A method for estimating the analysis error variance in a physical space data assimilation system

Abstract

The error variance of a meteorological analysis is an important quantity, both as a measure of confidence in the analysed product, and as an initial condition for the forecast error variance in a cycling data assimilation system. Modem assimilation systems that rely on global solutions of the analysis equations typically do not include an estimate of this quantity, even though the equation for the full analysis error covariance matrix is well-known. The reason is that this equation is far too costly to implement directly. In this article we analyse the analysis error covariance equation of the Kalman filter, and we propose a computationally efficient method for estimating the analysis error variance, i.e. the diagonal elements of the covariance matrix. The estimate is shown to be conservative in the sense that the analysis error variance is overestimated everywhere. We illustrate the performance of the method in the context of simple two-dimensional analysis experiments as well as in a global, three-dimensional ozone data assimilation system. These experiments show that both quantitatively and qualitatively the method captures the main features of the variance calculated by the full covariance equation at a small fraction of the cost.