Validation of a subglacial hydrology model with analytical and semi-analytical solutions

Subglacial hydrology is a key component in ice sheet dynamics. The presence of subglacial water at the ice-bed interface can significantly reduce basal friction and facilitate rapid ice flow, which could lead to the formation of surges and ice streams. The action of the subglacial network on ice flow is simulated by a range of numerical models. Validating these models is essential to ensure that the important physical processes are included, and that the numerical methods provide accurate solutions. In addition to field measurements, which are challenging to obtain at the ice-bed interface, a common validation technique includes inter-comparison with other numerical models. Even though such a technique is beneficial, it does not provide an equivalent validation as exact solutions. Here we present analytical and semi-analytical solutions for confined and unconfined flows in porous layers to validate subglacial hydrology models, which are based on an effective porous medium (EPM) approach. We then apply them to validate the confined-unconfined aquifer scheme (CUAS) model. We find that the numerical results are consistent with the analytical solutions, which provides more confidence that CUAS accurately solves the hydrology equations. Because of their generality, our solutions are readily applicable to other subglacial hydrology models that are based on an EPM approach. We anticipate that a validated hydrology model with our solutions can achieve more credible results in subglacial network simulations.