The MODIS land surface temperature (LST) products contain large areas of missing data due to cloud contamination. Interpolating clear-sky equivalent LSTs on those areas is a first step in a stepwise approach toward fully recovering missing data. A previous study (viz. the Yu method) has implemented an effective clear-sky interpolation method, especially targeting large-area missing data. The Yu method postulates several global reference LST images that contain over 90% of valid pixels and that are assumed to have a close statistical relationship to the interpolated images. However, in practice, such reference images are rarely available throughout a one-year cycle, and the time gaps between the available reference images and the interpolated images are often huge, resulting in compromised interpolation accuracy. In this study, we intended to address those weaknesses and propose a novel clear-sky interpolation approach. The proposed approach uses multiple temporally proximate images as reference images, with which multiple initial estimates are made by an empirically orthogonal function method and then fused by a Bayesian approach to achieve a best estimate. The proposed approach was compared through two experiments to the Yu method and two other widely used methods, i.e., harmonic analysis of time series and co-kriging. Both experiments demonstrate the superiority of the proposed approach over those established methods, as evidenced by higher spatial correlation coefficients (0.90–0.94) and lower root-mean-square errors (1.19–3.64 °C) it achieved when measured against the original data that were intentionally removed.

中文翻译：

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一种用于在具有大量缺失数据的区域内插值晴空 MODIS 地表温度的贝叶斯方法

由于云污染，MODIS 地表温度 (LST) 产品包含大面积的缺失数据。在这些区域内插晴空等效 LST 是逐步恢复丢失数据的第一步。之前的一项研究（即 Yu 方法）实施了一种有效的晴空插值方法，特别是针对大面积缺失数据。Yu 方法假定多个全局参考 LST 图像包含超过 90% 的有效像素，并且假定这些图像与插值图像具有密切的统计关系。然而，在实践中，这样的参考图像很少能在一年的周期内获得，并且可用参考图像和插值图像之间的时间间隔往往很大，导致插值精度受到影响。在这项研究中，我们打算解决这些弱点并提出一种新颖的晴空插值方法。所提出的方法使用多个时间上接近的图像作为参考图像，通过经验正交函数方法对其进行多个初始估计，然后通过贝叶斯方法进行融合以获得最佳估计。所提出的方法通过两个实验与 Yu 方法和另外两种广泛使用的方法进行了比较，即时间序列的调和分析和协同克里金法。两个实验都证明了所提出的方法优于那些已建立的方法，这可以通过更高的空间相关系数 (0.90–0.94) 和较低的均方根误差 (1.19–3.64 °C) 来证明，当针对原始数据进行测量时，被故意删除。