Second-order non-stationary modeling approaches for univariate geostatistical data

A fundamental decision to make during the analysis of geostatistical data is the modeling of the spatial dependence structure as stationary or non-stationary. Although second-order stationary modeling approaches have been successfully applied in geostatistical applications for decades, there is a growing interest in second-order non-stationary modeling approaches. This paper provides a review of modeling approaches allowing to take into account the second-order non-stationarity in univariate geostatistical data. One broad distinction between these modeling approaches relies on the way that the second-order non-stationarity is captured. It seems unlikely to prove that there would be the best second-order non-stationary modeling approach for all geostatistical applications. However, some of them are distinguished by their simplicity, interpretability, and flexibility.