# Comparison of Methods for Reconstructing MODIS Land Surface Temperature under Cloudy Conditions
## 1 Introduction  
Land surface temperature (LST) is one of the most important parameters associated with the land-atmosphere interface, and has important research significance in many fields, including climate, ecology, hydrology, and habitat chemistry [1; 2; 3]. It reflects the physical process of the interaction between the land surface and the atmosphere on regional and global scales, and is an indispensable and important parameter for the study of climate change, the urban heat island effect, and so on [4; 5; 6]. In recent years, with the rapid development of remote sensing technology, the acquisition of LST no longer depends on the radiometers at weather stations, but on satellite datasets from around the world. Remote sensing is playing an increasingly important role in thermal infrared research associated with LST [7]. Currently, the available LST satellite datasets include the Moderate-Resolution Imaging Spectrometer (MODIS), the Advanced Very-High-Resolution Radiometer (AVHRR), and the Advanced Along-Track Scanning Radiometer (AATSR) [8]. Among these, the MODIS sensors carried on the Terra and Aquasatellites are one of the most widely used sources of satellite-derived LST, because of their superior spatial and temporal resolution. MODIS provides multiple daily LST products from thermal infrared bands using a split window algorithm [9; 10]. However, the algorithm is only effective when the data have been acquired under clear-sky conditions. In the case of cloudy weather or other atmospheric interference with radiation transmission, the retrieval of LST is greatly affected. As a result, MODIS LST suffers from contamination by cloud-top temperature, which leads to the greater or lesser appearance of null-value pixels in the LST products [11; 12]. Only under clear-sky conditions do pixels in LST products have valid values. For regions with undesirable weather conditions that lead to extensive cloud cover, little valid information can be found in daily LST products [10]. Cloudy-sky conditions have a greatly negative influence on these regions, because their presence means the surface energy is not truly reflected, which greatly limits the subsequent applications in related fields [13]. Therefore, the MODIS LST products need to be improved in order to overcome these limitations before being used in research. In other words, research into MODIS LST reconstruction is of great significance [11]. At present, mainly interpolation methods are used in the reconstruction of MODIS LST, and many novel interpolation methods have been proposed for daily MODIS LST reconstruction [14; 15; 16] that only use limited spatiotemporal information. Methods for the reconstruction of MODIS LST can be divided into three kinds of methods: spatial, temporal, and spatiotemporal [12]. For temporal methods, invalid values are estimated on a pixel-by-pixel basis, and the values of geographically adjacent pixels are not considered. Spatial methods only consider the values of adjacent pixels and do not include values from different periods [17]. Spatiotemporal methods consider neighboring pixels in both the temporal and spatial domains. Among the spatial methods, a method based on the assumption that LST is related to elevation was proposed by [PERSON] et al., 2012 [18]. For each invalid pixel, an adaptive window was used to recover it based on the linear relationship between other valid pixel values with elevation. On this basis, ordinary least squares (OLS) regression is performed, in which LST is modeled as a linear function of elevation. Then the missing value can be interpolated on the basis of evaluation of the exported function at the elevation of the pixel center. Among the temporal methods, [PERSON], 2016 [19] and [PERSON] et al., 2015 [20] adopted the Linear Temporal method. For each invalid value on the image, the rate of change in the LST between the closest preceding and succeeding 8-day periods with data is determined, and a linear equation is constructed.