Development and Application of Balanced Dynamical Models

虽然最准确的预测和模拟来自原始的方程模型，但我们对大气行为的大多数物理见解来自“平衡”模型，它代表了通过一些近似简化的基本方程的版本。最近，舒伯特博士在概括半地转理论（一种平衡模型理论）方面取得了进展，其中包括地球球形的全部影响。这些结果为将半地转应用从天气尺度扩展到行星尺度现象提供了可能性。这个理论的一个优雅的方面（当用等熵和球面地转坐标组合表述时）是它简单的数学结构——一个位势涡的预测方程和一个诊断方程或可逆性原理。在这个奖项下，舒伯特博士将进一步发展和应用这一理论。广义半地转理论的一个缺点是不能很好地模拟高度弯曲的流动。首席研究员希望能够通过使用一种公式（数学上简单）来克服这个问题，该公式结合了两个特殊的坐标系和非线性平衡近似。他还将用几种不同类型的模式进行中纬度风暴和热带系统的模拟，并系统地比较结果。

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.