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Robert E. Schlesinger

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Robert E. Schlesinger

Abstract

This study involves the dynamics of a deep convective cloud in conditionally unstable surroundings with moderate mid-tropospheric shear. A two-dimensional, anelastic numerical model is used to simulate convection of the squall-line type.

A prototype experiment is run with liquid water drag, liquid precipitation, and effects of pressure perturbations upon the buoyancy included. The roles of these forces are inferred by running variations upon the prototype with one force suppressed in each case. In another variation, a sharp upper jet replaces a flat upper wind maximum. It is found that.

  1. The prototype storm exhibits a quasi-steady mature stage characterized by nearly time-independent streamline patterns for both air parcels and precipitation particles in and near the cloud core. Potentially warm low-level air feeds the updraft from downshear, while potentially cool middle-level air feeds the downdraft from upshear.

  2. During maturity, thermal buoyancy is the dominant vertical force, but is strongly opposed by the vertical perturbed pressure gradient force. The buoyancy due to pressure perturbations is appreciable, with a maximum value about one-fourth that for the thermal buoyancy. Liquid water drag is intermediate in importance between the two buoyancy components. The vertical and horizontal net accelerations are comparable to each other and to the pressure buoyancy.

  3. Dynamic entrainment of potentially cool air into the sides of the cloud eventually contributes to dissipation as the downdraft spreads laterally and isolates the updraft.

  4. Liquid water drag limits updraft intensity but is not necessary for downdraft formation, which is due instead to evaporative cooling.

  5. Fallout of precipitation is essential to storm dissipation; without fallout, liquid water accumulation at low levels is insufficient for significant downdraft development, and the cloud core evolves to a steady state.

  6. Negative pressure buoyancy in the upper portion of the cloud slightly limits the intensity of the developing updraft, but positive pressure buoyancy at and near the foot of the updraft reinforces its intensity during maturity.

  7. A sharp upper-level jet in place of a broad upper-level wind maximum delays and slightly prolongs the mature stage, but does not lead to a more intense updraft.

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Robert E. Schlesinger

Abstract

The mature stage of an isolated convective storm in sheared surroundings is studied by means of an anelastic three-dimensional numerical model. Liquid precipitation and turbulence are included in parameterized form.

Three comparative experiments are run with different vertical profiles of ambient wind: no ambient wind, uni-directional shear, and multi-directional shear dominated by strong low-level veering, the first shear profile being the west-east projection of the second. The cases are compared in regard to airflow, pressure, potential temperature and liquid water. The results were as follows:

  1. Both sheared storms exhibit a quasi-erect high-speed updraft, a deep cyclonic-anticylonic vortex couplet aloft, middle-level barrier flow around the updraft, and gradual splitting into cyclonic and anti-cyclonic cells moving to the right and left of the mean winds.

  2. The model storms show a slightly weaker growing stage with shear than without, but the mature stage is stronger and more persistent. Without shear, the main downdraft develops directly beneath the updraft, whereas with shear the main downdraft develops upshear of the updraft. Surface convergence between updraft inflow and downdraft outflow is much stronger with shear than without.

  3. The perturbed pressure field shows highs beneath the downdraft and at the updraft summit, and low pressure at intermediate levels. With shear, the low pressure shows two centers at the left and right flanks, inducing a divergent horizontal pressure gradient force field that may contribute to splitting.

  4. Thermal buoyancy and the perturbed vertical pressure gradient force oppose each other, in particular enabling parcels to accelerate upward against negative buoyancy at the bases of the sheared updrafts.

  5. With directional shear, the respective right and left flanks move slower and faster than the mean winds, and the right flank is stronger than the left.

  6. With shear, surface rainfall is lighter and less widespread than without shear, but maximum liquid water content aloft is greater and decreases much slower with time.

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Robert E. Schlesinger

Abstract

Two- and three-dimensional anelastic numerical modeling experiments with common environmental profiles are used to study two aspects of the pressure perturbation field in strongly sheared convective storms: 1) the physical roles of the so-called “buoyant” and “dynamic” pressure components, and 2) the distinction between the buoyant and hydrostatic pressure perturbations. The two- and three-dimensional models are analogous except that the two-dimensional grid domain is about 50% longer in order to accommodate a broadening of the two-dimensional storm circulation with time.

