Simulation of conditional non-Gaussian random fields with directional asymmetry

Abstract

Observed environmental are usually the results of physical, chemical, or biological processes. These processes often introduce asymmetries which should be considered when analysing and modelling the observed variables. In a geostatistical context, there are two main types of asymmetry. The first is rank-asymmetry, i.e., low and high values exhibit different spatial dependence structures. The second is order-asymmetry, i.e., the spatial dependence structure is distinguishable in different directions. Both asymmetries, if significant, indicate that the corresponding random field has a non-Gaussian dependence structure. These asymmetries are not part of the classical geostatistical workflow. Taking asymmetry into account however is likely to improve the estimation and the uncertainty assessment at unobserved locations. In this contribution a stochastic model which can be used to simulate asymmetrical random fields with any of the asymmetries or with their combination is presented. Synthetically simulated flow fields and the well known Walker lake dataset are used to demonstrate the methodology.