A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis
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Abstract: 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.
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Figure 2. Spread of observational information using the L-BFGS scheme when
$ \beta $ = 0.6 (a), 1.2 (b), 1.8 (c) and 2.6 (d), respectively.
Figure 3. Spread of observational information in the MSRF scheme when
$ \beta' $ = 0.35. a−d are the results at iteration 70, 120, 140, and 160, respectively.
Figure 4. Surface plot of the MSRF scheme (a) and the SMRF scheme (b). The results at iteration 210.
Figure 5. SSMIS Arctic sea ice concentration observation on August 14, 2023 (a) and the location of selected observation points for data assimilation (b).
Figure 6. Sea ice concentration analyzed field on August 14, 2023 solved by using the L-BFGS scheme when
$ \beta $ = 110 (a),$\beta $ = 200 (b),$\beta $ = 450 (c), and$\beta $ = 700 (d).
Figure 7. Sea ice concentration analyzed field (left column) and the descent direction (
$ -\nabla \mathrm{J} $ ) (right column) from the L-BFGS scheme ($ \beta $ = 110) at iteration 3, 5, and 7, respectively.
Figure 8. Sea ice concentration analyzed field from the MSRF scheme with
$ \beta' $ = 35 and$ M $ = 215 (a) and SIC analyzed field from the SMRF scheme (b) on August 14, 2023.
Figure 9. Sea ice concentration analyzed field (left column) and the descent direction (right column) of the MSRF scheme (
$ \beta' $ = 35) at iteration 7, 80, and 140.
Figure 10. Differences between the analyzed field and the true sea ice concentration field in the MSRF scheme (a) and the SMRF scheme (b). The blue and pink pentagrams are located at (87°N, 88°E) and (80.5°N, 150°W), respectively.
Figure 11. Histogram of the deviation between the analyzed field and the true sea ice concentration field in the MSRF scheme (a) and SMRF scheme (b).
Figure 12. Comparison of RMSE (a) and MAD (b) in the MSRF scheme and the SMRF scheme from August 11 to August 31, 2023.
Table 1. Comparison of RMSE, MAD and CPU computation time between the MSRF scheme and SMRF scheme on August 14, 2023 and August 8, 2022 (bold)
Scheme RMSE MAD Iteration step CPU time/s MSRF scheme 0.0652 0.0297 215 12.137 0.0655 0.0289 215 12.558 SMRF scheme 0.0656 0.0307 500 88.936 0.0660 0.0301 500 85.161 
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Cao Xiaoqun, Huang Sixun, Zhang Weimin, et al. 2008. Modeling background error covariance in regional 3D-VAR. Scientia Meteorologica Sinica (in Chinese), 28(1): 8–14 Cavalieri D J, Parkinson C L, DiGirolamo N, et al. 2012. Intersensor calibration between F13 SSMI and F17 SSMIS for global sea ice data records. IEEE Geoscience and Remote Sensing Letters, 9(2): 233–236, doi: 10.1109/LGRS.2011.2166754 Chen Dake. 2011. A Collection of Argo Research Papers (in Chinese). Beijing: China Ocean Press, 1–16 Hayden C M, Purser R J. 1995. Recursive filter objective analysis of meteorological fields: applications to NESDIS operational processing. Journal of Applied Meteorology, 34(1): 3–15, doi: 10.1175/1520-0450-34.1.3 He Guangxin, Li Gang, Zhang Hua. 2011. The scheme of high-order recursive filter for the GRAPES-3DVar with its initial experiments. Acta Meteorologica Sinica (in Chinese), 69(6): 1001–1008 He Zhongjie, Xie Yuanfu, Li Wei, et al. 2008. Application of the sequential three-dimensional variational method to assimilating SST in a global ocean model. Journal of Atmospheric and Oceanic Technology, 25(6): 1018–1033, doi: 10.1175/2007JTECHO540.1 Huang Xiangyu. 