论文标题
通过层次空间和正交功能平滑改善分段线性雪密度模型
Improving Piecewise Linear Snow Density Models through Hierarchical Spatial and Orthogonal Functional Smoothing
论文作者
论文摘要
雪密度估计作为深度的函数用于理解气候过程，评估极性区域的水积累趋势以及估计冰川质量平衡。雪密度的常见且可解释的物理衍生的微分方程模型是分段线性的，这是深度的函数（在变换的尺度上）。因此，他们无法捕获重要的数据功能。此外，微分方程参数显示出强烈的空间自相关。为了解决这些问题，我们允许物理模型的参数，包括超过深度的随机变化点，以空间变化。我们还开发了一个框架，以便在功能上平滑物理动机的模型。为了保留可解释的物理模型的推断，我们将平滑函数投影到物理模型的空间变化空间中。提出的在空间和功能平滑的雪密度模型可以更好地适合数据，同时保留对物理参数的推断。使用此模型，我们发现控制雪致密化的参数的显着空间变化。
Snow density estimates as a function of depth are used for understanding climate processes, evaluating water accumulation trends in polar regions, and estimating glacier mass balances. The common and interpretable physically-derived differential equation models for snow density are piecewise linear as a function of depth (on a transformed scale); thus, they can fail to capture important data features. Moreover, the differential equation parameters show strong spatial autocorrelation. To address these issues, we allow the parameters of the physical model, including random change points over depth, to vary spatially. We also develop a framework for functionally smoothing the physically-motivated model. To preserve inference on the interpretable physical model, we project the smoothing function into the physical model's spatially varying null space. The proposed spatially and functionally smoothed snow density model better fits the data while preserving inference on physical parameters. Using this model, we find significant spatial variation in the parameters that govern snow densification.
