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Sensitivity Test of POP System Matrices—An Application of Spectral Portrait of a Nonsymmetric Matrix

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  • 1 Department of Atmospheric Sciences, University of Washington, Seattle, Washington
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Abstract

By using the POP (principal oscillation pattern) system matrices as examples, this study introduces to the meteorological community the concept and application of spectral portrait (or pseudospectra) of a nonsymmetric matrix. An analytical formula is provided to estimate the system error of a POP matrix due to the inversion of a covariance matrix. By comparing the spectral portrait and the system error, this study demonstrates a possible tool to test the sensitivity of a POP analysis.

Corresponding author address: Yuang Zhang, Max-Planck-Institut für Meteorologie, Bundesstrasse 55, D-20146 Hamburg, Germany.

Abstract

By using the POP (principal oscillation pattern) system matrices as examples, this study introduces to the meteorological community the concept and application of spectral portrait (or pseudospectra) of a nonsymmetric matrix. An analytical formula is provided to estimate the system error of a POP matrix due to the inversion of a covariance matrix. By comparing the spectral portrait and the system error, this study demonstrates a possible tool to test the sensitivity of a POP analysis.

Corresponding author address: Yuang Zhang, Max-Planck-Institut für Meteorologie, Bundesstrasse 55, D-20146 Hamburg, Germany.

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