Agricultural Water Management 216 (2019) 294–305

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Agricultural Water Management
journal homepage: www.elsevier.com/locate/agwat

Measuring full-range soil hydraulic properties for the prediction of cropwater availability using gamma-ray attenuation and inverse modelingT

Everton Alves Rodrigues Pinheiroa,b, , Quirijn de Jong van Liera, Leonardo Inforsatoa,
Jirka Šimůnekb
⁎ab

CENA/University of São Paulo, P.O. Box 96, 13416-900, Piracicaba, SP, Brazil
Department of Environmental Sciences, Univ. of California, Riverside, CA, 92521, USA

ARTICLE INFOABSTRACT

Keywords:
Evaporation experimentParameter optimization
Soil hydraulic conductivity
Root water uptake

Accurate knowledge of soil hydraulic properties (K-θ-h) for the entire range of crop available water is essential
for the prediction of soil water movement and related processes by mechanistic models, including the partitioning of surface energy fluxes into transpiration and evaporation and the dynamics of root water uptake,mandatory processes for adjustments of crop water use efficiency. We implemented an experimental and numerical protocol to obtain K-θ-h of eleven soils with a broad spectrum of texture and land use. Measurements ofthe soil water content during evaporation experiments using gamma-ray beam attenuation, a non-invasive
technique, were adopted as an alternative approach to conventional measurements of the soil water pressure
head. Inverse parameter optimization was performed using Hydrus-1D. The optimized K-θ-h functions wereinterpreted with respect to crop available water, where results calculated by a proposed “dynamic” method werecompared with those determined using the conventional “static” criteria with standardized pressure heads. The
evaporation experiment protocol allowed the determination of the K-θ-h relationships by inverse modeling fromnear-saturation to the dry range (∼ −150 m) with satisfactory accuracy. Soil water retention curves of the finetextured soils determined by the conventional method (pressure plates) deviated from those estimated by the
inverse optimization near saturation and in the dry range, with the conventional method predicting larger watercontent values. In terms of crop available water, the “dynamic” method allowed incorporating system characteristics (atmospheric demand and crop properties) and K-θ-h in a process-based way, contrarily to the “static”
method. Considering a specific scenario, for the fine-textured soils the “static” and “dynamic” approaches performed similarly, however, for the coarse-textured soils, they diverged significantly. No tendency could be revealed for crop water availability under different land uses, and, in general, crop available water for soils under
forest use was very similar to their counterparts under agricultural use.

1. Introduction
Soil water is a key element in partitioning of surface energy fluxes
into plant transpiration and soil evaporation (Vogel et al., 2017). It
controls the global net biomass productivity and couples energy andbiogeochemical budgets by the establishment and maintenance of
natural and agricultural ecosystems (Wang et al., 2012; Pinheiro et al.,2018; Minasny and McBratney, 2018). Soil water availability to crops
can be estimated using simple empirical formulations based on theupper and lower limits of available soil water, commonly defined solely
on pressure head values, and thus relegating the dynamic process of soil
water flow in the unsaturated zone. On the other hand, the same empirical formulations can acquire an increased physical meaning if their⁎pressure head threshold values are calculated taking into consideration
properties and variables that control the root water uptake process(e.g., the hydraulic conductivity and hydraulic conductivity gradients,
together with the spatial root distribution and the atmospheric energy
demand). Alternatively, robust simulations of soil water availability
while dynamically linking soil-plant-atmosphere processes by the implementation of state-of-the-art vadose zone hydrology models such as
Hydrus-1D (Šimůnek et al., 2016) and SWAP (Kroes et al., 2017) arehighly desired. In either way, both approaches are dependent on theaccurate assessment of soil hydraulic properties (SHP).
The traditional method to obtain soil water retention properties isbased on establishing a hydrostatic equilibrium between a soil sample
and a porous medium such as a filter paper, fine sand, or a porous

Corresponding author at: CENA/University of São Paulo, P.O. Box 96, 13416-900, Piracicaba, SP, Brazil.
E-mail addresses: pinheiroear@usp.br (E.A.R. Pinheiro), qdjvlier@usp.br (Q. de Jong van Lier), inforsato@usp.br (L. Inforsato), jsimunek@ucr.edu (J. Šimůnek).

https://doi.org/10.1016/j.agwat.2019.01.029
Received 8 August 2018; Received in revised form 30 January 2019; Accepted 30 January 20190378-3774/ © 2019 Elsevier B.V. All rights reserved.

Agricultural Water Management 216 (2019) 294–305

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ceramic, at a certain pressure head. In soil physics labs around theworld, various equipment such as sand boxes, tension tables, andpressure plates are commonly used to subject an initially saturated soil
sample to a series of gradually decreasing pressure heads (Cresswell
et al., 2008; Bittelli and Flury, 2009). The obtained data pairs θ(h) ofpressure heads, h, and soil water contents, θ, are then fitted using someselected analytical model of the soil-water retention function (e.g.,
Brooks and Corey, 1964; Campbell, 1974; van Genuchten, 1980;
Durner, 1994; Groenevelt and Grant, 2004). Although this method does
not provide any information about the unsaturated soil hydraulic conductivity, K(θ), a common practice in many vadose zone hydrologicalstudies is to adopt the Mualem (1976) capillary bundle model together
with independent measurements of the saturated hydraulic conductivity, Ks, and assign a pore connectivity value (λ) of 0.5 as found by
Mualem (1976). However, this practice subjects simulations of soilhydrology-related processes to large uncertainties (Schaap and Leij,
2000; Vereecken et al., 2010), especially in the dry and wet ranges ofsoils with regular and hierarchical pore geometry, respectively.
Models that deal with root water uptake in a detailed manner bynumerically solving the Richards equation with a root water uptake
sink term are highly dependent on unsaturated hydraulic conductivity
functions in the dry range (Javaux et al., 2008; de Jong van Lier et al.,2008, 2015; Cai et al., 2018) and require special attention to soil hydraulic parameterization. One way to reduce the uncertainty caused by
the determination of SHP is to assess soil water retention and unsaturated hydraulic conductivity simultaneously. A well-establishedmethod to do so is to use the inverse parameter estimation of transientwater flow experiments (e.g., Šimůnek et al., 1998; Peters et al., 2015).
The evaporation method is one of the most popular transient flow experiments. Several modifications of this method have been proposed(e.g., Wind, 1968; Schindler, 1980; Wendroth et al., 1993; Šimůnek
et al., 1998; Durner and Iden, 2011) since its introduction by Gardnerand Miklich (1962). In general, the laboratory evaporation method uses
tensiometers that are inserted horizontally or vertically in a soil corethat is placed on a balance. While tensiometers are used to measuretemporal variations of the pressure head in the soil core, a balance isused to determine temporal variations of the actual evaporation rate.
The method is usually limited by the operation range of tensiometers(commonly h > −10 m). Another drawback besides the narrow operation range are constrained measurements in a thin soil layer aroundtensiometer ceramic cups, which are relatively large compared to thesmall soil sample. The contact between sensors and soil may also be
limited, especially in soils that shrink and swell due to a high clay
content or organic matter.
Measurements of the soil water content during evaporation experiments using gamma-ray beam attenuation, a non-invasive technique with high spatial resolution and allowing the use of the same soil
samples throughout the entire process (Luo and Wells, 1992; Oliveira
et al., 1998; Pires et al., 2005; Lobsey and Rossel, 2016), can represent
an alternative approach to conventional measurements of the soil waterpressure head. The main objectives of this study thus are a) to investigate this alternative method for the determination of SHP in soil
samples, b) to interpret the resulting SHP with respect to crop water
availability, and c) to compare crop water availability obtained using a
proposed “dynamic” method with that determined using the conventional criteria of “static” pressure head values that define field capacity(FC) and the wilting point (WP).

