Exceptional-point signatures of scale-selective basal hydrology-sliding coupling in a two-state glacier model

Basal sliding is regulated by how heat and water partition within thin, mixed icewater layers at glacier beds, yet the transition from distributed to efficient drainage remains difficult to express in a compact form that connects energy balance, transport and observable. Here we show that a coarse-grained two-patch reduction of basal enthalpy dynamics yields a linear non-Hermitian generator that can be written in an anti-parity-time (anti-PT) symmetric form in the balanced-loss (µ) limit. In this representation, a detuning δ(k) set by along-flow transport asymmetry across a heterogeneity scale and a dissipative coupling κ set by hydraulic/thermal exchange compete to produce an exceptional-point (EP) condition δ(k) 2 = κ 2 that marks a sharp regime boundary. Because δ depends on Fourier wavenumber k, the EP selects bed-parallel length scales that are predicted to switch from mode-selective localization to damped oscillatory exchange of ice-rich and water-rich basal states. Mapping δ, κ and µ to measurable glaciological quantities links the framework to distributed drainage laws and GlaDS-type outputs, and yields testable signatures in radar-derived basal reflectivity, subglacial lake storage and transient speed-up/slow-down events. The resulting EP proximity provides a physics-based, scale-selective criterion for when basal hydrology most strongly amplifies sliding sensitivity to modest perturbations in melt supply or drainage efficiency.