Articles | Volume 29, issue 4 
            
                
                    
                    
                        
            
            
            https://doi.org/10.5194/hess-29-969-2025
                    © Author(s) 2025. This work is distributed under 
the Creative Commons Attribution 4.0 License.
                the Creative Commons Attribution 4.0 License.
Special issue:
                        
                    https://doi.org/10.5194/hess-29-969-2025
                    © Author(s) 2025. This work is distributed under 
the Creative Commons Attribution 4.0 License.
                the Creative Commons Attribution 4.0 License.
A mathematical model to improve water storage of glacial lake prediction towards addressing glacial lake outburst floods
Miaomiao Qi
                                            Yunnan Key Laboratory of International Rivers and Transboundary Eco-Security, Yunnan University, Kunming 650091, China
                                        
                                    
                                            Institute of International Rivers and Eco-Security, Yunnan University, Kunming 650091, China
                                        
                                    
                                            Yunnan International Joint Laboratory of China–Laos–Bangladesh–Myanmar Natural Resources Remote Sensing Monitoring, Kunming 650091, China
                                        
                                    
                                            School of Earth Sciences, Yunnan University, Kunming 650500, China
                                        
                                    
                                            Yunnan Key Laboratory of International Rivers and Transboundary Eco-Security, Yunnan University, Kunming 650091, China
                                        
                                    
                                            Institute of International Rivers and Eco-Security, Yunnan University, Kunming 650091, China
                                        
                                    
                                            Yunnan International Joint Laboratory of China–Laos–Bangladesh–Myanmar Natural Resources Remote Sensing Monitoring, Kunming 650091, China
                                        
                                    Zhifang Zhao
CORRESPONDING AUTHOR
                                            
                                    
                                            Yunnan International Joint Laboratory of China–Laos–Bangladesh–Myanmar Natural Resources Remote Sensing Monitoring, Kunming 650091, China
                                        
                                    
                                            School of Earth Sciences, Yunnan University, Kunming 650500, China
                                        
                                    Yongpeng Gao
                                            Faculty of Geography, Yunnan Normal University, Kunming 650500, China
                                        
                                    
                                            Key Laboratory of Resources and Environmental Remote Sensing for Universities in Yunnan, Kunming 650500, China
                                        
                                    Fuming Xie
                                            Yunnan Key Laboratory of International Rivers and Transboundary Eco-Security, Yunnan University, Kunming 650091, China
                                        
                                    
                                            Institute of International Rivers and Eco-Security, Yunnan University, Kunming 650091, China
                                        
                                    Georg Veh
                                            Institute of Environmental Science and Geography, University of Potsdam, Potsdam, Germany
                                        
                                    Letian Xiao
                                            Yunnan Key Laboratory of International Rivers and Transboundary Eco-Security, Yunnan University, Kunming 650091, China
                                        
                                    
                                            Institute of International Rivers and Eco-Security, Yunnan University, Kunming 650091, China
                                        
                                    Jinlong Jing
                                            School of Mathematics and Statistics, Yunnan University, 650091 Kunming, China
                                        
                                    
                                            Yunnan Key Laboratory of International Rivers and Transboundary Eco-Security, Yunnan University, Kunming 650091, China
                                        
                                    
                                            Institute of International Rivers and Eco-Security, Yunnan University, Kunming 650091, China
                                        
                                    Kunpeng Wu
                                            Yunnan Key Laboratory of International Rivers and Transboundary Eco-Security, Yunnan University, Kunming 650091, China
                                        
                                    
                                            Institute of International Rivers and Eco-Security, Yunnan University, Kunming 650091, China
                                        
