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Patrick T. Haertel, David A. Randall, and Tommy G. Jensen

Abstract

A Lagrangian numerical model is used to simulate upwelling in an idealized large lake. This simulation is carried out to test the model's potential for simulating lake and ocean circulations.

The model is based on the slippery sack (SS) method that was recently developed by the authors. It represents the lake as a pile of conforming sacks. The motions of the sacks are determined using Newtonian dynamics. The model uses gravity wave retardation to allow for long time steps and has pseudo-Eulerian vertical mixing.

The lake is exposed to northerly winds for 29 h. Upwelling develops in the eastern edge of the basin, and after the winds shut off, upwelling fronts propagate around the lake. This case was previously simulated using a height- and sigma-coordinate ocean model. The SS model produces circulations that are similar to those produced by the other models, but the SS simulation exhibits less mixing.

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David A. Randall, Qingqiu Shao, and Chin-Hoh Moeng

Abstract

Bulk mass-flux models represent the large eddies that are primarily responsible for the turbulent fluxes in the planetary boundary layer as convective circulations, with an associated convective mass flux. In order for such models to be useful, it is necessary to determine the fractional area covered by rising motion in the convective circulations. This fraction can be used as an estimate of the cloud amount, under certain conditions. “Matching” conditions have been developed that relate the convective mass flux to the ventilation and entrainment mass fluxes. These are based on conservation equations for the scalar means and variances in the entrainment and ventilation layers. Methods are presented to determine both the fractional area covered by rising motion and the convective mass flux. The requirement of variance balance is used to relax the “well-mixed” assumption. The vertical structures of the mean state and the turbulent fluxes are determined analytically. Several aspects of this simple model's formulation are evaluated using results from large-eddy simulations.

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Max J. Suarez, Akio Arakawa, and David A. Randall

Abstract

A planetary boundary layer (PBL) parameterization for general circulation models (GCMs) is presented. It uses a mixed-layer approach in which the PBL is assumed to be capped by discontinuities in the mean profiles. Both clear and cloud-topped boundary layers are parameterized.

Particular emphasis is placed on the formulation of the coupling between the PBL and both the free atmosphere and cumulus convection. For this purpose a modified σ-coordinate is introduced in which the PBL top and the lower boundary are both coordinate surfaces. The use of a bulk PBL formulation with this coordinate is extensively discussed.

Results are presented from a July simulation produced by the UCLA GCM. PBL-related variables are shown, to illustrate the various regimes the parameterization is capable of simulating.

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Chin-Hoh Moeng, Shaohua Shen, and David A. Randall

Abstract

Within the stratus-topped boundary layer many physical processes are involved: longwave radiation cooling, entrainment, latent heating, surface heating, solar heating, drizzling, etc. How all processes combine to maintain the turbulence within the stratus-topped boundary layer remains an unsolved problem. The large-eddy simulation technique is used to examine the first four physical processes mentioned. First, the contribution of each physical process to the thermodynamic differences between the updraft and downdraft branches of turbulent circulations is examined through a conditional sampling. Second, these mean thermodynamic differences are shown to express well the vertical distributions of heat and moisture fluxes within stratus-topped boundary layers.

These provide a method to validate the process-partitioning technique. (This technique assumes that the net flux profile can be partitioned into different component-flux profiles according to physical processes and that each partitioned component flux is linear in height.) In this paper, the heat and moisture fluxes are process partitioned, and each component flux is found to contribute to the net flux in a way that is consistent with its corresponding process contribution to the mean thermodynamic differences between updrafts and downdrafts. Also, the net flux obtained by summing all component fluxes agrees well with that obtained directly from the large-eddy simulations.

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Ross P. Heikes, David A. Randall, and Celal S. Konor

Abstract

This paper discusses the generation of icosahedral hexagonal–pentagonal grids, optimization of the grids, how optimization affects the accuracy of finite-difference Laplacian, Jacobian, and divergence operators, and a parallel multigrid solver that can be used to solve Poisson equations on the grids. Three different grid optimization methods are compared through an error convergence analysis. The optimization process increases the accuracy of the operators. Optimized grids up to 1-km grid spacing over the earth have been created. The accuracy, performance, and scalability of the multigrid solver are demonstrated.

