Published online 3 October 2006
Published in Vadose Zone J 5:1093-1109 (2006)
DOI: 10.2136/vzj2005.0104
© 2006 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH
A Field Application of the Scaled-Predictive Method for Unsaturated Soil
M. J. Thomassona,*,
P. J. Wierengab and
T. P. A. Ferréc
a Errol L. Montgomery & Associates, Inc., 1550 East Prince Rd., Tucson, AZ 85719
b Dep. of Soil, Water and Environmental Science, Univ. of Arizona, Tucson, AZ
c Dep. of Hydrology and Water Resources, Univ. of Arizona, Tucson, AZ
* Corresponding author (mthomasson{at}elmontgomery.com)
Received 22 August 2005.
 |
ABSTRACT
|
|---|
Unsaturated hydraulic conductivity is important to many vadose zone processes. However, there is uncertainty regarding how laboratory- and field-measured hydraulic property measurements can be combined with soil textural data to improve the description of the unsaturated hydraulic conductivity function at the field scale. In this investigation, we examine a scaled-predictive method for defining the hydraulic conductivity function. This approach uses field-measured data to adjust the hydraulic conductivity relationship developed using either laboratory measurements or soil textural data. In addition, both hydraulic property models were scaled using field-measured data collected during a controlled infiltration experiment. Data from a second controlled infiltration experiment were used to evaluate the hydraulic property models based on accuracy of prediction of the arrival time of a wetting front and the water content distribution with time. The unadjusted laboratory-derived parameters provide the best first approximation for predicting the wetting front arrival. Both hydraulic property models gave more accurate predictions of the wetting front arrival after adjustment with field-measured data. Both scaled models predicted the water content distributions poorly. These predictions were improved, especially for the pedotransfer model, if the scaling was applied to only the lower portion of the soil profile.
Abbreviations: LDP, laboratory-derived hydraulic properties • NN, neural network • RMS, residual squared errors • S-P, scaled-predictive
|
INTRODUCTION
|
|---|
ACCURATE NUMERICAL MODELS of water flow and solute transport are critical for use by regulatory agencies. With the continued advances of numerical models and computing capabilities, the accuracy of predictions of flow models is often limited by the adequacy of hydraulic property estimations. Specifically, predictions of the movement of water and solutes through the unsaturated zone are highly sensitive to the water content–pressure head relationship 
(h) and the hydraulic conductivity–pressure head relationship K(h) (Butters and Duchateau, 2002). Many approaches have been taken to define the K(h) relationship (Luckner et al., 1989; Yates et al., 1992; Mace et al., 1998), including the scaled-predictive methods, which match the predicted and experimental hydraulic conductivities at fluid phase contents less than full saturation (Luckner et al., 1989; Yates et al., 1992; Mace et al., 1998).
The objective of this study is to examine the effectiveness of the scaled-predictive method for adjusting the unsaturated hydraulic conductivity relationship to improve the accuracy of predictions of unsaturated flow numerical models. Specifically, we investigate whether commonly measured properties, such as tension and water content, combined with the scaled-predictive method can offer a relatively quick and simple approach in adjusting the unsaturated hydraulic conductivity relationship. We also examine whether soil hydraulic properties measured in laboratory columns offer an advantage over properties estimated using a neural network (NN) analysis based on soil texture. The effectiveness of the parameter estimation schemes is evaluated based on the ability of a numerical model to predict the arrival time of a wetting front and the water content distribution with time during two controlled field infiltration experiments.
|
METHODS, MATERIALS, AND THEORY
|
|---|
Study Site Description
The experimental plot is located on the Maricopa Agricultural Center, approximately 150 km northwest of Tucson, AZ. The plot lies within a northwest trending alluvial basin, situated within the Basin and Range region, which is characterized by northwest to southeast trending mountain ranges separated by broad alluvial valleys (Corell and Corkhill, 1994). The alluvium in the basin varies in thickness from 60 to 150 m (m), and is comprised primarily of unconsolidated to slightly consolidated sands and gravels. Some finer grained lenses are distributed throughout the unit. Soil textural characterization at the entire field site is generally classified as the Casa Grande soil, a fine-loamy, mixed, hyperthermic Typic Natrargrids soil (Thompson et al., 2000). The regional groundwater table is at approximately 200-m depth. Localized perched zones of groundwater are present at approximately 11- to 12-m depth. The region is in a semiarid environment and receives approximately 20 cm (cm) of rainfall annually.
