Stéphanie Roulier

Analysis of Inverse Procedures for Estimating Parameters Controlling Macropore Flow and Solute Transport in the Dual-Permeability Model MACRO

the best simulation of the data giving the desired parameter set. The best-fit condition is reached by minimizing Because they are objective and reproducible, inverse modeling an objective function, which expresses the discrepancy procedures are increasingly used to identify model parameters that cannot be easily measured. This study investigated the feasibility of between the experimental data and the simulation. Inusing inverse methods to estimate parameters describing macropore verse modeling procedures are thus objective, reproducflow, transport, and transformation processes in the dual-permeability ible, and unambiguous, providing the problem is well model MACRO. MACRO was linked to the inverse modeling package posed (i.e., the solution exists, is unique, and depends SUFI, and we used numerically generated data representing transient continuously on the initial data). Ill-posed problems, leaching experiments for tracers and reactive solutes in microlysimearising from insufficient data in terms of quality and ters (21-cm height). Attention was focused on parameter sensitivity, quantity with respect to the parameters to be estimated, availability of experimental data (flux and resident concentrations), lead to problems of nonuniqueness and unreliable pathe degree of macropore flow in the system, and the significance of rameter estimates (Dubus et al., 2002). experimental errors. Reliable results were obtained in the case of strong macropore flow, but both resident and flux concentrations To date, inverse methods have been widely applied were needed. However, the uncertainty in d, the parameter describing in soil physics to derive soil hydraulic properties and in mass exchange between microporosity and macroporosity, remained large-scale distributed hydrological models (Hopmans large, and the adsorption coefficient could not be estimated accurately. and Simunek, 1999; Madsen, 2003), but very little is curResponse surface analysis showed that this was due to a lack of sensitivity to d and to internal correlation between adsorption and rently known about the possibilities and potential probdegradation parameters. In the case of equilibrium flow, the model lems of inverse modeling techniques applied to macwas overparameterized, and the parameters related to macropore flow ropore flow problems. Durner et al. (1999) showed that were not sensitive enough to be estimated properly. Experimental the parameters of bimodal water retention and hydrauerrors did not affect the feasibility of the procedure, although the lic conductivity functions assumed in some dual-permeuncertainty in the estimates increased. SUFI linked to MACRO apability models could be determined by inverse modeling pears to be a promising tool for optimization of the system parameters against measured water outflows from multistep outflow in soils affected by macropore flow, but the “experimental” design experiments. They claimed that the procedure was roneeds to be improved for reliable determination of the mass exchange bust, leading to unique solutions with limited data (waparameter and the adsorption coefficient. ter outflows only), irrespective of the number of parameters included, providing the underlying model accurately represented the true soil hydraulic properties. Schwartz M flow in the unsaturated zone is a signifiet al. (2000) attempted to estimate the parameters of a cant process that has a major impact on leaching dual-permeability model by inverse modeling on steadyand has been demonstrated in many field experiments state bromide breakthrough experiments on a variably (e.g., Flury, 1996; Jarvis, 2002). A number of models charged tropical soil, where the Br ion could be considaccounting for macropore flow are now available (Jarered as a weakly sorbed reactive solute. They encounvis, 1998; Feyen et al., 1998). The most widely adopted tered great difficulties in obtaining physically realistic concept is to divide the porosity into two or more reestimates of two critical parameters, namely the dispergions, each characterized by a water pressure (or water sion coefficient in the micropores and the fraction of content), water flow rate, and solute concentration. sorption sites in the macropores. They concluded that However, the introduction of additional parameters deinverse procedures are problematic even for the simple scribing the macropore region in such dual-permeability case of steady water flow with four unknown parameters models makes the task of parameter estimation even to estimate and were also pessimistic about the potential more difficult, and this is the main obstacle to the application of macropore flow models. Inverse modeling, also to estimate macropore flow parameters under transient termed automatic calibration, is a promising alternative conditions in the field. These findings highlight the need method to derive parameters that cannot be estimated to investigate the feasibility of inverse procedures beby accurate independent measurement or by expert fore applying them to actual data, to avoid the risk of judgment. Parameter values are derived from the comidentifying physically inappropriate parameter values. parison of model simulations with experimental data, In particular, it remains to be seen whether robust estimation of model parameters regulating macropore flow is possible for transient leaching experiments with reacS. Roulier and N. Jarvis, Department of Soil Sciences, SLU, Box 7014, tive solutes. 750 07, Uppsala, Sweden. Received 14 Feb. 2003. Original Research Paper. *Corresponding author (stephanie.roulier@mv.slu.se). This study focused on the development and testing of an inverse procedure to derive soil hydraulic properPublished in Vadose Zone Journal 2:349–357 (2003). ties and adsorption and transformation parameters in  Soil Science Society of America 677 S. Segoe Rd., Madison, WI 53711 USA simulation models which account for rapid nonequi-