                                    Related authors
Fuming Xie, Shiyin Liu, Yongpeng Gao, Yu Zhu, Tobias Bolch, Andreas Kääb, Shimei Duan, Wenfei Miao, Jianfang Kang, Yaonan Zhang, Xiran Pan, Caixia Qin, Kunpeng Wu, Miaomiao Qi, Xianhe Zhang, Ying Yi, Fengze Han, Xiaojun Yao, Qiao Liu, Xin Wang, Zongli Jiang, Donghui Shangguan, Yong Zhang, Richard Grünwald, Muhammad Adnan, Jyoti Karki, and Muhammad Saifullah
                                    Earth Syst. Sci. Data, 15, 847–867, https://doi.org/10.5194/essd-15-847-2023, https://doi.org/10.5194/essd-15-847-2023, 2023
                                    Short summary
                                    Short summary
                                            
                                                In this study, first we generated inventories which allowed us to systematically detect glacier change patterns in the Karakoram range. We found that, by the 2020s, there were approximately 10 500 glaciers in the Karakoram mountains covering an area of 22 510.73 km2, of which ~ 10.2 % is covered by debris. During the past 30 years (from 1990 to 2020), the total glacier cover area in Karakoram remained relatively stable, with a slight increase in area of 23.5 km2.
                                            
                                            
                                        Jakob Steiner, William Armstrong, Will Kochtitzky, Robert McNabb, Rodrigo Aguayo, Tobias Bolch, Fabien Maussion, Vibhor Agarwal, Iestyn Barr, Nathaniel R. Baurley, Mike Cloutier, Katelyn DeWater, Frank Donachie, Yoann Drocourt, Siddhi Garg, Gunjan Joshi, Byron Guzman, Stanislav Kutuzov, Thomas Loriaux, Caleb Mathias, Biran Menounos, Evan Miles, Aleksandra Osika, Kaleigh Potter, Adina Racoviteanu, Brianna Rick, Miles Sterner, Guy D. Tallentire, Levan Tielidze, Rebecca White, Kunpeng Wu, and Whyjay Zheng
                                        Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2025-315, https://doi.org/10.5194/essd-2025-315, 2025
                                    Preprint under review for ESSD 
                                    Short summary
                                    Short summary
                                            
                                                Many mountain glaciers around the world flow into lakes – exactly how many however, has never been mapped. Across a large team of experts we have now identified all glaciers that end in lakes. Only about 1% do so, but they are generally larger than those which end on land. This is important to understand, as lakes can influence the behaviour of glacier ice, including how fast it disappears. This new dataset allows us to better model glaciers at a global scale, accounting for the effect of lakes.
                                            
                                            
                                        Yu Zhu, Shiyin Liu, Junfeng Wei, Kunpeng Wu, Tobias Bolch, Junli Xu, Wanqin Guo, Zongli Jiang, Fuming Xie, Ying Yi, Donghui Shangguan, Xiaojun Yao, and Zhen Zhang
                                    Earth Syst. Sci. Data, 17, 1851–1871, https://doi.org/10.5194/essd-17-1851-2025, https://doi.org/10.5194/essd-17-1851-2025, 2025
                                    Short summary
                                    Short summary
                                            
                                                This study compiled a near-complete inventory of glacier mass changes across the eastern Tibetan Plateau using topographical maps. These data enhance our understanding of glacier change variability before 2000. When combined with existing research, our dataset provides a nearly 5-decade record of mass balance, aiding hydrological simulations and assessments of mountain glacier contributions to sea-level rise.
                                            
                                            
                                        Natalie Lützow, Bretwood Higman, Martin Truffer, Bodo Bookhagen, Friedrich Knuth, Oliver Korup, Katie E. Hughes, Marten Geertsema, John J. Clague, and Georg Veh
                                    The Cryosphere, 19, 1085–1102, https://doi.org/10.5194/tc-19-1085-2025, https://doi.org/10.5194/tc-19-1085-2025, 2025
                                    Short summary
                                    Short summary
                                            
