water
Review

A Review of HYDRUS 2D/3D Applications for Simulations of
Water Dynamics, Root Uptake and Solute Transport in Tree
Crops under Drip Irrigation
Giasemi Morianou 1,2, *, Nektarios N. Kourgialas 2, *1

2*

Citation: Morianou, G.; Kourgialas,
N.N.; Karatzas, G.P. A Review of
HYDRUS 2D/3D Applications for
Simulations of Water Dynamics, Rootand George P. Karatzas 1

School of Chemical and Environmental Engineering, Technical University of Crete, Polytechneioupolis,
73100 Chania, Greece
Water Recourses-Irrigation Environmental Geoinformatics Laboratory, Institute of Olive Tree, Subtropical
Crops and Viticulture, Hellenic Agricultural Organization (ELGO Dimitra), Agrokipio, 73134 Chania, Greece
Correspondence: morianou@elgo.gr (G.M.); kourgialas@elgo.gr (N.N.K.)

Abstract: Orchards with tree crops are of critical importance to the global economy and to theenvironment due to their ability to be productive for many years without the need for replanting.
They are also better adapted to extreme climatic conditions compared to other crops. However, newchallenges are emerging as climate change threatens both tree production and water supply. Drip
irrigation (surface and subsurface) is an irrigation method that has the potential to save water andnutrients by placing water directly into the root zone and minimizing evaporation. Many irrigation
designs and strategies have been tested to best perform drip irrigation for any given soil, crop and/or
climate conditions. The researchers’ need to find the optimal combination of irrigation managementand design in the most economical and effortless way led to the use of comprehensive numericalmodels such as HYDRUS 2D/3D. HYDRUS 2D/3D is a widely used mathematical model for studying
vadose zone flow and transport processes. A review of HYDRUS 2D/3D applications for simulationsof water dynamics, root uptake and solute transport under drip irrigation in the four most common
categories of tree crops (citrus, olive, avocado and deciduous fruit/nuts) is presented in this study.
The review promotes a better understanding of the effect of different drip irrigation designs andtreatments, as well as the reliability provided by HYDRUS 2D/3D in the evaluation of the above. This
manuscript also indicates gaps and future challenges regarding the use of the model in simulationsof drip irrigation in tree crops.

Uptake and Solute Transport in Tree
Crops under Drip Irrigation. Water
2023, 15, 741. https://doi.org/

Keywords: HYDRUS 2D/3D; drip irrigation; trees; irrigation system; irrigation treatment; model
efficiency

10.3390/w15040741
Academic Editor: Giovanni
Ravazzani
Received: 7 December 2022
Revised: 31 January 2023
Accepted: 8 February 2023
Published: 13 February 2023

Copyright: © 2023 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
Worldwide, water resources are under pressure as population growth and agriculturalintensification have resulted in an increased demand. Climate change combined with theresulting desertification, will exacerbate the problem and increase the areas characterized
by severe drought [1]. According to the FAO [2], agriculture is the largest consumer ofwater, accounting for almost 70% of global freshwater withdrawals, while 10% is used fordomestic consumption and the rest for industry. Due to water shortage and water–climate
effects, in the last decades an alternative practice for irrigation has become the use ofwastewater [3]. However, the use of wastewater is still being tested for potential negative
effects on soil and plants after long-term applications [4]. Thus, the need for more efficientand optimized use of water in irrigation is still critical [5].
Micro-irrigation, such as micro-sprinkler irrigation, drip irrigation, microtubing, etc.,
is the preferred method of irrigation by farmers owing to its low cost and water efficiency,with drip irrigation being one of the most common practices for vegetable and perennial
crops such as fruit trees. Drip irrigation provides the possibility of precise water andWater 2023, 15, 741. https://doi.org/10.3390/w15040741

