Response of Marine-Terminating Glaciers to Forcing: Time Scales, Sensitivities, Instabilities, and Stochastic Dynamics

Recent observations indicate that many marine-terminating glaciers in Greenland and Antarctica are currently retreating and thinning, potentially due to long-term trends in climate forcing. In this study, we describe a simple two-stage model that accurately emulates the response to external forcing of marine-terminating glaciers simulated in a spatially extended model. The simplicity of the model permits derivation of analytical expressions describing the marine-terminating glacier response to forcing. We find that there are two time scales that characterize the stable glacier response to external forcing, a fast time scale of decades to centuries, and a slow time scale of millennia. These two time scales become unstable at different thresholds of bed slope, indicating that there are distinct slow and fast forms of the marine ice sheet instability. We derive simple expressions for the approximate magnitude and transient evolution of the stable glacier response to external forcing, which depend on the equilibrium glacier state and the strength of nonlinearity in forcing processes. The slow response rate of marine-terminating glaciers indicates that current changes at some glaciers are set to continue and accelerate in coming centuries in response to past climate forcing and that the current extent of change at these glaciers is likely a small fraction of the future committed change caused by past climate forcing. Finally, we find that changing the amplitude of natural fluctuations in some nonlinear forcing processes, such as ice shelf calving, changes the equilibrium glacier state. Plain Language Summary We develop a very simple mathematical model to explain how change in climate causes change in marine glaciers. The model shows that this response mostly occurs in two phases, a fast phase over tens to hundreds of years, and a slow phase over thousands of years. Glaciers have a larger response when they are on flat bedrock or when changes in the length of their ice shelf occur due to iceberg detachment. Even though some glaciers have not thinned or retreated significantly in recent years because they sit on steep downward sloping bedrock, they may experience rapid thinning and retreat in the future as they continue to respond to past climate change over thousands of years. Noise in climate and other processes that cause glaciers to be noisy can potentially cause permanent changes in glacier size. These results indicate that we should include noise when making predictions of glaciers changes so that we can calculate uncertainty in future projections and the impact of noise on permanent glacier size.