Error Estimation Using Wavelet Analysis for Data Assimilation: EEWADAi

Abstract

A new method is presented for estimating numerical errors in simulations as a function of space and time. This knowledge of numerical errors can provide critical information for the effective assimilation of external data. The new method utilizes wavelet analysis for the detection of deviation from low-order polynomial structure in the computational data indicating regions of the domain where relatively large numerical errors will occur. This wavelet-based technique has a very low computational cost, and in practice the cost can be considered negligible compared to the computational cost of the simulation. It is proposed here that this be used in the field of data assimilation for fast and efficient assimilation of external data, and a numerical example illustrating that the new method performs better than the existing method of optimal interpolation is given.