                                                As the atmosphere warms, thinning glacier dams impound smaller lakes at their margins. Yet, some lakes deviate from this trend and have instead grown over time, increasing the risk of glacier floods to downstream populations and infrastructure. In this article, we examine the mechanisms behind the growth of an ice-dammed lake in Alaska. We find that the growth in size and outburst volumes is more controlled by glacier front downwaste than by overall mass loss over the entire glacier surface.
                                            
                                            
                                        Yu Zhu, Shiyin Liu, Ben W. Brock, Lide Tian, Ying Yi, Fuming Xie, Donghui Shangguan, and Yiyuan Shen
                                    Hydrol. Earth Syst. Sci., 28, 2023–2045, https://doi.org/10.5194/hess-28-2023-2024, https://doi.org/10.5194/hess-28-2023-2024, 2024
                                    Short summary
                                    Short summary
                                            
                                                This modeling-based study focused on Batura Glacier from 2000 to 2020, revealing that debris alters its energy budget, affecting mass balance. We propose that the presence of debris on the glacier surface effectively reduces the amount of latent heat available for ablation, which creates a favorable condition for Batura Glacier's relatively low negative mass balance. Batura Glacier shows a trend toward a less negative mass balance due to reduced ablation.
                                            
                                            
                                        Monika Pfau, Georg Veh, and Wolfgang Schwanghart
                                    The Cryosphere, 17, 3535–3551, https://doi.org/10.5194/tc-17-3535-2023, https://doi.org/10.5194/tc-17-3535-2023, 2023
                                    Short summary
                                    Short summary
                                            
                                                Cast shadows have been a recurring problem in remote sensing of glaciers. We show that the length of shadows from surrounding mountains can be used to detect gains or losses in glacier elevation.
                                            
                                            
                                        Natalie Lützow, Georg Veh, and Oliver Korup
                                    Earth Syst. Sci. Data, 15, 2983–3000, https://doi.org/10.5194/essd-15-2983-2023, https://doi.org/10.5194/essd-15-2983-2023, 2023
                                    Short summary
                                    Short summary
                                            
                                                Glacier lake outburst floods (GLOFs) are a prominent natural hazard, and climate change may change their magnitude, frequency, and impacts. A global, literature-based GLOF inventory is introduced, entailing 3151 reported GLOFs. The reporting density varies temporally and regionally, with most cases occurring in NW North America. Since 1900, the number of yearly documented GLOFs has increased 6-fold. However, many GLOFs have incomplete records, and we call for a systematic reporting protocol.
                                            
                                            
                                        Dharmaveer Singh, Manu Vardhan, Rakesh Sahu, Debrupa Chatterjee, Pankaj Chauhan, and Shiyin Liu
                                    Hydrol. Earth Syst. Sci., 27, 1047–1075, https://doi.org/10.5194/hess-27-1047-2023, https://doi.org/10.5194/hess-27-1047-2023, 2023
                                    Short summary
                                    Short summary
                                            
                                                This study examines, for the first time, the potential of various machine learning models in streamflow prediction over the Sutlej River basin (rainfall-dominated zone) in western Himalaya during the period 2041–2070 (2050s) and 2071–2100 (2080s) and its relationship to climate variability. The mean ensemble of the model results shows that the mean annual streamflow of the Sutlej River is expected to rise between the 2050s and 2080s by 0.79 to 1.43 % for SSP585 and by 0.87 to 1.10 % for SSP245.
                                            
                                            
                                        Fuming Xie, Shiyin Liu, Yongpeng Gao, Yu Zhu, Tobias Bolch, Andreas Kääb, Shimei Duan, Wenfei Miao, Jianfang Kang, Yaonan Zhang, Xiran Pan, Caixia Qin, Kunpeng Wu, Miaomiao Qi, Xianhe Zhang, Ying Yi, Fengze Han, Xiaojun Yao, Qiao Liu, Xin Wang, Zongli Jiang, Donghui Shangguan, Yong Zhang, Richard Grünwald, Muhammad Adnan, Jyoti Karki, and Muhammad Saifullah
                                    Earth Syst. Sci. Data, 15, 847–867, https://doi.org/10.5194/essd-15-847-2023, https://doi.org/10.5194/essd-15-847-2023, 2023
                                    Short summary
                                    Short summary
                                            
