J. Hydrol. Hydromech., 66, 2018, 2, 161–169
DOI: 10.1515/johh-2017-0046

Further tests of the HYPROP evaporation method for estimating
the unsaturated soil hydraulic properties
Camila R. Bezerra-Coelho1, Luwen Zhuang2, Maria C. Barbosa1, Miguel Alfaro Soto3,
Martinus Th. van Genuchten2, 4*
1

Department of Civil Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, Brazil.
Department of Earth Sciences, Utrecht University, Utrecht, Netherlands.
3
Department of Applied Geology, São Paulo State University, UNESP, Rio Claro, SP, Brazil.
4
Department of Nuclear Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, Brazil.
*
Corresponding author. E-mail: rvangenuchten@hotmail.com
2

Abstract: Many soil, hydrologic and environmental applications require information about the unsaturated soil hydraulicproperties. The evaporation method has long been used for estimating the drying branches of the soil hydraulic functions.
An increasingly popular version of the evaporation method is the semi-automated HYPROP© measurement system(HMS) commercialized by Decagon Devices (Pullman, WA) and UMS AG (München, Germany). Several studies werepreviously carried out to test the HMS methodology by using the Richards equation and the van-Genuchten-Mualem(VG) or Kosugi-Mualem soil hydraulic functions to obtain synthetic data for use in the HMS analysis, and then to compare results against the original hydraulic properties. Using HYDRUS-1D, we carried out independent tests of the
HYPROP system as applied to the VG functions for a broad range of soil textures. Our results closely agreed with previous findings. Accurate estimates were especially obtained for the soil water retention curve and its parameters, at least
over the range of available retention measurements. We also successfully tested a dual-porosity soil, as well as an extremely coarse medium with a very high van Genuchten n value. The latter case gave excellent results for water retention, but failed for the hydraulic conductivity. In many cases, especially for soils with intermediate and high n values, an
independent estimate of the saturated hydraulic conductivity should be obtained. Overall, the HMS methodology performed extremely well and as such constitutes a much-needed addition to current soil hydraulic measurement techniques.
Keywords: Soil hydraulic properties; Evaporation method; HYPROP; HYDRUS-1D; van Genuchten-Mualem equations.
INTRODUCTION
Reliable data about the unsaturated soil hydraulic propertiesare crucial for many hydrologic, agricultural and environmental
applications. A large number of experimental methodologies
have been developed and tested over the years to estimate thesoil water retention and unsaturated soil hydraulic conductivity(Dane and Hopmans, 2002; Klute (Ed.), 1986). A direct approach for the soil water retention function is to measure aseries of water content (θ) and pressure head (h) pairs, and thento fit a particular function to the data. Direct measurement
techniques include methods using a hanging water column orsand box, pressure cells, pressure plate extractors, suction tables, soil freezing, and many other approaches as reviewed by
Looney and Falta (Eds.) (2000), Dane and Hopmans (2002),
and Bittelli and Flury (2009), among others. Once the pairs of θand h data are obtained, the results may be analyzed in terms ofspecific analytical functions such as those by Brooks and Corey(1964), van Genuchten (1980), Fredlund and Xing (1994),
Kosugi (1996), or Assouline et al. (1998). Several convenient
software packages are available for this purpose (van Genuchten et al., 1991; Wraith and Or, 1998). Alternatively, the data
could be analyzed without assuming specific analytical functions, for example by using linear, cubic spline or other interpolation techniques (Bitterlich et al., 2004; Kastanek and Nielsen,
2001).
Similar direct approaches involving pairs of conductivity
and pressure head or water content data are in principle also
possible for the K(h) or K(θ) functions (Dane and Hopmans,
2002; Klute and Dirksen, 1986), including for the saturated

