Sensitivity Operator Inverse Modeling Framework for Advection-Diffusion-Reaction Models with Heterogeneous Measurement Data

Air quality monitoring systems vary in temporal and spatial coverage, the composition of the observed chemicals, and the data's accuracy. The developed inverse modeling approach [1] is based on sensitivity operators and ensembles of adjoint equations solutions. An inverse problem is transformed to a quasi-linear operator equation with the sensitivity operator. The sensitivity operator is composed of the sensitivity functions, which are evaluated on the adjoint ensemble members. The members correspond to the measurement data elements. 

This 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 analyzing the inverse problem. More specifically, by analyzing the sensitivity operator's singular structure, we can estimate the informational content in the measurement data with respect to the considered process model. This type of analysis can estimate the inverse problem solution before its actual solution and evaluate the monitoring system efficiency with respect to the considered inverse modeling task [1,2]. 

Numerical experiments with the emission source identification problem for air pollution transport and transformation model were carried out to illustrate the developed framework. In the numerical experiments, we considered in-situ, image-type, and integral-type measurement data.

The work was supported by the grant №075-15-2020-787 in the form of a subsidy for a Major scientific project from Ministry of Science and Higher Education of Russia (project "Fundamentals, methods and technologies for digital monitoring and forecasting of the environmental situation on the Baikal natural territory").

References

[1] Penenko, A. Convergence analysis of the adjoint ensemble method in inverse source problems for advection-diffusion-reaction models with image-type measurements // Inverse Problems & Imaging, American Institute of Mathematical Sciences (AIMS), 2020, 14, 757-782 doi: 10.3934/ipi.2020035

[2] Penenko, A.; Gochakov, A. & Penenko, V. Algorithms based on sensitivity operators for analyzing and solving inverse modeling problems of transport and transformation of atmospheric pollutants // IOP Conference Series: Earth and Environmental Science, IOP Publishing, 2020, 611, 012032 doi: 10.1088/1755-1315/611/1/012032