                                                In this study, first we generated inventories which allowed us to systematically detect glacier change patterns in the Karakoram range. We found that, by the 2020s, there were approximately 10 500 glaciers in the Karakoram mountains covering an area of 22 510.73 km2, of which ~ 10.2 % is covered by debris. During the past 30 years (from 1990 to 2020), the total glacier cover area in Karakoram remained relatively stable, with a slight increase in area of 23.5 km2.
                                            
                                            
                                        Yu Zhu, Shiyin Liu, Junfeng Wei, Kunpeng Wu, Tobias Bolch, Junli Xu, Wanqin Guo, Zongli Jiang, Fuming Xie, Ying Yi, Donghui Shangguan, Xiaojun Yao, and Zhen Zhang
                                        Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2022-473, https://doi.org/10.5194/essd-2022-473, 2023
                                    Preprint withdrawn 
                                    Short summary
                                    Short summary
                                            
                                                In this study, we presented a nearly complete inventory of glacier mass change dataset across the eastern Tibetan Plateau by using topographical maps, which will enhance the knowledge on the heterogeneity of glacier change before 2000. Our dataset, in combination with the published results, provide a nearly five decades mass balance to support hydrological simulation, and to evaluate the contribution of mountain glacier loss to sea level.
                                            
                                            
                                        Adam Emmer, Simon K. Allen, Mark Carey, Holger Frey, Christian Huggel, Oliver Korup, Martin Mergili, Ashim Sattar, Georg Veh, Thomas Y. Chen, Simon J. Cook, Mariana Correas-Gonzalez, Soumik Das, Alejandro Diaz Moreno, Fabian Drenkhan, Melanie Fischer, Walter W. Immerzeel, Eñaut Izagirre, Ramesh Chandra Joshi, Ioannis Kougkoulos, Riamsara Kuyakanon Knapp, Dongfeng Li, Ulfat Majeed, Stephanie Matti, Holly Moulton, Faezeh Nick, Valentine Piroton, Irfan Rashid, Masoom Reza, Anderson Ribeiro de Figueiredo, Christian Riveros, Finu Shrestha, Milan Shrestha, Jakob Steiner, Noah Walker-Crawford, Joanne L. Wood, and Jacob C. Yde
                                    Nat. Hazards Earth Syst. Sci., 22, 3041–3061, https://doi.org/10.5194/nhess-22-3041-2022, https://doi.org/10.5194/nhess-22-3041-2022, 2022
                                    Short summary
                                    Short summary
                                            
                                                Glacial lake outburst floods (GLOFs) have attracted increased research attention recently. In this work, we review GLOF research papers published between 2017 and 2021 and complement the analysis with research community insights gained from the 2021 GLOF conference we organized. The transdisciplinary character of the conference together with broad geographical coverage allowed us to identify progress, trends and challenges in GLOF research and outline future research needs and directions.
                                            
                                            
                                        Yanxing Hu, Tao Che, Liyun Dai, Yu Zhu, Lin Xiao, Jie Deng, and Xin Li
                                        Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2022-63, https://doi.org/10.5194/essd-2022-63, 2022
                                    Preprint withdrawn 
                                    Short summary
                                    Short summary
                                            
                                                We propose a data fusion framework based on the random forest regression algorithm to derive a comprehensive snow depth product for the Northern Hemisphere from 1980 to 2019. This new fused snow depth dataset not only provides information about snow depth and its variation over the Northern Hemisphere but also presents potential value for hydrological and water cycle studies related to seasonal snowpacks.
                                            
