Emulation with uncertainty quantification of regional sea-level change caused by the Antarctic Ice Sheet

TL;DR

This work investigates rapid emulation of regional sea-level change driven by Antarctic Ice Sheet mass loss, comparing physics-informed sensitivity kernels with neural-network emulators (NN and CVAE) using ISMIP6-2100 AIS projections. It trains emulators to predict sea-level changes at 27 coastal sites from high-dimensional AIS-thickness inputs and couples them with uncertainty quantification methods (linear post-processing and split-conformal inference) to produce calibrated prediction intervals. Results show the kernel emulator is most accurate and fastest to deploy, while ML models are viable but generally lag the physics-based approach in accuracy, with MC dropout providing unreliable uncertainty. The study demonstrates how emulators can generate probabilistic RSL distributions at large scale (Monte Carlo ensembles) with substantial speedups, informing decision-relevant coastal risk assessments and highlighting directions for future extensions to global, sector-based, and viscoelastic-Earth scenarios.

Abstract

Projecting sea-level change in various climate-change scenarios typically involves running forward simulations of the Earth's gravitational, rotational and deformational (GRD) response to ice mass change, which requires high computational cost and time. Here we build neural-network emulators of sea-level change at 27 coastal locations, due to the GRD effects associated with future Antarctic Ice Sheet mass change over the 21st century. The emulators are based on datasets produced using a numerical solver for the static sea-level equation and published ISMIP6-2100 ice-sheet model simulations referenced in the IPCC AR6 report. We show that the neural-network emulators have an accuracy that is competitive with baseline machine learning emulators. In order to quantify uncertainty, we derive well-calibrated prediction intervals for simulated sea-level change via a linear regression postprocessing technique that uses (nonlinear) machine learning model outputs, a technique that has previously been applied to numerical climate models. We also demonstrate substantial gains in computational efficiency: a feedforward neural-network emulator exhibits on the order of 100 times speedup in comparison to the numerical sea-level equation solver that is used for training.

Figures (12)

• Figure 1: Illustration of RSL fingerprints for given AIS thickness changes for two samples representative of small and large AIS mass change. a) Modeled AIS grounded-ice thickness change between 2015 and 2100 for sample from training dataset with third smallest total AIS mass change. b) Calculated RSL change fingerprint for AIS mass loss in a. c) Modeled AIS grounded-ice thickness change between 2015 and 2100 for sample from training dataset with third largest total AIS mass change. d) Calculated RSL change fingerprint for AIS mass loss in c. Note different colorbar ranges for each plot and that values exist beyond the ranges shown. The 27 long-term tide gauge sites selected by Meyssignac2017a that we used as emulation targets are shown with black dots in b and d.
• Figure 2: Illustration of the CVAE architecture. The encoder, in the left-most box, is a feed-forward neural network that maps to the latent space in the middle of the diagram. This latent space is lower dimensional than the input space. For generating output, a latent multivariate normal vector, depicted with a density plot, is sampled and concatenated with conditional information, and then it is subsequently passed through the decoded network to produce a prediction. Note that this a generative model as multiple outputs can be generated with the same conditional information so long as new latent vectors are sampled.
• Figure 3: R-squared comparison between calibrated emulator predictions and actual simulated sea-level change values. R-squared values indicate that the kernel is most accurate, followed by the CVAE, and then the NN. All emulators show a high level of accuracy; see following linear plots in addition to these boxplots. The variation these display is over the 27 locations examined in this study.
• Figure 4: Root mean squared error (RMSE) comparison between calibrated emulator predictions and actual simulated sea-level change values, in units of cm. RMSE values indicate similar insights as the previous figure, in that the kernel is most accurate, followed by the CVAE, and then the NN. The variation these boxplots display is over the 27 locations examined in this study. The median RMSE values are about 0.3 cm for the kernel emulator, 0.5 cm for the CVAE, and 0.7 cm for the NN emulator.
• Figure 5: Comparison of empirical prediction interval coverage rates over the three emulator methods (kernel, CVAE, and NN) and two UQ methods (linear model, subscripted as "lm", and split-conformal inference, subscripted as "conf"). For the 85% and 90% prediction intervals, the empirical coverages meet the nominal rate, excepting slight undercoverage for the kernel split-conformal intervals. For the 95% and 99% intervals, the split-conformal methods come closest to meeting the nominal coverage rate. Horizontal dashed line depicts the nominal coverage rate that ideally all methods are close to. The variation in these boxplots is over the 27 locations examined in this study.