Spatial Interpolation of Hydraulic Conductivity using Radial-Basis Function Networks

Geological evolution determines the spatial distribution of hydraulic conductivity in natural field. This pattern is often characterized using geostatistics and estimates at unmeasured locations are obtained from kriging. In this paper, the potential of a special class of artificial neural networks (ANNs) called radial-basis function (RBF) networks is explored to perform spatial interpolation of hydraulic conductivity. These networks derive their structure and interpretation from the theory of interpolation in multidimensional spaces. Such networks, almost invariably, consist of three layers — a transparent input layer, a hidden layer with sufficiently large number of nodes to allow good mapping capabilities without overfitting, and an output layer. Radially-symmetric basis functions are used as activation functions of hidden layer nodes. By implementing concepts of interpolation theory into network design, the training of radial-basis function networks can be accomplished faster than artificial neural networks that use back-propagation. In case of hydraulic conductivity mapping, the location coordinates are used as inputs to RBF networks, and the hydraulic conductivity value as output. Two sites within the Kings Creek watershed of the Konza Prairie Research Area in Kansas were utilized for spatial analysis of infiltration properties. Plots of size 6m by 6m were selected at each site, and experiments for infiltration properties, including saturated hydraulic conductivity, were conducted at 37 locations at each. These data were used to interpolate the hydraulic conductivity values over the entire plot using RBF networks and the kriging technique from geostatistics. The two methods yield different surfaces of hydraulic conductivity. The similarities between the two methods and their respective interpolation philosophies, strengths and limitations are discussed.