Bainian Liu, Academy of Ocean Science and Engineering, National University of Defense Technology, Changsha 410075, China
A Modified Nonlinear Wavelet thresholding filter in ensemble data Assimilation
Abstract: Estimates of background-error in Ensemble data assimilation often contains sampling noise due to limited ensemble size. Objective filter technology (Raynaud, et al., 2009) has been successfully applied in server operational ensemble data assimilation systems, such as in ECMWF and Meteo-France. But, one of main shortages is that this homogeneous filter cannot adapt to the local structure of the signal. Thus, heterogeneous filtering methods such as nonlinear wavelet thresholding technology is employed. As the noise level varies in different scales, the threshold determined by iterative algorithms (Azzalini, 2005) is no longer suiting for noise. To dress this problem, Pannekoucke et al. (2014) uses a multiplicative factor to adjust the filtering strength based on the optimization of the trade-off between the removal of the noise and the averaging of the useful signal. However, the tuning of choose α is not so obvious, especially in real operational context. In our work, the threshold of wavelet is modified accounting to the distribution of the wavelet coefficients whose modulus is smaller than threshold value. Its validity and performance are examined in one dimensional model. Results show that our method outperforms previous filter . Its filtering performance has improved almost 13.28%.