Agricultural Water Management 288 (2023) 108492

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

Quantifying water and salt movement in a soil-plant system of a corn fieldusing HYDRUS (2D/3D) and the stable isotope method
Yuehong Zhang a, c, Xianyue Li a, c, *, Jiří Šimůnek b, Haibin Shi a, Ning Chen a, Qi Hu aaCollege of Water Conservancy and Civil Engineering, Inner Mongolia Agricultural University, Hohhot 010018, China
Department of Environmental Sciences, University of California Riverside, Riverside, CA 92521, USAc
Collaborative Innovation Center for Integrated Management of Water Resources and Water Environment in the Inner Mongolia Reaches of the Yellow River, Hohhot,
Chinab

A R T I C L E I N F O

A B S T R A C T

Handling editor: Dr R Thompson

Brackish water has been increasingly used worldwide for irrigation to relieve crop water stress. However, crop
yield reductions inevitably occur under uncontrolled irrigation with saline waters, especially in areas withshallow and saline groundwater. It is essential to quantify the movement of soil water and salts in a soil-plantsystem and to optimize irrigation patterns with brackish water to alleviate the harm of salt stress on crop
growth. Therefore, a two-year cornfield experiment was carried out during 2020–2021 to evaluate differences insoil water and salt movement under different irrigation regimes: a) brackish water irrigation with high (HB),
medium (MB), and low (LB) irrigation depths, and b) freshwater irrigation with medium irrigation depths (MF).
Moreover, the HYDRUS (2D/3D) model was used to evaluate soil water contents (SWC), electrical conductivitiesof the saturation paste extract (ECe), and fluxes, distributions, and mass balances of soil water and salts for the
HB, MB, LB, and MF regimes. Meanwhile, oxygen isotope (18O) was used to calibrate and verify the simulation
accuracy of the HYDRUS (2D/3D) model by determining the proportion of water and salt sources in a soil-plantsystem.The results showed that HYDRUS (2D/3D) could precisely capture SWC and ECe under different irrigation
treatments, with the root mean square error (RMSE) of 0.004–0.017 cm3 cm− 3 and 0.023–0.372 dS m− 1 for SWC
and ECe, respectively. The highest differences in SWCs and ECe in plots under brackish water and freshwater
irrigations occurred in the 0–20 cm soil layer. The stress areas in the soil profile due to water and salt stresses
under MB decreased and increased by 1.8 cm2 and 2010.0 cm2, respectively, compared with MF, accounting for
0.04% and 40.2% of the root zone. However, average root water uptake (RWU) in both years under MB
decreased by 1.9% compared to MF. Additionally, RWU showed a nonlinear relationship with irrigation depth
when brackish water was used for irrigation. The highest RWU occurred under MB, where the average RWU inboth years increased by 7.7% and 12.4% compared with HB and LB, respectively. Therefore, the MB treatment
could be recommended to increase crop yield and alleviate the freshwater shortage in agricultural production.
Moreover, the findings of this study improve our understanding of the mechanisms of soil water and salt
movement and groundwater contributions in a system under brackish water irrigation with different irrigation
depths.

Keywords:
Brackish water
Stable oxygen isotope
The proportion of water and salt
Water and salt movement
Corn yield
HYDRUS

1. Introduction
The shortage of freshwater resources represents a "bottleneck" forsustainable agricultural development in arid and semi-arid regions (Sacoet al., 2007; Zhang et al., 2019; Ortiz and Jin, 2021). However, there is alarge number of brackish water resources in most arid and semi-arid
regions (Liu et al., 2022), such as in Afghanistan (Ragab and Christel,2002), Spain (Aparicio et al., 2019), Mexico (Ozturk et al., 2018), andChina (Chen et al., 2022b). For example, the Hetao irrigation district ofChina has about 8.9 billion m3 of brackish water. Therefore, brackish
water has been widely recommended to replace freshwater as an irri­
gation water source to relieve the shortage of freshwater (Jabeen et al.,2022; Fakharany and Salem, 2021). However, the reduction in crop
yield inevitably occurs when irrigation with brackish water is used dueto the accumulation of soil salts in the crop root zone (Bonachela et al.,2022). Therefore, to alleviate a crop growth reduction due to salt stress,* Corresponding author at: College of Water Conservancy and Civil Engineering, Inner Mongolia Agricultural University, Hohhot 010018, China.
E-mail address: lixianyue80@126.com (X. Li).
https://doi.org/10.1016/j.agwat.2023.108492
Received 25 June 2023; Received in revised form 21 August 2023; Accepted 23 August 2023
0378-3774/© 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).

