On Balance and Initialization

The Initialization problem Is defined as the problem of obtaining the initial data that are required in order to solve a well posed initial-and-boundary-value problem for the equations of large scale dynamical meteorology. In our treatment of this problem complete knowledge at a given instant of the atmospheric temperature and surface-pressure fields, as well as of their time derivatives, is assumed to be at our disposal; and the problem of computing the velocity field at that instant from this ' nowledge is studied. The methods used are based on the exact mathematical treatment of the differential equations of atmospheric motion, rather than on perturbation-type or numerical methods, A simple solution of the initialization problem thus formulated is exhibited in a particular case. It is sho n, however, that in general the problem is indeterminate and additional information is required to uniquely find the velocity field. Four-dimensional data assimilation is also discussed.