land
ArticleModeling Irrigation of Tomatoes with Saline Water in Semi-Arid
Conditions Using Hydrus-1D
Sabri Kanzari 1 , Jiří Šimůnek 2, * , Issam Daghari 3 , Anis Younes 4 , Khouloud Ben Ali 1 , Sana Ben Mariem 1
and Samir Ghannem 1,5
1

2
3
4

5

*

Citation: Kanzari, S.; Šimůnek, J.;
Daghari, I.; Younes, A.; Ali, K.B.;
Mariem, S.B.; Ghannem, S. Modeling
Irrigation of Tomatoes with Saline
Water in Semi-Arid Conditions Using
Hydrus-1D. Land 2024, 13, 739.

National Institute of Rural Engineering, Waters, and Forestry, University of Carthage, Ariana 2080, Tunisia;
sabri.kanzari@iresa.agrinet.tn (S.K.)
Department of Environmental Sciences, University of California Riverside, Riverside, CA 92507, USA
National Institute of Agronomy, University of Carthage, Tunis 1082, Tunisia
Institut Terre et Environnement de Strasbourg, Université de Strasbourg, CNRS, ENGEES, UMR 7063,
67084 Strasbourg, France
Faculty of Sciences of Bizerte (FSB), University of Carthage, Jarzouna 7021, Tunisia
Correspondence: jiri.simunek@ucr.edu

Abstract: In arid and semi-arid regions like Tunisia, irrigation water is typically saline, posing a riskof soil and crop salinization and yield reduction. This research aims to study the combined effects ofsoil matric and osmotic potential stresses on tomato root water uptake. Plants were grown in pot andfield experiments in loamy-clay soils and were irrigated with three different irrigation water qualities:
0, 3.5, and 7 dS/m. The Hydrus-1D model was used to simulate the combined dynamics of subsurface
soil water and salts. Successful calibration and validation of the model against measured water andsalt profiles enabled the examination of the combined effects of osmotic and matric potential stresseson root water uptake. Relative yields, indirectly estimated from actual and potential transpiration,
indicated that the multiplicative stress response model effectively simulated the measured yields andthe impact of saline water irrigation on crop yields. The experimental and modeling results provide
information to aid in determining the salinity levels conducive to optimal crop growth. The findings
indicate that the selected salinity levels affect tomato growth to varying degrees. Specifically, thesalinity levels conducive to optimal tomato growth were between 0 and 3.5 dS/m, with a significant
growth reduction above this salinity level. The gradual salinization of the root zone further evidenced
this effect. The scenario considering a temperature increase of 2 ◦ C had no significant impact on crop
yields in the pot and field experiments.

https://doi.org/10.3390/
land13060739

Keywords: soil; saline water supply; irrigation; tomato; Hydrus-1D; Tunisia

Academic Editors: Tiago Brito Ramos,
Maria da Conceição Gonçalves andMohammad Farzamian
Received: 2 May 2024
Revised: 22 May 2024
Accepted: 22 May 2024
Published: 24 May 2024

Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms andconditions of the Creative Commons
Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

1. Introduction
Saline water poses a significant challenge to agricultural sustainability in Tunisia, acountry characterized by arid and semi-arid climates. With limited freshwater resources,
Tunisia heavily relies on alternative water sources for irrigation, including saline waters(waters containing high concentrations of dissolved salts), which presents both opportunities and challenges for agriculture in Tunisia. The use of saline water for irrigation is
widespread in Tunisia, driven by the scarcity of freshwater resources and the increasing
demands of agriculture [1]. Saline water sources include groundwater with elevated levels of dissolved salts and treated wastewater from various sources [2]. In some regions,desalination plants have also been established to convert seawater into usable irrigationwater [3]. Brackish water requires careful management to avoid negative impacts on soil
quality and crop productivity [4,5].
When saline water is applied to the soil, salts accumulate over time, increasing soil
salinity levels. It can also contribute to soil erosion and degradation, further exacerbating
land degradation issues in Tunisia [6]. In addition to soil salinization, saline water irrigation

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can directly impact crop health and productivity. Many crops are sensitive to high soil andirrigation water salt concentrations. Excessive salt levels can cause physiological stress inplants, leading to reduced growth, yield losses, and even crop failure [7]. Certain crops,
such as tomatoes, are particularly sensitive to salinity stress, making them susceptible toyield reductions when irrigated with saline water [8]. Despite these drawbacks, saline
water irrigation also has some benefits for agriculture in Tunisia. Waters containing highconcentrations of dissolved salts are often more readily available and less expensive thanfreshwater sources, providing an alternative water supply for irrigation during water
scarcity [9].
Modeling irrigation with saline water is crucial for understanding its effects and implementing effective mitigation strategies. Modeling can be performed using hydrologicalmodels, such as Hydrus-1D [10]. These models simulate water movement and solutetransport in soils, allowing researchers and farmers to predict how saline water affects soil
salinity, crop growth, and yields over time [11]. Using different data for soil hydraulic properties, irrigation practices, and water quality, these models can simulate various scenarios
and assess the effectiveness of different management strategies [12]. Modeling can also aid
in identifying the most suitable crops for irrigation with water of a given salinity. Indeed,some crops have higher salt tolerance than others, and modeling can help determine whichcrops are best suited for cultivation in saline environments. Additionally, models canevaluate the impact of different irrigation strategies, such as drip irrigation or leaching, on
soil salinity levels and crop productivity [13].
Several models have been developed to simulate water flow and solute transport
in soil profiles with plants, such as Hydrus-1D [14,15], SWAP [16], and SALTMOD [17].
In this study, we use the Hydrus-1D model because of its distinct advantages over theother models in modeling root water uptake under various environmental stresses. The
Hydrus-1D model offers superior capabilities in simulating water and salt dynamics inthe soil profiles with plants under saline irrigation conditions, allowing more accurate
predictions of crop responses to varying salinity levels [18,19].
Increased temperatures due to climate change can severely affect tomato production [20].
Increased temperatures can accelerate evaporation, potentially depleting soil moisture [21].
This can negatively impact tomato plants, affecting their growth and yield [22]. Higher
temperatures can also alter the phenological stages of tomato plants, affecting flowering, fruit
set, and ripening [23]. As temperatures rise, evaporation rates increase, concentrating salts inthe soil. This increased soil salinity can adversely affect tomato plants, reducing their ability toabsorb water and nutrients, stunting growth, and reducing yields [5].
The objectives of this study are: (i) to integrate the effects of soil matric and osmotic
potentials into modeling water and salts transport, (ii) to study the effects of saline water
irrigation on tomatoes cultivated under semi-arid conditions to provide a framework for understanding the complex interactions between soil, water, and crops in saline environments,and (iii) to evaluate the effects of an increase in mean air temperature on soil water andsalts dynamics and tomatoes’ root water uptake and, ultimately, yield. Haut du formulaire.
2. Materials and Methods
2.1. Experiment Design and Measurements
The experimental trials were conducted on a land parcel (36◦ 51′ 36.791′′ N, 10◦ 11′ 36.795′′ E)in the Ariana region, a semi-arid area in north Tunisia, during the year 2018. The soil isloamy clay. The study focused on a tomato variety, Rio Grande, commonly cultivated in
Tunisia. Planting was done on 16 March 2018 in the pot experiment and on 17 April 2018 in
the field experiment. A spacing of 25 cm between plants and 50 cm between rows was usedin the field experiment. Tomato harvesting occurred on 10 June 2018 in pot cultivation and on
3 August 2018 in field cultivation. Both pot and field experiments were conducted under naturalmeteorological conditions. The field and pot experimental data are not compared against eachother (since they were not carried out at the same time). Instead, they are used to calibrate andvalidate the Hydrus-1D model and assess its ability to account for environmental stresses.

