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Discharge from marine-terminating outlet glaciers accounts for up to half the recent mass loss from the Greenland ice sheet, yet the causal factors are not fully understood. Here we assess the factors controlling the behaviour of Humboldt Glacier (HG), allowing us to evaluate the influence of basal topography on outlet glacier response to external forcing since part of HG's terminus occupies a large overdeepening. HG's retreat accelerated dramatically after 1999, coinciding with summer atmospheric warming of up to 0.19°C a-1 and sea-ice decline. Retreat was an order of magnitude greater in the northern section of the terminus, underlain by a major basal trough, than in the southern section, where the bedrock is comparatively shallow. Velocity change following retreat was spatially non-uniform, potentially due to a pinning point near HG's northern lateral margin. Consistent with observations, numerical modelling demonstrates an order-of-magnitude greater sensitivity to sea-ice buttressing and crevasse depth (used as a proxy for atmospheric warming) in the northern section. The trough extends up to 72km inland, so it is likely to facilitate sustained retreat and ice loss from HG during the 21st century. [ABSTRACT FROM AUTHOR]