Numerical methods of model quality estimations and assimilation of observations

The methods of the combined use of mathematical models and observed data for the environmental monitoring and forecasting purposes are described. The interaction between models and data are based on variational principle. It includes the reconstruction of state functions, identification of parameters and diagnostic estimation of the model quality on the observed data; consistence of information from diverse observational systems; investigation of model sensitivity to the variations of input parameters; observational experiment design. The application of these techniques to the models of atmospheric hydrodynamics and transport of pollutants are presented.