Todd D. Ringler

A Multiscale Nonhydrostatic Atmospheric Model Using Centroidal Voronoi Tesselations and C-Grid Staggering

AbstractThe 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 acc...

A unified approach to energy conservation and potential vorticity dynamics for arbitrarily-structured C-grids

A numerical scheme applicable to arbitrarily-structured C-grids is presented for the nonlinear shallow-water equations. By discretizing the vector-invariant form of the momentum equation, the relationship between the nonlinear Coriolis force and the potential vorticity flux can be used to guarantee that mass, velocity and potential vorticity evolve in a consistent and compatible manner. Underpinning the consistency and compatibility of the discrete system is the construction of an auxiliary thickness equation that is staggered from the primary thickness equation and collocated with the vorticity field. The numerical scheme also exhibits conservation of total energy to within time-truncation error. Simulations of the standard shallow-water test cases confirm the analysis and show convergence rates between 1st- and 2nd-order accuracy when discretizing the system with quasi-uniform spherical Voronoi diagrams. The numerical method is applicable to a wide class of meshes, including latitude-longitude grids, Voronoi diagrams, Delaunay triangulations and conformally-mapped cubed-sphere meshes.

Modeling the Atmospheric General Circulation Using a Spherical Geodesic Grid: A New Class of Dynamical Cores

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 in...

Numerical representation of geostrophic modes on arbitrarily structured C-grids

A C-grid staggering, in which the mass variable is stored at cell centers and the normal velocity component is stored at cell faces (or edges in two dimensions) is attractive for atmospheric modeling since it enables a relatively accurate representation of fast wave modes. However, the discretization of the Coriolis terms is non-trivial. For constant Coriolis parameter, the linearized shallow water equations support geostrophic modes: stationary solutions in geostrophic balance. A naive discretization of the Coriolis terms can cause geostrophic modes to become non-stationary, causing unphysical behaviour of numerical solutions. Recent work has shown how to discretize the Coriolis terms on a planar regular hexagonal grid to ensure that geostrophic modes are stationary while the Coriolis terms remain energy conserving. In this paper this result is extended to arbitrarily structured C-grids. An explicit formula is given for constructing an appropriate discretization of the Coriolis terms. The general formula is illustrated by showing that it recovers previously known results for the planar regular hexagonal C-grid and the spherical longitude-latitude C-grid. Numerical calculation confirms that the scheme does indeed give stationary geostrophic modes for the hexagonal-pentagonal and triangular geodesic C-grids on the sphere.

Analysis of discrete shallow-water models on geodesic Delaunay grids with C-type staggering

The properties of C-grid staggered spatial discretizations of the shallow-water equations on regular Delaunay triangulations on the sphere are analyzed. Mass-conserving schemes that also conserve either energy or potential enstrophy are derived, and their features are analogous to those of the C-grid staggered schemes on quadrilateral grids. Results of numerical tests carried out with explicit and semi-implicit time discretizations show that the potential-enstrophy-conserving scheme is able to reproduce correctly the main features of large-scale atmospheric motion and that power spectra for energy and potential enstrophy obtained in long model integrations display a qualitative behavior similar to that predicted by the decaying turbulence theory for the continuous system.

Exploring a Multiresolution Modeling Approach within the Shallow-Water Equations

The ability to solve the global shallow-water equations with a conforming, variable-resolution mesh is evaluated using standard shallow-water test cases. While the long-term motivation for this study is the creation of a global climate modeling framework capable of resolving different spatial and temporal scales in differentregions,theprocessbeginswithananalysisoftheshallow-watersysteminordertobetterunderstand the strengths and weaknesses of the approach developed herein. The multiresolution meshes are spherical centroidal Voronoi tessellations where a single, user-supplied density function determines the region(s) of fine- and coarse-mesh resolution. The shallow-water system is explored with a suite of meshes ranging from quasi-uniform resolution meshes, where the grid spacing is globally uniform, to highly variable resolution meshes, where the grid spacing varies by a factor of 16 between the fine and coarse regions. The potential vorticity is found to be conserved to within machine precision and the total available energy is conserved to within a time-truncation error. This result holds for the full suite of meshes, ranging from quasi-uniform resolution and highly variable resolution meshes. Based on shallow-water test cases 2 and 5, the primary conclusion of this study is that solution error is controlled primarily by the grid resolution in the coarsest part of themodeldomain.Thisconclusionisconsistentwithresultsobtainedbyothers.Whenthesevariable-resolution meshes are used for the simulation of an unstable zonal jet, the core features of the growing instability are foundtobelargelyunchangedasthevariationinthemeshresolutionincreases.Themaindifferencesbetween the simulations occur outside the region of mesh refinement and these differences are attributed to the additional truncation error that accompanies increases in grid spacing. Overall, the results demonstrate support for this approach as a path toward multiresolution climate system modeling.

