## 1 Introduction  
Terrestrial snow cover and glaciers are major components of the cryosphere, representing two of the fastest-changing geographical features on the earth's surface. They occur over a large proportion of the Earth's continents. They are also sensitive indicators of climate change because they show a wide range of responses to variations in global temperature. Snow cover extent in the Northern Hemisphere is greatest in January of each year, encompassing an average area of 46.5 million\(\cdot\)km\({}^{2}\). The annual average areal cover is approximately 25.3 million\(\cdot\)km\({}^{2}\), with a standard deviation of 1.1 million\(\cdot\)km\({}^{2}\)[1]. In arid regions such as the Tarm River Basin in China, mountain-fed rivers are the only available water sources that can meet societal needs such as public supply, agriculture, irrigation, and hydropower. Hence, variation in the extent of snow cover in the Tarm Basin might affect subsequent spring and summer river runoff, which could have an impact on the socioeconomic development of the region, disturb fragile ecosystems, and even lead to an increase in the frequency of droughs and/or flood-related disasters [2]. The mapping of snow cover is important for both the calculation of energy balances and the prediction of climate patterns; therefore, its accurate determination is of paramount importance [3]. Recent technological advances in remote sensing have made it possible to use satellite data to extract historical and near real-time information on the areal amount and extent of snow cover. Of the many options available, the Snow Cover Daily L3 Global 500-m Grid (MOD10A1) dataset is used widely to monitor daily changes in the spatiotemporal distribution of snow over large areas. This freely available global dataset, which has undergone many reprocessing steps, has proven highly useful for the monitoring and mapping of snow cover changes at high temporal frequency [4; 5; 6]. One MODIS (MODerate-resolution Imaging Spectroradiometer) scan line is composed of 2708 observations at 500-m intervals, where the sensor zenith angle (SZA) approaches 65\({}^{\circ}\) at the end of each profile [7]. Pixels representing snow cover in MOD10A1 are selected by a scoring algorithm that uses observations obtained nearest to local noon and closest to the SZA nadir [8]. However, the large cross-track scan angle of MODIS has raised doubts about the quality of MOD10A1 data at the end of each scan line. Uncertainty related to the estimation of snow cover at high values of SZA is mentioned in the MOD10A1 official documentation [9], which has led many workers to investigate the effect of viewing geometry on the image reflectance, normalized index, and pixel areas [10]. Associated studies have also been conducted into the influence of topography or underlying surface conditions [11]. Variations in the SZA and solar zenith angle in relation to the canopy reflectance of wheat have shown that the ratio of off-nadir to nadir radiance increases (or decreases) as SZA increases (or decreases) [12]. MODIS Level-3 data have also been used to quantify the effects of SZA on the cloud properties of MODIS, which revealed that the amount of cloud \"observed\" by MODIS increases remarkably between the nadir and the scan-line terminus [13]. A lower SZA was found to coincide with higher reflectance, and vice versa [14], which led to the discovery of inaccuracies in snow cover pixels at off-nadir viewing angles. The primary source of error in this case is thought to stem from pixel expansion at off-nadir viewing angles, which leads to neighboring (non-snow-covered) pixels adopting incorrect reflectance values [15]. A semiempirical parametric model of the angular pattern of snow cover in forested areas has been established [16]. Errors in snow cover estimation are exacerbated for large SZAs in forested areas [17] because the snow-covered canopy causes the sensor to interpret a greater snow cover fraction at near-nadir views. By contrast, observable snow cover is reduced at the end of a MODIS scan line.