Abstract
This paper concerns the parameter model which is used in the numerical weather prediction. The expression of the atmospheric motion with a finite number of parameters can never satisfy the original equations of motion and the thermodynamic equation completely for all the levels of the atmosphere, but it can only fulfill the equations approximately. The prognostic equations in the parameter model, therefore, are derived in such a way that the deviations of the parameterized solution of motion from the real solution of equations may become minimum for the domain concerned. Along this line, non-filtered prognostic equations in three-parameter model were derived with the use of the variational principle, and then those for the balanced system of equations were obtained by filtering the prognostic equations.
