Continuous Dynamic Grid Adaptation in a Global Atmospheric Model

Joseph M. Prusa and William J. Gutowski
Iowa State University
Ames, IA 50011

Summary

The purpose of this project is to develop and advance the use of continuous grid adaptation in global atmospheric models. Such adaptation allows global models to continuously adjust their computational grid (by deforming in time and space) to focus resolution in selected regions of interest. In particular, this capability for grid adaptation allows local enhancements of accuracy by up to an order of magnitude compared to uniform grids with the same overall number of nodes. Grid adaptation may offer the best hope for the climate modeling and forecasting community to (i) reach kilometer, cloud resolving resolution (in selected mesoscale to regionally sized domains) and (ii) improve the predictions of climate statistics in the next 5-15 years.

Astonishing progress in numerical solvers and computational hardware/software during the past two decades have finally made realistic three dimensional transient climate simulations feasible. However, difficulties with boundary and initial conditions (which can have global impact on computed solutions), grid resolution (a few million nodes distributed around the globe results only in horizontal resolutions of hundreds of km), and sub-grid-scale physics (turbulence models, soil-vegetation processes, air/sea interface exchange, and so on), limit the accuracy that may be obtainable with available resources.

Global models with resolutions ~10 km (several times beyond current state of the art using modern solvers and highly parallel machines) require approximately 1000 times the computational power that is required at ~100 km resolution. This scale just barely begins to resolve important weather features like tropical storms. Even higher resolutions of ~ 1 km - necessary to more fully resolve these features would require another 1000 fold increase in computational power. During the next 15 years, although we may anticipate a factor of 1000 increase in computational power, we may be very hard pressed to reach a uniform global resolution of one kilometer.

In this study, we are continuing development and implementation of a coordinate transformation technique for the computational model Eulag (initially developed by Dr. Piotr Smolarkiewicz, NCAR – Eulag has been used successfully for simulations in engineering, oceanic, atmospheric, and even solar applications) that enables migration of computational grid points from regions of low interest (e.g., calm conditions) to high interest (e.g., severe weather systems). Due to this transformation, our computational model is able to accommodate global or regional simulations with equal facility.

The model–code has been written in a generalized form suitable for computation on a number of independent as well as parallelizable hardware platforms. Recently, we have successfully simulated idealized, global climates using the code in multi-processor mode on the IBM SP Blackforest supercomputer at the National Center for Atmospheric Research (NCAR). We have also run the code in single processor mode on Linux workstations at Iowa State University. Depending upon the example application, use of multiple processors has allowed speedups of from 10 to 100 times compared to the computational times required using a single processor.

At the present time, the coordinate transformation has been rigorously implemented throughout the dynamical core of Eulag and tested using an idealized "Held-Suarez" climate. For these tests we have developed a set of analytically specified transformations that focus grid adaptation into selected regions of interest. Recent results also include a numerical 1D grid generator that is built out of the nonoscillatory, forward in time (NFT) advection schemes that form the backbone of Eulag. We successfully used it to simulate a traveling gravity-wave packet by focusing a localized region of high grid point resolution around the packet. This type of grid generator has significant potential to be much faster and more robust than the more traditional (elliptic) type grid generators currently in use throughout much of the engineering and scientific community.

In addition to the global atmospheric simulations that are the core of our study, as a direct result of our collaborative efforts several other applications are now underway that were not previously possible. These include ocean basin climate simulations by Smolarkiewicz at NCAR, atmospheric simulations with time variable upper boundaries by N. P. Wedi at ECMWF, and aircraft wing vortex simulations by A. Dornbrack at DLR. What the coordinate transformation enables in each of these studies is (i) irregularly shaped boundaries that more realistically simulate ocean domains, (ii) more physically realistic upper boundaries such as constant pressure surfaces in atmospheric and ocean simulations, and (iii) grid adaptation near the core of vortices.

The future utility of our efforts resides in the scalability of our code in massively parallel environments as much as it depends upon the particular mathematical and physical merits of our model and NFT algorithms. Continued collaborations with A. A. Wyszo-grodzki (who produced the parallelized, multi-platform version of Eulag) at LANL provide the resource for us to continue to pursue these scalability issues. NCAR continues to provide massively parallel platforms for us to compute with, both on Blackforest – and on the new machine Bluesky. With peak computational speeds of approximately 2 and 6 teraflops, respectively, these hardware resources are sufficient for the duration of the project.

Current and near-term work consists of:

1. Generalizing the advective generator to a 2D form suitable for tracking multiple regions of interest.
2. Ongoing collaborations with Smolarkiewicz at NCAR to extend the transformation to the viscous and diagnostic routines.
3. Examining direct effects of gravity-waves on the general circulation of the atmosphere.
4. Examining–maintaining–improving the conservation properties of the model– code.
5. Ongoing collaborations with Wyszo-grodzki at LANL on increasing multi-processor scalability.
6. Establishing the multiprocessing capability of the code on the Linux cluster at ISU.

For further information on this subject contact:
Dr. David Bader, Program Manager
Climate Change Prediction Program
Office of biological and Environmental Research
Phone: 301-903-5329
dave.bader@science.doe.gov

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