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The formulation of a fully compressible nonhydrostatic atmospheric model called the Model for Prediction Across Scales–Atmosphere (MPAS-A) is described. The solver is discretized using centroidal Voronoi meshes and a C-grid staggering of the prognostic variables, and it incorporates a split-explicit time-integration technique used in many existing nonhydrostatic meso- and cloud-scale models. MPAS can be applied to the globe, over limited areas of the globe, and on Cartesian planes. The Voronoi meshes are unstructured grids that permit variable horizontal resolution. These meshes allow for applications beyond uniform-resolution NWP and climate prediction, in particular allowing embedded high-resolution regions to be used for regional NWP and regional climate applications. The rationales for aspects of this formulation are discussed, and results from tests for nonhydrostatic flows on Cartesian planes and for large-scale flow on the sphere are presented. The results indicate that the solver is as accurate as existing nonhydrostatic solvers for nonhydrostatic-scale flows, and has accuracy comparable to existing global models using icosahedral (hexagonal) meshes for large-scale flows in idealized tests. Preliminary full-physics forecast results indicate that the solver formulation is robust and that the variable-resolution-mesh solutions are well resolved and exhibit no obvious problems in the mesh-transition zones.

Kinetic energy (KE) spectra derived from global high-resolution atmospheric simulations from the Model for Prediction Across Scales (MPAS) are presented. The simulations are produced using quasi-uniform global Voronoi horizontal meshes with 3-, 7.5-, and 15-km mean cell spacings. KE spectra from the MPAS simulations compare well with observations and other simulations in the literature and possess the canonical KE spectra structure including a very-well-resolved shallow-sloped mesoscale region in the 3-km simulation. There is a peak in the vertical velocity variance at the model filter scale for all simulations, indicating the underresolved nature of updrafts even with the 3-km mesh. The KE spectra reveal that the MPAS configuration produces an effective model resolution (filter scale) of approximately 6Δx. Comparison with other published model KE spectra highlight model filtering issues, specifically insufficient filtering that can lead to spectral blocking and the production of erroneous shallow-sloped mesoscale tails in the KE spectra. The mesoscale regions in the MPAS KE spectra are produced without use of kinetic energy backscatter, in contrast to other results reported in the literature. No substantive difference is found in KE spectra computed on constant height or constant pressure surfaces. Stratified turbulence is not resolved with the vertical resolution used in this study; hence, the results do not support recent conjecture that stratified turbulence explains the mesoscale portion of the KE spectrum.

A solver for the nonhydrostatic deep-atmosphere equations of motion is described that extends the capabilities of the Model for Prediction Across Scales-Atmosphere (MPAS-A) beyond the existing shallow-atmosphere equations solver. The discretization and additional terms within this extension maintain the C-grid staggering, hybrid height vertical coordinate, and spherical centroidal Voronoi mesh used by MPAS, and also preserve the solver’s conservation properties. Idealized baroclinic wave test results, using Earth-radius and reduced-radius sphere configurations, verify the correctness of the solver and compare well with published results from other models. For these test cases, the time evolution of the maximum horizontal wind speed, and the total energy and its components, are presented as additional solution metrics that may allow for further discrimination in model comparisons. The test case solutions are found to be sensitive to the configuration of dissipation mechanisms in MPAS-A, and many of the differences among models in previously published test case solutions appear to arise because of their differing dissipation configurations. For the deep-atmosphere reduced-radius sphere test case, small-scale noise in the numerical solution was found to arise from the analytic initialization that contains unstable lapse rates in the tropical lower troposphere. By adjusting a parameter in this initialization, the instability is removed and the unphysical large-scale overturning no longer occurs. Inclusion of the deep-atmosphere capability in the MPAS-A solver increases the dry dynamics cost by less than 5% on CPU-based architectures, and configuration of either the shallow- or deep-atmosphere equations is controlled by a simple switch.

The role of vertical mesh spacing in the convergence of full-physics global atmospheric model solutions is examined for synoptic, mesoscale, and convective-scale horizontal resolutions. Using the MPAS-Atmosphere model, convergence is evaluated for three solution metrics: the horizontal kinetic energy spectrum, the Richardson number probability density function, and resolved flow features. All three metrics exhibit convergence in the free atmosphere for a 15-km horizontal mesh when the vertical grid spacing is less than or equal to 200 m. Nonconvergence is accompanied by noise, spurious structures, reduced levels of mesoscale kinetic energy, and reduced Richardson number peak frequencies. Coarser horizontal mesh solutions converge in a similar manner but contain much less noise than the 15-km solutions for coarse vertical resolution. For convective-scale resolution simulations with 3-km cell spacing on a variable-resolution mesh, solution convergence is almost attained with a vertical mesh spacing of 200 m. The boundary layer scheme is the dominant source of vertical filtering in the free atmosphere. Although the increased vertical mixing at coarser vertical mesh spacing depresses the kinetic energy spectra and Richardson number convergence, it does not produce sufficient dissipation to effectively halt scale collapse. These results confirm and extend the results from a number of previous studies, and further emphasize the sensitivity of the energetics to the vertical mixing formulations in the model.