https://www.mdpi.com/journal/water

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chemical application in terms of both quantity and location, and therefore maximal waterand nutrient uptake, while minimizing leaching from the root zone [6]. In addition, drip
irrigation can be adapted to a wide range of topographic features, soil conditions and crop
types [7]. Drip irrigation systems consist of small emitters that are either buried (subsurface
drip irrigation) or placed on the soil surface (surface drip irrigation) and deliver water at acontrolled rate [8]. In this regard, drip irrigation provides a high level of management, andallows for the accurate application of irrigation according to crop water needs, especially
under orchard conditions [9].
Quantifying soil moisture content and chemical nutrient concentrations under a microirrigation system is a challenging task due to variations in soil hydraulic properties, emitter
discharge rates, irrigation volume and frequency and water uptake by roots. Due to these
uncertainties, sub-root zone seepage and nutrient leaching may occur, even though theapplied water is equal to or less than the crop demand [6,10]. In addition, field experiments
and measurements to determine water movement and chemical concentration are very
time-consuming and expensive [11]. Therefore, mathematical/conceptual models havebeen developed for estimating water and solute transport in the vadose zone [12–16]. The
modeling approach, although considered to be a useful alternative to field measurements,
constantly includes uncertainties. Thus, using the best-fit model can produce more reliable
results for sustainable agriculture policymakers. The most complete, reliable and widelyused software package for simulating water, heat and solute movement in two- and threedimensional variably saturated porous media is HYDRUS 2D/3D [17]. An important
advantage of HYDRUS 2D/3D compared to other similar models is that there are no
limitations to a specific spatial or temporal scale [18]. The model has been used for many
applications over the years and especially for agricultural applications. Compared toother unsaturated zone models, HYDRUS provides users with more options for evaluating
different irrigation schedules [19–22], studies on root water uptake [23–27] and leachingof nutrients and contaminants [6,28–33]. It has also been used extensively to evaluate theeffects of different irrigation and fertigation strategies/treatments [6,34–36].
Since Skaggs et al. [37] effectively compared HYDRUS-2D simulations of drip irrigation with experimental field observations, the model has proven to be highly suitable forstudies of drip irrigation studies under many kinds of cultivation [21,38–45]. Althoughthese studies indicate the importance of numerical modeling in designing irrigation andfertigation systems for different crops, most studies are conducted for annual crops. The
literature on modeling studies of drip irrigation for perennial horticultural crops, suchas fruit and nut trees, is extremely limited. Depending on the age of the tree, the cropdevelopment stage, the percentage of soil cover and the local conditions, the water requirements of trees can be considered as quite high. In addition, trees control factors such as soil
moisture dynamics through canopy interception and shading [46], root water uptake andtranspiration [23]. All these factors distinguish tree crops from annual crops by the way
in which irrigation water and nutrients are applied. This fact makes further investigation
imperative (given the existing gap) involving simulations of water and solvent movementin the root zone of a tree under drip irrigation using models such as the widely used
HYDRUS (2D/3D) model.
This review is intended to provide an overview of the HYDRUS 2D/3D applications
for simulating water dynamics, root uptake and solute transport in tree crops under drip
irrigation. In the present work, tree crops are divided into the four most common categories:
citrus trees, olive trees, avocado trees and deciduous fruit (pear, apple and jujube) andnut (almond, pistachio, etc.) trees. These crop categories differ in their water stress tolerance, cultivation and fertilization practices and yield/harvest time. The numerical model
HYDRUS 2D/3D is presented in Section 2. The application of the model to drip-irrigatedcitrus trees, olive trees, avocado trees and deciduous fruit and nut trees is presented in
Sections 3, 4, 5 and Section 6, respectively.

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2. HYDRUS 2D/3D Software
The Windows-based HYDRUS 2D/3D model [18] (Figure 1) simulates water flow, heatmovement and the transport of solutes of variably saturated porous media in two and three
dimensions (2D/3D) using various numerical and mathematical techniques. Many studies
have evaluated the software and analyzed its potential for predicting water and nutrient
movement for various drip irrigation methods [37,47].

Figure 1. The Windows-based HYDRUS 2D/3D model software package. (a) Project navigator—data(interface), (b) domain types (2D/3D) and (c) main simulation modules.

A general schematic presentation of the transport domain of a -drip-irrigated treewith the main hydrological fluxes is shown in Figure 2a,b which also describes the main
modules of the HYDRUS program for the simulation of these fluxes. The water flow module
includes the saturated and unsaturated water flow and incorporates various models for theestimation of soil hydraulic properties. A sink term accounting for water uptake by plantroots is also included. For the heat and solute transport modules, HYDRUS uses convection–
dispersion-type equations. The heat transport equation considers movement by conduction
as well as convection with flowing water. The governing flow and transport equations
are solved numerically using Galerkin-type linear finite element schemes. The inverse
optimization is also included in the HYDRUS program which is an indirect approachfor estimating the unsaturated soil hydraulic and/or solute transport parameters fromtransient flow and/or transport data [48]

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Figure 2. (a) Schematic of the main water and solute fluxes and (b) schematic of the HYDRUS
modular structure.

The HYDRUS 2D/3D software numerically solves the Richards’ equation (Equation (1))
for both saturated and unsaturated water flow using convection/dispersion equations forheat and solute transport [14].







∂
∂h
∂
∂h
∂
∂h
∂θ
=
K (h)
+
K (h)
+
K (h)
+1 −S
(1)
∂t
∂x
∂x
∂y
∂y
∂z
∂z
where θ is the volumetric water content of the soil [L3 L−3 ], t is time [T], K is the hydraulicconductivity [LT−1 ], h is the soil water pressure head [L], x and y are the horizontal spatial
coordinates [L], z is the vertical spatial coordinates [L] and S is the sink term representing
root water uptake [T−1 ]).
The sink term S in Equation (1) represents the volume of water removed per unit timefrom a unit volume of soil by the plant water uptake. Feddes [49] defined S as:
S(h, z) = a(h)·Smax (h, z)(2)where the water stress response function α(h) is a prescribed dimensionless function of soil
water pressure head (0 ≤ α ≤ 1), Smax is the maximum possible root water extraction rate
when soil water is not a limiting factor [L3 L−3 T−1 ] and z is soil depth [L].
Soil hydraulic properties are calculated using the water retention function and hydraulicconductivity described by the van Genuchten–Mualem constitutive relationship [50,51]:

