Published November 22, 2019

Original ResearchCore Ideas• Soil-specific pedotransfer functions can be incorporated into the
HYDRUS model.
• Electrolyte concentration reduces
the adverse effect of pH and Na on
soil structural stability.
• Clay content is important in governing soil hydraulic reduction
dynamics due to pH.

A. Ali, A.J.W. Biggs, J. Šimůnek, and J.McL.
Bennett, Univ. of Southern Queensland,
Centre for Sustainable Agricultural Systems,
West St, Toowoomba, QLD 4350, Australia; A.J.W. Biggs, Dep. of Natural Resources,
Mines and Energy, Tor St, Toowoomba, QLD
4350, Australia; J. Šimůnek, Dep. of Environmental Sciences, Univ. of California,
Riverside, CA 92521. *Corresponding author(aram.ali@usq.edu.au).
Received 7 July 2019.
Accepted 28 Oct. 2019.
Citation: Ali, A., A.J.W Biggs, J. Šimůnek, andJ.M. Bennett. 2019. A pH-based pedotransfer function for scaling saturated hydraulicconductivity reduction: Improved estimationof hydraulic dynamics in HYDRUS. Vadose
Zone J. 18:190072. doi:10.2136/vzj2019.07.0072© 2019 The Author(s). This is an open access article
distributed under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-ncnd/4.0/).

A pH-Based Pedotransfer Function for
Scaling Saturated Hydraulic Conductivity
Reduction: Improved Estimation of
Hydraulic Dynamics in HYDRUS
Aram Ali,* Andrew J.W. Biggs, Jirka Šimůnek,and John McL. Bennett
Hydraulic conductivity is a key soil property governing agricultural production
and is thus an important parameter in hydrologic modeling. The pH scaling factor for saturated hydraulic conductivity (Ks) reduction in the HYDRUS model was
reviewed and evaluated for its ability to simulate Ks reduction. A limitation of themodel is the generalization of Ks reduction at various levels of electrolyte concentration for different soil types, i.e., it is not soil specific. In this study, a newgeneralized linear regression model was developed to estimate Ks reduction fora larger set of Australian soils compared with three American soils. A nonlinear
pedotransfer function was also produced, using the Levenberg–Marquardt optimization algorithm, by considering the pH and electrolyte concentration of theapplied solution as well as the soil clay content. This approach improved the estimation of the pH scaling factor relating to Ks reduction for individual soils. The
functions were based on Ks reduction in nine contrasting Australian soils using two
sets of treatment solutions with Na adsorption ratios of 20 and 40; total electrolyte
concentrations of 8, 15, 25, 50, 100, 250, and 500 mmolc L−1; and pH values of 6, 7,
8, and 9. A comparison of the experimental data and model outputs indicates thatthe models performed objectively well and successfully described the Ks reduction due to the pH. Further, a nonlinear function provided greater accuracy than
the generalized function for the individual soils of Australia and California. This
indicates that the nonlinear model provides an improved estimation of the pH
scaling factor for Ks reduction in specific soils in the HYDRUS model and should
therefore be considered in future HYDRUS developments and applications.
Abbreviations: EC, electrolyte concentration; SAR, sodium adsorption ratio.

Soil hydraulic conductivity is a critically important soil physical property usedin determining water and solute transport, infiltration rate, groundwater recharge, andother agricultural and hydrological processes (Ben-Hur et al., 2009; Smith et al., 1995).
Soil hydraulic conductivity is strongly dependent on soil structural status and stability andthe geometry of pore spaces in the soil (Assouline and Narkis, 2011). The use of marginal
quality irrigation water is likely to cause deterioration in the soil structure; a change inthe ratio of solids, water, and air within the soil; and reduced hydraulic conductivity due
to clay disaggregation and dispersion processes (Bennett et al., 2019; Quirk and Schofield,
1955; Rengasamy and Olsson, 1991). A reduction in hydraulic conductivity often occurs
as a result of excess Na within the soil solution (measured as the sodium adsorption ratio,
SAR), which can result in both intra- and inter-crystalline swelling, leading to clay dispersion (Dang et al., 2018b; Ezlit et al., 2013). The magnitude of the reduction in hydraulicconductivity depends on the electrolyte concentration (EC) in the soil solution (Quirk and
Schofield, 1955; Shainberg and Letey, 1984). Furthermore, Suarez et al. (1984) showedthat the pH of the solute percolating a soil, in combination with high SAR and low EC,
was likely to lead to decreased hydraulic conductivity beyond the combined SAR andEC effect alone. The effects of pH, EC, and SAR of an applied solution on soil hydraulicconductivity have been broadly investigated, experimentally and mathematically, using

Vadose Zone Journal | Advancing Critical Zone Sciencepredictive models (Chorom et al., 1994; Ezlit et al., 2013; McNeal
and Coleman, 1966; Suarez and Rubio, 2010).
Predictive models have become efficient tools to investigate
water flow and solute movement in soils under irrigation. The
performance of multiple simulations considering various equilibrium and kinetic nonequilibrium chemical reactions between
major ions allows industry and research to quickly interrogate
the dynamics of systems. However, the development of models
for the prediction of soil structural degradation and hydraulicconductivity dynamics will only be as good as the functions andassumptions that underlie them. Saturated hydraulic conductivity reduction remains a challenging task due to the combined
effects of sodicity, salinity, pH, and alkalinity within the context
of the soil being an inherently heterogeneous and complex material that is non-rigid (Campbell and Paustian, 2015; Miller andWhite, 1998). Therefore, the effect of a given solution chemistry
can lead to unique soil structural dynamics within soils of different origin (Bennett et al., 2019; Bennett and Warren, 2015;
Menezes et al., 2014; Quirk and Schofield, 1955), soil clay content and mineral suite (Bell, 1996; Goldberg and Glaubig, 1987),
soil organic matter (Oades, 1984), the pH of soil solution (Bolanet al., 1996; Suarez et al., 1984), and the ionicity of the soil aggregate system (Bennett et al., 2019; Marchuk and Rengasamy, 2012;
Zhu et al., 2019). Moreover, the magnitudes and the interrelationship of these factors provide variable levels of resilience ofsoils to structural degradation for a given intervention. Therefore,soil hydraulic dynamics should not be expected to be simply predicted with a generalized model.
The HYDRUS model is perhaps the most widely utilized
soil hydraulic model (Šimůnek et al., 2016). The empirical andsemiempirical equations for the adverse effects of SAR, EC, andpH of solutions are described within the HYDRUS program
manual (Šimůnek et al., 2013). McNeal (1968) used a semiempirical equation based on the experimental clay swelling function
for montmorillonite clay treated with combined sodic and saline
solutions to fit experimental curves related to the relative saturated hydraulic conductivity (Ks). The effect of solution pH on
the Ks is derived from Suarez et al. (1984), whereby the change in
Ks is characterized by a negative effect of pH on the soil hydraulicconductivity, independent of EC and SAR, which is explained byan additional scaling factor. Suarez et al. (1984) investigated theeffects of pH on the Ks of three soils from California for a combination of solution SAR and EC concentrations; i.e., pH cannot bethought of as completely independent of the SAR and EC, as this is
not physically possible. The results of the Suarez et al. (1984) study,
using a narrow range of soils, have become the main dataset forthe prediction of Ks reduction due to the pH of the applied solution. Furthermore, this dataset was subsequently used to produce a
linear function (see Eq. [4] below) to simulate rKs reduction due to
pH in the UNSATCHEM and HYDRUS mathematical modelsof Suarez and Šimůnek (1997) and Šimůnek and Suarez (1997).
The use of this reduction model is likely to provide less accurate prediction of Ks for different soils (Šimůnek and Suarez, 1997)

