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A Geodesic Climate Model with Quasi-Lagrangian Vertical Coordinates

PI: David A. Randall
Todd D. Ringler, and Wayne H. Schubert (CSU)
Akio Arakawa (UCLA)
Albert J. Semtner, Jr. (Naval Postgraduate School)
Scott R. Fulton (Clarkson University)
John R. Baumgarder, Phillip W. Jones (LANL)

Summary

The goal of this research is to development a comprehensive model of the Earth’s climate using superior numerical and computational techniques. All components of this climate model employ spherical geodesic grids to tessellate the surface of the sphere. These grids cover the globe in a highly uniform and isotropic manner. Further, the atmosphere and ocean model components use quasi-Lagrangian vertical coordinates. These coordinates mimic the physical system where large-scale transport is predominately along material surfaces. The software that is being developed targets massively parallel architectures. The algorithms are written in a modular and hierarchal manner to expedite model development and portability. Comprehensive climate models, such as the one we are developing here, that target supercomputer architectures will be indispensable to the climate research community as we continue to analyze the natural variability of the climate system and assess the impact of anthroprogenic forcing.

We can loosely characterize a model of the Earth’s climate system as being composed of an atmosphere, a land-surface, an ocean, and sea-ice. Each of these climate system components span three spatial directions; two directions extend along the surface of the sphere and the third direction points toward the local vertical. When we attempt to model the continuous climate system using numerical models, we are forced to assign discrete nodes to represent patches of space. The climate modeling community is still trying to determine how to best distribute these nodes in space. For instance, what is the optimal distribution of nodes to cover, or tessellate, the surface of the sphere? Furthermore, what is the optimal method to model the highly-stratified vertical direction of the atmosphere and ocean? It has been demonstrated that the quality of the simulation and the numerical efficiency of the algorithms are strongly dependent on the choice of the horizontal tessellation and the vertical tessellation.

All the model components utilize spherical Voronoi tessellations to span the surface of the sphere. These grids are generated by recursively bisecting an icosahedron inscribed to a sphere. This procedure results in a grid that covers the sphere in a highly uniform manner. The finite-difference operator representing the divergence, curl, and gradient operators have been tested extensively over the last twelve-month period. These finite-difference operators show a high level of consistency with their continuous counterparts and are sufficiently accurate to proceed forward. Discrete forms of higher-order operators, such as the stress tensor, that are required in the sea-ice model have been developed and are currently being analyzed. A monotone advection scheme for the transport of mass and per-unit mass scalar fields, such as ocean salt or atmospheric water vapor, has been developed for use with this grid system. We currently have a full physics atmospheric general circulation model that uses the spherical Voronoi grid. Furthermore, we have a prototype ocean model that is also situated on this grid.

As opposed to the horizontal directions, the vertical direction of the atmosphere and ocean is characterized by a relatively high level of stratification. Stated alternatively, the basic state of the atmosphere and ocean show more rapid change when moving in the vertical direction than in the horizontal direction. The numerical diffusion and numerical dispersion that are associated with transport algorithms can erroneously mix quantities in the vertical direction. One technique to mitigate this problem is to allow the vertical nodes to move with the fluid as material surfaces. This greatly reduces, and sometimes completely eliminates, excessive numerical transport between nodes. Both the atmosphere and ocean models are testing prototypes of this technique to reduce numerical transport between nodes.

In addition to developing new algorithms for the spatial discretization, we are also developing software to facilitate the time-integration of the model components. We have developed a time-integration facility that is component-independent and will abstract the complexity of time-integration into a single algorithm. We have also developed an algorithm, called a "coupler", to allow the climate components to communicate in a computationally efficient manner on massively parallel architectures.

We continue to search for collaborators to facilitate the development of this comprehensive climate model. We have initiated collaborations with two other SciDAC projects: the TSTT project with Patrick Knupp as the point of contact and the TOPS project with Tom Manteuffel as the point of contact.

A component of the TSTT project is the development of a robust grid optimization algorithm (MESQUITE). Starting from our unmodified grid, Knupp and colleagues applied various grid-smoothing techniques in an attempt to further improve our horizontal discretization. The results of this work will be presented at the SIAM conference at San Diego in February.

A part of the TOPS project is to provide to the community efficient PDE solvers. The numerical algorithms we are pursing require the inversion of elliptic operators at every time step in the integration. This type of PDE is amiable to multi-grid methods; the TOPS project includes many experts in multi-grid methods. While this collaboration is still forming, we expect to make use of the TOPS project algorithms in our model development.

Furthermore, our search for collaborators is not strictly limited to other SciDAC projects. We have completed a productive collaboration with Chris Ding from LLNL who developed an algorithm to facilitate the registration and communication between model components. This software is called Model Program Handshake (MPH) and it is now a part of our software development library. In addition, we are staying abreast of the Earth System Modeling Framework project.

We continue to make steady progress towards our goal of delivering a comprehensive climate model to DOE by the end of this project. Such a large undertaking that targets the rapidly changing supercomputer architectures requires the development of basic library-level numerical algorithms. We are obtaining these algorithms from external sources when possible. We expect that over the next year we will complete the assembly of each component and begin the testing of the entire coupled system. In addition to solving the scientific problems that this coupling will surely present, we will increasingly focus on algorithm optimization.

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