Bivariate DeepKriging for Large-scale Spatial Interpolation of Wind Fields

TL;DR

The paper tackles large-scale, non-Gaussian, bivariate wind-field interpolation where cokriging struggles computationally and statistically. It introduces Bivariate DeepKriging (BDK), a spatially dependent multioutput DNN that uses radial-basis embeddings of locations and bootstrap ensembles for distribution-free uncertainty quantification, linking to the classical LMC under certain conditions. Across simulations, BDK matches cokriging in Gaussian setups but outperforms it in non-Gaussian and nonstationary settings, while delivering substantial speedups (often 20x or more) on large datasets. The method is applied to wind data over Saudi Arabia (506k locations), producing high-resolution wind-field maps and illustrating the practicality of scalable, nonparametric downscaling for wind-energy and climate applications, with code and supplementary materials provided for reproducibility.

Abstract

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.

Figures (6)

• Figure 1: Structure of the spatially dependent neural network with embedding
• Figure 2: Boxplot of MSPE for the three different models CMK, CLK and BDK over $100$ replicates for the non-Gaussian simulation.
• Figure 3: Boxplot of MSPE for the three different models CMK, CLK and BDK over $100$ replicates for the nonstationary simulation.
• Figure 4: Prediction interval for variable 1 and variable 2 for the nonstationary simulation. Here the red interval signifies the prediction interval generated by CMK and the blue interval is for BDK.
• Figure 5: Total computation time (in secconds) for different models in log scale for different number of locations