NOTES ON THE THEORY OF LARGE-SCALE DISTURBANCES IN ATMOSPHERIC FLOW WITH APPLICATIONS TO NUMERICAL WEATHER PREDICTION

摘要

The problem of predicting the behavior of large-scale disturbances in the mean horizontal flow of the earth's atmosphere, which is directly connected with the problem of predicting the day-to-day changes of surface weather conditions, has been studied from the standpoint of formulating and solving the hydro-dynamical equations which govern the flow. Owing to the difficulty of solving the complete system of equa¬tions (whose very generality implies the existence of several irrelevant, but possible, types of solutions), it is convenient to develop a "scale theory" whereby the various possible types of atmospheric motion, each corresponding to a distinct type of solution, can be distinguished and classified. As it turns out, each type of motion is characterized by its phase speed and frequency. The large-scale disturbances, for example, are distinguished from all other types of motion by the fact that their characteristic phase speed is much less than that of sound waves and of high-speed internal gravity waves.nBy explicitly introducing this information into a mean vorticity equation for adiabatic flow, it is then possible to reduce the system to a single equation from which the extraneous solutions have been excluded and which is otherwise free of major difficulties. The resulting "prognostic equation," which governs the large-scale motions of a fictitious two-dimensional fluid whose velocity is a vertically integrated mean value of the horizontal component of velocity in the real three-dimensional atmosphere, forms the basis for a method of numerical prediction.nAn iterative scheme, based on the solutions of a succession of linear equations, has been proposed for solving the nonlinear prognostic equation. In the course of developing this method, the complete solutions for forced oscillations induced by irregular terrain and for linear transient disturbances have been presented in readily computable form, in terms of known initial values and the appropriate Green's functions. Finally, the prediction formulas for large-scale transient disturbances have been applied to observed initial data, with generally favorable results.