Approximation and Inversion of a Complex Meteorological System via Local Linear Filters

Frederic Schoenberg Department of Statistics, University of California, Los Angeles, Los Angeles, California

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Richard Berk Department of Statistics, University of California, Los Angeles, Los Angeles, California

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Robert Fovell Department of Atmospheric Science, University of California, Los Angeles, Los Angeles, California

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Cheng Li Department of Statistics, University of California, Los Angeles, Los Angeles, California

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Rong Lu Department of Atmospheric Science, University of California, Los Angeles, Los Angeles, California

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Robert Weiss Department of Biostatistics, University of California, Los Angeles, Los Angeles, California

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Abstract

Dynamical models involving systems of numerous differential equations are commonly used to describe meteorological behavior. Approximations to such systems are often desired, particularly for inversion problems when the model’s adjoint is unavailable. A method for approximating a general, nonlinear system is explored here. The method is particularly useful for inverse problems. An application to a complex multivariate dynamic model for southern California air quality is given, and the method is shown to provide satisfactory estimates of vehicle emission-rate inputs using ozone concentration estimates for the Los Angeles basin.

Corresponding author address: Frederic Schoenberg, Dept. of Statistics, 8130 Math–Science Bldg., University of California, Los Angeles, Los Angeles, CA 90095-1554.

frederic@ucla.edu

Abstract

Dynamical models involving systems of numerous differential equations are commonly used to describe meteorological behavior. Approximations to such systems are often desired, particularly for inversion problems when the model’s adjoint is unavailable. A method for approximating a general, nonlinear system is explored here. The method is particularly useful for inverse problems. An application to a complex multivariate dynamic model for southern California air quality is given, and the method is shown to provide satisfactory estimates of vehicle emission-rate inputs using ozone concentration estimates for the Los Angeles basin.

Corresponding author address: Frederic Schoenberg, Dept. of Statistics, 8130 Math–Science Bldg., University of California, Los Angeles, Los Angeles, CA 90095-1554.

frederic@ucla.edu

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