Infiltration Experiments
The study site consisted of a 50 by 50 m field plot with two access culverts installed vertically in the ground. These allowed access to undisturbed soil through ports in the culvert walls (Fig. 1). Tensiometers were installed through the access culvert walls approximately 0.6 to 0.9 m into the undisturbed soil, from 0.5 to 3.0 m depth in 0.5 m intervals. Tension and neutron probe data used in this study came from the east side of the southern culvert, and a neutron probe access tube located between the two access culverts (Fig. 1).
During two successive infiltration experiments, water was applied to the experimental plot using 164 parallel drip lines spaced 0.3 m apart, with self-cleaning emitters every 0.3 m along the line. A total of 27 000 emitters were distributed over the 50 by 50 m area. Water meters were used to measure the volume of water applied over the irrigated area. The experimental plot was covered by a 60 by 60 m, 0.081 cm thick, Hypalon pond liner (DuPont, Wilminton, DE) to minimize surface evaporation. Additional information about the experiments can be found in Young et al. (1999).
Experiment 1 lasted 93 d, starting 28 Apr. 1997 and ending on 30 July 1997. Water was applied from 28 Apr. 1997 to 21 May 1997, at an average flux of 1.85 cm per day (cm d–1) with a coefficient of variation (CV) of 1.9% for a total of 44.4 cm of water over 24 d. Redistribution was measured for 93 d following the end of infiltration.
Experiment 2 lasted 210 d starting on 3 Dec. 1997 and ending 1 July 1998. Water was applied at an average flux of 1.91 cm d–1 (computed CV of 12%) for 34 d (total of 64.8 cm) with redistribution measured for 177 d following the end of infiltration.
Modeling Water Flow
HYDRUS 1-D (Simunek et al., 1998) was used to simulate the flow of water through the soil profile. HYDRUS 1-D solves a mixed form of Richards' equation. The governing equation, without a source or sink term, is:
 | [1] |
where t is time (day), K is hydraulic conductivity (cm d–1), h is the water pressure head (cm), and z is elevation increasing upward (cm).
The initial and boundary conditions that represent the first field experiment are:
 | [2] |
 | [3] |
 | [4] |
 | [5] |
where to is the initial time of the experiment and hi(z) are measured values. A free drainage condition is imposed at the lower boundary. A flux boundary condition is imposed on the upper boundary. In the second field experiment the flux upper boundary condition was specified as 1.91 cm d–1 for the first 33 d and zero (0) thereafter.
The soil-hydraulic functions of Mualem (1976) and van Genuchten (1980) are:
 | [6] |
 | [7] |
 | [8] |
where r and s are the residual and saturated water content (cm3 cm–3), respectively, I is a pore connectivity factor (-), 
(1/cm) and n (-) are empirical coefficients that affect the shape of the hydraulic functions, and Se is the effective saturation. Equations [6] and [7] are subject to the m = 1 – 1/n condition (n > 1) (Mualem, 1976; van Genuchten, 1980). The initial distribution of pressure head for the unsaturated-flow model was obtained from the observed initial averaged water contents (Fig. 2) given by the neutron probe data.
View larger version (16K):
[in this window]
[in a new window]
|
Fig. 2. Model initial conditions and observed initial conditions. The circles and squares represent the mean observed soil water contents for Exp. 1 and 2, respectively. The solid line represents the interpolated soil water contents used in the model (HYDRUS).
|
|
Determination of Hydraulic Properties
Laboratory-Derived Properties
Laboratory-derived hydraulic properties (LDP) of the soil from the field site were estimated by Fleming (2001) from 11 core samples (Table 1). The cores were collected from a north–south transect in the center of the plot at a depth of approximately 1.5 m. Saturated hydraulic conductivity and saturated water content were determined on all 11 of the intact soil cores using a constant head Marriott system (Soil Measurement Systems, Tucson, AZ) and repacked soil cores. At the end of the saturated conductivity determination, the entire soil core assembly was reweighed to obtain an estimate of saturated volumetric water content (Fleming, 2001). The residual water content as well as the van Genuchten (1980) parameters of , n, and I were estimated using an upward infiltration laboratory method combined with an inverse numerical procedure (Fleming, 2001). The intact soil cores measured 7.6 cm in diameter and height. An average flux of 0.015 cm min–1 was applied to the lower boundary for the 215 min experiment.
