Lawrence Berkeley National Laboratory

Abstract Glacier flow plays a major role in current and future rates of globally averaged sea‐level rise. The viscosity of glacial ice, controlling the rate of flow, decreases as stress increases and is highly sensitive to the value of the stress exponent, , in the constitutive equation for viscous flow. Glaciologists and climate modelers almost exclusively assume when modeling ice flow and projecting sea‐level rise through forward modeling. However, recent work suggests that better fits observations, prompting the question: How sensitive are projections of sea‐level rise to the value of ? We use an established community ice flow model and standard benchmark experiments designed as an idealized representation of Pine Island Glacier, West Antarctica. While initializing an model to match observations of an ice sheet is possible, we find that incorrectly assuming when in fact dramatically underestimates rates of sea‐level rise. The scale of this error grows nonlinearly with the magnitude of the climate forcing, acting to increase projection uncertainties. Additionally, we find that models often account for this stress‐dependent rheology mismatch during model initialization in a way that masks this rheological effect in the short term while leaving model outputs vulnerable to larger biases in longer‐term projections. Initializations to observations of Pine Island Glacier display similar rheology‐mismatch fingerprints to our idealized example. Plain Language Summary The ice found in glaciers and ice sheets responds to applied stresses with reduced resistance to flow and deformation: push twice as hard, get more than twice the flow. We can model this behavior with a stress‐dependent viscosity whose exponent, , governs the sensitivity of flow to changes in stress. Recent work suggests that in many regions, departing from the current standard practice of , a pervasive assumption that underpins all existing sea level projections that depend on modeling the flow of ice sheets. We ask: If numerical ice sheet models have been using incorrect values of , how does that affect their model projections for ice sheet change? We show that in benchmark models of marine ice sheets typically found in Antarctica, using when should be four leads to underestimates of 100‐year sea‐level rise contributions of between 21% and 35% depending on the climate forcing. Our work highlights that a simple quantity prescribed for the physical behavior of ice has far reaching implications for modeling of ice sheets and understanding future sea level rise. Key Points Ice sheet model projections are sensitive to the choice of flow law exponent, which governs how ice viscosity responds to changes in stress Models incorrectly assuming can be initialized to match glaciers, but significantly underestimate ice loss in retreat benchmarks This bias increases with the speed of retreat, indicating a need to assess uncertainty from ice rheology mismatches in sea level projections