Published online 1 February 2008
Published in Vadose Zone J 7:87-96 (2008)
DOI: 10.2136/vzj2007.0099
© 2008 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH
Performance Evaluation of Models That Describe the Soil Water Retention Curve between Saturation and Oven Dryness
Muhammed Khlosia,*,
Wim M. Cornelisa,
Ahmed Douaikb,
Martinus Th. van Genuchtenc and
Donald Gabrielsa
a Dep. of Soil Management and Soil Care, Coupure Links 653, B-9000 Ghent, Belgium
b Research Unit on Environment and Conservation of Natural Resources, National Institute of Agricultural Research, BP 415, Ave. de la Victoire, 10000 Rabat, Morocco
c USDA, U.S. Salinity Lab., 450 W. Big Springs, Riverside, CA 92507
* Corresponding author (Muhammed.Khlosi{at}UGent.be).
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Received 24 May 2007.
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ABSTRACT
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The objective of this work was to evaluate eight closed-form unimodal analytical expressions that describe the soil-water retention curve across the complete range of soil water contents. To meet this objective, the eight models were compared in terms of their accuracy (RMSE), linearity (coefficient of determination, R2, and adjusted coefficient of determination, R2adj), and prediction potential. The latter was evaluated by correlating the model parameters to basic soil properties. Retention data for 137 undisturbed soils from the Unsaturated Soil Hydraulic Database (UNSODA) were used for the model comparison. The samples showed considerable differences in texture, bulk density, and organic matter content. All functions were found to provide relatively realistic fits and anchored the curve at zero soil water content for the coarse-textured soils. The performance criteria were similar when averaged across all data sets. The criteria were found to be statistically different between the eight models only for the sandy clay loam soil textural class. An analysis of the individual data sets separately showed that the performance criteria were statistically different between the models for 17 data sets belonging to six different textural classes. We found that the Khlosi model with four parameters was the most consistent among different soils. Its prediction potential was also relatively good due to significant correlation between its parameters and basic soil properties.
Abbreviations: OM, organic matter • SSE, sum of squared errors • SWRC, soil water retention curve • UNSODA, Unsaturated Soil Hydraulic Database
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INTRODUCTION
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The unsaturated soil hydraulic properties are key factors governing the partitioning of rainfall and irrigation into soil water storage, evapotranspiration, and deep drainage. The hydraulic properties involve the soil water retention curve (SWRC), which relates the matric potential (
) with the soil water content (
) and the hydraulic conductivity function. Discrete (, ) data sets can be obtained from either laboratory or field measurements, or predicted from other soil properties using pedotransfer functions or other approaches. Both methods yield discontinuous sets of – data pairs within the range of matric potentials used for the measurements. For modeling purposes, a continuous and smooth representation of the SWRC is preferred, which can be obtained by fitting a closed-form analytical expression to a discrete data set. To date, various expressions appear in the literature to represent the SWRC (e.g., Brooks and Corey, 1964; van Genuchten, 1980; Kosugi, 1999). Most of the retention models are successful in the wet part of the SWRC. The dry part of the SWRC, however, is equally important in a number of water-related processes affected by water contents well below the residual value, such as deflation of soil particles by wind (Cornelis et al., 2004), microbial activity and N mineralization in soils (De Neve and Hofman, 2002), CH4 oxidation in soils (De Visscher and Van Cleemput, 2003), and applications in colloid science (Blunt, 2001).
There is, hence, a pressing need to accurately represent the SWRC for all matric potentials. In the last few years and decades, several attempts have been made to represent the complete retention curve (Ross et al., 1991; Campbell and Shiozawa, 1992; Rossi and Nimmo, 1994; Fayer and Simmons, 1995; Morel-Seytoux and Nimmo, 1999; Webb, 2000; Groenevelt and Grant, 2004; Khlosi et al., 2006). All of these models, except the equation of Groenevelt and Grant (2004), were tested on data reported by Campbell and Shiozawa (1992) and Schofield (1935), who measured water contents far below –1500 kPa. All models performed relatively well; however, when testing the Rossi and Nimmo (1994) sum model against data sets in which ranged between –1 and –1500 kPa, Cornelis et al. (2005) found that this model behaved rather poorly compared with the van Genuchten (1980) and Kosugi (1999) models, despite its physically realistic shape. In this study, we therefore compared eight closed-form unimodal analytical expressions to describe the SWRC across the complete range of soil water contents. The comparison includes expressions by Campbell and Shiozawa (1992), Rossi and Nimmo (1994), Fayer and Simmons (1995), Webb (2000), Groenevelt and Grant (2004), and Khlosi et al. (2006), which were tested using a limited number of data pairs (e.g., UNSODA), as is most often the case in practice. Three statistical criteria were considered to define the best models: accuracy (RMSE), linearity (R2 and R2adj), and prediction potential (the correlation between model parameters and basic soil properties).
