# The Influence of Glacier Mass Balance on River Runoff in the Typical Alpine Basin
## 1 Introduction  
Alpine glaciers are important indicators of climate change. According to the latest report from the IPCC (Intergovernmental Panel on Climate Change) [1], previous claims about the melting of alpine glaciers causing a rise in sea levels have been exaggerated [2]. According to the IPCC's sixth report [3], global climate warming and the increasing frequency of extreme weather events have caused the temperatures in alpine and polar areas torise at a faster rate than coastal and oceanic areas, thereby accelerating the retreat of alpine glaciers [4]. In the High Asia region, especially in the Tibetan Plateau and its surrounding areas, there is a significant distribution of alpine glaciers, which serve as important sources of natural and human-induced water downstream. The state of glaciers exhibits systematic differences influenced by factors such as regional temperature and precipitation [5]. However, the majority of alpine glaciers are undergoing a mass loss and reduction in area [6; 7; 8], with an accelerated trend of glacier retreat [9; 10; 11; 12], particularly in recent decades. The potential consequences of increasingly vulnerable glaciers include an unsustainable water supply for rivers and the occurrence of glacier-related hazards such as glacier lake expansion, glacier lake outburst, and floods. These changes have profound implications for the socio-economic development and water resource allocation downstream [13]. Therefore, conducting the mapping and monitoring of alpine glaciers holds significant scientific and realistic importance [14]. Remote-sensing technology can relatively easily monitor changes in the area and the length of alpine glaciers [15]. However, changes in glacier area alone do not fully reflect changes in glacier mass. In comparison to glacier area, changes in glacier mass are more sensitive to climate change, have a more direct impact, and provide a more effective reflection of contributions to glacier meltwater [16]. Currently, the methods for estimating changes in glacier mass include the area-thickness empirical method, the area-volume empirical method, and glacier physical models for glacier mass estimation [17; 18]. Changes in glacier area often lead to changes in glacier volume and thickness. During glacier area measurements, the presence of abundant debris on the glacier surface often hinders accurate area determination. Therefore, changes in GSE become crucial information for monitoring glaciers [19]. By acquiring the changes in GSE and incorporating glacier density, it is possible to convert the information on the GSE change into GMB [17; 20]. Remote-sensing technology such as optical stereo-photogrammetry, LiDAR (Light Detection and Ranging), and SAR (Synthetic Aperture Radar) have become important methods for the large-scale monitoring of GSE change, estimating glacier volume change, and determining GMB [21]. Currently, remote-sensing technology for monitoring GSE change include D-InSAR (Differential Interferometric Synthetic Aperture Radar) measurement, DEM difference method, and LiDAR-based elevation measurement. Laser altimetry satellites utilized for glacier elevation measurements include Jason-2, Jason-3, GryoSat SARin, GEDI (Global Ecosystem Dynamics Investigation), ICESat-1 (Ice, Cloud, and Land Elevation Satellite-1), and ICESat-2 (Ice, Cloud, and Land Elevation Satellite-2). Laser altimetry satellites can only provide elevation measurements at specific laser footprint locations, and the distribution of laser footprints along the entire glacier is often sparse. This leads to significant uncertainties in obtaining the surface elevation of the entire glacier through interpolation. Due to the challenging terrain and inaccessibility of glacier areas, it is difficult to obtain ground-truth measurements of ice surface elevation changes. In such cases, the multi-source DEM difference method based on geodetic principles can be used to cover the entire glacier or the entire area, providing more representative results of GSE.