Published in Vadose Zone Journal 2:297-312 (2003)
© 2003 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH PAPER
Simulation of Large-Scale Field Infiltration Experiments Using a Hierarchy of Models Based on Public, Generic, and Site Data
Wenbin Wanga,
Shlomo P. Neuman*,b,
Tzung-mow Yaoc and
Peter J. Wierengac
a Water Management Consultants, 3025 N. Campbell Ave. #281, Tucson, AZ
b Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721
c Department of Soil, Water, and Environmental Science, University of Arizona, Tucson, AZ 85721
* Corresponding author (neuman{at}hwr.arizona.edu).
Received 19 November 2002.
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ABSTRACT
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Comparative simulations of a large-scale field infiltration experiment at the Maricopa Agricultural Center (MAC) near Phoenix, AZ, were conducted using a hierarchy of models based on public, generic, and site data joined with pedotransfer functions and an inverse procedure. Our purpose was to investigate the ability of simple models and relatively inexpensive data to reproduce and predict reliably the time evolution of water content profiles in nine 10-m-deep neutron monitoring boreholes at the site. By relying solely on public sources of information one might conclude that soil at the MAC site is uniform to a depth of 16 m, with a water table at about 22 m. Upon collecting soil samples at the site, we learned the soils are layered and laterally discontinuous, with a perched water table at about 13 m. To identify the least level of complexity required to simulate infiltration at the MAC, we compared models that consider one- and two-dimensional flow in a uniform soil, a soil consisting of uniform layers, and a stratified soil with laterally distinct zones. There is a paucity of hydraulic characterization data for the site. To investigate the feasibility of obtaining hydraulic parameter estimates for the models on the basis of soil type, we ascribed uniform properties to each layer or zone using mean values of three generic databases. To improve these estimates, we ascribed variable soil hydraulic properties to individual soil samples using regression and neural network pedotransfer functions based on soil type and bulk density; we then used them to obtain Bayesian updates of mean hydraulic properties in each layer or zone. We used the various models and mean parameter estimates to simulate water contents during one of several infiltration experiments at the MAC. None of the results compared well with measured water contents, although one set of generic mean parameter values yielded much better results than the other two. Estimating parameters using pedotransfer functions and Bayesian updating does not lead to improved simulations. Only when the parameters are estimated by means of an inverse procedure does one notice a significant improvement in model fit. We compared and ranked the various models and parameter estimates using likelihood-based model discrimination criteria and confirmed our choice of best model by successfully simulating flow during an earlier infiltration experiment.
Abbreviations: MAC, Maricopa Agricultural Center
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INTRODUCTION
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ANALYSES OF WATER FLOW in the vadose zone are often hampered by a lack of adequate site data. Without such data, it is difficult to develop detailed predictive models of unsaturated flow in heterogeneous soils. Under what circumstances can relatively simple models based on data that are relatively easy to obtain provide reliable predictions of flow in the vadose zone? This question is acutely relevant to those charged with environmental safety assessment in common situations where time and resources are severely limited.
As the question is quite broad, we narrowed it down by asking what is the ability of simple models and relatively inexpensive data to reproduce and predict reliably the time evolution of water content profiles in nine 10-m-deep neutron monitoring boreholes during large-scale infiltration experiments at the MAC near Phoenix, AZ? To address this narrower question, we conducted comparative simulations of the experiments, using models of increasing complexity and a hierarchy of supporting data. The fastest and least expensive way to assess the geologic makeup and hydraulic properties of a site is to rely on public sources of information coupled with generic databases. Such information and data seldom support more than a very simple model of the site. A more accurate but time-consuming and costly approach is to describe site geology on the basis of disturbed soil samples collected at the site and to assess their hydraulic properties using pedotransfer functions. This may justify the postulation of a more detailed site model. Even more accurate but demanding and expensive is to collect relatively undisturbed soil samples for laboratory determination of their hydraulic properties. Additional alternatives include geophysical surveys and hydraulic tests conducted on site. The more numerous and reliable are such data, the more detailed and potentially accurate would be the model to simulate flow at the site. The accuracy of such simulations can only be assessed by comparing them with actual observations of system behavior. If the comparison proves unsatisfactory, one has the option of modifying the model and/or its parameters (usually through an inverse procedure) to improve the fit between model predictions and observations. Models so constructed can be ranked and compared using formal model discrimination criteria. The best among them can be validated by examining its ability to reproduce system behavior under conditions that are independent of those used to develop the model. We explored several of these site characterization and modeling options in reference to two of three infiltration experiments conducted at the MAC by Young et al. (1999).