hydraulic conductivity, Ks. The latter parameter can be measured in the laboratory using a variety of constant or falling head
methods, and in the field using single or double ring infiltrometers, constant head permeameters, and various auger-hole andpiezometer methods (Dane and Topp (Eds.), 2002). Unfortunately, pairs of K(h) or K(θ) data are not easily obtained in thevery dry range unless more specialized approaches are usedsuch as hot-air, centrifugation or dew-point techniques (Arya,
2002; Nimmo et al., 2002; Scanlon et al., 2002). Consequently,
unsaturated hydraulic conductivity properties often are still
estimated using inverse or parameter estimation procedures.
Parameter estimation methods generally involve measurements of several capacity and flow attributes (e.g., water contents, pressure heads, boundary fluxes), which are then used in
combination with a numerical solution of the Richards equation
to obtain estimates of the hydraulic parameters in the adopted
soil hydraulic functions. Popular methods include one-step andmulti-step outflow methods (Hopmans et al., 2002; Kool et al.,
1987; van Dam et al., 1994), tension infiltrometer methods(Šimůnek et al., 1998a) and evaporation methods (Šimůnek etal., 1998b), although many other laboratory and field methods
also exist or can be similarly employed (Hopmans et al., 2002).
One frequently used approach is the evaporation method,stemming from the early work by Gardner and Miklich (1962)
using horizontal columns, and subsequent modifications byWind (1968) and others. Measurements of the evaporation rate
and tension at multiple depths in the sample permitted the simultaneous direct estimation of the water retention and hydraulicconductivity. Key contributions have been by Halbertsma(1996), Klute and Dirksen (1986), Becher (1970), Plagge (1991),

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Camila R. Bezerra Coelho, Luwen Zhuang, Maria C. Barbosa, Miguel Alfaro Soto, Martinus Th. van Genuchten

Wendroth et al. (1993), Bertuzzi and Voltz (1997), and manyothers, including analyses of the data using parameters estimation
approaches (Šimůnek et al., 1998b, Iden and Durner, 2008). An
increasingly popular version of the evaporation method is the
HYPROP© measurement system (further referred to here asHMS), which allows semi-automated direct measurements ofwater retention and conductivity pairs over a relatively wide
range of pressure head values (Peters and Durner, 2008; Peters etal., 2015; Schindler et al., 2010a, b, and others). The HMS approach has been commercialized jointly by Decagon Devices(Pullman, WA, USA) and UMS AG (Munich, Germany), now
known as the METER group. The commercial system involves
pressure head measurements versus time at two depths within ashort 5-cm soil sample as water evaporates from its surface,with the evaporation rate determined by weighing the column.
Several studies have been carried out to test the HYPROP
evaporation approach against multistep outflow and othermethods (e.g., Schelle et al., 2010; Zhuang et al., 2017). Petersand Durner (2008) and Peters et al. (2015) tested the HMS
approach assuming synthetic (virtual) data for the two pressure
heads within the sample, as well as for the evaporation rate (andhence the sample weight), as a function of time as generated
with numerical solutions of the Richards equation. Peters andDurner (2008) used for this purpose the hydraulic functions of
van Genuchten-Mualem (1980), while Peters et al. (2015) usedthe equations of Kosugi (1996) as well as the PDI model ofPeters and colleagues (Iden and Durner, 2014; Peters, 2013,2014) to account for the effects of film, corner and isothermal
vapor flow in very dry soils.
In this study we follow a very similar approach using thestandard van Genuchten-Mualem approach to provide an independent test of the HYPROP evaporation method. HMS performance is studied in particular for a broad range of soils
having different van Genuchten α and n parameters, as well as
for a dual-porosity medium as described with the composite
hydraulic functions of Durner (1994). We first give a very brief
description of the HYPROP evaporation method. The
HYDRUS-1D software package (Šimůnek et al., 2016) is used
next to generate virtual (synthetic) pressure heads in the column,

