Elena Tsvetova

Methods of sensitivity theory and inverse modeling for estimation of source parameters

Abstract The source parameters estimation, based on environment pollution monitoring, and assessment of regions with high potential risk and vulnerability from nuclear sites are the two important problems for nuclear emergency preparedness systems and for long-term planning of socio-economical development of territories. For the discussed problems, most of modelers use the common back-trajectory techniques, suitable only for Lagrangian models. This paper discusses another approach for inverse modeling, based on variational principles and adjoint equations, and applicable for Eulerian and Lagrangian models. The presented methodology is based on both direct and inverse modeling techniques. Variational principles combined with decomposition, splitting and optimization techniques are used for construction of numerical algorithms. The novel aspects are the sensitivity theory and inverse modeling for environmental problems which use the solution of the corresponding adjoint problems for the given set of functionals. The methodology proposed provides optimal estimations for objective functionals, which are criterion of the atmospheric quality and informative content of measurements. Some applications of the suggested methods for source parameters and vulnerability zone estimations are discussed for important regions with environmental risk sites.

Variational approach and Euler’s integrating factors for environmental studies

Abstract We are promoting the use of variational principles as some generalizing idea that allows us to create consistent approximations of mathematical models. In this paper, we formulate a computing technology to solve direct and inverse problems of atmospheric dynamics and chemistry. For the implementation, we use functional decomposition methods, splitting techniques, and integrating factors designed as the solutions of some adjoint problems. One of the main purposes of the paper is to relate the theory of approximation with the concept of Eulerian integrating factors that plays the fundamental role in the theory of differential equations. We demonstrate the utility and versatility of the concept applying it to solve the systems of differential equations of convection–diffusion (with dominant convection) and stiff systems of kinetic equations. To identify the prospects of our approach, we briefly introduce how to use integrating factors in the case of unstructured grids.

Direct and Inverse Problems in a Variational Concept of Environmental Modeling

A concept of environmental forecasting based on a variational approach is discussed. The basic idea is to augment the existing technology of modeling by a combination of direct and inverse methods. By this means, the scope of environmental studies can be substantially enlarged. In the concept, mathematical models of processes and observation data subject to some uncertainties are considered. The modeling system is derived from a specially formulated weak-constraint variational principle. A set of algorithms for implementing the concept is presented. These are: algorithms for the solution of direct, adjoint, and inverse problems; adjoint sensitivity algorithms; data assimilation procedures; etc. Methods of quantitative estimations of uncertainty are of particular interest since uncertainty functions play a fundamental role for data assimilation, assessment of model quality, and inverse problem solving. A scenario approach is an essential part of the concept. Some methods of orthogonal decomposition of multi-dimensional phase spaces are used to reconstruct the hydrodynamic background fields from available data and to include climatic data into long-term prognostic scenarios. Subspaces with informative bases are constructed to use in deterministic or stochastic-deterministic scenarios for forecasting air quality and risk assessment. The results of implementing example scenarios for the Siberian regions are presented.

Aspects of Atmospheric Pollution in Siberia

This chapter considers specific atmospheric pollution problems in Siberia, the current state of studies and strategic activities, and peculiarities of Siberian environmental protection problems, risk assessment, and tendencies in atmospheric pollution in Siberia, including health-affecting pollutants, greenhouse gases, aerosols, etc. The chapter does not presume to cover all the aspects of atmospheric pollution in Siberia. Its main focus is a short general overview of the existing problems of airborne pollution in Siberia and methodological aspects of air pollution impact assessments followed by several examples of such studies for Siberia. In particular, the following issues are described: (1) sources and characteristics of air pollution in Siberia, (2) air quality and atmospheric composition characterization, (3) assessment of airborne pollution in Siberia from air and space, (4) methodology and models for air pollution assessment on different scales, and (5) case studies of long-range atmospheric transport of heavy metals from industries of the Ural and Norilsk regions.

