基于高光谱大气红外探测器模拟亮温的稳健变分反演研究

经典变分反演法是基于观测误差服从高斯分布的假定，对偏离均值较大的离群值较敏感。当实际观测数据包含离群值观测误差呈现非高斯分布时，如果采用经典反演法进行变分反演就会产生大的偏差，甚至导致变分反演的失败。使用经典变分反演法首先需要进行质量控制，剔除所谓的离群值，但有相当部分的离群值包含了一些亮点，如天气现象。如果对其“视而不见”，则对很多重要的信息就无法把握。基于此，研究采用稳健变分反演的思想同化这些离群值，主要思想是把M-估计法（L2、Huber、Fair和Cauchy一估计）的权重函数耦合到经典变分反演中，在每次变分反演极小化迭代过程中重新估计观测项对经典变分反演目标泛函的贡献率。采用高光谱大气红外探测器（AtmosphericInfraRedSounder，AIRS）的通道模拟亮温进行理想试验，结果表明：采用Huber一估计进行稳健变分反演对温度和湿度反演具有较好的效果；采用Cauchy-估计得到的效果反而更差，这是由Cauchy等分布函数固有的缺陷所决定的。因此，稳健变分反演观测误差非高斯分布是可行的，但依赖M-估计法权重函数的选取。

Study on Robust Variational Inversion Based on Hyper spectral Atmospheric InfraRed Sounder Simulated Brightness Temperature

Classical variational inversion method is based on the observation errors follow Gaussian distribution assumption, which is sensitive to the outliers that large deviation from the mean. When the observed data contain outliers and observation error meet non-Gaussian distribution, if adopting the classi- cal inversion method will get large deviation, and even lead to the failure of the variational inversion. U- sing classical variational inversion method, quality control is firstly required in order to remove the so- called outliers. But there are some outliers contain the highlights, such as weather phenomenon. If neg- lect these outliers, a lot of useful data will be lost. In this paper, the idea of robust variational inversion is used to assimilate these outliers. The main idea is to use weighting function of M-estimators（L2, Hu- bet, Fair and Cauchy-estimator） coupling to the classical variational inversion, re-estimate the contribu- tion rate of the observation items to the objective function during the each process of variational inversion minimization. The ideal experiments for using hyperspectral Atmospheric Infrared Sounder channel simu- lated brightness temperature, get the better inversion effect to inverse temperature and humidity by adopt Huber-estimator for robust variational inversion. But using Cauchy-estimator will have worse results than the classical one, this is determined by the inherent defects of Cauchy distribution function. These results indicate that the method is feasibly assimilating non-Gaussian by using robust variational inversion, but relies on selecting weight function of M-estimators.