as well as the evaporation rate (and hence the weight of the soil
sample), as a function of time. The data are subsequently usedin the HYPROP-Fit software (Pertassek et al., 2015) to estimate
the hydraulic properties of the assumed porous media, thus
providing a means for testing HMS performance. We also
investigated the use of different potential evaporation rates,
thus providing tests of the robustness of the HYPROP methodfor different soil types and environmental conditions.
THE HYPROP MEASUREMENT SYSTEM (HMS)The HMS setup involves pressure head measurements at two
depths within a standard 5-cm short soil column as water evaporates from the sample surface. Water contents and fluxes are
determined by weighing the sample. Measured pressure heads,
water contents, and evaporation fluxes are subsequently used toderive the water retention and unsaturated hydraulic conductivity functions (Pertassek et al., 2015; Peters and Durner, 2008;
Schindler et al., 2010a). The measurement range at the wet side
is restricted by limitations of pressure transducers to accurately
register very small pressure head differences, reason why it isoften recommended to measure the saturated hydraulic conductivity independently. At the dry side limitations are due to watercavitation in the tensiometers, usually at about –800 cm. Improved tensiometers are now being used that resist cavitation topressure heads as low as –3000 cm or more (Schindler et al.,2010a, b). Major advantages of the HYPROP method are its automation once the system is installed, and the fact that pairs of θ(h)and K(h) are being generated. The latter means that no preselected functional forms of the water retention and/or conductivity curve (such as those the Brooks and Corey or van
Genuchten-Mualem equations) need to be used. Once the data
are obtained, any set of hydraulic functions could potentially beapplied to the data.
Figure 1 shows the setup of the standard HMS system(Schindler et al., 2010a), sometimes referred to also as thesimplified evaporation method, SEM. Pressure heads versus
time are recorded at two locations (1.25 cm and 3.75 cm fromthe evaporating surface), while the evaporation rate is measured

Fig. 1. Schematic of the HYPROP measurement system, HMS (after Schindler et al., 2010a).

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Further tests of the HYPROP evaporation method for estimating the unsaturated soil hydraulic properties
Table 1. Values of the soil hydraulic parameters assumed in this study for relatively fine-textured (F), medium-textured (M), coarsetextured (C), and very coarse-textured (VC) soils, and for three medium-textured media (M1, M2, M3) having different pore- or particlesize distributions (psd) as reflected by the VG parameter n.
Case

Soil texture

F
M
C
VC

Fine
MediumCoarseVery coarse

0.0
0.0
0.0
0.1

M1
M2
M3

Broad psd
Medium psd
Narrow psd

0.0
0.0
0.0

θs
(cm3/cm3)

θr(cm3/cm3)

Ks(cm/day)

L
(–)

10.0
50.0
250.0
1000.0

0.50
0.50
0.50
0.50

Effect of the pore-size distribution, psd (broad to narrow)
0.450
0.016
1.30
50.0
0.450
0.016
1.80
50.0
0.450
0.016
2.50
50.0

0.50
0.50
0.50

θ ( h ) − θr1=mθs − θr1 + α h n 


n
(–)

Effect of soil texture (fine to very coarse)
0.500
0.00801.30
0.450
0.01601.80
0.400
0.03202.50
0.400
0.021910.0

by repeated weighting. Measurements continue until the upper
tensiometer reaches some limiting value (Schindler et al.,2010a). The data are subsequently analyzed from the averagewater content, the pressure head readings of the two tensiometers, and the mean total head gradients between the two tensiometers. We refer to Schindler et al (2010a, b) and Peters et al.
(2015) for detailed descriptions of the setup and the data analysis.
The data in our study were generated by running
HYDRUS-1D simulations, very similar as done by Peters andDurner (2008) and Peters et al. (2015). For most of the simulations we used a spatial discretization involving 61 nodes, withmesh refinement near the sample upper surface to accommodate higher local pressure head gradients during the simulations. More elements were used for soils having a narrow poresize distribution (i.e., large van Genuchten n values). In mostcases we imposed a relatively high potential evaporation rate of
1 cm/day, thus assuming that evaporation may have been enhanced by ventilation (e.g., Wendroth et al., 1993). Imposing
lower potential evaporation rates (e.g., 0.4 or 0.2 cm/day) were
not found to have significant effects on the results, except forslowing the experiments. The potential evaporation rate was
implemented as a system-dependent boundary conditions until
a critical pressure head, hcrit, was reached, after which a constant pressure head is imposed. We used for most cases the
HYDRUS-1D default value of –105 cm for hcrit, except for very
coarse-textured samples for which we used less extreme values
to limit numerical problems. The bottom boundary was a zero
fluid flux condition, while as initial condition we used an equilibrium profile with a pressure head of 4 cm at the bottom of
the 5 cm sample. We assumed that all of the virtual experiments
were carried out at a constant temperature of 20oC. Averagewater contents of the sample as needed for the HMS analysis
were estimated from the initial water content and the calculated
evaporation rates.
Soil hydraulic properties for most scenarios were describedusing the standard van Genuchten-Mualem formulation givenby (van Genuchten, 1980)