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Available Soil Water Retention Models
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A large number of functions have been proposed over the years to describe the SWRC across the complete range of soil water contents. Some of these functions are new, while others are extensions of existing models. The extended functions are mostly modifications of the popularly used models by Brooks and Corey (1964), van Genuchten (1980), and Kosugi (1999). These functions, which will be referred to in this study as the BC, VG, and KLN models, respectively, are given by
 | [1] |
 | [2] |
 | [3] |
respectively, where s is the saturated soil water content; r is the residual soil water content; b is the air-entry matric potential; md is the matric potential corresponding to the median pore radius; 
, 
, and n are curve-fitting parameters related to the pore-size distribution; 
is a dimensionless parameter to characterize the width of the pore-size distribution; and erfc denotes the complementary error function.
Unfortunately, Eq. [1], [2], and [3] have considerable difficulty in representing the retention of water as the degree of saturation approaches zero, often giving an unrealistic path of the retention curve. To overcome this problem, various improvements have appeared in the literature. A first attempt to cover the complete retention curve was made by Ross et al. (1991). They modified Campbell's (1974) equation, which is identical to the power function of the BC model with the residual water content taken as zero, to extend the SWRC to oven dryness. Campbell and Shiozawa (1992) and Schofield (1935) measured water contents of soils ranging from sand to silty clay at matric potentials far below = –1500 kPa. Inspection of their data suggests a log-linear relationship between the matric potential and the water content for matric potentials less than approximately –30 and –1000 kPa for sand and silt loam, respectively (the limiting values in their data set). Their silty clay soil showed an intermediate value. Based on these observations, Campbell and Shiozawa (1992) expressed the (, ) relationship in the low potential range as
 | [4] |
or simply as
 | [5] |
where a is a curve-fitting parameter representing the soil water content at = –1 m and o is the matric potential at oven dryness. Note that Campbell and Shiozawa (1992) expressed their matric potentials in units of meters and consequently a in their equations corresponds to the soil water content at –10 kPa or –1 m with a ln|a| value equal to zero. The value of o depends on the temperature, pressure, and humidity at which the soil is dried. Assuming a logarithmic behavior in the very dry range of the SWRC is consistent with the adsorption theory of Bradley (1936), which considers adsorbed molecules to build up in a layered film in which the net force of electrical attraction diminishes with increasing distance from the soil particle (Rossi and Nimmo, 1994). Incorporating Eq. [5] in a VG-type model, Campbell and Shiozawa (1992) described the SWRC from saturation to oven dryness as
 | [6] |
where A and m are curve-fitting parameters.
Rossi and Nimmo (1994) created a four-parameter sum model (RN1 model) and a three-parameter junction model (RN2 model) to represent the SWRC across the entire range from saturation to oven dryness. Both models are based on the Campbell (1974) model, with the residual water content taken as zero. Their four-parameter sum model (RN1), which consists of two functions joined at one point, was written as
 | [7] |
where i is the soil matric potential at the junction point where the two curves join, and β and 
are shape parameters. The term I represents the Hutson and Cass (1987) parabolic curve that joints the Campbell function (1974) at the junction point i. The Ross et al. (1991) correction is included in the expression for II. Further, using data sets from Schofield (1935) and Campbell and Shiozawa (1992), Rossi and Nimmo (1994) showed that at very low soil water content, the latter becomes proportional to the logarithm of the soil matric potential, as can be recognized as well in II. Equation [7] contains seven parameters; however, two of them can be determined from conditions that ensure continuity of both Eq. [7] and its first derivative with respect to i. Here we have chosen to explicitly determine β and as analytical functions of b, i, o, and (Cornelis et al., 2005):
 | [8] |
 | [9] |
By setting o arbitrarily at –106 kPa (Ross et al., 1991; Rossi and Nimmo, 1994) and using Eq. [8] and [9], the number of model parameters can be reduced to four.