A regional configuration of the atmospheric component of the Model for Prediction Across Scales (MPAS-A) is described and evaluated. It employs horizontally unstructured spherical centroidal Voronoi meshes (nominally hexagonal), and lateral boundary conditions used in rectangular grid regional models are adapted to the MPAS-A Voronoi mesh discretization. Test results using a perfect-model assumption show that the lateral boundary conditions are stable and robust. As found in other regional modeling studies, configurations using larger regional domains generally have smaller solution errors compared to configurations employing smaller regional domains. MPAS-A supports variable-resolution meshes, and when regional domains are expanded to include a coarser outer mesh, the variable-resolution configurations recover most of the error reduction compared to a configuration using uniform high resolution, and at much-reduced cost. The wider relaxation-zone region of the variable-resolution mesh also helps reconcile differences near the lateral boundary that evolve between the regional model solution and the driving solution, and the configuration is more stable than one using a uniform high-resolution regional mesh. At convection-permitting resolution, solutions produced using global variable-resolution MPAS-A configurations have smaller solution errors than the regional configurations after about 48 h.

Higher-order finite-volume flux operators for transport algorithms used within Runge–Kutta time integration schemes on irregular Voronoi (hexagonal) meshes are proposed and tested. These operators are generalizations of third- and fourth-order operators currently used in atmospheric models employing regular, orthogonal rectangular meshes. Two-dimensional least squares fit polynomials are used to evaluate the higher-order spatial derivatives needed to cancel the leading-order truncation error terms of the standard second-order centered formulation. Positive definite or monotonic behavior is achieved by applying an appropriate limiter during the final Runge–Kutta stage within a given time step. The third- and fourth-order formulations are evaluated using standard transport tests on the sphere. The new schemes are more accurate and significantly more efficient than the standard second-order scheme and other schemes in the literature examined by the authors. The third-order formulation is equivalent to the fourth-order formulation plus an additional diffusion term that is proportional to the Courant number. An optimal value for the coefficient scaling this diffusion term is chosen based on qualitative evaluation of the test results. Improvements using the higher-order scheme in place of the traditional second-order centered approach are illustrated within 3D unstable baroclinic wave simulations produced using two global nonhydrostatic models employing spherical Voronoi meshes.

Two time-splitting methods for integrating the elastic equations are presented. The methods are based on a third-order Runge-Kutta time scheme and the Crowley advection schemes. The schemes are combined with a forward-backward scheme for integrating high-frequency acoustic and gravity modes to create stable split-explicit schemes for integrating the compressible Navier-Stokes equations. The time-split methods facilitate the use of both centered and upwind-biased discretizations for the advection terms, allow for larger time steps, and produce more accurate solutions than existing approaches. The time-split Crowley scheme illustrates a methodology for combining any pure forward-in-time advection schemes with an explicit time-splitting method. Based on both linear and nonlinear tests, the third-order Runge-Kutta-based time-splitting scheme appears to offer the best combination of efficiency and simplicity for integrating compressible nonhydrostatic atmospheric models.

Results from aquaplanet experiments performed using the Model for Prediction across Scales (MPAS) hydrostatic dynamical core implemented within the Department of Energy (DOE)–NCAR Community Atmosphere Model (CAM) are presented. MPAS is an unstructured-grid approach to climate system modeling that supports both quasi-uniform and variable-resolution meshing of the sphere based on conforming grids. Using quasi-uniform simulations at resolutions of 30, 60, 120, and 240 km, the authors evaluate the performance of CAM-MPAS via its kinetic energy spectra, general circulation, and precipitation characteristics. By analyzing an additional variable-resolution simulation with grid spacing that varies from 30 km in a spherical, continental-sized equatorial region to 240 km elsewhere, the CAM-MPAS’s potential for use as a regional climate simulation tool is explored. Similar to other quasi-uniform aquaplanet simulations, tropical precipitation increases with resolution, indicating the resolution sensitivity of the physical parameterizations. Comparison with the finite volume (FV) dynamical core suggests a weaker tropical circulation in the CAM-MPAS simulations, which is evident in reduced tropical precipitation and a weaker Hadley circulation. In the variable-resolution simulation, the kinetic energy spectrum within the high-resolution region closely resembles the quasi-uniform 30-km simulation, indicating a robust simulation of the fluid dynamics. As suggested by the quasi-uniform simulations, the CAM4 physics behave differently in the high and low resolution regions. A positive precipitation anomaly occurs on the western edge of the high-resolution region, exciting a Gill-type response; this zonal asymmetry represents the errors incurred in a variable resolution setting. When paired with a multiresolution mesh, the aquaplanet test case offers an exceptional opportunity to examine the response of physical parameterizations to grid resolution.

In the Advanced Research Weather Research and Forecasting Model (ARW), versions 3.0 and earlier, advection of scalars was performed using the Runge–Kutta time-integration scheme with an option of using a positive-definite (PD) flux limiter. Large-eddy simulations of aerosol–cloud interactions using the ARW model are performed to evaluate the advection schemes. The basic Runge–Kutta scheme alone produces spurious oscillations and negative values in scalar mixing ratios because of numerical dispersion errors. The PD flux limiter assures positive definiteness but retains the oscillations with an amplification of local maxima by up to 20% in the tests. These numerical dispersion errors contaminate active scalars directly through the advection process and indirectly through physical and dynamical feedbacks, leading to a misrepresentation of cloud physical and dynamical processes. A monotonic flux limiter is introduced to correct the generally accurate but dispersive solutions given by high-order Runge–Kutta scheme. The monotonic limiter effectively minimizes the dispersion errors with little significant enhancement of numerical diffusion errors. The improvement in scalar advection using the monotonic limiter is discussed in the context of how the different advection schemes impact the quantification of aerosol–cloud interactions. The PD limiter results in 20% (10%) fewer cloud droplets and 22% (5%) smaller cloud albedo than the monotonic limiter under clean (polluted) conditions. Underprediction of cloud droplet number concentration by the PD limiter tends to trigger the early formation of precipitation in the clean case, leading to a potentially large impact on cloud albedo change.