Variational approach to the study of processes of geophysical hydro-thermodynamics with assimilation of observation data

This paper presents a variational approach to solving direct and inverse problems based on the joint use of mathematical models and data monitoring of processes of geophysical hydro-thermodynamics. This approach is used to solve problems related to environmental protection. A variational principle with weak constraints is formulated to account for uncertainties and errors in models and data. The inclusion of uncertainties makes it possible to develop direct non-iterative algorithms for sequential assimilation of data obtained by various observation systems. Some criteria and functions for controlling the quality of the natural environment are introduced into the modeling system to solve inverse problems of environmental risk assessment. A problem with data assimilation is considered for the Novosibirsk agglomeration.