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EXPERIMENTS AND SITE CHARACTERIZATION
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Brief Description of Infiltration Experiments
The three experiments (Young et al., 1999) were conducted by using a drip irrigation system to apply water uniformly at a controlled rate to a 50 by 50 m2 area (Fig. 1). The area was covered by a 60 by 60 m2, thick Hypalon (Colorado Lining, Parker, CO) pond liner to minimize evaporation. We consider the first and last of the three experiments. Experiment 1 lasted 93 d, starting 28 April and ending 30 July 1997. Water was applied to the field at an average rate of 1.85 cm d-1 for 24 d, with a bromide tracer added for the first 15 d at a mean concentration of 31.6 mg kg-1. The water application period was followed by a redistribution period of 69 d. Experiment 3 lasted more than 200 d; we consider the first 56 d, starting 24 April and ending 19 June 2001. Water was applied at an average rate of 2.66 cm d-1 for 28 d, and redistribution was measured for the following 28 d. Monitoring took place across the site by a variety of devices. We concentrate on the neutron probe readings of water content taken in nine boreholes down to a depth of 14 m at 0.25-m intervals (see Fig. 1).
Site Characterization Based on Public and Generic Data
Information about the MAC site and its surroundings is available from a variety of public sources, including United States Geological Survey, Arizona Department of Water Resources, Arizona Department of Agriculture, Arizona Land Department, Arizona Land Resource Information System, and Arizona Meteorological Network. They suggest that soils at the site consist of sandy loam to a depth of about 16 m, with the vadose zone extending to about 20 m. In the absence of more detailed information, one may be justified in simulating flow during the MAC infiltration experiments as if it took place downward at a horizontally uniform rate through a uniform layer of sandy loam. Public sources do not provide information about soil hydraulic properties at the site. To characterize the sandy loam hydraulically we ascribed to it mean parameter values taken from three generic databases: RAWLS (Rawls et al., 1982), ROSETTA (Schaap and Leij, 1998), and CARSEL (Carsel and Parrish, 1988; Meyer et al., 1997).
The RAWLS database includes 5401 soil samples from across the United States. Rawls et al. (1982) published a table of mean hydraulic parameter estimates and their standard deviations, based on the constitutive model of Brooks and Corey (1964), for 11 USDA soil texture classes The parameters include a pore size distribution index 
and the air-entry pressure head hb. These are related to van Genuchten's (1980) constitutive parameters 
and n through = n - 1 and hb = 1/.
The ROSETTA database is pooled from part of the AHUJA (Schaap and Leij, 1998), UNSODA (Leij et al., 1996), and RAWLS databases. It contains water retention parameters for 2134 soil samples and saturated hydraulic conductivity Ks for 1306 samples. Schaap and Leij (1998) tabulated mean values of these parameters for 12 USDA soil classes.
The CARSEL database contains 15737 soil textural samples collected by the Natural Resources Conservation Service (formerly Soil Conservation Service) from 42 of the United States. The database does not contain measured hydraulic parameters. On the basis of a regression model by Rawls and Brakensiek (1985) coupled with Monte Carlo simulations, Carsel and Parrish (1988) used the same database to derive probability distributions for saturated volumetric water content 
s, residual volumetric water content r, saturated hydraulic conductivity Ks, and van Genuchten's parameters and n for 12 USDA soil textural classes. Meyer et al. (1997) extended their results to include probability distributions for the Brooks and Corey parameters and hb, effective porosity, field capacity, wilting point, and available water content.
The distribution of samples among soil classes in RAWLS, ROSETTA, and CARSEL is quite uneven. While the sand portion of samples in RAWLS and ROSETTA is much larger than in CARSEL, the sandy loam portion in RAWLS is smaller, and there are fewer fine-textured samples in RAWLS and ROSETTA than in CARSEL. We assessed the extent to which these three databases are suitable for the modeling of infiltration at the MAC site.
