ON A PHYSICAL BASIS FOR NUMERICAL PREDICTION OF LARGE-SCALE MOTIONS IN THE ATMOSPHERE

J. G. Charney Institute for Advanced Study

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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 components in order to establish bounds for the influence region. It is found that numerical forecasts for periods of one or perhaps two days are now possible for certain areas of the earth but that forecasts for longer periods require a greater spread of observation stations than is available.

A method is given for reducing the three-dimensional forecast problem to a two-dimensional one by construction of an “equivalent-barotropic” atmosphere. The method is applied to the calculation of the 5OO-mb height tendency, and the results are compared with observation. A rule is derived for determining the positions of the isallohyptic centers from the field of the absolute-vorticity advection.

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 components in order to establish bounds for the influence region. It is found that numerical forecasts for periods of one or perhaps two days are now possible for certain areas of the earth but that forecasts for longer periods require a greater spread of observation stations than is available.

A method is given for reducing the three-dimensional forecast problem to a two-dimensional one by construction of an “equivalent-barotropic” atmosphere. The method is applied to the calculation of the 5OO-mb height tendency, and the results are compared with observation. A rule is derived for determining the positions of the isallohyptic centers from the field of the absolute-vorticity advection.

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