θ (h) =

θ s − θrθr + [1+(αh)n ]m

h<0




h≥0

θs

(3)

h

 m i2K (h) = Ks Se l 1 − 1 − Se 1/m(4)Water 2023, 15, 741

5 of 23

where θs is the saturated water content (L3 L−3 ); θr is the residual water content (L3 L−3 ); a
(L−1 ), m and n are empirical parameters that determine the shape of the soil water retention
curve where m = 1 − 1/n and l is the shape parameter; Ks is the saturated hydraulicconductivity (LT−1 ) and Se is the relative saturation (dimensionless) and is defined as:Se =θ − θrθ s − θr

(5)

The non-reactive solute transport in a homogenous medium is described by thegoverning advection–dispersion equation [52]:


∂θc
∂
∂c
∂q c
=
θDij
− i
(6)
∂t
∂xi
∂xi
∂xi
where θ is the volumetric water content; c is the solute concentration in liquid phase, ML−3 ;t is the time, T; xi and xj (i, j = 1, 2, 3) are the spatial coordinates L; qi (i = 1, 2, 3) are thewater fluxes in three directions L T−1 and Dij is the hydrodynamic dispersion coefficienttensor L2 T−1 .
3. Citrus Trees
Citrus is recognized as a particularly important horticultural crop for the global agricultural sector as there are 140 countries that produce citrus [53]. Citrus trees produce fruits,
including important crops such as oranges, lemons, grapefruits, pomelos and limes. Globally, citrus occupies 10,072,197.00 ha of agricultural land and reached 158,490,986.00 tons
in 2020 [2]. Most of the citrus growing areas are exposed to dry and hot summer weather.
The vast majority of citrus crops in these areas are oranges (56%), with the remainder
distributed among mandarins (28%), lemons and limes (15%) and grapefruit (1%) [2]. Citrus irrigation and nutrient management are critical, especially in areas of water scarcity.
Inadequate quantities of irrigation water or poor-quality water are factors that negatively
affect citrus tree productivity and fruit quality. Regarding citrus fertilization, nitrogen is
the key nutrient The increased use of nitrogen fertilizers in citrus results in nitrate leachingfrom the root zone and is a potential source of groundwater contamination [11]. Therefore,
optimal irrigation and fertilization scheduling in citrus production are major challenges
to the control of water and nitrogen losses below the root zone [54]. Therefore, efficientsimulation models such as HYDRUS 2D/3D have become valuable tools for studying water
dynamics and solute transport through the soil profile to design proper irrigation andfertigation systems for citrus cultivation [55].
3.1. HYDRUS 2D/3D Model Performance in Citrus Trees
There are many reasons as to why it is necessary to evaluate the performance ofnumerical models. A primary objective is to assess how well the model fits the observed
data by adjusting model parameter values (calibration—validation), then the ability of themodel to reproduce the historical and future behavior of agricultural/hydrologic systems
and finally to compare current modelling efforts with previous studies [56]. In general,models such as HYDRUS 2D/3D have proven very useful for simulating conditions that are
too expensive or technically impossible to test under field conditions. For citrus trees, the
HYDRUS 2D/3D model has been used to simulate soil water dynamics and solute transport
under both field conditions and more controlled experimental conditions (lysimeter).
In the lysimeter study by Phogat et al. [11], the model was calibrated using watercontent and drainage measurements under an orange tree. Simulations were also performed to evaluate nitrate leaching and fertigation management effects. Moisture content
distributions and leaching rates predicted by HYDRUS 2D/3D agreed well with measured
values in the lysimeter. The performance of the model was robust, as indicated by thestatistical measures used in the study.