Y. Zhang et al.

Agricultural Water Management 288 (2023) 108492

it is essential to quantify the movement of soil water and dissolved salts
in a soil-plant system under brackish water irrigation to optimize irri­
gation patterns with brackish water.
Specific impacts of brackish water irrigation have been studied in theliterature, such as on evapotranspiration (ET), crop yield, and waterproductivity (Cova et al., 2020; Fakharany and Salem, 2021; Lima et al.,2021). For example, ET of Hordeum vulgare in the high-salinity irriga­
tion water (ECiw=10 dS m− 1) treatment was 9.6% lower compared to thelow-salinity irrigation water (ECiw=0.8 dS m− 1) treatment in2015–2016 (Ozturk et al., 2018). Wheat yield and water productivity
under brackish water irrigation (ECiw=1.31 dS m− 1) in the 2017–2018
season decreased by 21.1% and 18.8%, respectively, compared to canalwater (i.e., freshwater) irrigation (Arshad et al., 2022). The movementof soil water and dissolved salts in the soil profile under brackish water
irrigation has also been studied in the literature. For example, Selim
et al. (2012) reported that the highest soil salt concentrations wererecorded between 50 and 70 cm below the soil surface in the tomato
field under brackish water irrigation with ECiw of 1 dS m− 1. However,
the impacts of groundwater salinity on the dynamics of soil water anddissolved salts in a soil-plant system were hard to quantify. This ismainly because the movement of soil water and salts in such a system
under brackish water irrigation is very complex, especially in areas withshallow and saline groundwater since soil water and salts in the crop
root zone are simultaneously affected by irrigation water and ground­water (Hosseini and Bailey, 2022). The dilution ratio in the crop rootzone would increase after irrigation since soluble salts would be dis­solved in soil water and migrate into the deeper soil (Che et al., 2022).
However, the soluble salts from shallow groundwater and deep soil
would also migrate to the crop root zone during non-irrigation periods
due to the capillary action against the direction of the soil water po­
tential gradient (Singh et al., 2021). Therefore, it is complicated toquantify the transport of soil water and salts in a soil-plant system underbrackish water irrigation.
Many techniques and methods can be used to accurately trace soil
water and salt dynamics, including long-term monitoring utilizing aseries of sensors (Bañón et al., 2019), labeling Deoxyribonucleic Acid
(DNA) (Zong et al., 2018), stable isotope tracers (Kohfahl et al., 2008),
and numerical models (Shah et al., 2021). However, many sensors areneeded due to soil spatial heterogeneity (Satoh and Kakiuchi, 2021).
Similarly, DNA labeling is associated with high costs and complicatedimplementation methods (Derbyshire et al., 2022).
On the other hand, isotopes are natural tracers that can precisely
trace sources of soil water and root water uptake (Dawson and Ehler­
inger, 1998; Asbjornsen et al., 2007; Wu et al., 2018; Tokarev et al.,2022). For example, Penna et al. (2020) studied water sources for cornroot water uptake using the stable isotope tracer technology and indi­cated that water mainly came from the 0–80 cm soil layer. Xu et al.
(2021) further found that about 68% of water in the spring corn stem
comes from the 40–60 cm soil layer.
However, the stable isotope tracer technology cannot continuously
monitor the source of root water uptake and the movement of soil waterand salts. Additionally, using a larger number of field monitoring points(than we did) would be highly time-consuming and costly, and the soil
profile would likely be more disturbed. Numerical models provide aquick and convenient way to quantify the migrations and distributionsof soil water and salts under different complex conditions. Among manyother models, the HYDRUS (2D/3D) model has been widely used tocapture the dynamics of soil water and salts, mainly due to its flexibility
in handling various boundary conditions, the friendly graphical userinterface, and the capacity to accurately reproducing field results (Chenet al., 2020; Khan et al., 2022). For instance, Ramos et al. (2011) eval­uated the effects of using synthetic saline water and freshwater on soil
salt movement in a corn field using the HYDRUS model and found thatthe soil salinity increased considerably after saline water irrigation anddecreased during the rainfall period due to salt leaching. Phogat et al.
(2018) quantified salinity dynamics in the root zone of almonds undersprinkler irrigation using the HYDRUS model and found that the averageroot zone ECe remained above the salinity tolerance threshold of al­
monds. Devkota et al. (2022) reported that soil salinity in the root zoneof the rice-wheat and cotton-wheat systems increased by 78% and 66%,
respectively, with increases in irrigation water salinity and evaporation
rates based on the long-term scenarios analysis. Feng et al. (2023) usedthe HYDRUS model to simulate water flow and salt transport for furrow
irrigation and indicated that ECe increased when ECiw was higher than
4.0 dS m− 1 below the drain depth of 80 cm. Ramos et al. (2023) assessed
the soil salinization risks in commercial orchards in southern Portugal
using the HYDRUS model and found that salinity stress did not reach aharmful level for plants even though salts tended to accumulate in theroot zone under the current climate conditions and a given irrigationwater quality. Ramos et al. (2023) recommended that tailored irrigation
solutions should be considered to alleviate salt stress in dry and very dry
years. Zhang et al. (2022) found, using the simulation result generated
by the HYDRUS (2D/3D) model, that a "semicircular low-salt wettingzone" was formed after brackish water irrigation.
However, the HYDRUS (2D/3D) model cannot be easily used todetermine the water sources for root water uptake. Using the model todetermine the contributions of irrigation and groundwater to root water
uptake is also challenging. Thus, the innovation of this study is thequantification of the water and salt dynamics in a soil-plant system
under brackish water irrigation by a combined use of stable isotope
tracers and the HYDRUS (2D/3D) model and the formulation of an
optimal irrigation schedule for irrigation with brackish water.
Therefore, the objectives of this study are: i) to calibrate and validate
the HYDRUS (2D/3D) model using multiple types of data, including soil
water, salts, and stable oxygen isotope; ii) to quantify the soil water andsalts dynamics, fluxes, and two-dimensional distributions under
different irrigation depths of brackish water; and iii) to determine theproportions and balances of soil water and salts in the soil-plant systemand crop yield under brackish water irrigation with different irrigation
depths.
2. Material and methods
2.1. Experimental site and design
A field experiment was conducted at the Jiuzhuang experiment site(40◦ 41’N, 107◦ 18’E), Inner Mongolia, China, during the 2020–2021
seasons. The area is in the warm temperature zone, with a mean accu­
mulation of sunshine hours of 3230 h. The mean annual precipitationfrom 1956 to 2020 was 139 mm. Potential evaporation measured using
the standard E601B evaporation pan made of fiberglass (with a diameterof 0.6 m and a depth of 0.6 m) reached 2332 mm. The average per­centages of sand, silt, and clay in the 0–100 cm soil layer were 5%, 70%,
and 25%, respectively. Thus, the soil texture at the experimental site wasclassified as silty loam based on the USDA soil triangle (United States
Department of Agriculture, 2010). The bulk density, field capacity, andwilting point within the 0–100 cm soil layer were 1.42 g cm3, 0.36 cm3
cm− 3, and 0.12 cm3 cm− 3, respectively. A completely random design
was adopted with four irrigation treatments and three replicates.
Therefore, the field was divided into 12 plots (Fig. 1). Each plot was 7.7
m wide and 20 m long, separated by a 3 m wide bar. Corn seeds (Zeamays L, cv. Junkai 918) were sown in early May (in 2020 and 2021) andharvested at the end of September. Seeds were planted 3.0 cm deep,
spaced at 30 cm at 4.5 seeds m− 2 into north-south oriented rows. The
spacings between paired rows and between pairs of rows were 50 and
70 cm, respectively. One drip line was introduced between two cornrows. The paired rows were mulched by plastic film, and the space be­
tween pairs of rows was not mulched (i.e., bare area) (Fig. 1). Brackish
groundwater with an average salinity (ECiw) of 3.7 dS m− 1 was used as
an irrigation source. The average groundwater table fluctuated from126 cm to 220 cm during the entire crop-growing season.
Meanwhile, a locally recommended brackish water irrigation depth2

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Agricultural Water Management 288 (2023) 108492

Fig. 1. The layouts of the experimental plot (a) and the planting pattern (b).

(23 mm) was adopted in this study based on the method proposed by
FAO29 (Ayers and Westcot, 1976), denoted a medium irrigation depth(MB). The leaching fraction of the brackish water irrigation treatment
was 0.185. The irrigation upper and lower limits under the MB treat­ment were 90% and 73% of field capacity, respectively, i.e., irrigation
was applied when the soil water content was less than 73% of field ca­
pacity. Additionally, the recommended irrigation depth was either
increased or decreased by 33.0% (7.5 mm) in the brackish groundwater
irrigation treatment, leading to the HB (30 mm) and LB (15 mm) sce­narios, respectively. To control the single variable, freshwater with anaverage salinity of 0.91 dS m− 1 was adopted as a control treatment withthe same irrigation depths as MB (MF). The irrigation schedules in the
HB, LB, and MF treatments were the same as in MB. A total of 12 irri­
gation events were performed during the crop-growing seasons (Fig. 2).

2.2. Measurements and calculations
Meteorological data, including air humidity, air temperature, rain­
fall, solar radiation, atmospheric pressure, and wind speed at a 2-m
height, were collected at a one-hour interval using an automatedmeteorological station (Onset Computer Inc., U30, Hobo, USA) locatedat the experimental site.
An automatic water level data logger (Onset Computer Inc.; U20L01, Hobo, USA) and an automatic water conductivity data logger(Onset Computer Inc.; U24–001, Hobo, USA) were installed in an
observation well in each plot to monitor the groundwater level and its
electrical conductivity. Data were averaged and recorded at one-day
intervals and stored in a data logger.
The soil water content (SWC) was measured using two TIME probes(IMKO GmbH Inc.; IPH, TRIME-PICO, Germany) installed in each plot in
the middle of the area under plastic film mulching and in the middle ofthe bare area (i.e., no mulching area) (Fig. 3) (Dalton and van

Fig. 2. Cumulative irrigation depth, rainfall (a, b), potential evaporation (Ep), potential transpiration (Tp), and the groundwater level (c, d) at the experimental site
during the crop growth seasons of 2020 (left) and 2021 (right).
3

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Agricultural Water Management 288 (2023) 108492

where Q is a flow quantity (cm3 d− 1), C is the isotopic composition, a
subscript t refers to water mixed from two sources, and subscripts u and v
refer to two different water sources, respectively.
The water flux ratio from sources u (Qu) and v (Qv) was determined by solving Eqs.
(2–3):Qu (δv − δt )=Qv (δt − δu )(4)

Similar to Eq. (4), the water flux ratio from source u (Qu) to thesource mixed from two sources (Qt) was determined as follows:
Qu (δt − δv )=Qt (δv − δu )where δt, δu, and δv are the ratios of δ2H or δ18O in water sources of t, u,and v (‰), respectively.
To quantify water and salt exchanges in the vertical and horizontal
directions, water sources were divided into eight types, i.e., (i) waterfrom the 0–40 cm soil layer under the entire soil surface (i.e., including
the mulched area and bare area) (WS 0–40), (ii) water from below the
40–100 cm soil layer under the entire soil surface (WS 40–100), (iii) waterfrom the 100–140 cm soil layer under the entire soil surface (WS 100–140),(iv) water from the 0–100 cm soil layer below the bare area (WB), (v)water from the 0–100 cm soil layer below the mulched area (WM), (vi)groundwater (WG), (vii) irrigation water (WI), and (viii) root water
uptake (WR). WS 0–40, WS 40–100, WS 100–140, WG, WI, and WR were used toquantify vertical water and salt fluxes, and WB and WM were used toquantify the horizontal water and salt fluxes.
The mutual contributions between WS 0–40, WS 40–100, WS 100–140, andWR were calculated using the following equations:()δWS0− 40 − δWI
QR=(6)(δWI − δR )QWS0− 40

Fig. 3. A schematic representation of the modeling domain, boundary condi­
tions, observation points, and sensor locations. The modeling domain was
divided into six zones, i.e., the 0–40 cm soil layer under the mulched area (I),the 40–100 cm soil layer under the mulched area (II), the 100–140 cm soil layer
under the mulched area (III), the 0–40 cm soil layer under the bare area (VI),the 40–100 cm soil layer under the bare area (V), and the 100–140 cm soil layer
under the bare area (IV).

