Glacier models need a sliding law — a mathematical relationship between the traction at the base of the ice and the velocity at which the glacier slides over its bed. For decades, modelers have sought the correct law: power-law, Coulomb friction, regularized Coulomb, or some hybrid. Each works in some settings and fails in others. The result is a field where the same glacier can be modeled with contradictory physics depending on which research group builds the simulation.
A comprehensive review of basal sliding processes suggests the search for a single universal law is misconceived. The ice-bed interface is not a clean contact between two surfaces — it is a zone. The authors call it a “sliding layer,” a region where myriad overlapping processes operate simultaneously: regelation around obstacles, enhanced creep in warm basal ice, till deformation, hydrological pressurization, fracture at bedrock asperities. These processes are setting-dependent and scale-dependent, meaning their relative contributions shift as you move from one glacier to another, or even from one part of a glacier bed to another.
The practical consequence is that the tunable coefficient most models use — a single number varied spatially to make model output match observations — is not a physical parameter. It is a fudge factor absorbing the aggregate behavior of processes the model cannot resolve. The sliding relationship, the authors argue, should fall within a sum of regularized-Coulomb and power-law components, with surface roughness mattering more than traditional classifications of bed hardness.
The deeper insight is about resolution and aggregation. When a system's behavior arises from many concurrent sub-processes operating at scales below your model's resolution, no single constitutive law will capture the aggregate. The law you need depends on which processes dominate — and that depends on conditions you may not know.