Abstract

Complex mathematical computer models are employed within climate science in order to: improve the understanding of the behaviour of climate and ice-sheet interactions; study past, present and future climate and ice-sheet evolution; and guide policy decisions. These are often in the form of asynchronous coupled climate and ice-sheet models. However, there are major limitations to the direct use of such computer models including: their complex structure; high-dimensional input parameter spaces and large numbers of model outputs, which includes spatial-temporal fields. This is further compounded by the high computational cost of running the coupled model which in turn places physical constraints on the ice-sheet geometries for which simulations are available.

Surface Mass Balance (SMB); the difference in the accumulation of ice due to snow fall versus the loss due to melting and other processes, is an output of the substantially more computationally expensive climate model which is then input to the quick to evaluate ice-sheet model. This is of great importance in understanding ice-sheet instabilities. The aim is therefore to construct an emulator for SMB, referred to as SMB-Gen, and to couple this with an ice-sheet model. However, serious difficulties are presented as for each simulation, SMB is an incomplete spatial field with values only returned by the climate model within grid cells, defined by geographical locations and ice-sheet elevation, where there is a positive surface ice fraction. Consequently, each simulation yields a different shaped SMB spatial field dependent on the ice fraction; another complex spatial field returned by the ice-sheet model. Glaciologists deem the ice fraction to be an important input for modelling SMB. Moreover, there exists various climate and ice-sheet parameters which may also be useful predictors for SMB. The aforementioned challenges render standard multivariate and spatial field emulation techniques inadequate.

We develop novel Bayesian emulation methodology for SMB exploiting a latent Gaussian process model to mitigate the challenges associated with the incomplete spatial field structure of the SMB output. This is applied to the FAMOUS-Glimmer model for the North American ice-sheet during the last glacial maximum. The ultimate aim is to constrain projections of ice-sheet instabilities and hence obtain robust estimates of future sea level rise by enabling large numbers of model evaluations for use in uncertainty quantification calculations.