                                            
                                        Melanie Fischer, Oliver Korup, Georg Veh, and Ariane Walz
                                    The Cryosphere, 15, 4145–4163, https://doi.org/10.5194/tc-15-4145-2021, https://doi.org/10.5194/tc-15-4145-2021, 2021
                                    Short summary
                                    Short summary
                                            
                                                Glacial lake outburst floods (GLOFs) in the greater Himalayan region threaten local communities and infrastructure. We assess this hazard objectively using fully data-driven models. We find that lake and catchment area, as well as regional glacier-mass balance, credibly raised the susceptibility of a glacial lake in our study area to produce a sudden outburst. However, our models hardly support the widely held notion that rapid lake growth increases GLOF susceptibility.
                                            
                                            
                                        Dahong Zhang, Xiaojun Yao, Hongyu Duan, Shiyin Liu, Wanqin Guo, Meiping Sun, and Dazhi Li
                                    The Cryosphere, 15, 1955–1973, https://doi.org/10.5194/tc-15-1955-2021, https://doi.org/10.5194/tc-15-1955-2021, 2021
                                    Short summary
                                    Short summary
                                            
                                                Glacier centerlines are crucial input for many glaciological applications. We propose a new algorithm to derive glacier centerlines and implement the corresponding program in Python language. Application of this method to 48 571 glaciers in the second Chinese glacier inventory automatically yielded the corresponding glacier centerlines with an average computing time of 20.96 s, a success rate of 100 % and a comprehensive accuracy of 94.34 %.
                                            
                                            
                                        Cited articles
                        
                        Bennett, M. R., Huddart, D., and McCormick, T.: The glaciolacustrine landform–sediment assemblage at Heinabergsjökull, Iceland, Geogr. Ann. A., 82, 1–16, https://doi.org/10.1111/j.0435-3676.2000.00107.x, 2000. 
                    
                
                        
                        Bolch, T., Kulkarni, A., Kääb, A., Huggel, C., Paul, F., Cogley, J. G., Frey, H., Kargel, J. S., Fujita, K., Scheel, M., Bajracharya, S., and Stoffel, M.: The state and fate of Himalayan glaciers, Science, 336, 310–314, https://doi.org/10.1126/science.1215828, 2012. 
                    
                
                        
                        Carrivick, J. L. and Quincey, D. J.: Progressive increase in number and water storage of ice-marginal lakes on the western margin of the Greenland Ice Sheet, Global Planet Change, 116, 156–163, https://doi.org/10.1016/j.gloplacha.2014.02.009, 2014. 
                    
                
                        
                        Carrivick, J. L. and Tweed, F. S.: Proglacial lakes: character, behaviour and geological importance, Quaternary Sci. Rev., 78, 34–52, https://doi.org/10.1016/j.quascirev.2013.07.028, 2013. 
                    
                
                        
                        Clague, J. J. and Evans, S. G.: A review of catastrophic drainage of moraine-dammed lakes in British Columbia, Quaternary Sci. Rev., 19, 1763–1783, https://doi.org/10.1016/S0277-3791(00)00090-1, 2000. 
                    
                
                        
                        Cook, K. L., Andermann, C., Gimbert, F., Adhikari, B. R., and Hovius, N.: Glacial lake outburst floods as drivers of fluvial erosion in the Himalaya, Science, 362, 53–57, https://doi.org/10.1126/science.aat4981, 2018. 
                    
                
                        
                        Cook, S. J. and Quincey, D. J.: Estimating the volume of Alpine glacial lakes, Earth Surf. Dynam., 3, 559–575, https://doi.org/10.5194/esurf-3-559-2015, 2015. 
                    
                
                        
                        Duan, H., Yao, X., Zhang, Y., Jin, H., Wang, Q., Du, Z., Hu, J., Wang, B., and Wang, Q.: Lake volume and potential hazards of moraine-dammed glacial lakes – a case study of Bienong Co, southeastern Tibetan Plateau, The Cryosphere, 17, 591–616, https://doi.org/10.5194/tc-17-591-2023, 2023. 
                    