according to location where each group of sites (1,2), (3,4), (5,6), (7,8),
and (9,10,11) represents different land uses on nearby and similar soils.
Five undisturbed soil cores (stainless steel cylinders with a height of
7 cm and an internal diameter of 7.4 cm) were collected from two
depths (between 0 and 0.15 m and between 0.3 and 0.45 m) at eachsite. The middle point of the cylinder length corresponds to the middle
depth of each interval. These sampling depths were selected based on
general root length density (RLD) observations performed by deWilligen and Van Noordwijk (1987), who showed that for the majorityof crops the most relevant root zone for root water uptake occurs between the soil surface and a depth of 0.4 m.
2.2. Evaporation experiments
Evaporation experiments were carried out in the lab to determine
unsaturated soil hydraulic properties of each sampled soil layer using
the undisturbed samples. For each soil layer, five replicates were slowly
saturated by capillarity from bottom to top using a 0.01 mol L−1 CaSO4
solution. Once full saturation was reached, the sample bottom wassealed with plastic foil, the soil samples were weighed, and the firstmeasurements of the soil water content were made by determining theattenuation of a collimated gamma-ray beam at five vertical positions,10, 15, 20, 35, and 50 mm below the soil sample surface. These measurements were performed twice at each vertical position, with thesample being turned by 90° between measurements (Fig. 2).
Samples were weighed and soil water contents recorded according
to this protocol each 24 h. The evaporation experiment was ceased
when the weight change during a 24-h period became negligible (< 1 g
d−1, corresponding to an average water content reduction less than
0.0035 m3 m-3 d−1), which usually took about three to four weeks. At
the end of the experiment, the final water content of the soil cores wasdetermined by oven drying at 105 °C.
Gamma-ray attenuation is a well-stablished technique that can beused for measuring soil-water content. Its advantages include the applicability to the entire range of water contents and a high accuracy. As
no sensor needs to be inserted inside the soil core, there is no alteration
at all of the sample structure (Pires et al., 2005). Additionally, unlike
many other measurement techniques, it does not require calibration foreach soil.
In this study, a collimated gamma-ray source of 137Cs with radioactivity of 11.1 GBq and an energy peak of 661.6 keV was used. The
source was coupled with a NaI(Tl) scintillation detector(7.62 × 7.62 cm), which was attached to a photomultiplier tube. A
photon counter was interfaced with a computer, which stores data
automatically. Circular collimators were adjusted and aligned between
a source (diameter 3 mm) and a detector (diameter 4.5 mm). Moredetails about the used gamma-ray attenuation device can be found in
Pires et al. (2005).
The soil core was positioned between the source and the detector.
The gamma-photons passing through the sample were counted by thedetector for 20 s and expressed as photon beam intensity I (m−2 s-1).
The volumetric soil water content, θ, was calculated using the BeerLambert attenuation law (Wang et al., 1975):=

2. Material and methods( )ln I0 Iµw w x(1)

where I0 (m−2 s-1) is the photon beam intensity crossing the experimental unit with oven-dry soil (corresponding to the same soil cores
used during the evaporation phase); μw (m2 kg-1) is the mass attenuation
coefficient of the water fraction for the corresponding radiation energy,
ρw (kg m-3) is the water density, and x (m) is the thickness of the soil
sample.

2.1. Sampling sites
Eleven sampling sites under several land use types and covering abroad spectrum of soil textures typical of a subtropical humid climatezone (Köppen Cwa) in the southeast of Brazil were selected for thisstudy (Fig. 1 and Table 1). Sampling sites can be grouped together
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E.A.R. Pinheiro, et al.

Fig. 1. Geographical locations and aerial images of the sampling sites.

2.3. Hypothetical experiments

and pressure head measurements, θi(ti) and hi(ti), respectively, were
simulated for five positions in a 7 cm high soil column and at potential
evaporation rate of 0.25 cm d−1. The true parameter values of soil
hydraulic properties of Clay and Sandy Loam were obtained from the
ROSETTA module (Schaap et al., 2001). To make the virtual dataset
more realistic, a normally distributed noise with a zero mean and astandard deviation of 1 cm was superimposed on the virtual datasethi(ti), similarly as done by Peters and Durner (2008). The perturbed
hi(ti) values were then converted to θi(ti) using the true sets of soil
hydraulic parameters.

