The Mechanism of Meteorological Noise

Using a simple atmospheric model, the difference between the solutions of the primitive and the quasi-hydrostatic equations is demonstrated. The results.show that the quasi-hydrostatic processes are largely determined by the initial field of pressure wherever the meteorological "noise"-phenomena (in the form of short-period oscillations about a trend of the meteorological elements) depend on the initial field of the non-geostrophic wind components. This trend can be computed with sufficient accuracy also by a numerical integration of the primitive equations, which are mathematically simpler to handle than the quasi-hydrostatic equations. In this case the initial wind fields can be computed from the observed pressure field by using the geostrophic approximation. To find the trend the results have to be smoothed. 1 //S.285// Hydrodynamic and thermodynamic equations, when applied to atmospheric processes, determine not only the so-called "quasi-static" processes, which proceed relatively slowly, but also of necessity certain short-period motions in which the velocities of propagation that arise are on the order of the speed of sound and thus are characterized as meteorological noise. In general, the only effect of these short-period processes, which have relatively low amplitudes, appears in the form of a perturbation in the temporal course of the processes. Furthermore, in synoptic charts, these perturbations are smoothed away, and so it might be deemed adequate to make a numerical prediction when determining which processes of change proceed quasi-statically. However, it is precisely the temporal course--that is, the partial temporal derivative--whose calculation is relatively simple even without complete integration by means of differential equations--that, when subjected to numerical methods of integration, is computed prognostically, that is, in order to determine the change in the observed large-scale conditions that will occur in the next time interval. If hydrodynamic and thermodynamic equations are used in their unaltered form to carry out these numerical calculations, unsmoothed momentum values are obtained in calculating the tendencies. As a result, it is possible to obtain changes only for the variable in question from the corresponding differential equations for a time interval that is small in comparison with the period of time during which the short-period processes introduce oscillation. This procedure requires a great deal of computation and makes it difficult to achieve an expedient numerical evaluation. The number of time steps required here can be drastically reduced if these short-period processes, which are themselves cumbersome and meteorologically uninteresting, are eliminated from the differential equations. //S.286// This also no doubt results in a fundamental change in the structure of the differential equations. In what follows, we shall attempt to isolate the short-period components from the quasi-static components and to evaluate them with the help of a simple atmospheric model. To achieve this, it appears 2 justified to us to eliminate the meteorological noise processes using a set of initial conditions that are defined by pressure and wind fields. 3 I. INITIAL EQUATIONS FOR THE BASIC ATMOSPHERIC MODEL The linearized equations for a homogeneous atmosphere, which have been previously discussed by Charney (1949), shall provide the basis for our initial equations. Assuming that the hydrostatic basic equation is valid and a basic state is defined by: U = ~ H = const k y