The Effect of Serially Correlated Observation and Model Error on Atmospheric Data Assimilation

Abstract

Observation error statistics are required in most atmospheric data assimilation systems. While observation errors are often assumed to be spatially correlated, serial correlations have received virtually no attention. In this article, the effect of serially correlated observation error is examined in the context of Kalman filter theory. It is shown that for spatially uncorrelated observation errors, serial correlations will only be detrimental for rapid-sampling instruments or low-flow regimes. In standard Kalman filter theory, it is assumed that the model error is not serially correlated. This assumption has been questioned in the past. In this article, certain types of serially correlated model errors are shown to have a serious detrimental effect on atmospheric data assimilation. It is also suggested that certain performance diagnostics may be capable of detecting serial correlations.