Land 2024, 13, 739

June 2018 in pot cultivation and on 3 August 2018 in field cultivation. Both pot and field
experiments were conducted under natural meteorological conditions. The field and pot
experimental data are not compared against each other (since they were not carried out at
the same time). Instead, they are used to calibrate and validate the Hydrus-1D model andassess its ability to account for environmental stresses.
3 of 16
The water requirements of the crops were estimated using climate data from the past
10-year period obtained from the National Institute of Meteorology. The average values
were used
estimate
the reference
using
theclimate
Penman–Monteith
The towater
requirementsof the evapotranspiration
crops were estimatedusingdata from theformula(FAO-56).
For obtained
calculating
the theactualevapotranspiration,
crop coeﬃcient
past 10-year
periodfrom
National
Institute of Meteorology.
Thevalues
averageforvalues
the threewere
fromevapotranspiration
those proposed byAllenal. (1998) [24].
weregrowth
used tostages
estimatethetakenreference
using
theetPenman–Monteith
formula(FAO-56).
For calculating
the actual
evapotranspiration,
crop0.8
coefficientvaluesThese
valuesare as follows:
Kc = 0.6 (initialstage),
1.15 (mid-stage), and(final stage).
the three growthstages(FAO,
were1998;
takenFAO,
from2009)
thosewasproposed
et al.the(1998)[24].
TheforCROPWAT
8.0 software
utilizedbytoAllen
establish
irrigaThese
valuesareasfollows:K=
0.6(initial
stage),
1.15(mid-stage),
and0.8(finalstage).
tion schedule. Water requirementsc for tomato cultivation are approximately 720 mm.
The
CROPWAT
8.0 software(FAO,
1998; FAO,
was
utilized totomato
establish
the Theirrigation
Surfaceirrigation
was used
to deliver
water2009)
to eachindividual
plant.
irschedule.
Water requirements
forfield
tomatocultivationmean
are approximately
rigationschedulingin the pot andexperiments,
temperatures,720
andmm.
reference
Surface irrigation
was usedintoFigure
deliver
to eachindividual
tomato plant.
Theevapotranspiration
are presented
1. water
No rainfall
eventswere recorded
duringschedulingin theexperiments,
mean temperatures,and reference
theirrigation
tomato growing
season.
Inpottheandfieldfield
experiments,
irrigation
was applied every
threepresented
in Figure
1. No rainfall eventswere 1).
recordedor evapotranspiration
four days based onare
100%
of estimatedevapotranspiration(FigureIn the during
pot ex-thetomatogrowingseason.
In
the
field
experiments,
irrigation
wasappliedevery
three orperiments, irrigation was applied every two or three days until the soil water content
four
days
based
on
100%
of
estimated
evapotranspiration(Figure
1).
In
the
pot
experiments,
reached field capacity (34% in terms of the volumetric soil water content). Soil field cairrigation
was applied
every
two or plate
three apparatus
days until (forthe soilwater content
field
pacitywas measured
using
a pressure
a pressure
head ofreached−300 cm).
(34%
in terms
of werethe volumetric
soil
water
capacitywas
Thecapacity
amountsof water
addedrecorded foreach
pot content).
(Figure 1).Soil
Thefield
averagewettedmeasuredusingapressureplate
apparatus(forapressure
head
of
−
300
cm).
The
amounts
area was 45% in the field experiment and 65% in the pot experiment. Irrigation waterof watertoadded
were recorded
each potqualities:(Figure 1).
The average
was of45%
provided
the plants
had threefor
diﬀerent
distilledwaterwettedwith aarea
salinity
0 in
the
field
experiment
and
65%
in
the
pot
experiment.
Irrigation
water
providedtotheplantsdS/m, saline water with a salinity of 3.5 dS/m, and saline water with a salinity of 7 dS/m.
had threesoil
different
distilledwaterusing
withthea salinityof 0 dS/m,salinewithVolumetricwater qualities:
content wasmeasuredgravimetricmethod,andwatersoil saa
salinity
of
3.5
dS/m,
and
salinewater
withasalinityof
7dS/m.
Volumetric
soil
water
linity was measured using the saturated paste extract method [25] with three replicates.
content
was measured
the gravimetricsoiluntil
salinity
was ofmeasuredusing
In thepot experiment,
soilusingsamples
were taken method,
every tenanddays
the endthe tomato
thecyclesaturated
paste extract
[25]
with
replicates.
In thepot experiment,plant
to characterizesoilmethod
water andsoil
saltthreecontent.
In the field
experiment,
the soilsoil
samples were taken every ten days until the end of the tomato plant cycle to characterizewater content was measured on days 1, 30, 60, and 109 after planting every 20 cm down
soil water and soil salt content. In the field experiment, the soil water content was measured
to a depth of 80 cm.
on days 1, 30, 60, and 109 after planting every 20 cm down to a depth of 80 cm.

