High resolution simulation of nonstationary Gaussian random fields

Simulation of random fields is a fundamental requirement for many spatial analyses. For small spatial networks, simulations can be produced using direct manipulations of the covariance matrix. Larger high resolution simulations are most easily available for stationary processes, where algorithms such as circulant embedding can be used to simulate a process at millions of locations. We discuss an approach to simulating high resolution nonstationary Gaussian processes that relies on generating a stationary random field followed by a nonlinear deformation to produce a nonstationary field. A spatially varying variance coefficient accounts for local scale effects. The nonstationary covariance function is estimated nonparametrically, and the deformation function is then estimated in a variational framework. We illustrate the proposed approach on synthetic datasets, a challenging temperature dataset over the state of Colorado and a regional climate model over North America.