The pressure analysis helps to clarify certain marked differences between the two-dimensional and three-dimensional storms, most notably a much weaker main updraft in two dimensions pronounced downshear tilt of the two-dimensional storm core versus an erect three-dimensional storm core, and a dry secondary updraft downshear of the main cloudy updraft in two dimensions with no analog in three dimensions:

  1. In the main updraft, strong midlevel thermal buoyancy is partly opposed by a downward-perturbed vertical pressure gradient force, but to a much greater extent in two dimensions than in three dimensions contributing to smaller net upward accelerations. This difference resides fully in the buoyant pressure component.

  2. In three dimensions the dominant mesolow is a few kilometers aloft within the active cloudy updraft, whereas in two dimensions it is at the surface, far downshear of the active updraft, and roughly three times stronger. Parcels feeding the main updraft therefore accelerate downshear earlier and more strongly in two dimensions than in three dimensions.

  3. The intense mesolow in two dimensions contributes strongly to a density deficit beneath the anvil, i.e., induces an upward “pressure buoyancy force” that helps drive the dry secondary updraft.

  4. The contrasting mesolow strengths in two dimensions and three dimensions reflect largely the buoyant component, which in two dimensions attains large negative values at low levels due to excessive overlying warming from previous strong environmental subsidence exaggerated by the two-dimensional slab geometry.

  5. The dynamic pressure minimum lies well above and downshear of the buoyant pressure minimum in three dimensions, but is colocated with it in two dimensions, further contributing to the very deep two-dimensional mesolow.

Formally, in both two dimensions and three dimensions, the buoyant and hydrostatic pressure perturbations satisfy elliptic diagnostic equations which are similar except that a horizontal Laplacian in the linear operator for the buoyant field is absent for the hydrostatic field. Thus, while both fields are intimately related to the distribution of total buoyancy (thermal buoyancy plus liquid water drag), the buoyant pressure perturbation is smoother and of lower amplitude than its hydrostatic counterpart. For the model experiments reported here, this distinction is far greater in three dimensions than in two dimensions, in association with the smaller horizontal scale of the active convection in three dimensions. Beneath the main updraft core, the maximum hydrostatic deficit is some 250% greater than the maximum buoyant deficit in three dimensions, but only about 50% greater in two dimensions.

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Robert E. Schlesinger

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This paper considers some mathematical aspects of the nonlinear eddy-viscosity turbulence parameterization with quasi-isotropic partitioning of turbulent kinetic energy in three-dimensional anelastic flow. The parameterization, which several investigators have used with the Boussinesq approximation in simulating boundary layer flow and shallow cumulus convection, is generalized in a reasonable way, modifying the formulations of subgrid velocity variances and mean flow deformation to take nonzero three-dimensional divergence into account.

It is shown that while strict dissipation of domain-integrated mean kinetic energy due to turbulence is insured for Boussinesq flow, a source/sink term analogous to the pressure-divergence term is also formally present for anelastic flow. Also, in seeking a straightforward parameterization of turbulent kinetic energy so as to insure mathematical realizability for the turbulent velocity variance and covariances, it is found that the formulation of Lilly (1967) meets these requirements provided that his proportionality factor is suitably restricted. In turn, this places a restriction on the relative magnitudes of two universal constants that arise in a more recent formulation of Deardorff (1973). (1973).

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Robert E. Schlesinger

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Robert E. Schlesinger

Abstract

This project uses a three-dimensional anelastic cloud model with a simple ice phase parameterization to evaluate the feedback of isolated deep convective clouds over a horizontal scale comparable to one grid cell in typical mesoscale numerical weather prediction models. A more specific focus in this paper is the sensitivity of the feedback to modest changes in the initial vertical wind shear intensity and low-level moisture supply, as well as to the ice phase.

Two parallel sets of comparative simulations are run for a quasi-steady severe Oklahoma supercell thunderstorm in strong vertical wind shear versus a weaker, less persistent, and narrower tropical Atlantic cumulonimbus with a slowly decaying and pulsating updraft in much weaker shear. The horizontal Reynolds averaging approach of Anthes is adopted to diagnose the budgets for heat, moisture, and horizontal momentum. Several similarities and differences between the midlatitude and tropical control experiments were delineated in Part I. The main findings of the sensitivity study are described below.