Spatial Variability Models Based on Pedologic Site Data
To justify postulating a more detailed flow model for the MAC, one must rely on site data. Pedologic data at the site include soil composition to a depth of 15 m and bulk density to 5 m (Young et al., 1999). Most of the samples are concentrated in the upper 1.8 m of the soil. Histograms and statistics of soil composition at the site can be found in Wang (2002). The data exhibit pronounced spatial variability, which makes it difficult to postulate a simple model of soil makeup for the site. This task is facilitated by a variogram analysis of percentage of sand, silt, and clay conducted by Wang down to a depth of 15 m. The variograms have a vertical range (distance beyond which spatial autocorrelation effectively vanishes) of about 2 m (Wang, 2002), suggesting that it might be feasible to model flow at the site as if it took place through uniform horizontal layers having average thickness of 2 m. This is supported by a visual examination of soil profiles in boreholes and neutron count ratios, which correlate with soil compositional data.
Upon conducting an omnidirectional variogram analysis of sand, silt, and clay percentages in 30-cm soil intervals to a depth of 1.8 m, Wang (2002) determined that these variables have a horizontal range of 20 to 25 m. This suggests postulating yet another, more complex model in which the layers consist of uniform segments measuring 20 to 25 m in the horizontal direction. Though one might postulate more detailed models of spatial variability at the MAC, we shall see that this laterally discontinuous layered model allows us to simulate two infiltration experiments at the site with adequate (though not perfect) fidelity.
On the basis of these and additional data from deeper boreholes near the site, we represented the 20-m-thick vadose zone at the MAC site by 10 layers consisting of four different soil types (sandy loam, gravelly loam sand, sand, and sandy clay loam), as illustrated in Fig. 2. We included in the model a perched water table at a depth of about 13 m across the site that was revealed by the neutron data.
Hydraulic Characterization Using Pedotransfer Functions
Because there is a paucity of hydraulic parameter measurements for the MAC site, we relied on pedotransfer functions (Bouma and van Lanen, 1987) to translate soil pedologic data into hydraulic parameters. First we associated each soil class with mean hydraulic parameter values of the three generic databases. To improve these generic values, we estimated the soil hydraulic properties (saturated water content s, residual water content r, van Genuchten's and n, saturated hydraulic conductivity Ks) of individual soil samples across the site on the basis of their particle size distribution and bulk density using regression equations of Rawls and Brakensiek (1985) and the Rosetta neural network software of Schaap et al. (1998). Soil samples are available for three of the four soil types found within the upper 15.5 m (Fig. 2): sandy loam, gravely loamy sand, and sand. No soil samples are available at the site for the deeper sandy clay loam. The results and some related statistics are listed in Table 1. These provide continuously varying soil hydraulic property estimates across the entire triangle of possible soil compositions, which we treated as local "measurements". We then conditioned the original (prior) CARSEL estimates of hydraulic parameters for each soil class on these site "data" by means of a Bayesian updating code developed for this purpose by Meyer et al. (1997).
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Table 1. Hydraulic parameter estimates derived from site measurements of soil size fraction and density using two different pedotransfer models.
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The original (prior) CARSEL estimates (including standard deviation) and their Bayesian (posterior) updates are listed in Table 2 for the three soil types sampled at the site. The Bayesian approach of Meyer et al. (1997) equates the variance of prior mean values with that of soil hydraulic parameters in the CARSEL database. In this sense, the prior standard deviation can be viewed as representing the estimation error of prior mean values. The site data are considered to be error-free. As expected, Bayesian updating brought about a change in the mean (reduction in bias) and a drastic reduction in its estimation variance, regardless of which pedotransfer model was used to obtain the "measurements".
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Table 2. Prior (based on CARSEL database) and posterior (following Bayesian updating) mean and standard deviation (SD) of hydraulic parameter estimates by soil class.