View this table:
[in this window]
[in a new window]
|
Table 1. Mean hydraulic properties and the statistical parameters for the core samples obtained by laboratory methods.
|
|
Neural Network-Derived Hydraulic Properties
Hydraulic properties of the soil at the access culvert were estimated using soil samples taken from locations surrounding the access culvert. The soil at the access culvert is classified texturally as sandy loam to a depth of 2.0 m and as loamy sand from approximately 2.0 to 3.0 m (Fig. 3). The textural data were used to delineate one approximate gradational boundary at a depth of 1.5 to 2.0 m. The textural classifications were used in conjunction with a NN program ROSETTA (Schaap et al., 2001) to define values for the saturated hydraulic conductivity, the saturated and residual water contents, and the van Genuchten parameters of , n, and I.
Water Budget
The amount of water applied to the upper surface of the plot was compared to the change in the measured change in the length of water stored within the soil profile. The water storage change was determined by integrating the field measured water contents with depth at different times during the experiment. The water storage error was calculated as:
 | [9] |
 | [10] |
 | [11] |
where E is the water storage error (cm), Lmeasured is the length (cm) of water stored in the unsaturated zone, Lapplied is the length (cm) of the water applied (using water flow meters), 
z is the vertical depth measurement interval of the neutron probe (25 cm), and is the volumetric water content (cm3 cm–3) change from the initial water content, and k1 is the number of neutron probe measurements. The water storage error was calculated for various locations and times. In all cases, the depth interval and times over which the water storage errors were calculated were chosen to ensure that the profile extended below the wetting front.
Scaled-Predictive Method
An approach similar to the scaled-predictive (S-P) method presented by Luckner et al. (1989), Yates et al. (1992), and Mace et al. (1998) was used in this study. In the S-P method, the predictive K(h) relationship (Eq. [7]) is scaled using a single measurement of unsaturated hydraulic conductivity at a known water content that replaces the saturated hydraulic conductivity as the matching point. Typically, the unsaturated hydraulic conductivity relationship is predicted using a soil hydraulic model such as Eq. [7], which uses one or more parameters from the soil water retention model (Eq. [6]) as well as a measured reference value for hydraulic conductivity, usually Ks. As pointed out by Luckner et al. (1989) and Yates et al. (1992) use of Ks often yields large errors in the unsaturated hydraulic conductivity due to the steep slope of Eq. [7] near saturation. Mace et al. (1998) applied the method to six laboratory cores and found that use of an unsaturated hydraulic conductivity value to scale the predictive relationship improved estimates of K(h) markedly while Yates et al. (1992) applied the method to 36 unsaturated hydraulic conductivity distributions for 23 soils obtained from the literature and found that the method did not significantly improve the estimates of the unsaturated hydraulic conductivity. All of the studies (Luckner et al., 1989; Yates et al., 1992; Mace et al., 1998) suggested using an unsaturated hydraulic conductivity value at a water content below saturation but within the wet range for the matching point as an alternative to Ks. The approach used here makes use of unsaturated hydraulic conductivity measurements for each depth where tensiometers are installed to scale the unsaturated hydraulic conductivity relationship according to:
 | [12] |
where ßK is the scaling factor and K*(h*) is the reference relationship defined by the LDP or NN soil hydraulic properties. Thus, both the h and reference h* values have the same numeric value and the entire K*(h*) relationship is adjusted (or shifted) so that it passes through a field-derived matching point. This linear scaling transformation is based on the similar media concept introduced by Miller and Miller (1956).
The field-derived matching points were computed by determining an average wetting front velocity from the observed tensiometer data and combining this velocity with the observed mean water content at that depth to derive a flux value assuming a unit gradient condition behind the wetting front according to:
 | [13] |
where z is the depth interval (50 cm) the wetting front travels, is the water content change at that depth based on neutron probe measurements, t is the time of the wetting front arrival at depth z (determined from tensiometer readings). Tension data were not used to determine the hydraulic gradient because the transducer calibration data were incomplete (data were not available within the dry range). However, based on tension data within the wet range, behind the wetting front (where transducer calibration data were available), the unit gradient assumption was valid. It is also assumed that the water content immediately achieves steady-state conditions behind the wetting front.
