An Objective Method for Inferring Sources of Model Error

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  • 1 NASA/Goddard Laboratory for Atmospheres, Greenbelt, Maryland
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Abstract

A restricted statistical correction (RSC) approach is introduced to assess the sources of error in general circulation models (GCMs). RSC models short-term forecast error by considering linear transformations of the GCM's forcing terms, which produce a “best” model in a restricted least squares sense. The results of RSC provide 1) a partitioning of the systematic error among the various GCM's forcing terms, and 2) a consistent partitioning of the nonsystematic error among the GCM forcing terms, which maximize the explained variance. In practice, RSC requires a substantial reduction in the dimensionality of the resulting regression problem: the approach described here projects the fields on the eigenvectors of the error covariance matrix.

An example of RSC is presented for the Goddard Earth Observing System (GEOS) GCM's vertically integrated moisture equation over the continental United States during spring. The results are based on the history of analysis increments (“errors”) from a multiyear data assimilation experiment employing the GEOS model. The RSC analysis suggests that during early spring the short-term systematic forecast errors in the vertically integrated moisture are dominated by errors in the evaporation field, while during late spring the errors are large in both the precipitation and evaporation fields. The RSC results further suggest that one-quarter to one-half of the nonsystematic forecast errors in the vertically integrated moisture may be attributable to GCM deficiencies.

Limitations of the method resulting from ambiguities in the nature of the analysis increments are discussed. While the RSC approach was specifically developed to take advantage of data assimilation experiments, it should also be useful for analysing sequences of somewhat longer GCM forecasts (∼1 day) as long as they are short enough to consider the errors approximately local.

Abstract

A restricted statistical correction (RSC) approach is introduced to assess the sources of error in general circulation models (GCMs). RSC models short-term forecast error by considering linear transformations of the GCM's forcing terms, which produce a “best” model in a restricted least squares sense. The results of RSC provide 1) a partitioning of the systematic error among the various GCM's forcing terms, and 2) a consistent partitioning of the nonsystematic error among the GCM forcing terms, which maximize the explained variance. In practice, RSC requires a substantial reduction in the dimensionality of the resulting regression problem: the approach described here projects the fields on the eigenvectors of the error covariance matrix.

An example of RSC is presented for the Goddard Earth Observing System (GEOS) GCM's vertically integrated moisture equation over the continental United States during spring. The results are based on the history of analysis increments (“errors”) from a multiyear data assimilation experiment employing the GEOS model. The RSC analysis suggests that during early spring the short-term systematic forecast errors in the vertically integrated moisture are dominated by errors in the evaporation field, while during late spring the errors are large in both the precipitation and evaporation fields. The RSC results further suggest that one-quarter to one-half of the nonsystematic forecast errors in the vertically integrated moisture may be attributable to GCM deficiencies.

Limitations of the method resulting from ambiguities in the nature of the analysis increments are discussed. While the RSC approach was specifically developed to take advantage of data assimilation experiments, it should also be useful for analysing sequences of somewhat longer GCM forecasts (∼1 day) as long as they are short enough to consider the errors approximately local.

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