George H. Bryan

Resolution Requirements for the Simulation of Deep Moist Convection

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 research community, O(100 m) grid spacing is recommended for most applications, because a modeling system that is well founded should be desired for most purposes.

A benchmark simulation for moist nonhydrostatic numerical models

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.

Sensitivity of a Simulated Squall Line to Horizontal Resolution and Parameterization of Microphysics

Idealizedsimulations ofthe 15May2009 squalllinefromthe SecondVerification ofthe OriginsofRotation 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: Dx 5 4, 1, or 0.25 km (with identical vertical grids). Overall, results show that simulated squall lines are sensitive to both microphysical setupandhorizontalresolution,althoughsomequantities(i.e.,surfacerainfall)aremoresensitiveto Dxinthis study. Simulations with larger Dx 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 highestresolution simulations have substantially more cloud water evaporation, which is partly attributable to the development of resolved turbulence. For a given Dx, 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 Dx 5 0.25 km producesthemostrealisticsimulationbecause(i)thissimulationproducesrealisticdistributionsofreflectivity associatedwithconvective,transition,andtrailingstratiformregions,(ii)thecoldpoolpropertiesarereasonably close to analyses from VORTEX2, and (iii) relative humidity in the cold pool is closest to observations.

The Maximum Intensity of Tropical Cyclones in Axisymmetric Numerical Model Simulations

Abstract 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 26°C), the authors conduct model sensitivity tests to determine the sensitivity of maximum azimuthal velocity (υmax) to uncertain aspects of the modeling system. For fixed mixing lengths in the turbulence parameterization, a converged value of υmax is achieved for radial grid spacing of order 1 km and vertical grid spacing of order 250 m. The fall velocity of condensate (Vt) changes υmax by up to 60%, and the ...

The Bow Echo and MCV Experiment: Observations and Opportunities

The Bow Echo and Mesoscale Convective Vortex Experiment (BAMEX) is a research investigation using highly mobile platforms to examine the life cycles of mesoscale convective systems. It represents a combination of two related investigations to study (a) bow echoes, principally those that produce damaging surface winds and last at least 4 h, and (b) larger convective systems that produce long-lived mesoscale convective vortices (MCVs). The field phase of BAMEX utilized three instrumented research aircraft and an array of mobile ground-based instruments. Two long-range turboprop aircraft were equipped with pseudo-dual-Doppler radar capability, the third aircraft was a jet equipped with dropsondes. The aircraft documented the environmental structure of mesoscale convective systems (MCSs), observed the kinematic and thermodynamic structure of the convective line and stratiform regions (where rear-inflow jets and MCVs reside), and captured the structure of mature MCVs. The ground-based instruments augmented sou...

Mechanisms Supporting Long-Lived Episodes of Propagating Nocturnal Convection within a 7-Day WRF Model Simulation

Abstract A large-domain explicit convection simulation is used to investigate the life cycle of nocturnal convection for a one-week period of successive zonally propagating heavy precipitation episodes occurring over the central United States. Similar to climatological studies of phase-coherent warm-season convection, the longest-lived precipitation episodes initiate during the late afternoon over the western Great Plains (105°–100°W), reach their greatest intensity at night over the central Great Plains (100°–95°W), and typically weaken around or slightly after sunrise over the Midwest (95°–85°W). The longest-lived episodes exhibit average zonal phase speeds of ∼20 m s−1, consistent with radar observations during the period. Composite analysis of the life cycle of five long-lived nocturnal precipitation episodes indicates that convection both develops and then propagates eastward along an east–west-oriented lower-tropospheric frontal zone. An elevated ∼2-km-deep layer of high-θe air helps sustain convect...