The three-parameter junction model of Rossi and Nimmo (1994) (RN2 model) consists of three functions, which are continuous at the two points where the functions are joined:
 | [10] |
where i and j are the soil matric potentials at the two junction points, and β' and ' are shape parameters. To describe the shape of the SWRC near saturation, Rossi and Nimmo combined the parabolic equation proposed by Hutson and Cass (1987) with the BC model (as described by II). The equation for II is a power law for smaller than the air-entry value b. The simple power law overestimates the water content at very low matric potentials. For this reason, a third part, III, as proposed by Ross et al. (1991), was added to obtain a water content of zero at o. In this case, there are six parameters other than s, as well as four conditions by imposing continuity of the global function and its first derivative at the two junction points. Four parameters (β', i, j, and ') can be calculated from analytical functions of the remaining two fitted parameters, b and :
 | [11] |
 | [12] |
 | [13] |
 | [14] |
The three free parameters of the RN2 model are then s, b, and . Rossi and Nimmo (1994) obtained better accuracy with their four-parameter sum model, however, than with their three-parameter junction model.
Fayer and Simmons (1995) further modified the Brooks–Corey and van Genuchten functions by replacing the residual water content with the adsorption equation of Campbell and Shiozawa (1992) to obtain
 | [15] |
 | [16] |
where a is a curve-fitting parameter representing the soil water content at = –1 kPa, and o is the matric potential at oven dryness. Equations [15] and [16] are denoted here as FS1 and FS2, respectively.
Morel-Seytoux and Nimmo (1999) extended the BC model to oven dryness using the three-parameter junction model (RN2). They divided the matric potential values into three levels: a low-potential level (from oven dryness to near field capacity), a middle level (field capacity to about air-entry matric potential), and a high level (air-entry matric potential to zero suction). For the low-potential level, a slightly modified form of the RN2 model (III) was selected. For the high-potential level, the following algebraic relation was adopted:
 | [17] |
where Se is effective saturation, Se = ( – r)/( s – r), Sem is effective saturation at the matching point, m is the corresponding matric potential, M = 1/, and aMS is defined as
 | [18] |
In this case, there are certain conditions of continuity and smoothness to be satisfied to reattach Eq. [17] with the traditional BC model for the middle potential range.
Webb (2000) proposed a new approach (W model) to combine the VG model with a dry-region expression. This model does not necessitate refitting of experimental data and consists of two regions. Region 1 is an adsorption region described with a linear function on a semilog plot of log() vs. soil water content (). Region 2 is a capillary-flow region described with the VG model (or any other desired function) in which any previous fitting parameter is retained. The linear relation between and on a semilog plot for the dry region was expressed by Webb (2000) as
 | [19] |
where
 | [20] |
m and m are, respectively, the matric potential and water content at the matching point, and µ is the slope of Eq. [19]. Different steps are required for determining the water content at matching point m. First, we rewrite Eq. [19] as
 | [21] |
Second, the VG model is formulated in terms of and its slope is calculated. Third, the slope of the VG model is combined with Eq. [21] to give the intercept at o as
 | [22] |
where
 | [23] |
Finally, the value of m is determined from Eq. [22] by iteration. Since the value of o in Eq. [22] should equal –106 kPa, one can give an initial estimate of m and adjust this estimate until the proper value of o is obtained.
Recently, a new three-parameter model for the SWRC was developed by Groenevelt and Grant (2004) (GG model). This model anchors the curve at zero soil water content using the logarithmic scale in a model for which the pF, defined as log(–), with expressed in units of centimeters (Schofield, 1935), is the independent variable. They found the equation for the model to be capable of fitting pF curves with remarkable success across the complete range from saturation to oven dryness. The soil water content hence would be a function of pF as
 | [24] |
where k0, k1, and 
are the three dimensionless parameters and 6.9 is the pF value at oven dryness according to the Schofield equation (Schofield, 1935).