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Experiments under field conditions used HYDRUS 2D/3D to predict seasonal water,
salt and nitrate dynamics in citrus. Statistical comparisons of measured values withmodeling results showed a consistent performance of the model [57]. In addition, Phogat
et al. [57] observed discrepancies between predicted and observed nitrate–nitrogen (NO3− N) and soil solution salinity (ECsw) concentrations (mean absolute errors within acceptable
limits). This is likely due to the assumption of a constant boundary flux at the surface during
a given daily time step or because the model considers only a simple linear movementof nitrogen, rather than all complex processes (mineralization, denitrification, microbialinteractions, etc.). Phogat et al. [58] claimed that most studies only evaluate a portion of
the model and not its overall behavior. Therefore, they used eleven statistical measures tocompare the values of water content, ECsw and NO3− -N dynamics simulated by HYDRUS2D with field-measured values obtained under drip-irrigated mandarins. The objective
was to determine which set of statistical measures was most appropriate for evaluating
model performance. They concluded that for the reliable evaluation of model performancein field applications, a combination of different statistical criteria must be included with anevaluation of absolute or relative volume error.
3.1.1. Findings Regarding the Design of Drip Irrigation Systems
In the literature, citrus cultivation is usually found growing under advanced fertigation
systems that combine drip irrigation and fertilizer application to deliver water and nutrients
directly to the roots of the plants. Therefore, there is a need to evaluate these systems
because significant leaching of contaminants (especially nitrogen) can occur near drip lines.
There are few studies investigating the importance of numerical modelling for the design
and management of irrigation and fertigation systems in citrus, and even fewer studies
using the HYDRUS 2D/3D model (Table 1). The first attempt to study the fate of nitrates
in citrus using HYDRUS 2D/3D was conducted by Phogat et al. [11] in an experimental
lysimeter. The design of the irrigation system used in this study, while quite common in
fruit tree irrigation, has not been found in any other work where the drip irrigation system
was simulated using the HYDRUS 2D/3D model. The emitters were placed on a circle
25 cm from the tree trunk equidistant from each other and the irrigation was modelled as a
circular line source with a uniform water flux along the drip line. The other three works in
the literature on simulating drip irrigation in citrus using HYDRUS 2D/3D were conductedunder field conditions [55,57,58]. In these studies, irrigation water was supplied througha surface drip irrigation system, with drip lines placed 60 cm apart on either side of thetree line. Of the four studies with citrus trees, only Panigrahi and Sharma [55] made acomparison between the irrigation methods. They compared surface and subsurface drip
irrigation and tested the distance of lateral lines from the tree trunk. It was found that theproper distribution of water in the root zone of citrus plants was possible when drip lines
were placed at a distance 60 cm from the tree trunk (surface drip irrigation). In addition,
subsurface drip irrigation produced higher yields by maintaining a relatively high watercontent in the root zone by placing the drip line at a depth of 30 cm. They also conclude
that the distance of the irrigation line from the tree trunk depends on the age of the plant
and the depth of the root system.
3.1.2. Findings Regarding Irrigation and Fertigation Strategies
In arid and semi-arid regions there is a growing need for irrigation methods thatconserve water and maintain crop production. Traditionally, citrus plants are grown underadvanced fertigation systems, and for this reason it is critical to keep nutrients in theroot system, increase root uptake and avoid deep percolation. Deficit irrigation strategies
can contribute to this end, stabilize yield and maximize water productivity. The maintypes of deficit irrigation in citrus production are sustained-deficit irrigation (SDI) andregulated-deficit irrigation (RDI). SDI is based on applying a specified level of constantwater stress (a ratio of ETC ) throughout crop growth, without regard for the phenologicalperiod [59]. In RDI strategies, water stress is applied during specific crop stages. More

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specifically, the effects of RDI treatments depend on the phenological period in which thewater restriction is applied. For instance, the application of RDI in citrus during period I(spring, flowering and fruit set) could diminish the final yield due to the fall of flowers andyoung fruits [60–62]. González-Altozano and Castel [63–65] carried out several RDI tests
on an experimental orchard of ‘Clementina de Nules’ citrus trees and they concluded that theapplication of RDI during period II (initial fruit enlargement, July–August) did not affectyield, fruit size or quality and allowed significant water savings. They also observed thatwater deficit during period III (final stages of crop development, end of summer–autumn)
resulted in a decrease the fruit size.
In this context, using HYDRUS 2D/3D Phogat et al. [9] evaluated scenarios in whichless irrigation water (50% and 75% of ETc) is applied. The results show that a higher uptake
efficiency was achieved when less water was applied. In another study, Phogat et al. [53]evaluated certain scenarios that focused on reducing irrigation and N application by 10–20%
through the growing season. These scenarios resulted in a reduction in N leaching andwater drainage, but also in a decrease in N uptake and water uptake compared to normal
practice. At the same time, salinity was increased. The main problem with these scenarios
was that a reduction in plant water and N uptake would have a major impact on plant
growth and yield. They also tested scenarios with a 10–50% reduction in irrigation in thesecond half of the growing season. They concluded that a 30% reduction in irrigation
during this period was the best scenario, reducing both water and nitrate leaching andincreasing crop N uptake compared to full irrigation. They found that further reductions in
irrigation of 40% and 50% greatly reduced water and nitrate infiltration and also increased
soil solution salinity (ECsw, dSm−1 ) in the root zone to a level much higher than thetolerance threshold of the crop.
Other parameters studied with the HYDRUS 2D/3D model are related to the form of
irrigation strategy in terms of time intervals and duration of irrigation/fertigation. Nitrate
management and irrigation strategies also include increasing or decreasing the frequency of
application. In a scenario by Phogat et al. [57], increasing the irrigation frequency with short
irrigation events while maintaining the same irrigation volume had no effect on the deep
percolation of water and nutrients. However, an increase in salinity was observed compared
to traditional practices. Simulations in citrus examined the influence of application timing
and showed that it did not have a large impact in a normal fertigation schedule with small
and frequent N doses within an irrigation event in both pulsed and continuous irrigation
scenarios [11,57].
3.2. Summary of HYDRUS 2D/3D Application in Citrus Trees
The application of the HYDRUS 2D/3D model to drip-irrigated citrus trees is notextensive enough to draw conclusions about the optimal irrigation scheme in terms ofthe number of laterals and drippers or the optimal position of the dripper (radial, deep).
Only one study compares surface and subsurface irrigation and concludes that subsurface
irrigation produced higher yields by maintaining relatively higher water content in theroot zone. On the other hand, all HYDRUS 2D/3D studies on irrigation strategies in citrus
show that deficit irrigation is a good agricultural practice to conserve water and maintainproduction. Although caution should be used when applying high water stress, there is arisk of increasing soil salinity. This risk also exists when the frequency is changed and whenshort irrigation events are applied. Otherwise, frequency does not affect other factors suchas percolation, water and nutrients. It is also worth mentioning that due to the applicationof fertigation to citrus, the fate of nitrates in the soil is also studied, which has not been
explored to a large extent in simulations with tree crops.