Land 2024, 13, x FOR PEER REVIEW

4 of 17

FigureMeantemperatures,reference
evapotranspiration(top),
andtomatoirrigation
scheduling
Figure1. 1.
Mean
temperatures,reference
evapotranspiration(top),
andtomatoirrigation
scheduling(bottom)
in
the
pot
and
field
experiments.
(bottom) in the pot and field experiments.

2.2. Hydrus-1D Model
2.2.1. Theory
Hydrus-1D [14,15] is a numerical model that uses the Galerkin finite element

Land 2024, 13, 739

4 of 162.2. Hydrus-1D Model
2.2.1. Theory
Hydrus-1D [14,15] is a numerical model that uses the Galerkin finite element method
to solve the Richards equation governing water dynamics in the unsaturated zone:
 

∂θ
∂h
∂
K
=
+1 −S
(1)
∂t
∂z
∂z
where h is the water pressure head [L], θ is the soil volumetric water content [L3 L−3 ], t is
time [T], z is the depth measured from the land surface (positive downward) [L], S is a sinkterm [L3 L−3 T−1 ], and K is the soil unsaturated hydraulic conductivity [LT−1 ].
Hydrus-1D uses the van Genuchten–Mualem soil hydraulic functions to represent
soil hydraulic properties. The soil water retention [26] and hydraulic conductivity [27]functions are as follows:(θr + θs −θrn m h < 0(1+|αh| )θ (h) =
(2)
θs
h≥0
h

 m i2K (h) = Ks Se0.5 1 − 1 − Se 1/m
Se =θ − θrθ s − θr(3)
(4)

where θ r is the residual water content [L3 L−3 ]; θ s is the saturated water content [L3 L−3 ];α [L−1 ], n (n > 1), and m = 1 − 1/n are shape parameters; Se is the effective saturation; andKs is the saturated hydraulic conductivity [LT−1 ].
Hydrus-1D uses the Galerkin finite element method to solve the advection–dispersion
equations (ADE) governing solute transport:


∂θC
∂
∂C
∂qθC
=
θD
−
(5)
∂t
∂z
∂z
∂z
where C is the solute concentration of the liquid phase [ML−3 ], D is the dispersion coefficient[L2 T−1 ], and q is the Darcy velocity [LT−1 ]. When neglecting molecular diffusion, thedispersion coefficient is defined as:
D = λq(6)
where λ is the soil longitudinal dispersivity [L].
The sink term, S, represents the volume of water removed from a unit volume of soil
per unit time due to plant water uptake. The Feddes model, as described by [18], wasemployed to simulate root water uptake. Three stress response function models available in
Hydrus-1D were evaluated for the simulation of salt stress: the additive model (Additive),
the threshold model (T-Model), and the S-shape model (S-Model). The last two models
are multiplicative models, combining the Feddes model [28], accounting for saturationstress, with either the “Threshold and Slope” model of Mass [29] or the S-shape model ofvan Genuchten [30], accounting for salinity stress. The theoretical underpinnings of thesemodels are elaborated in the Hydrus-1D manual, with specific parameter values provided
for tomato crops.
2.2.2. Soil Hydraulic Properties and Solute Transport Parameters
The estimation of the soil hydraulic parameters, namely the van Genuchten parametersin the water content–pressure head (Equation (2)) and conductivity–saturation (Equation (3))
relationships, was based on soil column evaporation experiments [31].
The dispersion coefficient, a crucial parameter in solute transport in unsaturated
soils, cannot be measured, and we thus resorted to indirect methods. Experiments on soilcolumns were conducted using PVC tubes with a diameter of 15 cm filled with 10 cm of

Land 2024, 13, 739

5 of 16

soil. The columns were slowly saturated from the top with distilled water. A Mariotte
bottle was placed at the top of the column to maintain a constant pressure head of about
3 cm and steady-state flow conditions. A pulse (50 mL) of a potassium chloride solution(0.8 M, 8.4 dS/m) was manually applied [32,33]. Effluent samples of approximately 100 cm3
were used to measure soil electrical conductivity and determine the solute breakthroughcurve (BTC). The experimental BTC values were fitted using the analytical solution of the
ADE using CXTFIT 2.1 software [34] to estimate the dispersion coefficient.
2.2.3. Model Calibration and Validation
The Hydrus-1D model was calibrated using measured soil water content and salinity
profiles in both pots and field experiments irrigated with fresh water (i.e., 0 dS/m). The
validation of the Hydrus-1D model was carried out by keeping the same input parameters
and only changing the water quality in both cases of this study (pot and field experiments).
2.3. Statistical Evaluation of Modeling Results
Simulation results were evaluated graphically and statistically. In the graphicalmethod, the measured and simulated volumetric water content values were plotted as afunction of soil depth. The statistical approach involved calculating the root mean squareerror (RMSE; in %):r1∑in=1 (si − mi )²
RMSE =
× × 100(7)nmwhere si is the simulated value, mi is the measured value, m is the average observed value,
and n is the number of observations.
3. Results and Discussion
3.1. Soil Water Content Dynamics
The variations in the soil water content in the pot experiments are presented in Figure 2.
Duringthe first month after the start of irrigation, the water content gradually increased
toLand 2024, 13, x FOR PEER REVIEW
6 of 17reach the field capacity (34%) in all three pots irrigated with different water qualities [35–37].
The water content of the soil irrigated with the saltiest water (7 dS/m) remained at thefield capacity. As the soil salinity increased with frequent irrigations, osmotic pressure also
two water preventing
qualities did
not
block
water Irrigations
extraction by
the
plant
and thesoil water
increased,
root
water
uptake.
withtheotherroots,
two water
qualities
didcontent
decreased
over
time.
The
soil
irrigated
with
fresh
water
(0
dS/m)
had
the
lowestnot block water extraction by the plant roots, and the soil water content decreased overwaterThe
content
values, as
thefreshplantwaterroots(0extracted
water
withoutwater
any content
osmoticvalues,
potential
time.
soil irrigatedwithdS/m) hadthe lowest
asconstraints.
the plant roots extracted water without any osmotic potential constraints.