VZJ | Advancing Critical Zone Sciencebut to some extent helps to identify the degree of Ks reduction due
to the pH of applied solutions. Therefore, there is a global need to
optimize and validate the model parameters for pH-induced Ks
reduction within the HYDRUS model and more broadly for use asa pedotransfer function. However, the approaches to validate andcalibrate the models vary depending on the complexity involvedin parameterizing of the models. Šimůnek et al. (2012) indicatedthat model calibration and inverse parameter estimation can be
performed using a relatively simple, gradient based, local optimization approach based on the Marquardt–Levenberg method,which is directly implemented into the HYDRUS codes; it is also
important that the estimated model is both efficient and robust.
This study reviewed the HYDRUS model for Ks reduction due tothe pH of the applied solution and developed modifications to thecurrent reduction model and its parameters. This was achieved by
combining Levenberg–Marquardt nonlinear parameter optimization involving the EC and pH of the applied solution, as well as
the soil clay content, to improve the accuracy of the modeled soluteand water movement on a soil-specific basis.

66Theoretical Background
Within HYDRUS, the reduction of the hydraulic conductivity K is calculated by multiplying a scaling factor r with the initialsaturated hydraulic conductivity Ks and the relative hydraulic conductivity Kr. The scaling factor r is a function of the soil solution
pH, SAR, and EC, and the relative hydraulic conductivity Kr is afunction of the hydraulic pressure head:
K (h, p H, SAR, EC )= r (pH, SAR, EC )K s K r (h )[1]where K is the hydraulic conductivity (cm d−1), h is the pressure
head (cm), pH is the solution pH (−log[H+]), SAR is the sodium
adsorption ratio, EC is the total electrolyte concentration of thesolution (mmolc L−1), and r is a scaling factor (a function of pH,
SAR, and EC). Subsequently, the scaling parameter, r, is divided
into two sub-factors:r (pH, SAR, EC )= r1 (SAR, EC)r2 (pH )[2]where r1 is a function of SAR and EC, providing the disaggregation (inter- and intra-crystalline swelling) and dispersion effects
on the hydraulic conductivity, as described by Quirk and Schofield(1955), Dang et al. (2018b), and Bennett et al. (2019), while r 2
represents the effects of solution pH on the hydraulic conductivity(Suarez et al., 1984). The assumption is that the scaling parameters
r1 and r 2 can be applied for the entire range of pressure heads underunsaturated conditions. Where the values of r1 and r 2 equate to 1.0,
the soil chemistry supports the maximum hydraulic conductivity.
The scaling parameter r1 is based on the clay-swelling modelof McNeal (1968). This describes the reduction of Ks in terms of
the exchangeable sodium percentage (ESP) and electrolyte concentration using a montmorillonite interlayer swelling factor. The
relationship between r1 and the clay-swelling model (x) was calculated by McNeal (1968) and can be written asp. 2 of 13

r1 (SAR, EC)= 1-cx n
1 + cx n[3]

where c and n are empirical parameters for a given soil within a
specified range of soil ESP, and x is the clay-swelling model calculated by McNeal (1968) based on the adjusted ESP and solution
concentration. While beyond the scope of this study, it is noted
here that the McNeal (1968) model was modified by Ezlit et al.
(2013) to function on a soil-specific basis via a semiempirical disaggregation approach. Dang et al. (2018c) validated the specificity
and the disaggregation model for field soils, while Bennett et al.
(2019) demonstrated the magnitude of soil variability, even for thesame soil orders. Therefore, in seeking to improve the soil-water
dynamics of HYDRUS, it is prudent to utilize the semiempiricalapproach of Ezlit et al. (2013) as well as to seek to improve theincorporation of pH effects.
The r 2 scaling factor, for the effect of pH on the hydraulicconductivity, was calculated from the experimental data of Suarez
et al. (1984) after first seeking to correct Ks reduction for theadverse effects of low electrolyte concentration and high exchangeable Na using r1 (Eq. [3])—an attempt to provide the pH effect as
independent of the SAR and EC combined effects. The following equation was developed by Suarez and Šimůnek (1997) andŠimůnek and Suarez (1997) based on the negative effects of thepH of the applied solution from the study of Suarez et al. (1984):

ìï1.0,
for pH £ 6.83
ïï
ï
r2 (pH )= í3.46 - 0.36pH, for 6.83 < pH < 9.3
ïïïïî0.1,for pH ³ 9.3[4]

The upper and lower pH limits are an assumption of nochange in rKs or near-complete reduction for the specified pH
ranges. We will refer to this model as the HYDRUS K–pH-dependent function. Consequently, the final hydraulic conductivity
reduction due to the pH, SAR, and EC of the applied solution is
calculated (Šimůnek and Suarez, 1997) as

K (h, pH, SAR, EC )= r (pH, SAR, EC )K s K r (h )= r1 (SAR, EC)r2 (pH )K s K r (h )[5]Equation [5] assumes that r1 and r 2 have an equivalentweighted effect on the hydraulic reduction of the system, whichallows the pH scaling factor to assert a large amount of control on
the hydraulic system that may not necessarily be warranted.

66Materials and Methods

Soil Selection and Initial Characterization

Nine soils were collected from the 0- to 30-cm depth of soils
located in Queensland and New South Wales states, Australia(Table 1). The selection of these soils was based on their difference in initial pH and alkalinity as the primary selection factor. A
secondary selection factor was the soil clay mineralogy and texture.
The soils were air dried and crushed with sufficient energy to break

VZJ | Advancing Critical Zone Sciencedown the aggregates to pass through a 2-mm sieve; care was taken
to not apply energy greater than that required in order to maintainthe physical bonds of the aggregates <2 mm. Using standard methods from Rayment and Lyons (2011), the electrical conductivity(Method 3A1), pH (Method 4A1), and soluble and exchangeable
cations (Method 15A2) were measured. The alkalinity was determined using a Radiometer Analytical Titrator (TIM845, Titration
Manager). Published methodologies were used to determine thesoil particle size distribution (Gee and Bauder, 1986), clay mineralogy by X-ray diffraction (Jackson, 2005), and organic C (Walkley
and Black, 1934). The soil characteristics are presented in Table 1.