The midlatitude storm evolves to maturity somewhat later (earlier) for stronger (weaker) shear, though with little effect on peak updraft speed or basic storm structure. Quantitatively, the convection is more sensitive to moisture supply changes, although basic structure is again preserved. With increased moisture the peak updraft speed increases by ∼15% and the apparent heating and drying amplitudes by ∼40%, and vice versa for the drier run. The vertical eddy fluxes are the main modulating factors. Without ice the peak updraft is ∼10% weaker, though with no systematic effect on downdraft speed, the later stages show gradual weakening in contrast to the quasi-steady control case, and the apparent heating and drying amplitudes are ∼25% lower due to decreased condensation and also (for heat) the absence of any latent heat release by glaciation.

The tropical cumulonimbus is for the most part less sensitive to shear intensity than its midlatitude counterpart. The pulsations are weaker in stronger shear and vice versa, but varying the shear has no systematic effect on either downdraft intensity or updraft evolution, affecting the budgets to a modest degree chiefly through the vertical eddy transport profiles. Omitting ice also affects the tropical cumulonimbus less than the midlatitude supercell storm, only slightly affecting updraft speed and the various budgets, especially for momentum.

However, the tropical cumulonimbus is much more sensitive to moisture supply than the midlatitude supercell. The updraft is almost 25% weaker in the dry run and ∼45% stronger with slower decay and stronger pulsations in the moist run, which also produces a deeper cloud with less downshear tilt and a more extensive anvil. Apparent heating and drying amplitudes are roughly doubled in the moist run and halved in the dry run, modulated mainly by condensation and vertical eddy transport amplitudes. The momentum budget is also notably sensitive to moisture supply, especially in the moist variation, in which the upper-level horizontal pressure gradient force promotes the enhanced anvil blowoff and reduced cloud tilt.

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Robert E. Schlesinger

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This paper presents preliminary results from an investigation into the feedback between convective storms and their new surroundings, using output from a three-dimensional anelastic cloud-scale model. Convective feedback budgets for heat, moisture and horizontal momentum are diagnosed from horizontally Reynolds-averaged governing equations, analogous to the theory of Anthes. There is limited horizontal scale separation between the active convection area and the averaging area, which at 30 km on a side is comparable to one grid cell of a typical mesoscale numerical weather prediction model.

The simulation is run with an idealized midlatitude severe thunderstorm sounding. The resulting storm displays several supercell features. These include a vigorous erect large-diameter updraft that splits at lower levels, a vaulted weak echo region in the lower part of the main (right flank) updraft core, and a midlevel mesovortex couplet with cyclonic vorticity in the main updraft.

The vertical profiles of the various budget terms show several findings of potential relevance to cumulus parameterization. The vertical eddy transport (flux divergence) is highly important to each budget; it significantly raises the height of the maximum apparent heat source and lowers the height of the maximum apparent moisture sink, and acts to reduce the net tropospheric vertical wind shear. At the same time, the horizontal eddy momentum transport and the mean horizontal pressure gradient force both act strongly to sharpen the tropopause-level jet, so that the net shear is little changed. The horizontal eddy transport is much less important to the heat budget, and remains negligible for moisture. Mean storage contributes significantly to the apparent source for each budget under consideration. Other terms derived by Anthes but ignored in existing cumulus parameterizations (the resultant of eddy storage, transport of mean fields by the eddy wind, and transport of eddy fields by the mean wind) become quite appreciable. These terms partially oppose the condensational heating and drying, and the processes that sharpen the tropopause-level jet.

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Robert E. Schlesinger

Abstract

This project uses a three-dimensional anelastic cloud model with a simple ice phase parameterization to evaluate the feedback between isolated deep convective clouds and their near surroundings. The horizontal Reynolds averaging approach of Anthes is adopted to diagnose the vertical profiles of the individual budget terms for heat, moisture, and horizontal momentum, as well as the resultant effects of each budget as defined by apparent sources or sinks. The averaging area, 33.75 km on a side, is comparable to one grid cell for typical mesoscale numerical weather prediction models.