An Incremental Remapping Transport Scheme on a Spherical Geodesic Grid

Weather and climate models contain equations for transporting conserved quantities such as the mass of air, water, ice, and associated tracers. Ideally, the numerical schemes used to solve these equations should be conservative, spatially accurate, and monotonicity-preserving. One such scheme is incremental remapping, previously developed for transport on quadrilateral grids. Here the incremental remapping scheme is reformulated for a spherical geodesic grid whose cells are hexagons and pentagons. The scheme is tested in a shallow-water model with both uniform and varying velocity fields. Solutions for standard shallow-water test cases 1, 2, and 5 are obtained with a centered scheme, a flux-corrected transport (FCT) scheme, and the remapping scheme. The three schemes are about equally accurate for transport of the height field. For tracer transport, remapping is far superior to the centered scheme, which produces large overshoots, and is generally smoother and more accurate than FCT. Remapping has a high startup cost associated with geometry calculations but is nearly twice as fast as FCT for each added tracer. As a result, remapping is cheaper than FCT for transport of more than about seven tracers.

Projected Future Changes in Vegetation in Western North America in the Twenty-First Century

Rapid and broad-scale forest mortality associated with recent droughts, rising temperature, and insect outbreaks has been observed over western North America (NA). Climate models project additional future warming and increasing drought and water stress for this region. To assess future potential changes in vegetation distributions in western NA, the Community Earth System Model (CESM) coupled with its Dynamic Global Vegetation Model (DGVM) was used under the future A2 emissions scenario. To better span uncertainties in future climate, eight sea surface temperature (SST) projections provided by phase 3 of the Coupled Model Intercomparison Project (CMIP3) were employed as boundary conditions. There is a broad consensus among the simulations, despite differences in the simulated climate trajectories across the ensemble, that about half of the needleleaf evergreen tree coverage (from 24% to 11%) will disappear, coincident with a 14% (from 11% to 25%) increase in shrubs and grasses by the end of the twenty-first century in western NA, with most of the change occurring over the latter half of the twenty-first century. The net impact is a ;6 GtC or about 50% decrease in projected ecosystem carbon storage in this region. The findings suggest a potential for a widespread shift from tree-dominated landscapes to shrub and grass-dominated landscapesin westernNA becauseof future warmingandconsequentincreases in waterdeficits.These results highlight the need for improved process-based understanding of vegetation dynamics, particularly including mortality and the subsequent incorporation of these mechanisms into earth system models to better quantify the vulnerability of western NA forests under climate change.

Exploring a Global Multiresolution Modeling Approach Using Aquaplanet Simulations

AbstractResults 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 ...

Observed Scaling in Clouds and Precipitation and Scale Incognizance in Regional to Global Atmospheric Models

AbstractObservations of robust scaling behavior in clouds and precipitation are used to derive constraints on how partitioning of precipitation should change with model resolution. Analysis indicates that 90%–99% of stratiform precipitation should occur in clouds that are resolvable by contemporary climate models (e.g., with 200-km or finer grid spacing). Furthermore, this resolved fraction of stratiform precipitation should increase sharply with resolution, such that effectively all stratiform precipitation should be resolvable above scales of ~50 km. It is shown that the Community Atmosphere Model (CAM) and the Weather Research and Forecasting model (WRF) also exhibit the robust cloud and precipitation scaling behavior that is present in observations, yet the resolved fraction of stratiform precipitation actually decreases with increasing model resolution. A suite of experiments with multiple dynamical cores provides strong evidence that this “scale-incognizant” behavior originates in one of the CAM4 pa...