Solution Preparation
The desired levels of pH, EC, and SAR of the experimental
treatment solutions were obtained by mixing NaHCO3, NaCl, and
MgCl2×6H2O chemical compounds. Mixtures of Na and Mg salts
rather than Na and Ca salts were used to prepare the solutions at
each pH to prevent CaCO3 precipitation at high pH and low SAR.
The Mg concentration was calculated based on the soil-specificflocculation power from cation flocculation concentration experiments relative to Ca (Table 1) based on the modified method of
Rengasamy and Oades (1977). The leaching solutions, SAR 20
and 40, were prepared at total electrolyte concentrations of 8, 15,
25, 50, and 100 mmolc L−1 for SAR 20 and 8, 15, 25, 50, 100, 250,
and 500 mmolc L−1 for SAR 40 solutions. Both the SAR 20 and
40 solutions were then prepared at a equilibrated pH values of 6,7, 8, and 9 according to the methodology of Suarez et al. (1984).
The effective SAR (SAReff ) values were calculated based on theeffective flocculation power of Mg:
SAR eff =Na
X Mg 2[6]where X is the effective flocculation power of Mg exhibited for eachsoil (Table 1), and Na and Mg are concentrations (in mmolc L−1).
The desired pH was achieved by adjusting the HCO3−/C1−
ratio and CO2 partial pressure (P CO2) to ±0.05 units of thedesired pH; the pH 9 and 6 solutions were the same exceptthat the pH 9 solutions were equilibrated at atmospheric CO2(PCO2 » 35 Pa) and the pH 6 solution at PCO2 » 97 kPa using
CO2 gas with 99.9% purity. This was consistent with the methodology of Suarez et al. (1984) to allow direct comparison with
their results. This approach was used, rather than the additionof other alkali or acidic compounds, for pH adjustment to avoid
a change in ionic composition and electrolyte concentration ofsolutions. The pH 6 solutions were achieved by continuously
bubbling CO2 gas into the 5.0-L solution container. The pHof the solution was measured in the solution container before
degassing could occur.

Preparation for, and Measurement of,
Saturated Hydraulic Conductivity
An aliquot (300 g) of each soil was carefully packed into
polyvinyl chloride columns (87.5-mm inner diameter)—meshp. 3 of 13† EC, electrolyte concentration; SAR, sodium adsorption ratio; CROSS, cation ratio of soil structural stability; ESP, exchangeable sodium percentage; EDP, exchangeable dispersive percentage; CEC, cation exchange capacity; CFC of (Mg), the equivalent effectiveness of the flocculation power of Mg relative to Ca.

26°51¢19.3² S,
152°59¢23.46² E
Beerwah, QLD
25°21¢36² S,
27°35¢44.9² S,
152°44¢40.44² E
152°18¢20.1² E
Maryborough, QLD Gatton, QLD
27°13¢48² S,
151°19¢12² E
Dalby, QLD
Location in Australia

28°58¢29² S,
150°26¢38² E
Wariven, NSW

28°54¢50.48² S,
150°16¢18.6² E
Eldorado, NSW

27°49¢50² S,
150°9¢13.9² E
Moonie, QLD

27°48¢32.8² S,
27°58¢8.4² S,
151°54¢22.2² E
148°22¢51.6² E
Greenmount, QLD St. George, QLD

Gray Chromosol

Alfisol
Alfisol

Yellow Chromosol
Gray Kurosol

Ultisol
Inceptisol

Red Kandosol
Brown Vertosol

Vertisol

Black Vertosol

Vertisol

Gray Vertosol

Vertisol

Red Dermosol
Brown Dermosol

Inceptisol

Australian

USDA

Taxonomic class

Inceptisol

85.8

4.8
10.0

80.0
62.5

22.5
5.0

82.5

13.8

56.0

15.8

21.9

6.3

47.5

16.3
12.8

58.5

Silt, %

Sand, %

50.0

9.5

0.66
0.71

10.0
15.0

0.62
0.49

12.5

0.58

30.3

0.73

62.3

0.73

46.3

0.71

33.8

0.63

28.8

CFC of (Mg)

60.0
18.0
NO3 –N, mg L−1

60.0
174.0
Cl−, mg kg−1

Clay, %

10.0

0.1
0.6

10.0
33.0

1.0
0.7
17.0
1200.0

20.0
30.0
120.0
8.0

0.1

1.3

58
18

1.6
1.5

20

1.6

1.6

469

1.3
1.6
1.1

0.6

154
139

306

647

76

9.2
10
5.2
2

CEC, mmolc kg−1
Organic C, mg kg−1

12.5
4.4
EDP, %

11

1.6

2.3

8.2

2.0
2.5

7.7
3.2

1.2
0.5

0.6

0.3

0.4

3.5

0.2

6.7
4.6

11.68

2.5

3.0

CROSS (mmolc L−1)−0.5

ESP, %

9.9

7.0

1.8
1.9

15.7

0.2
3.1

0.9

0.0

0.1

89.3
75.0

6.0
1.9
SAR, (mmolc L−1)−0.5

4.3

207.2
Total alkalinity, mg L−1

157.1

164.3

55.0

5.2

0.02
0.05

5.3
4.5

0.08
0.05
0.09
0.19

7.1
7.4
7.3

0.33
0.34

8.3
8.8
8.9
pH (1:5)

EC (1:5), ­dS m−1

0.30

9
8
7
6
5
4
3
2
1
Property†

Soil

Table 1. Physical and chemical properties of the selected soils (0–30-cm depth).

VZJ | Advancing Critical Zone Sciencebottoms and a fast filter paper wereused to allow drainage—to attain themean bulk density (1.4 g cm−3) for thenine soils. In a disturbed soil column,
the bulk density is somewhat arbitrary,hence the mean value was considered an
appropriate selection. The soil columns
were initially saturated with the appropriate solution by capillary tension fromthe bottom of the core. Subsequently,
the same solution was applied to the topof the column to measure the hydraulic conductivity at a constant hydraulichead of 2.0 cm, in accordance with Klute(1965). Leaching commenced with themost concentrated solution of the desired
pH and SAR (Fig. 1 and 2). When the Ksof the soil columns and pH of the effluent had stabilized, the sequentially lower
EC concentration solution of the same
SAR and pH was applied. This process
was continued until the culminationof the final solution in the sequence.
The leachate solutions were collectedfrom each column at time intervals to
calculate Ks using Darcy’s law. For the
purposes of comparison, the Ks values
were compared with the initial Ks values
determined as the Ks occurring with thegreatest electrolyte concentration (forSAR 20, the greatest EC was 100 mmolc
L−1, and for SAR 40 it was 500 mmolcL−1). The Ks was calculated at sequential
time intervals (t) using Darcy’s law:

Ks =

VL
AHt

[7]

where V is the volume of solution (cm3),
L is the length of the soil core (cm), A
is the cross-sectional area of the soilcolumn (cm2), and H is the water headextending from the top of the ponded
solution to the depth of the soil core (cm).
Three replicates for each treatment andsoil were used to determine Ks, creatinga total of 216 soil cores for all soils usedin this study.
The changes in hydraulic conductivity between treatments were represented
as a relative hydraulic conductivity (rKs):
rK s =

K s( i +n j )
K si

[8]

p. 4 of 13

Fig. 1. Relative hydraulic conductivity (rKs) vs. electrolyte concentration for soils at a Na adsorption ratio of 20 and pH of 6, 7, 8, and 9.

where the initial Ks, denoted by i, was compared with the i + nj
sequential Ks to provide a hydraulic conductivity reduction fromthe initial Ks, where nj is the jth sequential solution in the sequenceof n solutions.

