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Understanding glacio-hydrological processes is crucial to water resources management, especially under increasing global warming. However, data scarcity makes it challenging to quantify the contribution of glacial melt to streamflow in highly glacierized catchments such as those in the Tienshan Mountains. This study aims to investigate the glacio-hydrological processes in the SaryDjaz-Kumaric River (SDKR) basin in Central Asia by integrating a degree-day glacier melt algorithm into the macro-scale hydrological Soil and Water Assessment Tool (SWAT) model. To deal with data scarcity in the alpine area, a multi-objective sensitivity analysis and a multi-objective calibration procedure were used to take advantage of all aspects of streamflow. Three objective functions, i.e., the Nash-Sutcliffe efficiency coefficient of logarithms (LogNS), the water balance index (WBI), and the mean absolute relative difference (MARD), were considered. Results show that glacier and snow melt-related parameters are generally sensitive to all three objective functions. Compared to the original SWAT model, simulations with a glacier module match fairly well to the observed streamflow, with the Nash-Sutcliffe efficiency coefficient (NS) and R-2 approaching 0.82 and an absolute percentage bias less than 1%. Glacier melt contribution to runoff is 30-48% during the simulation period. The approach of combining multi-objective sensitivity analysis and optimization is an efficient way to identify important hydrological processes and recharge characteristics in highly glacierized catchments.