                
                        
                        Emmer, A. and Vilímek, V.: New method for assessing the susceptibility of glacial lakes to outburst floods in the Cordillera Blanca, Peru, Hydrol. Earth Syst. Sci., 18, 3461–3479, https://doi.org/10.5194/hess-18-3461-2014, 2014. 
                    
                
                        
                        Fischer, M., Korup, O., Veh, G., and Walz, A.: Controls of outbursts of moraine-dammed lakes in the greater Himalayan region, The Cryosphere, 15, 4145–4163, https://doi.org/10.5194/tc-15-4145-2021, 2021. 
                    
                
                        
                        Fujita, K., Sakai, A., Takenaka, S., Nuimura, T., Surazakov, A. B., Sawagaki, T., and Yamanokuchi, T.: Potential flood volume of Himalayan glacial lakes, Nat. Hazards Earth Syst. Sci., 13, 1827–1839, https://doi.org/10.5194/nhess-13-1827-2013, 2013. 
                    
                
                        
                        Gao, Y., Liu, S., Qi, M., Xie, F., Wu, K., and Zhu, Y.: Glacier-related hazards along the International Karakoram Highway: status and future perspectives, Front. Earth Sci., 9, 611501, https://doi.org/10.3389/feart.2021.611501, 2021. 
                    
                
                        
                        Golledge, N. R. and Phillips, E.: Sedimentology and architecture of De Geer moraines in the western Scottish Highlands, and implications for grounding-line glacier dynamics, Sediment Geol., 208, 1–14, https://doi.org/10.1016/j.sedgeo.2008.03.009, 2008. 
                    
                
                        
                        Harrison, S., Kargel, J. S., Huggel, C., Reynolds, J., Shugar, D. H., Betts, R. A., Emmer, A., Glasser, N., Haritashya, U. K., Klimeš, J., Reinhardt, L., Schaub, Y., Wiltshire, A., Regmi, D., and Vilímek, V.: Climate change and the global pattern of moraine-dammed glacial lake outburst floods, The Cryosphere, 12, 1195–1209, https://doi.org/10.5194/tc-12-1195-2018, 2018. 
                    
                
                        
                        Liu, S., Wu, T., Wang, X., Wu, X., Yao, X., Liu, Q., Zhang, Y., Wei, J., and Zhu, X.: Changes in the global cryosphere and their impacts: A review and new perspective, Sci. Cold Arid Reg., 12, 343–354, https://doi.org/10.3724/SP.J.1226.2020.00343, 2020. 
                    
                
                        
                        Lützow, N., Veh, G., and Korup, O.: A global database of historic glacier lake outburst floods, Earth Syst. Sci. Data, 15, 2983–3000, https://doi.org/10.5194/essd-15-2983-2023, 2023. 
                    
                
                        
                        Mergili, M., Pudasaini, S. P., Emmer, A., Fischer, J.-T., Cochachin, A., and Frey, H.: Reconstruction of the 1941 GLOF process chain at Lake Palcacocha (Cordillera Blanca, Peru), Hydrol. Earth Syst. Sci., 24, 93–114, https://doi.org/10.5194/hess-24-93-2020, 2020. 
                    
                
                        
                        Murton, D. K. and Murton, J. B.: Middle and Late Pleistocene glacial lakes of lowland Britain and the southern North Sea Basin, Quaternary Int., 260, 115–142, https://doi.org/10.1016/j.quaint.2011.07.034, 2012. 
                    
                
                        
                        Nie, Y., Deng, Q., Pritchard, H. D., Carrivick, J. L., Ahmed, F., Huggel, C., Liu, L., Wang, W., Lesi, M., Wang, J., Zhang, H., Zhang, B., Lü, Q., and Zhang, Y.: Glacial lake outburst floods threaten Asia's infrastructure, Sci. Bull., 68, 1361–1365, https://doi.org/10.1016/j.scib.2023.05.035, 2023. 
                    
