Information content of measurements from tracer microlysimeter experiments designed for parameter identification in dual-permeability models
Introduction
Dual-permeability solute transport models account for preferential flow by including a separate flow domain describing rapid non-equilibrium flow in soil macropores with first-order mass exchange between the two domains (Feyen et al., 1998, Šimůnek et al., 2003). In this respect they are more complex than models based solely on the convection-dispersion equation since they require additional parameters to describe macropore flow. One difficulty with these models has been the lack of reliable procedures for estimating these parameters (FOCUS, 1995, Šimůnek et al., 2003), since some are either difficult or impossible to measure. One example of this type of model is MACRO (Jarvis, 1994, Larsbo et al., 2003), which couples classical treatments of flow and transport processes in the soil matrix to a macropore region where flow is assumed to be gravity-driven.
Parameters regulating the degree of preferential flow in MACRO (the mass exchange coefficient, the saturated micropore hydraulic conductivity and the kinematic exponent governing the flow in macropores) have been shown to be among the most sensitive for pesticide leaching in a structured soil under field conditions (Dubus and Brown, 2002). A reduction in the uncertainty of these parameters is of paramount importance for reliable model predictions. Attempts have been made to identify parameters by inverse modelling in preferential flow models on data from column experiments (Schwartz et al., 2000, Kätterer et al., 2001, Roulier and Jarvis, 2003). These authors found that the parameter determining the mass exchange between flow domains was difficult to identify. This was attributed to parameter insensitivity (Kätterer et al., 2001, Roulier and Jarvis, 2003), failure of the first-order mass transfer concept used in the model to handle different time scales (Schwartz et al., 2000) and a sparse parameter sampling scheme (Roulier and Jarvis, 2003). Roulier and Jarvis (2003) also suggested that higher time resolution data for both flux and resident concentrations might facilitate parameter identification. Recently, Larsbo et al. (2005) studied the possibilities to identify four key parameters regulating preferential flow in high time-resolution tracer microlysimeter experiments. They successfully constrained the mass exchange coefficient but could not satisfactorily reduce the uncertainty in the kinematic exponent describing macropore tortuosity. This was attributed to correlation with the macroporosity.
The success of an inverse method depends on how well the problem is posed (Hopmans and Šimůnek, 1999). Whether a parameter estimation problem is solvable is determined by its stability, identifiability and uniqueness. Even though theoretically the problem of ill-posedness is not always solvable, a parameter estimation problem might become well-posed if sufficient experimental data is obtained. The usefulness of adding more data to solve the non-uniqueness problem has lately been questioned and focus has shifted towards data quality rather than quantity (Yapo et al., 1996, Gupta et al., 1998). Vrugt et al., 2001, Vrugt et al., 2002 developed a calibration method entitled parameter identification method based on the localization of information (PIMLI). In contrast to other parameter identification methods, PIMLI is specifically designed to locate the most informative measurements for parameter identification.
The objectives of this study were (i) to find an improved temporal measurement scheme for identification of parameters governing the degree of preferential flow in the MACRO model using laboratory microlysimeter experiments and (ii) to study the possibilities to identify these parameters. We used the PIMLI method proposed by Vrugt et al. (2001) for the parameter identification exercise and to identify the most informative measurements. We examined two plausible measurement approaches, (i) high time-resolution measurements of percolation rate, effluent concentration and resident solute concentrations at six depths and (ii) measurements of percolation rate, effluent concentration, and one resident solute concentration profile (six depths) at the end of the experiment. All analyses were performed on two hypothetical soils representing one typical clay and one typical loam. A limited sensitivity analysis was first conducted to identify the most sensitive parameters for the different groups of data for the experimental set-up.
Section snippets
Model description
MACRO 5.1 is a physically based one-dimensional dual-permeability model for water flow and solute transport through the unsaturated zone (Larsbo et al., 2003, Larsbo et al., 2005). The soil porosity is divided into a micropore domain and a macropore domain. The pore domains are characterized by different flow rates and solute concentrations. Only the most relevant aspects of the model concerning this study are given here.
The division between flow domains is given by a water potential, Ψb (m),
Laboratory setup and artificial data
The model was parameterized for a laboratory microlysimeter experiment (18 cm high columns with a radius of 9.6 cm) designed for identification of parameters regulating preferential flow and solute transport (Roulier and Jarvis, 2003, Larsbo et al., 2005). Numerical reference data were generated for a hypothetical clay soil with a slow exchange between pore domains and a hypothetical loam soil with a faster exchange (Table 1). Water contents at the start of the simulations corresponded to
Sensitivity analysis
Sensitivity analysis (SA) is used to identify parameters that have the greatest effect on model outputs (Fontaine et al., 1992). Parameters that are identified as insensitive can be held constant during a calibration to reduce the computational demand. Since results from SA tend to depend on the site and scenario considered, it is often useful to make a limited sensitivity analysis when conditions are different from those from which prior sensitivity information is available (Ferreira et al.,
PIMLI
Vrugt et al. (2001) introduced a parameter identification method based on the localization of information (PIMLI) and successfully used it for calibration of the parameters in the van Genuchten water retention equation (van Genuchten, 1980) and the hydraulic conductivity function given by Mualem (1976) using numerically generated data from a multistep outflow experiment. The general idea behind PIMLI is to identify subsets of data containing the most information for the identification of each
Morris sensitivity analysis
Average elementary effects for the hypothetical clay soil calculated for high time-resolution data of percolation rate and effluent and resident concentrations are presented in Fig. 3(a). For the percolation rate, θmac,sat was by far the most sensitive parameter followed by Kb, Kmac,sat, n* and α (van Genuchten α). This is not surprising since these parameters govern the distribution of infiltration between pore domains and the water flow rates in both flow domains. The diffusion pathlength, θ
Parameter identification
The results from the PIMLI exercise are summarised in Table 2 for the hypothetical clay and in Table 3 for the hypothetical loam. For the clay, uncertainties were reduced by more than 50% for six parameters using all data. The prior distributions for the remaining six parameters were left unaltered or only slightly changed by the process. These parameters were also least sensitive according to the Morris analysis (Fig. 3(a)). The true values of d, n*, Kb and Dv were within one standard
Measurement scheme
One other aim of the PIMLI analysis was to identify which type of measurement contains most information for parameter identification and in which phase of the experiment these measurements are located. A sampling scheme for a microlysimeter experiment should focus on these phases. The patterns of ICs for each group of data and the relative importance of different groups were generally similar throughout the iterative process. As an example, results for Dv for the clay soil using all data are
Conclusions
Artificial data from laboratory microlysimeter experiments consisting of high resolution ‘measurements’ of percolation rate, effluent concentration and resident concentrations at six depths were used with a parameter identification method based on the localisation of information (PIMLI) in the dual-permeability model MACRO. The data contained enough information to successfully reduce the uncertainty in the parameter governing mass exchange between pore domains, the micropore saturated hydraulic
Acknowledgements
This project was funded by VR (The Swedish Research council) in the project ‘Regulation of preferential water flow and reactive solute transport by lateral mass exchange: Critical examination of the first-order assumption’.
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