A typical goal of a geostatistical analysis is to perform spatial prediction. Geostatistical models traditionally take the form of regression models with spatially correlated errors, employing covariate information in the mean function. The random process in such models is indexed in terms of the locations of the study region. The machine learning community employs Gaussian processes for many tasks, and these processes may be indexed on information that statisticians would term as covariates. We compare the predictive ability of a traditional geostatistical model with that of a non-traditional Gaussian process model, which has a constant mean and whose random process is indexed on orographic covariates. The models we compare are both simply parametrized, fit with straightforward inference methods, and use classical kriging predictors. The non-traditional model achieves non-stationarity in the geographic space. We apply the two models to soil moisture data sets, which have extensive spatial sampling, and we apply the models to six separate days of data. In terms of quantitative measures, we find that the models' predictive abilities are comparable, with the non-traditional outperforming the traditional model perhaps slightly. Qualitatively, the non-traditional model's predictions may be more closely linked to the orographic covariates. Copyright © 2014 John Wiley & Sons, Ltd.