The determination of SHP from a conventional evaporation experiment usually relies on pressure heads, h(t), measured using tensiometers at selected positions in a soil sample. These pressure headmeasurements are used to define the objective function to be minimized
during the inverse parameter optimization process. In our experimental
setup, tensiometer readings were replaced with gamma-ray attenuation
measurements, resulting in water contents rather than pressure heads.
To evaluate the performance of the inverse parameter optimization
process when the objective function (Φ, a sum of squared deviations
between measured and simulated values) is defined in terms of soil
water contents versus time, θi(ti), rather than in terms of conventionalpressure heads versus time hi(ti), a hypothetical evaporation experiment
was simulated using Hydrus-1D.
The sample geometry and measurement positions in the hypothetical experiment were the same as in the real experiment. Water content

2.4. Inverse parameter optimization
Both laboratory and hypothetical soil evaporation experiments were
evaluated using the Hydrus-1D software package (Šimůnek et al.,2016), which simulates one-dimensional variably-saturated water flowin porous media by numerically solving the Richards equation. Hydrus296

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1D additionally implements the Marquardt-Levenberg parameter estimation method for inverse optimization of soil hydraulic parameters.
This method is a gradient-type minimization one, which is sensitive tothe initial estimates (Abbaspour et al., 2001).
Unsaturated soil hydraulic properties were assumed to be describedby the analytical K-θ-h functions defined by the van Genuchten-Mualem
model (Mualem, 1976; van Genuchten, 1980):

Table 1
Particle size distribution, soil texture class, and current land use at the 11
sampling sites.
Site

1
2
3
4
5
6
7
8
9
10
11

Depth
m

Particle size fraction (kg kg-1)
Sand

Silt

Clay

0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45

0.885
0.856
0.835
0.835
0.204
0.221
0.181
0.139
0.481
0.509
0.427
0.388
0.233
0.278
0.202
0.168
0.856
0.845
0.847
0.850
0.856
0.862

0.027
0.031
0.027
0.015
0.167
0.125
0.127
0.106
0.113
0.061
0.092
0.081
0.076
0.055
0.045
0.038
0.031
0.029
0.039
0.024
0.031
0.012

0.088
0.113
0.138
0.150
0.629
0.654
0.692
0.755
0.406
0.430
0.481
0.531
0.691
0.667
0.753
0.794
0.113
0.126
0.114
0.126
0.113
0.126

Soil
textureclass

Land use

Loamy
fine sand
Sandy
Loam
Clay

PastureClay

Sugarcane

Sandy
clay
Clay

Native Forest

Clay

Native Forest

Clay

Annual crops

Loamyfine sandLoamyfine sandLoamyfine sand

Sugarcane= [1 + | h| n ] (1 / n)Sugarcane
Fallow

K = Ks

[1

(1

(2)

1

n / (n 1) )1(3)(1 / n) ] 2
3−3

with = () is ther )/( sr ) is the effective saturation, θ (m mwater content, h (m) is the pressure head, and K (m d-1) is the unsaturated hydraulic conductivity. Six parameters define the SHPs andwill be referred to as the VGM parameters: θr (residual water content),θs (saturated water content), Ks (saturated hydraulic conductivity), andshape parameters α (m-1), n, and λ.
The upper and lower water flow boundary conditions were set as
atmospheric and constant (zero) flux boundary conditions, respectively.
In the analysis of laboratory experiments, the surface evaporation flux
was calculated for each time interval from the observed mass difference
over a time interval and used as a time-variable boundary condition. In
the analysis of hypothetical experiments, the constant potential evaporation rate of 0.25 cm d−1 was used as the upper boundary flux.
Soil water contents measured at five positions versus time were
included in the objective function Φ to be minimized by Hydrus-1D in
the analysis of laboratory experiments. In the analysis of hypothetical

PastureNative Forest
Eucalyptus(planted
forest)Fig. 2. Schematic illustration of the gamma attenuation measurement protocol (5 heights and 2 rotations).

297

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experiments, the perturbed θi(ti) and hi(ti) were used separately to define the objective function Φ. In the case when Φ was defined usinghi(ti), the final total water volume in the soil sample was included in Φ
as well, in order to position the retention curve along the θ axis(Šimůnek et al., 1998).
To avoid physically unrealistic estimates in the analysis of laboratory experiments, the initial set of soil hydraulic parameters was selected using the neural network module ROSETTA (Schaap et al., 2001)
and the parameters optimized using data obtained from pressure plateapparatus experiments. For both soil evaporation experiments (laboratory and hypothetical), the five optimized VGM soil hydraulicparameters were: θs, α, n, Ks, and λ. The residual water content, θr, wasset equal to the final measured value of the soil water content, when thesoil was close to air-dry. For the laboratory experiment, a set of hydraulic parameters was estimated for each of the five replicates. To
transform these five sets of parameters into a single set, the optimized
VGM parameters for each replicate were used to generate 100 values of
K and θ in the pressure head observation range (from −150 to−0.1 m). The resulting 500 data pairs were then processed using the
RETC software (van Genuchten et al., 1991) to generate a unique hydraulic parameter set for each soil layer.

The limiting water content, θlim, and the water content at wilting
point, θwp, can be related to the matric flux potential M, a convenient
property in detailed studies on root water uptake (Raats, 1977; de Jongvan Lier at al., 2008; Pinheiro et al., 2018). M (m2 d−1) is defined as theintegral of the hydraulic conductivity function K(h) (m d−1) over apressure head interval starting at an arbitrary reference pressure headhref (m):hM=Mlim =RMSE =

1
( i
n i=1

2
i*)
¯i )2

(7)
−1

where Mlim (m d ) is the limiting matric flux potential, Tp is thepotential transpiration rate (m d-1), k is the number of soil layers, Li (m)and Ri (m-2) are the thickness and active root length density (RLD) for
layer i. The value of an empirical constant p was calibrated to be equal
to 5.3 when using href = −150 m by Pinheiro et al. (2018). To calculate
Mlim using Eq. (7), the following hypothetical scenario with an active
RLD decreasing with depth is defined: Tp = 4·10-3m d−1, L1 = 0.25 m,
R1 = 100 m-2, L2 = 0.35 m, and R2 = 10 m-2. Using these values, theresulting Mlim equals 2.37 10-4 m2 d−1. The Tp rate was chosen to represent an average subtropical condition under moderate temperature(Allen et al., 1998), while the active RLD values were based on the
scenarios simulated by de Jong van Lier et al. (2006).
To determine the matric flux potential at wilting point, Mwp, Tp in
Eq. (7) was substituted by a minimum (residual) transpiration at wilting
point Twp= fTp, allowing a dynamic prediction of the wilting point. We
used f = 0.01, resulting in Mwp = 2.37 10−6 m2 d-1. The value for factor
f = 0.01 is arbitrary, but was considered reasonable since a residualtranspiration is maintained due to epidermal conductance (water loss
through incompletely closed stomata and cuticular conductance) when
the soil available water has been completely depleted (Sinclair andLudlow, 1986; Sinclair et al., 2005). As discussed in Sinclair andLudlow (1986), this residual transpiration can vary considerably among
species.
M is uniquely correlated to θ and h. The M-θ-h relations are available for several standard soil hydraulic property models (including thevan Genuchten functions) and Mlim or Mwp can be easily converted incorresponding values of water contents or pressure heads.

