Parallel Kriging Analysis for Large Spatial Datasets

We investigate the problem of kriging analysis for estimating quantities at unknown locations given a set of observations. Widely known in the geostatistical community, kriging bases spatial prediction on a closed-form model for the spatial co variances between observations, deriving interpolation parameters that minimize variance. While kriging produces predictions with high accuracy, a standard implementation based on maximum likelihood involves repeated covariance factorization, forward-solve, and inner product operations. The resulting computational complexity renders the method infeasible for application to large datasets on a single node. To facilitate large-scale kriging analysis, we develop and implement a distributed version of the algorithm that can utilize multiple computational nodes as well as multiple cores on a single node. We apply kriging analysis for making predictions from a medium-sized weather station dataset, and demonstrate our parallel implementation on a much larger synthetic dataset consisting of 65536 points using 512 cores.