Numerical Models
Three numerical approaches were used to simulate infiltration for Exp. 1. The results obtained with these three modeling approaches were compared to the measured tension and water content data collected at the access culvert. The tensiometer responses were used to delineate the arrival of the wetting front and the beginning of the drainage phase at all depths. The tensiometers were used rather than the neutron probe data, because they were very responsive to the changes in water content and they were collected more frequently (6-h time intervals). The first approach was a single layer homogeneous model that uses the LDP hydraulic properties. The second approach was a two layer model (based on the textural analysis) that uses the hydraulic properties from the NN analysis. The hydraulic properties used in the first and second models were then manually adjusted using the S-P method by use of the scaling factor, ßK. The predictions from both models were then recompared to the measured tension and water content data collected at the access culvert during the first infiltration experiment.
For the third approach all known information for the site was used. This resulted in a two layer model with the laboratory-derived hydraulic parameters providing the initial estimates for the upper sandy loam layer (0–200 cm) and the NN hydraulic parameters providing the initial estimates for the lower loamy sand layer (200–300 cm). The inverse capabilities of HYDRUS were used to simultaneously match the measured water content data at all depths, allowing all of the soil hydraulic parameters except I (r, s, , n, and Ks) to vary during inversion. For the inverse procedure, the measured water content data at each depth was used for fitting purposes rather than the tension data because the transducer calibration data were incomplete (data were not available within the dry range).
A post audit was performed on these models using the measured data from the second infiltration experiment. The initial conditions and boundary conditions were changed accordingly. The initial hydraulic properties used in the models are shown in Table 2.
The goodness of fit for the simulations is evaluated using three criteria. The first criterion is the goodness of fit of the simulated arrival time of the wetting front to the observed arrival time of the wetting front at different depths. The second criterion was the root mean of residual squared errors (RMS) for the observed versus predicted water contents for each depth according to:
 | [14] |
where i and 
i, are the measured and predicted volumetric water contents respectively, for a particular depth, and k2 is the total number of time intervals available for each measurement depth. The third criterion was the r2 value, calculated by HYDRUS 1-D, for regression of the observed vs. fitted soil water content distributions at specific times.
|
RESULTS AND DISCUSSION
|
|---|
Water Budget
The computed depth of water application at the neutron access tube was compared to the depth of water applied through the drip system as measured by the water flow meters for each available irrigation day. The computed depth of water stored in the soil profile at the neutron probe access tube exceeded the actual amount of water applied by an average of 22% through the period of irrigation for the first infiltration experiment. This agrees with data from Graham (2004), who found, using a different analysis of the same data, that the average water balance error for the nine locations within the plot was 19% during the first experiment.
Simulations Using Laboratory- and NN-derived Hydraulic Properties
Water contents were plotted vs. time in Fig. 4 for the 100-, 200-, and 300-cm depths. The wetting front arrival time was defined as the time at which the water content rose to the midpoint between the minimum and maximum values at that depth. The simulated wetting fronts, using the LDP values, arrived at the 1.0, 2.0, and 3.0 m depths at approximately 9.6, 15.8, and 23.3 d, respectively. The wetting fronts computed using the NN properties arrived at these depths after approximately 12.5, 22.2, and 30.8 d. The percent differences between observed and simulated arrival times are listed in Table 3. The LDP model performed better than the NN model by 47.3% and 2.0% based on their fits to the observed wetting front arrival times and RMS of the soil water content profiles, respectively (Table 3 and 4). The LDP model does a reasonable job predicting the increases in water content (Fig. 4, left panes), but, it overpredicts the wetting front arrival time by an average of 44% (Table 3). The NN model overpredicts both the increases in water content and the arrival times by an average of 92% (Fig. 4, right panes).