                
                        
                        Qi, M., Liu, S., Wu, K., Zhu, Y., Xie, F. M., Jing, H. A., Gao, Y. P., and Yao, X. J.: Improving the accuracy of glacial lake water storage estimation: a case study in the Poiqu basin, central Himalayas, J. Hydrol., 610, 127973, https://doi.org/10.1016/j.jhydrol.2022.127973, 2022. 
                    
                
                        
                        Qi, M., Liu, S., Gao, Y., Xie, F., Pan, X., Zhang, Z., Yao, X., Zhang, C., and Zhu, Y.: Water volume changes and assessment of potential outburst triggers for glacial lakes in the Nidu Zangbo basin southeastern Tibet – case study of Tanong Co, J. Glaciol. Geocryol., 45, 1205–1219, https://doi.org/10.7522/j.issn.1000-0240.2023.0092, 2023. 
                    
                
                        
                        Richardson, S. D. and Reynolds, J. M.: An overview of glacial hazards in the Himalayas, Quatern. Int., 65, 31–47, https://doi.org/10.1016/S1040-6182(99)00035-X, 2000. 
                    
                
                        
                        Rounce, D. R., Hock, R., Maussion, F., Hugonnet, R., Kochtitzky, W., Huss, M., Berthier, E., Brinkerhoff, D., Compagno, L., Copland, L., Farinotti, D., Menounos, B., and McNabb, R. W.: Global glacier change in the 21st century: Every increase in temperature matters, Science, 379, 78–83, https://doi.org/10.1126/science.abo1324, 2023. 
                    
                
                        
                        Rubensdotter, L. and Rosqvist, G.: Influence of geomorphological setting, fluvial-, glaciofluvial-and mass-movement processes on sedimentation in alpine lakes, Holocene, 19, 665–678, https://doi.org/10.1177/0959683609104042, 2009. 
                    
                
                        
                        Sattar, A., Haritashya, U. K., Kargel, J. S., Leonard, G. J., Shugar, D. H., and Chase, D. V.: Modeling lake outburst and downstream hazard assessment of the Lower Barun Glacial Lake, Nepal Himalaya, J. Hydrol., 598, 126208, https://doi.org/10.1016/j.jhydrol.2021.126208, 2021. 
                    
                
                        
                        Seddik, H., Greve, R., Sugiyama, S., and Naruse, R.: Numerical simulation of the evolution of glacial valley cross sections, Phys. Rev. D., 61, 210–211, https://doi.org/10.1103/PhysRevD.61.114016, 2009. 
                    
                
                        
                        Shugar, D. H., Burr, A., Haritashya, U. K., Kargel, J. S., Watson, C. S., Kennedy, M. C., Bevington, A. R., Betts, R. A., Harrison, S., and Strattman, K.: Rapid worldwide growth of glacial lakes since 1990, Nat. Clim. Chang., 10, 939–945, https://doi.org/10.1038/s41558-020-0855-4, 2020. 
                    
                
                        
                        Veh, G., Korup, O., and Walz, A.: Hazard from Himalayan Glacier Lake Outburst Floods, P. Natl. Acad. Sci. USA, 117, 907–912, https://doi.org/10.1073/pnas.1914898117, 2019a. 
                    
                
                        
                        Veh, G., Korup, O., von Specht, S., Roessner, S., and Walz, A.: Unchanged frequency of moraine-dammed glacial lake outburst floods in the Himalaya, Nat. Clim. Chang., 9, 379–383, https://doi.org/10.1038/s41558-019-0437-5, 2019b. 
                    
                
                        
                        Veh, G., Lützow, N., Kharlamova, V., Petrakov, D., Hugonnet, R., and Korup, O.: Trends, breaks, and biases in the frequency of reported glacier lake outburst floods, Earth's Future, 10, e2021EF002426, https://doi.org/10.1029/2021EF002426, 2022. 
                    
