Numerical simulation of atmospheric convection in many instances will require the solution of a diagnostic equation to determine the pressure distribution. This relationship, called the balance equation, is elliptic and hence subject to solution by relaxation or iterative techniques. However, these methods have failed to give the degree of accuracy which is required to carry out other steps in the simulation procedure. An alternate and quite general technique is developed which is based upon a matrix transformation procedure given by Polozhii 1965. This transformation method readily can be adapted to various boundary conditions, grid spacings, and finite-difference formulations although the discussion primarily is concerned with a case of derivative boundary conditions and non-uniform grid. A proof is given of the existence of a numerical solution when the transform method is applied to a two-dimensional balance equation. The accuracy of the method is tested by application to two cases for which the correct distributions of pressure are known. An extension of the transform method to a solution of the balance equation over a three-dimensional region is outlined. A computer routine for solving the two-dimensional problem is described. Author
Report on Project THEMIS, Prediction of Environmental Parameters.