Some of the functions described above utilize existing fitted curves. The Fayer and Simmons (1995) approach uses existing fitted curves to estimate the parameters in their modified SWRC expressions. Morel-Seytoux and Nimmo (1999) linked up existing SWRCs with a dry-region expression such that existing fitted curves can be directly used. To utilize other existing fitted curves, Khlosi et al. (2006) used the adsorption equation of Campbell and Shiozawa (1992) to modify the Kosugi (1999) model. The new expression (KCGS model) hence combines the adsorption equation of the CS model with the KLN model as
 | [25] |
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Materials and Methods
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Sources of Soil Water Retention Curve Data
Soil water retention curve measurements for a selected set of undisturbed soils from different parts of the world for various soil types were used in this study. The set consisted of 137 undisturbed soils selected from the UNSODA database (Nemes et al., 2001). The 137 soils were selected using the following criteria: (i) SWRC data were available from at least near saturation to, when possible, near oven dryness (some of the soils had measurements at matric potentials far below = –1500 kPa), (ii) nearly all soil texture classes were represented (Fig. 1
), and (iii) their basic soil properties were known (notably clay, silt, sand, and organic matter content and bulk density). The organic matter content ranged from 0.7 to 214.0 g kg–1, while bulk densities varied from 0.59 to 1.76 Mg m–3 (Fig. 2
).
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FIG. 1. Textural distribution of 137 soils from the UNSODA database (Nemes et al., 2001) used in model development: sandy (sand and loamy sand), loamy (sandy loam, loam, silt loam, and silt), and clayey (sandy clay loam, silty clay loam, clay loam, sandy clay, silty clay, and clay) soils.
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Models for the Data Fit
From available SWRC models, we selected eight models: those proposed by Campbell and Shiozawa (1992), Rossi and Nimmo (1994) (RN1 and RN2 models), Fayer and Simmons (1995) (FS1 and FS2), Webb (2000), Groenevelt and Grant (2004), and Khlosi et al. (2006).
The parameters of the chosen models were obtained by nonlinear least-squares fitting of the models to the observed SWRCs. We used, for this purpose, a quasi-Newton algorithm (Press et al., 1992), which is an iterative method starting with some initial estimates of the parameters. The approach is based on partitioning of the total sum of squares of the observed values into a part described by the fitted model and a residual part of observed values around those predicted with the model. The goal of the curve-fitting process is to find an equation that maximizes the sum of squares associated with the model while minimizing the residual sum of squares or sum of squared errors (SSE). The latter reflects the degree of bias and a contribution of random errors, conventionally expressed as
 | [26] |
where b is a parameter vector containing the p unknowns that need to be estimated; j = 1, 2, ..., N; N is the number of soil-water retention data for each soil sample (ranging between 5 and 27), j is the soil water content corresponding to the jth data pair for each soil, and "obs" and "fit" denote measured and fitted values, respectively.
The quasi-Newton routine was performed using the mathematical software program MathCad (PTC Corp., Needham, MA). Initial estimates for the model parameters in the iterative procedure were selected using reported literature values for the different soils, if available. When not available, we routinely reran the program with different initial parameter estimates to prevent convergence to local minima in the objective function. To avoid unrealistically large positive (or even negative) values for a, r, , and b in the CS, RN1, FS1, FS2, W, and KCGS models, we constrained their parameters to > 0 for the CS model, b > i for the RN1 model, r 
0 for the W model, and a by the range of values found for the same texture class for the CS, FS2, and KCGS models.
Comparison Methods
Goodness-of-Fit Statistics
Various statistical measures can be used to compare the fitting accuracy of the SWRC models. In this study, we used as measures the RMSE, the coefficient of determination (R2), and the adjusted coefficient of determination (R2adj), which were calculated for each soil sample. The mean square error (MSE) and RMSE were derived from the SSE using
 | [27] |
 | [28] |
respectively. The RMSE (m3 m–3) is an indication of the overall error of the evaluated function and should approach zero for the best model performance. The value of R2 reflects the proportion of the total sum of squares (SST) that is partitioned into the model sum of squares (SSM) since SST is equal to SSM plus SSE:
 | [29] |
An R2 value that approaches unity means that the model explains most of the variability in the observed data, meaning that SSE is very small compared with SSM.
