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.

Idealized simulations of the 15 May 2009 squall line from the Second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2) are evaluated in this study. Four different microphysical setups are used, with either single-moment (1M) or double-moment (2M) microphysics, and either hail or graupel as the dense (rimed) ice species. Three different horizontal grid spacings are used: Δx = 4, 1, or 0.25 km (with identical vertical grids). Overall, results show that simulated squall lines are sensitive to both microphysical setup and horizontal resolution, although some quantities (i.e., surface rainfall) are more sensitive to Δx in this study. Simulations with larger Δx are slower to develop, produce more precipitation, and have higher cloud tops, all of which are attributable to larger convective cells that do not entrain midlevel air. The highest-resolution simulations have substantially more cloud water evaporation, which is partly attributable to the development of resolved turbulence. For a given Δx, the 1M simulations produce less rain, more intense cold pools, and do not have trailing stratiform precipitation at the surface, owing to excessive rainwater evaporation. The simulations with graupel as the dense ice species have unrealistically wide convective regions. Comparison against analyses from VORTEX2 data shows that the 2M setup with hail and Δx = 0.25 km produces the most realistic simulation because (i) this simulation produces realistic distributions of reflectivity associated with convective, transition, and trailing stratiform regions, (ii) the cold pool properties are reasonably close to analyses from VORTEX2, and (iii) relative humidity in the cold pool is closest to observations.

The Radiative‐Convective Equilibrium Model Intercomparison Project (RCEMIP) is an intercomparison of multiple types of numerical models configured in radiative‐convective equilibrium (RCE). RCE is an idealization of the tropical atmosphere that has long been used to study basic questions in climate science. Here, we employ RCE to investigate the role that clouds and convective activity play in determining cloud feedbacks, climate sensitivity, the state of convective aggregation, and the equilibrium climate. RCEMIP is unique among intercomparisons in its inclusion of a wide range of model types, including atmospheric general circulation models (GCMs), single column models (SCMs), cloud‐resolving models (CRMs), large eddy simulations (LES), and global cloud‐resolving models (GCRMs). The first results are presented from the RCEMIP ensemble of more than 30 models. While there are large differences across the RCEMIP ensemble in the representation of mean profiles of temperature, humidity, and cloudiness, in a majority of models anvil clouds rise, warm, and decrease in area coverage in response to an increase in sea surface temperature (SST). Nearly all models exhibit self‐aggregation in large domains and agree that self‐aggregation acts to dry and warm the troposphere, reduce high cloudiness, and increase cooling to space. The degree of self‐aggregation exhibits no clear tendency with warming. There is a wide range of climate sensitivities, but models with parameterized convection tend to have lower climate sensitivities than models with explicit convection. In models with parameterized convection, aggregated simulations have lower climate sensitivities than unaggregated simulations.

An axisymmetric numerical model is used to evaluate the maximum possible intensity of tropical cyclones. As compared with traditionally formulated nonhydrostatic models, this new model has improved mass and energy conservation in saturated conditions. In comparison with the axisymmetric model developed by Rotunno and Emanuel, the new model produces weaker cyclones (by ;10%, in terms of maximum azimuthal velocity); the difference is attributable to several approximations in the Rotunno-Emanuel model. Then, using a single specification for initial conditions (with a sea surface temperature of 268C), the authors conduct model sensitivity tests to determine the sensitivity of maximum azimuthal velocity (y max ) to uncertain aspects of the modeling system. For fixed mixing lengths in the turbulence parameterization, a converged value of y max is achieved for radial grid spacing of order 1 km and vertical grid spacing of order 250 m. The fall velocity of condensate (V t ) changes y max by up to 60%, and the largest y max occurs for pseudoadiabatic thermodynamics (i.e., for V t . 10 m s 21 ). The sensitivity of y max to the ratio of surface exchange coefficients for entropy and momentum (C E /C D ) matches the theoretical result, y max ; (C E /C D ) 1/2 , for nearly inviscid flow, but simulations with increasing turbulence intensity show less dependence on C E /C D ; this result suggests that the effect of C E /C D is less important than has been argued previously. The authors find that y max is most sensitive to the intensity of turbulence in the radial direction. However, some settings, such as inviscid flow, yield clearly unnatural structures; for example, y max exceeds 110 m s 21 , despite a maximum observed intensity of ;70 m s 21 for this environment. The authors show that turbulence in the radial direction limits maximum axisymmetric intensity by weakening the radial gradients of angular momentum (which prevents environmental air from being drawn to small radius) and of entropy (which is consistent with weaker intensity by consideration of thermal wind balance). It is also argued that future studies should consider parameterized turbulence as an important factor in simulated tropical cyclone intensity.