Longitudinal stress induced by basal slippery patch

Supraglacial lake drainages create spatially finite regions of reduced basal friction, slippery patches, at the ice-bed interface that perturb local stresses in the overlying ice, potentially sufficiently to trigger cascading hydrofracture-driven lake drainage events. We derive analytical solutions for the perturbed stress response to such slippery patches using the shallow shelf approximation and validate these solutions against 2d full-Stokes numerical simulations for Newtonian $n=1$ and Glen $n=3$ rheologies, spanning a range of flow parameters. The stress perturbation magnitude scales as $\rho g \alpha \ell/4$, linear in surface slope $\alpha$ and patch length $\ell$, and decays exponentially into the ice away from the patch over a decay lengthscale $(2Bh/C)^{n/(n+1)}$, dependent on ice thickness $h$, rheological parameters $n, B$, and basal sliding coefficient outside the patch, $C$. The stress decay lengthscale increases with larger ice thickness and smaller basal traction. Combining stress magnitude and decay lengthscale, we define an absolute coupling length as the distance over which the perturbed stress remains above a given threshold, which is largest in the Greenland ablation zone. We discuss implications of these results for the magnitude and spatial reach of stress communication among lake drainage events, especially under a warming climate.