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Table 1. Summary of HYDRUS 2D/3D simulations in citrus trees.
Research
ReportCrop

Soil Type

Irrigation
System 1

Irrigation
Treatment 2

HYDRUS
2D/3D

Simulation
Processes

DI -on a circle
and fertigation

Ip vs. Ic

2D

Water flow
Root uptake
Nitrate dynamics

DI -2 drip lines
and fertigationdifferent
schedules

2D

Water flow
Root uptake
Salinity and Nitrate
dynamics

SubDI vs. DI-

2D

Water flow
Root uptake

DI-2 drip lines
and fertigation-

2D

Water flow
Root uptake
Salinity and Nitrate
dynamics(0–60 cm soil
depth): loamy sandPhogat et al.
[11]orange(lysimeter)(60–85 cm soil
depth): sandy
Loam(85–110 cm soil
depth): sandPhogat et al.
[57]

mandarin(0–90 cm soil
depth): sandy loam
(90–150 cm soil
depth): loam
(0–40 cm soil
depth): sandy loam

Panigrahi andSharma [55]Phogat et al.
[58]

mandarinmandarin(40–100 cm soil
depth): sandy clay
loam
(0–90 cm soil
depth): sandy loam
(90–150 cm soil
depth): loam

Notes: 1 SubDI: Subsurface Drip Irrigation; DI: Drip Irrigation. 2 FI: Full Irrigation; RDI: Regular Deficit Irrigation;
SDI: Sustained Deficit Irrigation; Ip: Pulsed Irrigation; Ic: Continuous Irrigation.

4. Olive Trees
Olive cultivation is considered one of the most important and oldest agriculturalactivities. The most common olive varieties encountered are Arbequina, Wilsoni, Chemlali,
Hojiblanca, Frantoio, Coratina, Leccino, Kalamata, etc. According to the FAO’s statistics(2021), southern Europe produces about 60% of the world’s olive production. In the past,olive trees (Olea europaea L) were mainly grown under rainfed conditions. However, in
recent decades, due to climate change and increased crop water demands, olive producers
have opted for irrigation to achieve optimal yields, using drip systems in most cases [66].
However, water limitations in the main olive-growing areas have led farmers to consider
different adaptation strategies and irrigation systems. For example, many farmers apply
deficit irrigation strategies to save water while maintaining crop profitability. The HYDRUS
2D/3D model is widely used in the scientific literature for the design and management ofdrip irrigation systems.
4.1. HYDRUS 2D/3D Model Performance in Olive Trees
Only four studies were found in the literature evaluating drip irrigation systems
and strategies for olive trees using the HYDRUS 2D/3D model (Table 2). These studies
only concern simulations of soil water content as no studies of nitrate–nitrogen (NO3− N) or soil solution salinity (ECsw) dynamics in olive trees have been conducted using
this model. In their study, Egea et al. [67] found a good level of agreement between
simulated and observed soil–moisture contents across all treatments and probe locations
studied. However, they also found that model accuracy decreased when regulated deficit
irrigation was considered compared to full irrigation treatments, which could be due topossible inaccuracies and oversimplifications in modeled root water uptake under drought
conditions. The orchard used for the experiments and simulations by Egea et al. [67] wasalso used by Fernandes et al. [68] four years later. The RMSE and MAE values obtained
from the comparison of measured and simulated soil water contents were similar to thoseWater 2023, 15, 741

