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The ice shelves buttressing the Antarctic ice sheet determine the rate ofice-discharge into the surrounding oceans. The geometry of ice shelves, andhence their buttressing strength, is determined by ice flow as well as by thelocal surface accumulation and basal melt rates, governed by atmospheric andoceanic conditions. Contemporary methods resolve one of these rates, buttypically not both. Moreover, there is little information of how they changedin time. We present a new method to simultaneously infer the surfaceaccumulation and basal melt rates averaged over decadal and centennialtimescales. We infer the spatial dependence of these rates along flow linetransects using internal stratigraphy observed by radars, using a kinematicforward model of internal stratigraphy. We solve the inverse problem usingsimulation-based inference (SBI). SBI performs Bayesian inference by trainingneural networks on simulations of the forward model to approximate theposterior distribution, allowing us to also quantify uncertainties over theinferred parameters. We demonstrate the validity of our method on a syntheticexample, and apply it to Ekstr\"om Ice Shelf, Antarctica, for which newlyacquired radar measurements are available. We obtain posterior distributions ofsurface accumulation and basal melt averaging over 42, 84, 146, and 188 yearsbefore 2022. Our results suggest stable atmospheric and oceanographicconditions over this period in this catchment of Antarctica. Use of observedinternal stratigraphy can separate the effects of surface accumulation andbasal melt, allowing them to be interpreted in a historical context of the lastcenturies and beyond.

Simulation-Based Inference of Surface Accumulation and Basal Melt Rates of an Antarctic Ice Shelf from Isochronal Layers