66Modification of the Hydraulic

Reduction Scaling Factor for pH
Generalized Equation

An inverse empirical model for the prediction of the Ks reduction scaling factor, due to the adverse effects of irrigation waterpH, was developed from the observed rKs data (Fig. 1 and 2). Ther 2 scaling factor in HYDRUS proposed by Šimůnek and Suarez

VZJ | Advancing Critical Zone Science

(1997) (Eq. [8]) was recalculated using the experimental rKs values
from the study of Suarez et al. (1984). Subsequently, these rKs
values were compared with the rKs values for the current experimental results observed at pH 6 [rKs(pH6)] for each EC value andSAR of 20 and 40. This provided an initial determination of therelative scaling factor (rSF) for comparison purposes:rSF =rK s(i , ni )rK s(i )[9]where rSF is the rKs reduction ratio compared with the rKs at pH 6
[rKs(i)], and nj is the sequential solution pH in the solution sequence.
After calculating the parameters from Eq. [9], a new r2 pH scaling
factor was then calculated using a linear regression analysis. Linear
p. 5 of 13

Fig. 2. Relative hydraulic conductivity (rKs) vs. electrolyte concentration for soils at a Na adsorption ratio of 40 and pH of 6, 7, 8, and 9.

regression was investigated in terms of the rKs for each pH and individual soil using the statistical program Minitab V.17 (Fig. 3). Fromthese data, a generalized r2 function was also formed using the same
approach as Šimůnek and Suarez (1997), based on the results of rKs
for the soils used in the study of Ali et al. (2019) and presented in(Fig. 1 and 2). This new generalized function isìï1.0,
for pH < 7.2ïïïr2 (pH )= í2.242 - 0.172pH, for 7.2 £ pH £ 9.5
ïïïïî0.60
for pH > 9.5[10]

and the statistical parameters are presented in Table 2. We willrefer to this model as the new generalized model.

VZJ | Advancing Critical Zone Science

Nonlinear Regression Using theLevenberg–Marquardt Method
After calculating the parameters for Eq. [9] by comparisonof the K s reduction data, a stepwise regression was then performed with solution pH, solution EC, soil pH and clay content
included. As a result of this, soil pH was dropped from themodel, with the remaining parameters significant and includedin the model. Therefore, the solution pH, solution EC, andclay content were included in a nonlinear forecast model basedon the observed training data using the statistical program
Minitab V.17.
To find the coefficients of the nonlinear equation
expressing the pH dependence of the soil K s reduction, ap. 6 of 13

Fig. 3. The new generalized function and
HYDRUS K–pH-dependent function to calculate the hydraulic conductivity scaling factor(r2) due to the pH of the solution. The shaded
region represents the range of variations for r2= 1.0 and r2 = 0.1 for nine soils compared with
the HYDRUS K–pH-reduction function; thecentral dotted line represents the r1 and r2 conditions for the generalized equation of thesesame nine soils.

Levenberg–Marquardt simulation optimization algorithm(Marquardt, 1963) was used, which served to iteratively solve
an optimization problem of minimizing errors between theobserved and computed values of the Ks reduction in relation tochanges in the pH and EC of the solution and the clay content
of the soils. This optimization was used to develop a prediction model for forward solutions. This approach works wellin modeling situations because it specifically simulates the Ks
reduction due to the pH of irrigation water and is amenable tocontinuous and adaptive solution EC, solution pH, and soil clay
content, which is extremely desirable in governing Ks temporaland spatial dynamics (Benson and Trast, 1995; Frenkel et al.,1978). The r 2 scaling factor model, based on the Levenberg–
Marquardt approach isrLM =1.25 - pH´ ln (EC)21.72 - 7.42´ pH + 28.8´ ln (EC )+ 0.33´CC[11]

where rLM is the predicted scaling factor for Ks reduction due to the
pH of the percolating solution (pH), in tandem with the solution EC
and clay content (CC); EC is measured in mmoles of charge per liter,while CC is a percentage of the total soil particle size analysis. The
model parameters and associated statistics are presented in Table 3.
We will refer to this model as the nonlinear model.

66Evaluation of the Developed Models
The models were trained and evaluated against the measured
Ks reduction data obtained for nine contrasting Australian soils atfour different pH levels (Fig. 1 and 2). The observed rKs values werecompared with the predicted rKs of the corresponding HYDRUS
K–pH-dependent function, the new generalized model, and thenonlinear model developed by using the Levenberg–Marquardt
optimization approach; rKs values were calculated using Eq. [8].
For the nonlinear model, the standard error, the root meansquare error (RMSE), and the coefficient of determination (R2) ofboth predicted and measured results were compared and slightly
diverged from each other, showing a higher coefficient of determination (R2 = 0.82 and t-test = 2.45) between the observed values
and model-simulated rKs than the current HYDRUS and new generalized functions. Conversely, the HYDRUS K–pH-dependent
model produced the highest standard error and RMSE and thelowest coefficient of determination (R 2 = 0.51 and t-test = 8.45)
compared with the new generalized and nonlinear models forobserved and simulated rKs values (Table 4).
The statistical analysis was also conducted among predicted
rKs values for the HYDRUS K–pH-dependent function, the newgeneralized model, and the nonlinear function. A significant difference was observed (P < 0.001) for the new generalized model

Table 2. Statistical parameters for the HYDRUS K–pH-dependent function and the new generalized function calculated in this study using linear
regression analysis, including the standard error of the regression (SE), Durbin–Watson statistic to detect the presence of autocorrelation (DWS), theroot mean square error (RMSE), the coefficient of determination (R 2), adjusted coefficient of determination (R 2ADJ), and predicted coefficient ofdetermination (R 2PRED); F value and P value are statistical tests to determine whether the term is associated with the response.
Equation

SE

DWS

RMSE

R2

R2ADJ

R2PREDF value

P valueHYDRUS K–pH-dependent function

0.53

2.14

0.78

0.36

0.33

0.22

14.3

0.001

New generalized function

0.17

2.14

0.2

0.56

0.55

0.52

59.2

<0.001VZJ | Advancing Critical Zone Sciencep. 7 of 13

Table 3. Statistical characteristics pertaining to Eq. [11] from the nonlinear regression analysis using the Levenberg–Marquardt algorithm.
Parameter†

Eq. [11]
Summary

Table 4. Summary statistical characteristics of the observed relative
hydraulic conductivity (rKs) and predicted rKs using the HYDRUS K–
pH-dependent model, the new generalized model, and the nonlinear
model, which are shown in Fig. 4, using the analysis of variance and thet-test methods.

Iterations

24

Final SSE

5.64

StatisticHYDRUS K–pHdependent function

New generalized
function

Nonlinear function

DFE

427

SE

0.25

0.17

0.14

MSE

0.013

RMSE

0.32

0.18

0.16

SE

0.11

R2

0.51

0.77

0.81

R

0.72

0.88

0.90

df

211

t-test

8.45

2.86

2.45

SS

2.759

F value

71.35

8.16

6.01

MS

0.013

P value<0.001

0.005

0.015

F value

0.98

P value

0.56

Lack of fit

Parameter estimates
95% Confidence interval
Coefficient

Estimate

SE estimate

Table 5. Summary statistical characteristics of the observed relative
hydraulic conductivity (rKs) from the study of Suarez et al. (1984) andpredicted rKs using the HYDRUS K–pH-dependent model, the newly
developed generalized equation, and the nonlinear equation, which are
shown in Fig. 5, using the analysis of variance and the t-test methods.