                
                        
                        Wang, X., Guo, X., Yang, C., Liu, Q., Wei, J., Zhang, Y., Liu, S., Zhang, Y., Jiang, Z., and Tang, Z.: Glacial lake inventory of high-mountain Asia in 1990 and 2018 derived from Landsat images, Earth Syst. Sci. Data, 12, 2169–2182, https://doi.org/10.5194/essd-12-2169-2020, 2020. 
                    
                
                        
                        Westoby, M. J., Glasser, N. F., Brasington, J., Hambrey, M. J., Quincey, D. J., and Reynolds, J. M.: Modelling outburst floods from moraine-dammed glacial lakes, Earth-Sci. Rev., 134, 137–159, https://doi.org/10.1016/j.earscirev.2014.03.009, 2014. 
                    
                
                        
                        Wu, G., Yao, T., Wang, W., Zhao, H., Yang, W., Zhang, G., Li, S., Yu, W., Lei, Y., and Hu, W.: Glacial hazards on Tibetan Plateau and surrounding alpines, Bull. Chin Acad. Sci., 34, 1285–1292, CNKI:SUN:KYYX.0.2019-11-012, 2019. 
                    
                
                        
                        Yao, X. J., Liu, S. Y., Han, L., Sun, M. P., and Zhao, L. L.: Definition and classification system of glacial lake for inventory and hazards study, J. Geogr. Sci., 28, 229–241, https://doi.org/10.1007/s11442-018-1467-z, 2018. 
                    
                
                        
                        Zhang, G., Bolch, T., Yao, T., Rounce, D. R., Chen, W., Veh, G., King, O., Allen, S. K., Wang, M., and Wang, W.: Underestimated mass loss from lake-terminating glaciers in the greater Himalaya, Nat. Geosci., 16, 333–338, https://doi.org/10.1038/s41561-023-01150-1, 2023. 
                    
                
                        
                        Zheng, G., Allen, S. K., Bao, A., Ballesteros-Cánovas, J. A., Huss, M., Zhang, G., Li, J., Yuan, Y., Jiang, L., Yu, T., Chen, W., and Stoffel, M.: Increasing risk of glacial lake outburst floods from future Third Pole deglaciation, Nat. Clim. Chang., 11, 411–417, https://doi.org/10.1038/s41558-021-01028-3, 2021a. 
                    
                
                        
                        Zheng, G., Mergili, M., Emmer, A., Allen, S., Bao, A., Guo, H., and Stoffel, M.: The 2020 glacial lake outburst flood at Jinwuco, Tibet: causes, impacts, and implications for hazard and risk assessment, The Cryosphere, 15, 3159–3180, https://doi.org/10.5194/tc-15-3159-2021, 2021b. 
                    
                
                        
                        Zhou, L. X., Liu, J. K., and Li, Y. L.: Calculation method of mathematical model of the moraine dammed lake storage capacity, Sci. Technol. Eng., 20, 9804–9809, https://doi.org/10.3969/j.issn.1671-1815.2020.24.016, 2020.  
                    
                
                        
                        Zhu, S., Liu, B., Wan, W., Xie, H., Fang, Y., Chen, X., and Hong, Y.: A new digital lake bathymetry model using the step-wise water recession method to generate 3D lake bathymetric maps based on DEMs, Water, 11, 1151, https://doi.org/10.3390/w11061151, 2019. 
                    
                Short summary
            Here we propose a new mathematically robust and cost-effective model to improve glacial lake water storage estimation. We have also provided a dataset of measured water storage in glacial lakes through field depth measurements. Our model incorporates an automated calculation process and outperforms previous ones, achieving an average relative error of only 14 %. This research offers a valuable tool for researchers seeking to improve the risk assessment of glacial lake outburst floods.
            Here we propose a new mathematically robust and cost-effective model to improve glacial lake...
            
         
 
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
             
             
            