Bivariate DeepKriging for Large-scale Spatial Interpolation of Wind
  Fields
Pratik Nag Ying Sun Brian J Reich
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.