View larger version (25K):
[in this window]
[in a new window]
|
Fig. 4. Soil water content vs. time for three soil depths and two sets of hydraulic property parameters. Circles are the measured soil water contents; dashed lines represent tension obtained with tensiometers. Solid lines represent predicted soil water contents. Experiment 1, unadjusted models.
|
|
Both the LDP and NN models simulate the water content distribution poorly (Fig. 5). Differences between measured and predicted water contents are as large as 10% by volume. The r2 values were calculated for water content distributions for selected times, and presented in Table 5. Neither model exhibited a r2 value higher than 0.51 (neglecting the initial conditions, Day 0). Furthermore, comparison of the modeled water content distributions with the measured water content distributions seems to indicate that the use of a homogeneous profile in the LDP model is not valid with respect to capturing the water content distribution. However, the two layer NN model also did a very poor job predicting the water content distribution with a correlation coefficient of 0.37 for the Day 26 water content distribution. During the drainage phase (and without layering in the model), the simulated profile drains toward a uniform water content with depth and a homogeneous profile. Both models fail to accurately predict the shape of the soil water profile as the drainage phase progresses (Days 42 and 93) as reflected by the r2 values (Table 5) and figures (Fig. 5).
View larger version (16K):
[in this window]
[in a new window]
|
Fig. 5. Measured (circles) and predicted soil water contents (solid lines) for Days 18, 26, and 42. Experiment 1, unadjusted models.
|
|
Simulations Using the Scaled-Predictive Method and Inverse Method
A version of the scaled-predictive method was applied to adjust the hydraulic conductivity relationships of the LDP and NN models (referred to as LDP + S-P and NN + S-P, respectively) using a field-based calculated unsaturated hydraulic conductivity value for each depth, (Table 6, Fig. 6). After scaling the hydraulic conductivity values to those shown in Table 6, the hydraulic conductivity curve passes through the field calculated values, while the original curve based on an average laboratory-derived hydraulic conductivity value of 44.6 cm d–1 underpredicts the field calculated values by 72 to 98% (Fig. 6) (treating the field calculated values as the known values). For the relationships using the NN, the curves based on NN hydraulic conductivity values of 37.1 and 67.8 cm d–1 also underpredict the field calculated values significantly (Fig. 6). For all depths, scaling the NN unsaturated hydraulic conductivity relationships resulted in scaling factors >5 (Table 6) with the 50-cm depth resulting in a scaling factor of 129. This is in contrast to the LDP + S-P model where for all depths scaling the unsaturated hydraulic conductivity relationships resulted in scaling factors >2 with the largest scaling factor (also at 50 cm) of 18.5.
View larger version (26K):
[in this window]
[in a new window]
|
Fig. 6. Hydraulic conductivity vs. water content. Symbols are the field-calculated hydraulic conductivity values for 50- to 300-cm depths in 50 cm intervals; (A) the dashed line is based on a laboratory-derived value of 44.6 cm d–1 for Ks, the solid lines represent the adjusted hydraulic conductivity relationships and (B) the dashed lines are based on a neural network values of 37.09 and 67.83 cm d–1 for Ks, the solid lines represent the adjusted hydraulic conductivity relationships.
|
|
As expected, after adjusting the unsaturated hydraulic conductivity relationship using the S-P method, the ability of both the LDP and NN model to predict the wetting front arrival improved greatly (Fig. 7). Adjusting the LDP and NN models resulted in both models overestimating the wetting front arrival time (all depths averaged) by 7.5 and 3.3%, respectively, as compared to wetting front arrival times measured with tensiometers.
View larger version (25K):
[in this window]
[in a new window]
|
Fig. 7. Soil water content vs. time for three soil depths and two sets of hydraulic property parameters. Circles are the measured soil water contents; dashed lines represent tension obtained with tensiometers. Solid lines represent predicted soil water contents. Experiment 1, adjusted models.
|
|
The LDP + S-P model more accurately predicted the vertical water content distribution than the NN + S-P model (Fig. 8). This is expected since application of the scaled-predictive method effectively transforms the LDP model to a six layer heterogeneous model (LDP + S-P). The results of the LDP + S-P model with respect to both wetting front arrival and water content distribution indicate that the hydraulic conductivity is the controlling property. Although the NN + S-P model is also a six layer model, it did not perform as well as the LDP + S-P model in predicting the water content distribution (Table 5).
