A mathematical model to improve water storage of glacial lakes prediction towards addressing glacial lake outburst floods

Abstract. Moraine-dammed glacial lakes are vital sources of freshwater but also pose a hazard to mountain communities if they drain in sudden glacial lake outburst floods. Accurately measuring the water storage of these lakes is crucial to ensure sustainable use and safeguard mountain communities downstream. However, thousands of glacial lakes still lack a robust estimate of their water storages because bathymetric surveys in remote regions are difficult and expensive. Here we geometrically approximate the shape and depths of moraine-dammed lakes and provide a cost-effective model to improve lake water storage estimation. Our model uses the outline and the terrain surrounding a glacier lake as input data, assuming a parabolic lake bottom and constant hillslope angles. We validate our model using ten new bathymetrically surveyed glacial lakes on the Qinghai-Tibet Plateau, and compiled data from 34 recently measured lakes. Our model overcomes the autocorrelation issue inherent in earlier area/depth-water storage relationships and incorporates an automated calculation process based on the topography and geometrical parameters specific to moraine-dammed lakes. Compared to other models, our model achieved the lowest average relative error of approximately 14 % when analyzing 44 observed data, surpassing the >44 % average relative error from alternative models. Finally, the model is used to calculate the water storage change of moraine-dammed lakes in the past 30 years in High Mountain Asia. The model has been proven to be robust and can be utilized to update the water storage of lake water for conducting further management of glacial lakes with the potential for outburst floods in the world.