The scheme of high-order recursive filter for the GRAPES3DVar with its initial experiments

The background error covariance (B) and the calculation of the inverse of B are one of the core problems in the 3D variational assimilation. The recursive filter with the isotropic Gaussian covariance is applied to the horizontal transformation of the background error covariance in the GRAPES-3DVar system. In the original scheme, the one-order recursive filter does not converge fast enough, i.e. it should be utilized 10 times in order to make the objective function convergence. Using the method of Purser and Wu (2003a), this paper develops a high-order recursive filter suitable for the GRAPES3DVar system. The results from the ideal experiments show that the objective function can ensure a quick convergence by using the fourth-order recursive filter only once. The resulting output field adheres better to the Gaussian distribution than the one developed by a continuous four times application of the simple first-order filter. Also, in order to make the power spectrum of Gaussian type function adhere closer to the spectrum attenuation of the actual atmospheric, a linear combination of three sequential four-order recursive filters with different intrinsic scales is carried out. The preliminary experimental results indicate that the new four-order recursive filter can show some mesoscale information clearly with the original largescale information retained.