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

TL;DR

The paper introduces a simulation-based inference framework to jointly recover spatially varying surface accumulation $\\dot{a}$ and basal melt $\\dot{b}$ rates along ice-shelf flow lines from radar-detected internal isochronal horizons. By integrating a forward model based on SSA with a fast layer-tracing scheme and a calibrated noise model, the authors train neural posterior estimators (NPE) to obtain full posterior distributions over mass-balance parameters, enabling uncertainty quantification. The method is validated on synthetic data and applied to Ekström Ice Shelf, yielding posterior ages for IRHs and demonstrating consistency with independent stake measurements. The approach provides a principled, uncertainty-aware means to interpret past accumulation and melt histories from internal stratigraphy, with potential extensions to non-steady-state regimes and broader glaciological settings.

Abstract

The ice shelves buttressing the Antarctic ice sheet determine the rate of ice-discharge into the surrounding oceans. The geometry of ice shelves, and hence their buttressing strength, is determined by ice flow as well as by the local surface accumulation and basal melt rates, governed by atmospheric and oceanic conditions. Contemporary methods resolve one of these rates, but typically not both. Moreover, there is little information of how they changed in time. We present a new method to simultaneously infer the surface accumulation and basal melt rates averaged over decadal and centennial timescales. We infer the spatial dependence of these rates along flow line transects using internal stratigraphy observed by radars, using a kinematic forward model of internal stratigraphy. We solve the inverse problem using simulation-based inference (SBI). SBI performs Bayesian inference by training neural networks on simulations of the forward model to approximate the posterior distribution, allowing us to also quantify uncertainties over the inferred parameters. We demonstrate the validity of our method on a synthetic example, and apply it to Ekström Ice Shelf, Antarctica, for which newly acquired radar measurements are available. We obtain posterior distributions of surface accumulation and basal melt averaging over 42, 84, 146, and 188 years before 2022. Our results suggest stable atmospheric and oceanographic conditions over this period in this catchment of Antarctica. Use of observed internal stratigraphy can separate the effects of surface accumulation and basal melt, allowing them to be interpreted in a historical context of the last centuries and beyond.

Figures (14)

• Figure 1: Estimation of mass balance parameters from a steady state ice shelf with two methods. The Eulerian Mass Budget method (left) detects the difference of surface accumulation and basal melt within two flux gates (blue vertical lines) by considering flux divergence $\nabla\cdot(\bf{v}H)$. Often, the basal melt rates $\dot b$ are inferred assuming that the surface accumulation ($\dot{a}_{\text{obs}}$) is known. In the Internal Reflection Horizon (IRH) method we are given information on the internal stratigraphy of the shelf. This information is used to decouple the known total mass balance into individual estimates of surface accumulation and basal melt ($\dot{a}_{\text{avg}},\dot{b}_{\text{avg}}$ respectively). These estimates correspond to the time-averaged value over the age of the IRH. The inset plots show different surface accumulation and basal melt parameterizations which give rise to the same total mass balance and overall shape of the ice shelf, but different internal stratigraphy.
• Figure 2: Simulation-based inference workflow. In the training phase, accumulation rates are randomly sampled from a prior distribution, the corresponding basal melt rates are obtained using total mass balance, and the resulting internal stratigraphy is calculated using the forward model. These simulations from the prior are used to train a neural network which parameterizes conditional distributions. In the evaluation phase, the trained network is conditioned on the observed IRH and outputs the Bayesian posterior distribution over the parameters (without any additional calls to the forward model).
• Figure 3: Overview of the Ekström Ice Shelf.a: Satellite view of Ekström Ice Shelf along with location of the radar transect along the central flow line (red line) and the Kottas traverse (blue line). An independent estimate of surface accumulation via stake arrays is available on Kottas traverse, which we use to validate our results. b: Vertical cross-section view of the radar transect, along with ice surface and base take from BedMachine Antarctica Morlighem2017, starting at the grounding line (GL). Red lines indicate four picked Internal Reflection Horizons (IRHs). c: Zoom in on box in B. The IRHs are numbered 1--4 in order of increasing depth.
• Figure 4: Two dimensional flow tube domain setup for the synthetic example. Map view of the simulated ice shelf's surface. Flow lines (grey lines) converge to the central flow line (red). Colour indicates ice thickness. The input variables for the internal stratigraphy model are evaluated on the central flow line.
• Figure 5: Prior and posterior (predictive) for the synthetic dataset. a and c: Prior and posterior over surface accumulation and basal melt rates respectively for layer 1 of the synthetic ice shelf, of age 50 years. Solid line is the distribution mean, the shaded region represents the 5th and 95th percentiles. The ground truth (GT) parameters used to generate the reference isochronoal layer are also shown. b: Cross section of the ice shelf. Prior and posterior predictive distributions for the layer closest matching the ground truth isochronal layer. The vertical dashed line represents the LMI boundary for this isochronal layer. The posterior predictive reconstructs the observed layer with higher accuracy and lower uncertainty. The posterior predictive distribution of the age of the isochronal layer is $60^{+9}_{-12}$ years (meaning a median of 60 years, and 16th and 84th percentiles of 48 and 69 years respectively). The average root mean square error relative to the GT isochronal layer is 3.9 m for the posterior and 11.5 m for the prior.