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Charles Cohen

Abstract

In a series of experiments with a two-dimensional mesoscale numerical model that uses the Frank-Cohen cumulus parameterization, different types of large-scale forcing are held constant and the response of the model atmosphere is examined. A dynamic equilibrium between convection and the specified large-scale forcing is achieved in many of the 24 h simulations, with the convection oscillating around a mean state.

In the numerical experiments, the different physical processes that make up the large-scale forcing in the model are examined. Removing the adiabatic cooling and including only the moisture convergence effect of the modeled intertropical convergence zone ITCZ causes a substantial decrease in the precipitation. Including just the adiabatic cooling, without the moisture convergence, produces the same total rainfall over 24 h as including just the moisture convergence. The large-scale upward motion of the ITCZ, as one component of the grid-scale upward mass flux at cloud base, strengthens the parameterized convection temporarily, but over a few hours the total amount of convection is limited by the stability. Other experiments examine the influence of radiative cooling and synoptic easterly waves.

With different types of large-scale forcing, the resulting vertical profiles of changes in temperature and water vapor mixing ratio show some common features. The parameterized tropical convection causes the domain- averaged virtual potential temperature sounding to move closer to a true moist adiabat.

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Charles Cohen

Abstract

Four cumulus parameterizations in the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (Penn State–NCAR) Mesoscale Model (MM5) are compared in idealized sea-breeze simulations, with the aim of discovering why they work as they do. Compared to simulations of real cases, idealized cases produce simpler results, which can be more easily examined and explained. By determining which features of each parameterization cause them to produce differing results, a basis for improving their formulations and assisting modelers who may design new cumulus parameterizations can be provided.

The most realistic results obtained for these simulations are those using the Kain–Fritsch scheme. Rainfall is significantly delayed with the Betts–Miller scheme, due to the method of computing the reference sounding. Another version of this parameterization, which computes the reference sounding differently, produces nearly the same timing and location of deep convection as the Kain–Fritsch scheme, despite the very different physics.

In applying the quasi-equilibrium closure, the Grell parameterization uses horizontal and vertical advection to compute the rate of destabilization. In the present simulation, the parameterized updraft is always derived from the top of the mixed layer, where vertical advection predominates over horizontal advection in increasing the moist static energy, instead of from the most unstable layer. By doing this, it evades the question of whether horizontal advection generates instability or merely advects an existing unstable column.

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Charles Cohen

Abstract

A method is developed that uses numerical tracers to make accurate diagnoses of entrainment and detrainment rates and of the properties of the entrained and detrained air in numerically simulated clouds. These rates and properties are averaged horizontally and over time, and are produced independently of each other. There are no restrictions on the types of clouds to which the procedure can be applied.

Cumulonimbus clouds are simulated with a variety of initial thermodynamic soundings. In the simulations, updraft entrainment rates are large near and above cloud base, through the entire depth of the conditionally unstable layer. Stronger updrafts in a more unstable environment are better able to entrain relatively undisturbed environmental air, while weaker updrafts in a less unstable environment can entrain only air that has been modified by the clouds.

Smaller convective clouds in more stable environments mix more with their environment but do not necessarily have larger entrainment rates. How much air is entrained depends on the low-level convective available potential energy (CAPE) and on the convective inhibition of the environmental air.

Strong updrafts that are produced when the low-level CAPE is large include parcels with a wide range of equivalent potential temperature and are more likely to have an undilute core and to reach or exceed their level of neutral buoyancy than the weaker and more horizontally uniform updrafts that are produced when low-level CAPE is small.

These results help to explain previous observations that convective updraft cores are stronger in midlatitude continental clouds than they are in tropical maritime clouds.

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Charles Cohen and William M. Frank

Abstract

Observations in the tropics have shown that the lapse rate of virtual Potential temperature θv normally resembles that of a reversible moist adiabat. In the present study, a mesoscale numerical model with parameterized convection is used to examine the adjustment to equilibrium of the tropical atmosphere in the presence of large-scale forcing. The physical processes that enable the model to produce an equilibrium lapse rate similar to what is observed are examined. The results indicate that a spectrum of cloud sizes, which is produced by a variable entrainment rate, is essential to enable the atmosphere to approach an equilibrium state of small conditional instability in the presence of large-scale destabilization. Lateral detrainment is not essential for modeling the large-scale stability of the atmosphere, despite its significance for modeling individual mesoscale convective systems.