Figure 2.
2. Measured
Measured soil
soil water
water content%) inin thethe pot
pot experiments
experiments irrigatedirrigated with
with different
diﬀerent water
water
Figurecontent (in(in %)
qualities
(0,
3,
and
7
dS/m).
qualities (0, 3, and 7 dS/m).

soil water
waterprofiles,
profiles,measured
measuredevery
every3030days
days
field
experiment
with
tomaThe soil
ininthethefield
experimentwithtomatoes
toes irrigatedwater,are illustrated
in Figure3a. Thisfigureshows
the variairrigatedwithwith
freshfresh
water,are illustrated
in Figure3a. Thisfigureshows
the variations
insoilinwatercontent
without
significant
osmotic
potential
effects.eﬀects.
Indeed,the soilthe
water
tions
soil watercontent
without
significant
osmotic
potential
Indeed,soil
content
profilesprofiles
show dynamics
that reflect(wetting)(wetting)and evaporation(drying)
water content
show dynamics
thatinfiltrationreflect infiltrationand evaporation(drying) episodes. After 109 irrigation days, the water content exceeded the field capacity, indicating that the roots did not undergo water stress.

Figure 2. Measured soil water content (in %) in the pot experiments irrigated with diﬀerent water
qualities (0, 3, and 7 dS/m).

Land 2024, 13, 739

The soil water profiles, measured every 30 days in the field experiment with tomatoes irrigated with fresh water, are illustrated in Figure 3a. This figure shows the varia6 of 16
tions in soil water content without significant osmotic potential eﬀects. Indeed, the soil
water content profiles show dynamics that reflect infiltration (wetting) and evaporation(drying) episodes. After 109 irrigation days, the water content exceeded the field capaciepisodes. After 109 irrigation days, the water content exceeded the field capacity, indicatingty, indicating that the roots did not undergo water stress.
that the roots did not undergo water stress.

(a)

(b)

FigureFigure3.3.Measured
Measuredsoil
soilwaterwatercontent
content(in(in%)%)ininthe
thefieldfieldexperiments
experimentswith
withtomatoes
tomatoesirrigatedirrigatedwith
with(a)(at(at30,30,
60,60,
and109109d) and(b) (b)watersof diﬀerent
salinities(0, 3,(0,and
7 dS/m)(at 109(at(a)freshfreshwater
water
and
d) andwatersof different
salinities
3, and
7 dS/m)days).
109 days).

FigureFigure3b3bshows
showsthethewaterwatercontent
contentprofiles
profilesmeasured
measuredafter
after109109irrigation
irrigationdays
daysininfield
fieldexperiments
experimentsirrigatedirrigatedwith
withwaters
watersofofdiﬀerent
differentqualities.
qualities.The
Thewaterwatercontent
contentininthe
thesurfacesurfacelayers
layersisisvery
veryclose
closetotofield
fieldcapacity
capacity(34%),(34%),while
whileititincreases
increasesconsiderably
considerablywith
withdepth,
deepwater
infiltration.
TheTheirrigation
strategy
based
on calculating
thedepth,indicating
indicating
deep
water
infiltration.
irrigation
strategy
based
on calculatingwater
needsneeds
usingusing
climatic
parametersfromthe theprevious
tentenyears
totoestimate
the water
climatic
parametersfrompreviousyears
estimateactual
actualevapotranspiration
evapotranspirationsucceeded
succeededininnot
notsubjecting
subjectingthe
thecropcroptotowater
waterstressstress[38].
[38].However,
However,
deeppercolation
percolationshows
showsthatthatcrop
cropwaterwaterneeds
needswere
wereoverestimatedoverestimated[39].
[39].
deep
Land 2024, 13, x FOR PEER REVIEW 3.2. Soil Salinity Dynamics

7 of 173.2. Soil Salinity Dynamics
Thevariations
variationsininthe
theaverage
average soil
soil salinity
salinity inThein thethe pot
pot experiments
experimentsirrigatedirrigatedwith
withwaters
waof different
qualities
areareshown
in in
Figure
4. 4.
This
figureshows
tersof diﬀerent
qualities
shown
FigureThisfigureshowsa anearly
nearlyconstantconstantlevel
levelofofsalinitysoils
irrigatedwith
withfresh
freshwater
waterandandaagradual
gradualincrease
increasein
in soilsoil salinity
salinity in soils
salinity
in in
soils
irrigated
irrigated with lower-quality
lower-quality waters,
waters, reachingreaching 88dS/m
dS/m when 3.5 dS/m
dS/m water
water waswas used
used andand
12 dS/mdS/mwhen
when77dS/mdS/mwaterwaterwaswasused.
used.

FigureFigure 4. Soil
Soil salt content (ECe) in the pot experiments irrigated with waters of diﬀerent
different salinities(0,(0, 3,
3, andand 77 dS/m).
dS/m).

experiment irrigatedirrigated with
with fresh
fresh water, the variations
variations inin thethe soil
soil salinity
salinityIn the field experimentindicated continuous
continuous leachingleaching ofof the initial salinity
salinity
profiles measured every thirty days indicated
In contrast,
contrast, surface
surface salinity
salinity significantly
significantly increased
increased during
during irrigations
irrigations with
(Figure 5a). In
saline waters of 3.5 dS/m and 7 dS/m, reaching 7 dS/m and 12 dS/m, respectively, at theend of the crop cycle (Figure 5b). Soil salinity is higher near the surface than at depth,
mainly due to evapotranspiration causing salt accumulation near the soil surface [40].

Figure 4. Soil salt content (ECe) in the pot experiments irrigated with waters of diﬀerent salinities(0, 3, and 7 dS/m).
Land 2024, 13, 739

In the field experiment irrigated with fresh water, the variations in the soil salinity
7 of 16
profiles measured every thirty days indicated continuous leaching of the initial salinity(Figure 5a). In contrast, surface salinity significantly increased during irrigations withsalineand
7 dS/m,reaching
7 dS/mand and
12 dS/m,respectively,
at theatsalinewaters
watersofof3.5
3.5dS/mdS/m
and7 dS/m,reaching
7 dS/m
12 dS/m,respectively,
end
of
the
crop
cycle
(Figure5b).
Soilsalinityishighernear
thesurfacethanatdepth,
the end of the crop cycle (Figure 5b). Soil salinity is higher near the surface than at depth,
mainlymainlydueduetotoevapotranspiration
evapotranspirationcausing
causingsalt
saltaccumulation
accumulationnear
nearthethesoilsoilsurface
surface[40].
[40].

