Arti fi cial Neural Network Estimation of Saturated Hydraulic Conductivity

cial neural networks have become a common tool for modeling complex “input–output” dependencies. In the past, neural network models have been used as a special class of pedotransfer functions (PTFs) using feed-forward back propagation or radial basis functions to approximate any continuous (nonlinear) function (Hecht-Nielsen, 1990; Pachepsky et al., 1996; Schaap and Bouten, 1996; Minasny and McBratney, 2002; Pachepsky and Schaap, 2004). Studies in which ANNs have been examined from a statistical perspective indicate that ANN models with certain geometries, connectivities, and internal parameters are either equivalent or close to existing statistical models (White, 1989; Cheng and Titterington, 1994; Hill et al., 1994; Sarle, 1994). Moreover, they are fl exible and simple; by altering the transfer function or architecture, one can vary model complexity. They can also be easily extended from univariate to multivariate cases incorporating nonlinearities effortlessly. In neural networks, the concern is primarily one of estimation or prediction accuracy and methods that work, whereas the main objective of statisticians is to develop a universal methodology and to achieve statistical optimality (Breiman, 1994; Tibshirani, 1994). Saturated hydraulic conductivity, among other soil hydraulic properties, is important for initializing climate and hydrologic models. However, measuring Ks is time consuming and expensive. As a result of the high variability associated with soil hydraulic properties (Warrick and Nielson, 1980; Wilding, 1984), most work performed in the past has been limited to the use of empirical and physical relationships referred to as pedotransfer functions (Bouma and van Lanen, 1987; Bouma, 1989; Rawls et al., 1992) and in recent times, ANN (Pachepsky et al., 1996; Schaap and Bouten, 1996; Schaap et al., 1999; Minasny and McBratney, 2002). Terrain plays a fundamental role in modulating the earth surface and atmospheric processes because the landform confi guration frequently governs the movement of materials and water on the landscape (Burt and Butcher, 1986; Moore et al., 1993; Gessler et al., 1995; Western and Blöschl, 1999; Park and Vlek, 2002; Romano and Chirico, 2004) and, consequently, the catchment hydrology at the topo-scale (Wilson and Gallant, 2000). The use of terrain attributes for modeling Ks may serve as a suitable alternative, as terrain data are fairly easy to collect compared to intensive soil sampling. The inclusion of terrain data infl uence on PTFs for estimating soil water content, van Genuchten hydraulic parameters, has recently been studied (Romano and Artifi cial Neural Network Estimation of Saturated Hydraulic Conductivity