Se ( h ) =α(cm–1)(1)(

K ( Se ) = K s Se L 1 − 1 − Se1/ m


m 2

) 

where Se is effective saturation [–], θs and θr are the saturated
and residual water contents, respectively [L3L–3], Ks is the saturated hydraulic conductivity [LT–1], α [L–1] and n [–] are semiempirical shape parameters, m = 1–1/n, and L is a poreconnectivity parameter [–], which we fixed in the HYDRUS1D simulations at 0.5 following the original study by Mualem(1976).
We explored the effects of a wide range of hydraulic parameters values on the HMS results, notably by varying values of
the hydraulic parameters α and n. Table 1 lists only those examples that are specifically discussed in this paper. The examples in Table 1 are separated into two sets covering (1) a rangeof values typical of fine-, medium-, coarse-, and very coarsetextured soils, and (2) several medium-textured samples having
increasingly narrow pore-size distributions as reflected byincreasingly larger n values. Our study assumed the residual
water content, θr, to be zero, except for the very coarse (VC)
example. The analyses would be essentially the same if fixed
non-zero θr values were used. We fixed θr in our study byreasoning that additional independent water retention measurements often are needed (especially for fine-textured media) todefine the very dry side of the hydraulic functions, such as
conventional pressure plate extractor and/or WP4 dew-point
potentiometer measurements (e.g., Gubiani et al., 2012). We
note that Peters et al. (2015) were also concerned about possible vapor flow and other complications in the very dry side of
the hydraulic properties. We decided not to address these issues
within the context of the HMS studies, but to focus instead only
on the hydraulic properties at relatively wet and intermediatewater contents.
We additionally explored the performance of a dual-porosity
soil whose hydraulic properties are described using the composite hydraulic functions of Durner (1994) and Priesack andDurner (2006) for Se(h) and K(Se) given by

S e ( h) =

θ ( h) − θ r
w1
w2
=
+
n1 m1
θs − θr[1+ |α1h| ][1+ |α 2 h|n2 ]m2( w1 S1 + w2 S2 ) {w1α1[1 – (1 – S11/ m ) m ] + w2α 2 [1 – (1 – S21/ m ) m ] }K ( Se ) = K s2( w1α1 + w2α 2 )
L

(2)

1

1

2

(3)

2

2

(4)

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Camila R. Bezerra Coelho, Luwen Zhuang, Maria C. Barbosa, Miguel Alfaro Soto, Martinus Th. van Genuchten

respectively, where Si, αi, ni, and mi (i = 1,2) are the same as in(1) and (2) for the macropore and micropore regions, respectively (or of the fracture and matrix regions if interpreted forunsaturated fractured rock), while w defines the division of theporous medium in macropore and micropore regions. Values ofthe various parameters used in Eqs. (3) and (4) were θr = 0.10,
θs = 0.50, L = 0.50, Ks = 50 cm d–1, w1 = w2 = 0.5, α1 = 0.2 cm–1,
n1 = 2.5, α2 = 0.002 cm–1, and n2 = 2.0.
Once the pressure heads and actual evaporation rates (andhence sample weights) were generated using HYDRUS-1D, the
HYPROP-Fit analysis was applied to the synthetic numerical
data, leading to estimates of the original soil hydraulic parameters. HYPROP-Fit used the root mean square error (RMSE) to
quantify differences between the synthetic (yi) water retention
or unsaturated hydraulic conductivity data, and calculated values (yic) based on the fitted VG curves. RMSE values were
calculated using
np

RMSE =1 n (y − y )
i =1

c
i

2

i

(5)

p

where np is the number of data points, and yi refers to either
water content, θi, or the logarithm of the unsaturated hydraulicconductivity, log(Ki).
RESULTS AND DISCUSSION
Figure 2, 3 and 4 show results for, respectively, the finetextured (F), medium-textured (M) and coarse-textured (C)soils as identified in Table 1. The top left plot in each figure
shows calculated pressure heads, h1(t) and h2(t), of the top andlower tensiometers, respectively, of the HMS setup, while the
top right plot shows the cumulative actual evaporation rate (orcumulative weight loss per cm2 sample area), W(t), as obtainedwith HYDRUS-1D. Calculated pressure heads and evaporation

