Modeling pressure extremes in subglacial drainage systems

One of the important reasons for studying subglacial hydrology is to predict the distribution and variation of effective pressure, which acts as a key control on basal sliding. Borehole measurements of water pressure show that there are often large variations on seasonal and diurnal time scales: it is common for the pressure to exceed the overburden stress in the ice (ie. for the effective pressure to become negative), or to decrease to atmospheric pressure. Most current models of subglacial drainage are not appropriate when the pressure passes these extremes, implicitly assuming that the water pressure lies between atmospheric and ice overburden. In this work, we describe a new method to account for the different physics that occur when water pressure reaches overburden or decreases to atmospheric. In the first case, the ice is assumed to separate from the bed and the water allowed to spread out in order to prevent higher water pressures; in the second, an air or vapor-filled gap is created between the ice and the water so the drainage space is only partially-filled. The model is thus able to simulate drainage systems for which most other models would unphysically predict negative water pressure or negative effective pressure. We predict overburden is reached most commonly when the water discharge is large, the ice surface slope is shallow, or the discharge increases rapidly. Atmospheric pressure and a partially-filled drainage system are predicted when the discharge is low, the ice is shallow, or the surface slope is steep.