Genuchten, 1986). The SWC measurements using the TIME probes weretaken at soil depths of 0–20, 20–40, 40–60, 60–80, 80–100, and
100–140 cm every 5–7 days. Moreover, the gravimetric method wasused to verify moisture probes once every 7–14 days.
Sampling locations and intervals for measuring the electrical con­ductivities of the saturation paste extract (ECe) and isotope concentra­
tions (using the gravimetric method) were the same as for SWCs. ECe
was determined by the saturated paste method (Rhoades, 1993) and wasmeasured by a standard conductance meter (Shanghai Youke Instrument
and Meter Co., Ltd.; DDS-307A, CHN).
Isotope measurements included irrigation water, soil water, rainfall,groundwater, and corn stem water. 100 mL of irrigation water andgroundwater were collected to determine isotopes after irrigation. 15 gof rootless soil was placed into a ziplock bag with parafilm to prevent
evaporation and used to determine the isotopes of soil water. The corn
stem was collected before and after irrigation and cut into smaller seg­ments. Then, crop samplings were placed inside a ziplock bag todetermine the isotopes of corn stem. The soil and corn stem samples’
water were extracted using a cryogenic vacuum distillation system (LI2000, LICA United Technology Limited, China) (Ehleringer andOsmond, 1989). The isotopic measurements for irrigation water, soil
water, rainfall, groundwater, and corn stem water were carried out
using a water vapor isotope analyzer (PICARRO L2140-I, Picarro, Santa
Clara, USA). The isotope compositions (δ2H and δ18O) were calculated asfollows:() ()
Rsampleδ18 O orδ2 H =− 1 × 1000
(1)
Rstandard(2)

Q t Ct = Q u Cu + Q v Cv

(3)

(
)
δWS0− 40 − δWI
QWS40− 100)=(
QWS0− 40
δWI − δWS40− 100

(7)

(
)
δW
− δWS100− 140
QWS0− 40)
= ( S40− 100
QWS40− 100
δWS100− 140 − δWS0− 40

(8)

(
)
δW
− δWS0− 40
QWS100− 140)= ( S40− 100
QWS40− 100
δWS0− 40 − δWS100− 140(9)where QR/QWS 0–40 is the contribution rate of the corn stem water to soil
water from the 0–40 cm soil layer, QWS 40–100/QWS 0–40 is the contri­
bution rate of soil water from the 40–100 cm soil layer to soil water fromthe 0–40 cm soil layer, QWS 0–40/QWS 40–100 is the contribution rate ofsoil water from the 0–40 cm soil layer to soil water from the 40–100 cm
soil layer, QWS 100–140/QWS 40–100 is the contribution rate of soil waterfrom the 100–140 cm soil layer to soil water from the 40–100 cm soil
layer, δWS 0–40 is the isotopic ratio of δD or δ18O of soil water from the
0–40 cm soil layer (‰), δWS 40–100 is the isotopic ratio (‰) of δD or δ18Oof soil water from the 40–100 cm soil layer (‰), δWS 100–140 is the iso­
topic ratio (‰) of δD or δ18O of soil water from the 100–140 cm soil
layer (‰), and δWI is the isotopic ratio (‰) of δD or δ18O of irrigationwater.
Similar to Eqs. (6–9), the mutual contributions between WS 40–100,
WS 100–140, WB, and WM were calculated using the following equations:
(
)
δW
− δWG
QWS40− 100)(10)= ( S100− 140
QWS100− 140
δWG − δWS40− 100

where 2H and 18O represented the isotopes of hydrogen (H) and oxygen(O), respectively, Rsample and Rstandard are isotope ratios of 2H or 18O of
the water sample and standard water (Vienna Standard Mean Ocean
Water), respectively, and the analytical precision is less than 0.1‰.
According to the laws of mass conservation (Trenberth, 1991) and
Moore (Chien and Karamcheti, 2013), the contribution rates of different
water sources can be calculated as follows:
Qt = Qu + Qv

(5)

QWB
(δWM − δWI )=(δWI − δWB )
QWM

4

(11)

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Agricultural Water Management 288 (2023) 108492

QWM(δWB − δWG )=(δWG − δWM )QWB

using the dual Kc method (Allen et al., 1998):(12)

where QWS 40–10/QWS 100–140 is the contribution rate of soil water fromthe 40–100 cm soil layer to soil water from the 100–140 cm soil layer,
QWB/QWM is the contribution rate of soil water from the bare area to soil
water from the mulched area, QWm/QWB is the contribution rate of soil
water from the mulched area to soil water from the bare area, δWG is theisotopic ratio of δD or δ18O in groundwater (‰), δWP is the isotopic ratioof δD or δ18O of soil water from the mulched area (‰), and δWB is theisotopic ratio of δD or δ18O of soil water from the bare area (‰).
Soil water fluxes in different zones were determined based on thecalculated contribution rate from Eqs. (6− 12) and soil water content:)(
QWS40− 100
QWS0− 40
Wf40 = 10(13)
θ0− 40 H0− 40 −
θ40− 100 H40− 100
QWS0− 40
QWS40− 100)(
QWS100− 140
QWS40− 100
Wf100 = 10
θ40− 100 H40− 100 −θ100− 140 H100− 140
QWS40− 100
QWS100− 140(
WfM− B = 10H0− 100

QWB
QWM
θM −
θB
QWM
QWB

(14)
(15)

(23)

{

(

)

(

)}

(
−

)

∂qx c ∂qz c
+
∂x
∂z

(25)
where θ is the soil water content (cm− 3 cm− 3), h is the pressure head(cm), K(h) is the unsaturated hydraulic conductivity (cm day− 1), S isroot water uptake (day− 1), c is the solute concentration (mg cm− 3), Dxx,Dzz, Dxz, and Dzx are the components of the effective dispersion coeffi­
cient tensor (cm− 2 day− 1), qx and qz are the components of the volu­
metric flux density (cm day− 1), t is time (day), x is the horizontal
coordinate (cm), and z is the vertical coordinate (cm).
Root water uptake in Eq. (24) was computed using the Feddes model(Feddes et al., 1978) that considers water and salinity stresses
simultaneously:{Tpωω > ωc
S(h, hφ , x, z) = α(h, hφ )b(x, z) , ω =(26)
ωc ω < ωcω

(18)

where α(h, hφ) is the simultaneous stress response function repre­
senting water and osmotic stresses (-), b(x,z) is the normalized distri­bution of root density in the two-dimensional soil domain (cm− 2), andω is a dimensionless water stress index. The water stress reduction
function of Feddes et al. (1978), the threshold and slope function ofMaas (1990), and the compensation approach of Jarvis (1989) wereadopted to represent water and salt stresses, respectively.
The soil hydraulic functions θ(h) and K(h) in Eq. (24) were describedusing the van Genuchten model (van Genuchten, 1980):⎧⎪⎨ θr + θs − θrn m h < 0[1 + |αh| ]θ(h) =(27)⎪⎩
θs h ≥ 0

where Sf40 and Sf100 are the soil salt fluxes at the 40 and 100 cm soil
depths (mg cm− 2 d− 1), respectively, Sf M-B is the soil salt flux between
bare and mulched areas (mg cm− 2 d− 1), c0–40, c40–100, c100–140, cB, and cP
are the salt concentrations in the 0–40, 40–100, and 100–140 cm soil
layers, the bare area, and the mulched area (mg cm− 3), respectively. The
salt concentration in Eqs. (16–19) was calculated as follows (Allen et al.,1998):(19)

where c is the salt concentration (mg cm− 3), and ECe is the electricalconductivity of the saturation extract (dS m− 1).
Reference crop evapotranspiration (ET0) was calculated using the
FAO56 Penman-Monteith equation (Allen et al., 1998):
0.408Δ(Rn −Δ + γ(1 + 0.34u2 )Ep = Ke ⋅ET0

∂θc
∂
∂c
∂c
∂
∂c
∂c
=
θDxx + θDxz+
θDzx + θDzz
∂x
∂z
∂t
∂x
∂z
∂x
∂z

(17)

ET0 =

(22)