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Wang (2002) conducted a variogram analysis of saturated water content (s) and log saturated hydraulic conductivity (log Ks) estimates obtained using the Rosetta neural network software. They exhibited vertical ranges between 1 and 2 m and horizontal ranges (down to a depth of 1.8 m) between 20 and 36 m; some fit linear variogram models that do not possess finite correlation scales. As expected, the results correspond closely to those of the soil composition data from which the hydraulic "measurements" originated.
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FORWARD FLOW MODELING
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Forward Modeling Based on Public and Generic Data
As mentioned above, publicly available data suggest that soils at the experimental site consist of sandy loam to a depth of about 16 m, with a regional water table located at a depth of 22 m. In the absence of more detailed information, one might be justified in simulating flow during the MAC infiltration experiments as if it took place downwards at a horizontally uniform rate through a uniform layer of sandy loam. To characterize the sandy loam hydraulically, we ascribed to it mean parameter values taken from the RAWLS, ROSETTA, and CARSEL generic databases.
Volumetric water contents were obtained from neutron probe readings using a calibration curve developed by Young et al. (1999). The calibration was based on measured water contents from core samples and neutron probe readings at depths of 3.0 m or less. We adopted water content measurements in Borehole 422 (Fig. 1) before Exp. 3 as initial values and treated the water table at a depth of about 13 m (indicated by the same measurements) as a constant head boundary. (Setting the water table at a depth of 22 m, as indicated by information from public sources, did not affect the model results at depth down to 10 m.) A constant flux of 2.66 cm d-1 was maintained at the soil surface during the first 28 d of the experiment. During the remainder of the experiment, the soil surface constituted a no-flow boundary. We solved Richards' equation subject to these initial and boundary conditions on a one-dimensional grid of rectangular cells measuring 10 cm along the vertical and 1 m along the horizontal, using the finite volume code TOUGH2 developed by Pruess et al. (1999).
Figures 3 and 4 compare measured and simulated water contents in Borehole 422 derived using mean hydraulic parameters from ROSETTA and CARSEL, respectively. Results using mean parameter values from RAWLS are visually very similar to those in Fig. 3. Only the CARSEL parameters yielded acceptable matches with observations at depths of <4.0 m.
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Fig. 3. One-dimensional forward simulation of infiltration into uniform soil during Exp. 3 at Borehole 422 using mean hydraulic parameters from ROSETTA.
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Fig. 4. One-dimensional forward simulation of infiltration into uniform soil during Exp. 3 at Borehole 422 using mean hydraulic parameters from CARSEL.
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We conclude that relying entirely on public and generic data, even with initial conditions based on site measurements, led to a poor reproduction of observed infiltration at the Maricopa site. Among the three generic databases examined, the best results were obtained with the CARSEL set.
Forward Modeling Based on Site Data
On the basis of available site characterization data we postulated a model of uniform layers that may be rendered nonuniform through further subdivision in the lateral direction. We considered three corresponding infiltration models of Exp. 3 that increase in complexity from one-dimensional vertical flow across uniform layers to two-dimensional flow across uniform and nonuniform layers. All models were based on Richards' equation and were conducted using the TOUGH2 code of Pruess et al. (1999). In two-dimensional simulations, flow takes place across 9 to 10 layers (depending on borehole; see Fig. 2) in a vertical plane measuring 110 m horizontally and extending down to a no-flow boundary at 20 m depth. The plane was discretized into rectangular cells measuring 2.0 m horizontally and 10 cm vertically. Neutron probe data suggested that the perched water table at the eastern and northern boundaries is higher by about 0.2 m than at the western and southern boundaries; we assigned constant head boundary conditions along the lower portions of the lateral grid boundaries to reflect these measurements and no-flow conditions at higher elevations. A constant flux of 2.66 cm d-1 was maintained at the soil surface during the first 28 d of the experiment within the irrigated plot, and a flux of zero outside this plot. During the remainder of the experiment, the soil surface constituted a no-flow boundary.
Figure 5 shows the results of a one-dimensional forward simulation in Borehole 402 (Fig. 1) using mean hydraulic parameters from CARSEL. The computed response (curves) captured in a very crude way the observed behavior (dots). However, there were large differences between measured and computed water contents and wetting-front arrival times. Much poorer results were obtained when we adopted mean hydraulic parameters from RAWLS or ROSETTA (Wang, 2002).
