A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency, a multi-scale second-order autoregressive recursive filter (MSRF) method is designed. The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter (SMRF) method. The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations. Moreover, compared with the SMRF scheme, the MSRF scheme improves computational accuracy and efficiency to some extent. The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation, but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2 % compared to the SMRF scheme. On the other hand, compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed, the MSRF scheme only needs to perform two filter processes in one iteration, greatly improving filtering efficiency. In the two-dimensional experiment of sea ice concentration, the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme. This means that the MSRF scheme can achieve better performance with less computational cost, which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.