We propose a technique of data assimilation in solving the problem on estimating the concentration and total outcome of a passive impurity. The forecast of changes in the impurity concentration fields in time is given using semi-Lagrangian model of a passive impurity transfer and diffusion applied to the Northern hemisphere. The algorithm of data assimilation being used in the problem on estimating the fields of concentration and total outcome of a passive impurity is based on the Kalman theory of optimal filtering. In calculating the covariance matrices assumption is made of the ergodicity of the random fields of errors considered. In this paper we present the results of numerical experiments with model data on the passive impurity concentration using methane as an example. Efficiency of the approaches to the assimilation problem proposed is shown.