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Fig. 5. One-dimensional simulation of infiltration into layered soil during Exp. 3 at Borehole 402 using mean hydraulic parameter values from CARSEL at various depths.
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Figure 6 depicts results obtained using Bayesian updates of ROSETTA parameter estimates. Though there was some improvement in comparison with results obtained without updating, the results were still poorer than those obtained using mean hydraulic parameters from CARSEL. The same happened when we use updated parameter estimates from RAWLS (Wang, 2002).
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Fig. 6. One-dimensional simulation of infiltration in Exp. 3 at Borehole 402 using Bayesian updates of saturated hydraulic conductivity, van Genuchten's and n based on ROSETTA estimates.
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These and similar simulations corresponding to Borehole 422, summarized in Table 3, indicated that mean hydraulic parameters from CARSEL provided best-fit simulations to measured water content data in all cases. Bayesian updates improved the accuracy of generic ROSETTA and RAWLS hydraulic parameters, but not significantly.
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Table 3. Results of forward simulations using one-dimensional layered models. Bayesian updates refer to CARSEL database.
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Figure 7 compares two-dimensional forward simulations and measurements along a north–south uniformly layered transect passing through Boreholes 402, 422, and 442 (Fig. 1), using mean hydraulic parameter values from CARSEL. The quality of the results varied with depth, and simulated wetting front arrival times lagged by up to 10 d behind those measured. Results obtained using mean parameter estimates from ROSETTA or RAWLS, as well as those obtained using Bayesian updates of these parameters, were much less satisfactory (Wang, 2002). The same was true for a central east–west transect through Boreholes 422, 423, and 425 (Fig. 1). A summary of all these runs in Table 4 indicates that hydraulic parameter estimates from CARSEL were generally superior to those from ROSETTA, RAWLS, or their Bayesian updates. However, none of the forward simulations were entirely satisfactory, and there is an obvious need to calibrate the models against observed system behavior.
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Fig. 7. Two-dimensional forward simulation along north–south uniformly layered transect, using mean hydraulic parameter values from CARSEL at various depths.
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Table 4. Results of forward simulations for north–south (N-S) and east–west (E-W) transects, using two-dimensional uniformly layered models. Bayesian updates refer to CARSEL database.
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INVERSE FLOW MODELING BASED ON SITE DATA
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We used the inverse code iTOUGH2 (Finsterle, 1999a,b) to calibrate our one- and two-dimensional flow models against observed water contents at the MAC. The inverse code estimates hydraulic parameters by minimizing a negative log likelihood criterion equal to the weighted sum of squared water content and parameter residuals. Water content residuals are differences between simulated and observed water contents, the square of each being weighted by the inverse variance of the corresponding observation error. Parameter residuals are differences between posterior (inverse) and prior (input) parameter estimates, the square of each being weighted by the inverse variance of the corresponding prior estimation error.
Parameter estimates obtained on the basis of Bayesian updating had very small variances (Table 2) and therefore very large weights. The latter allowed only minute departure of the posterior parameters from their initial (input) values, which is not enough to yield a significant improvement in model fit (reduction in the weighted sum of squared water content residuals). As unsaturated flow equations are highly nonlinear and soil hydraulic parameter estimates are correlated with each other, it is difficult to identify soil hydraulic properties uniquely using inversion. The more accurate the input parameters, the higher the prospect of obtaining meaningful inverse estimates. Since the CARSEL database yielded the best results in the forward simulations, we adopted the mean and variance of hydraulic parameters from Meyer et al. (1997) as input into the inverse code.
Calibrating a one-dimensional model consisting of a single uniform layer against water content data in various boreholes during Exp. 3 brought about only a minor improvement over the uncalibrated model (Wang 2002). This model is clearly inferior to the multilayer models we consider below.
Because the sandy loam at depths 0 to 2 m has a different bulk density than deeper sandy loam layers, we estimated its hydraulic properties separately. This yielded a total of four materials for each sequence of layers: sandy loam in the top layer, sandy loam in deeper layers, gravel loamy sand, and sand. Sensitivity analysis about the prior parameter estimates suggested (see Wang, 2002, for details) that it should be possible to estimate independently the saturated hydraulic conductivity Ks and van Genuchten's and n for each of these materials, so this was what we did.
