The spatial resolution appropriate for the simulation of deep moist convection is addressed from a turbulence perspective. To provide a clear theoretical framework for the problem, techniques for simulating turbulent flows are reviewed, and the source of the subgrid terms in the Navier-Stokes equation is clarified. For decades, cloud-resolving models have used large-eddy simulation (LES) techniques to parameterize the subgrid terms. A literature review suggests that the appropriateness of using traditional LES closures for this purpose has never been established. Furthermore, examination of the assumptions inherent in these closures suggests that grid spacing on the order of 100 m may be required for the performance of cloud models to be consistent with their design. Based on these arguments, numerical simulations of squall lines were conducted with grid spacings between 1 km and 125 m. The results reveal that simulations with 1-km grid spacing do not produce equivalent squallline structure and evolution as compared to the higher-resolution simulations. Details of the simulated squall lines that change as resolution is increased include precipitation amount, system phase speed, cloud depth, static stability values, the size of thunderstorm cells, and the organizational mode of convective overturning (e.g., upright towers versus sloped plumes). It is argued that the ability of the higher-resolution runs to become turbulent leads directly to the differences in evolution. There appear to be no systematic trends in specific fields as resolution is increased. For example, mean vertical velocity and rainwater values increase in magnitude with increasing resolution in some environments, but decrease with increasing resolution in other environments. The statistical properties of the simulated squall lines are still not converged between the 250-and 125-m runs. Several possible explanations for the lack of convergence are offered. Nevertheless, it is clear that simulations with O(1 km) grid spacing should not be used as benchmark or control solutions for resolution sensitivity studies. The simulations also support the contention that a minimum grid spacing of O(100 m) is required for traditional LES closures to perform appropriately for their design. Specifically, only simulations with 250-and 125-m grid spacing resolve an inertial subrange. In contrast, the 1-km simulations do not even reproduce the correct magnitude or scale of the spectral kinetic energy maximum. Furthermore, the 1-km simulations contain an unacceptably large amount of subgrid turbulence kinetic energy, and do not adequately resolve turbulent fluxes of total water. A guide to resolution requirements for the operational and research communities is proposed. The proposal is based primarily on the intended use of the model output. Even though simulations with O(1 km) grid spacing display behavior that is unacceptable for the model design, it is argued that these simulations can still provide valuable information to operational forecasters. For the researc...
A benchmark solution that facilitates testing the accuracy, efficiency, and efficacy of moist nonhydrostatic numerical model formulations and assumptions is presented. The solution is created from a special configuration of moist model processes and a specific set of initial conditions. The configuration and initial conditions include: reversible phase changes, no hydrometeor fallout, a neutrally stable base-state environment, and an initial buoyancy perturbation that is identical to the one used to test nonlinearly evolving dry thermals. The results of the moist simulation exhibit many of the properties found in its dry counterpart. Given the similar results, and acceptably small total mass and total energy errors, it is argued that this new moist simulation design can be used as a benchmark to evaluate moist numerical model formulations. The utility of the benchmark simulation is highlighted by running the case with approximate forms of the governing equations found in the literature. Results of these tests have implications for the formulation of numerical models. For example, it is shown that an equation set that conserves both mass and energy is crucial for obtaining the benchmark solution. Results also suggest that the extra effort required to conserve mass in a numerical model may not lead to significant improvements in results unless energy is also conserved.
Enhanced infrared satellite imagery and conventional surface and sounding data are used to document the existence and climatological characteristics of mesoscale convective complexes (MCCs) over midlatitude South America (south of 20°S) and in the tropical region (20°N to 20°S) between North and South America. The implications of the results, with regard to the structure and dynamics of MCCs, are discussed. It is found that MCCs occur with approximately the same frequency in mid‐latitude South America as they do in mid‐latitude North America. For the most part the characteristics of mid‐latitude South American MCCs are similar to those of MCCs in the United States. The most notable difference between North and South American MCCs is that the South American systems are, on the average, about 60% larger than MCCs in the United States. In addition to the large population of mid‐latitude South American MCCs, an even larger number of low‐latitude (tropical) systems were found. In general, both the mid‐latitude and tropical populations of MCCs are nocturnal and continental; i.e., the great majority of systems occur at night over land. Of the systems that do occur over water, a significant fraction develop into tropical storms. Large populations of MCCs occur in each of the physiographically similar mid‐latitude areas of North and South America where low‐level nocturnal jets frequently develop. Very few MCCs occur over the Amazon River Basin or over the southeastern United States, even though both of these areas exhibit large amounts of deep convective activity. All of the various MCC population centers occur in latitudinal zones of westerlies or easterlies and are concentrated immediately downwind of major mountain ranges. One of the 2 years of data that was investigated was an El Niño year. During the El Niño period the number of mid‐latitude South American systems was more than double the number in the non‐El Niño year. Moreover, several MCCs formed over the anomalously warm water that appeared along the Peruvian coast. Thus on the basis of this very small sample, there may be a direct connection between MCC activity and El Niño.
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