(4)

n

i*)

pTp
k
LR
i=1 i i2

The mean water content values of the soil cores calculated from thesample weight change over time were compared with the simulated
mean water content values for the same time intervals. The mean watercontent simulated by the Hydrus-1D was obtained by dividing the volume of water in the entire flow domain by the column height. The
accuracy was quantified using the Nash-Sutcliffe efficiency (NSE) androot mean squared error (RMSE) coefficients:
n
( i
i=1
n
( i
i=1

(6)

Pinheiro et al. (2018) proposed to determine the limiting soil hydraulic condition as the onset of the falling rate phase of transpiration.
For a layered soil, they obtained:

2.5. Further verification of the accuracy of the optimized soil hydraulicparameters

NSE = 1

K (h) dh
href

2

(5)

respectively, where n is the number of data points, θi is the measured
value of the mean water content in the soil column at time ti, i*is thecorresponding simulated value by the Hydrus-1D, and i is the meanvalue of the water content over the entire experiment.
2.6. Crop water availability

3. Results and discussion

The optimized soil hydraulic parameters were used to predict the
total and readily available water (TAW and RAW, respectively) of theanalyzed soils. The threshold values for calculating crop water availability are customarily defined as the water content at field capacity(θfc), the upper limit of TAW and RAW, the limiting water content(θlim), the lower limit of RAW, and the water content at wilting point(θwp), the lower limit of TAW. Values of θfc, θlim, and θwp are commonly
calculated using fixed pressure heads. Common pressure head values
used to assess field capacity hfc are −3.3 m or −1.0 m, for hlim are
between −2.0 m and −10 m (Taylor and Ashcroft, 1972), and for hwp
are most commonly assumed equal to −100 m or −150 m.
The approach of determining water content values for field capacity
and critical and wilting point conditions based on fixed pressure heads
will be compared with their estimation using “dynamic” criteria. The
water content at field capacity, θfc, can be determined by simulating adrainage experiment without plants, rainfall, and evaporation using aflux density criterion of 1 mm d−1 (e.g., Twarakavi et al., 2009) at thelower soil boundary (here considered at a depth of 0.6 m). The adopted
criterion of the bottom flux of 1 mm d−1 is reasonable also for tropicalsoils (de Jong van Lier and Wendroth, 2016; de Jong van Lier, 2017).

3.1. Hypothetical experiment
Table 2 shows the overall performance of the parameter optimization with the objective function (Φ) defined in terms of θ(t) or h(t) for
selected initial parameter estimates.
Despite the inserted noise in h(t) and θ(t) used to define the objective function Φ, the inverse solution repeatedly converged to a set ofsoil hydraulic parameters comparable to the original true set, producing
low values of Φ and RMSE for all three initial parameter estimates.
Although some optimized parameters, especially α, showed differenceswith original values, depending on the initial estimate, the general
performance of the inverse solution was quite satisfactory. In general,
both types of Φ produced similar fitted parameter values, indicatingthat the θ(t) dataset contains, similarly to the h(t) dataset, substantial
information for the determination of SHP using the inverse optimization approach (Ritter et al., 2003; Vereecken et al., 2008; Ines andMohanty, 2008; Bourgeois et al., 2016). The lack of exactness for individual VGM parameters does not seem to be an essential issue(Bezerra-Coelho et al., 2018). For instance, Siltecho et al. (2015)298

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Table 2Inverse optimization results for hypothetical evaporation experiments with Clay and Sandy Loam soils and with a normally distributed noise imposed on the virtual
dataset of h(t) and θ(t). Different sets of initial parameter estimates corresponding to different texture classes from ROSETTA (Schaap et al., 2001) were used.
Case

Initial estimate

θr—m3 m−3—

θs

α
m−1

n
−

Ks
m d−1

λ
−

Φ
−

RMSE

True parameters
h(t)
θ(t)
h(t)
θ(t)
h(t)
θ(t)
True parameters
h(t)
θ(t)
h(t)
θ(t)
h(t)
θ(t)

Clay
Clay

0.068
−
−
−
−
−
−
0.065
−
−
−
−
−
−

0.380
0.380
0.380
0.379
0.380
0.360
0.380
0.410
0.410
0.409
0.409
0.409
0.409
0.410

0.800
0.800
0.804
0.760
0.737
0.552
0.549
7.500
7.500
7.436
7.534
7.134
7.487
7.634

1.090
1.090
1.090
1.091
1.091
1.108
1.096
1.890
1.891
1.910
1.893
2.041
1.900
1.834

0.048
0.048
0.048
0.044
0.046
0.024
0.039
1.061
1.064
1.073
1.081
1.186
1.054
1.039

0.500
0.498
0.504
0.472
0.665
0.001
1.181
0.500
0.500
0.523
0.497
0.737
0.490
0.398

−
1.4∙10−6
8.7∙10−6
7.3∙10−6
9.0∙10−6
1.0∙10−3
9.6∙10−6−
8.0∙10−4
6.6∙10−3
8.1∙10−4
7.6∙10−3
8.1∙10−4
6.8∙10−3−
2.6∙10−5 m
5.9∙10-5 m3 m-3
5.9∙10−5 m
6.0∙10−5 m3 m-3
7.7∙10−4 m
6.2∙10−5 m3 m-3−
3.6∙10−4 m
1.0∙10−3 m3 m-3
3.6∙10−4 m
1.1∙10−3 m3 m-3
3.6∙10−4 m
1.0∙10−3 m3 m-3

Silt
Sandy Clay
Sandy Loam
Sandy Loam
Loamy sandSiltdemonstrated that individual values of the VGM parameters, especiallythe parameters n and Ks, are highly dependent on the measurement
technique. However, this individual dependency is not translated into
noticeable differences in further simulations of state variables.
The highest parameter correlation was between α and n whenminimizing Φ[θ(t)], and between α and Ks when minimizing Φ[h(t)](Table 3).
Although the level of uncertainty is expected to be higher forparameters that display a high correlation (Šimůnek et al., 1998), eventhese optimized parameters were close to their true values (seeTable 2). The tortuosity factor (λ), which exhibited a relatively low
correlation with the other parameters, produced the highest deviations
from its true values, both for Φ[θ(t)] and Φ[h(t)]. Initial estimates close
to the true values always produced a good fit. Similar findings using thesame type of Φ were reported by Šimůnek et al. (1998) and Siltecho
et al. (2015), who found that unrealistic fits can be avoided by choosing
initial parameter values reasonably close to their true values.

