Dataset for: A Model for Antarctic Surface Mass Balance and Ice Core Site Selection

In this study, we develop a model for Antarctic surface mass balance (SMB) that allows us to assess regional and global uncertainty in SMB estimation and carry out a model-based design to propose new measurement sites. For this analysis, we use a quality-controlled aggregate dataset of SMB field measurements with significantly more observations than previous analyses; however, many of the measurements in this dataset lack quality ratings. In addition, these data demonstrate spatial autocorrelation, heteroscedasticity, and non-Gaussianity. To account for these data attributes, we pose a Bayesian Gaussian process generalized linear model for SMB. To address missing reliability ratings, we use a mixture model with different variances to add robustness to our model. In addition, we present a novel approach for modeling the variance as a function of the mean to account for the heteroscedasticity in the data. Using this model, we predict Antarctic SMB and compare our estimates with previous estimates. In addition, we create prediction maps with uncertainty to visualize spatial patterns in SMB and to identify regions of high SMB uncertainty. Our model estimates total SMB to be 2156 Gton/yr over the range of our data, with 95\% credible interval (2081,2234) Gton/yr. Overall, our results suggest lower Antarctic SMB than previously reported. This lower SMB estimate may be indicative of a more dire diagnosis of the long-term health of the Antarctic ice sheets. Lastly, we use our model to propose 25 new measurement sites for field study utilizing a sequential design minimizing integrated mean squared error.

本研究构建了南极表面质量平衡 (SMB) 模型，可用于评估SMB估算中的区域与全局不确定性，并基于模型设计提出新的野外测量点位。本次分析采用了经过质量控制的SMB野外实测汇总数据集，其观测样本量显著多于既往研究；但该数据集中的多数测量数据缺乏质量评级。此外，这些数据存在空间自相关 (spatial autocorrelation)、异方差性 (heteroscedasticity) 与非高斯性 (non-Gaussianity) 特征。为适配这些数据特性，我们构建了面向SMB的贝叶斯高斯过程广义线性模型 (Bayesian Gaussian process generalized linear model)。针对缺失的可靠性评级问题，我们采用带有不同方差的混合模型以提升模型的鲁棒性。此外，我们提出了一种新颖的方差建模方法，将方差表示为均值的函数，以此解决数据中的异方差性问题。利用该模型，我们对南极SMB进行了预测，并将估算结果与既往研究的估值进行了对比。同时，我们生成了带有不确定性的预测地图，以可视化SMB的空间分布模式，并识别出SMB不确定性较高的区域。本模型估算得到研究数据覆盖范围内的南极总SMB为2156 Gton/yr，95%置信区间 (credible interval) 为(2081, 2234) Gton/yr。总体而言，我们的结果表明南极SMB低于既往报道的估值。这一偏低的SMB估算结果，或意味着南极冰盖长期健康状况的诊断结果更为严峻。最后，我们利用该模型，通过采用最小化积分均方误差 (integrated mean squared error) 的序贯设计方法，提出了25个可供野外研究的新测量点位。