The applications of perturbation and control theories to numerical simulation of the atmosphere and ocean are discussed.

It is a characteristic of mathematical simulation of the atmosphere and ocean that input parameters of the models and initial fields are defined fairly roughly and often only the range of parameters is known. Therefore, a problem arises in defining the influence upon a simulation of (a) input parameter variations, and (b) the method of estimation of parameter values from observational data.

Methods are considered for the construction of discrete models and for numerical analysis and prediction of meteorological fields, as well as for the investigation of the model sensitivity to input parameter variations. The computational algorithms are based on a variational principle in combination with a splitting method. The latter provides stability and economy of computation.

Methods based on perturbation and control theories make it possible to carry out a qualitative analysis of a particular numerical model to determine the influence of different factors, and to aid rational design of numerical experiments.

In particular, application of sensitivity methods and control theory to initialization allows one to adjust the scales of processes described by the atmospheric model to correspond to the scales of the processes described by the input observational data.

One of the applications of the sensitivity theory is to the design of numerical experiments for evaluation of the effect of man's activity upon the climatic system.