Richard Menard, Environment and Climate Change Canada
Variance loss of ensemble-based error covariances for chemical transport models
Abstract: It has been argued since the early development of four-dimensional data assimilation that the propagation of error covariances is an essential component of truly optimal data assimilation schemes. Yet the accuracy of the error covariance propagation with the numerical models has almost is rarely examined or challenged. Indeed, because of moment closure issues, analytical solution of the propagation of error covariances exists only in rare cases, such as with linear Gaussian dynamics, which turn out to be applicable to chemical transport problems. This study examines the convergence of the numerical simulation of error covariances to an exact solution of the propagation of error covariance as a function of model resolution, time-step, correlation length-scales and ensemble size. In this work we use a linear 3D chemical transport model from the BASCOE system to generate ensemble-based error covariances and compare with the analytical solution of the corresponding PDE. The results show a significant loss of variance in the ensembles compared with the solution of the PDE. The variance loss depends principally on the correlation length-scale and resolution of the model, and is nearly insensitive to the number of members. The variance loss is also accompanied with an augmentation of the correlation length. Some ideas to correct or address this issue are also discussed.