The HYDRUS (2D/3D) model (Šimůnek et al., 2016; Šimůnek et al.,2018) was used to simulate the movement of water and soluble salts inthe soil-plant system under different irrigation depth treatments. The
variation in the ion composition of irrigation water during fertigation
was neglected in the modeling. The Richards equation and theconvection-dispersion equation were used to solve water flow and solutetransport in the model, respectively:
[
]
[
(
)]
∂θ ∂
∂h
∂
∂h
(24)
=
K(h)
+
K(h)
+ 1 − S(h, hφ )
∂z
∂t ∂x
∂x
∂z

(
)
QW
QWS40− 100
Sf100 = 10 c40− 100 S100− 140 θ40− 100 H40− 100 − c100− 140
θ100− 140 H100− 140
QWS40− 100
QWS100− 140900G) + γ T+273
u2 VPDTp = Kcb ⋅ET0

2.3. HYDRUS (2D/3D) model

where Wf40 and Wf100 are the soil water fluxes at the 40 and 100 cm soil
depths (mm d− 1), respectively, Wf M-B is the soil water flux between thebare and mulched areas (mm d− 1), θ1, θ2, θ3, θB, and θM are soil watercontents in the soil layers of 0–40, 40–100, and 100–140 cm, the barearea, and the mulched area (cm3 cm− 3), respectively, and H is the soil
depth (cm).
Soil salt fluxes were determined based on soil water fluxes calculated
by Eqs. (13–15):()
QW
QWS0− 40
Sf40 = 10 c0− 40 S40− 100 θ0− 40 H0− 40 − c40− 100
θ40− 100 H40− 100(16)
QWS0− 40
QWS40− 100

c = 0.64ECe(21)

where Ke is the soil evaporation coefficient, and Kcb is the basal crop
coefficient.

)

(
)
QW
QW
SfM− B = 10H0− 100 cP B θM − cB M θB
QWM
QWB

ETp = Ep + Tp

⎡

⎛

⎞m ⎤2

1
θ − θr⎢⎜⎟ ⎥K(h) = Ks ⋅Sle ⎣1 − ⎝1 − Se ⎠ ⎦ , m = 1 − , Se =n
θ s − θr
1
m

(20)

(28)

where θs is the saturated volumetric water content (cm3 cm− 3), θr is
the residual volumetric water content (cm3 cm− 3), Ks is the saturated
hydraulic conductivity (cm day− 1), α (cm− 1), n (-), and m (-) areempirical parameters, Se is the effective saturation (-), and l is the poreconnectivity parameter (-).

where Rn is net radiation (MJ m− 2 day− 1), G is the soil heat flux density(MJ m− 2 day− 1), T is the air temperature at a 2 m height (◦ C), u2 is thewind speed at a 2 m height (m s− 1), VPD is the saturation vapor pressure
deficit (kPa), Δ is the slope of the vapor pressure curve (kPa ◦ C− 1), and γ
is a psychrometric constant (kPa ◦ C− 1).
Potential crop evapotranspiration (ETp) was divided into potential
transpiration (Tp) and potential evaporation (Ep) (Fig. 2), which were
determined by multiplying ET0 by the crop coefficient (Kc) obtained5

Y. Zhang et al.

Agricultural Water Management 288 (2023) 108492

2.4. Initial and boundary conditions and auxiliary lines

Table 1
Adjusted basal crop coefficients during the initial (Kcb ini adj), middle (Kcb mid adj),
and late (Kcb late adj) crop growth stages, the fraction of the surface wetted byirrigation (fw irrigation), the fraction of the surface wetted by rainfall (fw rainfall),the maximum depth of water that can be evaporated from the surface soil layer(TEW), readily evaporable water (REW), the evaporation depth (Ze), the mean
crop height (hc), the mean daily minimum relative humidity (RHmin), the mean
wind speed at the 2-m height (u2), and the lengths and dates of different crop
growth stages.

A two-dimensional area 220 cm deep and 55 cm wide was defined as
the modeling domain. The initial SWC and the electrical conductivity ofsoil water (ECsw) calculated from the measured ECe (ECsw = 2ECe) (Ayers
and Westcot, 1976) were specified in the modeling domain based on
their actual distributions. The initial SWC and ECe values were obtainedby measurements one day before sowing.
Four boundary conditions were defined, i.e., on the upper boundary,
the bottom boundary, the left lateral boundary, and the right lateralboundary (Fig. 3). The upper boundary was divided into three parts torepresent the emitter (0–2 cm away from the dripper), the mulched area
(i.e., the area under plastic film mulching, 2–35 cm away from thedripper), and the bare area (no mulching area, 35–55 cm away from thedripper) (Fig. 3). The emitter and the mulched area were assigned the"time-variable flux" and "no-flux" boundary conditions, respectively. The
bare area was assigned an "atmospheric" boundary condition. Rainfall
and potential evaporation fluxes were provided for the "atmospheric"boundary condition. The potential transpiration flux was associatedwith the entire surface boundary and distributed over the root zone
using the normalized distribution of root density (see Eq. 26). The bot­tom boundary was assigned the "time-variable head" boundary condi­tion representing the shallow groundwater level. The two lateralboundaries were assigned "no-flux" boundary conditions. The third-type(i.e., Cauchy) boundary condition was used for salt transport at theupper and bottom boundaries.
Two horizontal auxiliary lines were defined in the transport domain
in the 40 cm and 100 cm soil depths to capture the dynamics of soil
water and salts in the soil profile. Moreover, a vertical auxiliary line wasdefined 40 cm away from the dripper. As a result, the modeling domain
was divided into six zones, i.e., the 0–40 cm soil layer under the mulchedarea (I), the 40–100 cm soil layer under the mulched area (II), the100–140 cm soil layer under the mulched area (III), the 0–40 cm soil
layer under the bare area (VI), the 40–100 cm soil layer under the barearea (V), and the 100–140 cm soil layer under the bare area (IV) (Fig. 3).

Parameters

Years

Kcb ini adj
Kcb mid adj
Kcb late adj
fw, irrigation
fw, rainfall
TEW
REW
Ze
hc
RHmin (%)
u2 (m s-1)
The initial crop growthstage
The middle crop growthstage
The late crop growth
stage

2020

2021

0.15
1.21
0.55
0.32
0.20
22
8
0.15
1.8
24.5
1.85
May 4 - June 4 (32 d)

0.15
1.19
0.55
0.32
0.20
22
8
0.15
1.7
45.4
1.57
May 10 - June 23 (45 d)June 5 - August 16 (73 d)June 24 - August 30 (68 d)

August 17 - September 20(35 d)

August 31 - September 26(27 d)

2.7. Model performance criteria
Agreement and bias between simulated and observed values of SWC
and ECe were evaluated using the root mean square error (RMSE), themean relative error (MRE), the determination coefficient (R2), and thepercentage bias (PBIAS) (Chen et al., 2023):
RMSE =

2.5. Modeling parameters

1

MRE = nThe soil hydraulic parameters for different soil layers were initiallyestimated using the pedotransfer functions (based on the neural network
method, Schaap et al., 2001) from the soil textural information and thebulk density. These parameters were then manually adjusted bycomparing simulated and observed SWC and ECe values until good ac­
curacy was achieved. The calibrated soil hydraulic parameters are
summarized in Table 1.
Soil longitudinal (DL) and transverse dispersivities (DT) are needed todetermine the components of the dispersion tensor. In this study, DL was
set to 50 cm in the 0–20 cm soil layer, 28 cm in the 20–40 cm soil layer,
25 cm in the 40–60 cm soil layer, and 26 cm in the 60–100 cm soil layer.
The transverse dispersivity (DT) was taken as one-tenth of DL (e.g.,
Phogat et al., 2020).
The root water uptake parameters for corn proposed by Wesselingand Brandyk (1985) were used in this study. The root "anaerobic" point(h1), the pressure head when optimal root water uptake starts (h2), thepressure head when optimal root water uptake ends (h3), and the wilting
point pressure head (h4) were set to − 15, − 30, − 600, and − 8000 cm,
respectively. Moreover, corn’s salinity threshold and slope values were
set to 1.7 dS m− 1 and 12%, respectively (Ayers and Westcot, 1976).