Lower limit

Upper limit

a1

1.25

0.033

1.196

1.31

a2

21.72

9.63

6.91

40.1

a3

−7.42

1.58

−10.76−4.95

StatisticHYDRUS K–pHdependent function

New generalized
function

Nonlinear function

a4

28.76

2.96

24.0

34.54

SE

0.30

0.24

0.20

a5

0.33

RMSE

0.37

0.25

0.22

R2

0.45

0.67

0.75

R

0.67

0.82

0.86

t-test

5.1

2.15

2.13

F value

25.77

4.5

4.4

P value<0.001

0.034

0.035

0.056

0.23

0.45

† SSE, sum of squared errors; DFE, error degrees of freedom; MSE, mean squareerror; SE, standard error; df, degrees of freedom; SS, sum of squared deviations; F value and P value are statistical tests to determine whether the term is
associated with the response that includes the predictors in the current model;
a1–a5, coefficient estimates to describe the relationship between the response(rLM) and the predictors (pH, electrical conductivity, and clay content).

and the nonlinear equation compared with the HYDRUS K–pHdependent function, while no significant difference was detected(P = 0.71) between predicted rKs for the generalized and nonlinear
equations. These statistics indicate that there was a better fit by
the nonlinear model to the observed rKs data.

66Validation of the New Scaling Factors
The two new regression models were validated against theexperimentally observed rKs values of the California soils from thestudy of Suarez et al. (1984). Additionally, the HYDRUS K–pHdependent model (Šimůnek and Suarez, 1997)—developed fromthe Suarez et al. (1984) data—was evaluated against the same
California dataset to determine the magnitude of improvement thatthe new models provided. Statistical parameters for the observed vs.
predicted values for each model are presented in Table 5.
Using the t-test and analysis of variance for the null hypothesis of no difference, the statistical tests showed that there wasa significant difference between predicted and measured valuesof rKs using the HYDRUS K–pH-dependent model (t-test = 5.1,
P < 0.001, R 2 = 0.45). A comparison was also made between

VZJ | Advancing Critical Zone Sciencethe newly proposed generalized and nonlinear models and theobserved rKs values of Suarez et al. (1984), providing t-test = 2.15,
P < 0.034, R 2 = 0.67 and t-test = 2.13, P < 0.035, R 2 = 0.75,
respectively. The tests indicated that there was a higher correlation
between predicted and observed rKs values for these models thanthe HYDRUS K–pH-dependent function at the 0.05 probability
level (Table 5). The statistics also showed a significant difference(P < 0.001) for the proposed generalized and nonlinear equations
for the data from the Suarez et al. (1984) soils compared with the
HYDRUS K–pH-dependent model; no significant difference was
detected (P = 0.93) between the predicted rKs values of the generalized and nonlinear models.
Figures 4 and 5 indicate that the rKs data points are consistently better predicted using the new nonlinear equation, although
the new generalized linear equation performs reasonably wellin comparison. Interestingly, the HYDRUS K–pH-dependent
model does not perform well on the data from which it was created. We propose that the better performance of the nonlinear
equation suggests that soil-specific attributes of soils will be
important in explaining the reduction in hydraulic dynamics.
This result is not surprising, given the literature indicating that soil
p. 8 of 13

Fig. 4. The relation between the observed relative hydraulic conductivity (rKs) and rKs predicted using (A) the HYDRUS K–pH-dependent model, (B)the new generalized model, and (C) the nonlinear function (Levenberg–Marquardt algorithm). The diagonal dotted line is the 1:1 line, and the solidline is the regression fit for the observed data.

hydraulic reduction is soil specific (Bennett et al., 2019; Marchuk
and Rengasamy, 2011), but it does reinforce the need to updatesuch parameters within soil-water models.

Observed vs. Predicted Reductionin Hydraulic Conductivity
The statistical analysis showed the accuracy of the predicted
rKs for each model for each dataset (Tables 4 and 5). For r 2 optimization, the new generalized and nonlinear models demonstrated
better performance, as indicated by their lower RMSE and t-testvalues and higher coefficients of determination for the Australianand California soils. For both datasets, when the nonlinear model
was used, the predicted outcomes were generally in closer agreement with the observations of rKs than the other two models.
Naturally, the observed rKs values are dependent on the EC,
SAR, and pH of the solution, as well as the soil clay content andmineralogy (Bennett et al., 2019; McNeal and Coleman, 1966;

VZJ | Advancing Critical Zone ScienceSuarez et al., 1984). The relatively high accuracy and performanceof the nonlinear model was mainly due to its capability of predicting pH effects more specifically by considering electrolyte
concentration and clay content. The r 2 scaling factor for the nonlinear model (r 2LM) is mainly controlled by the pH and EC of thesolution and the clay content of the soil, as shown by

K LM (h, pH, SAR, EC, CC )=rLM (pH, SAR, EC, CC )K s K r (h )[12]Comparatively, the r2 scaling factor for the generalized models
is simply based on the pH of the solution (Eq. [2]). Accordingly,
the predicted rKs values were calculated using Eq. [5] and Eq. [13]to calculate the rKs of the generalized models and nonlinear model,
respectively:rLM (pH, SAR, EC, CC )=r1 (SAR,EC)r2LM (pH,EC,CC )[13]

p. 9 of 13

Fig. 5. The relation between the observed relative hydraulic conductivity (rKs) from the study of Suarez et al. (1984) and predicted rKs using (A) the
HYDRUS K–pH-dependent model, (B) the new generalized model, and (C) the nonlinear model (Levenberg–Marquardt algorithm). The diagonal
dotted line is the 1:1 line, and the solid line is the regression fit for the observed data.

where KLM is the hydraulic conductivity based on the Levenberg–
Marquardt nonlinear model (r 2LM; Eq. [11]), rLM is the saturated
hydraulic conductivity reduction as a result of adverse effects of
EC, SAR, and pH (using the nonlinear function), and CC is theclay content (%).
Another limitation of the predicted hydraulic conductivity
is that the final rKs is also dependent on the degradative effectsof EC and SAR (r1; Eq. [3]). The r1 scaling factor has been generalized and determined empirically and its parameter values
developed using only a narrow range of soils. In that matter, theuse of generalized parameters would increase errors related to theuncertainty in the weighted scaling factors and result in reducing
the accuracy of rKs prediction. The extent of uncertainty of the
pH scaling factor (r 2LM) is somewhat reduced by including EC
and clay content in the calculation of the scaling factor for thehydraulic dynamic reduction (Eq. [13]). This is a clear indicationof the improvement of rKs prediction using the nonlinear function,

VZJ | Advancing Critical Zone Science

although it could be further improved by combining r1 and r 2 in asingle nonlinear equation.