Evaluation of an analytical model for the maximum intensity of tropical cyclones

Several studies have shown that the intensity of numerically simulated tropical cyclones can exceed (by 50%) a theoretical upper limit. To investigate the cause, this study evaluates the underlying components of Emanuel’s commonly cited analytic theory for potential intensity (herein referred to as E-PI). A review of the derivation of E-PI highlights three primary components: a dynamical component (gradient-wind and hydrostatic balance); a thermodynamical component (reversible or pseudoadiabatic thermodynamics, although the pseudoadiabatic assumption yields greater intensity); and a planetary boundary layer (PBL) closure (which relates the horizontal gradients of entropy and angular momentum at the top of the PBL to fluxes and stresses at the ocean surface). These three components are evaluated using output from an axisymmetric numerical model. The present analysis finds the thermodynamical component and the PBL closure to be sufficiently accurate for several different simulations. In contrast, the dynamical component is clearly violated. Although the balanced portion of the flow (yg, to which E-PI applies) appears to also exceed E-PI, it is shown that this difference is attributable to the method used to calculate yg from the model output. Evidence is shown that yg for a truly balanced cyclone does not exceed E-PI. To clearly quantify the impact of unbalanced flow, a more complete analytic model is presented. The model is not expressed in terms of external conditions and thus cannot be used to predict maximum intensity for a given environment; however, it does allow for evaluation of the relative contributions to maximum intensity from balanced and unbalanced (i.e., inertial) terms in the governing equations. Using numerical model output, this more complete model is shown to accurately model maximum intensity. Analysis against observations further confirms that the effects of unbalanced flow on maximum intensity are not always negligible. The contribution to intensity from unbalanced flow can become negligible in axisymmetric models as radial turbulence (i.e., viscosity) increases, and this explains why some previous studies concluded that E-PI was an accurate upper bound for their simulations. Conclusions of this study are also compared and contrasted to those from previous studies.

Moist Absolute Instability: The Sixth Static Stability State

It is argued that a sixth static stability state, moist absolute instability, can be created and maintained over mesoscale areas of the atmosphere. Examination of over 130 000 soundings and a numerical simulation of an observed event are employed to support the arguments in favor of the existence of moist absolutely unstable layers (MAULs). Although MAULs were found in many different synoptic environments, of particular interest in the present study are the deep (≥ 100 mb) layers that occur in conjunction with mesoscale convective systems (MCSs). A conceptual model is proposed to explain how moist absolute instability is created and maintained as MCSs develop. The conceptual model states that strong, mesoscale, nonbuoyancy-driven ascent brings a conditionally unstable environmental layer to saturation faster than small-scale, buoyancy-driven convective elements are able to overturn and remove the unstable state. Moreover, since lifting of a moist absolutely unstable layer warms the environment, the temper...

Explicit Numerical Diffusion in the WRF Model

Abstract Diffusion that is implicit in the odd-ordered advection schemes in early versions of the Advanced Research core of the Weather Research and Forecasting (WRF) model is sometimes insufficient to remove noise from kinematical fields. The problem is worst when grid-relative wind speeds are low and when stratification is nearly neutral or unstable, such as in weakly forced daytime boundary layers, where noise can grow until it competes with the physical phenomena being simulated. One solution to this problem is an explicit, sixth-order numerical diffusion scheme that preserves the WRF model’s high effective resolution and uses a flux limiter to ensure monotonicity. The scheme, and how it was added to the WRF model, are explained. The scheme is then demonstrated in an idealized framework and in simulations of salt breezes and lake breezes in northwestern Utah.

A Multimodel Assessment of RKW Theory’s Relevance to Squall-Line Characteristics

Abstract The authors evaluate whether the structure and intensity of simulated squall lines can be explained by “RKW theory,” which most specifically addresses how density currents evolve in sheared environments. In contrast to earlier studies, this study compares output from four numerical models, rather than from just one. All of the authors’ simulations support the qualitative application of RKW theory, whereby squall-line structure is primarily governed by two effects: the intensity of the squall line’s surface-based cold pool, and the low- to midlevel environmental vertical wind shear. The simulations using newly developed models generally support the theory’s quantitative application, whereby an optimal state for system structure also optimizes system intensity. However, there are significant systematic differences between the newer numerical models and the older model that was originally used to develop RKW theory. Two systematic differences are analyzed in detail, and causes for these differences ...