Development and Application of Balanced Dynamical Models

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Although the most accurate predictions and simulations come from primitive equation models, most of our physical insights into atmospheric behavior come from "balanced" models, which represent versions of the basic equations simplified through a number of approximations. Recently, Dr. Schubert has made progress in formulating generalizations of the semi-geostrophic theory (a type of balanced model theory) to include the full effects of the earth's sphericity. The results open the possibility of extending semi-geostrophic applications from synoptic scale to planetary scale phenomena. An elegant aspect of the theory (when formulated in combined isentropic and spherical geostrophic coordinates) is its simple mathematical structure - one prognostic equation for potential vorticity and one diagnostic equation or invertibility principle. Under this award, Dr. Schubert will further develop and apply this theory. One weakness of the generalized semi-geostrophic theory is that highly curved flows are not properly simulated. The principal investigator hopes to be able to overcome this problem through the use of a formulation (mathematically simple) which combines two special coordinate systems and a non-linear balance approximation. He also will carry out simulations of midlatitude storm and tropical systems with several different types of models and systematically compare the results.