Frank B. Lipps

Numerical Simulation of Deep Tropical Convection Associated with Large-Scale Convergence

Abstract A set of four-hour simulations has been carried out to study deep moist convection characteristic of the Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment (GATE). The present model includes warm rain bulk cloud physics and effects associated with a large-scale, time-invariant convergence. The convection took approximately two hours to develop from a random moisture disturbance. The cloud efficiency, in terms of the total water vapor condensed, was near 40%. The heat and moisture budgets and the time–mean vertical fluxes of mass, heat, and moisture were calculated for the last 80 minutes of the simulations. In this study the primary emphasis was placed upon run A, the three-dimensional calculation. For this calculation, the layer centered near 4.0 km was a region of low mean cloudiness but of strong convection. The upward mass flux was strong and upward heat and moisture fluxes had maximum values in this layer. The strongest downward mass flux was due to weak downward velocit...

On the Anelastic Approximation for Deep Convection

Abstract A brief review of the scale analysis of Lipps and Hemler is given without any reference to the parameters G and B. The resulting anelastic equations conserve energy, in contrast to the modified anelastic set of equations analyzed by Durran. In addition, the present equations give an accurate solution for the frequency of gravity waves in an isothermal atmosphere. The present anelastic equations have these characteristics in common with the pseudo-incompressible equations introduced by Durran. The equations obtained from the scale analysis are appropriate for numerical integration of deep convection. The associated Poisson equation can be solved using standard procedures. For the pseudo-incompressible set of equations, the Poisson equation is more difficult to solve.

Some Results from a Simplified Three-Dimensional Numerical Model of Atmospheric Turbulence

Abstract A simplified set of subgrid-scale transport equations is used to compute the stresses in a three-dimensional model of thermal convection in the atmosphere. Terms appearing in the full transport equations thought not to be essential to the large-scale dynamics are discarded, leaving prognostic equations to be solved for the subgrid-scale energy and the virtual potential temperature variance only. Equations for the Reynolds stresses and the subgrid-scale temperature-velocity correlations are considerably simplified and can be solved algebraically. A scale analysis of the full transport equations is offered as partial justification for the present approach in the case of nearly isotropic turbulence. The problem studied is that of a well-mixed layer bounded above by a region of strong stable stratification. The present model gives a significant improvement in the representation of the large-scale variables as compared with the more conventional eddy viscosity approach. In three experiments testing di...

BAROTROPIC STABILITY AND TROPICAL DISTURBANCES

Abstract This paper attempts to determine under what conditions horizontal shear in the mean zonal flow can provide the initial source of energy for the traveling disturbances of low latitudes. A three-zone barotropic model is constructed in order to examine the stability of an idealized mean zonal current. The width and total wind shear associated with this mean current are varied. The form of growing disturbances and their amplification rates are found. A stability analysis is also carried out for a basic flow which has a hyperbolic tangent variation with latitude. Results obtained by numerical integration for this basic flow are similar to those found previously with the three-zone model. In discussing his easterly wave model, Yanai indicates a basic flow which has a total wind shear of about 8 m sec–1 occurring over approximately 6° of latitude. Results obtained for a basic flow with these characteristics show that the fastest growing wave has a wavelength near 2500 km and an e-folding time of about 7...

A Study of Turbulence Parameterization in a Cloud Model

Abstract A diagnostic second-order turbulence parameterization has been incorporated into a shallow anelastic three-dimensional numerical cloud model. The turbulence closure scheme for the subgrid-scale motions includes the effects of buoyancy, condensation and liquid water drag. This model has been used to study trade wind cumuli which are roughly 1200 m thick. The simulated cloud has many features in common with observed clouds (Malkus, 1954); however, the observed clouds are made up of several thermal elements instead of one as in the numerical simulation, and they persist over a much longer time period. When comparing the present model with another using deformation eddy viscosity, the following results are obtained: 1) The deformation model has a larger smoothing effect on the horizontally averaged potential temperature and water vapor mixing ratio. 2) Early in the clouds development, the subgrid-scale kinetic energy is larger than the computed-scale kinetic energy. At the mature stage, the subgrid-...