View larger version (17K):
[in this window]
[in a new window]
|
Fig. 8. Measured (circles) and predicted soil water contents (solid and dashed lines) for Days 18, 26, and 42. Experiment 1, adjusted models.
|
|
The predictions from the inverse model were compared to the LDP + S-P model. The LDP + S-P model produced better predictions of the water content profile (Table 5; Fig. 8) than the inverse model (Fig. 9). This is because the inverse model adjusts the hydraulic parameters to fit the observed water content data vs. time for each depth rather than the water content profiles at specific times. As expected, the inverse model did a better job predicting the water contents for each depth with RMS and standard deviation values of 3.2 and 0.9, respectively, vs. 5.0 and 1.6, respectively, for the LDP + S-P model. The poor fit of the inverse model with respect to the wetting front arrival (Fig. 10) is attributable to the fact that water content data measured with the neutron probe does not capture the wetting front arrival clearly due to noise inherent in the data and because the measured data is discontinuous. The LDP + S-P model is not subject to this limitation because we used the measured tensiometer data to delineate the wetting front arrival time and adjusted the hydraulic parameters manually.
View larger version (10K):
[in this window]
[in a new window]
|
Fig. 9. Measured (circles) and predicted soil water contents (solid and dashed lines) for Days 18, 26, and 42. Experiment 1, inverse (adjusted) model.
|
|
View larger version (15K):
[in this window]
[in a new window]
|
Fig. 10. Soil water content vs. time for three soil depths for the inverse model. Circles are the measured soil water contents; dashed lines represent tension obtained with tensiometers. Solid lines represent predicted soil water contents. Experiment 1, inverse (adjusted) model.
|
|
The predictions of the wetting front arrival times from the LDP and NN models improved using the S-P method, as shown by the percent error calculations, and gave better predictions of the wetting front arrival than the inverse model (Table 3). However, the inverse model gave better results than both the LDP + S-P and NN + S-P models in predicting the values of the observed water content values with a RMS of 3.2% vs. 5.0% and 5.2%, respectively (Table 4). The six layer LDP + S-P model was more accurate in predicting the water content profile than the six layer NN + S-P and two layer inverse models. This indicates that certain detailed site specific information (laboratory measured hydraulic properties) is more advantageous to accurate simulations. For our experiment, using unadjusted hydraulic parameters, the laboratory-derived parameters provide a better first approximation for predicting the wetting front arrival and the shape of the curves than parameters estimated using a NN model based on textural considerations.
Post-audit Using the Second Infiltration Data
All three models (LDP, NN, and inverse models) were re-run, and predictions were compared to observed data from the second infiltration experiment. The upper boundary and initial conditions of the models were changed to reflect the second infiltration experiment conditions. The LDP + S-P, NN + S-P and inverse models grossly underpredict the wetting front arrival times by 79, 78, and 95%, respectively (Table 3; Fig. 11 and Fig. 12). While the length of the irrigation phase for the second experiment increased from 24 to 34 d, the rate increased only slightly from 1.85 to 1.91 cm d–1. There are several possible explanations for this large increase in the underestimation of the wetting front arrival. The soil profile is initially much wetter before the start of the second infiltration experiment as compared to the start of the first infiltration experiment (0.21 vs. 0.13 cm3 cm–3, averaged). This could significantly affect the infiltration process since water typically infiltrates drier soil profiles at a higher initial rate under constant head conditions. This could result in much larger scaling factors since the first experiment had much drier conditions especially near the surface (Fig. 2). Assumptions used in calculating the unsaturated hydraulic conductivity values used to scale the hydraulic conductivity relationship may also have been breached because the assumption of a unit gradient may be in error. Assuming the upper portion of the soil profile behind the wetting front is not in equilibrium, the hydraulic gradient may be larger than one, resulting in smaller unsaturated hydraulic conductivity values (Eq. [13]) and translating to lower scaling factors. The assumption that the wetting front travels at a rate given by z/t could also be in error. The response of the tensiometers to a pressure wave created by the wetting front would result in a rate greater than the actual rate of the wetting front. This would result in larger unsaturated hydraulic conductivity values, creating larger scaling factors. Finally, preferential flow around the access culvert could also result in larger apparent unsaturated hydraulic conductivity values, leading to larger scaling factors. Supporting the possibility that one of these factors, such as the infiltration process, has skewed the scaling factors to the higher side is the observation that the LDP and NN models using unadjusted hydraulic parameters more accurately predicted the wetting front arrival time than the adjusted models (Table 3, Fig. 13).
