Efficient Estimation of Non-stationary Spatial Covariance Functions with Application to High-resolution Climate Model Emulation
Efficient Estimation of Non-stationary Spatial Covariance Functions with Application to High-resolution Climate Model Emulation
复制标题
非平稳空间协方差函数的有效估计及其在高分辨率气候模型仿真中的应用
作者：
Yuxiao Li;Ying Sun
在许多气候和环境应用中，空间过程表现出非平稳性。基于卷积的方法常用于构造高斯过程中的非平稳协方差函数。虽然基于卷积的模型是灵活的，但当数据集很大时，它们的计算非常昂贵。现有的方法大多依赖于局部拟合各向异性但平稳的模型，然后重建空间变化的参数。在本研究中，我们提出了一种新的估计方法，通过局部多项式拟合协方差参数来近似一类非平稳mat<s:1>协方差函数。该方法可以有效地估计更丰富的非平稳协方差函数，局部平稳模型是一个特例。我们还开发了一种在小尺度上具有非平稳特征的快速高分辨率模拟方法，并将其应用于气候模式输出的降水数据。
Spatial processes exhibit nonstationarity in many climate and environmental applications. Convolution-based approaches are often used to construct nonstationary covariance functions in Gaussian processes. Although convolutionbased models are flexible, their computation is extremely expensive when the data set is large. Most existing methods rely on fitting an anisotropic, but stationary model locally, and then reconstructing the spatially varying parameters. In this study, we propose a new estimation procedure to approximate a class of nonstationary Matérn covariance functions by local-polynomial fitting the covariance parameters. The proposed method allows for efficient estimation of a richer class of nonstationary covariance functions, with the local stationary model as a special case. We also develop an approach for a fast high-resolution simulation with nonstationary features on a small scale and apply it to precipitation data in climate model outputs.