(a)

(b)

FigureFigure5.5.Measured
Measuredsoil
soilsaltsaltcontent
contentininthe
thefieldfieldexperiments
experimentswith
withtomatoes
tomatoesirrigatedirrigatedwith
with(a)(a)fresh
fresh
water
water(at(at30,
30,60,
60,andand109109d)d)and
and(b)(b)waters
watersofofdiﬀerent
differentsalinities
salinities(0,(0,3,3,andand77dS/m)
dS/m)(at(at109
109days).
days).

3.3.Numerical
NumericalModeling
ModelingofofWater
WaterandandSalt
SaltDynamics
Dynamicswith
withRoot
RootWater
WaterUptake
Uptake3.3.
3.3.1.Inputs
InputstotoHydrus-1D
Hydrus-1D
3.3.1.
The soil was considered homogeneous in pot experiments, consisting of a single layer
The soil was considered homogeneous in pot experiments, consisting of a singleof 30 cm. In the field experiment, water content and salinity measurements were taken
layer of 30 cm. In the field experiment, water content and salinity measurements wereevery 20 cm down to a depth of 80 cm. Four soil layers (horizons) of 20 cm thickness weretaken every 20 cm down to a depth of 80 cm. Four soil layers (horizons) of 20 cm thickconsidered in the simulations. The values of the van Genuchten–Mualem parameters forness were considered in the simulations. The values of the van Genuchten–Mualem pathe four soil layers are presented in Table 1. The simulation period lasted 87 days in the pot
rameters for the four soil layers are presented in Table 1. The simulation period lasted 87
experiments, with three output dates of 30, 60, and 87 days. On the other hand, the fielddays in the pot experiments, with three output dates of 30, 60, and 87 days. On the other
trial lasted 109 days, and the output dates were 30, 60, and 109 days.
hand, the field trial lasted 109 days, and the output dates were 30, 60, and 109 days.
Table 1. The soil hydraulic parameters of different soil layers.
Layer (cm)θr (cm3 ·cm−3 )θs (cm3 ·cm−3 )α (cm−1 )n (-)

Ks (cm·d−1 )

0.27

1.11

6.41

Pot experiment
-

0.1

0.41
Field experiment

0–20 cm

0.078

0.546

0.07

1.067

8.87

20–40 cm

0.078

0.544

0.07

1.079

8.87

40–60 cm

0.078

0.445

0.10

1.073

12.6

60–80 cm

0.078

0.443

0.03

1.078

12.5

The dispersivity of the different soil layers varied around 5 cm, except for the 60–80 cm
layer, where it was equal to 3 cm. The distribution coefficient of the adsorption isotherm
ranged between 0.1 g/cm3 and 0.3 g/cm3 for all soil layers. Hydrus-1D includes a databasethat provides stress response function values for many crops, including tomatoes, which wereconsidered here. The initial soil water content and soil salinity values as a function of depth in
the field experiment are shown in Figure 6. In the pot experiment, the initial water content was
20%, and the initial soil salinity was 1.2 dS/m.
For the simulation of field experiments, we used the rainfall and evapotranspiration
data from the National Institute of Meteorology and crop coefficients from [24].

Land 2024, 13, 739

cm layer, where it was equal to 3 cm. The distribution coeﬃcient of the adsorption isotherm ranged between 0.1 g/cm3 and 0.3 g/cm3 for all soil layers. Hydrus-1D includes a
database that provides stress response function values for many crops, including tomatoes, which were considered here. The initial soil water content and soil salinity values asa function of depth in the field experiment are shown in Figure 6. In the pot experiment,
8 of 16
the initial water content was 20%, and the initial soil salinity was 1.2 dS/m.

(a)

(b)

Figureinitial(a) (a)water
content
andand(b) salinity
as a functionof soilofdepth
in the infield
Figure6.6.Measured
Measured
initialwater
content(b) salinity
as a function
soil depththeexperiment.
field experiment.

3.3.2.
Simulation
ResultsFor
the simulationof field experiments, we used the rainfall and evapotranspiration
data fromthe Nationalmodel
Institute
Meteorology
andcoeﬃcients
fromand[24].salts in both
The Hydrus-1D
wasofused
to simulate
thecrop
movementof waterpot and field soils, considering root water uptake under the combined effects of soil matric3.3.2.
Simulation
Results
and osmotic
potentials.

The Hydrus-1D model was used to simulate the movement of water and salts in
Model
both
potCalibrationand field soils, considering root water uptake under the combined eﬀects of soilmodel was calibrated using measured soil water content and salinity
matricTheandHydrus-1D
osmotic potentials.
profiles in both pots and field experiments irrigated with fresh water (i.e., 0 dS/m). The
measuredand simulated water content and salinity values for both experiments are presented
Model
Calibrationin Figures 7–9. The measured soil water content values are quite close to the simulated values.
The Hydrus-1D model was calibrated using measured soil water content and salinIn the field experiment (Figures 7 and 8), the Hydrus-1D model underestimated the measured
Land 2024, 13, x FOR PEER REVIEW
9 of 17
ity profiles in both pots and field experiments irrigated with fresh water (i.e., 0 dS/m).
water content on day 30 and overestimated it on the other output dates. The model slightly
The measured and simulated water content and salinity values for both experiments areoverestimated the volumetric water content in the pot experiment (Figure 9).
presented in Figures 7–9. The measured soil water content values are quite close to thesimulated values. In the field experiment (Figures 7 and 8), the Hydrus-1D model underestimated the measured water content on day 30 and overestimated it on the other
output dates. The model slightly overestimated the volumetric water content in the pot
experiment (Figure 9).

Figure(calibration)soilsoilwater
content(in %)(in(top)(in dS/m)
Figure 7.7. Measured
Measuredandandsimulated
simulated(calibration)
water
content%) and(top)salinity
and salinity
(in
dS/m)
(bottom)
in
the
field
experimentirrigated
with
fresh
water
at
30
(left),
60(middle),and109(bottom) in the field experiment irrigated with fresh water at 30 (left), 60 (middle), and 109 (right)days.
(right) days.