Two comparative simulations are run, one for a severe Oklahoma thunderstorm in strong vertical wind shear and the other for a tropical Atlantic cumulonimbus in much weaker shear. The midlatitude cloud evolves to a vigorous quasi-steady mature stage with several supercell characteristics including an erect large-diameter updraft, a strong and vertically extensive mesolow, and a well-developed highly asymmetric cold pool that spreads rapidly. In contrast, the tropical updraft is much narrower and slower with a shallow weak midlevel mesolow, leans markedly downshear, and evolves early into slow decay modulated by bubblelike pulsations, while the cold pool is weak and quasi-circular and spreads slowly.

There are several similarities between corresponding budgets in the two runs. Most notably: 1) The heat and moisture budgets are dominated by condensation, which is maximized in the midtroposphere. 2) The horizontal pressure gradient force dominates the momentum budget. 3) Vertical eddy transport (flux divergence) is highly important to each budget. Thermodynamically, it acts to mainly cool and dry the lower troposphere, while warming and moistening the upper troposphere, though with a lower crossover level for moisture than for heat. 4) The altitudes of the peak apparent heat sources are determined by the vertical eddy transport of heat. 5) Net evaporation has ∼40% as much amplitude as the condensation. 6) Horizontal eddy transport contributes little to the heat and moisture budgets. 7) Other terms derived by Anthes but ignored in existing cumulus parameterizations (the resultant of eddy storage, transport of mean fields by the eddy wind, and transport of eddy fields by the mean wind) oppose significant portions of the apparent sources or sinks in each budget, though not quite proportionally.

On the other hand, the tropical budgets differ from their midlatitude counterparts in several aspects. Most notably: (i) The amplitudes of the feedback terms are an order of magnitude smaller. (ii) The condensational heating and drying have sharper and narrower peaks, and glaciation of rain is much smaller in relation to the condensation. (iii) The evaporative cooling and moistening have a sharp midtropospheric peak associated with an altostratus shelf that is absent in the midlatitude case. (iv) Vertical eddy transport of heat is less important in relation to condensational warming, and is more oscillatory with height than in the midlatitude case. (v) Vertical eddy transport does not contribute to the forcing of the principal peak in the apparent moisture sink. (vi) Horizontal eddy transport of momentum, significant in the midlatitude storm, is negligible in the tropical cloud.

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Robert E. Schlesinger

Abstract

This study concerns the influence of ambient conditions upon the behavior of deep moist convection in the atmosphere. By means of a two-dimensional numerical model, an anelastic system of hydrodynamic and thermodynamic equations is integrated in order to simulate convection of the squall-line type. Liquid precipitation and the effect of pressure perturbations upon the buoyancy are included.

The joint influence of low-level relative humidity and mid-tropospheric wind shear upon the intensity and persistence of the convection at maturity is investigated. Nine comparative experiments are performed using three values of each parameter, including cases without shear. The various cases are compared with regard to airflow and rainfall patterns. Basic features of the perturbation fields for flow, temperature and pressure are interrelated.

It is found that the greater the moisture supply and the weaker the shear, the more intense is the convection in terms of both peak updraft velocity and rainfall rate. Strength and persistence do not necessarily correspond. Specifically:

  1. With a very large moisture supply and weak shear, an intense but relatively short-lived updraft results. The main rainfall and downdraft occur downshear of the updraft, isolating it from its source.

  2. A long-lived or quasi-steady updraft of moderate to strong intensity is supported by moderate shear, or even strong shear if moisture is sufficiently abundant. Rainfall and downdraft develop upshear of the updraft, tending to perpetuate it.

  3. With insufficient moisture, strong shear cannot support an intense or long-lived storm. Rainfall and downdraft are upshear of the updraft, but the lowest-lying air flows under and past it, limiting its buoyancy.

Low-level evaporative cooling produces a surface meso-high under the mature storm core. Mid-level warming due to compensatory subsidence contributes to surface meso-lows on either side, the downshear meso-low being further enhanced by warm outflow into the anvil.

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