View larger version (22K):
[in this window]
[in a new window]
|
Fig. 11. Soil water content vs. time for three soil depths and two sets of hydraulic property parameters. Circles are the measured soil water contents; dashed lines represent tension obtained with tensiometers. Solid lines represent predicted soil water contents from the models. Experiment 2, adjusted models.
|
|
View larger version (14K):
[in this window]
[in a new window]
|
Fig. 12. Soil water content vs. time for three soil depths for the NN + S-P model. Circles are the measured soil water contents; dashed lines represent tension obtained with tensiometers. Solid lines represent predicted soil water contents from the models. Experiment 2, adjusted model.
|
|
View larger version (22K):
[in this window]
[in a new window]
|
Fig. 13. Soil water content vs. time for three soil depths and two sets of hydraulic property parameters. Circles are the measured water contents; dashed lines represent tension obtained with tensiometers. Solid lines represent predicted soil water contents. Experiment 2, unadjusted models.
|
|
The LDP model performed better than the NN model, underestimating the wetting front arrival time by an average of 13%. The LDP + S-P and NN + S-P models were re-run with the scaling from the upper soil layer (0–50 cm) removed to further investigate the possibility that the scaling procedure adversely affect predictions. The ability of both models to predict the arrival of the wetting front improved dramatically (Fig. 14). The LDP + S-P model predictions improved from underpredicting the arrival of the wetting front by 79% to underpredicting the arrival by 31% (all depths averaged, Table 3). The NN + S-P model predictions improved from underpredicting the arrival of the wetting front by 78% to overpredicting the arrival by 5.3% (all depths averaged).
View larger version (22K):
[in this window]
[in a new window]
|
Fig. 14. Soil water content vs. time for three soil depths and two sets of hydraulic property parameters. Circles represent the measured soil water contents; dashed lines represent tension obtained with tensiometers. Solid lines represent predicted soil water content. Experiment 2, adjusted models, upper soil layer not scaled.
|
|
The performance of the three models in predicting the water contents and the water content distributions from the second simulations were comparable to the results from the first simulations (Table 4 and Table 5). The LDP + S-P model was able to capture the general shape of the water content profile (Fig. 15 and Fig. 16) but was unable to capture the details. This is probably due to soil profile heterogeneities that are not represented in the model despite having six layers distributed over 3 m. There was no significant improvement in the predictions of the water content profiles for the LDP + S-P and NN + S-P models with no scaling in the upper soil layer (0–50 cm). It is interesting to note that while the homogeneous LDP model performed almost as well as the other layered models with respect to the mean correlation coefficients, the water content profiles for the layered models are more visually similar to the observations than the LDP model. This would indicate that care should be taken in simply quantifying the performance of numerical models using the r2 value; such statistics can average differences of model results to a value that is not necessarily representative of the model performance.
View larger version (17K):
[in this window]
[in a new window]
|
Fig. 15. Measured (circles) and predicted soil water contents (solid and dashed lines) for Days 7, 33, and 37. Experiment 2, adjusted models.
|
|
View larger version (9K):
[in this window]
[in a new window]
|
Fig. 16. Measured (circles) and predicted soil water contents (solid and dashed lines) for Days 7, 33, and 37. Experiment 2, inverse (adjusted) model.
|
|
|
SUMMARY AND CONCLUSIONS
|
|---|
The arrival of a wetting front and the water content distribution from two field infiltration events were simulated and compared to observed data. Three numerical models were developed using hydraulic properties derived using LDP based on measurements made on soil cores, NN-derived values based on soil textural analyses, and an inverse modeling approach. Soil cores were only collected at one depth, so the LDP model only included one layer. Soil samples for textural analysis were collected from 50 to 300 cm at 50 cm intervals around the access culvert. These samples supported developing a two layer NN-based model. The hydraulic conductivity relationship of these two models was then adjusted using a scaled-predictive method. A third two- layer model used an inverse approach to estimate the hydraulic parameters. The predictions from all models were compared to observed data from an infiltration experiment to adjust the soil hydraulic parameters. The relative performance of these models was then assessed by comparing the predictions of wetting front arrival time and water content profile against measured data from a second infiltration experiment performed under different conditions.
