rosetta: a computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions
Introduction
A broad array of methods currently exists to determine soil hydraulic properties in the field or in the laboratory (cf. Klute, 1986, Leij and van Genuchten, 1999). While measurements permit the most exact determination of soil hydraulic properties, they often require a substantial investment in both time and money. Moreover, many vadose zone studies are concerned with large areas of land that may exhibit substantial spatial variability in the soil hydraulic properties. It is virtually impossible to perform enough measurements to be meaningful in such cases, thus indicating a need for inexpensive and rapid ways to determine soil hydraulic properties.
Many indirect methods for determining soil hydraulic properties have been developed in the past (cf. Rawls et al., 1991, van Genuchten and Leij, 1992, Leij and van Genuchten, 1999). Most of these methods can be classified as pedotransfer functions (PTFs, after Bouma and van Lanen, 1987) because they translate existing surrogate data (e.g. particle-size distributions, bulk density and organic matter content) into soil hydraulic data. All PTFs have a strong degree of empiricism in that they contain model parameters that were calibrated on existing soil hydraulic databases. A PTF can be as simple as a lookup table that gives hydraulic parameters according to textural class (e.g. Carsel and Parrish, 1988, Wösten et al., 1995) or include linear or nonlinear regression equations (e.g. Rawls and Brakensiek, 1985, Minasny et al., 1999). PTFs with a more physical foundation exist, such as the pore-size distribution models by Burdine (1953) and Mualem (1976), which offer a method to calculate unsaturated hydraulic conductivity from water retention data. Models by Haverkamp and Parlange (1986) and Arya and Paris (1981) use the shape similarity between the particle- and pore-size distributions to estimate water retention. Tyler and Wheatcraft (1989) combined the Arya model with fractals mathematics, while Arya et al., 1999a, Arya et al., 1999b recently extended the similarity approach to estimate water retention and unsaturated hydraulic conductivity.
Practical applications of most PTFs are often hampered by their very specific data requirements. Some authors established PTFs that provided the best results for their data set, which sometimes produced models that require many input variables (cf. Rawls et al., 1991) or detailed particle-size distributions (Arya and Paris, 1981, Haverkamp and Parlange, 1986). However, users of PTFs are frequently confronted with situations where one or several input variables needed for a PTF are not available. Another problem is that PTFs provide estimations with a modest level of accuracy. It would therefore be useful if PTFs could accept input data with varying degrees of detail and if PTF predictions could include reliability measures.
Recently, neural network analysis was used to establish empirical PTFs (Pachepsky et al., 1996, Schaap and Bouten, 1996, Minasny et al., 1999, Pachepsky et al., 1999). An advantage of neural networks, as compared to traditional PTFs, is that neural networks require no a priori model concept. The optimal, possibly nonlinear, relations that link input data (particle-size data, bulk density, etc.) to output data (hydraulic parameters) are obtained and implemented in an iterative calibration procedure. As a result, neural network models typically extract the maximum amount of information from the data. Schaap et al. (1998) used neural network analyses to estimate van Genuchten (1980) water retention parameters and saturated hydraulic conductivity. To facilitate the practical use of the PTFs, they designed a hierachical structure to allow input of limited and more extended sets of predictors. The combination with the bootstrap method (Efron and Tibshirani, 1993) provided the reliability for the PTF estimations (Schaap and Leij, 1998).
Yet, while neural network-based PTFs may provide relatively accurate estimates, they contain a large number of coefficients that do not permit easy interpretation or publication in explicit form. To facilitate application of the PTFs, we have developed the computer program rosetta that implements some of the models published by Schaap et al., 1998, Schaap and Leij, 1998 and Schaap and Leij (2000). The objectives of this paper are (i) to present the rosetta program in terms of hydraulic parameters, calibration data sets, selection of predictors, and characterization of model performance, and (ii) to discuss the uncertainty of estimated hydraulic parameters as a function of suction and texture.
Section snippets
Materials and methods
Much of this section has been published before in Schaap et al., 1998, Schaap and Leij, 1998, Schaap and Leij, 2000. However, we describe the most important methodology here to provide the reader a concise documentation about the background of rosetta. This section will also present methodology that was not used in previous publications.
Model characteristics
An overview of the performance of the hierarchical models for estimation of water retention parameters and Ks is given in Table 1. Not surprisingly, the results show that correlations between fitted and estimated parameters increase and RMSE values decrease when more predictors are used (H1–H5). Residual water content is difficult to estimate with all models, while saturated water content is difficult to estimate without information about bulk density. The correlation for α increases
Discussion
Even with the best predictive models, i.e. H5 for retention and C2-Fit for unsaturated conductivity, the correlations between estimated and fitted or measured hydraulic parameters were modest at best (cf. Table 1, Table 2). The differences between RMSE and ME values of estimation and direct fits (Fig. 2, Fig. 3, Fig. 4, Fig. 5) further suggest that the models in this study could be improved upon. However, the direct fits only give the theoretically minimum attainable errors for PTFs because ,
Description of rosetta
Named somewhat whimsically after the Rosetta Stone that allowed translation of ancient Egyptian hieroglyphs into Old Greek, rosetta allows user-friendly access to models H1–H5 for water retention and saturated hydraulic conductivity and models C2-Fit and C2-H1–C2-H5 for unsaturated hydraulic conductivity. In this section, we will review the most important features of rosetta. More information about various aspects of the program and file specifications may be obtained through the help system
Concluding remarks
This study presents the computer program rosetta which implements a number of PTFs for estimation of water retention parameters, the saturated and unsaturated hydraulic conductivity as well as associated uncertainties. The models were characterized in terms of their calibration data sets and the accuracy of their estimations. For the estimation of water retention and saturated hydraulic conductivity, it turned out that the hierarchical models performed reasonably well if more predictors were
Acknowledgements
The authors gratefully acknowledge the support by NSF and NASA (EAR-9804902), and the ARO (39153-EV).
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