Variational methods for targeted monitoring of atmospheric quality by specified cost criteria

The creation of problem-oriented monitoring strategies for the study of natural processes in the atmosphere-Earth system based on use of mathematical models in combination with observational data is discussed. Major objects of a modeling system are described. These are: a model of processes of transport and transformation of substances in the gas and aerosol state, data and models of observations. We develop a variational approach that provides formulation, construction, and implementation of solutions to direct and inverse problems. To formulate the variational principle, some target functionals are defined. They serve for forecasting, assimilating observational data, controlling atmospheric quality, etc. Data assimilation techniques play a significant role in successful management of environmental objectives. The result of the study is a version of the so-called "seamless" modeling technology in which five classes of the required functions are calculated. These are state functions, adjoint functions, uncertainty functions, and two functions of sensitivity with respect to variations of model parameters and monitoring data. We can solve inverse problems of strategic operational assessments of hazardous situations and identification of sources of intensive technogenic impacts to organize the targeted monitoring.