[
]1/2
2
1∑n
(S
−
O
)
i
i
n i=1
∑n

i=1 |Si −

Oi

Oi |

× 100%∑ni=1 (Oi − O)(Si − S)√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
R2 = √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
∑n∑n
i=1 (Oi − O)
i=1 (Si − S)

(29)

(30)
(31)

n
∑

(Si − Oi )PBIAS = i=1 ∑× 100%
n
Oi

(32)

i=1

where Si and Oi are the simulated and observed values, respectively, andn is the number of data points.
3. Results
3.1. Model evaluation
The HYDRUS (2D/3D) model was calibrated and validated using theobserved data from 2020 and 2021, respectively. The results showedthat HYDRUS (2D/3D) could precisely simulate the dynamics of soil
water and salts under different irrigation treatments. In the calibration
period (2020), the variation range of RMSE, MRE, R2, and PBIAS under
different irrigation treatments were 0.005–0.018 cm3 cm− 3, 7.0–14.8%,
0.62–0.84, and − 6.3–8.2% for SWC, respectively, while they were0.012–0.348 dS m− 1, 2.9–11.9%, 0.63–0.98, and − 7.5–8.9% for ECe,
respectively. In the validation period (2021), the variation range of
RMSE, MRE, R2, and PBIAS under different irrigation treatments were

2.6. Scenario analysis
Five additional irrigation depth scenarios (i.e., 7.5, 15.0, 22.5, 30.0,
and 37.5 mm) were evaluated using the HYDRUS (2D/3D) mode toassess further the effects of different irrigation depths on the soil waterand salt balances. Water salinity in different scenarios was the same andequal to 3.7 dS m− 1.
6

Y. Zhang et al.

Agricultural Water Management 288 (2023) 108492

0.004–0.017 cm3 cm− 3, 6.9–10.6%, 0.62–0.80, and − 5.2–8.7% for
SWC, respectively, while they were 0.023–0.372 dS m− 1, 5.6–11.8%,
0.74–0.99, and − 4.4–9.0% for ECe (Table 2). High variations of RMSE
for SWC and ECe could be attributed to SWCs and ECe in the surface soil
layer (10 cm soil layer) that were greatly affected by meteorologicalfactors. The simulation accuracy of SWC and ECe in the surface soil layer
was lower than in the deeper soil layer. The highest simulation accuracy
under HB, MB, LB, and MF treatments occurred in the MF treatment,with average RMSE, MRE, R2, and PBIAS of 0.008 cm3 cm− 3, 8.2%,
0.73%, and 2.6% for SWC, respectively, and average RMSE, MRE, R2,
and PBIAS of 0.047 dS m− 1, 7.5%, 0.87%, and 3.0% for ECe, respec­tively. Visual verification also shows a high agreement between simu­
lated and observed values (Fig. 4).

There are apparent differences in water exchanges between different
regions under different irrigation treatments. In the vertical direction,water migrated mainly from a deep to shallow soil layer. Water ex­change between zones I and II was significantly lower than between
zones II and III (Fig. 5). The average water volume that migrated fromzone I to zone II under HB, MB, LB, and MF was 123.4, 72.7, 41.3, and69.0 mm, respectively, while it was 205.4, 219.8, 228.3, and 238.3 forzones III to II. Additionally, the average water volume that migrated
from zone II to zone I under HB, MB, LB, and MF was 182.3, 197.6,
184.1, and 207.1, respectively. The average water volume that migrated
from zone II to zone III under HB, MB, LB, and MF was 142.9, 91.2, 61.0,
and 87.5 mm, respectively. In the horizontal direction, water migrated
mainly from the mulched area to the bare area (Fig. 6). The averagewater volume that migrated from zone I to zone VI under HB, MB, LB,
and MF was 75.1, 53.3, 32.1, and 53.4 mm, respectively. On the other
hand, the average water volume that migrated from zone VI to zone I
was 42.7, 47.9, 48.0, and 49.5 mm, respectively.
Similarly, apparent differences in the salt exchange between
different regions under different irrigation treatments were found. In thevertical direction, salt mainly migrated from a deep soil layer to ashallow soil layer. The salt exchange between zones I and II was higher
than between zones II and III (Fig. 5). The average salt amount that
migrated from zone I to zone II under HB, MB, LB, and MF was 194.0,
93.5, 40.4, and 18.6 mg cm− 1, respectively, while it was 71.3, 129.7,
141.5, and 146.3 mg cm− 1 from zone III to zone II. Additionally, theaverage salt amount that migrated from zone II to zone I under HB, MB,
LB, and MF was 273.3, 252.0, 163.5, and 62.3 mg cm− 1, respectively.
The average salt amount that migrated from zone II to zone III under HB,
MB, LB, and MF was 44.6, 43.7, 37.9, and 44.3 mg cm− 1, respectively. In
the horizontal direction, salt mainly migrated from the bare area to themulched area (Fig. 6). The average salt amounts that migrated from themulched area (zones I and II) to the bare area (zones IV and V) under HB,
MB, LB, and MF were 90.6, 55.0, 26.1, and 15.8 mg cm− 1, respectively,
while from the bare area to the mulched area, they were 94.8, 92.8, 65.7
and 22.4 mg cm− 1, respectively.

3.2. The dynamics of soil water and salts under different irrigation depths
There were apparent differences in SWCs in the 0–20 cm soil layer
under different irrigation treatments after irrigation (Fig. 4). The
average SWC under MB in both years was 7.9% higher than under LB,
while it decreased by 10.5% compared with HB. However, there were noapparent differences in SWCs between the MB and MF treatments. The
average SWC under MB in both years increased by only 0.04% comparedwith MF. No differences in SWCs under different treatments wereapparent in the 20–100 cm soil layer. The average SWCs under HB, MB,
LB, and MF in both years were 0.3608, 0.3602, 0.3601, and 0.3603 cm3
cm− 3, respectively. In general, SWC increased by 0.002 cm3 cm− 3 inresponse to an increase of 10 mm in the brackish water irrigation depth.
(Table 3).
ECe in the 0–100 cm soil layer under different treatments increased
with crop growth. Average ECe in both years under the HB, MB, LB, andMF treatments one day after harvesting was 14.3, 12.1, 9.7, and 4.1
times higher than one day before sowing. Moreover, ECe under brackish
water irrigation was higher than under freshwater irrigation. The
average ECe in the 0–20 cm soil layer under brackish water irrigation(HB, MB, and LB) was 2.7 times higher than under MF. However, ECe
under different irrigation treatments decreased with increased soil
depth. The average ECe in the 20–40, 40–60, and 60–100 cm soil layers
under different irrigation treatments was 18.1%, 64.5%, and 70.4%
lower than in the 0–20 cm soil layer, respectively.
There were apparent differences in ECe under different irrigation
depths with brackish water. The average ECe in the 0–100 cm soil layer
under HB increased by 12.2% and 39.8% compared with MB and LB in
2020, respectively, while under HB, ECe increased by 14.7% and 17.9%
compared with MB and LB in 2021, respectively. Overall, ECe increased
by 0.03 dS m− 1 in response to an increase of 1 mm of the brackish water
irrigation depth.

3.4. Two-dimensional distributions of soil water and salts under different
irrigation depths
The two-dimensional distributions of soil water and salts weresimilar in both years. Therefore, only three days in 2020 were selected toassess the effects of irrigation events and evaporation on the spatial
distributions of SWC and ECe under different irrigation treatments, i.e.,
one day before irrigation (DAS 66), one day after irrigation (DAS 67),
and on the last day of the crop growing season (DAS 140).
On DAS 66, SWC under different irrigation treatments was relatively
low while showing an increasing trend with soil depth (Fig. 7). On theother hand, ECe displayed an opposite trend to the SWC distribution.
Meanwhile, SWC in the horizontal direction gradually increased fromthe dripper towards the bare area, while ECe gradually decreased. In
general, SWCs and salt concentrations under brackish water irrigation(MB, HB, and LB) were higher than under freshwater irrigation (MF).
The stress areas under MB due to water (SWC<0.29 cm3 cm3) and salt
(ECe >1.70 dS m− 1) stress decreased and increased by 1.8 cm2 and2010.0 cm2, respectively, compared with MF. Conversely, the stressareas due to water and salt stress decreased and increased, respectively,
in response to an increase in the irrigation depth with brackish water.
The water stress areas under HB were 5.9% and 11.2% lower than under
MB and LB, respectively, while the salt stress areas were 10.8% and42.8% larger.
On DAS 67, SWC decreased in the horizontal direction from thedripper towards the bare area, while it decreased in the vertical direc­
tion with the soil depth. However, ECe showed an uneven distribution in
the two-dimensional profile, especially in the vertical direction. ECe firstincreased and then decreased with an increase in the soil depth. The
highest ECe occurred in the 20–30 cm soil layer (Fig. 7). Salt stress areas

3.3. Soil water and salt fluxes under different irrigation depths
Simulated water and salt fluxes were validated using the δ18O datafrom 2020 to 2021. Visual verification confirms that the agreement
between simulated and measured values is good (Fig. 5 and Fig. 6).
Table 2The initial estimates and calibrated values of the soil hydraulic parameters for
the 0–40 and 40–100 cm soil layers. θr is the residual soil water content (cm3
cm− 3), θs is the saturated soil water content (cm3 cm− 3), α (cm− 1) and n (–) areshape parameters, Ks is the saturated hydraulic conductivity (cm day− 1), and l is
the tortuosity parameter in the conductivity function (–).

