An Optimal Spatial Finite-Difference Operator which Reduces Truncation Error to a Minimum

Highly accurate spatial discretization is essentially required to perform numerical climate and weather prediction. The difference between the differential and the finite-difference operator is however a primitive error source in the numerics. This paper presents an optimization of centered finite-difference operator based on the principle of constrained cost function, which can reduce the truncation error to minimum. In the optimization point of view, such optimal operator is in fact an attempt to minimize spatial truncation errors in atmospheric modeling, in a simple way and indeed a quite innovative way to implement Variational Continuous Assimilation (VCA) technique.Furthermore, the optimizing difference operator is consciously designed to be meshing-independent. so that it can be used for most Arakawa-mesh configurations, such as un-staggered (Arakawa-A) or commonly staggered (Arakawa-B, Arakawa-C, Arakawa-D) mesh. But for the calibration purpose, the pro posed operator is implemented on an un-staggered mesh in which the truncation oscillation is mostly excited, and it thus makes a severe and indeed a benchmark test for the proposed optimal scheme. Both theoretical investigation and practical modeling indicate that the aforementioned numerical noise can be significantly eliminated.