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Gregory J. Tripoli and William R. Cotton

Abstract

Previous studies have shown liquid water potential temperature to be an inappropriate choice for a thermodynamic variable in a deep cumulus convection model. In this study, an alternate form of this variable called ice-liquid water potential temperature (θu) is derived. Errors resulting from approximations made are discussed, and an empirical form of the θu equation is introduced which eliminates much of this error. Potential temperature lapse rates determined in saturated updrafts and unsaturated downdrafts by various θu approximations, an equivalent potential temperature approximation and a conventional irreversible moist thermodynamic approximation are then compared to the potential temperature lapse rate determined from a rigorously derived reversible thermodynamic energy equation. These approximations are then extended to a precipitating system where comparisons are again made. It is found that the errors using the empirical form of the θu equation are comparable to those made using conventional irreversible moist thermodynamic approximations. The advantages of using θu as an alternative to θ in deep convection and second-order closure models also are discussed.

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Michael J. Weissbluth and William R. Cotton

Abstract

Currently, there is no adequate cumulus parameterization suitable for use in mesoscale models having horizontal resolutions between 5 and 50 kilometers. Based on the similarity of the temporal and spatial evolution of the vertical variances between a CCOPE supercell and a generic tropical squall line as explicitly simulated by the Regional Atmospheric Modeling System developed at Colorado State University, a convective parameterization scheme is developed that represents microscale turbulence with a modified second-order closure scheme and cumulus draft-scale eddies with a convective adjustment scheme. The microscale turbulence scheme is based upon the Mellor and Yamada 2.5-level closure modified to predict solely on ww and includes Zeman and Lumley's formulation for the buoyancy-driven mixed layer to close the pressure term and the eddy transport term. If deep convection is indicated, the microscale turbulence scheme includes contributions from cumulus draft-scale fluxes determined from a cloud model and uses different length scales to represent the planetary boundary-layer eddies and the in-cloud eddies.

The cumulus draft-scale tendencies of heat, moisture, and hydrometeors are specified by a mesoscale compensation term and a convective adjustment term. The convective adjustment term is the difference between a cloud model-derived properly and its environmental value, and is modulated by a time scale determined through a moist static energy balance. The mesoscale compensation term is a product of the vertical gradient of the appropriate scalar and a convective velocity equal to (ww)½. The cloud model is calibrated and generalized by comparisons with conditionally sampled data from the two explicitly simulated storms.

One unique feature of this approach is that the parameterization is not simply a local grid column scheme; ww is transported by the turbulence as well as the mean horizontal and vertical winds. Thus, the scheme responds to shear and is more global in nature than current cumulus parameterizations, and maintains a memory of previous convective activity. Furthermore, the scheme provides explicit cumulus source functions for all hydrometeor species. Results from a simple two-dimensional simulation of deep cumulus indicate the satisfactory performance of this scheme. Part II of this paper will compare explicit simulations of two- and three-dimensional Florida sea-breeze convection with parameterized simulations on various coarser grids.

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Brian J. Gaudet and William R. Cotton

Abstract

An idealized simulation of a supercell using the Regional Atmospheric Modeling System (RAMS) was able to produce a low-level mesocyclone near the intersection of the forward- and rear-flank downdrafts. The creation of the low-level mesocyclone is similar to previous studies. After 3600 s, the low-level mesocyclone underwent a period of rapid intensification, during which its form changed from an elongated patch to a compact center. This transition was also accompanied by a sudden decrease in pressure (to 12 mb below that of the neighboring flow), and was found to occur even in the absence of nested grids.

It is shown that the stage of strong intensification does not begin aloft, as in the dynamic pipe effect, and then descend to the surface. Rather, the vortex is initiated near the surface, and then builds upward. The process is completed in 5 min, and the final vortex can be clearly distinguished from the larger-scale mesocyclone at the cloud base. The reduction of pressure can be explained as a consequence of the evacuation of mass in the horizontal convergence equation. This is in contrast to axisymmetric models of vortex intensification, which generally rely on the evacuation of mass in the vertical divergence equation. In the latter cases a positive horizontal convergence tendency is what initiates the concentrated vortex. However, nondivergent models prove that vorticity concentration can occur in the absence of any horizontal convergence. Here the concentration is associated with a negative horizontal convergence tendency.

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M. J. Manton and W. R. Cotton

Abstract

A parameterization of the constant flux surface layer is developed in order to provide boundary conditions for numerical models of the atmospheric boundary layer and moist convective layer. Algebraic expressions are found for the turbulence covariances in the surface layer under all stability conditions.

