In meteorology the weather analysis can provide a reference against which one can check the quality of observations. The analysis can be reduced to an interpolation problem, if the model state is overdetermined by the observations. For the under-determined problem it is not a straight forward how to perform analysis because data is sparse and only indirectly related to the model variables. In order to solve the problem we need to rely on some background information in the form of a priori estimate of the model state, where any physical constrains on the analysis can be helpful. One of the ways to approach this problem is through applying the data assimilation method to it. In this talk I will try to present some basic theory which goes with the DA method and illustrate it on an example.