Miyakoda, K., and R. W. Moyer, 1968: A method if initialization for dynamical weather forecasting. Tellus, 20 (1), 115-128.

Abstract: A new technique to solve the balance of equations for a given geopotential field is tested. The non-filtered thermo-hydrodynamical equations are used as the basis, and the balance solution is obtained iteratively by filtering out the high-frequency modes through the use of the Euler-backward time differencing scheme.
The merit of this technique as compared to conventional methods is that equations which include complicated processes, such as friction or heating, can be treated without difficulty, and that the balanced solution thus obtained appears completely consistent with the prognostic equations. Furthermore, it is no longer necessary to artificially modify the observed geopotential as in conventional schemes, so as to meet the ellipticity condition of the differential equations.