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Frank B. Lipps and Richard S. Hemler

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Frank B. Lipps and Richard S. Hemler

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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-Vsisälä 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.

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Frank B. Lipps and Richard S. Hemler

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A three-dimensional numerical model with warm rain bulk cloud physics is used to investigate the shallow convection observed on day 226 of GATE. This convection had cloud tops at 3.0 km, cloud bases at 0.4 km and approximately 0.1 cm of rain at the surface. The simulated convection shows a strong sensitivity to the criterion for the onset of autoconversion of cloud water into rain water. The strongest convection occurs for the case in which no rain water forms. This case, however, does not conform to the observed convection, lacking the downdraft below cloud base and the observed strong surface outflow.

The primary simulation produces a “finger” of convection propagating to the northeast, perpendicular to the northwest–southeast orientation of the larger-scale line of convection. The orientation and propagation speed of the calculated convection are in excellent agreement with observed radar data. This simulation also has a well-defined leading edge and strong surface outflow as observed. In poorer agreement, the cloud base was too high and the rainfall at the surface was less than observed.

Present calculations indicate that the boundary layer air is flowing through the line from southwest to northeast below cloud base. The primary moisture source for the cloud is the upper half of the subcloud layer, with nearly horizontal flow entering the cloud.

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Frank B. Lipps and Richard S. Hemler

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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.

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Frank B. Lipps and Richard S. Hemler

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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 moving faster than the line behind the gust front, the strong easterlies in the lower cloud levels, and the cold boundary layer behind the gust front.

Two-hour time means of the vertical momentum flux are calculated in a 60-km-wide domain (east–west) following the squall line. The vertical disturbance momentum flux for momentum normal to the line agrees with observations and is primarily confined to this region adjacent to the squall line. Horizontal-averaged time-mean momentum budgets are also calculated in this domain. For the normal component of momentum, this budget is in a quasi-steady state. It cannot be in a fully steady state as the gust front moves 1.2 m s−1 faster than the area of rain behind the line for the 2-h time mean.

The parameterization of Schneider and Lindzen for the vertical momentum flux associated with active clouds is compared with mean data from the simulation. Their parameterization accounts for the in-cloud vertical momentum flux reasonably well, but ignores the remaining flux associated with convective-scale downdrafts, which is significant in lower levels.

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Franik B. Lipps and Richard S. Hemler

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A scale analysis valid for deep moist convection is carried out. The approximate equations of motion are anelastic with the time scale set by the Brunt- Väisälä frequency. A new assumption is that the base state potential temperature is a slowly varying function of the vertical coordinate. It is this assumption that eliminates the energetic inconsistency discussed by Wilhelmson and Ogura (1972) for a non-isentropic base state. Another key result is that the dynamic pressure is an order of magnitude smaller than the first-order temperature and potential temperature. In agreement with observations, the kinetic energy is found to be an order of magnitude smaller than the first-order thermodynamic energy.

A set of six numerical simulations representing moderately deep moist convection is carried out. The base state is an idealized maritime tropical sounding with no vertical wind shear. The first calculation (Run A) shows the growth and dissipation of a typical shower cloud. The remaining calculations have small changes in either initial conditions or model equations from Run A. These calculations indicate the sensitivity of the present model to different approximations and give additional evidence for the validity of the scale analysis.

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Frank B. Lipps and Richard S. Hemler

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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 velocities in the rainy area below cloud base.

Time-mean data were also calculated for vertical velocity cores and compared with observed data. In run A, virtually all updraft cores are in-cloud and for a deep layer between 2.5 and 8.0 km the in-cloud up-ward mass flux is nearly all associated with cores. In this layer the upward mass flux due to cores is approximately twice the mass flux associated with the large-scale convergence. The fractional area of updraft cores is small, varying between 2.5% and 4.0% for vertical levels between 1 and 11 km. Calculated values of core diameter D̄ are in relatively good agreement with the observed data. For values of mean vertical velocity ¯ω, however, the agreement is not nearly as good. For downdraft cores, values of ¯ω, are significantly smaller than the observations. For updraft cores, values of ω at lower levels are small, whereas values in the upper levels are in reasonable agreement with observations. The weak updraft cores at lower levels may be related to the absence of strong gust fronts in the present simulations.

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Richard S. Hemler, Frank B. Lipps, and Bruce B. Ross

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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. Without the observed small-scale forcing, which was unresolved in the Severe Environmental Storms and Mesoscale Experiment (SESAME) dataset, the model is unable to generate the squall line until a larger-scale convergence area evolves, some 2–3 h after the appearance of the observed squall line.

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Brian J. Soden, Anthony J. Broccoli, and Richard S. Hemler

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Uncertainty in cloud feedback is the leading cause of discrepancy in model predictions of climate change. The use of observed or model-simulated radiative fluxes to diagnose the effect of clouds on climate sensitivity requires an accurate understanding of the distinction between a change in cloud radiative forcing and a cloud feedback. This study compares simulations from different versions of the GFDL Atmospheric Model 2 (AM2) that have widely varying strengths of cloud feedback to illustrate the differences between the two and highlight the potential for changes in cloud radiative forcing to be misinterpreted.

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Kevin Hamilton, R. John Wilson, and Richard S. Hemler

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The large-scale circulation in the Geophysical Fluid Dynamics Laboratory “SKYHI” troposphere–stratosphere–mesosphere finite-difference general circulation model is examined as a function of vertical and horizontal resolution. The experiments examined include one with horizontal grid spacing of ∼35 km and another with ∼100 km horizontal grid spacing but very high vertical resolution (160 levels between the ground and about 85 km). The simulation of the middle-atmospheric zonal-mean winds and temperatures in the extratropics is found to be very sensitive to horizontal resolution. For example, in the early Southern Hemisphere winter the South Pole near 1 mb in the model is colder than observed, but the bias is reduced with improved horizontal resolution (from ∼70°C in a version with ∼300 km grid spacing to less than 10°C in the ∼35 km version). The extratropical simulation is found to be only slightly affected by enhancements of the vertical resolution. By contrast, the tropical middle-atmospheric simulation is extremely dependent on the vertical resolution employed. With level spacing in the lower stratosphere ∼1.5 km, the lower stratospheric zonal-mean zonal winds in the equatorial region are nearly constant in time. When the vertical resolution is doubled, the simulated stratospheric zonal winds exhibit a strong equatorially centered oscillation with downward propagation of the wind reversals and with formation of strong vertical shear layers. This appears to be a spontaneous internally generated oscillation and closely resembles the observed QBO in many respects, although the simulated oscillation has a period less than half that of the real QBO.

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