Land 2024, 13, 739

Figure 7. Measured and simulated (calibration) soil water content (in %) (top) and salinity (indS/m) (bottom) in the field experiment irrigated with fresh water at 30 (left), 60 (middle), and9109
of 16(right) days.

Figure8.8.Measured
Measuredandandsimulated
simulated(validation)(validation)soil
soilwaterwatercontent
content(in(in %;%; top)(top))
andsalinity
salinity(in(indS/m;dS/m;Figureand(bottom))
in
the
field
experiments
irrigatedwithsalinewatersof
3.5
dS/m(left)
and7
dS/m(right)bottom) in the field experiments irrigated with saline waters of 3.5 dS/m (left) and 7 dS/m (right) at
theof theat endthe endof experiment.
the experiment.

The measured soil salinity profiles during the two pot and field experiments withtomatoes irrigated with saline waters and simulated using the Hydrus-1D model arepresented in Figure 9. Overall, the measured and simulated values are similar on all three
output dates. The simulated soil electrical conductivities generally overestimated themeasured values in both experiments.
Model Validation
The validation of the Hydrus-1D model was carried out by keeping the same input
parameters and only changing the water quality in both cases of this study (pot and field
experiments). Figures 6 and 7 show that the simulated soil water content profiles agree wellwith the measured profiles for both pot and field experiments. Indeed, for all the output
dates, the simulated profiles are very close to the measured ones.
The model’s performance was evaluated qualitatively (Figures 7–9) and assessedusing statistical evaluations and the RMSE values (Tables 2 and 3). These values are low(<10%) and highlight the model’s reliability for simulating water and salt dynamics forboth experiments and during the calibration and validation processes [41].
Table 2. Root mean square errors (RMSE, in %) assessing the Hydrus-1D calibration process.
Variable
Soil Water Profile
Soil Salinity Profile

Experiment

Date 1

Date 2

Date 3

Field

9.30

7.30

6.40

Pot

10.30

11.10

8.30

Field

5.30

2.10

4.60

Pot

2.00

4.50

1.70

Land 2024, 13, x FOR PEER REVIEWLand 2024, 13, 739

10 of 17
10 of 16

Water quality (3.5 dS/m)

Water quality (7 dS/m)
(a)

(b)

Figure9.9.Measured
Measuredandandsimulated
simulatedtime
timeseries
seriesof
ofsoilsoilwaterwatercontent
content(%)(%)(left)(left)andandsalinity
salinity(dS/m)(dS/m)
Figure(right) in the pot experiments irrigated with (a) freshwater (top) (calibration) and (b) saline waters(right) in the pot experiments irrigated with (a) freshwater (top) (calibration) and (b) saline waters ofof 3.5 dS/m (middle) and 7 dS/m (bottom) (validation).
3.5 dS/m (middle) and 7 dS/m (bottom) (validation).

The measured soil salinity profiles during the two pot and field experiments withtomatoes irrigated with saline waters and simulated using the Hydrus-1D model arepresented in Figure 9. Overall, the measured and simulated values are similar
all three
RMSEon(%)
Experiment
Irrigation Water Quality
outputVariable
dates. The simulated
soil electricalconductivities generally(onoverestimatedthe Final Day) the
measured values in both experiments.
3.5 dS/m
9.10

Table 3. Root mean square errors (RMSE, in %) assessing the Hydrus-1D validation process.

Soil Water Profile

Model Validation

Field

7 dS/m

1.10

3.5 dS/m
3.00
The
validation
model was carried out by keeping the same input
Pot
Soil
Water
Profile of the Hydrus-1D
1.10 and fieldparameters and only changing the water quality in7 dS/mboth cases of this study (potexperiments). Figures 6 and 7 show that the simulated
soil water content 10.20
profiles agree
3.5 dS/m
Soilwith
Salinity
Field for both pot and field experiments. Indeed, for all thewelltheProfile
measured profiles
7 dS/m5.70
output dates, the simulated profiles are very close to the measured ones.
3.5 dS/m
5.20
model’s
SoilTheSalinity
Profileperformance
Potwas evaluated qualitatively (Figures 7–9) and assessed
dS/m 2 and 3). These values
3.00 are low
using statistical evaluations and the RMSE values7(Tables

Land 2024, 13, 739

Soil Water Profile

Pot

Soil Salinity Profile

Field

Soil Salinity ProfilePot

7 dS/m
3.5 dS/m
7 dS/m
3.5 dS/m
7 dS/m

1.10
10.20
5.70
5.20
3.00

11 of 16

3.3.3. Crop Yield
3.3.3. Crop Yield
The Hydrus-1D model cannot directly estimate the crop yield. However, according
The Hydrus-1D model cannot directly estimate the crop yield. However, according
to Oster et al. (2012), the relative yield (Yr) can be estimated as the ratio between the acto Oster et al. (2012), the relative yield (Yr ) can be estimated as the ratio between thetual and potential (or maximum) transpiration, which are both provided in the model’s
actual and potential (or maximum) transpiration, which are both provided in the model’s
output files [42]. Figures 10 and 11 show the relative yields for tomatoes irrigated with
output files [42]. Figures 10 and 11 show the relative yields for tomatoes irrigated withwaters of diﬀerent qualities for both experimental pot and field trials simulated using thewaters of different qualities for both experimental pot and field trials simulated using
three models mentioned above (Additive, T-Model, and S-Model) to represent the eﬀects
the three models mentioned above (Additive, T-Model, and S-Model) to represent theof osmotic and matric potentials on crop root water uptake. The simulated relative yields
effects of osmotic and matric potentials on crop root water uptake. The simulated relative
decreased with increased irrigation water salinity (ECw) for all three stress response
yields decreased with increased irrigation water salinity (ECw ) for all three stress response
functions (Figure(Figure 10).
10). Thewith
tomatoes
irfunctions
Therelative
relativeyield
yieldisis0.98
0.98ininthe
thefieldfieldexperimentexperimentwithtomatoesrigated
with
fresh
water
(0
dS/m)
for
all
three
stressresponsefunctions.
However,intheirrigated with fresh water (0 dS/m) for all three stress response functions. However, in the
potcase,case,YYr equals
equals 0.33
0.33 forforfreshwater
freshwater irrigation.
irrigation. The
The reduced
reduced root
root development
development inin potspots
potr
compared
to
the
field
accountsfor
this
reductioninrelative
yield
[43].
compared to the field accounts for this reduction in relative yield [43].

