Application of a novel constrained wavelet threshold denoising method in ensemble-based background-error variance

A more efficient noise filtering technique is needed in ensemble data assimilation, to improve traditional spectral filtering methods that cannot reflect the local characteristics of spatial scales. In this paper, we present the design of a novel constrained wavelet threshold denoising method (CWTDNM) by introducing an improved threshold value and a new constraining parameter. The proposed method aims to filter noise swamped over different scales. We prepared an ideal experiment object based on the two-dimensional barotropic vorticity equation. A suitable wavelet basis function (i.e., Db11) and the optimal number of decomposition levels (i.e., five) were first selected. The results show that, given the wavelet coefficients are constrained by the parameter, the CWTDNM can produce better filtering results with the smallest root mean square error (RMSE) compared to similar methods. In addition, the filtering accuracy of 10 ensemble sample variances using the CWTDNM is equivalent to that estimated directly from 80 ensemble samples, but with the runtime reduced to approximately one-seventh. Furthermore, a large peak signal-to-noise ratio, which implies a low RMSE, suggests that the proposed method suitably preserves most of the information after denoising.