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Gregory J. Tripoli and William R. Cotton

Abstract

A detailed analysis of the dynamics and thermodynamics responsible for the structure, growth and propagation of an orogenic mesoscale convective system simulated in two dimensions is made. The process of scale interaction is addressed through Fourier analysis and Reynolds averaging analysis of representative predicted variables, diabatic forcing and momentum acceleration terms. Additional dynamical analysis is accomplished through sensitivity experiments in which Coriolis, diabatic heating and ambient airflow are varied.

The general conclusion is that the simulated orogenic development is a geostrophic adjustment process to convective heating which is itself modulated and maintained by orographically induced flow systems. The heating scales range over a nearly continuous spectrum ranging from 10–250 km. The heating occurs in response to primary advective gravity modes. The larger-scale gravity-wave disturbances modulate the smaller scales by organizing mean upward vertical motion patterns. The largest gravity-wave modes are modulated by constraints of the slope flow circulation, namely a phasing of an advective mode with a localized break in the plains inversion.

The simulated growth to mesoα-scale proportions occurs from the horizontal expansion of the disturbance through interaction with the mountain-plains scale slope flow circulation. Similar to upscale two-dimensional turbulence cascade, the mountain plains solenoid deforms thermal patterns, increasing their scale. As the scale reaches mesoα-scale proportions, geostrophic adjustment frequencies are sufficient to allow the thermal fields to persist. Implications to the problem of cumulus parameterization and limitations of the two-dimensional framework of this numerical study are discussed.

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William R. Cotton and Gregory J. Tripoli

Abstract

A three-dimensional model of deep, moist convection is described. The model is fully compressible and utilizes a “time-splitting” method of integration in order to make the model economically feasible.

This study represents an extension of the numerical experiments reported by Cotton (1975). In that work the profiles of the ratio of average cloud water content to the moist-adiabatic water content (c/QA) predicted by a one-dimensional Lagrangian (1DL) and a one-dimensional time-dependent (1DTD) model are compared with case study observed data and the average c/QA profiles reported by Warner (1970a). In this work, data predicted by a three-dimensional (3D) cloud simulation in a stagnant environment and a 3D cloud simulation in the observed shear flow are compared with observed data and the earlier model calculations. The results of this study demonstrated that all the cloud simulations in an initially stagnant environment, including the 1DL, 1DTD and 3D models, predicted profiles of c/QA which exhibited very high magnitudes near the top of the rising cloud. The predicted magnitudes of c/QA near the top of the rising cloud exceeded the observed magnitude by as much as a factor of 3. In contrast, the 3D simulation in the observed shear flow predicted profiles of c/QA and magnitudes of peak c/QA which were in good agreement with observations.

What is most surprising is that the improved prediction of cloud liquid water content was not at the expense of the prediction of cloud-top height. Instead the cloud-top heights predicted in both the no-motion and shear-flow simulations were identical and equal to the observed cloud-top height. This is in contrast to the earlier 1DL and 1DTD model numerical experiments reported by Cotton using the same sounding. In those calculations, predicted cloud-top height varied considerably (over several kilometers) with different entrainment rates and eddy exchange coefficients. As a further benefit, the prediction of cloud-scale averaged vertical velocity in the shear-flow simulation was also better than that predicted in the no-motion simulation.

It is thus concluded that the interaction of a cumulus cloud with an environment characterized by vertical shear of the horizontal wind is a major control on the prediction of cloud internal properties. Associated with the improved prediction of c/QA, the 3D simulation in shear flow also exhibited major changes in the structure of the cloud circulation. A particularly interesting feature was the formation of rotating cloud elements in several portions of the main cloud element.

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Michael J. Weissbluth and William R. Cotton

Abstract

Vertical divergence of the mountain wave's momentum flux has recently been hypothesized to be an important contribution to the global momentum budget. Wavebreaking theories and envelope orography have been employed to explain the divergence of the momentum flux. Here, cloud-top radiational cooling is shown to locally destabilize the environment and disrupt the propagation of the mountain wave in idealized two-dimensional simulations, thus drastically altering the expected momentum flux profile. Also, simulations of two-dimensional mountain waves indicate that nonlinearities can increase the wave response if the lower layer is decoupled from the flow aloft or decrease the wave response by providing multiple reflection levels for the incident mountain wave. The onset of wavebreaking and the level at which the wave breaks can be influenced by the ambient thermodynamic profile.