An additional measure of fit is the R2adj (Neter et al., 1996), which is designed to take into account the number of parameters in the model. The R2adj better reflects how the degree of correlation between observed and fitted data will change as additional parameters are added to or deleted from the model. The R2adj is defined by
 | [30] |
where p is the number of model parameters. The R2adj statistic can take on any value 
1, with a value closer to 1 indicating a better fit.
In general, a model with more parameters can fit the observational data better. Although R2adj is generally one of the best indicators of the quality of the fit when adding additional parameters to the SWRC model, overparameterization should be avoided since it results in a nonidentifiable model (i.e., a model leading to sample configuration probabilities identical to those of a simpler model with fewer parameters), in large variances of the estimated model parameters for similar soils, or in a high degree of correlation between the parameters (or low parameter uniqueness) if the number of observations is limited, as is often the case with laboratory-determined SWRCs (Cornelis et al., 2005). Moreover, it is advantageous to minimize the number of model parameters when attempting to predict the SWRC from readily available data using pedotransfer functions.
To check if the R2, R2adj, and RMSE of the eight models are similar or different, a statistical test of significance is needed. Regarding the coefficients of determination or, equivalently, their corresponding coefficients of correlation, the initial hypothesis is that all eight correlation coefficients are equal (Steel and Torrie, 1980):
 | [31] |
with r being either R or Radj, and 1 to 8 referring to the eight models. The first step is then to transform the correlation coefficients into a new variable z such that:
 | [32] |
with loge being the natural logarithm. Since we have the same number of data for the eight models for a given data set, the variable 
2obs is next calculated as
 | [33] |
where 
is the arithmetic mean of zi. This variable is subsequently compared with a theoretical value (2theor) at the 95% confidence level having (p – 1) degrees of freedom. Hypothesis [31] is rejected, meaning that the eight correlation coefficients and thus the coefficients of determination are statistically different, when
 | [34] |
For RMSE, the test of significance is possible for variances. For this purpose, we first square RMSE to calculate MSE, which represents variances. The hypothesis for homogeneity of variances, also called homoscedasticity (Hartley, 1950), is then
 | [35] |
where 2 is the MSEs, with 1 to 8 referring to the eight models. The Hartley test is now applied by first computing the observed value:
 | [36] |
in which 2max and 2min are, respectively, the maximum and minimum values among the eight MSEs. This observed value is compared with a theoretical one (Htheor) at the 95% confidence level with p and (N – 1) degrees of freedom. Hypothesis [35] is rejected, meaning that the eight MSEs and thus the RMSEs are statistically different, when
 | [37] |
To conveniently compare the goodness of fit of the eight models, RMSE, R2, and R2adj were calculated separately for each model and for each data set. Next, we calculated the mean values of these performance criteria for each of the 11 soil textural classes, as well as the mean values for the whole data sets for the same performance criteria.
Comparing Models Parameters with Basic Soil Properties
To provide further insight, the rsp, the Pearson coefficient of correlation between the model parameters and several basic soil properties, was computed for each soil sample. Mean values were calculated also for each model. The soil properties considered here were bulk density, 
b, organic matter content (OM), and sand, silt, and clay content. The Pearson coefficient of correlation was used as a measure for the prediction potential of a model in that the closer rsp is to either 1 or –1, the higher the prediction potential of the parameters in the model. High correlations between model parameters and basic soil properties are useful keys in developing reliable pedotransfer functions for the model parameters. The statistical significance of the correlation coefficients was tested using the same procedure as for R2 and R2adj (Eq. [31–34]). Results are reported only for the mean correlation coefficients for the whole data sets.
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Results and Discussion
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Evaluation of the Models
Parameter values for the different models and for different soil textural classes (Table 1
) were obtained by curve fitting the models to the entire data set for each soil textural class. These values can serve as useful initial estimates when attempting to use one of the evaluated expressions.