For our experiment, the unadjusted laboratory-derived parameters provide a better first approximation for predicting the wetting front arrival and the shape of the curves than parameters estimated using a NN model based on textural considerations. Initial efforts scaling the unsaturated hydraulic conductivity relationship offered no advantage for predicting the wetting front velocity. This is likely due in part to the need to use a field-based estimate of unsaturated hydraulic conductivity closer to saturation to scale the unsaturated hydraulic conductivity relationship. This estimate is offered to some degree by the saturated hydraulic conductivity estimated in the laboratory using soil cores and hence the better performance of the unadjusted models during the post-audit. Removing the scaling factor from the upper soil layer (0–50 cm) both the LDP + S-P and NN + S-P models were re-run resulting in more accurate predictions from both models with the NN + S-P model performing best. It is encouraging that the performance of the model developed using hydraulic properties derived from the NN analysis of soil textural analyses performed as well or better on average than the model developed using more labor intensive hydraulic properties derived from laboratory soil cores. The results indicate that under specific conditions (scaling points available within the wet range) the scaled-predictive method does provide a means to improve model predictions and reduce the number of parameters that need to be estimated. If data are unavailable within the wet range scaling should be applied to the soil profile below the upper soil layer.
|
ACKNOWLEDGMENTS
|
|---|
The authors acknowledge the support of the U.S. Nuclear Regulatory Commission, Washington, DC., under contract NRC-04-97-056. Thomas J. Nicholson is Project Manager.
|
REFERENCES
|
|---|
- Butters, G.L., and P. Duchateau. 2002. Continuous flow method for rapid measurement of soil hydraulic properties; I. Experimental considerations. Vadose Zone J. 1:239–251.[Abstract/Free Full Text]
- Corell, S.W., and E.F. Corkhill. 1994. A regional groundwater flow model of the salt river valley. Phase II, Phoenix active management area, numerical model, calibration, and recommendation. Model Rep. 08. Arizona Dep. of Water Resources, Phoenix.
- Fleming, J. 2001. Applications of the inverse approach for estimating unsaturated hydraulic parameters from laboratory flow experiments. Ph.D. Thesis, The Univ. of Arizona, Tucson.
- Graham, A. 2004. In situ characterization of unsaturated soil hydraulic properties at the Maricopa Environmental Monitoring Site. M.S. thesis. The Univ. of Arizona, Tucson.
- Luckner, L., M.T. van Genuchten, and D.R. Nielsen. 1989. A consistent set of parametric models for the two-phase flow of immiscible fluids in the subsurface. Water Resour. Res. 25: 2187–2193.
- Mace, A., D.L. Rudolph, and R.G. Kachanoski. 1998. Suitability of parametric models to describe the hydraulic properties of an unsaturated coarse sand and gravel. Ground Water 36:465–475.[CrossRef][ISI]
- Miller, E.E., and R.D. Miller. 1956. Physical theory for capillary flow phenomena. J. Appl. Phys. 27:324–332.[CrossRef][ISI]
- Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12:513–522.[CrossRef]
- Schaap, M.G., F.J. Leij, and M.T. van Genuchten. 2001. Rosetta: A computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions. J. Hydrol. 251:163–176.[CrossRef]
- Simunek, J., M. Sejna, and M.T. van Genuchten. 1998. The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably-saturated media. Version 2.0. U.S. Salinity Lab., USDA, ARS, Riverside, CA.
- Thompson, T.L., T.A. Doerge, and R.E. Godin. 2000. Nitrogen and water interactions in subsurface drip-irrigated cauliflower: I. Plant response. Soil Sci. Soc. Am. J. 64:406–411.[Abstract/Free Full Text]
- van Genuchten, M.T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892–898.[ISI]
- Yates, S.R., M.T. van Genuchten, A.W. Warrick, and F.J. Leij. 1992. Analysis of measured, predicted, and estimated hydraulic conductivity using the RETC computer program. Soil Sci. Soc. Am. J. 56:347–354.[ISI]
- Young, M.H., P.J. Wierenga, A.W. Warrick, L.L. Hofmann, and S.A. Musil. 1999. Variability of wetting front velocities during a field-scale infiltration experiment. Water Resour. Res. 35:3079–3087.[CrossRef]
TOP
ABSTRACT
INTRODUCTION