Land 2024, 13, x FOR PEER REVIEW

Additive

12 of 17

T-Model

S-ModelFigure10.
10.TheTheeffecteﬀectofofsaline
salineirrigation
irrigationwater
wateronontomatoes’
tomatoes’
relativeyield(top)andandthethereFigure
relative
yield
(Yr(Y
) [r)−[−]] (top)relalationships
betweentheactual(Y)
andsimulated(Ys) yields (kg/plant) (bottom) using the threetionships between the actual (Y) and simulated (Ys ) yields (kg/plant) (bottom) using the three stressstress response models (Additive, T-Model, and S-Model) incorporated in Hydrus-1D (field exresponse models (Additive, T-Model, and S-Model) incorporated in Hydrus-1D (field experiments).
periments).

The actual yields measured in the two trials with different irrigation water qualities
were compared to the simulated yields to identify the most suitable stress response function
model for studying the combined effects of osmotic and matric potentials. According to
FAO Note 66 (2012), Yr = Y/Ymax , where Y is the actual yield, and Ymax is the maximum (orpotential) yield. In our experiments, Ymax is calculated for irrigations with fresh water. The
Ymax value equals 2.53 kg/plant for the field experiment and 4.16 kg/plant for the pot trial.
The values of the simulated relative yields were calculated using these values [42].
Figures 10 and 11 also present linear correlations between the measured and simulated
relative yields. The relative yields simulated using the additive model (Feddes) and themultiplicative T-Model (combining the Feddes et al. [28] model for saturation stress withthe threshold and slope model of Mass [29] for osmotic stress) were least correlated with themeasured relative yields in both pot and field trials. The multiplicative S-Model (combining
the Feddes model [28] for saturation stress with the S-shape model of van Genuchten [30]Land 2024, 13, 739

Additive

T-Model

S-Model12 of 16

Figure 10. The eﬀect of saline irrigation water on tomatoes’ relative yield (Yr) [−] (top) and the relationships between the actual (Y) and simulated (Ys) yields (kg/plant) (bottom) using the threestress response models (Additive, T-Model, and S-Model) incorporated in Hydrus-1D (field exfor osmotic stress) is the only model capable of reproducing the measured relative yields
periments).

with a correlation coefficient R² close to 1 for both pot and field experiments.

Additive

T-Model

S-ModelFigure11.
11.TheTheeffecteﬀectofofsaline
salineirrigation
irrigationwater
wateronontomatoes’
tomatoes’
relativeyield(top)andandthethereFigure
relative
yield
(Yr(Y
) [r)−[−]] (top)relas) yields (kg/plant) (bottom) using the threelationships
betweentheactual(Y)
andsimulated(Y
tionships between the actual (Y) and simulated (Ys ) yields (kg/plant) (bottom) using the three stressstress response models (Additive, T-Model, and S-Model) incorporated in Hydrus-1D (pot experresponse models (Additive, T-Model, and S-Model) incorporated in Hydrus-1D (pot experiments).
iments).

3.4. Effect of Temperature Increase
The actual toyieldsmeasuredin thetwo trials with
diﬀerent
qualities
According
the IPCC(2021),
temperatures
in Tunisia
are irrigation
expected water
to increasebywerecomparedtothesimulatedyieldstoidentifythemostsuitablestressresponse◦
2 C over the coming decades. The effects of this temperature increase on tomato cultivation
functionmodel
for studying
the combined
eﬀects of osmotic
andmatricpotentials.
Acwerestudied(numerically)by increasing
the temperatureby 2 ◦ C.
To thisaim,
the reference
cording
to
FAO
Note
66
(2012),Y
r = Y/Ymax, where Y is the actual yield, and Ymax is theevapotranspiration (ET0 ) values were recalculated, and simulations were rerun using the
maximum
potential) yield. In our experiments, Ymax is calculated for irrigations with
updatedET(or0 values while all other model parameters were kept unchanged.
freshThe
water.
The
Ymaxthese
valuesimulations
equals 2.53 are
kg/plant
for theinfield
experiment
kg/plant
results ofpresented
Figures
12 and and13. 4.16
In the
field
for
the
pot
trial.
The
valuesofthesimulated
relativeyieldswere
calculated
using
these
experiment, soil water content exceeded field capacity in the root zone. In deeper layers
values [42].
between
40 and 80 cm, soil water content decreased after the 60th day, indicating infiltration
Figures
10zone.
and 11linearcorrelations
betweenmeasuredsimubeyond
the root
Onalsothe present
other hand,in thepot experiment,
thethewatercontentand
remained
lated relative
yields.field
The relative
simulatedthe
using
the additive
andconstant
and below
capacity.yields
Additionally,
accumulation
ofmodelsalts in(Feddes)
the surface
the multiplicative(combining
thewaters
Feddeset increased
al. [28] model
for saturationstresslayer
increased dueT-Modelto irrigation
with saline
andevaporation.
The salinity
in the root zone reached an average value of 6 dS/m, and the relative yields estimatedusing the S-Model did not change compared to the measured relative yields. An increasein temperature, thus, did not significantly affect the tomato yields in either trial [20].

Land 2024, 13, 739

remained constant and below field capacity. Additionally, the accumulation of salts inthe surface layer increased due to irrigation with saline waters and increased evaporation. The salinity in the root zone reached an average value of 6 dS/m, and the relative
yields estimated using the S-Model did not change compared to the measured relative
yields. An increase in temperature, thus, did not significantly aﬀect the tomato 13
yieldsof 16 ineither trial [20].

Land 2024, 13, x FOR PEER REVIEW

14 of 17

Figure 12. Eﬀects of a temperature increase of 2 ◦°C on tomatoes cultivated in field conditions: relaFigure 12. Effects of a temperature increase of 2 C on tomatoes cultivated in field conditions:tive yield as a function of irrigation water salinity (top left); soil water content profiles at 30, 60, andrelative yield as a function of irrigation water salinity (top left); soil water content profiles at 30,
109 days when irrigated with freshwater (top right); soil salinity profiles at 30, 60, and 109 days
60, and 109 days when irrigated with freshwater (top right); soil salinity profiles at 30, 60, and(middle row) when irrigated with fresh water (left) and saline waters of 3.5 (middle) and 7 (right)
109 days (middle row) when irrigated with fresh water (left) and saline waters of 3.5 (middle)
dS/m; and average root zone salinity when irrigated with fresh water and saline waters of 3.5 and 7
and 7 (right) dS/m; and average root zone salinity when irrigated with fresh water and saline
dS/m (bottom).
waters of 3.5 and 7 dS/m (bottom).

