Ross Heikes

Numerical Integration of the Shallow-Water Equations on a Twisted Icosahedral Grid. Part I: Basic Design and Results of Tests

Abstract The streamfunction-velocity potential form of shallow-water equations, implemented on a spherical geodesic grid, offers an attractive solution to many of the problems associated with fluid-flow simulations in a spherical geometry. Here construction of a new type of spherical geodesic grid is outlined, and discretization of the equations is explained. The model is subjected to the NCAR suite of seven test cases for shallow-water models.

Numerical Integration of the Shallow-Water Equations on a Twisted Icosahedral Grid. Part II. A Detailed Description of the Grid and an Analysis of Numerical Accuracy

Abstract The finite-difference scheme for the Laplace and flux-divergence operators described in the companion paper (Part I) is consistent when applied on a grid consisting of perfect hexagons. The authors describe a necessary and sufficient condition for this finite-difference scheme to be consistent when applied on a grid consisting of imperfect hexagons and pentagons, and present an algorithm for generating a spherical geodesic grid on a sphere that guarantees that this condition is satisfied. Also, the authors qualitatively describe the error associated with the operators and estimate their order of accuracy when applied on the new grid.

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...

Climate modeling with spherical geodesic grids

A new approach to climate simulation uses geodesic grids generated from an icosahedron and could become on attractive alternative to current models. We implemented an atmospheric general circulation model using a geodesic discretization of the sphere. Our model uses the message-passing interface and runs efficiently on massively parallel machines.

FDTD modeling of a novel ELF Radar for major oil deposits using a three-dimensional geodesic grid of the Earth-ionosphere waveguide

This paper reports the first application of an optimized geodesic, three-dimensional (3-D) finite-difference time-domain (FDTD) grid to model impulsive, extremely low-frequency (ELF) electromagnetic wave propagation within the entire Earth-ionosphere cavity. This new model, which complements our previously reported efficient 3-D latitude-longitude grid, is comprised entirely of hexagonal cells except for a small, fixed number of pentagonal cells. Grid-cell areas and locations are optimized to yield a smoothly varying area difference between adjacent cells, thereby maximizing numerical convergence. Extending from 100 km below sea level to an altitude of 100 km, this technique can accommodate arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities/anisotropies of the excitation, ionosphere, lithosphere, and oceans. We first verify the global model by comparing the FDTD-calculated daytime ELF propagation attenuation with data reported in the literature. Then as one example application of this grid, we illustrate a novel ELF radar for major oil deposits.

Optimized Icosahedral Grids: Performance of Finite-Difference Operators and Multigrid Solver

AbstractThis paper discusses the generation of icosahedral hexagonal–pentagonal grids, optimization of the grids, how optimization affects the accuracy of finite-difference Laplacian, Jacobian, and divergence operators, and a parallel multigrid solver that can be used to solve Poisson equations on the grids. Three different grid optimization methods are compared through an error convergence analysis. The optimization process increases the accuracy of the operators. Optimized grids up to 1-km grid spacing over the earth have been created. The accuracy, performance, and scalability of the multigrid solver are demonstrated.

Efficient data IO for a Parallel Global Cloud Resolving Model

Execution of a Global Cloud Resolving Model (GCRM) at target resolutions of 2-4 km will generate, at a minimum, 10s of Gigabytes of data per variable per snapshot. Writing this data to disk, without creating a serious bottleneck in the execution of the GCRM code, while also supporting efficient post-execution data analysis is a significant challenge. This paper discusses an Input/Output (IO) application programmer interface (API) for the GCRM that efficiently moves data from the model to disk while maintaining support for community standard formats, avoiding the creation of very large numbers of files, and supporting efficient analysis. Several aspects of the API will be discussed in detail. First, we discuss the output data layout which linearizes the data in a consistent way that is independent of the number of processors used to run the simulation and provides a convenient format for subsequent analyses of the data. Second, we discuss the flexible API interface that enables modelers to easily add variables to the output stream by specifying where in the GCRM code these variables are located and to flexibly configure the choice of outputs and distribution of data across files. The flexibility of the API is designed to allow model developers to add new data fields to the output as the model develops and new physics is added. It also provides a mechanism for allowing users of the GCRM code to adjust the output frequency and the number of fields written depending on the needs of individual calculations. Third, we describe the mapping to the NetCDF data model with an emphasis on the grid description. Fourth, we describe our messaging algorithms and IO aggregation strategies that are used to achieve high bandwidth while simultaneously writing concurrently from many processors to shared files. We conclude with initial performance results.

Modeling Rossby Wave Breaking in the Southern Spring Stratosphere

AbstractRossby wave breaking (RWB) plays a central role in the evolution of stratospheric flows. The generation and evolution of RWB is examined in the simple dynamical framework of a one-layer shallow-water system on a sphere. The initial condition represents a realistic, zonally symmetric velocity profile corresponding to the springtime southern stratosphere. Single zonal wavenumber Rossby waves, which are either stationary or traveling zonally with realistic speeds, are superimposed on the initial velocity profile. Particular attention is placed on the Lagrangian structures associated with RWB. The Lagrangian analysis is based on the calculation of trajectories and the application of a diagnostic tool known as the “M” function. Hyperbolic trajectories (HTs), produced by the transverse intersections of stable and unstable invariant manifolds, may yield chaotic saddles in M. Previous studies associated HTs with “cat’s eyes” generated by planetary wave breaking at the critical levels. HTs, and hence RWB, ...

3-D FDTD modeling of ULF/ELF propagation within the global Earth-ionosphere cavity using an optimized geodesic grid

We discuss an emerging application of finite-difference time-domain (FDTD) computational electrodynamics: modeling transient ultra-low frequency (ULF) and extremely low frequency (ELF) propagation within the global Earth-ionosphere cavity. This permits for the first time a direct, three-dimensional, time-domain calculation of round-the-world ULV/ELF propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities and anisotropies of the excitation, ionosphere, lithosphere, and oceans.

A Flexible Atmospheric Modeling Framework for the CESM

We have created two global dynamical cores based on the unified system of equations and Z-grid staggering on an icosahedral grid, which are collectively called UZIM (Unified Z-grid Icosahedral Model). The z-coordinate version (UZIM-height) can be run in hydrostatic and nonhydrostatic modes. The sigma-coordinate version (UZIM-sigma) runs in only hydrostatic mode. The super-parameterization has been included as a physics option in both models. The UZIM versions with the super-parameterization are called SUZI. With SUZI-height, we have completed aquaplanet runs. With SUZI-sigma, we are making aquaplanet runs and realistic climate simulations. SUZI-sigma includes realistic topography and a SiB3 model to parameterize the land-surface processes.