Improvements to the Canadian 3D-Var Background Error Statistics

Mark Buehner

Massachusetts Institute of Technology


The goal of this study is to explore new approaches for estimating and representing the forecast error covariances used in variational data assimilation in meteorology. Firstly, the effect of relaxing the usual assumptions of homogeneity and isotropy of the horizontal error correlations is evaluated. This is accomplished by representing the covariances with a truncated eigenvalue decomposition and imposing the constraint that the horizontal correlations approach zero at large separation distances. It is found that this representation can resolve the effects of baroclinicity and orography on the covariances. Secondly, the stationary error covariances calculated from the ensemble spread of 6 hour forecasts from an ensemble forecast system are compared with those obtained using a more standard approach. The comparison shows that the error statistics estimated from the ensemble system are only weakly consistent with the between-variable covariances related to the geostrophic and Ekman balances. This result illustrates the potential importance of how the ensemble is constructed when being used for estimating error covariances (such as in the ensemble Kalman filter algorithm). Thirdly, an approach for estimating the analysis error covariances is evaluated. The analysis error covariances can be used to produce more accurate estimates of the forecast error statistics using one of several approaches. Preliminary results are presented from using a Monte Carlo approach to propagate the analysis error statistics according to the model dynamics. Finally, a new approach for obtaining flow-dependent error statistics is also outlined that combines several of the approaches examined in this study.