Initialvalue
Calibration

Soil
layer
(cm)

θr (cm3
cm− 3)θs (cm3
cm− 3)αn (–)

Ks (cmday− 1)

l
(–)

0–40
40–100
0–40
40–100

0.039
0.038
0.042
0.040

0.380
0.377
0.371
0.366

0.00660.00690.00640.0067

1.60
1.59
1.64
1.63

50.1
49.6
50.8
49.4

0.5
0.5
0.5
0.5

(cm− 1)7

Y. Zhang et al.

Agricultural Water Management 288 (2023) 108492

Fig. 4. Simulated and observed soil water contents (SWC, left) and saturated extract electrical conductivities (ECe, right) in the 0–20 (top), 20–40, 40–60, and
60–100 (bottom) cm soil depths under brackish water irrigation with high (HB), medium (MB), and low (LB) irrigation depths (different colors), and underfreshwater with medium irrigation depths (MF) in 2020 (first and third columns) and 2021(second and fourth columns).

were not found under the MF treatment, while under HB, MB, and LB,
they were 2341.5, 2073.8, and 1681.6 cm2, respectively.
On DAS 140, visible differences in the distributions of soil water andsalts were found under different irrigation treatments. The largest water
stress area occurred under the HB treatment and was 7.8% and 14.2%
larger than under MB and LB, respectively. However, the HB treatment
had the largest salt stress area with 2625.3 cm2, which was 1.08 and1.14 times larger than under MB and LB, respectively.

the 0–40 cm and 40–100 cm soil layers under MB was 147.8% and28.2% higher than under MF, respectively. Soil salts in the 0–40 cm soil
layer under MB mainly come from salts dissolved in irrigation water,while soil salts in the 0–40 cm soil layer under MF mainly come fromsalts dissolved in groundwater. While 57.9% of salts in the 0–100 cm soil
layer originated from irrigation water in the MB treatment, 92.7% ofsalts in this soil layer came from groundwater in the MF treatment.
RWU showed a nonlinear relationship with irrigation depth whenbrackish water was used for irrigation. The highest RWU occurred under
MB (i.e., the inflection point of a nonlinear curve), and the average RWU
in both years under MB increased by 7.7% and 12.4% compared with HB
and LB, respectively. However, the capillary rise decreased with an in­crease in irrigation depth. Similarly, the soil salt storage in the 0–40 cm
soil layer under brackish water irrigation increased with increased
irrigation depth. Additionally, the relative contribution of irrigationwater to RWU increased with irrigation depth increasing. The relative
contribution of irrigation water to RWU under HB was 22.5% and 39.8%
higher than under MB and LB, respectively. However, the relative con­tributions of the soil water and groundwater to RWU decreased withirrigation depth increasing. The relative contribution of groundwater to
RWU under HB was 5.9% and 9.5% lower than under MB and LB,
respectively. The soil salt storage in the 0–40 cm soil layer under HB was
14.9% and 23.3% higher than under MB and LB, respectively. However,the soil salt storage in the 40–100 cm soil layer under brackish water
irrigation decreased with increased irrigation depth. The soil salt storage
in the 40–100 cm soil layer under HB was 33.4% and 75.6% lower thanunder MB and LB, respectively.

3.5. Proportions and balances of soil water and salts
There were apparent differences in soil water balance components
under different irrigation treatments. In general, root water uptake(RWU) and evaporation under brackish water irrigation were lower thanunder freshwater irrigation (Fig. 8). Average RWU and evaporation inboth years under MB were 1.9% and 9.1% lower than under MF,
respectively. Meanwhile, the average capillary rise in both years under
MB was 10.4% lower than under MF. RWU under MB occurs mainly in
the 0–40 cm soil layer. Overall, the relative contributions of irrigationwater, soil water (including rainfall), and groundwater to RWU under
MB were 92.5%, 2.5%, and 5.0%, respectively. However, there was noapparent difference in the relative contributions of different water re­sources between MB and MF. Significant differences in soil salt balancecomponents were found for different irrigation treatments. The soil saltstorage in the 0–40 cm soil layer under brackish water irrigation was
higher than under freshwater irrigation. On the other hand, the soil saltstorage in the 40–100 cm soil layer under brackish water irrigation was
lower than under freshwater irrigation. The average soil salt storage in8

Y. Zhang et al.

Table 3
Statistical performance of the HYDRUS (2D/3D) model for soil water contents (SWC) and electrical conductivities (ECe) in the 0–20, 20–40, 40–60, and 60–100 cm soil layers in the mulched and bare areas under brackish
water irrigation with high (HB), medium (MB), and low (LB) irrigation depths, and under freshwater irrigation with medium irrigation depths (MF) during calibration (2020) and validation (2021). RMSE, MRE, R2, and
PBIAS are the root mean square error, the mean relative error, the determination coefficient, and the percentage bias, respectively.
Indexes

Soil depth (cm)Mulched area

Bare area

2020
SWC

RMSE
(cm3cm− 3)
MRE(%)

R2
(-)

9
PBIAS
(%)
ECe

RMSE
(dS m− 1)
MRE(%)

PBIAS
(%)

2020

2021

HB

MB

LB

MF

HB

MB

LB

MF

HB

MB

LB

MF

HB

MB

LB

MF

0.01
0.01
0.005
0.01
14.81
8.97
6.99
7.58
0.73
0.84
0.67
0.73
-4.39
7.09
6.14
4.46
0.34
0.35
0.22
0.07
9.60
10.92
11.92
8.57
0.95
0.95
0.95
0.94
7.70
-3.48
-1.39
7.41

0.02
0.01
0.01
0.01
11.31
10.25
7.54
7.37
0.76
0.81
0.67
0.66
3.18
3.36
2.48
1.02
0.26
0.18
0.09
0.04
7.89
6.35
6.28
8.70
0.47
0.98
0.98
0.78
8.87
7.29
6.63
-7.45

0.02
0.01
0.01
0.01
11.19
9.46
7.72
7.12
0.76
0.76
0.62
0.69
-3.56
3.37
8.26
4.66
0.19
0.22
0.09
0.02
7.85
8.64
9.56
4.12
0.96
0.96
0.95
0.72
2.01
8.58
5.62
-0.44

0.01
0.01
0.01
0.01
9.69
10.02
7.63
7.02
0.72
0.83
0.65
0.67
-2.93
5.34
-6.32
3.01
0.07
0.06
0.03
0.01
9.82
7.60
5.83
2.94
0.94
0.95
0.93
0.65
8.79
-7.08
4.70
6.63

0.02
0.01
0.01
0.01
10.23
9.89
7.42
7.12
0.72
0.79
0.79
0.68
8.66
-5.19
3.94
6.08
0.22
0.37
0.22
0.04
6.40
11.75
11.47
8.58
0.98
0.94
0.96
0.96
6.38
7.98
4.93
-0.27

0.01
0.01
0.01
0.01
9.81
10.54
7.45
7.50
0.73
0.73
0.71
0.64
4.61
5.52
8.51
2.00
0.33
0.22
0.09
0.03
8.08
5.65
6.76
6.65
0.95
0.97
0.96
0.75
4.57
1.42
8.51
3.72

0.01
0.01
0.00
0.01
9.85
9.21
6.88
7.10
0.71
0.70
0.62
0.75
-4.92
6.59
8.17
6.22
0.20
0.21
0.06
0.02
7.05
8.01
7.71
6.19
0.96
0.96
0.94
0.81
-0.16
4.41
2.74
-0.74

0.02
0.01
0.01
0.004
10.57
8.85
7.11
6.92
0.74
0.80
0.72
0.67
6.86
-0.34
7.55
-1.21
0.08
0.08
0.04
0.03
8.21
9.75
9.88
7.35
0.97
0.95
0.90
0.74
1.57
6.81
8.62
0.52