values, we did not incorporate all final measurements into Φ of Hydrus1D. After performing several tests, we concluded that for the soil
samples and laboratory conditions, 10–12 days of water content measurements were enough to reach pressure heads in the range of −140 to−180 m during the optimization process.
The only VGM parameter not fitted during the inverse simulations
was θr. In general, θr and θs are assumed to be easily determined bydirect measurements. Once determined, they can be either introducedin the objective function in a Bayesian sense or used directly as true
values, reducing the overall parameter uncertainty (Siltecho et al.,2015). Šimůnek et al. (1998) found a high correlation between parameters θr and n and observed a substantial improvement in the inverse
solution when θr was either inserted in the objective function or fixed at
its true value. In our case, as we kept the experiment running until quasi
air-dry conditions, the last recorded value of water content was set as
the true value of θr.
Regarding θs, it may be unrealistic to consider the measured total
porosity to be a proxy for θs for field conditions, because it is very
unlikely for a soil profile, or even a soil sample, to reach the state of fullsaturation due to water repellency and entrapped or dissolved air(Pachepsky et al., 2001; Vereecken et al., 2010). In our experiments, a
low correlation between θs and other parameters was observed for all
soils (ranging from −0.001 to 0.3) and θs was thus kept as a fitting
parameter. Fitted θs values were similar to the measured initial total
water content in the soil samples.
The λ parameter, which is related to the tortuosity and pore spaceconnectivity, is usually assumed to be equal to 0.5 according to Mualem(1976), but its true value is hardly ever determined over the full rangeof pressure heads. Since for inverse parameter optimization problems,
reducing the number of fitting parameters increases the uniqueness andstability of the solution, a fixed λ of 0.5 has often been adopted instudies dealing with parameter optimization (e.g., Šimůnek et al., 1998;
Siltecho et al., 2015; Brunetti et al., 2016). Although the physicalmeaning of λ is frequently questioned (e.g., Vereecken et al., 2010;
Peters, 2013), the unsaturated hydraulic conductivity function (K) is
highly sensitive to λ values (Van Dam et al., 1994; Schaap and Leij,
2000), especially in the near-wilting range, and the standard practice ofusing fixed λ may lead to underpredictions of K and poor simulations ofcrop water availability (de Jong van Lier et al., 2015). For all soil
samples used in this research, fitted λ values were either zero or close tozero (Table 4). Similar results were reported in de Jong van Lier (2017)and Pinheiro et al. (2018) for tropical soils. As discussed in Vereecken
et al. (2010), many studies have revisited the parameter λ and foundvalues strongly deviating from 0.5.
The average Ks for the coarse (sand content > 80%) and fine textured soils was 0.40 ± 0.39 ( ± standard deviation) m d−1 and3.2. Soil hydraulic properties of real soils
Optimized soil hydraulic parameters for all analyzed soils are given
in Table 4. A satisfactory agreement (relatively low standard errors)
was observed between the replicates. This is worth noting because
undisturbed soil samples taken from field sites may naturally exhibit ahigh heterogeneity.
The VGM description of soil hydraulic properties only accounts forthe capillary water retention and conductivity (Peters, 2013) and may
produce an erroneous description in the very dry range. Although theexperiments were carried out for about three weeks, down to very dry
conditions when daily sample weight changes reached negligible
Table 3
Correlation matrix for the inverse solution for the hypothetical experiment(Clay soil) with Φ defined in terms of θ(t) and h(t).
Definition of Φ

Parameter

θs

α

n

Ks

λ

θ(t)

θs
α
n
Ks
λ
θs
α
n
Ks
λ

1.0
0.22
−0.20
0.05
−0.22
1.0
−0.66
−0.41
−0.51
0.53

−
1.0
−0.99
0.48
−0.60
−
1.0
−0.39
0.94
−0.01

−
−
1.0
−0.44
0.64
−
−
1.0
−0.47
−0.57

−
−
−
1.0
0.40
−
−
−
1.0
0.30

−
−
−
−
1.0
−
−
−
−
1.0

h(t)

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Table 4
Optimized van Genuchten-Mualem parameters and statistics of Hydrus-1D inverse solutions: average values of the objective function (Φ) and root mean squared error(RMSE). The values between parentheses are the standard errors representative of the five replicas.
Site

Layer

θr1
——m3 m−3——

θs

α
m−1

n
−

Ks
m d−1

λ
−

Φ
−

RMSE
m3m−3

1

0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45
0.00-0.15
0.30-0.45

0.025 (0.0021)
0.025 (0.0019)
0.042 (0.0010)
0.034 (0.0010)
0.046 (0.0140)
0.069 (0.0072)
0.049 (0.0104)
0.060 (0.0046)
0.042 (0.0060)
0.046 (0.0053)
0.030 (0.0068)
0.028 (0.0095)
0.048 (0.0066)
0.054 (0.0107)
0.053 (0.0154)
0.063 (0.0147)
0.034 (0.0022)
0.031 (0.0041)
0.040 (0.0029)
0.039 (0.0028)
0.036 (0.0011)
0.035 (0.0013)

0.324 (0.0024)
0.320 (0.0024)
0.344 (0.0016)
0.344 (0.0017)
0.395 (0.0011)
0.415 (0.0013)
0.378 (0.0010)
0.372 (0.0010)
0.350 (0.0013)
0.344 (0.0010)
0.362 (0.0010)
0.350 (0.0010)
0.410 (0.0011)
0.415 (0.0020)
0.427 (0.0012)
0.419 (0.0010)
0.290 (0.0015)
0.306 (0.0023)
0.357 (0.0054)
0.368 (0.0040)
0.351 (0.0026)
0.368 (0.0046)

2.221 (0.0930)
2.816 (0.1230)
2.031 (0.0420)
2.693 (0.0480)
0.950 (0.0340)
1.783 (0.0840)
1.379 (0.0480)
1.747 (0.0560)
1.080 (0.0050)
1.400 (0.0290)
0.888 (0.0330)
1.608 (0.0610)
1.482 (0.0600)
1.129 (0.0670)
1.205 (0.0440)
0.783 (0.0210)
2.211 (0.0850)
2.361 (0.1410)
4.272 (0.3800)
2.752 (0.1830)
3.096 (0.0980)
4.738 (0.2340)

