Methods for the combined use of mathematical models and observational data for studying and forecasting the evolution of natural processes in the atmosphere, ocean, and environment are presented. Variational principles for estimation of functionals defined on a set of functions of state, parameters and sources of models of processes are a theoretical background. Mathematical models with allowance for uncertainties are considered as constraints to the class of functions. Attention is focused on methods of successive data assimilation and on inverse problems.

Variational approach and sensitivity theory methods are used to construct algorithms for solving the problems of environmental forecast and design. When studying the behavior of the model in the...

Air quality monitoring systems differ in composition and accuracy of observations and their temporal and spatial coverage. A monitoring system’s performance can be assessed by evaluating the accuracy of the emission sources identified by its data. In the considered inverse modeling approach, a source identification problem is transformed to a quasi-linear operator equation with the sensitivity operator. The sensitivity operator is composed of the sensitivity functions evaluated on the adjoint ensemble members. The members correspond to the measurement data element aggregates. Such ensemble construction allows working in a unified way with heterogeneous measurement data in a single-operator equation. The quasi-linear structure of the resulting operator equation allows both solving and predicting solutions of the inverse problem. Numerical experiments for the Baikal region scenario were carried out to compare different types of inverse problem solution accuracy estimates. In the considered scenario, the projection to the orthogonal complement of the sensitivity operator’s kernel allowed predicting the source identification results with the best accuracy compared to the other estimate types. Our contribution is the development and testing of a sensitivity-operator-based set of tools for analyzing heterogeneous air quality monitoring systems. We propose them for assessing and optimizing observational systems and experiments.