2000. Variational analysis using spatial filters. Monthly Weather Review, 128(7): 2588–2600, doi: 10.1175/1520-0493(2000)128<2588:VAUSF>2.0.CO;2 Li Dong, Wang Xidong, Zhang Xuefeng, et al. 2011. Multi-scale 3D-VAP based on diffusion filter. Marine Science Bulletin (in Chinese), 30(2): 164–171 Li Wei, Xie Yuanfu, He Zhongjie, et al. 2008. Application of the multigrid data assimilation scheme to the China Seas’ temperature forecast. Journal of Atmospheric and Oceanic Technology, 25(11): 2106–2116, doi: 10.1175/2008JTECHO510.1 Lorenc A. 1992. Iterative analysis using covariance functions and filters. Quarterly Journal of the Royal Meteorological Society, 118(505): 569–591 Meier W N, Stewart J S, Wilcox H, et al. 2021. Near-Real-Time DMSP SSMIS Daily Polar Gridded Sea Ice Concentrations, Version 2. [Indicate subset used]. Boulder, CO, USA: NASA National Snow and Ice Data Center Distributed Active Archive Center Moré J J, Thuente D J. 1994. Line search algorithms with guaranteed sufficient decrease. ACM Transactions on Mathematical Software, 20(3): 286–307, doi: 10.1145/192115.192132 Peng Shiqiu, Xie Lian, Liu Bin, et al. 2010. Application of scale-selective data assimilation to regional climate modeling and prediction. Monthly Weather Review, 138(4): 1307–1318, doi: 10.1175/2009MWR2974.1 Purser R J, Wu Wanshu, Parrish D F, et al. 2003a. Numerical aspects of the application of recursive filters to variational statistical analysis. Part I: spatially homogeneous and isotropic Gaussian covariances. Monthly Weather Review, 131(8): 1524–1535, doi: 10.1175//1520-0493(2003)131<1524:NAOTAO>2.0.CO;2 Purser R J, Wu Wanshu, Parrish D. 2003b. Numerical aspects of the application of recursive filters to variational statistical analysis. Part II: spatially inhomogeneous and anisotropic general covariances. Monthly Weather Review, 131(8): 1536–1548, doi: 10.1175//2543.1 Vandenberghe F, Kuo Y H. 1999. Introduction to the MM5 3D-VAR data assimilation system: theoretical basis. NCAR Technical Note 917, https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=93c68ddfd4ababe95cda33ba8d5eea25d60cdab1 Wu Xinrong, Han Guijun, Li Dong, et al. 2011. A three-dimensional variational analysis using sequential filter. In: Proceedings of the 2011 Fourth International Joint Conference on Computational Sciences and Optimization. Washington, DC, USA: IEEE Computer Society, 1016–1020 Wu Yang, Xu Zhifang, Wang Ruichun, et al. 2018. Improvement of GRAPES_3Dvar with a new multi-scale filtering and its application in heavy rain forecasting. Meteorological Monthly (in Chinese), 44(5): 621–633 Xie Y, Koch S, McGinley J, et al. 2011. A space-time multiscale analysis system: a sequential variational analysis approach. Monthly Weather Review, 139(4): 1224–1240, doi: 10.1175/2010MWR 3338.1 Yang Lu, Li Dong, Zhang Xuefeng, et al. 2022. A multi-scale high-order recursive filter approach for the sea ice concentration analysis. Acta Oceanologica Sinica, 41(2): 103–115, doi: 10.1007/s13131-021-1940-x Zeng Zhongyi. 2006. Inverse Problems in Atmospheric Science (in Chinese). Taiwan, China: National Editorial Library, 323–326 Zhang Hua, Xue Jishan, Zhuang Shiyu, et al. 2004. Idea experiments of GRAPeS three-dimensional variational data assimilation system. Acta Meteorologica Sinica (in Chinese), 62(1): 31–41 Zhang Xuefeng, Yang Lu, Fu Hongli, et al. 2020. A variational successive corrections approach for the sea ice concentration analysis. Acta Oceanologica Sinica, 39(9): 140–154, doi: 10.1007/s13131-020-1654-5 Zhuang Zhaorong, Li Xingliang. 2021. The application of superposition of Gaussian components in GRAPES-RAFS. Acta Meteorologica Sinica (in Chinese), 79(1): 79–93 Zhuang Zhaorong, Li Xingliang, Chen Chungang. 2021. Properties of horizontal correlation models and its application in GRAPES 3DVar system. Chinese Journal of Atmospheric Sciences (in Chinese), 45(1): 229–244 -
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