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Development of an Atmospheric Climate Model with Self-Adapting Grid and Physics

J. E. Penner, M. Herzog, Q. Stout, B. van Leer, K. Powell, University of Michigan

Summary

One of the most important advances needed in global climate models is the development of models that can reliably treat convection. This project will result in a climate model that self-adjusts the grid resolution and the complexity of the physics model to the atmospheric flow conditions. To accomplish this, we expect to implement a fully 3-dimensional non-hydrostatic model within a hydrostatic climate model code while using a block-structured grid that allows for the implementation of smaller grid resolution within both the hydrostatic and non-hydrostatic portion of the grid.

The goal of this research project is to develop adaptive grid techniques for future climate model and weather prediction. This approach will lead to new insights into small-scale and large-scale flow interactions which are unresolved by current uniform grid approaches. Adaptive mesh refinement (AMR) techniques provide an attractive framework for atmospheric motions since they allow improved horizontal resolution in a limited region without requiring a fine grid resolution throughout the entire model domain. Therefore, the model domain to be resolved with higher resolution is kept at a minimum, greatly reducing computer memory and speed requirements.

Adaptive grid techniques are being applied to a parallel version of NASA's next generation climate model, the NASA/NCAR Finite-Volume Community Climate Model, which has been developed at the NASA Goddard Space Flight Center (GSFC, Data Assimilation Office). This global hydrostatic model is based on NCAR physics and the so-called Lin-Rood finite volume dynamical core that provides highly efficient algorithms for high performance computing.

This research project is characterized by an interdisciplinary approach involving atmospheric science, computer science and mathematical/numerical aspects. The work is done in close collaboration between the Atmospheric Science, Computer Science and Aerospace Engineering Departments at the University of Michigan and NASA/GSFC.

The adaptive version of the NASA finite volume dynamical core will be based on a reduced grid design near the polar regions. The main objective is to limit the Courant-Friedrich-Levy (CFL) numbers in both longitudinal and latitudinal directions. In addition to the advantage of polar coarsening to decrease time steps, this technique may allow the use of efficient polar filters. Polar filters are applied in order to stabilize high-frequency gravity waves that are unnecessarily resolved in polar regions. At present, the NASA finite volume dynamical core uses a global Fourier filtering mechanism that involves all data points in longitudinal direction. Since the revised 2D block-structured model does not provide this information without additional MPI communication the use of local polar filtering mechanisms is under investigation.

The reduced grid implementation makes use of a spherical adaptive grid library. This communication library for parallel processors is being developed in the Department of Computer Science at the University of Michigan. Choosing the right data structure in AMR applications is very important since it not only determines the algorithmic strategy but also the computational efficiency of the code. The adaptive data structure chosen here is based on the cache-efficient block-structured data layout. As refinement occurs the adaptive grid library maintains the adjacency information and provides functions to iterate through all of the blocks and to transfer the data efficiently between the blocks. Each block including its ghost region is an independent object. During each time step the atmospheric transport equations are solved block by block before ghost cell updates become necessary.

The library provides efficient load-balancing algorithms in order to optimize the distribution of blocks among the distributed memory processors. Additionally, OpenMP shared memory constructs can be used within a block, e.g. in the vertical direction.

In the original Lin and Rood algorithm, transport is treated with a 1D advective operator in one horizontal direction (say, the x-direction) followed by a 1D flux-form operator in other horizontal direction (the y-direction). In order to solve the transport equations for the non-hydrostatic code, flux form operators are required in both directions. Rather than changing operators at the boundary of the two regions, we have investigated using a flux form operator in both directions in the hydrostatic portion of the code.

Figure 2 shows a test of the transport scheme in the original Lin and Rood model and that proposed for use here. The test consisted of a solid body rotation of a guassian hill with a rotation angle of 45 degrees.

Figure 2. (a) Initialization field used to test transport schemes (b) flow field from the transport scheme in the original Lin and Rood (1997) code and (c) from applying a flux-form operator in each horizontal direction.

The results show that after 1 rotation of the initial Gaussian hill, the amplitude is slightly better preserved in the fully flux-form scheme. In addition, in the original Lin and Rood scheme, the signal is stretched along the direction of advection.

Our next step will be to add the adaptive block library to this new advective version and then to explore the addition of the non-hydrostatic code.

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