Methods based on the joint use of models and observational data in the framework of variational approach to forecasting weather and atmospheric composition quality

Presented is a new version of the methods ofvariational assimilation ofmeasurement data from various observational systems including imagery. The base of these methods is the technique of variational principles formulated with weak constraints and applied to the joint models of hydrothermodynamics and chemistry ofthe atmosphere. To implement assimilation schemes, direct algorithms are proposed which are based on splitting techniques and enable solving the four-dimensional problems of forecasting with the assimilation of available monitoring data in the operational mode.

Sequential data assimilation algorithms for air quality monitoring models based on a weak-constraint variational principle

A data assimilation problem for unsteady models is considered as a sequence of coupled inverse problems of reconstruction of the space-time structure of the state functions with various sets of measurement data. The data assimilation is carried out jointly with the identification of an additional unknown function, which is interpreted as a function of model uncertainty. A variational principle serves as the basis for constructing the algorithms. Various versions of the algorithms are presented and analyzed. Based on the principle of the residual, a computationally efficient algorithm for data assimilation in a locally one-dimensional case is constructed. A theoretical estimate of its performance is obtained. This algorithm is one of the main components of a data assimilation system based on a splitting scheme for unsteady three-dimensional transport and transformation models of atmospheric chemistry.

Development of variational approach for direct and inverse problems of atmospheric hydrodynamics and chemistry

The development of a variational approach for solving interrelated problems of atmospheric hydrodynamics and chemistry is presented. The variational approach allows expanding the class of concerned problems for a complex study of different-scale physical and chemical processes using the methods of direct and inverse modeling for these purposes. A technology of constructing consistent mathematical models and methods of their numerical implementation based on the variational principle in the weak constraint statement is described. Solutions of local and global adjoint problems are of great importance for constructing the algorithms of direct and inverse modeling. Implementing the idea of adjoint integrating factors provides unconditionally monotone and stable discrete-analytic approximations for convection-diffusion-reaction problems.

Methods of sensitivity theory and orthogonal decomposition for studying climate dynamics and pollution

Development of the methodology of forward and inverse modeling for climatic and environmental protection studies is presented. The focus is on the methods of orthogonal decomposition of fields. The application is made to construction of deterministic-stochastic scenarios for ecological studies and forecasts on the base of joint use of models and climatic data. The main algorithms are shortly described. Reanalysis data base is used for estimations of seasonal variation of informativeness of the leading subspace.

Energy centers of the climate system and their connection with ecological risk domains

Problems of ecological risks and vulnerability of territories with respect to human induced effects stand on the intersection of the fields and interests of climatic and ecological studies. The purpose of this paper is to lay the concept on interconnections between energetically active regions in the climatic system and zones of increased ecological risks as well as to describe the mathematical background that we develop for realization of the concept. The studies are fulfilled on the base of a joint use of the models and measured data. To calculate the influence domains of thermodynamic factors and the regions of ecological risk the numerical models of atmospheric hydrodynamics and pollutants transport are used in forward and inverse modes. The system organization of the approach are based on the combination of numerical tools, namely, orthogonal decomposition of function spaces, factor analysis and selection of the main components and factors, sensitivity methods with respect to the parameter perturbations for the models and functionals, and forward and inverse techniques with data assimilation procedures. The results of the modeling scenarios with global atmospheric models with the use of NCEP reanalysis data for 53 years are presented.

Sequential Variational Data Assimilation Algorithms at the Splitting Stages of a Numerical Atmospheric Chemistry Model

A variational data assimilation algorithm is studied numerically. In situ concentration measurement data are assimilated into transport and transformation model of atmospheric chemistry. The algorithm is based on decomposition and splitting methods with solution of variational data assimilation problems for separate splitting stages. A direct algorithm without iterations is used for the linear transport stage. An iterative gradient algorithm is applied for data assimilation at the non-linear chemical transformation stage. In a realistic numerical experiment, the contributions of data assimilation algorithms for the different splitting stages are compared.