Enhanced submarine ice-shelf melting strongly controls ice loss in the Amundsen Sea embayment (ASE) of West Antarctica, but its magnitude is not well known in the critical grounding zones of the ASE's major glaciers. Here we directly quantify bottom ice losses along tens of kilometres with airborne radar sounding of the Dotson and Crosson ice shelves, which buttress the rapidly changing Smith, Pope and Kohler glaciers. Melting in the grounding zones is found to be much higher than steady-state levels, removing 300-490 m of solid ice between 2002 and 2009 beneath the retreating Smith Glacier. The vigorous, unbalanced melting supports the hypothesis that a significant increase in ocean heat influx into ASE sub-ice-shelf cavities took place in the mid-2000s. The synchronous but diverse evolutions of these glaciers illustrate how combinations of oceanography and topography modulate rapid submarine melting to hasten mass loss and glacier retreat from West Antarctica.