Non-separable Nearest-Neighbor Gaussian Process Model for Antarctic Surface Mass Balance and Ice Core Site Selection

Surface mass balance (SMB) is an important factor in the estimation of sea level change, and data are collected to estimate models for prediction of SMB over the Antarctic ice sheets. Using a quality-controlled aggregate dataset of SMB field measurements with significantly more observations than previous analyses, a fully Bayesian nearest-neighbor Gaussian process model is posed to estimate Antarctic SMB and propose new field measurement locations. A corresponding Antarctic SMB map is rendered using this model and is compared with previous estimates. A prediction uncertainty map is created to identify regions of high SMB uncertainty. The model estimates net SMB to be 2345 Gton $\text{yr}^{-1}$, with 95% credible interval (2273,2413) Gton $\text{yr}^{-1}$. Overall, these results suggest lower Antarctic SMB than previously reported. Using the model's uncertainty quantification, we propose 25 new measurement sites for field study utilizing a design to minimize integrated mean squared error.