1.622 (0.0201)
1.565 (0.0168)
1.788 (0.0091)
2.160 (0.2045)
1.206 (0.0133)
1.180 (0.0066)
1.202 (0.0107)
1.173 (0.0044)
1.242 (0.0094)
1.217 (0.0066)
1.208 (0.0076)
1.197 (0.0100)
1.183 (0.0060)
1.201 (0.0107)
1.192 (0.0126)
1.180 (0.0109)
1.471 (0.0141)
1.397 (0.0180)
1.428 (0.0148)
1.455 (0.0135)
1.817 (0.0188)
1.727 (0.0197)

0.473 (0.0654)
0.520 (0.0721)
0.211 (0.0115)
0.570 (0.0501)
0.070 (0.0100)
0.285 (0.0350)
0.136 (0.0170)
0.150 (0.0130)
0.094 (0.0110)
0.301 (0.0220)
0.096 (0.0100)
0.102 (0.0130)
0.233 (0.0240)
0.293 (0.0460)
0.217 (0.0320)
0.054 (0.0060)
0.515 (0.0590)
0.316 (0.0550)
0.502 (0.1040)
1.586 (0.2420)
0.034 (0.0040)
0.680 (0.1260)

0.100 (0.0639)
0.006 (0.0567)
0.000 (−)
0.028 (0.0358)−0.011 (0.1261)
0.00 (−)−0.015 (0.1005)
0.000 (−)
0.000 (−)
−0.002 (0.0585)
0.000 (−)
−0.010 (0.0934)
0.000 (−)
0.000 (−)
0.261 (0.1443)−0.012 (0.1236)
0.005 (0.0548)
0.013 (0.0828)
0.000 (−)
0.000 (−)
0.040 (0.0491)
0.194 (0.0603)

0.031
0.039
0.017
0.025
0.022
0.023
0.027
0.026
0.025
0.015
0.015
0.022
0.024
0.025
0.041
0.073
0.025
0.039
0.080
0.090
0.048
0.060

0.023
0.029
0.016
0.019
0.020
0.022
0.022
0.025
0.020
0.022
0.021
0.023
0.025
0.028
0.028
0.036
0.021
0.027
0.037
0.039
0.029
0.030

2
3
4
5
6
7
8
9
10
11
1

θr was fixed at its true value during the inverse solutions.

0.15 ± 0.09 m d−1, respectively. Ks showed a positive correlation withα (0.3 to 0.8) and negative correlation with n (-0.2 to -0.9) for most
replicates and for all soil textures. However, the correlation with λ was
low and ranged from negative to positive values. In a broad sense, theparameters n and α are empirical and determine the shape of the retention curve. Van Genuchten (1980) related α to the average poresizes, and a larger α enhances Ks. Šimůnek et al. (1998) also found astrong negative correlation between fitted Ks and the parameter n for a
specific scenario. The drop of the hydraulic conductivity near saturation is controlled by the n parameter to a much higher extent than by
the λ parameter (Vereecken et al., 2010).
In general, several studies have shown that many uncertainties are
involved in the Ks fitting of Eq. (3), and similar to λ, n, and α, Ks must betreated and interpreted as an empirical shape parameter (Schaap andLeij, 2000; Vereecken et al., 2010). In fact, according to Schaap and Leij
(2000), fitted Ks values are usually almost one order of magnitude
lower than independent measurements of the saturated hydraulic conductivity. Eq. (3) does not account for macropore flow, which is expected to take place under pressure head values higher than −10 cm(Jarvis, 2007; Weynants et al., 2009), and therefore, using independentmeasurements of the saturated hydraulic conductivity in Eq. (3) is
problematic.
A very good agreement was found between mean soil water contentsof the soil cores obtained from measured core weight changes over timeand corresponding simulated values. The average values of NSE and
RMSE were 0.956 ± 0.037 and 0.018 ± 0.007 m3 m−3, respectively,
for the coarse-textured soils, and 0.903 ± 0.043 and 0.024 ± 0.005
m3 m−3, respectively, for the fine-textured soils. Since measured valuesof mean water contents obtained during the experiments from weightrecords were not used in the objective function of the inverse solution,
this good agreement indicates that the optimized sets of soil hydraulicparameters can predict transient water flow process in the evaluatedsoils with relatively robustness.
Using Eqs. (2) and (3) together with the optimized VGM parametersfrom Table 4, water contents and hydraulic conductivities for selectedvalues of the pressure head in the range of crop available water were
calculated for the surface layer of the evaluated soils (Table 5). In
general, the known effect of texture on the soil hydraulic behavior canbe readily identified. For coarser textured soils (loamy fine sands), a

sharp drop in θ and K can be observed for pressure heads close to saturation. For these soils, K at h= −150 m reaches values three to fourorders of magnitude lower than for finer textured soils. In terms of root
water uptake in water-limited scenarios, a non-stressed condition is
attained when a local drop in the K value is compensated by an increasein the hydraulic gradient between the bulk soil and the root surface. A
sharp gradient increase will force the root system to exert a very negative pressure head even when the bulk soil is still relatively wet,making the onset of the drought stress (hlim) to occur at a less negative
pressure head (de Jong van Lier et al., 2006; Pinheiro et al., 2018).
Consequently, according to results presented in Table 5, the most restrictive surface soil layer for root water uptake is site 11, having thelowest values of K over an entire dry range of pressure heads. The
importance of K for unsaturated conditions on the root water uptake
process justifies the need of its determination with a good accuracy inthe dry range. De Jong van Lier et al. (2015) showed in detail thatwithout reliable soil hydraulic properties, especially K, drought stresscannot be correctly predicted in most cases.
3.3. Comparison of retention curves obtained using the pressure plateapparatus and the inverse solutions
Retention curves (RC) obtained using the inverse parameter estimation corresponded relatively well to those obtained using the pressure plate apparatus (PPA). Fig. 3 shows four examples of RC obtainedusing the PPA and the inverse solution together with independent pairsof h(θ) measured using a dew point device.
For the coarse-textured soils (sites 1–2 and 9–11), the two approaches produced very similar curves in the entire range of soil watercontents. On the other hand, for fine-textured soils (sites 3–8), RC obtained using the PPA overestimated soil water contents in the dry range.
Dew point measurements performed on independent samples subjected
to a pressure head of −150 m on the PPA for 15, 30, and 100 days
matched values obtained by the inverse solution, suggesting the PPA
values are overestimated at lower pressure heads for fine textured soils(Fig. 3). The three dew point measurements after different equilibriumtimes were practically the same. Several studies discuss errors in low
pressure head values of the RC determined using the PPA, especially forfine-textured soils (e.g., Cresswell et al., 2008; Bitelli and Flury, 2009;300

