Continuous Dynamic Grid Adaptation in a Global Atmospheric Model

J.M. Prusa and W.J. Gutowski, Iowa State University

Summary

1. Introduction

State of the art global models are just beginning to approach resolutions ~10 km. Yet this scale only begins to resolve important weather features like tropical storms. Even higher resolutions of ~ 1 km and less – necessary to more fully resolve these features – would require more than a 1000 fold increase in computational power. During the next 15 years, 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 effecting CDGA capability in the computational model Eulag (initially developed by P. 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., storms). The capability for grid adaptation derives from the model's formulation in a generalized coordinate system that is determined by transforming an a priori specified physical coordinate system such as Cartesian or spherical coordinates (Prusa and Smolarkiewicz, JCP 2003). The coordinate transformation may be specified analytically, determined numerically, or be a combination of both.

2. Recent Developments

Recent work has emphasized two parallel efforts. The first, a collaboration between J. Prusa and P. Smolarkiewicz, has extended the coordinate transformation technique for differential operators needed for vorticity, strain rate, scalar and stress divergence. Although classical results for these formulae have been known for some 50 years, the forms applicable for our nonoscillatory, forward-in-time (NFT) model differ in subtle, yet important, ways and are new. At present, the analysis for these operators is largely complete. The coding and testing of these new formulae is well underway, and will set the foundations for important future developments such as turbulence modeling with CDGA. This material forms the basis of a new paper authored by Smolarkiewicz and Prusa.

The second major effort focuses more directly on computation. Eulag is fully parallel and we have recently used it in multi-processor mode on the IBM SP supercomputer, Blackforest , at NCAR to successfully simulate idealized, Held-Suarez (HS) global climates. We have also run the code in single processor mode on Linux workstations at Iowa State University. Significant computations can be done in this mode if fast processors (~ Ghz) are available. Since Eulag is an anelastic model, it does not explicitly compute a thermodynamic pressure field. Thus we have developed and are gaining experience with a pressure recovery algorithm. Intimately tied to this is an investigation on the role of anelastic reference profiles on the solution. Other developments have been made in the diagnosis of baroclinic dynamics in the Held-Suarez climate; and finally, grid generating code has been developed and ported into the parallel version of Eulag.

At present, successful HS simulations have been made using dynamic adaptation of the horizontal grid over a featureless globe as well as for several stationary adapted grids with regions of enhanced local resolution over an idealized Andes Mountains topography. Fig. 1 shows results comparing the potential temperature fields in the region of topography for the stretched grid vs. a uniform grid result with the same total number of grid points. Although still relatively crude, the adapted grid more faithfully replicates the topographic profile, as well as better depicts deformations in the stability profile above the peak that are indicative of vertically propagating gravity waves. Due to the enhanced resolution near the topography, the global model is explicitly resolving these waves .

3. Scientific Relevance

As Fig. 1 illustrates, grid adaptation can enhance a global model's ability to explicitly resolve physical processes that would otherwise have to be relegated to sub-grid parameterizations. In principle, such effects can have an impact on climate, even with terascale computations. The role of adaptation in improving climate statistics is still largely unknown, however. Our goal is to provide new insights on the operational calculus and the robust grid generators needed for CDGA to deliver on this promise of enhanced climate projection.

Figure 1. Potential temperature contours for flow over an idealization of the Andes Mountains. Horizontal extent depicts 3000 kms of longitude, west to east; and 30 kms of vertical depth. Top figure shows results using grid adapted to have 3x higher horizontal resolution over the mountains than the bottom figure, which has a uniform grid with the same overall number of grid points.

For further information on this subject contact:
Dr. J. M. Prusa
Teraflux Corporation
Boca Raton, FL
E-mail: jprusa@bellsouth.net

Dr. W. J. Gutowski, Jr.
Iowa State University
Ames, IA
E-mail: gutowski@iastate.edu

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