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Rachel R. McCrary, David A. Randall, and Cristiana Stan

Abstract

The relationship between African easterly waves and convection is examined in two coupled general circulation models: the Community Climate System Model (CCSM) and the “superparameterized” CCSM (SP-CCSM). In the CCSM, the easterly waves are much weaker than observed. In the SP-CCSM, a two-dimensional cloud-resolving model replaces the conventional cloud parameterizations of CCSM. Results show that this allows for the simulation of easterly waves with realistic horizontal and vertical structures, although the model exaggerates the intensity of easterly wave activity over West Africa. The simulated waves of SP-CCSM are generated in East Africa and propagate westward at similar (although slightly slower) phase speeds to observations. The vertical structure of the waves resembles the first baroclinic mode. The coupling of the waves with convection is realistic. Evidence is provided herein that the diabatic heating associated with deep convection provides energy to the waves simulated in SP-CCSM. In contrast, horizontal and vertical structures of the weak waves in CCSM are unrealistic, and the simulated convection is decoupled from the circulation.

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Todd D. Ringler, Ross P. Heikes, and David A. Randall

Abstract

This paper documents the development and testing of a new type of atmospheric dynamical core. The model solves the vorticity and divergence equations in place of the momentum equation. The model is discretized in the horizontal using a geodesic grid that is nearly uniform over the entire globe. The geodesic grid is formed by recursively bisecting the triangular faces of a regular icosahedron and projecting those new vertices onto the surface of the sphere. All of the analytic horizontal operators are reduced to line integrals, which are numerically evaluated with second-order accuracy. In the vertical direction the model can use a variety of coordinate systems, including a generalized sigma coordinate that is attached to the top of the boundary layer. Terms related to gravity wave propagation are isolated and an efficient semi-implicit time-stepping scheme is implemented. Since this model combines many of the positive attributes of both spectral models and conventional finite-difference models into a single dynamical core, it represents a distinctively new approach to modeling the atmosphere’s general circulation.

The model is tested using the idealized forcing proposed by Held and Suarez. Results are presented for simulations using 2562 polygons (approximately 4.5° × 4.5°) and using 10 242 polygons (approximately 2.25° × 2.25°). The results are compared to those obtained with spectral model simulations truncated at T30 and T63. In terms of first and second moments of state variables such as the zonal wind, meridional wind, and temperature, the geodesic grid model results using 2562 polygons are comparable to those of a spectral model truncated at slightly less than T30, while a simulation with 10 242 polygons is comparable to a spectral model simulation truncated at slightly less than T63.

In order to further demonstrate the viability of this modeling approach, preliminary results obtained from a full-physics general circulation model that uses this dynamical core are presented. The dominant features of the DJF climate are captured in the full-physics simulation.

In terms of computational efficiency, the geodesic grid model is somewhat slower than the spectral model used for comparison. Model timings completed on an SGI Origin 2000 indicate that the geodesic grid model with 10 242 polygons is 20% slower than the spectral model truncated at T63. The geodesic grid model is more competitive at higher resolution than at lower resolution, so further optimization and future trends toward higher resolution should benefit the geodesic grid model.

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Xin Lin, David A. Randall, and Laura D. Fowler

Abstract

The simulated diurnal cycle is in many ways an ideal test bed for new physical parameterizations. The purpose of this paper is to compare observations from the Tropical Rainfall Measurement Mission, the Earth Radiation Budget Experiment, the International Satellite Cloud Climatology Project, the Clouds and the Earth’s Radiant Energy System Experiment, and the Anglo-Brazilian Amazonian Climate Observation Study with the diurnal variability of the Amazonian hydrologic cycle and radiative energy budget as simulated by the Colorado State University general circulation model, and to evaluate improvements and deficiencies of the model physics. The model uses a prognostic cumulus kinetic energy (CKE) to relax the quasi-equilibrium closure of the Arakawa–Schubert cumulus parameterization. A parameter, α, is used to relate the CKE to the cumulus mass flux. This parameter is expected to vary with cloud depth, mean shear, and the level of convective activity, but up to now a single constant value for all cloud types has been used. The results of the present study show clearly that this approach cannot yield realistic simulations of both the diurnal cycle and the monthly mean climate state. Improved results are obtained using a version of the model in which α is permitted to vary with cloud depth.

