Information Content of Data for Identifying Soil Hydraulic Parameters from Outflow Experiments

However, using this conventional approach, problems are often encountered with the non-uniqueness of the Process-oriented models of open systems often contain parameters optimized parameters. Non-uniqueness leads to more that cannot be measured directly but can only be obtained by inverse modeling. A conventional inverse method is typically based on the than one set of parameters, each yielding minimum valminimization of an objective function that lumps the discrepancies ues for the objective function determined by local minin time series of observed values and predicted model response. Howima or by the same global minimum at more than one ever, problems are often encountered with the non-uniqueness of the point in the parameter space (Gupta and Sorooshian, parameter estimates. Non-unique parameter estimates result in case 1985; Duan et al., 1992). of low parameter sensitivity, mutual parameter dependency, and high Seemingly there was a widespread conviction that the measurement noise. These problems can be solved partly if we do best way to solve the non-uniqueness problem was to not use the entire data set but focus on subsets where the model is include additional and more accurate measurements most sensitive to changes in the unknown parameters. Therefore we (Eching and Hopmans, 1993; Van Dam et al., 1994). propose PIMLI (Parameter Identification Method based on the LocalHowever, research into data requirements has led to ization of Information), that uses the variability in time of the model sensitivity for the various parameters to split the total set of measurethe understanding that the information content of the ments into disjunctive subsets that each contain the most information data is far more important than the amount of data used on one of the model parameters. Thereupon, each distinguished subset for model calibration (Kuczera, 1982; Sorooshian et al., is used to constrain its corresponding parameter. To illustrate PIMLI 1983; Gupta and Sorooshian, 1985; Yapo et al., 1996; we chose a simulated multi-step outflow (MSO) experiment in which Gupta et al., 1998). Therefore, we developed a parameonly cumulative outflow is measured because of its well-known probter identification technique entitled PIMLI (Parameter lems with the uniqueness of the identified soil hydraulic properties. Identification Method based on the Localization of InThe results show that PIMLI not only leads to unique parameter sets formation) that treats the data in such a way as to preof soil hydraulic properties for a range of soils but also significantly serve the specific information with respect to the various improves the understanding of uniqueness problems related to paramparameters and that uses the information content of eter identification. data to identify the model parameters. For illustrating PIMLI we used the MSO experiment that only measures cumulative outflow, because of its well-known problems M for environmental applications vary in regarding the non-uniqueness of the identified paramesophistication and complexity, ranging from simters for unsaturated flow (Hopmans and Šimůnek, ple data-oriented models to highly complex process1999). oriented models. These models give an approximate The use of inverse methods for determining the unsatdescription of the system under study and contain sevurated flow parameters from transient experiments was eral unknown quantities, such as parameters. Often, first reported by Zachmann (1981). Kool et al. (1985a,b) these model parameters cannot be measured directly used this inverse modeling approach to determine soil but can only be obtained by inverse modeling. If these hydraulic properties from one-step outflow (OSO) exmodels are to be applied without calibration, then transperiments, but experienced problems with the nonfer functions must be found to link these model parameuniqueness of the parameter estimation. Further investiters to other properties that can be measured indepengations of the inverse method demonstrated the need dently (Schaap et al., 1998). The uniqueness of a set of for additional u(h) data (Hudson et al., 1991; Van Dam calibrated parameters is a prerequisite to finding these et al., 1992; Bohne et al., 1993) or tensiometer measuretransfer functions. ments inside the soil sample (Kool and Parker, 1988; The simplest form of parameter estimation is curve Toorman et al., 1992; Eching and Hopmans, 1993) to fitting in which measured data are represented by a overcome the problem of non-uniqueness of paramestatic function with parameters that provide the best ters. The benefit of including tensiometer measurements possible fit to the data (van Genuchten et al., 1991). A is apparent, as the optimized soil water retention is more complex form of parameter estimation is inverse forced to match the observed u(h) data. Another way modeling, where parameters are optimized while minto realize more reliable parameter estimates is to increimizing a suitable objective function that expresses the mentally increase the pneumatic pressure in several discrepancy between the output of a dynamic model steps, the MSO experiment, instead of a single pressure and the measurements (Janssen and Heuberger, 1995). increment (Van Dam et al., 1994). The objective of this study was to analyze the tempoJ.A. Vrugt, W. Bouten, and A.H. Weerts, Institute for Biodiversity and Ecosystem dynamics, University of Amsterdam, Nieuwe PrinsenAbbreviations: MSO, multi-step outflow; MVG, Mualem–van Gengracht 130, Amsterdam, 1018 VZ, the Netherlands. Received 17 Sept. uchten; OSO, one-step outflow; PIMLI, Parameter Identification 1999. *Corresponding author ([email protected]). Method based on the Localization of Information; SWIF, soil water in forested ecosystems model. Published in Soil Sci. Soc. Am. J. 65:19–27 (2001).