Table 2
contains results of the statistical measures computed for each expression to compare their goodness of fit at three levels: each separate data set (137 values for each statistical measure), each soil textural class (11 values), and all of the data sets combined (one value). Based on the mean value of the three performance criteria over all data sets, Table 2 (last column) and Fig. 3
show that the mean RMSE values varied between 0.0105 and 0.0161. The statistical analysis shows that the eight models do not differ between each other regarding their RMSEs. The same table and figure also show that relatively high values were found for the mean R2 (>0.97) and mean R2adj (>0.96) for all models, thus indicating that all equations can be considered valid. Indeed, the test of significance for both R2 and R2adj further suggests that the eight models do not differ. A more detailed analysis was done by considering each textural class separately (Table 2). The test of significance shows that the eight models differ in terms of RMSE only for the silty clay loam but not for the remaining 10 textural classes.
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FIG. 3. Boxplots of (a) RMSE, (b) R2, and (c) adjusted R2 (R2adj) values for different soil-water retention curve models: Campbell and Shiozawa (CS); Rossi and Nimmo four-parameter sum (RN1); Rossi and Nimmo three-parameter junction (RN2); Fayer and Simmons modified Brooks–Corey (FS1); Fayer and Simmons modified van Genuchten (FD2); Webb (W); Groenevelt and Grant (GG); and Khlosi et al. (KCGS). The box plots summarize the distribution of RMSE, R2, and R2adj. The horizontal full line in each box signifies the median value and the mean in a dotted line, whereas the bottom and top of the box represent the 25th and 75th percentile. The whiskers display the 10th and 90th percentile, while the points indicate the outliers.
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Regarding R2 and R2adj, the eight models differ statistically for the class sandy clay loam, while they can be considered to give similar results for the 10 remaining textural classes. Because of the differences in results between all data sets combined and those from each textural class, we further analyzed our data by considering each data set separately and focusing mainly on R2adj. The results show that for 17 out of the 137 data sets, the eight models were statistically different, while they gave similar R2adj values for the remaining 120 data sets classified as silty clay loam (one data set), silty clay (two data sets), silt (three data sets), loamy sand (11 data sets), and clay loam (five data sets). The 17 data sets were classified as sand (three data sets out of 18), sandy loam (one out of 19), silty loam (two out of 41), loam (five out of 23), sandy clay loam (three out of four), and clay (three out of 10). These results reflect the fact that mean values sometimes will not reveal differences when individual data sets are used. To further examine the goodness of fit of the various models, we plotted the distributions of RMSE, R2, and R2adj for all soil samples in Fig. 3. Each boxplot shows the median (solid line), mean (dotted line), the 25 and 75% percentiles (top and bottom of the box), the 10 and 90% percentiles (whiskers), and the outliers (circles). Notice that the fitting errors for the FS2, W, and KCGS models were smaller than those for the other models. This is because of the better representation of these models for all soil samples. Results suggest that the KCGS model is the most suitable for describing the observed data.
Table 3
lists the Pearson correlation coefficients, rsp, between all parameters and the basic soil properties. The KCGS and FS2 models produced the highest correlation values for r (or a) with b and clay content, while most models showed high correlation of s with b and clay content. Notice that s was highly correlated to b and to a lesser extent to clay content while the opposite was true for a. The other parameters, which mostly affect the shape of the SWRC, showed much lower correlations except for the KCGS, W, FS1, RN2, and GG models. This was to be expected for the RN2 and GG models, since RN2 does not contain r (or a) while GG does not have r (or a) and s. Relatively high values were also obtained for the FS1 and W models. The KCGS model showed high correlations for its additional parameters as well as for a and s. Other models such as CS, RN1, and FS2 showed good correlation with at least one additional parameter.
These results indicate that the KCGS model performed best. This model performed as good as the other models in terms of the goodness of fit, and showed significant correlation between all of its parameters and the basic soil properties. Compared with the KCGS model, CS expression exhibited two main disadvantages. One is that the correlation between model parameters and basic soil properties was far less than that of the KCGS model for all parameters. A second disadvantage is related to the fact that the boxplot of the RMSE, R2, and R2adj values showed many outliers for CS compared with KCGS. This suggests that CS is less consistent when applied to different soils. The FS2 model, which showed the same fitting performance as the KCGS and CS models, did not represent the dry range well without having (, ) data below a matric potential of –100 kPa (Khlosi et al., 2006). Although the W model does not necessitate the refitting of observed data, this model does not require many iterations to find the matching point.
