双变量深度克里金法用于大尺度风场空间插值
Bivariate DeepKriging for Large-scale Spatial Interpolation of Wind Fields
AI总结：
本文提出双变量深度克里金法，通过空间依赖深度神经网络提升大尺度风场空间插值效率与精度。
摘要：
高空间分辨率的风数据对于气候、海洋学和气象研究中的各种应用至关重要。对具有二维速度的双变量风场进行大尺度空间插值或降尺度是一项具有挑战性的任务，因为风数据往往非高斯分布，具有高度的空间变异性与异质性。在空间统计中，共克里金法常用于预测双变量空间场。然而，共克里金预测器除非在高斯过程中才最优。此外，共克里金法在大规模数据集上计算上是不可行的。在本文中，我们提出了一种方法，称为双变量深度克里金法，这是一种具有嵌入层的空间依赖深度神经网络（DNN），该嵌入层由空间径向基函数构建，用于双变量空间数据预测。我们随后开发了一种基于bootstrap和集成DNN的无分布不确定性量化方法。我们提出的方法在传统共克里金预测器上表现更优，特别是在常用的协方差函数如共区域化线性模型和灵活的双变量Matérn协方差函数上。我们展示了所提出的DNN模型的计算效率和可扩展性，计算速度平均比传统技术快20倍。我们将双变量深度克里金法应用于中东地区506771个地点的风数据。所提出方法的预测性能优于共克里金预测器，并显著减少了计算时间。
英文摘要：
High spatial resolution wind data are essential for a wide range of applications in climate, oceanographic and meteorological studies. Large-scale spatial interpolation or downscaling of bivariate wind fields having velocity in two dimensions is a challenging task because wind data tend to be non-Gaussian with high spatial variability and heterogeneity. In spatial statistics, cokriging is commonly used for predicting bivariate spatial fields. However, the cokriging predictor is not optimal except for Gaussian processes. Additionally, cokriging is computationally prohibitive for large datasets. In this paper, we propose a method, called bivariate DeepKriging, which is a spatially dependent deep neural network (DNN) with an embedding layer constructed by spatial radial basis functions for bivariate spatial data prediction. We then develop a distribution-free uncertainty quantification method based on bootstrap and ensemble DNN. Our proposed approach outperforms the traditional cokriging predictor with commonly used covariance functions, such as the linear model of co-regionalization and flexible bivariate Matérn covariance. We demonstrate the computational efficiency and scalability of the proposed DNN model, with computations that are, on average, 20 times faster than those of conventional techniques. We apply the bivariate DeepKriging method to the wind data over the Middle East region at 506,771 locations. The prediction performance of the proposed method is superior over the cokriging predictors and dramatically reduces computation time.
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