A Fast Particle-based Approach for Calibrating a 3-D Model of the Antarctic Ice Sheet
Sea level projections strongly influence the design of coastal risk management strategies; however, our understanding of future sea-level rise depends on highly uncertain projections of the Antarctic ice sheet’s mass loss. Antarctic ice sheet models provide projections of the long-term mass loss, but these models rely on poorly constrained parameters (“inputs”). Uncertainty in the model inputs often propagates to highly uncertain sea-level projections. Bayesian calibration methods can “tune” the unknown model parameters by assimilating modern observations. However, existing calibration methods are limited to two broad classes of ice sheet models - simple ice models with many model parameters or complex models with very few parameters. Simpler lower-resolution models have shorter model run times, but may not accurately represent the underlying physical processes. Complex high-resolution models can better capture the key ice dynamics, but the long run times and high computational overhead place strict limits on the total number of model evaluations. We focus on the Pennsylvania State University 3D ice sheet model (PSU3D-ICE), which operates at moderate spatio-temporal resolutions, has shorter single model run times (~15 minutes), and includes many model parameters (11). PSU3D-ICE is complex enough to capture the important ice dynamics without greatly increasing the computational costs. Our approach employs sequential Monte Carlo with an adaptive tempering schedule and mutation stage. In addition, our implementation takes advantage of the massive parallelization (2000+ cores) inherent to high-performance computing environments. Though we developed our novel particle-based calibration method expressly for PSU3D-ICE, our method can be extended to other computer models with moderate run times (~15 minutes) and many model parameters (5-20).
Key Result 1: Calibrating fewer model parameters (three inputs) using a well-known approach (emulation-calibration) leads to overconfident and considerably lower projections of sea-level rise. Our particle-based approach accounts for more model parameters (11 inputs) and projects higher uncertainty in sea-level projections. For 2300, the tail area risk increases by a factor of 65 when accounting for more unknown model inputs.
Key results 2: Our approach enables computer experiments that were computationally infeasible using existing methods. We find that improving our knowledge of the Antarctic ice sheet during the Pliocene era can potentially lead to sharper projections of future sea-level rise. Another experiment suggests that sea-level projections are sensitive to our prior knowledge of the model parameters. Hence, overly constraining the model parameters could possibly underestimate future sea-level rise.
Key Result 3: Our novel method makes an important contribution to the methodological literature as a computationally efficient approximate approach for computer model calibration. Based on the results of our numerical study, our approach provides good approximations and drastically reduces overall calibration wall times by using distributed computing.
We consider the scientifically challenging and policy-relevant task of understanding the past and projecting the future dynamics of the Antarctic ice sheet. The Antarctic ice sheet has shown a highly nonlinear threshold response to past climate forcings. Triggering such a threshold response through anthropogenic greenhouse gas emissions would drive drastic and potentially fast sea level rise with important implications for coastal flood risks. Previous studies have combined information from ice sheet models and observations to calibrate model parameters. These studies have broken important new ground but have either adopted simple ice sheet models or have limited the number of parameters to allow for the use of more complex models. These limitations are largely due to the computational challenges posed by calibration as models become more computationally intensive or when the number of parameters increases.
Here, we propose a method to alleviate this problem: a fast sequential Monte Carlo method that takes advantage of the massive parallelization afforded by modern high-performance computing systems. We use simulated examples to demonstrate how our sample-based approach provides accurate approximations to the posterior distributions of the calibrated parameters. The drastic reduction in computational times enables us to provide new insights into important scientific questions, for example, the impact of Pliocene era data and prior parameter information on sea-level projections. These studies would be computationally prohibitive with other computational approaches for calibration such as Markov chain Monte Carlo or emulation-based methods. We also find considerable differences in the distributions of sea-level projections when we account for a larger number of uncertain parameters. For example, based on the same ice sheet model and data set, the 99th percentile of the Antarctic ice sheet contribution to sea-level rise in 2300 increases from 6.5 m to 13.1 m when we increase the number of calibrated parameters from three to 11. With previous calibration methods, it would be challenging to go beyond five parameters. This work provides an important next step toward improving the uncertainty quantification of complex, computationally intensive, and decision-relevant models.