High resolution simulation of nonstationary Gaussian random fields

Abstract

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.

Stochastic representations of model uncertainties at ECMWF: state of the art and future vision

“…Schlather (2012) and Kroese and Botev (2013) give recent overviews of fast algorithms to simulate stationary or isotropic random fields. The efficient generation of non-stationary Gaussian random fields at high spatial resolution is discussed by Kleiber (2016).…”

Efficient Estimation of Non-stationary Spatial Covariance Functions with Application to High-resolution Climate Model Emulation

“…Nychka et al (2015) introduced an idea based on Gaussian Markov random fields (GMRFs) and spatial autoregressive (SAR) models for nonstationary processes. Kleiber (2016) proposed an efficient nonstationary simulation method based on spatial deformation. However, it is computationally expensive to estimate the deformation function before performing the simulation.…”

“…High-resolution nonstationary simulations are also challenging. Kleiber (2016) proposed combining the approaches of circular embedding and deformation to achieve an exact simulation. We propose a different approach using a sequentially conditional simulation.…”

Sparse vector Markov switching autoregressive models. Application to multivariate time series of temperature

“…The residual process is a spatial Gaussian process. For weather derivatives markets application, its standard deviation is written as the product of a deterministic season and a GARCH process (Campbell and Diebold, 2011) while in case of the weather generators, full spatial models are used and the modelling effort mainly focuses on the covariance of the residual process (Kleiber, 2016). In the context of stochastic weather generators, it has been found that the introduction of regimes corresponding to typical weather patterns may help to better capture the non linearities of the meteorological variables (see (Ailliot et al, 2015a) and references therein).…”