The Structure of Background-error Covariance in a Four-dimensional Variational Data Assimilation System: Single-point Experiment

A four dimensional variational data assimilation (4DVar) based on adimension-reduced projection (DRP-4DVar) has been developed as a hybrid ofthe 4DVar and Ensemble Kalman filter (EnKF) concepts. Its goodflow-dependent features are demonstrated in single-point experiments throughcomparisons with adjoint-based 4DVar and three-dimensional variational data(3DVar) assimilations using the fifth-generation Pennsylvania StateUniversity-National Center for Atmospheric Research Mesoscale Model (MM5).The results reveal that DRP-4DVar can reasonably generate a background errorcovariance matrix (simply B-matrix) during the assimilation window from an initial estimation using a number of initial condition dependent historical forecast samples. In contrast, flow-dependence in the B-matrix of MM5 4DVar is barely detectable. It is argued that use of diagonal estimation in the B-matrix of the MM5 4DVar method at the initial time leads to this failure. The experiments also show that the increments produced by DRP-4DVar areanisotropic and no longer symmetric with respect to observation location dueto the effects of the weather trends captured in its B-matrix. This differs from the MM5 3DVar which does not consider the influence of heterogeneous forcing on the correlation structure of the B-matrix, a condition that is realistic for many situations. Thus, the MM5 3DVar assimilation could only present an isotropic and homogeneous structure in its increments.