Figure 8 depicts matches between simulated (curves) and measured (dots) water contents in Borehole 402 considering one-dimensional infiltration into a layered medium during Exp. 3 following inversion. Inverse modeling is seen to have improved these matches significantly, compared with the forward modeling results in Fig. 5. It also brought about a significant change in the estimate (mean) and reduction in the estimation error (variance) of each parameter. The same happened when we calibrate our one-dimensional layered model individually against water content data from Boreholes 422, 442, 423, and 425.
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Fig. 8. One-dimensional simulation of infiltration into layered soil during Exp. 3 in Borehole 402 using inverse estimates of saturated hydraulic conductivity and van Genuchten's and n.
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Figure 9 shows the results of two-dimensional inverse modeling along the western north–south transect by considering the soil to consist of horizontally uniform layers. The matches are seen to be much better than those obtained before inversion in Fig. 7. While some simulation results fit the data well, other were systematically too low or too high. For example, water content in the top sandy loam layer in Borehole 402 was systematically underpredicted, whereas in sandy loam and sand layers at depths 6 to10 m in Boreholes 422 and 442 it was systematically overpredicted. Figure 9 suggests indirectly that computed wetting-front arrival times in deeper sections of Borehole 442 lagged considerably behind the measured values. Similar results were obtained for the central east–west transect (Wang, 2002). We conclude that it may be necessary to account for lateral variations in layer properties.
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Fig. 9. Two-dimensional simulation of infiltration in Exp. 3 along western north–south transect (Boreholes 402, 422, 442), using inverse estimates of saturated hydraulic conductivity and van Genuchten's and n and assuming uniform soil layers.
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Variogram analysis has shown that the dominant horizontal correlation scale of soil hydraulic parameters at the MAC is 20 to 25 m. We therefore subdivided the transect into three horizontal segments, one per borehole. We ascribed to each segment initial parameter values equal to those previously obtained from corresponding one-dimensional inverse modeling results, which yielded a total of 36 parameters per transect.
Figure 10 compares simulated and observed water contents using inverse parameter estimates along the western north–south transect. The fit is seen to be good in all cases. A histogram of residuals (Fig. 11) suggests that they are close to normal with a near-zero mean and small standard deviation. At a confidence level of 95%, only 14 out of the 300 residuals were identified as outliers. The parameter estimates differed only slightly from their one-dimensional counterparts. Similar results were obtained for the central east–west transect (Wang, 2002).
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Fig. 10. Two-dimensional simulation of infiltration in Exp. 3 along western north–south transect (Boreholes 402, 422, 442), using inverse estimates of saturated hydraulic conductivity and van Genuchten's and n and assuming nonuniform layers.
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Fig. 11. Histogram of differences between observed and simulated water contents along western north–south transect (Boreholes 402, 422, 442) following inversion. Nonuniform layers.
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Tables 5 and 6 compare the various one- and two-dimensional models along the western north–south and central east–west transects, respectively, following inversion. The quality of model fit was compared on the basis of a D-optimality criterion equal to the determinant of the covariance matrix of parameter estimation errors, an A-optimality criterion equal to the trace of this matrix, an E-optimality criterion equal to the largest absolute eigenvalue of the same matrix (Steinberg and Hunter, 1984), the negative log likelihood criterion that is minimized during the inverse process, and the logarithm of the corresponding likelihood function (which is being maximized). These model fit criteria can be used to compare the quality of different models that have similar structure and number of parameters (such as our north–south and east–west two-dimensional models with uniform layers), but not models that have different structures or numbers of parameters (such as our two-dimensional models with uniform and non-uniform layers). To validly compare the quality of all models in Tables 5 and 6, we employed likelihood-based model discrimination criteria of Akaike (1974) and Kashyap (1982), as done previously by Carrera and Neuman (1986a)(b, c). The smaller (or more negative) are these criteria, the better the model. The model discrimination criteria consistently identified the uniform one-dimensional model as being the worst among those considered, and the two-dimensional nonuniformly layered model as being the best.
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Table 5. Model quality criteria for four one-dimensional (1-D) and two two-dimensional (2-D) models associated with the north–south (N–S) transect.
