通过机载双天线微波辐射计的观测数据层析反演出云液水的空间分布是一个有限角度的图像重建问题。为提高这一反问题的适定性, 本文对已有的正则化方法进行了改进: 根据云液水的分布特征选择W1,2空间范数的离散形式作为正则项; 通过数值模拟试验确定双天线仰角的最优设置方案为 (30°, 90°) 等。为避免已有方法中对目标函数进行线性化处理而产生的模型误差, 采用L-BFGS-B算法对非线性目标函数直接求解。按照侧边界内云液水分布是否已知将反演模型分为已界模型和未界模型。已界模型的反演结果表明, 反演误差在8.6%～12.3%之间, 反演图像可以反映出不同云型的结构特征。敏感性试验表明, 影响反演精度的主要因素为投影数据的角度分辨率、 辐射计观测噪声以及侧边界云液水分布的不确定性; 受云液水含量、 正则算子特性及边界因素的综合影响, 不同云型的反演精度存在差异。为使微波辐射计探测云液水分布能够独立于其它探测手段, 本文针对未界模型提出嵌套反演方法。数值模拟试验表明, 嵌套反演方法可以为目标区域的反演提供足够的侧边界信息。
Retrieving spatial distributions of cloud liquid water content (LWC) from the airborne double-antenna microwave radiometer data by tomography method is a limited-angle image reconstruction. In order to enhance the well-posedness of this inverse problem, this paper improves the current regularization methods through using the discrete form of the norm in W1, 2 space as the regular term according to the characteristic of LWC distribution and choosing (30°, 90°) as the best combination of the double antenna elevation angles according to the results of numerical simulations. The L-BFGS-B algorithm is used to solve the nonlinear optimization problem to avoid the model error caused by the linearization. The retrieval model falls into two types according as the LWC distribution in the lateral boundary is known or unknown and they are called Yijie model and Weijie model for short. The retrieval results of the Yijie model show that the relative error is 8.6%－12.3% and the structure of different cloud types can be showed in the retrieval images. Sensitivity studies indicate that the number of scanning angles, the radiometer noise level, and the uncertainty of LWC in the lateral boundary affect the retrieval accuracy most. Besides, the retrieval accuracy also varies in different cloud types because of the magnitude of the LWC, the characteristic of the regular operator, and the lateral boundary factor. In order to make the remote sensing of LWC distributions independent of other instruments, the nesting retrieval method is developed to retrieve the Weijie model. The numerical simulation shows that the nesting method can offer enough information of the lateral boundary for retrieving the LWC distribution in the target area.