A Simulation of a Squall Line Using a Nonhydrostatic Cloud Model with a 5-km Horizontal Grid

Abstract A three-dimensional nonhydrostatic cloud model is used to simulate the squall line observed in central Texas on 11 April 1979. The cloud model covers an area 400 × 400 km2 with a 5-km horizontal resolution and is supplied initial and boundary conditions by a larger hydrostatic mesoscale model. The model produces a back-building squall line ahead of the surface cold front, as would be expected based on an analysis of the pre-squall-line environment. A well-defined gust front and cold pool develop with the squall line. At the end of the 5-h simulation, deep convection is found along a line nearly 400 km long. The simulated squall line compares favorably both with observations and with a higher-resolution model simulation in an environment of similar shear, suggesting that the 5-km horizontal resolution is adequately representing the significant features of the squall line. The major shortcoming of this study is the failure of the cloud model to produce the observed squall line at the proper time. W...

Another Look at the Thermodynamic Equation For Deep Convection

Abstract The study considers deep moist convection involving only a liquid-vapor phase change. An alternative form of the classical thermodynamic equation for reversible saturated flow is derived. Four approximate forms of this equation are obtained and their relative errors compared to the full equation are evaluated by using parcel theory. The best approximation is found to be an adequate representation of the full equation throughout the total depth of the convection. The two best approximations are compared with some forms of the thermodynamic equation used by other investigators.

Another Look at the Scale Analysis for Deep Moist Convecton

Abstract In this note, a more rational approach is given to specify the parameters G and B in the scale analysis of Lipps and Hemier. The thermodynamic equation is written in a different form so that a closed expression for B can be derived. The present values of G and B are very similar to those in the previous scale analysis. A new result is that the time scale is expressed in terms of the moist convective instability rather than the inverse of the Brunt-Vsisala frequency. The ratio of volume integrated kinetic energy to volume integrated first-order sensible heat is also discussed in more detail. It is found that for an accurate estimate of sensible beat the region of compensating downward motion between the active clouds must be taken into account. As indicated by earlier authors, the amount of sensible heat produced inside the clouds is relatively small.

Numerical Modeling of a Midlatitude Squall Line: Features of the Convection and Vertical Momentum Flux

Abstract A 4-h simulation is carried out for the 22 May 1976 squall line that passed through the mesonetwork of the National Severe Storm Laboratory in central Oklahoma. This squall line was more than 100 km wide, oriented north-south and traveled eastward at approximately 14 m s−1. It produced rainfall of 2-h duration at surface stations. The simulation was obtained from a three-dimensional convective cloud model with open lateral boundary conditions on the east and west, and periodic conditions on the north and south boundaries. The model domain is 96 km long (east–west) and 32 km wide (north-south) with a horizontal grid resolution of 1.0 km and a vertical resolution of 0.5 km. A squall line develops and moves eastward at 13.7 m s−1 during the last two hours of the simulation. The present mesoγ-scale model, however, can only simulate the leading edge of the squall line, with rain at specific surface locations lasting only 30 min. Realistic features of the modeled flow include the surface westerlies mov...

On the downward transfer of tritium to the ocean by a cloud model

Observational evidence analyzed by Eriksson [1965] and Weiss and Roether [1980] suggests that over the globe the ratio of tritium deposition into the ocean by vapor diffusion to that by rainfall should be near or slightly greater than two, while Koster et al. [1989] found in a general circulation model study that the diffusion to rainout ratio was closer to one. This study investigates the convective transport of tritium from the atmosphere to the ocean using a two-dimensional warm-rain cloud model. It is found that the deposition ratio is strongly dependent on the frequency and duration of rain events, with typical values for a monotonic tritium profile being about 1.0, but with values as low as 0.7 when long-duration events occur frequently and as high as 1.9 when convective events are short-lived and infrequent. On the basis of this study it appears that explicit treatment of convection in the general circulation model would not resolve the discrepancy in the deposition ratio between the model and the observations. It is also shown that the process of isotopic adjustment of tritium between the rain and the vapor phases is a key factor in determining the deposition ratio, since this process allows tritium to escape from the raindrops and ultimately diffuse to the surface. When tritium is “frozen” in the droplets, deposition ratios are reduced significantly.