Figure 13. Cont.

Land 2024, 13, 739

14 of 16◦

Figure13.
13.Eﬀects
Effectsofofaatemperaturetemperature increase
increase of
C on
Figureof 22 °Con tomatoes
tomatoescultivatedcultivatedininpot
potconditions:conditions: relarelative
yield
as
a
functionofirrigationwater
salinity(topleft);
average
soil
water
when
tive yield as a function of irrigation water salinity (top left); average soil watercontent
content
when irriirrigated
fresh
water
(top
right);
averagesoil
soilsalinity
salinityinin thethe 0–30
left);
gatedwithwith
fresh
water
(top
right);
average
0–30 cmcmsoilsoillayer
layer(bottom(bottomleft); andandzoneroot zone
salinity
5 cm
depth)
forirrigations
irrigations with
with fresh
salinewatersof 3.5ofandroot
salinity(at 5(atcm
depth)
forfreshwater
waterandandsalinewaters
3.5 and 7
7 dS/m(bottomright).
dS/m(bottomright).

4. Conclusions

4. Conclusions

The aridity of regions like Tunisia has prompted the intensification of irrigation pracTheariditythe
ofscarcity
regions
like Tunisiawaterhas resources
promptedirrigation
tices.
However,of good-quality
hastheled intensification
to the necessity ofofusing
practices.
However,the scarcity
of good-quality
water
has
ledsuchto thenecessity
brackish waterin agriculture.
The accumulationof salts
dueresources
to irrigationwithwatershas
detrimental
effects
on
both
soil
and
crop
yields.
Experiments
conducted
using
tomatoesof using brackish water in agriculture. The accumulation of salts due to irrigation withgrown
in pots
the field andirrigatedwithsoilthreedifferent
water qualities
ranginginsuchwatershasanddetrimental
eﬀectson bothandcrop yields.
Experiments
conducted
salinity
from
0
dS/m
to
7
dS/m
provided
data
to
study
the
variations
in
soil
water
and
using tomatoes grown in pots and the field and irrigated with three diﬀerent water
salt dynamics. In both pot and field trials, the water content in the root zone (0–30 cm)
qualities ranging in salinity from 0 dS/m to 7 dS/m provided data to study the variations
remained close to field capacity throughout the crop cycle. The variations in salt proinfiles
soilshowedwater andsalt dynamics.
In bothdepending
pot and fieldtrials, thewatercontent
in the root
progressive
soil salinization
on irrigationwater
salinity,
reaching
zone
(0-30
cm)
remained
close
to
field
capacitythroughoutthecropcycle.
The
variations
12 dS/m in the pot soil and 8 dS/m in the field soil. Crop reactions to these water qualities
inweresalt evaluatedprofiles showed
progressive
soil
salinization
on irrigationwater salinusing water
movement
andsalt transferdepending
modeling using
the Hydrus-1D
ity,reaching
12 dS/m effects
in the ofpotsoil anddS/mpotentials
in the fieldsoil.
Crop reactions
to thesemodel.
The combined
osmotic
and8matricwere
evaluatedusing threestressqualities
response werefunctionmodels: using
the additive
and twomultiplicative
the usingwater
evaluatedwater model
movement
andsalt transfermodels,modeling
T-Modeland S-Model.
estimated
relativecrop ofyieldsshowedthatmatric
only the
S-Model weretheHydrus-1Dmodel.The
The
combined
eﬀectsosmotic
andpotentials◦ C temperature increase
could reproduce
the measured
relative yields.
A hypotheticalevaluatedusing threestress response
functionmodels: the2additivemodel and two muldid not significantly affect crop yields. Soil salinization slightly increased due to increased
tiplicative models, the T-Model and S-Model. The estimated relative crop yields showedtemperature and evaporation.
that only
the S-Model could reproduce the measured relative yields. A hypothetical 2 °C
Adopting a modeling approach based on soil geochemical characterization and thetemperature
increaseofdid
not significantly
aﬀect
crop transportyields. Soilslightly inUnsatChem module
HYDRUS[14,15], which
considers
andsalinization
reactions between
2+
2+
+
+
2
−
2
−
−
creaseddue
toincreased
temperatureandevaporation.
major ions (e.g., Ca , Mg , Na , K , SO4 CO3 , Cl ), would be an alternative approach to this study, where the risks of soil alkalization and salinization could be morethoroughly explored for strategic crops like tomatoes. Moreover, to obtain more accurate
yield predictions, using specialized crop models, such as AquaCrop and DSSAT, would be
advisable. These crop models are specifically designed to simulate and predict crop growthand yield under varying environmental conditions and provide more reliable estimates ofagricultural productivity. Therefore, while Hydrus-1D excels in soil water and salinity dynamics, including crop models such as AquaCrop and DSSAT would improve the accuracyof yield predictions.
Author Contributions: Conceptualization, S.K., I.D. and K.B.A.; Data curation, S.K., K.B.A., S.B.M.
and S.G.; Formal analysis, S.K., J.Š. and S.B.M.; Funding acquisition, S.K. and S.B.M.; Investigation,
S.K., J.Š., I.D., A.Y., K.B.A., S.B.M. and S.G.; Project administration, S.K. and S.B.M.; Resources,
S.K. and S.B.M.; Software, J.Š.; Supervision, S.K. and S.B.M.; Visualization, S.K., J.Š., I.D., A.Y.,
K.B.A., S.B.M. and S.G.; Writing—original draft, S.K. and J.Š.; Writing—review and editing, S.K.,

Land 2024, 13, 739

15 of 16

J.Š., I.D., A.Y., K.B.A., S.B.M. and S.G. All authors have read and agreed to the published versionof the manuscript.
Funding: This research received no external funding.
Data Availability Statement: The data supporting the findings of this research are available inthe manuscript.
Conflicts of Interest: The authors declare no conflict of interest.

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