Variational Approach to the Study of Processes of Geophysical Hydrothermodynamics with Assimilation of Detailed Observation Data
V. V. Penenko, A. V. Penenko, E. A. Tsvetova
Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: математическое моделирование, модели гидродинамики и химии атмосферы, вариационный принцип, усвоение данных наблюдений, Новосибирская агломерация, mathematical modeling, model of hydrodynamics and chemistry of the atmospheric, variational principle, assimilation of observational data, Novosibirsk agglomeration
Abstract
This paper presents a variational approach to the solution of direct and inverse problems based on the joint use of mathematical models and monitoring data for processes of geophysical hydrothermodynamics. This approach is used to solve problems related to environmental protection. A variational principle with weak restrictions is formulated to account for uncertainties and errors in models and data. Inclusion of uncertainties makes it possible to construct direct non-iterative algorithms for sequential assimilation of data obtained by various observational systems. Criteria and functions for controlling the quality of the natural environment are introduced into the modeling system to solve inverse problems of environmental safety. The problem with data assimilation for the Novosibirsk agglomeration is considered.
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