0.01
0.01
0.01
0.01
10.59
8.26
7.38
7.85
0.72
0.72
0.63
0.70
4.74
6.00
0.60
6.80
0.27
0.23
0.07
0.03
10.26
9.42
8.67
8.87
0.97
0.97
0.97
0.88
6.55
4.91
3.71
3.50

0.01
0.01
0.01
0.01
10.15
7.87
7.07
7.14
0.76
0.73
0.68
0.78
-2.06
8.22
-5.03
1.38
0.19
0.19
0.04
0.01
7.01
10.08
5.41
3.57
0.98
0.97
0.92
0.73
-3.95
4.16
8.53
2.36

0.01
0.01
0.01
0.01
8.02
7.81
6.98
7.17
0.80
0.72
0.67
0.78
5.59
6.83
1.32
-2.66
0.16
0.12
0.02
0.01
9.61
7.45
4.07
3.78
0.97
0.96
0.92
0.63
0.31
0.62
3.00
5.75

0.01
0.00
0.01
0.01
8.45
7.46
7.02
6.99
0.82
0.75
0.63
0.71
-4.93
7.86
1.03
0.28
0.09
0.05
0.02
0.01
9.74
6.98
4.10
3.40
0.97
0.95
0.72
0.74
6.53
7.27
-7.46
-6.86

0.01
0.01
0.01
0.01
10.10
10.19
7.43
7.38
0.73
0.71
0.78
0.70
6.27
7.49
3.73
-2.34
0.25
0.17
0.09
0.03
8.01
8.59
10.80
8.82
0.98
0.99
0.95
0.84
0.76
-2.56
7.55
3.13

0.01
0.01
0.01
0.01
9.38
7.68
7.19
7.48
0.73
0.72
0.67
0.70
5.09
8.02
6.51
4.61
0.31
0.17
0.03
0.02
9.25
7.62
8.18
7.11
0.97
0.98
0.91
0.72
1.36
8.99
4.16
-4.37

0.01
0.01
0.01
0.01
8.80
7.89
7.17
7.1
0.70
0.74
0.75
0.72
-2.17
4.23
6.27
-1.68
0.13
0.16
0.04
0.03
6.96
9.93
7.35
8.26
0.98
0.98
0.94
0.81
6.59
6.78
-1.44
5.83

0.01
0.02
0.01
0.01
9.20
10.40
6.99
7.10
0.72
0.76
0.71
0.70
7.91
6.61
2.51
8.02
0.06
0.07
0.03
0.03
8.98
8.68
7.28
9.81
0.98
0.96
0.68
0.84
-0.04
6.03
4.85
7.70

Agricultural Water Management 288 (2023) 108492

R2
(-)

10
30
50
80
10
30
50
80
10
30
50
80
10
30
50
80
10
30
50
80
10
30
50
80
10
30
50
80
10
30
50
80

2021

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Agricultural Water Management 288 (2023) 108492

Fig. 5. Simulated and observed fluxes of water (a-d) and salts (e-h) in the vertical direction between the 0–40 cm soil layer in the mulched area (I), the 40–100 cm
soil layer in the mulched area (II), and the 100–140 cm soil layer in the mulched area (III) under brackish water irrigation with high (HB), medium (MB), and low(LB) irrigation depths, and under freshwater with medium irrigation depths (MF) in 2020 (left) and 2021 (right).

3.6. The mass balance components for soil water and salts under different
irrigation depths

affected by irrigation depths. In general, the capillary rise (G) decreased
with an increase in the irrigation depth. The cause of this phenomenon isa decrease in the soil water potential gradient between the corn rootzone and groundwater (Schulthess et al., 2019). The soil water potential
in the corn root zone increased with an increase in the irrigation depth,
which resulted in a decrease in the soil water potential gradient between
the corn root zone and the groundwater table. Therefore, water flow (i.
e., the capillary rise) from the groundwater table to the corn root zone
decreased.
Meanwhile, higher soil water potential would promote water flowfrom the soil to the plant, and the apoplastic pathway of water move­
ment is dominant (Steudle and Peterson, 1998; Steudle, 2001; Bramley
et al., 2009). Nevertheless, RWU decreased when the irrigation depth
increased from medium (MB) to high (HB) irrigation depth. For
example, we found that RWU under HB was 7.7% lower than under MB.
The reasons for this phenomenon are manifold. On the one hand, theThe results of the five additional irrigation depth scenario simula­tions showed that RWU increased by 22.5% with a 5 mm increase in theirrigation depth when the irrigation depth was less than 23 mm, while G
decreased by 20.9 mm (Fig. 9). However, when the irrigation depth
exceeded 23 mm, RWU decreased by 10.4% in response to a 5 mm in­crease in the irrigation depth. Additionally, SL increased by 10.3% with a
5 mm increase in the irrigation depth, while SG decreased by 61.7%.
4. Discussion
4.1. Effects of different irrigation depths on soil water and salt balances
The soil water and salt balances in the corn root zone were markedly
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Agricultural Water Management 288 (2023) 108492

Fig. 6. Simulated and observed fluxes of water (a, b) and salts (c, d) in the horizontal direction between the 0–100 cm soil layer in the mulched area (zones I and II)
and the 0–100 cm soil layer in the bare area (zones IV and V) under brackish water irrigation with high (HB), medium (MB), and low (LB) irrigation depths, andunder freshwater with medium irrigation depths (MF) in 2020 (left) and 2021 (right).

oxygen content in the soil decreased with a rapid increase in SWC due tothe large drip irrigation rate (2.4 L h− 1) used in this experiment, whichcaused a decrease in root activity (Noah and Friedman, 2018; Baramet al., 2022).
On the other hand, soil salinity under brackish water irrigation
increased with an increase in the irrigation depth, which may haveresulted in a decrease in the feruloylation of arabinoxylans in the rootsof corn due to severe salt stress (Oliveira et al., 2020). Meanwhile, thelignification of the cell wall in response to salt stress led to its stiffening
and contributed to a decrease in RWU (Meychik et al., 2010). For
instance, this study found that the salt stress degree (i.e., average ECe in
the root zone minus ECe threshold) under HB was 26.3% higher than under
MB. However, RWU under HB was slightly higher than under LB. The
cause of this was mainly attributed to the shallow groundwater table inthis region. Although the irrigation depth under LB was lower thanunder HB, G under LB increased by 62.6% compared with HB due to theshallow groundwater table. Moreover, the difference in RWU under the
MB and MF treatments was also negligible. The reason was mainly
attributed to the root activity under MF not being severely limited bysalt stress due to the low salt input.
Additionally, the leached salt mass (SL) increased in response to anincreased irrigation depth for brackish water. For example, the leachedsalt mass under HB was higher by 1.9 and 3.2 t ha− 1 than under MB and
LB, respectively. However, there is an opposite relationship between thesalt mass migrating from groundwater into the root zone (SG) and theirrigation depth. The lowest SG occurred in the HB treatment under
different irrigation treatments. The reason can be attributed to a low
capillary rise under the HB treatment.

irrigation (Li et al., 2023). For example, the depth and width of the "wetsoil area" under HB were 10.3 and 5.7 cm larger than under MB,
respectively, and 14.8 and 14.1 cm larger compared with LB. After
irrigation, soil water and salts mainly accumulated in the vertical di­rection in the 30–40 cm soil layer. However, Wang et al. (2016) illus­
trated that the largest soil salt concentrations occurred in the 60–80 cm
soil layer after brackish water irrigation. The reason for this difference isthe different soil textures at the two experimental sites. Soil texture at
the experimental site of Wang et al. (2016) was classified as sandy soil,
and sandy soils tend to have larger hydraulic conductivities, dispersion
coefficients, and distribution depths. Additionally, in the horizontal di­rection, SWC in the mulched area was lower than in the bare area before
irrigation, while the soil salt distribution showed the opposite trend
compared to the soil water distribution. Soil salt concentrations in themulched area increased by 37.5% compared with the bare area (Fig. 7).
This can be mainly attributed to higher RWU in the mulched area thanevaporation in the bare area, which caused soil water movement fromthe bare area to the mulched area in the direction of the soil water po­
tential gradient.
As a result of water flow from the bare area to the mulched area,
corresponding salts dissolved in soil water accumulate in the mulched
area. A similar result has also been found in the earlier literature (Zhang
et al., 2021). For example, soil salt concentrations in the mulched area
were 63.5% higher than in the bare area (Chen et al., 2022a). However,there are different conclusions in the earlier literature. Zribi et al. (2017)
reported that soil salt concentrations in the mulched area were lower
than in the bare area before irrigation. This discrepancy could be
attributed to differences in rainfall at the two experimental sites. The
overall rainfall at the experimental site of Zribi et al. (2017) reached
252 mm, with higher rainfall in the bare area than in the mulched area.
Therefore, SL in the bare area was higher than in the mulched area, while
the soil salt concentrations in the bare area were lower.
Although soil salt concentrations in the crop root zone increased withan increase in the irrigation depth during brackish water irrigation, theimpact of salt concentrations on the hydraulic conductivity of the root
wall was negligible when the ionic strength of the soil solution was
lower than the threshold (Meychik et al., 2021). Meanwhile, RWU and4.2. Effect of different irrigation depths on the distributions of soil waterand salts
There is an apparent impact of the irrigation depth on the distribu­
tions of soil water and salts, especially for brackish water irrigation. In
general, the "wet soil area" (with the soil matric potential thresholds
exceeding − 20 kPa) and the "salt accumulation area" increased in
response to an increase in the irrigation depth for brackish water11