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Table 6. Model quality criteria for three one-dimensional (1-D) and two two-dimensional (2-D) models associated with the east–west (E–W) transect.
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CONFIRMATION OF INVERSE MODELING RESULTS
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Our conceptual model and inverse hydraulic parameter estimates were based on data collected during infiltration Exp. 3. We used them to simulate water contents at the MAC site during Exp. 1.
Figure 12 shows a two-dimensional simulation of Exp. 1 along the western north–south transect using the nonuniform layered model with hydraulic parameters obtained through calibration against water contents observed during Exp. 3. The good matches between simulated and observed water contents for Exp. 1 constitute a confirmation of the calibrated model. Similar results were obtained for the central east–west transect (Wang, 2002).
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Fig. 12. Two-dimensional simulation of Exp. 1 along the north–south transect (Boreholes 402, 422, 442), using layered nonuniform conceptual model and hydraulic parameters obtained from Exp. 3.
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CONCLUSIONS
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Our comparison of various data sources and modeling approaches in simulating large-scale infiltration experiments at the MAC site led to the following conclusions:- Publicly available data suggest that soils at the experimental MAC site consist of sandy loam down to a depth of about 16 m. Site data indicated instead that the soil profile down to a depth of 20 m consists of 10 layers composed of four different soil types (sandy loam, gravelly loam sand, sand, and sandy clay loam), which are laterally heterogeneous on scales exceeding 20 to 30 m.
- Publicly available data identify a regional water table that is locally about 22 m deep. Site data indicate the additional presence of a perched water table at a depth of about 13 m across the site.
- Relying entirely on publicly available data, even with locally determined initial water contents, leads to a poor reproduction of observed water contents during infiltration at the MAC site. Hence, generic flow models of the kind used by some regulatory agencies for environmental assessment, which avoid site exploration, are a poor substitute for site-specific models that are tailored to local conditions and compatible with relevant site data.
- Mean hydraulic parameter estimates based on the generic CARSEL database, published by Meyer et al. (1997) on the basis of data assembled by Carsel and Parrish (1988), allow a much better reproduction of observed water contents at the MAC than do estimates based on the RAWLS (Rawls et al., 1982) or ROSETTA (Schaap and Leij, 1998) databases. Bayesian updating of mean hydraulic parameters associated with the CARSEL database, based on neural network and regression estimates of site hydraulic parameters, leads to only a marginal improvement in their ability to reproduce observed water contents at the site.
- Regardless of our choice of database, pedotransfer function or flow model, we were unable to reproduce observed water contents at the site without calibrating the flow model against such observations. Hence, uncalibrated flow models of the kind used by some regulatory agencies for environmental assessment, which avoid site monitoring of relevant dependent variables such as water content or pressure head, are a poor substitute for models whose parameters are estimated by inverse procedures based in part on observed system behavior. We used the mean and variance of hydraulic parameters associated with the CARSEL database as inputs into our inverse flow models.
- Calibrating a one-dimensional model consisting of a single uniform layer against water content data in various boreholes during Exp. 3 brings about only a minor improvement over the uncalibrated model. This model is clearly inferior to the multilayer models we considered for the site.
- Inverse modeling brings about a significant improvement in our ability to reproduce observed water contents at the MAC using multilayer models regardless of whether the latter are one- or two-dimensional, with uniform or laterally heterogeneous layers. Inverse modeling is accompanied by a significant change in the estimate (mean) and reduction in the estimation error (variance) of each hydraulic parameter.
- Likelihood-based model discrimination criteria consistently identify the uniform one-dimensional model as being the worst among those considered and the two-dimensional model, with laterally heterogeneous layers as being the best.
- The latter model, calibrated against water content data observed during Exp. 3, reproduces with fidelity water content data observed during Exp. 1.
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ACKNOWLEDGMENTS
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This work was supported by the U.S. Nuclear Regulatory Commission under contract number NRC-04-97-056. We thank Thomas J. Nicholson, our NRC project manager, for his support and Philip D. Meyer of Pacific Northwest National Laboratory, and Arthur W. Warrick and Donald E. Myers of the University of Arizona for their valuable inputs.