66Discussion

Improvement of HYDRUS

The literature demonstrates that the HYDRUS models
have been effectively applied to laboratory and field experiments(Ramos et al., 2011, 2012; Rasouli et al., 2013) using soil hydraulicconductivity and solute transport model parameters. Šimůnek etal. (2012) argued that the HYDRUS codes are physically basedmodels and may require little or no calibration when all required
input parameters are experimentally determined. However, interms of hydraulic conductivity dynamic decline, there is no physical parameter that can be measured, and the functions describing
reduction do not allow for soil-specific nuances. This is an
important limitation of the current HYDRUS model family andp. 10 of 13

modules. Our work suggests that an updated generalized equation
could be utilized, but it also further suggests that the inclusion ofsoil-specific attributes could provide a consistently better relation
between observed and predicted results, which supports the use ofand further development of the nonlinear function.
Using a broad range of soils, the principal goal of this current study was to evaluate the existing scaling factor (r 2) and
its applicability, with the intent of improving on the existing
HYDRUS reduction function to include soil-specific attributes.
We have demonstrated that the generalized equation for the r 2
scaling factor of the HYDRUS model leads to a unique solution
and can be updated using a broader range of soils. This allows theformation of soil-specific equations, in which the predicted rKs
values are compared with observed rKs values for the 12 examinedsoils of Australia and California (Fig. 4 and 5). While the newgeneralized equation provided reasonable results over the existing linear HYDRUS equation, the nonlinear validated approachfor K s reduction will provide more confidence in the ability of
the HYDRUS model to estimate dynamic K s reduction. Soils are
inherently heterogeneous in their properties and their resiliency
to retain soil structure under conditions such as alkaline pH, lowsolution salinity, and adverse monovalent cation concentrations(dispersive potential varies). The Levenberg–Marquardt optimization allows the inclusion of multiple factors in a manner thatprovides a better fit to the complex nonlinear dynamics of soil
hydraulic reduction.

Nonlinear Performance and Future Directions
The nonlinear inverse modeling included additional parameters, such as solution EC and soil clay content, which are critical
governing factors in the management of the extent of Ks reduction (Agassi et al., 1981; Cook et al., 2006; Dang et al., 2018a,
2018c; Zhu et al., 2016). An increase in EC generates the osmoticpressure that compresses the diffuse double layer repulsive effecton the clay domains (Quirk, 2001), subsequently diminishing thecontribution of pH and SAR on the diffuse double layer expansion (Sumner, 1993). The clay content is also an important factor
in determining the extent of the hydraulic conductivity reduction and subsequently the resilience of the soil structure stability(Bennett et al., 2019). Concomitantly, the clay content of a soil
has also been documented to affect the resilience of soil structure
to the pH of the applied solution (Lieffering and McLay, 1996;
Nyamangara et al., 2007). For lower clay content soils, the absolutedecrease in Ks is greater than for clay soils, indicating the potential for negative effects of pH on Ks (Lieffering and McLay, 1996;
Suarez et al., 1984). A similar trend was observed for Ks reductionin this study. Furthermore, in terms of the relative hydraulic reduction percentage, clay content will have an effect whereby highly
sandy soils may require complete dispersion of the existing clay tocause a reduction percentage in Ks equivalent to the disaggregation
properties in highly clay-dominant soils. This is considered as afunction of the greater frequency of pores with smaller pore diameter and clay domain swelling without dispersion where sufficient

VZJ | Advancing Critical Zone Scienceclay exists. However, the agreement between the observed and predicted results for the nonlinear equation suggests that there is stilla need for improvement in predictive capability.
Bennett et al. (2019) suggested that soil-specific hydraulicconductivity reduction functions require the consideration of clay
properties, especially the quantification of clay mineral type, size,and surface charge, which reinforces the assertions of Quirk (2001).
Additionally, and related to the clay specificity, the concept of ionicity affecting the net negative charge (Marchuk and Rengasamy,2011) is also required to be incorporated into a soil-specific structural model (Bennett et al., 2019). Heterogeneous properties andthe soil-specific behavior under the pH of applied solutions are
known to affect the net negative charge (Chorom et al., 1994) andthereby provide a means of improving the prediction of hydraulicconductivity reduction.
It is also important to reflect on the fact that this study, and thestudy of Suarez et al. (1984)—the existing pH hydraulic reduction
function within HYDRUS—examined repacked soil cores rather
than undisturbed soils. This was to avoid heterogeneity factors that
potentially mask the process effect of the mechanisms controlling
hydraulic reduction. Importantly, we contend that the mechanisms
controlling hydraulic conductivity reduction dynamics within a poreare consistent across all pore size ranges under both saturated andunsaturated conditions. This means that the scaling factor would
apply uniformly to all pore sizes but that the absolute differencesin hydraulic conductivity would depend on the pore size, inferringthat the results in this study are applicable to both saturated andunsaturated conditions. However, the effect of pH on the hydraulicdynamics in an unsaturated soil was outside the scope of the current
study and would be prudent to validate in future work.
Furthermore, there is merit in moving away from a scaling
factor model that seeks to separate the cation and pH effects.
Even with the improvement of the nonlinear model by including
EC, it still fails to include the effects of cations on the dispersive,
and thus hydraulic conductivity reductive, effects of SAR. The
current dataset is insufficient to achieve this, with only two
SAR levels; however, it does indicate that such a model can beachieved with reasonable confidence, given sufficient data. The
level of confidence is an important topic to consider also. Bennett
et al. (2019) demonstrated that a generalized equation for thesoil-specific threshold electrolyte concentration (C TH) varied byapproximately ±7.5 SAR units within one standard deviation,
concluding that this level of variation within a generalized equation was not reliable and was environmentally unsound. However,the current scaling factor within HYDRUS is worse. The Ezlit etal. (2013) disaggregation model, which the Bennett et al. (2019)
work is based on, was an improvement on the HYDRUS EC andSAR based reduction model (i.e., McNeal, 1968). On this basis, thefirst step would be to improve the current nonlinear approach toinclude the SAR effects within it and then incorporate this into
HYDRUS, with a level of confidence surrounding the output for
the user. Simultaneously, there is a requirement to improve thepredictive capability from a fundamental point of view.
p. 11 of 13

Soil Initial pH andHydraulic Conductivity Reduction
The soil initial pH was dropped from the stepwise regression
process, which led us to not include it within our models. This
may suggest that the initial soil pH is not important in predicting
the hydraulic conductivity decline. However, we caution that thisassumption is on the basis of the study of Ali et al. (2019), whodemonstrated that the initial soil pH and the clay content wereboth important in controlling the extent of the hydraulic conductivity reduction. The same nine soils were used in this work. It
was observed by Ali et al. (2019) that while there was a significant
reduction in soil structural characteristics for alkaline soils as pH
increased, the concomitant extent of the Ks reduction was not significant, although it consistently decreased as pH increased. Thatis, the size of the reduction effect appeared to be controlled by the
initial soil pH. The contrasting situation for an acidic initial soil
pH interacted with lower clay content and, as this current workshows, outweighed in terms of the effect of clay content. For thisreason, and the fact that the updated models were still developedon only 12 soils, it would be prudent to extend these studies to abroader range of soils that have varying pH and varying clay content within each pH subclass. As far as we are aware, combining
the nine Australian soils and three California soils constitutes themost comprehensive dataset to determine the pH effect on soil
hydraulic conductivity, which clearly identifies the requirement toincrease the dataset such that the soil specificity is better captured
within the nonlinear coefficients. This should further improve thenonlinear approach.

