基于L1范数正则项约束的不连续资料三维/四维变分融合研究

Discontinuous Data 3D/4D Variation Fusion Based on the Constraint of L1 Norm Regularization Term

经典三维/四维变分融合基于误差服从高斯分布,在极小化迭代时涉及到求解目标泛函梯度,若资料不连续则不可微,从而无法求解相应梯度,故理论要求所融合的资料必须具有"连续性"。采用扩展经典三维/四维变分融合方法,显式地基于L1范数把先验知识作为正则项约束项耦合到经典变分融合模型。在实施过程中把资料映射到小波域,采用新的融合模型在"小波空间"完成资料融合后,再采用小波逆变换映射回"观测空间"。通过线性平流扩散方程作为四维预报模式进行理想试验,试验设计融合背景和观测资料不连续,即在某些点左右导数不相等,试验结果表明文中采用的方法可行。进一步将该方法用于多源降水资料融合试验,采用基于GAMMA拟合函数的概率密度匹配法(Probability Density Function matching method,PDF)进行CMORPH反演降水资料订正,再将订正后的资料与地面站观测资料进行融合。通过与参考场结构相似性度量,得到该方法能更好地保留代表一些天气现象的"离群点"。该融合方法为不连续资料融合,尤其是"跳变点"的变分融合奠定了理论基础并提供了可借鉴的方法。

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 fourdimensional 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 Densi- ty Function, PDF） matching method based on GAMMA fitting function. Then corrected data was fused with the ob- servation 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 Ll-norm regularization variation fusion in this paper provided a possible way to deal with discrete data, especially for jump point.