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reported by Egea et al. [67] calculated for full irrigation (RMSE: 0.035–0.050 m3 m−3 andMAE: 0.030–0.040 m3 m−3 ), and slightly larger for deficit irrigation treatments (RMSE:
0.058–0.083 m3 m−3 and MAE: 0.047–0.075 m3 m−3 ). Therefore, both studies claim that thesimulations with the HYDRUS 2D/3D model are considered acceptably accurate. Autovino
et al. [22] investigated the performance of the HYDRUS-2D numerical model for predicting
soil water content and transpiration fluxes in an olive orchard irrigated with two different
irrigation systems. The measurements of the midday stem water potential were also used
for the calibration of the relative transpiration simulated by the model. The statisticalanalysis shows that the patterns of soil water contents generated by the model matchedwell with those measured in the experimental field. In addition, the model was also
capable of estimating actual transpiration with acceptable RMSE values for both years of
the experiment. Consequently, HYDRUS 2D/3D seems to be a suitable model to solve
the water mass balance of olive trees under Mediterranean climate conditions. Carlos
et al. [69] also wanted to test the efficiency of the model under desert conditions, namely inan olive orchard in Chile. The efficiency of the model was evaluated by comparing model
simulations with observations of volumetric water content and electrical conductivity inpores with five frequency domain reflectometry (FDR) sensors installed in the soil profile.
They concluded that HYDRUS 2D/3D represents the variations in volumetric water content
in olive trees in the desert with acceptable accuracy. However, the same conclusion was notreached for the simulation of electrical pore conductivity under the same conditions.
4.1.1. Findings Regarding the Design of Drip Irrigation Systems
Surface irrigation is used in all four olive orchard studies with HYDRUS 2D/3D. The
studies focused on the design of drip irrigation systems by evaluating the impact of thenumber of drip laterals and drippers. Egea et al. [67] evaluated the correctness of irrigation
design in an experimental olive orchard by analyzing the simulated soil water balancecomponents. In a HYDRUS 2D simulation scenario they reduced emitter discharge rates byhalf and doubled the number of drippers by adding another irrigation line. They found that
reducing emitter discharge by doubling the number of drip lines did not cause differencesin soil water balance components (soil water, evapotranspiration and drainage). A more
recent study by Fernandes et al. [68] reached the same conclusion. They also studied
the effects of using one or two drip irrigation pipes per tree row. The results showed noeffect of irrigation with one or two drip lines per tree row on leaf water potential, stomatal
conductance, growth and fruit production. We must emphasize here that both studies
were conducted in high density olive orchards and conclude that there are no benefits
from using two drip irrigation laterals instead of one. Another comparison between two
different irrigation systems was conducted by Autovino et al. [22]. They used HYDRUS
2D to predict soil water dynamics and transpiration fluxes in an olive orchard where asingle drip lateral per plant row was installed symmetrically on both sides of each tree,compared to an irrigation system that distributes water over the entire soil surface. They
found that with the second irrigation system, the distribution of water content in the soil
was more uniform than with a single drip system. In addition, because of the second
irrigation system (uniform irrigation throughout the field), the plants may have developed
a different root distribution and thus a locally altered water uptake. The lack of knowledge
about the temporal patterns of the active root system does not allow further speculation.
4.1.2. Findings Regarding Irrigation Strategies
The HYDRUS 2D/3D model was also used to simulate the components of soil waterbalance (irrigation, precipitation, evapotranspiration, water uptake by roots, drainage
and soil storage) to evaluate irrigation management in olive orchards under different
irrigation regimes. Simulations in drip-irrigated olive orchards show that differences insoil volume and soil surface area moistened by irrigation are not sufficient to affect thewater components studied [67,68]. Egea et al. [67] found that the differences in deep
percolation between full irrigation and deficit irrigation treatments were mainly caused byWater 2023, 15, 741

10 of 23a rainfall event towards the end of September and not by the irrigation strategy. Therefore,
deficit irrigation is a safe management option because it does not significantly affect thecomponents of the soil water balance. However, consideration must be given to the stageof vegetative growth at which is it implemented. Not applying irrigation can put the plantunder severe stress at the II stage of vegetative growth (flowering in mid-May) when it
is sensitive to water stress. The application of deficit irrigation (50% of ETc) during theperiod from mid-June to late August allows the measured midday water potential of thestems to always remain below the threshold for mild water stress [22]. Fernandes et al. [68]showed in their results that daily maximum leaf stomatal conductance, shoot growth andleaf area were greater during full irrigation than during regulated deficit irrigation (45% ofETc). Despite these differences, deficit irrigation did not cause differences in either fruitor oil yields. They also concluded that a deficit irrigation strategy minimized water losses
with respect to drainage, compared to full irrigation.
Other factors that affect soil water components and play a key role in designing theirrigation strategy are the frequency and timing of the application. Of the three studies
conducted in olive orchards using HYDRUS 2D/3D, only Egea et al. [67] evaluated theeffects of daytime versus nighttime irrigation and irrigation frequency on seasonal waterbalance components. They found that in the case of full irrigation, daytime irrigation
resulted in slightly higher water losses through deep percolation than nighttime irrigationand that, for the same irrigation amounts, root zone pressure head decreased as irrigation
frequency increased. Therefore, an irrigation strategy should also conclude the adjustmentof these factors for the treatment applied.
4.2. Summary of HYDRUS 2D/3D Application in Olive Trees
For olive trees only four papers were conducted to simulate drip irrigation using the
HYDRUS 2D/3D model. All studies concerned surface irrigation, and some tests were
performed with an increase in laterals and drippers, keeping the amount of water supplied
to the trees constant. The results show that the number of laterals has no effect on soil
water components. In olive trees, it also showed that deficit irrigation has no effect on
the components of water balance and fruit yield, but the absence of irrigation in the IIstage of vegetation can cause severe stress to the plant. Therefore, deficit irrigation is a safe
strategy that allows minimizing water losses due to drainage. One study also examined theeffects of irrigation timing and frequency and found that increasing irrigation frequency
can reduce the pressure head in the root zone. Salinity and nitrate dynamics have notyet been studied, mainly because fertigation is not usually applied to olives. However,fertilization is applied in winter, so the fate of nitrates in soils during winter rains mustalso be studied.
Table 2. Summary of HYDRUS 2D/3D simulations in olive trees.
Research
ReportCrop

Egea et al.
[67]

olive
arbequina

Autovino
et al. [22]olive
nocellara del Belice

Soil Type(soil depth 0–40):
sandy loam
(soil depth 40–100):
sandy clay
(homogenous soil depth):silty clay loam

Irrigation
System 1

Irrigation
Treatment 2

HYDRUS Simulation
2D/3D
Processes

FI: 100% ETc
DI-1 vs. 2 drip lines

2D

Water flow
Root uptake

2D

Water flow
Root uptake

RDI:
DI-1 drip line vs.
total surface irrig.