66Conclusion
This research identified the limitation of the HYDRUS
scaling factor (r 2) model and developed and validated two newmodels to optimize saturated hydraulic conductivity prediction.
The proposed models were produced using a similar approach as
in the HYDRUS model, with a nonlinear regression method further implemented. The nonlinear equation developed using theLevenberg–Marquardt algorithm considers the pH and EC of thesolution, as well as the soil clay content, which is an important
improvement toward soil-specific pedotransfer functions that may
be incorporated into HYDRUS. The overall performance of the
new models was significantly better than that of the existing linear
HYDRUS hydraulic reduction scaling model. This was the case forboth the current Australian dataset and for the California dataset
on which the HYDRUS model was based.
Even though the prediction of the reduction in the hydraulicconductivity still has room for improvement in terms of the sizeof the dataset and soil types that control hydraulic conductivity
reduction scaling factors and coefficients within the nonlinear
model, the results significantly build on the existing circumstance.
The nonlinear model, developed using the Levenberg–Marquardt
approach to substitute the r 2 scaling factor in the HYDRUS
program, provides a consistently more accurate estimate of the

VZJ | Advancing Critical Zone Science

hydraulic conductivity than the current HYDRUS r 2 reduction
model. Furthermore, the nonlinear equation is put forward as thebasis for further improvement for the incorporation of identified
soil properties suggested to govern soil structural dynamics.

Acknowledgments

Aram Ali wishes to acknowledge the University of Southern Queensland for provision of an international fee waiver and stipend scholarship in the pursuit of his
doctoral qualification.

References
Agassi, M., I. Shainberg, and J. Morin. 1981. Effect of electrolyte concentration and soil sodicity on infiltration
rate and crust formation. Soil Sci. Soc. Am. J. 45:848–851.
doi:10.2136/sssaj1981.03615995004500050004x
Ali, A., J. Bennett, A. Biggs, and A. Marchuk. 2019. Effect of irrigation water
pH on saturated hydraulic conductivity and electrokinetic propertiesof acidic, neutral and alkaline soils. Soil Sci. Soc. Am. J. 83:1671–1681.
doi:10.2136/sssaj2019.04.0123
Assouline, S., and K. Narkis. 2011. Effects of long-term irrigation withtreated wastewater on the hydraulic properties of a clayey soil. Water
Resour. Res. 47:W08530. doi:10.1029/2011WR010498
Bell, F. 1996. Lime stabilization of clay minerals and soils. Eng. Geol.
42:223–237. doi:10.1016/0013-7952(96)00028-2
Ben-Hur, M., G. Yolcu, H. Uysal, M. Lado, and A. Paz. 2009. Soil structurechanges: Aggregate size and soil texture effects on hydraulic conductivity under different saline and sodic conditions. Soil Res. 47:688–696.
doi:10.1071/SR09009
Bennett, J.M., A. Marchuk, S. Marchuk, and S. Raine. 2019. Towards
predicting the soil-specific threshold electrolyte concentration of soil as a reduction in saturated hydraulic conductivity:
The role of clay net negative charge. Geoderma 337:122–131.
doi:10.1016/j.geoderma.2018.08.030
Bennett, J.M., and B. Warren. 2015. Role of livestock effluent suspended
particulate in sealing effluent ponds. J. Environ. Manage. 154:102–109.
doi:10.1016/j.jenvman.2015.02.032
Benson, C.H., and J.M. Trast. 1995. Hydraulic conductivity of thirteen compacted clays. Clays Clay Miner. 43:669–681.
doi:10.1346/CCMN.1995.0430603
Bolan, N.S., J.K. Syers, M.A. Adey, and M.E. Sumner. 1996. Originof the effect of pH on the saturated hydraulic conductivity ofnon‐sodic soils. Commun. Soil Sci. Plant Anal. 27:2265–2278.
doi:10.1080/00103629609369702
Campbell, E.E., and K. Paustian. 2015. Current developments in soil organic matter modeling and the expansion of model applications: A review.
Environ. Res. Lett. 10:123004. doi:10.1088/1748-9326/10/12/123004
Chorom, M., P. Rengasamy, and R. Murray. 1994. Clay dispersion as influenced by pH and net particle charge of sodic soils. Soil Res. 32:1243–
1252. doi:10.1071/SR9941243
Cook, F.J., N.S. Jayawardane, D.W. Rassam, E.W. Christen, J.W. Hornbuckle,
R.J. Stirzaker, et al. 2006. The state of measuring, diagnosing, ameliorating and managing solute effects in irrigated systems. Tech. Rep.
04/06. Coop. Res. Ctr. for Irrig. Futures, Darling Heights, QLD, Australia.
Dang, A., J.M. Bennett, A. Marchuk, A. Biggs, and S. Raine. 2018a.
Evaluating dispersive potential to identify the threshold electrolyte concentration in non-dispersive soils. Soil Res. 56:549–559.
doi:10.1071/SR17304
Dang, A., J.M. Bennett, A. Marchuk, A. Biggs, and S.R. Raine. 2018b.
Quantifying the aggregation–dispersion boundary condition interms of saturated hydraulic conductivity reduction and the threshold electrolyte concentration. Agric. Water Manage. 203:172–178.
doi:10.1016/j.agwat.2018.03.005
Dang, A., J.M. Bennett, A. Marchuk, S. Marchuk, A. Biggs, and S. Raine.
2018c. Validating laboratory assessment of threshold electrolyte concentration for fields irrigated with marginal quality saline-sodic water.
Agric. Water Manage. 205:21–29. doi:10.1016/j.agwat.2018.04.037