When downdrafts are removed from the parameterized convection, the model only temporarily produces a realistic large-scale lapse rate. Other results suggest that the departure of observed θν soundings from adiabats around the melting level is due to ice processes. The feedbacks between convective-scale process and the environmental stability that allow the atmosphere to maintain a state of small conditional instability are discussed.

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William M. Frank and Charles Cohen

Abstract

A new cumulus parametefization is developed for ffse in mesoscale model simulations of precipitating convective systems. It is designed to estimate convective properties using a cloud model that interacts with the mesoscale model in a physically consistent manner. The cloud model is initiated by and interacts with the grid-scalecirculation without being constrained in instantaneous equilibrium with the grid-scale flow. The parameterization is designed for use in conjunction with explicit moist processes. Simulations of tropical convective lines performed using the scheme are presented in a companion paper (Part II).

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Charles Cohen and William M. Frank

Abstract

The new cumulns parameterization of Part I of this paper is used in a setes of simulations of tropical mesoscale convective lines. The structures and life cycles of the simulated systems are quite similar to those observed in many studies of tropical convection, supporting the use of the parametedzation in mesoscale model.

The modeled cloud lines formed extensive upper-level nimbostratus clouds, primarily from air detrained below cloud top by the parameterized convection. These clouds produced copious rainfall and tended to shift the net diabafic heating predicted by the model to higher levels. When a cloud model lacking lateral detrainment was used, the simulated cloud lines grew rapidly, had short lifetimes, did not develop nimbostratus ions and concentrated the diabatic heating in the upper levels. Radiative processes, though crudely simulated, were shownto have potentially large effects on the intensity of the conyective system Decreasing the intercept, No, in the drop size distribution in the explicit moisture scheme had relatively small effects on the structure of the simulated systems, but it inctsed the rainfall and caused a small upward shir in the vertical heating probe.

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William M. Frank and Charles Cohen

Abstract

A simple cloud model is developed which is designed for both diagnostic studies and mesoscale cumulus parameterization experiments. The cloud model is combined with an observed population of tropical convective updrafts and used to examine the vertical distributions of convective beating and moistening produced by tropical cloud ensembles.

Although the cloud model ensembles are dominated by deep cumulonimbi, their vertical beating and moistening profiles differ significantly from those of individual clouds. These profiles and the total rainfall are sensitive to assumptions that affect the vertical mass flux distributions of the clouds. The ensemble heating and moistening profiles are in general agreement with large-scale budget analyses except for a tendency for the former to concentrate more of the heating above 600 mb.

Modeled convective properties are found to be highly sensitive to assumptions concerning the convective environment immediately surrounding the updrafts and downdrafts. This has important implications for cumulus parameterization experiments, particularly in coarse-grid models.

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Eugene W. McCaul Jr. and Charles Cohen

Abstract

The sensitivities of convective storm structure and intensity to variations in the depths of the prestorm mixed layer, represented here by the environmental lifted condensation level (LCL), and moist layer, represented by the level of free convection (LFC), are studied using a three-dimensional cloud model containing ice physics. Matrices of simulations are generated for idealized environments featuring both small and large LCL = LFC altitudes, using a single moderately sheared curved hodograph trace in conjunction with convective available potential energy (CAPE) values of either 800 or 2000 J kg−1, with the matrices consisting of all four combinations of two distinct choices of buoyancy and shear profile shape. For each value of CAPE, the LCL = LFC altitudes are also allowed to vary in a separate series of simulations based on the most highly compressed buoyancy and shear profiles used for that CAPE, with the environmental buoyancy profile shape, subcloud equivalent potential temperature, subcloud lapse rates of temperature and moisture, and wind profile held fixed. Two other special simulations, one for each CAPE, are conducted using the high LFC and the lowered LCL, with a neutrally buoyant environmental thermal profile specified in between, such that the equivalent potential temperature was similar to that at the LCL. These latter two cases correspond to situations where the moist layer depth exceeds that of the mixed layer, whereas in all the other cases the two depths were equal.