Performance of the Models
The performance of the eight closed-form analytical expressions is further demonstrated below by fitting them to soil-water retention data of a relatively coarse-textured soil (loamy sand, b = 1.68 g m–3, OM = 3 g kg–1), a medium-textured soil (silt loam, b = 1.51 g m–3, OM = 5 g kg–1), and a fine-textured soil (clay, b = 1.47 g m–3, OM = 6 g kg–1). Figure 4
indicates that all models performed very well for the loamy sand in that they produced comparatively realistic fits and anchored the curves at zero soil water content. We can notice that the KCGS model still showed the best fit for all matric potentials. The correspondence between observed and fitted SWRCs for the silt loam exhibited deviations for the RN1, RN2, FS1, W, and GG models. The RN1 and RN2 models showed a poor match near saturation. This is because both models use the Hutson and Cass (1987) expression at high matric potentials, which is less flexible because of its parabolic shape. The RN1 and RN2 models further performed rather poorly in the dry range since these functions require many data points to provide a smooth match at the junction points. The FS1 model mostly missed the shape of the data near saturation due to its discontinuous character, which is an inherent feature of the original BC model. Figure 4 additionally shows that the GG model did not accurately match several points near saturation, not unlike some of the other models. This can be attributed to the discontinuity at = 1 cm (pF = 0), which decreases the flexibility of the curve in that region. By contrast, the CS, FS2, W, and KCGS models showed very good fits to the silt loam data, although CS seems to have a less realistic shape (linear) in the wet region. Slightly different results were obtained for the clay soil. The RN1 and RN2 models here again showed poor fits, as explained above. By keeping the oven-dryness pressure (o) as a free parameter, one can improve their fits but with the possibility of producing oven-dryness values lower than –106 in fine-textured soils. The GG model now showed a better match to the data, because it is more flexible when fewer data are presented near saturation. For the same reason, the discontinuous character of the FS1 model did not seem to be problematic for the clay soil. On the other hand, the CS model showed a biased curve since s was not considered here. The FS2, W, and KCGS models showed excellent fits also for the clay example.
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FIG. 4. Observed and fitted soil-water retention curves (SWRCs) for a loamy sand (LS), a silt loam (SiL), and a clay (C). Models are: Campbell and Shiozawa (CS); Rossi and Nimmo four-parameter sum (RN1); Rossi and Nimmo three-parameter junction (RN2); Fayer and Simmons modified Brooks–Corey (FS1); Fayer and Simmons modified van Genuchten (FD2); Webb (W); Groenevelt and Grant (GG); Khlosi et al. (KCGS); and van Genuchten (VG). The curve in the case of the GG model is only defined for potential values lower than –0.1 kPa (or –1 cm).
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Conclusions
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Using 137 soil samples from the UNSODA database, we compared eight closed-form unimodal analytical expressions for the soil-water retention curve. The expressions were evaluated in terms of their goodness of fit using different statistical indices. All eight models defined the soil water content vs. soil matric potential relationship below the residual water content. The performance of the models in terms of matching the data varied greatly depending on the degree of aggregation or desegregation of the data: individual SWRC data sets, averages of individual soil textural classes, or the overall mean. Our results show that lumping of the data without considering their textural class provided similar results for the eight models in terms of their ability to fit observed data. When the textural class was taken into account, however, the eight models were found to perform differently for the sandy clay loam class, while being not statistically different for the remaining 10 textural classes. An analysis for each data set separately showed that the eight models behaved differently for 17 of the individual 137 data sets, representing six different textural classes. The Khlosi et al. (2006) model with four parameters was found to be the most consistent for the different soils. Moreover, its prediction potential was relatively good because of significant correlation between its parameters and basic soil properties. Hence, we recommend this analytical formula for reliable modeling of the whole range of soil water contents of unsaturated soils, which can vary substantially in bulk density, soil texture, and organic matter content.
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S. Lu, T. Ren, Y. Gong, and R. Horton
Evaluation of Three Models that Describe Soil Water Retention Curves from Saturation to Oven Dryness
Soil Sci. Soc. Am. J.,
September 30, 2008;
72(6):
1542 - 1546.
[Abstract]
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