基于半连续空间数据的冰模型率定
Ice Model Calibration Using Semi-continuous Spatial Data
摘要：
人类活动造成的地球冰冻圈的迅速变化可能导致重大的环境影响。计算机模型为理解北极和南极冰盖的行为和预测未来提供了有用的工具。然而，这些模型通常受到很大的参数不确定性，由于约束条件差的模型输入参数，控制模拟冰盖的行为。计算机模型校准提供了一个正式的统计框架，使用观测数据推断参数，并量化由于这些参数的不确定性而导致的预测不确定性。冰盖模型的校准往往具有挑战性，因为相关的模型输出和观测数据采用半连续空间数据的形式，点质量为零，正值为右偏连续分布。目前的校准方法无法处理这些数据。在这里，我们介绍了一个分层的潜变量模型，处理二进制空间模式和积极的连续空间模式作为单独的组件。为了克服由于高维性的挑战，我们使用基于似然的广义主成分分析对空间依赖的潜在变量施加低维结构。我们应用我们的方法来校准南极冰盖的物理模型，并证明我们可以克服上述建模和计算的挑战。由于我们的校准，我们得到改进的未来冰量变化预测。
英文摘要：
Rapid changes in Earth's cryosphere caused by human activity can lead to significant environmental impacts. Computer models provide a useful tool for understanding the behavior and projecting the future of Arctic and Antarctic ice sheets. However, these models are typically subject to large parametric uncertainties due to poorly constrained model input parameters that govern the behavior of simulated ice sheets. Computer model calibration provides a formal statistical framework to infer parameters using observational data, and to quantify the uncertainty in projections due to the uncertainty in these parameters. Calibration of ice sheet models is often challenging because the relevant model output and observational data take the form of semi-continuous spatial data, with a point mass at zero and a right-skewed continuous distribution for positive values. Current calibration approaches cannot handle such data. Here we introduce a hierarchical latent variable model that handles binary spatial patterns and positive continuous spatial patterns as separate components. To overcome challenges due to high-dimensionality we use likelihood-based generalized principal component analysis to impose low-dimensional structures on the latent variables for spatial dependence. We apply our methodology to calibrate a physical model for the Antarctic ice sheet and demonstrate that we can overcome the aforementioned modeling and computational challenges. As a result of our calibration, we obtain improved future ice-volume change projections.
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