By thinning and accelerating, West Antarctic ice streams are contributing about 10% of the observed global sea level rise. Much of this ice loss is from Pine Island Glacier, which has thinned since at least 1992, driven by changes in ocean heat transport beneath its ice shelf and retreat of the grounding line. Details of the processes driving this change, however, remain largely elusive, hampering our ability to predict the future behaviour of this and similar systems. Here, a Lagrangian methodology is developed to measure oceanic melting of such rapidly advecting ice. High-resolution satellite and airborne observations of ice surface velocity and elevation are used to quantify patterns of basal melt under the Pine Island Glacier ice shelf and the associated adjustments to ice flow. At the broad scale, melt rates of up to 100 m yr−1 occur near the grounding line, reducing to 30 m yr-1 just 20 km downstream. Between 2008 and 2011, basal melting was largely compensated by ice advection, allowing us to estimate an average loss of ice to the ocean of 87 km3 yr-1, in close agreement with 2009 oceanographically constrained estimates. At smaller scales, a network of basal channels typically 500 m to 3 km wide is sculpted by concentrated melt, with kilometre-scale anomalies reaching 50% of the broad-scale basal melt. Basal melting enlarges the channels close to the grounding line, but farther downstream melting tends to diminish them. Kilometre-scale variations in melt are a key component of the complex ice-ocean interaction beneath the ice shelf, implying that greater understanding of their effect, or very high resolution models, are required to predict the sea-level contribution of the region.