Singular Vector Analysis for Atmospheric Chemical Transport Models

Wenyuan Liao Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, Virginia

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Adrian Sandu Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, Virginia

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Gregory R. Carmichael Center for Global and Regional Environmental Research, University of Iowa, Iowa City, Iowa

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Tianfeng Chai Center for Global and Regional Environmental Research, University of Iowa, Iowa City, Iowa

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Abstract

The singular vectors of a chemical transport model are the directions of maximum perturbation growth over a finite time interval. They have proved useful for the estimation of error growth, the initialization of ensemble forecasts, and the optimal placement of adaptive observations. The aim of this paper is to address computational aspects of singular vector analysis for atmospheric chemical transport models. The distinguishing feature of these models is the presence of stiff chemical interactions. A projection approach to preserve the symmetry of the tangent linear–adjoint operator for stiff systems is discussed, and extended to 3D chemical transport simulations. Numerical results are presented for a simulation of atmospheric pollution in East Asia in March 2001. The singular values and the structure of the singular vectors depend on the length of the simulation interval, the meteorological data, the location of the optimization region and the selection of optimization species, the choice of error norms, and the size of the optimization region.

Corresponding author address: Dr. Adrian Sandu, Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061. Email: sandu@cs.vt.edu

Abstract

The singular vectors of a chemical transport model are the directions of maximum perturbation growth over a finite time interval. They have proved useful for the estimation of error growth, the initialization of ensemble forecasts, and the optimal placement of adaptive observations. The aim of this paper is to address computational aspects of singular vector analysis for atmospheric chemical transport models. The distinguishing feature of these models is the presence of stiff chemical interactions. A projection approach to preserve the symmetry of the tangent linear–adjoint operator for stiff systems is discussed, and extended to 3D chemical transport simulations. Numerical results are presented for a simulation of atmospheric pollution in East Asia in March 2001. The singular values and the structure of the singular vectors depend on the length of the simulation interval, the meteorological data, the location of the optimization region and the selection of optimization species, the choice of error norms, and the size of the optimization region.

Corresponding author address: Dr. Adrian Sandu, Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061. Email: sandu@cs.vt.edu

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