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Abstract Sít’ Tlein (Malaspina Glacier), located in Southeast Alaska, has a complex flow history. This piedmont glacier, the largest in the world, is fed by three main tributaries that all exhibit similar flow patterns, yet with varying surge cycles. The piedmont lobe is dramatically reshaped by surges that occur at approximately decadal timescales. By combining historical accounts with modern remote sensing data, we derive a surge history over the past century. We leverage the Stochastic Matrix Factorization, a novel data analysis and interpolation technique, to process and interpret large datasets of glacier surface velocities. A variant of the Principal Component Analysis allows us to uncover spatial and temporal patterns in ice dynamics. We show that Sít’ Tlein displays a wide range of behaviors, spanning quiescence to surge with seasonal to decadal variations of ice flow direction and magnitude. We find that in the lobe, surges dominate the velocity dataset’s variance (spanning 1984–2021), while seasonal variations represent a much smaller part of the variance. However, despite the regular surge pulses, the glacier lobe is far from equilibrium, and widespread retreat of the glacier is inevitable, even without further climate warming. 

Abstract. Sít' Tlein, located in the St. Elias Range, which straddles Alaska's Wrangell–St. Elias National Park and Kluane National Park in the Yukon, is the world's largest piedmont glacier. Sít' Tlein has thinned considerably over 30 years of altimetry, yet its low-elevation piedmont lobe has remained intact in contrast to the glaciers that once filled neighboring Icy and Disenchantment bays. In an effort to forecast changes to Sít' Tlein over decadal to centennial timescales, we take a data-constrained dynamical modeling approach in which we infer the parameters of a higher-order model of ice flow – the bed elevation, basal traction, and surface mass balance – with a diverse but spatiotemporally sparse set of observations including satellite-derived, time-varying velocity fields; radar-derived bed and surface elevation measurements; and in situ and remotely sensed observations of accumulation and ablation. Nonetheless, such data do not uniquely constrain model behavior, so we adopt an approximate Bayesian approach based on the Laplace approximation and facilitated by low-rank parametric representations to quantify uncertainty in the bed, traction, and mass balance fields alongside the induced uncertainty in model-based predictions of glacier change. We find that Sít' Tlein is considerably out of balance with contemporary (and presumably future) climate, and we expect its piedmont lobe to largely disappear over the coming centuries. If warming ceases, and surface mass balance remains at 2023 levels, then by 2073 (2173) we forecast a mass loss (expressed in terms of 95 % credible interval) of 323–444 km3 (546–728 km3). If instead surface mass balance continues to change at the same rate as inferred over the historical period, then we forecast a 2073 (2173) mass loss of 383–505 km3 (740–900 km3). In either case, the resulting retreat and subsequent replacement of glacier ice with a marine embayment or lake will yield a significant modification to the regional landscape and ecosystem. 

Emulators of ice flow models have shown promise for speeding up simulations of glaciers and ice sheets. Existing ice flow emulators have relied primarily on convolutional neural networks (CNN’s), which assume that model inputs and outputs are discretized on a uniform computational grid. However, many existing finite element-based ice sheet models such as the Ice-Sheet and Sea-level System model (ISSM) benefit from their ability to use unstructured computational meshes. Unstructured meshes allow for greater flexibility and computational efficiency in many modeling scenarios. In this work, we present an emulator of a higher order, finite element ice flow model based on a graph neural network (GNN) architecture. In this architecture, an unstructured finite element mesh is represented as a graph, with inputs and outputs of the ice flow model represented as variables on graph nodes and edges. An advantage of this approach is that the ice flow emulator can interface directly with a standard finite element –based ice sheet model by mapping between the finite element mesh and a graph suitable for the GNN emulator. We test the ability of the GNN to predict velocity fields on complex mountain glacier geometries and show how the emulated velocity can be used to solve for mass continuity using a standard finite element approach. 

Abstract. Numerical simulations of ice sheets rely on the momentum balance to determine how ice velocities change as the geometry of the system evolves. Ice is generally assumed to follow a Stokes flow with a nonlinear viscosity. Several approximations have been proposed in order to lower the computational cost of a full-Stokes stress balance. A popular option is the Blatter–Pattyn or higher-order model (HO), which consists of a three-dimensional set of equations that solves the horizontal velocities only. However, it still remains computationally expensive for long transient simulations. Here we present a depth-integrated formulation of the HO model, which can be solved on a two-dimensional mesh in the horizontal plane. We employ a specific polynomial function to describe the vertical variation in the velocity, which allows us to integrate the vertical dimension using a semi-analytic integration. We assess the performance of this MOno-Layer Higher-Order (MOLHO) model to compute ice velocities and simulate grounding line dynamics on standard benchmarks (ISMIP-HOM and MISMIP3D). We compare MOLHO results to the ones obtained with the original three-dimensional HO model. We also compare the time performance of both models in time-dependent runs. Our results show that the ice velocities and grounding line positions obtained with MOLHO are in very good agreement with the ones from HO. In terms of computing time, MOLHO requires less than 10 % of the computational time of a typical HO model, for the same simulations. These results suggest that the MOno-Layer Higher-Order formulation provides improved computational time performance and a comparable accuracy compared to the HO formulation, which opens the door to higher-order paleo simulations.