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Mass balance of glaciers in High Mountain Asia (HMA) varies substantially across the region. While the spatial variability is attributed to differences in climatic setting and sensitivity of these glaciers to climate change, an assessment of these factors to date has only been performed on a small sample of glaciers and a small set of climate perturbation scenarios. To advance the assessment to larger datasets, we first reconstruct the time series of reference-surface mass balance for 1952-2014 periods using an empirical model calibrated with observed mass balance from 45 glaciers across the HMA. Forcing the model with a set of independent stepwise changes of temperature (+/- 0.5 K to +/- 6 K) and precipitation (+/- 5% to +/- 30%), we assess the reference-surface mass balance sensitivity of each glacier in the sample. While the relationship between the change in mass balance and the change in precipitation is linear, the relationship with the change in temperature is non-linear. Spatial heterogeneity in the simulated mass balance sensitivities is attributed to differences in climatic setting, elevation, and the sensitivity of mass-balance profile (gradient) to changes in temperature and precipitation. While maritime and low-lying continental glaciers show high sensitivity to temperature changes and display a uniform mass-balance sensitivity with elevation, the high-lying continental glaciers show high sensitivity to precipitation changes and display a non-uniform mass-balance sensitivity with elevation. Our analysis reveals the dominant drivers of spatial variability in the mass balance sensitivity across the region: temperature as a single driver for maritime glaciers, and a superposition of temperature, precipitation seasonality, and snow/rain differentiation for continental glaciers. Finally, a set of sensitivity tests with perturbed model parameters confirms the robustness of our results. The model's ability and robustness to resolve spatial patterns in the sensitivities and their drivers implies that simple modeling approaches remain a powerful tool for analyzing glacier response to climate change in HMA.