An Analytical View of Updating Meteorological Variables: Part II. Weighted Assimilation

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  • 1 Department of Astro-Geophysics, University of Colorado, Boulder 80302
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Abstract

A simple theoretical approach is formulated, based on part I of this study, in which inadequate modelling of physical processes and the use of numerical algorithms are assumed to introduce random phase errors between model predictions of large-scale atmospheric disturbances and the true state of the atmosphere. An attempt is made to prevent excessive growth of these errors by updating the model predictions with error-contaminated observations, available either periodically or aperiodically. It is demonstrated that the root mean square prediction error can be controlled by updating,, when the technique of weighted assimilation is employed. This well-known technique uses both predicted and observed values of an atmospheric variable to form an estimate of the true state. In general, this estimate is a better data source than direct replacement by an observed value. However, the results show that when observation errors are relatively small, weighted assimilation is essentially equivalent to replacement by the observed variable. When the model prediction errors are relatively small, significant improvement over replacement by the observed value is attained. These results are displayed for various model and observation errors and for different length scales of the wave disturbance.

A critique of the present results and inherent difficulties that are met in application to numerical weather prediction are discussed.

Abstract

A simple theoretical approach is formulated, based on part I of this study, in which inadequate modelling of physical processes and the use of numerical algorithms are assumed to introduce random phase errors between model predictions of large-scale atmospheric disturbances and the true state of the atmosphere. An attempt is made to prevent excessive growth of these errors by updating the model predictions with error-contaminated observations, available either periodically or aperiodically. It is demonstrated that the root mean square prediction error can be controlled by updating,, when the technique of weighted assimilation is employed. This well-known technique uses both predicted and observed values of an atmospheric variable to form an estimate of the true state. In general, this estimate is a better data source than direct replacement by an observed value. However, the results show that when observation errors are relatively small, weighted assimilation is essentially equivalent to replacement by the observed variable. When the model prediction errors are relatively small, significant improvement over replacement by the observed value is attained. These results are displayed for various model and observation errors and for different length scales of the wave disturbance.

A critique of the present results and inherent difficulties that are met in application to numerical weather prediction are discussed.

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