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Table 5
Water contents and hydraulic conductivities for some values of pressure heads for the surface soil layer of the 11 analyzed soils (values calculated from soil hydraulicparameters in Table 4).
Site

1
2
3
4
5
6
7
8
9
10
11

Pressure head (m)Texture class

−0.1
−1.0
θ (m3 m−3)

−3.3

−10

−150

−0.1
K (m d−1)

−1.0

−3.3

−10

−150

Loamy fine sand
Sandy Loam
Clay
Clay
Sandy Clay
Clay loam
Clay
Clay
Loamy fine sandLoamy fine sandLoamy fine sand

0.315
0.337
0.392
0.373
0.346
0.359
0.404
0.422
0.282
0.333
0.335

0.110
0.108
0.311
0.285
0.260
0.285
0.313
0.332
0.133
0.141
0.083

0.068
0.070
0.263
0.241
0.213
0.238
0.268
0.283
0.093
0.103
0.055

0.033
0.045
0.172
0.161
0.132
0.150
0.183
0.191
0.051
0.060
0.038

1.8∙10−1
1.1∙10−1
1.1∙10−2
1.6∙10−2
1.7∙10−2
1.5∙10−2
2.2∙10−2
2.5∙10−2
1.4∙10−1
6.4∙10−2
1.4∙10−2

3.5∙10−3
2.3∙10−3
9.5∙10−4
9.5∙10−4
1.3∙10−3
1.5∙10−3
1.2∙10−3
1.7∙10−3
3.5∙10−3
6.1∙10−4
9.1∙10−5

9.0∙10−5
4.3∙10−59.9∙10−5
8.4∙10−5
1.2∙10−4
1.6∙10−4
1.1∙10−4
1.6∙10−4
1.4∙10−4
2.3∙10−5
1.3∙10−6

2.4∙10−6
8.6∙10−7
8.3∙10−6
6.7∙10−6
9.1∙10−6
1.3∙10−5
9.0∙10−6
1.2∙10−55.7∙10−6
9.9∙10−7
2.3∙10−8

3.2∙10−10
5.4∙10−11
1.3∙10−8
1.1∙10−8
1.2∙10−82.1∙10−8
1.6∙10−8
1.8∙10−8
2.0∙10−9
4.3∙10−10
1.1∙10−12

0.191
0.197
0.358
0.332
0.309
0.328
0.360
0.381
0.196
0.204
0.155

Solone et al., 2012; Roy et al., 2018). The main causes of PPA errors
reported in these studies are related to a poor soil-plate contact causedby drying, as well as to a low unsaturated hydraulic conductivity.
The difference between curves at near saturation was more evident
for fine-textured soils. The saturation of some of the soil cores used in
the PPA was up to 10–15% higher than of those (300 cm3) used in
evaporation experiments. Samples in evaporation experiments wereabout 5 times larger in volume than PPA samples, and larger samples
are more representative of field conditions, i.e., more prone to water
repellency and dissolved or entrapped air. According to Vereecken et al.
(2010), an accurate description of RC in the wet range remains achallenge due to regular failures in determining the soil water content
close to saturation. Saturated water contents are usually measured in
the laboratory on small soil samples used in the PPA or set equal to thetotal porosity, which is calculated from soil particle and soil bulk
densities. Such values of θs when extrapolated to transient field conditions may lead to unreliable simulations, as reported in Vereecken
et al. (2010), where discontinuities in the non-wetting phase nearsaturation (when air cannot access all the medium) cause worse correlations of the unsaturated hydraulic conductivity with water retention
at water contents higher than 85% of the saturated value.
3.4. Crop water availability evaluated for soils and land use
Soil hydraulic properties determine all processes related to soil
water flow, including drainage and flow towards roots, which is involved in crop water uptake. Nevertheless, threshold values for crop
available water (commonly expressed as field capacity, a transpiration
limiting condition, and a wilting point) are usually predicted using
empirically fixed values of pressure head. In a more process-based anddynamic approach, Table 6 shows a direct application of soil hydraulicparameters (Table 4) to calculate pressure head thresholds that define
crop water availability for a specific scenario of root length density andcrop transpiration.
The pressure head at field capacity (using the 1 mm d−1 bottom flux
criterion) showed a considerable variability among soils and layers,

Fig. 3. Water retention curves obtained using the inverse parameter estimation and the pressure plate apparatus (PPA) together with dew point measurement data.
301

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Table 6
Pressure heads (h) and water contents (θ) corresponding to dynamic criteria for field capacity (q60 = 1 mm d−1), limiting conditions (Mlim = 2.37∙10-4 m2 d−1), andwilting conditions (Mwp = 2.37∙10-6 m2 d−1).
Site

Layer

hfc
hlim
hwp
—————————————m—————————————

θfc
θlim
θwp
————————————m3 m−3——————————

1

0.00-0.25
0.25-0.60
0.00-0.25
0.25-0.60
0.00-0.25
0.25-0.60
0.00-0.25
0.25-0.60
0.00-0.25
0.25-0.60
0.00-0.25
0.25-0.60
0.00-0.25
0.25-0.60
0.00-0.25
0.25-0.60
0.00-0.25
0.25-0.60
0.00-0.25
0.25-0.60
0.00-0.25
0.25-0.60

−1.4
−1.2
−1.3
−1.1
−1.1
−0.9
−0.8
−0.6
−1.5
−1.3
−0.8
−0.6
−1.7
−1.5
−0.9
−0.7
−1.3
−1.1
−1.9
−1.8
−0.8
−0.7

0.166
0.166
0.173
0.116
0.355
0.366
0.339
0.339
0.293
0.289
0.334
0.316
0.358
0.356
0.385
0.397
0.180
0.207
0.168
0.194
0.174
0.163

2
3
4
5
6
7
8
9
10
11

−2.6
−2.1
−1.9
−1.3
−3.6
−3.2
−3.1
−1.9
−3.9
−5.6
−5.2
−1.8
−3.8
−7.7
−4.9
−3.7
−3.4
−2.5
−1.3
−4.5
−0.4
−0.9

