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 Mat\'ern 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.

翻译：高空间分辨率的风数据对于气候、海洋学和气象学研究的广泛应用至关重要。对具有二维速度的双变量风场进行大规模空间插值或降尺度是一项具有挑战性的任务，因为风数据往往呈现非高斯分布，且具有较高的空间变异性和异质性。在空间统计中，协克里金法通常用于预测双变量空间场。然而，除高斯过程外，协克里金预测器并非最优。此外，协克里金法在大数据集上计算代价高昂。本文提出一种名为双变量深度克里金法（Bivariate DeepKriging）的方法，该方法是一种空间相关的深度神经网络，其嵌入层由空间径向基函数构建，用于双变量空间数据预测。随后，我们开发了一种基于自助法和集成深度神经网络的无分布不确定性量化方法。与使用常用协方差函数（如协同区域化线性模型和灵活双变量Matérn协方差）的传统协克里金预测器相比，我们提出的方法性能更优。我们展示了所提深度神经网络模型的计算效率和可扩展性，其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506,771个位置的风数据。所提方法的预测性能优于协克里金预测器，并显著降低了计算时间。