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An Adjoint Sensitivity Method for the Adaptive Location of the Observations in Air Quality Modeling

Dacian N. DaescuInstitute for Mathematics and Its Applications, University of Minnesota, Minneapolis, Minnesota

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Gregory R. CarmichaelDepartment of Chemical and Biochemical Engineering, and The Center for Global and Regional Environmental Research, The University of Iowa, Iowa City, Iowa

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Abstract

The spatiotemporal distribution of observations plays an essential role in the data assimilation process. An adjoint sensitivity method is applied to the problem of adaptive location of the observational system for a nonlinear transport-chemistry model in the context of 4D variational data assimilation. The method is presented in a general framework and it is shown that in addition to the initial state of the model, sensitivity with respect to emission and deposition rates and certain types of boundary values may be obtained at a minimal additional cost. The adjoint modeling is used to evaluate the influence function and to identify the domain of influence associated with the observations. These essential tools are further used to develop a novel algorithm for targeting observations that takes into account the interaction among observations at different instants in time and spatial locations. Issues related to the case of multiple observations are addressed and it is shown that by using the adjoint modeling an efficient implementation may be achieved. Computational and practical aspects are discussed and this analysis indicates that it is feasible to implement the proposed method for comprehensive air quality models. Numerical experiments performed with a two-dimensional test model show promising results.

Corresponding author address: Dr. Dacian N. Daescu, Institute for Mathematics and Its Applications, University of Minnesota, 207 Church Street SE, 400 Lind Hall, Minneapolis, MN 55455. Email: daescu@ima.umn.edu

Abstract

The spatiotemporal distribution of observations plays an essential role in the data assimilation process. An adjoint sensitivity method is applied to the problem of adaptive location of the observational system for a nonlinear transport-chemistry model in the context of 4D variational data assimilation. The method is presented in a general framework and it is shown that in addition to the initial state of the model, sensitivity with respect to emission and deposition rates and certain types of boundary values may be obtained at a minimal additional cost. The adjoint modeling is used to evaluate the influence function and to identify the domain of influence associated with the observations. These essential tools are further used to develop a novel algorithm for targeting observations that takes into account the interaction among observations at different instants in time and spatial locations. Issues related to the case of multiple observations are addressed and it is shown that by using the adjoint modeling an efficient implementation may be achieved. Computational and practical aspects are discussed and this analysis indicates that it is feasible to implement the proposed method for comprehensive air quality models. Numerical experiments performed with a two-dimensional test model show promising results.

Corresponding author address: Dr. Dacian N. Daescu, Institute for Mathematics and Its Applications, University of Minnesota, 207 Church Street SE, 400 Lind Hall, Minneapolis, MN 55455. Email: daescu@ima.umn.edu

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