−19
−19
−11
−5
−74
−72
−67
−53
−71
−90
−90
−47
−79
−107
−85
−81
−36
−32
−15
−48
−3
−5

ranging from −1.9 m to −0.6 m. However, in general, the −1 mthreshold used in the “static” approach seems to be a reasonable proxy.
Transpiration limiting pressure heads vary from −1 to −8 m, which iscomparable to the order of magnitude used for the value of h3 in the
Feddes et al. (1978) reduction function (see the compilation by Taylorand Ashcroft, 1972) and in the same order of magnitude as the criterionof 70–80% of θfc (Zuo et al., 2006; Shi et al., 2015). Pressure head

0.124
0.130
0.144
0.102
0.308
0.317
0.288
0.305
0.253
0.234
0.266
0.279
0.307
0.285
0.314
0.346
0.132
0.164
0.191
0.143
0.235
0.151

0.054
0.056
0.067
0.048
0.191
0.214
0.181
0.203
0.150
0.150
0.163
0.165
0.199
0.192
0.207
0.231
0.067
0.080
0.093
0.075
0.088
0.067

values at wilting point ranged from −3 to −107 m, with a considerable
variability among soils and layers. As highlighted by Bouma (2018), thecommon value of −150 m for a wilting point (determined in the 1930s)
does not apply for many combinations of crops and soils, where wilting
may occur closer to saturation.
The general effect of the “dynamic” approach can be seen whencomparing the corresponding values of total and readily available water

Fig. 4. Total and readily available water (TAW and RAW) determined using “dynamic” and “static” criteria for pressure head thresholds in the 11 evaluated soils. The
asterisk indicates non-existent RAW in the surface layer.
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The “dynamic” approach not only considers the role of unsaturated
hydraulic properties, but it also allows for the direct analysis of how thetranspiration rate and root length density affect the onset of drought
stress. In the same soil (i.e., the same hydraulic properties), crops with ahigher RLD maintain the water potential at the root surface closer to theaverage pressure head in the surrounding soil since the flux density
toward the root surface to meet the transpiration rate is smaller, andhlim is lower, corresponding to a drier soil (de Jong van Lier et al., 2006;
dos Santos et al., 2017; Pinheiro et al., 2018). The effect of Tp on thelower limits of TAW and RAW determined using the “dynamic” method
is shown in Fig. 6. Higher Tp values lower the soil available water since
the drought stress and the wilting point will occur closer to the upper
limit of field capacity.
The effect of land use on crop water availability was more noticeable for coarse-textured soils (sites 1–2 and 9–11). For fine-textured
soils, the RAW values were practically identical for the same soils withdifferent land use. For three forest sites (4, 7, and 10), contrary to what
would commonly be expected, the RAW values were very similar to thevalues of the neighboring soil under intensive agricultural land use. In
general, forests are assumed to have higher organic matter content(Gajić, 2013), which may affect soil hydraulic properties and enhance
the soil water-holding capacity. Siltecho et al. (2015) found a negligible
influence of different land uses (forest, rubber plantation, and grass) on
soil hydraulic properties. Minasny and McBratney (2018) carried out ameta-analysis investigation and concluded that the effect of organic
matter on total available water was very modest. These authors used“static” pressure heads to retrieve TAW, which may have biased their
final conclusions. As commented by Bouma (2018), soil-water flow inthe vadose zone is a very dynamic process determined mainly by hydraulic properties, root depth, transpiration, and the rainfall pattern.
Therefore, Richards-equation based models require more data, but are
more powerful in combining soil, plant, and climate dynamically thanmodels that apply a simpler approach with fixed threshold values (field
capacity, limiting condition, and wilting point) for crop available water.

Fig. 5. Retention curve for the surface layer of site 9, illustrating differences
between typical water contents and available water (TAW and RAW) obtainedusing the “static” and “dynamic” pressure head approaches.

4. Conclusions
Fig. 6. Effect of potential transpiration on the limiting matric flux potential andthe lower thresholds of RAW and TAW (θlim and θwp) for the soil at Site 9.

Using experimental and numerical protocols for determining soil
hydraulic properties and assessing a process-based estimation of cropwater availability, we conclude that:(TAW and RAW) (Fig. 4). For fine-textured soils (sites 3–8), the TAW
and RAW values calculated using the “static” pressure heads are higher,
although very similar, than the values simulated using the “dynamic”
approach for the chosen scenario. On the other hand, the TAW andRAW values for coarse-textured soils estimated using the “dynamic”
approach are considerably lower than for the “static” method. In thesurface layer of sites 10 and 11 (both coarse-textured soils), θfc was
lower than θlim, causing a non-existing RAW. This fact (i.e., whendrainage quickly produces a water content limiting transpiration) is
physically plausible and may be expected in soils with a higher α and n,i.e., coarse-textured soils (soils with a high macroporosity and narrowpore-size distribution), in which drainage of water leads to a sharp dropin the pressure head. In these soils under rainfed condition, transpiration and crop growth would be always limited, except for a (short) time
period immediately following rainfall. In fact, de Jong van Lier (2017)
showed that a considerable fraction of crop water uptake occurs atwater contents higher than field capacity, and thus a non-existing RAW
does not necessary mean that the crops will always be under stress.
Fig. 5 shows details about the differences depicted in Fig. 4 for site
9. Whereas pressure head thresholds determined using the “dynamic”
approach take into consideration soil hydraulic properties (e.g., retention and unsaturated hydraulic conductivity), rooting characteristics,
and the atmospheric demand, the “static” values are based solely on
empirically determined “traditional” values, making them unable todistinguish between commonly varying features in soil, crops, and atmosphere.

1 An evaporation experiment performed with a non-invasive technique (gamma-ray attenuation) to measure water contents fromnear-saturation (∼ −0.1 m pressure head) to the dry range (∼−150 m) allowed the determination of unsaturated soil hydraulicproperties over the entire range by inverse modeling.
2 The determined soil hydraulic parameters could be employed to
calculate crop available water using the traditional “static” pressure
head method, as well as a multilayer “dynamic” approach.
Considering a specific scenario of atmospheric demand and active
root length density, the “static” and “dynamic” approaches performed similarly for the fine-textured soils. However, for the coarsetextured soils, the two approaches diverged significantly. Overall,
the “dynamic” method allows incorporating important systemcharacteristics (atmospheric demand and crop properties) and soil
hydraulic properties in a transparent (process-based) way, contrarily
to the “static” method.
3 No tendency could be revealed for crop water availability under
different land uses, and, in general, crop available water for soils
under forest use was very similar to their counterparts under agricultural use.
Acknowledgment
This work was supported by the São Paulo Research Foundation(FAPESP) (grant numbers 2016/16128-4 and 2017/17793-4).
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