rates were obtained at regular time intervals (e.g., every 10
seconds during the first hour, every 10 minutes during the next
9 hours, and every two hours after 10 hours). Using values atregular time intervals, as compared to irregular HYDRUS-1D
output times resulting from the self-adjusting numerical time
stepping scheme, was found to produce smoother values of thepressure heads and evaporation rates versus time, leading tomore accurate HMS results. Calculated values of the pressure
heads (as equivalent suctions) and sample weights were subsequently inserted in the HYPROP-Fit software (Pertassek et al.,2015) to generate the water retention and hydraulic conductivity data as shown in the bottom plots of Figures 2, 3 and 4.
Those plots also include the HMS fitted complete VG hydraulicfunctions.
Figure 2 shows the HMS estimated soil hydraulic properties
values and fitted VG hydraulic functions for the fine-textured
soil. As to be expected, the HMS estimated retention data covera limited range of water contents because of limitations imposed on possible tensiometer data. Still the HMS estimated
VG retention parameter values (Table 2) show very good
agreement with the original values (Table 2). Estimated values
for the saturated conductivity (Ks) and the pore connectivity
parameter (L) were reasonably close to the true values. Fixing
Ks to the assumed synthetic value of 10 cm/day produced amuch-improved value of L.
HMS water retention results for the medium-textured soil(M) in Figure 3 show a very nice coverage of the water contents, while the fitted water retention parameters were again
essentially identical to the originally assumed values (Table 2).
The HMS hydraulic conductivity values and fitted curve function were also in excellent agreement with the original values.
In this case there was little reason to fix Ks to the true value
since both Ks and L were estimated very well. This shows thatthe HMS approach worked well for the medium-textured soil,
without an obvious need to obtain independent estimates of Ks.

Fig. 2. HYDRUS-1D predictions of the pressure heads h1(t) and h2(t) and the cumulative weight loss W(t) (top plots) for the fine-textured
soil (F) obtained using the VG parameter values listed in Table 1, and plots of the HMS generated water retention and hydraulic conductivity data, together with the HYPROP-Fit estimated VG hydraulic functions using the parameters for case FH-1 (Table 2).

164

Further tests of the HYPROP evaporation method for estimating the unsaturated soil hydraulic properties

Fig. 3. HYDRUS-1D predictions of the pressure heads h1(t) and h2(t) and the weight loss W(t) (top plots) for the medium-textured soil(M) obtained using the VG parameter values listed in Table 1, and plots of the HMS generated water retention and hydraulic conductivity data, together with the HYPROP-Fit estimated VG hydraulic functions using the parameters for case MH-1 (Table 2).

Fig. 4. HYDRUS-1D predictions of the pressure heads h1(t) and h2(t) and the weight loss W(t) (top plots) for the coarse-textured soil(C) obtained using the VG parameter values listed in Table 1, and plots of the HMS generated water retention and hydraulic conductivity data, together with the HYPROP-Fit estimated VG hydraulic functions using the parameters for case CH-1 (Table 2).

The coarse-textured soil similarly provided excellent results
for soil water retention as shown by the lower left plot in Figure
4 and the HMS estimated retention parameters in Table 2.
However, estimation of the hydraulic conductivity parameters
Ks and L was relatively poor, with the correct values being
overestimated by more than 100%. However, fixing the valueof Ks to its correct values was found to produce very reasonablevalues of L. This shows the importance of obtaining independent estimates of the hydraulic conductivity at or near saturation
for coarse-texture media. Our result for the very coarse medium(VC), to be presented later, further supported this conclusion.

165

Camila R. Bezerra Coelho, Luwen Zhuang, Maria C. Barbosa, Miguel Alfaro Soto, Martinus Th. van Genuchten

Fig. 5. HMS generated results for the hydraulic properties of the medium-textured soils assuming increasingly higher n values indicative of morenarrow pore-size distributions. The plots from top to bottom are for n values of 1.3, 1.8, 2.5, and 10.0 representing cases B, M, N and VC in Table
2, respectively.

