On a Physical Basis for Numerical Prediction of Large-Scale Motions in the Atmosphere

Abstract The small-scale “noise” disturbances of the atmosphere create difficulties for the numerical integration of the equations of motion. For example, their existence demands that very small time differences be used in the integration of the finite-difference equations. To eliminate the noise, a filtering method is devised which consists essentially in replacing the primitive hydrodynamical equations by combining the geostrophic and hydrostatic equations with the conservation equations for potential temperature and potential vorticity. In this way a single equation in the pressure is obtained for the motion of the large-scale systems. A method is suggested for its numerical integration. The spread of data required for a short-period forecast is discussed in terms of the rate of spread of influences or “signal velocity” in the atmosphere. It is shown that a small disturbance is propagated both horizontally and vertically at a finite rate. Estimates are obtained for the maximum signal-velocity component...