The Greenland Ice Sheet is currently the largest individual contributor to global barystatic sea level rise. Our capacity to predict the future behavior of the ice sheet has not accelerated at the same rate as ice sheet change. A large part of this gap hangs on the question of where surface meltwater goes and how quickly it gets there. In this talk, I will discuss how I use radar imaging and inverse methods to reveal the internal structure of the Greenland Ice Sheet and the role of subsurface water transport and storage in ice sheet mass loss. Along the way, I will highlight some of the computational challenges our field faces as we try to bridge sparse field data, proxy observations from remote sensing, and numerical modeling across space and time to answer critical questions about the future of the Earth’s ice sheets.