Figures 2, 3 and 4 showed results for typical fine-, mediumand coarse-textured soils, with each case having different values of the van Genuchten α and n parameters. We wanted toinvestigate more specifically the effects of varying n values on
the HMS results, while keeping α constant. When n varies fromsmall to large, the slope of the retention curve becomes increasingly steeper as the pore-size distribution becomes narrower.
Figure 5 shows results when the value of n value for the medium-textured soil varies from 1.3 (case B) to 1.8 (M) to 2.5 (N).
Not further included in this figure are the HYDRUS-1D predicted values of heads h1(t), h2(t) and W(t). However, the figure
does contain results also for the very coarse medium (VC)
having an extremely large n value of 10.0. We note that n values of above 10.0 or even higher are not uncommon for somesoils (not necessarily coarse soils) such as golf course sands orother media such as quartz, carbonate sands and certain limestones (e.g., Sakaki et al., 2012; Wang et al., 2016).
The results in Figure 5 show excellent descriptions of thesoil water retention curves of all four soils, but especially whenn increases to the VC case. Again, this was to be expected since
the water retention data cover an increasingly narrower range ofwater contents. HMS estimated water retention data in all cases
essentially duplicated the originally assumed synthetic values(Table 2). However, as n increased, the descriptions of the166

hydraulic conductivity curves deteriorated, with the range of
estimated conductivity values becoming increasingly smaller up
to the VC case where HMS failed to produce any conductivity
data. This indicates that the HMS procedure does not work wellfor the hydraulic conductivity when applied to soils having very
narrow pore- or particle-size distributions.
We further tested HMS performance for several dualporosity soils whose hydraulic properties were described with
Eqs. (3) and (4). Results more or less followed the conclusions
obtained for the other soils in that they were most accurate
when a wide range of water retention and pressure head data
was covered by the tensiometers. Best results were again obtained for relatively small and intermediate values of n. Results
for a typical case are shown in Figure 6, with the fitted
dual-porosity parameters listed in Table 3. For some of thetrials we again fixed the very dry end of the retention curve byassuming that other methods (e.g., WP4 dew point measurements) were used to define that part of the curve. The water
retention parameters were estimated well, even when the valueof the residual water content was also estimated using the HMS
approach. The value of Ks was also estimated well (Table 3).
However, the tortuosity parameter L was poorly estimated, evenwhen Ks was fixed at the original (synthetic) value of 50
cm/day.

Further tests of the HYPROP evaporation method for estimating the unsaturated soil hydraulic properties
Table 2. Values of the HYPROP-Fit estimated soil hydraulic parameters for the various cases considered in this study. F, M, C and VC
represent relatively fine, medium, coarse- and very coarse-textured soils, respectively, as referred to in Table 1, while B, M and N are medium-textured soils representing relatively broad to more narrow pore-size distributions. Assumed hydraulic parameters used in the
HYDRUS simulations are in bold (see also Table 1), while the HYPROP-Fit generated parameters are identified with extra letters andnumbers (e.g., FH-1 and FH-2).
Case

Soil textureθs (cm3/cm3)

F
FH-1
FH-2
M
MH-1
MH-2
C
CH-1
CH-2
CH-3
VC
VCH-1

Fine
Fine
Fine
MediumMediumMediumCoarseCoarseCoarseCoarseVery coarse
Very coarse

0.500
0.499
0.500
0.450
0.449
0.449
0.400
0.399
0.398
0.400*
0.410
0.410

B
Broad
0.450
BH-1
Broad
0.450
BH-2
Broad
0.450*
M
Medium0.450
MH-1
Medium0.449
MH-2
Medium0.449
NNarrow
0.450
NH-1
Narrow
0.450
NH-2
Narrow
0.450*Fixed parameter value in the HYPROP-Fit optimization

α (cm–1)

L (–)
n (–)
Ks (cm/day)
Effect of soil texture (fine to very coarse)
0.008
1.30
10.0
0.50
0.0074
1.32
8.37
0.27
0.0078
1.31
10.0*
0.42
0.016
1.80
50.
0.50
0.0154
1.83
47.8
0.48
0.0154
1.80
50.0*
0.51
0.032
2.50
250.
0.50
0.0318
2.59
812.
1.16
0.0317
2.61
250*
0.56
0.0319
2.57
250*
0.58
0.0219
10.0
1000.
0.50
0.0215
10.0
1000*
5.94
Effect of pore-size distribution (broad to narrow)
0.016
1.30
50.0
0.50
0.0153
1.31
39,6
–0.04
0.0157
1.30
50.0*
0.31
0.016
1.80
50.0
0.50
0.0154
1.83
47.8
0.48
0.0154
1.80
50.0*
0.51
0.016
2.50
50.0
0.50
0.0157
2.52
38.4
0.19
0.0157
2.52
50.0*
0.42

