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Advances in Earth Science  2017, Vol. 32 Issue (7): 757-768    DOI: 10.11867/j.issn.1001-8166.2017.07.0757
Discontinuous Data 3D/4D Variation Fusion Based on the Constraint of L1 Norm Regularization Term
Wang Gen1, 2, Sheng Shaoxue1, Liu Huilan1, Wu Rong3, Yang Yin4
1.Anhui Meteorological Information Centre Anhui Key Laboratory of Atmospheric Science and Satellite Remote Sensing, Hefei 230031, China;
2.The Institute of Atmospheric Environment, China Meteorological Administration, Shenyang 110000, China;
3.Anhui Climate Center, Hefei 230031, China;
4.National Meteorological Center of China, Beijing 100081, China
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Abstract  Classical 3D/4D variation fusion is based on the theory that error follows Gaussian distribution. When using minimization iteration, the gradient of objective function is involved, and the solution of which requires the continuity of data. This paper adopted the extended classical 3D/4D variation fusion method, and explicitly applied the prior knowledge, which was based on L1-norm, as regularization constraint to the classical variation fusion method. Original data was firstly projected into the wavelet domain during the implementation process, and new fusion model was adopted for data fusion in wavelet space, then inverse wavelet transform was used to project the result to the observation space. Ideal experiment was carried out by using linear advection-diffusion equation as four-dimensional prediction model, which made a hypothesis of the discontinuity with the data between background and observation, and that meant the derivatives between left and right were not equal on some points. The result of the experiment showed that the method adopted here was practicable. A further research was also done for multi-source precipitation fusion. Firstly, CMORPH inversion precipitation data were corrected through PDF (Probability Density Function, PDF) matching method based on GAMMA fitting function. Then corrected data was fused with the observation one. By comparison with the reference field, the result showed that this method can keep some outliers better, which might represent certain weather phenomenon. The L1-norm regularization variation fusion in this paper provided a possible way to deal with discrete data, especially for jump point.
Key words:  L1-norm      Regularization term      Variation fusion      Wavelet space.      Discrete data     
Received:  26 February 2017      Published:  20 July 2017
ZTFLH:  P468  
Fund: Project supported by the Natural Science Foundation of Anhui Province“Generalised variational assimilation of AIRS water vapor channel brightness temperature and the application study in severe convective weather in Anhui Province”(No.1708085QD89); The Open Research Fund of Huai River Basin in Meteorological “Study of precipitation data fusion algorithm in Jianghuai Basin based on the ground and satellite observations”(No.HRM201407)
About author:  Wang Gen(1983-),male,Taizhou City, Jiangsu Province, Engineer. Research areas include satellite data assimilation, numerical simulation of GRAPES and multi-source data
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Wang Gen, Sheng Shaoxue, Liu Huilan, Wu Rong, Yang Yin. Discontinuous Data 3D/4D Variation Fusion Based on the Constraint of L1 Norm Regularization Term. Advances in Earth Science, 2017, 32(7): 757-768.

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