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Gregory J. Tripoli and William R. Cotton

Abstract

This study employs a revised version of the Colorado State University three-dimensional numerical cloud scale model to investigate the observed behavior of deep convection over South Florida on 17 July 1973. A brief description of recent model improvements is made. A combined balance and dynamics initialization procedure designed to introduce variable magnitudes and distributions of low-level wind convergence to the initial fields is described.

Using radiosonde and PIBAL data collected by the NOAA/ERL Florida Area Cumulus Experiment (FACE) and the National Weather Service at Miami on 17 July 1973, composite wind, temperature, pressure and moisture profiles were constructed to depict the state of the atmosphere at the time of deep convection. Mesoscale convergence was estimated from results of a mesoscale model simulation of low-level sea breeze convergence made by Pielke (personal communication) for the same case study day. Several numerical simulations were performed using the sounding data as a basic state. The initial magnitude and distribution of low-level convergence was varied and the sensitivity of the model to some micro-physical parameters was examined.

The results of the numerical experiments show that (i) the magnitude of surface convergence over a finite area has a pronounced influence on the simulated storm circulation, the eddy kinetic energy of the storm and the total rainfall of the storm system; (ii) the horizontal distribution of convergence has a relatively large effect on the rates of entrainment into the updraft below 5 km MSL resulting in significant modulations in predicted precipitation, but only moderate changes in storm kinetic energy; (iii) variations in terminal velocity of precipitation associated with the introduction of the ice phase has only a minor effect on precipitation and total kinetic energy of the storm; and (iv) increased rain evaporation rates result in a moderate increase in the kinetic energy of the simulated storm, but at the expense of surface precipitation. Pressure forces are also shown to play an important role in initiating downdrafts and in biasing the direction of downdraft-associated outflow. Implications of these results to the modification of convective clouds are discussed.

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Gregory J. Tripoli and William R. Cotton

Abstract

A three-dimensional numerical simulation of an intense, quasi-steady left-moving thunderstorm observed over mountainous terrain is presented. The observational analysis of the evolution of convection leading to this storm is presented in Part I, and a detailed analysis of the Doppler radar-observed storm structure is presented in Parts II and III. This storm was particularly interesting because it initially grew in an environment characterized by terrain-induced boundary layer convergence before a massive mesoscale cold front passed underneath. The front cooled and moistened low levels while veering the surface winds to the north, creating a hodograph of winds strongly backing with height. After frontal passage the initial storm cell grew explosively and turned to the left.

The observed storm evolution after the frontal passage was reproduced well by the numerical simulation. An observed secondary updraft which was not simulated, was attributed to residual effects of the prefrontal environment, which was not considered. The overall success of this simulation led to the conclusion that the storm structure was largely governed by the environmental wind shear and was only weakly influenced by its triggering mechanism.

The microphysical structure was reproduced only moderately well. The model had the greatest difficulty in simulating the echo intensity. This is attributed to the characteristics of the assumed Marshall–Palmer graupel distribution. However, no apparent degrading effects on the dynamical structure were found as a result.

The dynamical structure compared well with that of right-moving cells described observationally and simulated numerically by a number of authors. In particular, it was found that the leftward movement was induced by pressure forces projected to low levels within an anticyclonically rotating updraft in approximate cyclostrophic balance. The rotation was produced by the tilting of horizontal voracity (associated with the wind shear) into the vertical and subsequent stretching.

Trajectory analysis of updraft and downdraft parcels revealed the existence of both entrainment and pressure-forced downdrafts. It is demonstrated that much of the vertical pressure gradient acceleration of parcels may be accounted for by pressure in approximate hydrostatic equilibrium with the mean density anomaly of the local environment surrounding the parcel.

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Gregory J. Tripoli and William R. Cotton

Abstract

The interaction of topographically induced thermally and mechanically driven diurnal flow regimes in the lee of the Rockies is shown to lead to the growth of a mesoscale convective system (MCS). An organic MCS observed during the 1977 combined South Park Area Cumulus Experiment and High Plains Experiment is numerically simulated with a two-dimensional nonhydrostatic cloud model covering spatial scales of 1000 km. In this numerical investigation,mesoγ-, mesoβ- and mesoα-scales of motion are represented simultaneously. As a result, interesting features of cloud-mesoscale interaction are predicted that cannot be represented in cloud parameterization frameworks. Based on the results of this simulation, a six-stage conceptual model of orogenic development is given.

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