RMSE (θ)

RMSE (log K)–
0.00060.0009–0.00090.0009–0.00150.00150.0016–0.0001

–
0.033
0.041
–
0.042
0.043
–
0.079
0.138
0.144
–
–

–
0.00050.0007–0.00090.0009–0.00040.0004

–
0.013
0.033
–
0.042
0.043
–
0.011
0.029

Table 3. Values of the assumed (DP) and HYPROP-Fit (DPH) estimated soil hydraulic parameters for the dual-porosity soil, and RMSE
values of the optimizations.
Case
DP
DPH-1
DPH-2
DPH-3
DPH-4

θr
(cm3/cm3)
0.100
0.119
0.111
0.094
0.081

θs
(cm3/cm3)
0.500
0.504
0.504
0.500*
0.500*

w1
0.500
0.553
0.448
0.484
0.503

α1
(cm–1)
0.200
0.214
0.216
0.203
0.202

n1
(–)
2.50
2.15
2.15
2.25
2.28

α2
(cm–1)
0.002
0.002
0.002
0.002
0.002

n2
(–)
2.00
2.15
2.09
1.95
1.88

Ks
(cm/day)
50.0
43.6
50.0*
50.0*
50.0*

L
(–)
0.50
–0.083
0.071
0.37
0.50*

RMSE
(θ)
–
0.00150.00150.00150.0015RMSE(log K)–
0.03340.03610.03980.0422*Fixed parameter value in the HYPROP-Fit optimization

Fig. 6. HYDRUS-1D predictions of the pressure heads h1(t) and h2(t) and the cumulative weight loss W(t) (top plots) for the dual-porosity
soil (DP) obtained using the hydraulic parameter values listed in Table 3, and plots of the HMS generated water retention and hydraulicconductivity data, together with the HYPROP-Fit estimated dual-porosity functions using the parameters for case DPH-1 in Table 3.

167

Camila R. Bezerra Coelho, Luwen Zhuang, Maria C. Barbosa, Miguel Alfaro Soto, Martinus Th. van Genuchten

Overall, the dual-porosity examples indicate that reliable estimates will be obtained when the tensiometers and supporting
equipment (possibly WP4) cover a complete range of retention
data. Additional measurements of the saturated conductivity
will help, especially for determining the pore connectivity
parameter L. Still, we were very pleased with the results given
the many DP parameters involved and their possible correlations.
We conclude that the HMS approach is a very attractive addition of the current suite of measurement approaches for thesoil water retention and unsaturated hydraulic conductivity
properties. We were especially impressed by the accuracy andcompleteness of the retention measurements, including for soils
having narrow pore size distributions. The hydraulic conductivity measurements were in most cases very much acceptablealso, especially for relatively fine- and medium-textured soils
characterized by intermediate α and n values.
CONCLUDING REMARKS
The evaporation method has long been used for estimating
the drying branches of the soil hydraulic functions. The
HYPROP measurement system (HMS) is rapidly becoming an
increasingly popular alternative method for measurements ofthe soil water retention and unsaturated hydraulic conductivity
properties. Our tests of the HMS approach parallel results obtained in two earlier studies (Peters and Durner, 2008; Peters etal., 2015) carried out to assess the accuracy of the HMS methodology by using the Richards equation to obtain synthetic datefor use in the HMS analysis, and then to compare results
against the original properties. Our analysis covered a verybroad range of soils, including a soil with a very narrow poresize distribution as reflected by an n value of 10.0. Accurate
estimates were in most or all cases obtained for the soil water
retention curve and its parameters, at least over the range ofretention data used in the HMS analysis. The extremely coarse
medium (VC) with n = 10 gave excellent results for water retention, but failed for the hydraulic conductivity. Except for
relatively fine and intermediate soil textures, most cases do still
benefit from independent estimate of the hydraulic conductivity
at and/or near saturation. Overall, the HMS methodology performed very well and as such constitutes a much-needed addition to current soil hydraulic measurement techniques.
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Received 21 July 2017
Accepted 11 August 2017

Note: Colour version of Figures can be found in the web version of this article.

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