## 1 Introduction  
A large number of continental- and global-scale applications at 30 m resolution have been created and have pushed the discoveries using remote sensing at higher spatial resolution forward, since the Landsat series of satellite data have been made freely downloadable. These applications include the Finer Resolution Observation and Monitoring of Global Land Cover project [1], the Global ForestCover Change [2], etc. With increasing moderate to high spatial-resolution (MHSR) optical data available, the research and applications with higher spatial resolution at global scale is dramatically increasing. In particular, the satellite constellations with higher spatial resolution optical sensors will dramatically increase the observations with higher resolution, such as the Sentinle2 Multispectral Instrument (MSI) of European Space Agency (ESA), the Chinese GaoFen 1 (GF1) and GaoFen 6 (GF6) Wide Field Viewers (WFVs), and so on. However, the atmospheric effect on optical remote-sensing imagery usually degrades the applications and the temporal and spatial variation of aerosols are very difficult to completely remove [3; 4]. A better surface reflectance dataset with spatial and temporal consistency at global scale has been required by the global-scale applications at higher spatial resolution and some methods have been developed for this purpose, such as the Landsat Ecosystem Disturbance Adaptive Processing System (LEDAPS) algorithm [5] and the Moderate-resolution Imaging Spectroradiometer (MODIS)-based algorithms [6; 7]. Firstly, both of the methods used the MODIS aerosol optical depth (AOD) product [8; 9; 10] with a lower spatial resolution of 7-10 km, which is only 1/20-1/30 of the required resolution, and a large portion of void areas, especially arid areas, were interpolated; subsequently, the spatial distribution of aerosols at high resolution (30 m and higher) cannot be captured well, which causes spatial inconsistency. In addition, the situations in arid areas were not taken into consideration, which largely degraded the applications in these areas. For MHSR remote-sensing data, the dark target (DT) method [11] including dense dark vegetation (DDV) [8] is the most used and only partial areas of an image with dark objects are used to retrieve the AOD, which fails at areas without dense vegetation or shadow. The contrast reduction (CR) method [12] is developed specifically for stable surface and it use the variation of aerosol over stable surface from multi-temporal images to extract AOD; however, it needs a clear image as a reference, or it fails. ImAero-Landsat [13] is a hybrid method by integrating DDV and contrast reduction; the shortcoming of the contrast reduction method is not avoidable. The histogram-matching method [14] needs the identification of clear regions in an image in the first place, which is very difficult for automation and usually requires manual intervention [14]. Thus, the AOD retrieval and atmospheric correction for images over arid areas with bright surfaces remains a challenge. The method based on spatial expansion [15] has partially solved this problem; however, some images with very high resolution containing only bright surfaces will fail because of no initial AOD retrieved. In order to automatically retrieve accurate AOD over arid areas with bright surfaces from MHSR remotely sensed imagery, we present a new method that can better estimate the aerosols and retrieve surface reflectance from MHSR imagery in arid areas with bright surfaces. Land surface in arid areas is usually bright and stable and the variation of atmosphere in these areas is also very small; consequently, the land-surface characteristics, specifically the bidirectional reflectance distribution factor (BRDF), can be retrieved easily and accurately using time series of satellite images with relatively lower spatial resolution like MODIS with 500 m resolution and the retrieved BRDF is then used to retrieve the AOD from MHSR images.