Mapping complex soil patterns with multiple-point geostatistics

The commonly used variogram function is incapable of modelling complex spatial patterns associated with repetitive, connected or curvilinear features, because it is a two-point statistic. Because this was strongly limiting to petroleum- and hydrogeologists, they developed multiple-point geostatistics (MPG), an approach that replaces the variogram by a training image (TI). However, soil scientists also face complex spatial patterns and MPG might be of use to them as well. Therefore, this paper aims to introduce MPG to soil science and demonstrate its potential with a case study of polygonal subsoil patterns caused by Weichselian periglacial frost cracks in Belgium. A high-resolution proximal soil sensing survey provided a reference image from which a continuous (655 sensor data) and a categorical (100 point observations) dataset were extracted. As a continuous TI, we used the geophysical data of another part of the field, and as categorical TI we used a classified photograph of an ice-wedge network in Alaska. The resulting MPG maps reconstructed the polygonal patterns very well and corresponded closely to the reference image. Consequently, we identify MPG as a promising technique to map complex soil patterns and suggest that it should be added to the pedometrician's toolbox.