Bivariate DeepKriging for Large-Scale Spatial Interpolation of Wind Fields

High spatial resolution wind data play a crucial role in various fields such as climate, oceanography, and meteorology. However, spatial interpolation or downscaling of bivariate wind fields, characterized by velocity in two dimensions, poses a challenge due to their non-Gaussian nature, high spatial variability, and heterogeneity. While cokriging is commonly employed in spatial statistics for predicting bivariate spatial fields, it is suboptimal for non-Gaussian processes and computationally prohibitive for large datasets. In this article, we introduce bivariate DeepKriging, a novel method using a spatially dependent deep neural network (DNN) with an embedding layer constructed by spatial radial basis functions for predicting bivariate spatial data. Additionally, we devise a distribution-free uncertainty quantification technique based on bootstrap and ensemble DNN. We establish the theoretical basis for bivariate DeepKriging by linking it with the Linear Model of Coregionalization (LMC). Our proposed approach surpasses traditional cokriging predictors, including those using commonly used covariance functions like the linear model of co-regionalization and parsimonious bivariate Matérn covariance. We demonstrate the computational efficiency and scalability of the proposed DNN model, achieving computation speeds approximately 20 times faster than conventional techniques. Furthermore, we apply the bivariate DeepKriging method to wind data across the Middle East region at 506,771 locations, showcasing superior prediction performance over cokriging predictors while significantly reducing computation time.