Extended Data Fig. 7: Climatic and geometric controls on glacier mass balance.

(a-b) Temperature control on ice loss. The scatter plots in (a-b) show a similar relationship as Main text, Fig. 3f-g (T_s vs. ∆h/∆t), except the y-axis in (a-b) also includes the solid precipitation component. Specifically, F_out = P_solid − b, where P_solid is extracted from the downscaled NORA10 dataset⁵, and b is ∆h/∆t converted to m.w.e. yr⁻¹ using a density⁵⁷ of 850 kg m⁻³. Since the glacier-specific precipitation estimates are noisy, the plots in (a-b) show considerably more scatter than those in Main text, Fig. 3f-g. The advantage of examining the data in terms of F_out is that it enables us to extract the physical quantity k₁, which describes the expected increase in ice loss (m.w.e. yr⁻¹) for each 1 °C rise in mean summer temperature. The gray bands in (a-b) depict the 25th–75th percentile uncertainty envelopes of the T_s vs. F_out regressions (all glaciers). Note that the ice loss in marine-terminating glaciers is regulated not only by air temperature driving F_melt, but also by fjord temperature, bathymetry, and circulation controlling F_calving^31,73,99. We take a first-order approach and fit different k constants to land- vs. marine-terminating glaciers. In both (a-b), the k₁ coefficients are larger in land-terminating glaciers than marine-terminating glaciers. This observation of a weaker sensitivity of F_out to air temperature is consistent with the F_out in marine-terminating glaciers being driven partly by fjord processes that are decoupled from air temperature. Since the satellite-era observations (b) represent a shorter interval and therefore the ∆h/∆t data are more influenced by annual variability¹⁰⁰ and surge cycles¹⁰¹, we only fit glaciers with ∆h/∆t within the 10th–90th percentile range. Glaciers outside this range are depicted with gray dots. Note that the estimated k₁ coefficients from the 1936-2010 observations (a) and satellite-era datasets⁴ (b) are within uncertainty of each other. (c-d) Glacier slope modulates sensitivity to warming. (a) Simple theoretical glacier models⁷⁹ predict that glaciers with steeper slopes should be less sensitive to temperature rise. The rationale is that, for a lower-slope glacier, a given ELA rise of x meters will transfer a larger fraction of the glacier’s area from the accumulation zone to the ablation zone³⁸, causing a more substantial decrease in glacier-averaged ∆h/∆t. (b) We test whether there is evidence for a bed-slope control on glacier sensitivity to temperature rise⁷⁹ in our 1936-2010 dataset (Fig. 2) by estimating the relationship between T_s and ∆h/∆t for low, medium, and high slope glaciers. The bed slope is calculated as ∆z/∆x of the bed topography⁵⁹ along each glacier’s centerline⁵⁶. The distributions in (b) represent the regression slopes derived from weighted total least squares regressions on repeated random 50% subsamples of the dataset.