Results show that for the CAPE-starved environments (CAPE = 800 J kg−1) the simulated storms are supercells that are generally largest and most intense when LCL = LFC altitudes lie in the approximate range 1.5–2.5 km above the surface. The simulations show similar trends for the shear-starved (CAPE = 2000 J kg−1) environments, except that a tendency toward outflow dominance and multicell morphology is more evident when the LCL = LFC is high. For choices of LCL = LFC height within the optimal 1.5–2.5-km range, peak storm updraft overturning efficiency may approach 100% relative to parcel theory, while for lower LCL = LFC heights, overturning efficiency is reduced significantly. The enhancements of overturning efficiency with increasing LFC height are shown to be associated with systematic increases in both updraft effective diameter and the mean equivalent potential temperature of the low-level updraft, which reaches a maximum near the LFC. For the shear-starved environments, the tendency for outflow dominance is eliminated, but a large overturning efficiency maintained, when a low LCL is used in conjunction with a high LFC. The result regarding outflow dominance at large LCL derives from enhanced evaporation of precipitation in the deeper and drier subcloud layer, but the beneficial effect of a high LFC on convective overturning efficiency, at first glance surprising, derives from the enhanced depth of the moist layer containing the maximum CAPE. The importance of the moist layer depth is highlighted in tests that show that high-LFC storms simulated in environments where the neutrally buoyant sub-LFC layer contains a layer of reduced equivalent potential temperature experience a corresponding decrease in updraft strength. The simulation findings presented here appear to be consistent with statistics from previous severe storm environment climatologies, but provide a new framework for interpreting those statistics.

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Charles Cohen and Eugene W. McCaul Jr.

Abstract

A method is devised for diagnosing the condensation rate in simulations using the Regional Atmospheric Modeling System (RAMS) model, where ice-liquid water potential temperature is a prognostic variable and an iterative procedure must be used to diagnose the temperature and water vapor mixing ratio from ice-liquid water potential temperature. The condensation rate is then used to compute the microphysical precipitation efficiency (PE), which is defined as the ratio of the precipitation rate at the ground to the sum of the condensation and deposition rates. Precipitation efficiency is compared for pairs of numerical simulations, initialized with soundings having all key environmental parameters identical except for their temperature. The authors’ previous study showed that with a colder initial sounding, the conversion of cloud water to precipitation is relatively inefficient, but updrafts are stronger and there is relatively less evaporation of precipitation, with the net result being a larger climatological PE in the colder environment. Here, the authors consider the time lag between condensation and precipitation and demonstrate that in calculating a properly lagged microphysical PE, the combined effect of the decreased production of precipitation and the decreased evaporation is that the temperature of the initial soundings has no significant influence on the microphysical PE. To the authors’ knowledge, this is the first time that the lag has been used to compute PE. These results concerning PE are relevant only to deep convection.

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Charles Cohen and Eugene W. McCaul Jr.

Abstract

The sensitivity of cloud-scale simulations of deep convection to variations in prescribed microphysics parameters is studied, using the single-moment scheme in the Regional Atmospheric Modeling System (RAMS) model. Realistic changes were made to the shape parameters in the gamma distributions of the diameters of precipitating hydrometeors and of cloud droplets, in the number concentration of cloud droplets, and in the mean size of the hail and graupel. Simulations were performed with two initial soundings that are identical except for their temperature. The precipitation rate at the ground is not very sensitive to changes in the value of the shape parameter used for all precipitating hydrometeors (rain, hail, graupel, snow, and aggregates) or to the mean size of the hail and graupel, owing to counteracting effects. For example, with a larger shape parameter value, there is a greater production of precipitation by collection of cloud water, but also a larger rate of evaporation of the liquid precipitation. However, with a larger shape parameter value, the greater production of precipitation by collection and the increased evaporation result in more low-level cooling by the downdraft. Specifying larger hail and graupel results in less low-level cooling by the downdraft. The simulation with the cold initial sounding showed a change in storm propagation velocity when the specified sizes of hail and graupel were increased, but this did not occur when the warm initial sounding was used. With a larger shape parameter for cloud water or with a larger number concentration of cloud droplets, there is less autoconversion and less collection of cloud water and, consequently, much less precipitation at the ground and denser cirrus anvils. While the number concentration of cloud droplets can be forecast in some models with parameterized microphysics, at present the shape parameter for cloud water cannot and must, therefore, be carefully selected.

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