P-spline smoothing for spatial data collected worldwide

Spatial data collected worldwide from a huge number of locations is frequently used in environmental and climate studies. Spatial modelling for this type of data presents both methodological and computational challenges. In this work we illustrate a computationally efficient non-parametric framework in order to model and estimate the spatial field while accounting for geodesic distances between locations. The spatial field is modelled via penalized splines (P-splines) using intrinsic Gaussian Markov Random Field (GMRF) priors for the spline coefficients. The key idea is to use the sphere as a surrogate for the Globe, then build the basis of B-spline functions on a geodesic grid system. The basis matrix is sparse as is the precision matrix of the GMRF prior, thus computational efficiency is gained by construction. We illustrate the approach with a real climate study, where the goal is to identify the Intertropical Convergence Zone using high-resolution remote sensing data.