FI: 100% ETc
RDI: 50% ETc

Water 2023, 15, 741

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Table 2. Cont.
Research
ReportCrop

Soil Type

Fernandes
et al. [68]olivearbequina(soil depth 0–60):
sandy

Irrigation
System 1

Irrigation
Treatment 2

HYDRUS Simulation
2D/3D
Processes

FI: 100% Etc
DI-1 vs. 2 drip lines

SDI: 45% Etc

2D

Water flow
Root uptake

2D

Water flow
Root uptake

RDI: 45% Etc
Carlos et al.
[69]

olive

not listed

DI-2 drip lines-

Notes: 1 SubDI: Subsurface Drip Irrigation; DI: Drip Irrigation. 2 FI: Full Irrigation; RDI: Regular Deficit Irrigation;
SDI: Sustained Deficit Irrigation; Ip: Pulsed Irrigation; Ic: Continuous Irrigation.

5. Avocado Trees
The avocado is becoming one of the most important tropical crops for the world
market. In Europe, production and consumption of avocados have increased dramaticallyin recent decades [70]. The most widespread varieties are Hass, Pinterton, Lamb Hass,
Carmen Hass, Stewart, Holiday, Pryor, Opal, Fuerte, Zutano, etc. The increase in avocado
consumption and spread to new markets around the world, in countries where avocado
was not traditionally consumed before, has led to local production in new areas such as
the Mediterranean region [71]. This is because locally grown fruits can generally offer
consumers a higher quality in terms of taste, nutritional value, and organoleptic properties,
as well as better prices [72,73]. However, choosing the right location for planting avocados
should be carefully considered to reduce the likelihood of future problems. Regarding soil
conditions, important parameters are pH, carbonate content, soil drainage capacity andsalinity [74]. In addition, avocados are quite demanding in terms of water compared to othertree crops. The water requirements of avocado trees depend on various factors such as theage of the tree, the soil type and climatic conditions. Therefore, new irrigation techniquesthat combine irrigation monitoring and simulation will be useful tools to conserve water,
mitigate leaching and control soil salinity while ensuring good tree yield.
5.1. HYDRUS 2D/3D Model Performance in Avocado Trees
To date, there are only two research studies in the literature that use the HYDRUS
2D/3D model in irrigated avocado trees [75,76]. The two studies evaluated the effectsof irrigation with freshwater (FW) and wastewater (WW). The simulated results did not
aim to reproduce real field conditions but rather focused on soil hydraulic properties,
their difference in drip irrigation with FW and WW and their effects on water uptake andtranspiration.
5.1.1. Findings Regarding the Design of Drip Irrigation Systems
In both studies of drip irrigation of avocado orchards, the irrigation system in thefield consisted of two drip lines per row placed 25 cm on opposite sides of the trunk,with drippers delivering 1.6 L/h [76] discharge and 2 L/h [75], respectively, 50 cm apart.
However, Assouline et al. [76], in order to find the best combination between irrigation
management and design when using WW, conducted the following tests: (a) applying
different irrigation rates (halving or doubling the drip rate) for the same (shorter or longer)
duration at the same irrigation dose; (b) increasing the number of lateral drip lines pertree row from 2 to 4, 15 and 65 cm from the tree on both sides and (c) changing theirrigation frequency from one irrigation every 2 days to daily irrigation. The different
combinations are described in Table 3. The effects of these experiments were expressed,
in terms of changes in soil hydraulic properties and plant water uptake which is also
related to yield. The results show that increasing the number of driplines per row increases
actual transpiration in both FW and WW irrigation, and significantly reduces the difference
between the two treatments, mitigating the effects of WW irrigation. The authors also
pointed out that the above results could also be achieved by increasing the number ofWater 2023, 15, 741

