分层空间和正交函数平滑对分段线性雪密度模型的改进
Improving Piecewise Linear Snow Density Models through Hierarchical Spatial and Orthogonal Functional Smoothing
摘要：
作为深度函数的雪密度估计值用于了解气候过程，评估极地地区的水积累趋势，并估计冰川质量平衡。雪密度的常见和可解释的物理推导的微分方程模型是分段线性的，作为深度的函数（在变换的尺度上）;因此，它们可能无法捕获重要的数据特征。此外，微分方程参数表现出较强的空间自相关性。为了解决这些问题，我们允许物理模型的参数，包括深度上的随机变化点，在空间上变化。我们还开发了一个框架，功能平滑的物理动机的模型。为了保持对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的零空间中。建议的空间和功能平滑雪密度模型更好地拟合数据，同时保留物理参数的推断。使用这个模型，我们发现显着的空间变化的参数，管理积雪致密化。
英文摘要：
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.
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