A model for subglacial flooding through a preexisting hydrological network during the rapid drainage of supraglacial lakes

Increasingly large numbers of supraglacial lakes form and drain every summer on the Greenland Ice Sheet. Some of these lakes drain rapidly within the timescale of a few hours, and the vertical discharge of water during these events may find a preexisting film of water potentially within a distributed drainage system of linked cavities. Here we present a model for subglacial flooding applied specifically to such circumstances. One of many interesting results we find is that water flows in from the far field prior to the arrival of flooding. We systematically evaluate the effect of initial ice/bed opening on the degree of perturbation to the subglacial system. Of particular importance, we find that floods propagate much faster and vertical displacements are much greater for larger openings. For 10 and 1 cm of initial opening, for example, floods travel about 68% and 50% farther than in the fully coupled ice/bed scenario after 2 h of drainage, respectively. For the same choices of initial opening, the elastostatic displacement at the injection point is about 1.39 and 1.26 times that of the fully coupled scenario. Using the framework with a preexisting water film results in avoiding the pressure singularity that is inherent to classical hydrofracture models, thus opening an avenue for integrating the likes of our model within continuum subglacial hydrological models. Furthermore, we foresee that the theory presented can be used to potentially infer subglacial hydrological conditions from surface observables.