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REFERENCES
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- Akaike, H. 1974. New look at statistical model identification. IEEE Trans. Autom. Control. AC19:716–723.
- Bouma, J., and J.A. van Lanen. 1987. Transfer functions and threshold values: From soil characteristics to land qualities. p. 106–110. In K.J. Beek et al. (ed.) Quantified land evaluation. ITC Publ. 6. International Institute Aerospace Surv. Earth Sci., Enschede, the Netherlands.
- Brooks, R.H., and A.T. Corey. 1964. Hydraulic properties of porous media. Hydrol. Pap. 3. Colorado State Univ. Fort Collins.
- Carrera, J., and S.P. Neuman. 1986a. Estimation of aquifer parameters under transient and steady state conditions. 1. Maximum likelihood incorporating prior information. Water Resour. Res. 22:199–210.
- Carrera, J., and S.P. Neuman. 1986b. Estimation of aquifer parameters under transient and steady state conditions. 2. Uniqueness, stability, and solution algorithms. Water Resour. Res. 22:211–227.
- Carrera, J., and S.P. Neuman. 1986c. Estimation of aquifer parameters under transient and steady state conditions. 3. Application to synthetic and field data. Water Resour. Res. 22:228–242.
- Carsel, R.F., and R.S. Parrish. 1988. Developing joint probability distributions of soil water retention characteristics. Water Resour. Res. 24:755–770.
- Finsterle, S. 1999a. iTOUGH2 user's guide. Rep. LBNL-40040. Lawrence Berkeley National Lab., Berkeley, CA.
- Finsterle, S. 1999b. iTOUGH2 sample problems. Rep. LBNL-40042. Lawrence Berkeley National Lab., Berkeley, CA.
- Kashyap, R.L. 1982. Optimal choice of AR and MA parts in auto regressive moving average models. IEEE Trans. Pattern Anal. Mach. Intell. 4:99–104.
- Leij, F.J., W.J. Alves, and M.Th. van Genuchten. 1996. The UNSODA unsaturated soil hydraulic database. EPA, Ada, OK.
- Meyer, P.D., M.L. Rockhold, and G.W. Gee. 1997. uncertainty analyses of infiltration and subsurface flow and transport for SDMP sites. Rep. NUREG/CR-6565. U.S. Nuclear Regulatory Commission, Washington, DC.
- Pruess, K., C. Oldendurg, and G. Moridis. 1999. TOUGH2 user's guide. Version 2.0. Rep. LBNL-43134. Lawrence Berkeley National Laboratory, Berkeley, CA.
- Rawls, W.J., and D.L. Brakensiek. 1985. Prediction of soil water properties for hydrologic modeling. p. 293–299. In Proc. Watershed Management in the Eighties. American Society of Civil Engineering, New York.
- Rawls, W.J., D.L. Brakensiek, and K.E. Saxton. 1982. Estimation of soil water properties. Trans. ASAE 25:1316–1320.
- Schaap, M.G., and F.J. Leij. 1998. Database related accuracy and uncertainty of pedotransfer functions. Soil Sci. 163:765–779.
- Schaap, M.G., F.J. Leij, and M.Th. van Genuchten. 1998. Neural network analysis for hierarchical prediction of soil water retention and saturated hydraulic conductivity. Soil Sci. Soc. Am. J. 62:847–855.[Abstract/Free Full Text]
- Steinberg, D.M., and W.G. Hunter. 1984. Experimental design: Review and comment. Technometrics 28:71–97.
- van Genuchten, M.Th. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892–898.[Abstract/Free Full Text]
- Wang, W. 2002. Uncertainty analysis of groundwater flow and solute transport in unsaturated-saturated soil: Maricopa case. Ph.D. diss. University of Arizona, Tucson.
- Young, M.H., P.J. Wierenga, A.W. Warrick, L.L. Hofmann, S.A. Musil, M. Yao, C.J. Mai, Z. Zou, and B.R. Scanlon. 1999. Results of field studies at the Maricopa Environmental Monitoring Site, Arizona. Rep. NUREG/CR-5694. U.S. Nuclear Regulatory Commission, Washington, DC.
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ABSTRACT
INTRODUCTION