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Rachel R. McCrary, David A. Randall, and Cristiana Stan

Abstract

The West African monsoon seasonal cycle is simulated with two coupled general circulation models: the Community Climate System Model (CCSM), which uses traditional convective parameterizations, and the “superparameterized” CCSM (SP-CCSM), in which the atmospheric parameterizations have been replaced with an embedded cloud-resolving model. Compared to CCSM, SP-CCSM better represents the magnitude and spatial patterns of summer monsoon precipitation over West Africa. Most importantly, the region of maximum precipitation is shifted from the Gulf of Guinea in CCSM (not realistic) to over the continent in SP-CCSM. SP-CCSM also develops its own biases—namely, excessive rainfall along the Guinean coast in summer. Biases in rainfall from both models are linked to a misrepresentation of the equatorial Atlantic cold tongue. Warm sea surface temperature (SST) biases are linked to westerly trade wind biases and convection within the intertropical convergence zone. Improved SST biases in SP-CCSM are linked to increased tropospheric warming associated with convection. A weaker-than-observed Saharan heat low is found in both models, which explains why the main band of precipitation does not penetrate as far northward as observed. The latitude–height position of the African easterly jet (AEJ) is comparable to observations in both models, but the meridional temperature and moisture gradients and the strength of the jet are too weak in SP-CCSM and too strong in CCSM. Differences in the AEJ are hypothesized to be influenced by the contrasting representation of African easterly waves in both models; no wave activity is found in CCSM, and strong waves are found in SP-CCSM.

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Stefan N. Tulich, David A. Randall, and Brian E. Mapes

Abstract

This paper describes an analysis of large-scale [O(1000 km)] convectively coupled gravity waves simulated using a two-dimensional cloud-resolving model. The waves develop spontaneously under uniform radiative cooling and approximately zero-mean-flow conditions, with wavenumber 2 of the domain appearing most prominently and right-moving components dominating over left-moving components for random reasons. The analysis discretizes the model output in two ways. First, a vertical-mode transform projects profiles of winds, temperature, and heating onto the vertical modes of the model’s base-state atmosphere. Second, a cloud-partitioning algorithm sorts sufficiently cloudy grid columns into three categories: shallow convective, deep convective, and stratiform anvil.

Results show that much of the tilted structures of the waves can be captured by just two main vertical spectral “bands,” each consisting of a pair of vertical modes. The “slow” modes have propagation speeds of 16 and 18 m s−1 (and roughly a full-wavelength vertical structure through the troposphere), while the “fast” modes have speeds of 35 and 45 m s−1 (and roughly a half-wavelength structure). Deep convection anomalies in the waves are more or less in phase with the low-level cold temperature anomalies of the slow modes and in quadrature with those of the fast modes. Owing to the characteristic life cycle of deep convective cloud systems, shallow convective heating peaks ∼2 h prior to maximum deep convective heating, while stratiform heating peaks ∼3 h after. The onset of deep convection in the waves is preceded by a gradual deepening of shallow convection lasting a period of many hours.

Results of this study are in broad agreement with simple two-mode models of unstable large-scale wave growth, under the name “stratiform instability.” Differences here are that 1) the key dynamical modes have speeds in the range 16–18 m s−1, rather than 23–25 m s−1 (owing to a shallower depth of imposed radiative cooling), and 2) deep convective heating, as well as stratiform heating, is essential for the generation and maintenance of the slow modes.

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