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Agricultural Water Management 288 (2023) 108492

Fig. 7. Simulated two-dimensional distribu­
tions of soil water content (SWC) and electricalconductivity (ECe) one day before irrigation(DAS 66), one day after irrigation (DAS 67), andon the last day of the crop growing season (DAS140) under brackish water irrigation with high(HB), medium (MB), and low (LB) irrigation
depths and under freshwater with medium
irrigation depths (MF). Note that the arrow di­rections represent the soil water flow direction,
the arrow colors represent local SWC values,
and the arrow length has no meaning.

crop yield increased with increased irrigation depth under brackish
water irrigation. For example, crop yield under MB was 17.0% and19.8% higher than under HB and LB, respectively. This is mainly
attributed to the distribution of "suitable water and salt areas." In thisstudy, "suitable soil salts" areas under MB were 10.1% and 4.8% higher
than under HB and LB, respectively. In general, the MB treatment could
be recommended in agricultural production to increase crop yield andalleviate the freshwater shortage.

5. Conclusions
The oxygen stable isotope method was used to verify that HYDRUS(2D/3D) could precisely capture SWCs and ECe under different irrigation
treatments, with the RMSE of 0.004–0.017 cm3 cm− 3 and 0.023–0.372
dS m− 1 for SWC and ECe, respectively. There were apparent differencesin the dynamics of SWC and ECe under brackish water and freshwater
irrigation. The largest differences in SWCs and ECe under brackish water
irrigation and freshwater irrigation occurred in the 0–40 cm soil layer,
especially in the 0–20 cm soil layer. The stress areas due to water and
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Agricultural Water Management 288 (2023) 108492

Fig. 8. Soil water and salt balances (left figures of each treatment), and the isotope compositions of δ18O (‰) of soil water in the 0–40, 40–100, and 100–140 cm soil
layers, corn stem water, irrigation water, and groundwater, and the contributions rates (right figures of each treatment) under brackish water irrigation with high(HB), medium (MB), and low (LB) irrigation depths, and under freshwater with medium irrigation depths (MF). Note that positive (negative) values in the left figuresof each treatment represent inflow (outflow) fluxes for a particular soil layer. Meanwhile, positive values in the right figures of each treatment represent contribution
rates, and corresponding negative values represent the isotope compositions of δ18O.

salt stresses under MB decreased and increased by 1.8 cm2 and2010.0 cm2, respectively, compared with MF. Meanwhile, the averageamounts of water and salts migrating from zone I to zone II under MB
were 41.1% and 51.8% higher than under MF, respectively. However,
the average RWU in both years under MB was 1.9% lower than under
MF. Additionally, RWU under brackish water irrigation increased nonlinearly with an increase in the irrigation depth. The highest RWU
occurred under MB, and the average RWU in both years under MB
increased by 7.7% and 12.4% compared with HB and LB, respectively.
Therefore, the MB treatment could be recommended in agricultural
production to increase crop yields and alleviate freshwater shortages.

Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper: No conflict of interest exits in thesubmission of this manuscript, and manuscript is approved by all au­
thors for publication. I would like to declare on behalf of my co-authorsthat the work described was original research that has not been pub­lished previously, and not under consideration for publication else­
where, in whole or in part. All the authors listed have approved themanuscript that is enclosed.

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Agricultural Water Management 288 (2023) 108492

Fig. 9. The mass balance components for soil
water and salts for different irrigation depth(7.5, 15.0, 22.5, 30.0, and 37.5 mm) treat­ments. D is drainage, RWU is root water uptake,
E is soil evaporation, P is precipitation, G is acapillary rise from groundwater, I is the total
irrigation depth, ΔW0–40 is the change in soil
water storage in the 0–40 cm soil layer, and
ΔW40–100 is the change in soil water storage inthe 40–100 cm soil layer. SL is the salt massleached below the 100 cm soil depth, SI is thesalt mass added by irrigation water, SG is thesalt mass migrating from groundwater into theroot zone, ΔS0–40 is the change in soil saltstorage in the 0–40 cm soil layer, and ΔS40–100

is the change in soil salt storage in the 40–100 cm soil layer.

Data availability

and Development Program of China (2021YFC3201202), the Inner
Mongolia Autonomous Region Natural Science Foundation(2021CG0022), the Inner Mongolia Science and Technology Program(2022YFHH0039), the Natural Science Foundation of Inner Mongolia(2023MS05002), the Program for Grassland Elite in Inner Mongolia
Autonomous Region, and the Inner Mongolia autonomous region grad­uate education innovation plan subsidized the project (SZ2020081).

Data will be made available on request.
Acknowledgments
This research was jointly supported by the National Key Research

Appendix
The theory for the dual Kc method
The basal crop coefficient (Kcb) was estimated as follows:( )0.3hc
Kcb = Kcb (stand) + [0.04(u2 − 2) − 0.004(RHmin − 45)]3(1)

where Kcb (stand) is the basal crop coefficient in a standard climate condition, RHmin is the mean daily minimum relative humidity (%), and hc is themean crop height (m).
The soil evaporation coefficient (Ke) was calculated as follows:(3)

Ke = Kr (Kcmax − Kcb ) ≤ few Kcmax

where Kr is a dimensionless evaporation reduction coefficient, Kc max is the maximum value of Kc following rain or irrigation, and few is the fraction of
exposed and wetted soil.
Kc max represents an upper limit placed on E and T from the cropped surface and was estimated as follows:({)( )0.3 }h, Kcb + 0.05
1.2 + [0.04(u2 − 2) − 0.004(RHmin − 45)]
(4)
Kcmax = max
3
Variations in Kr were divided into two stages, i.e., a constant Kr during the first evaporation stage and a variable Kr during the second evaporation
stage, as follows:⎧⎨ TEW − De,j− 1 De,j− 1 > REW
Kr = TEW − REW(5)⎩
1
De,j− 1 ≤ REW
where TEW is the maximum depth of water subject to evaporation from the surface soil layer when this layer is completely saturated (mm), REW is
readily evaporable water (mm), and De, j-1 represents cumulative depletion of water from the soil surface layer at the end of day j-1.
De,j = De,j− 1 −

(

) Ij
Ej
Pj − ROj −++ Te,j + DPei,jfw few(6)

where Pj is precipitation on day j (mm), ROj represents runoff from the soil surface on day j (mm), Ij is the irrigation depth on day j, Ej is evaporation on
day j, Te,j is the depth of transpiration from the exposed and wetted fraction of the soil surface layer on day j (mm), and DPei,j is deep percolation fromthe soil surface layer on day j (mm):) Ij(DPei,j = Pj − ROj + − De,j− 1 , DPei,j ≥ 0
fw

(7)

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Agricultural Water Management 288 (2023) 108492(8)

few = min(1 − fc , fw )(fc =Kcb − Kcmin
Kcmax − Kcmin)1+0.5h(9)(10)

fw = max[1 − fm , 0.32]

where Kc min is the minimum value of Kc for dry bare soil, fw is the fraction of the surface soil wetted by irrigation or rainfall, fc is the fraction of thesurface soil effectively covered by vegetation, fm is the fraction of the mulched area and was approximately 0.80, and 0.32 is the measured fraction of
the surface soil wetted by irrigation under no mulching in a dripped system.

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