🤖 AI Summary
To address the challenges of non-Gaussianity, strong spatial heterogeneity, and computational intractability in large-scale bivariate wind field (2D wind vector) spatial interpolation, this paper proposes a spatially dependent deep neural network architecture. The method incorporates a radial basis function embedding layer to explicitly model spatial correlation, adopts a distribution-free bootstrap ensemble strategy for uncertainty quantification, and theoretically integrates a linear model of coregionalization (LMC) with a Matérn covariance structure. Evaluated on a massive dataset comprising 506,000 meteorological stations across the Middle East, the approach achieves significantly higher prediction accuracy than state-of-the-art cokriging methods, while accelerating inference by approximately 20×. It thus delivers a compelling balance of high accuracy, strong scalability, and theoretical interpretability—establishing a novel paradigm for high-resolution wind field modeling.
📝 Abstract
Abstract 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.
