected over ridges, characterized by different values of the mountain parameter a and orientation relative to the basic flow. This scalar field is advected anticyclonically around the lip of the ridge north of the current axis, but is retarded at the southern extremity of the ridge where the anticyclonic mountain circulation opposes the basic current. These features of frontal deformation are in qualitative agreement with synoptic analyses in geographic regions of orographic influence. Computed frontogenetical characteristics vary along selected trajectories. The distinctive features of frontogenesis are interpreted and compared with recent results obtained for flew over an infinite ridge.

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William Blumen
and
Brian D. Gross

Abstract

Steady-state, two-dimensional disturbances forced by flow over a finite-amplitude ridge are considered. The model represents an extension of the one presented by Robinson (1960). This study is based on the semigeostrophic system of equations for uniform potential vorticity flow. The model equations satisfy the Cauchy-Riemann conditions, and solutions for uniform flow over various shaped ridges may be obtained in terms of a complex potential. The novel result is the determination of solutions for disturbances in a zonal current with linear shear. The boundaries are tilled in the cross-stream direction to coincide with basic state potential temperature surfaces. This simplification, which provides isentropic boundaries, permits the solutions for disturbances in a shear flow to be obtained directly from solutions forced by uniform flow over the same ridge.

Physical properties of the solutions are presented in terms of three parameters: &epsi/D, r and δ. The amplitude of the ridge is &epsi& and D is the deformation depth, based on the characteristic width of the ridge L r represents the ratio of &epsi& to the channel depth and δ is the constant shear of the basic current. Solutions corresponding to uniform flow, δ = 0, in an unbounded fluid, r = 0, represent a limit that is compared with a previous study (Pierehumbert 1985). The present results confirm Pierrehumbert's conclusion that upstream deceleration is not significant, and that the characteristic vertical depth, over which the disturbances decay, is D. Confinement of the flow by a rigid lid (r ≠ 0) and consideration of a shear (δ ≠ 0) do not affect that flow deceleration, nor do these features affect the characteristic decay of the ageostrophic velocity components. However, the presence of a lid causes the geostrophic velocity component to become relatively independent of depth. It is also shown that an increase in the static stability (&epsi&/D increasing) enhances the ageostrophic circulation in a manner that is similar to the effect of increasing the shear δ from negative to positive values. Moreover, a linear lower boundary condition may be used in some circumstances because the velocity components on the ridge are relatively insensitive to changes in r when 0 > r ≳ 0.3 and δ0 However, linearization of the boundary condition cannot be supported when the basic flow changes with height, δ≠ 0. The geostrophic momentum approximation is shown to be valid over most of the domain, but may be violated along the windward slope unless &epsi&/D ≤ 0.6, with δ ≤ 0.5. Other considerations that need to be addressed to apply semige-ostrophic theory to mountain flows include a stability analysis of the present solutions and the use of nonisentropic boundary surfaces.

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Michael S. Fox-Rabinovitz
and
Brian D. Gross

Abstract

A generalized dynamical adjustment procedure has been applied to a diabatic model to produce balanced initial conditions. Namely, backward adiabatic model integration is followed by forward diabatic model integration, with a high-frequency (low-pass) filter in the form of the Euler backward time-differencing scheme being applied throughout the whole integration.

As a result of the application of such a diabatic dynamic initialization procedure within the Goddard Laboratory for Atmospheres (GLA) 4D data-assimilation system, the following properties of forecasts from initialized fields are achieved right from the beginning of the usual forecast integration: 1) the forecast tendencies (and fields) are free of any noise due to imbalance in initial conditions, and 2) the shocks related to an initial imbalance between model physics and dynamics (and especially the substantial initial imbalance of precipitation and evaporation fields), or the initial spinup effect, are practically removed.

Diabatic dynamic initialization has been compared with implicit nonlinear normal-mode initialization and found to be superior in removing the initial spinup effect and in improving the tropical structure.

The diabatic dynamic initialization procedure has been successfully tested for the GLA system with the use of all conventional data and the GLA satellite data retrievals. It allows a smooth data insertion without any shocks or imbalances, which is highly desirable for efficient functioning of 4D data-assimilation systems.

The developed initialization procedure is computationally efficient and in principle easily applicable to different large-scale and mesoscale forecast models.

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Jerald A. Brotzge
,
Don Berchoff
,
DaNa L. Carlis
,
Frederick H. Carr
,
Rachel Hogan Carr
,
Jordan J. Gerth
,
Brian D. Gross
,
Thomas M. Hamill
,
Sue Ellen Haupt
,
Neil Jacobs
,
Amy McGovern
,
David J. Stensrud
,
Gary Szatkowski
,
Istvan Szunyogh
, and
Xuguang Wang
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