p. 12 of 13

Ezlit, Y., J.McL. Bennett, S. Raine, and R. Smith. 2013. Modification of the
McNeal clay swelling model improves prediction of saturated hydraulic conductivity as a function of applied water quality. Soil Sci. Soc. Am.
J. 77:2149–2156. doi:10.2136/sssaj2013.03.0097
Frenkel, H., J. Goertzen, and J. Rhoades. 1978. Effects of clay type and content, exchangeable sodium percentage, and electrolyte concentration
on clay dispersion and soil hydraulic conductivity. Soil Sci. Soc. Am. J.
42:32–39. doi:10.2136/sssaj1978.03615995004200010008x
Gee, G., and J. Bauder. 1986. Particle-size analysis. In: A. Klute, editor,
Methods of soil analysis. Part 1. Physical and mineralogical methods.
2nd ed. SSSA Book Ser. 5. SSSA and ASA, Madison, WI. p. 383–411.
doi:10.2136/sssabookser5.1.2ed.c15
Goldberg, S., and R.A. Glaubig. 1987. Effect of saturating cation, pH, andaluminum and iron oxide on the flocculation of kaolinite and montmorillonite. Clays Clay Miner. 35:220–227. doi:10.1346/CCMN.1987.0350308
Jackson, M.L. 2005. Soil chemical analysis: Advanced course. 2nd rev. ed.
Parallel Press, Univ. of Wisconsin-Madison Libraries, Madison.
Klute, A. 1965. Laboratory measurement of hydraulic conductivity ofsaturated soil. In: C.A. Black et al., editors, Methods of soil analysis. Part
1. Physical and mineralogical properties. Agron. Monogr. 9. SSSA and
ASA, Madison, WI. p. 210–221. doi:10.2134/agronmonogr9.1.c13
Lieffering, R.E., and C.D.A. McLay. 1996. The effect of strong hydroxide
solutions on the stability of aggregates and hydraulic conductivity ofsoil. Eur. J. Soil Sci. 47:43–50. doi:10.1111/j.1365-2389.1996.tb01370.x
Marchuk, A., and P. Rengasamy. 2011. Clay behaviour in suspension isrelated to the ionicity of clay–cation bonds. Appl. Clay Sci. 53:754–759.
doi:10.1016/j.clay.2011.05.019
Marchuk, A., and P. Rengasamy. 2012. Threshold electrolyte concentrationand dispersive potential in relation to CROSS in dispersive soils. Soil
Res. 50:473–481. doi:10.1071/SR12135
Marquardt, D.W. 1963. An algorithm for least-squares estimationof nonlinear parameters. J. Soc. Ind. Appl. Math. 11:431–441.
doi:10.1137/0111030
McNeal, B. 1968. Prediction of the effect of mixed-salt solutions
on soil hydraulic conductivity. Soil Sci. Soc. Am. J. 32:190–193.
doi:10.2136/sssaj1968.03615995003200020013x
McNeal, B., and N. Coleman. 1966. Effect of solution composition
on soil hydraulic conductivity. Soil Sci. Soc. Am. J. 30:308–312.
doi:10.2136/sssaj1966.03615995003000030007x
Menezes, H., B. Almeida, C. Almeida, J. Bennett, E. Silva, and M. Freire.
2014. Use of threshold electrolyte concentration analysis to determine
salinity and sodicity limit of irrigation water. Rev. Bras. Eng. Agric. Ambient. 18:53–58. doi:10.1590/1807-1929/agriambi.v18nsupps53-s58
Miller, D.A., and R.A. White. 1998. A conterminous UnitedStates multilayer soil characteristics dataset for regional
climate and hydrology modeling. Earth Interact. 2:1–26.
doi:10.1175/1087-3562(1998)002<0001:ACUSMS>2.3.CO;2
Nyamangara, J., S. Munotengwa, P. Nyamugafata, and G. Nyamadzawo.
2007. The effect of hydroxide solutions on the structural stability andsaturated hydraulic conductivity of four tropical soils. S. Afr. J. Plant
Soil 24:1–7. doi:10.1080/02571862.2007.10634773
Oades, J.M. 1984. Soil organic matter and structural stability: Mechanisms and implications for management. Plant Soil 76:319–337.
doi:10.1007/BF02205590
Quirk, J. 2001. The significance of the threshold and turbidity concentrations in relation to sodicity and microstructure. Soil Res. 39:1185–1217.
doi:10.1071/SR00050
Quirk, J., and R. Schofield. 1955. The effect of electrolyte concentration on soil permeability. J. Soil Sci. 6:163–178.
doi:10.1111/j.1365-2389.1955.tb00841.x
Ramos, T.B., J. Šimůnek, M.C. Gonçalves, J.C. Martins, A. Prazeres, N.L. Castanheira, and L.S. Pereira. 2011. Field evaluation of a multicomponent

VZJ | Advancing Critical Zone Sciencesolute transport model in soils irrigated with saline waters. J. Hydrol.
407:129–144. doi:10.1016/j.jhydrol.2011.07.016
Ramos, T.B., J. Šimůnek, M.C. Gonçalves, J.C. Martins, A. Prazeres, and L.S.
Pereira. 2012. Two-dimensional modeling of water and nitrogen fatefrom sweet sorghum irrigated with fresh and blended saline waters.
Agric. Water Manage. 111:87–104. doi:10.1016/j.agwat.2012.05.007
Rasouli, F., A.K. Pouya, and J. Šimůnek. 2013. Modeling the effects of saline
water use in wheat-cultivated lands using the UNSATCHEM model.
Irrig. Sci. 31:1009–1024. doi:10.1007/s00271-012-0383-8
Rayment, G.E. and D.J. Lyons. 2011. Soil chemical methods: Australasia.
CSIRO Publ., Collingwood, VIC, Australia.
Rengasamy, P., and J. Oades. 1977. Interaction of monomeric and polymeric species of metal ions with clay surfaces: I. Adsorption of iron(III)species. Soil Res. 15:221–233. doi:10.1071/SR9770221
Rengasamy, P., and K. Olsson. 1991. Sodicity and soil structure. Soil Res.
29:935–952. doi:10.1071/SR9910935
Shainberg, I., and J. Letey. 1984. Response of soils to sodic and salineconditions. Calif. Agric. 52:1–57.
Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M.Th. van Genuchten. 2013.
The HYDRUS-1D software package for simulating the movement ofwater, heat, and multiple solutes in variably saturated media, Version
4.17. HYDRUS Software Ser. 3. Dep. of Environmental Sciences, Univ. of
California, Riverside.
Šimůnek, J., and D.L. Suarez. 1997. Sodic soil reclamation using multicomponent transport modeling. J. Irrig. Drain. Eng. 123:367–376.
doi:10.1061/(ASCE)0733-9437(1997)123:5(367)Šimůnek, J., M.Th. van Genuchten, and M. Šejna. 2012. HYDRUS:
Model use, calibration, and validation. Trans. ASABE 55:1263–1276.
doi:10.13031/2013.42239
Šimůnek, J., M.Th. van Genuchten, and M. Šejna. 2016. Recent developments and applications of the HYDRUS computer software packages.
Vadose Zone J. 15(7). doi:10.2136/vzj2016.04.0033
Smith, W.N., W.D. Reynolds, R. de Jong, R.S. Clemente, and E. Topp.
1995. Water flow through intact soil columns: Measurement
and simulation using LEACHM. J. Environ. Qual. 24:874–881.
doi:10.2134/jeq1995.00472425002400050013x
Suarez, D., J. Rhoades, R. Lavado, and C. Grieve. 1984. Effect of pH on
saturated hydraulic conductivity and soil dispersion. Soil Sci. Soc. Am.
J. 48:50–55. doi:10.2136/sssaj1984.03615995004800010009x
Suarez, D.L., and A.G. Rubio. 2010. Season-long changes in infiltration
rates associated with irrigation water sodicity and pH. In: R. Gilkes and
N. Prakongkep, editors, Soil Solutions for a Changing World: Proceedings of the 19th World Congress of Soil Science, Brisbane, Australia.
1–6 Aug. 2010. Vol. WG 3. Int. Union Soil Sci. p. 54–56.
Suarez, D.L., and J. Šimůnek. 1997. UNSATCHEM: Unsaturated water and solute transport model with equilibrium and kinetic chemistry. Soil Sci. Soc.
Am. J. 61:1633–1646. doi:10.2136/sssaj1997.03615995006100060014x
Sumner, M.E. 1993. Sodic soils: New perspectives. Soil Res. 31:683–750.
doi:10.1071/SR9930683
Walkley, A., and I.A. Black. 1934. An examination of the Degtjareff
method for determining soil organic matter, and a proposed
modification of the chromic acid titration method. Soil Sci. 37:29–38.
doi:10.1097/00010694-193401000-00003
Zhu, Y., A. Ali, A. Dang, A.P. Wandel, and J.M. Bennett. 2019. Re-examining the flocculating power of sodium, potassium, magnesiumand calcium for a broad range of soils. Geoderma 352:422–428.
doi:10.1016/j.geoderma.2019.05.041
Zhu, Y., A. Marchuk, and J.M. Bennett. 2016. Rapid method for assessment of soil structural stability by turbidimeter. Soil Sci. Soc. Am. J.
80:1629–1637. doi:10.2136/sssaj2016.07.0222

p. 13 of 13