Barotropic and baroclinic atmospheric processes manifest themselves in the numerous facets of large-scale weather phenomena. Typical examples are the formation and propagation of synoptic waves having wavelengths of several thousand kilometers and the characteristic life cycles of high- and low-pressure systems. The barotropic and baroclinic physics provides the physical basis of numerical weather prediction. In this chapter we will consider various aspects of barotropic models. It is realized that the prediction of the daily weather by means of barotropic models is no longer practiced by the national weather services. Nevertheless, by discussing the mathematical theory of the barotropic physics we can learn very well how physical variables are interconnected and how much care must be taken to construct even a very simple prediction model. The first numerical barotropic weather-prediction model was introduced by the renowned meteorologist C. G. Rossby and by the famous mathematician John von Neumann. Baroclinic models will be described in some detail in later chapters.

Barotropic models are short-range-prediction models that include only the reversible part of atmospheric physics. The consequence is that the atmosphere is treated as a one-component gas consisting of dry air. The irreversible physics such as non-adiabatic heating and cloud formation is not taken into account.

The basic assumptions of the barotropic model

The name of the model is derived from the assumption that the atmosphere is in a barotropic state throughout the prediction period. The condition of barotropy by itself, however, is not sufficient to construct a barotropic prediction model; additional assumptions are mandatory. The model described here rests on three basic assumptions.