SOIL SCIENCE SOCIETY OF AMERICA JOURNAL VOL. 62 JULY-AUGUST 1998 No. 4 DIVISION S-l—SOIL PHYSICS Neural Network Analysis for Hierarchical Prediction of Soil Hydraulic Properties Marcel G. Schaap,* Feike J. Leij, and Martinus Th. van Genuchten ABSTRACT The solution of many field-scale flow and transport problems re- quires estimates of unsaturated soil hydraulic properties. The objec- tive of this study was to calibrate neural network models for prediction of water retention parameters and saturated hydraulic conductivity, A' s , from basic soil properties. Twelve neural network models were developed to predict water retention parameters using a data set of 1209 samples containing sand, silt, and clay contents, bulk density, porosity, gravel content, and soil horizon as well as water retention data. A subset of 620 samples was used to develop 19 neural network models to predict K,. Prediction of water retention parameters and A', generally improved if more input data were used. In a more detailed investigation, four models with the following levels of input data were selected: (!) soil textural class, (ii) sand, silt, and clay contents, (iii) sand, silt, and clay contents and bulk density, and (iv) the previous variables and water content at a pressure head of 33 kPa. For water retention, the root mean square residuals decreased from 0.107 for the first to 0.060 m 3 nr' for the fourth model while the root mean square residual K, decreased from 0.627 to 0.451 log(cm d '). The neural network models performed better on our data set than four published pedotransfer functions for water retention (by ~ 0.01-0.05 m 3 m ') and better than six published functions for K, (by -0.1-0.9 order of magnitude). Use of the developed hierarchical neural network models is attractive because of improved accuracy and because it permits a considerable degree of flexibility toward available input data. C ONCERN ABOUT THE QUALITY of soil and water re- sources has motivated the development of increas- ingly sophisticated models for predicting water flow and solute transport in unsaturated soils. These models gen- erally require knowledge of the soil water retention, 0(/z), and unsaturated hydraulic conductivity, K(h), where 0 is the volumetric water content and h is the pressure head. Direct measurement of these properties USDA-ARS, U.S. Salinity Lab., 450 West Big Springs Rd., Riverside, CA 92507-4617. Received 2 June 1997. *Corresponding author (mschaap@ussl.ars.usda.gov). Published in Soil Sci. Soc. Am. J. 62:847-855 (1998). is often time consuming and expensive, while the results may not be accurate. An alternative is the use of pedo- transfer functions (PTFs), which estimate the hydraulic properties through correlation with more easily mea- sured or widely available soil parameters (Bouma and van Lanen, 1987; van Genuchten and Leij, 1992). A variety of PTFs with different mathematical con- cepts, predicted properties, and input data requirements have been developed. Quasi-physical methods by Arya and Paris (1981), Haverkamp and Parlange (1986), and Tyler and Wheatcraft (1989) use the concept of shape similarity between pore- and particle-size distributions. The vast majority of PTFs, however, are empirically based on relatively simple linear regression equations. Although considerable differences exist among PTFs in terms of the required input data, all of them use at least some information about the particle-size distribution. When only the textural classification is known, simple "class" PTFs can be used to provide average hydraulic properties for each soil textural class (Carsel and Par- rish, 1988; Wosten et al., 1995). When the actual particle- size distribution is known, PTFs that predict continu- ously changing hydraulic properties across the textural triangle can be used. Pedotransfer function predictions may be improved by extending the input data through addition of basic soil properties like bulk density, porosity, or organic matter content (Rawls and Brakensiek, 1985; Ver- eecken et al., 1989). Additional improvements may be achieved by including one or more water retention data points (Rawls et al., 1992; Williams et al., 1992). Ahuja et al. (1989) and Messing (1989) similarly improved pre- dictions of saturated hydraulic conductivity, K s , by using effective porosity data, which they defined as the total porosity minus the water content at 10 or 33 kPa pres- Abbreviations: PTF, pedotransfer function; p b , bulk density; EP 10 , effective porosity at 10 kPa; EP 33 , effective porosity at 33 kPa; EP lsgt> , effective porosity at 1500 kPa; HOR, horizon; POR, porosity; PTF, pedotransfer function; RMSR, root mean square residual, Eq. [4] and [5]; SSC, sand, silt, clay content; TXT, textural class. 847