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drippers per row (reducing the distance between them) or by using concentric loops ofdriplines around the trunk.
5.1.2. Findings Regarding Irrigation Strategies
The irrigation treatments tested on avocado trees using the HYDRUS 2D/3D model
are: (1) using wastewater versus freshwater treatments, (2) application of different irrigation rates (changing discharge and duration) and (3) changing irrigation frequency.
Assouline and Narkis [75] used the axisymmetric vertical flow solution (flow variables:i.e., velocity and pressure, do not vary with angular coordinate θ) from HYDRUS 2D tocreate a representation of water content distribution below the dripper in an FW and a
WW irrigation soil profile. The results indicate that although a similar amount of water
was applied in both treatments, the total wetted volume in the WW irrigation soil was
smaller and more saturated. This behavior was often explained by the hydrophobicity ofsoil caused by the WW application. In addition, WW was observed to have a negative
effect on soil hydraulic properties (saturated hydraulic conductivity, sorptivity, cumulative
infiltration and evaporation were consistently lower).
On the one hand, long-term use of WW for irrigation can degrade soil properties
which in turn affects crop water uptake and leads to lower yields. On the other hand, there
is a need to treat and recycle wastewater and use it whenever possible and appropriate
to conserve freshwater, especially in areas of water scarcity. For this reason, Assouline
et al. [76] studied the effects of mixing WW with FW. Four water qualities resulting frommixing FW and WW in different ratios for irrigation of an avocado orchard were considered.
In the simulation study the effects of salinity and related osmotic potential on root uptake
and transpiration were not considered, since the objective was not to reproduce real field
conditions, but to focus only on the aspect of soil hydraulic properties in drip irrigation with
FW and WW. Transpiration in FW-irrigated soil is about 10% higher than in WW-irrigatedsoil. In addition, the results at all soil depth show that the infiltration capacity of the soil
decreases as the percentage of WW in the irrigation water increases. Mixing FW withWW (a higher proportion of FW) allows the use of WW without affecting the hydraulicproperties of the soil, which become apparent after a few years of irrigation, and without
significantly affecting plant uptake and growth. The advantages of mixing are also the
reduction of freshwater demand, the use of water with nutrients and the minimization ofpollutant leaching into waterways [77].
As mentioned earlier, Assouline et al. [76] evaluated irrigation rate and frequency
for drip-irrigated avocado trees using the HYDRUS 2D model. They conclude from theirresults that there is no gain in increasing the dripper discharge if the current arrangementof the two drip lines and frequency remain the same (every 2 days). However, the use oflower discharge increases transpiration and decreases the difference between FW and WW
irrigated soils. On the other hand, increasing the irrigation frequency to daily irrigation had
a significant negative effect, especially on WW irrigated soil. The difference between actual
transpiration in the FW- and WW-irrigated soils is maximum at this irrigation frequency,
regardless of the amount of drip water used.
5.2. Summary of HYDRUS 2D/3D Application in Avocado Trees
The conclusion of the two studies is that long-term irrigation with WW negatively
affects the hydraulic properties of soil and affects the transpiration and yield of the tree.
However, Assouline et al. [76] indicated that the use of drippers with lower discharge rates
combined with an increase in the number of driplines which increases the wetted area pertree tends to reduce the negative effects. This can also be accomplished by increasing thenumber of drippers per line or by using concentric loops of driplines around the trunk.
The approach of more drippers per line or the use of concentric driplines should be further
investigated.
Another gap in the studies is that while the effluent retains increased salinity, there areno simulations for salt leaching or other nutrients. In addition, the two studies conductedWater 2023, 15, 741

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on avocado trees do not compare simulation results with field observations. The above
information is based on results of laboratory experiments conducted on disturbed soil
samples. Therefore, they cannot fully represent the behavior of the soil profile at the field
scale. This could be a challenge for future studies. Additionally, for future research it would
be of interest to examine the fate of mineral and organic loads of applied wastewater in soil
with the help of Hydrus submodules.
Table 3. Summary of HYDRUS 2D/3D simulations in avocado trees.
Research
ReportCrop

Soil Type

Irrigation
System 1

Assouline andNarkis [75]avocado(homogenous soil depth):clay

2 drip lines; 2.0 L/h

Irrigation
Treatment 2FW
WW

HYDRUS Simulation
2D/3D
Processes
2D

Water flow
Root uptake

2D

Water flow
Root uptake

2 drip lines; 48 h;
3.2 L/h2 drip lines; 48 h;
1.6 L/h2 drip lines; 48 h;
0.8 L/hAssouline et al.
[76]

avocado(homogenous soil depth):clay

2 drip lines; 24 h;
1.6 L/h2 drip lines; 24h; 0.8
L/h
4 drip lines; 24 h;
0.8 L/h
4 drip lines; 48 h;
1.6 L/h
4 drip lines; 48 h;
0.8 L/hFW

2/3 FW—1/3
WW

1/3 FW—2/3
WW

WW

Notes: 1 SubDI: Subsurface Drip Irrigation; DI: Drip Irrigation. 2 FI: Full Irrigation; RDI: Regular Deficit Irrigation;
SDI: Sustained Deficit Irrigation; Ip: Pulsed Irrigation; Ic: Continuous Irrigation; FW: freshwater irrigation; WW:wastewater irrigation.

6. Deciduous Fruit and Nut Trees
Fruit trees are divided into two groups, evergreen and deciduous, and most fruit
trees are classified as deciduous. Deciduous fruit trees and nut trees include those thatbloom in the spring and summer and lose all their leaves in the fall. These trees remainbare during the winter months and require the cold temperatures to produce leaves andflowers in the spring [78]. Major fruit crops include apples (Malus sylvestris), apricots(Prunus armeniaca), cherries (Prunus sp.), figs (Ficus carica), peaches (Prunus persica), pears(Pyrus communis), plums (Prunus sp.) and prunes (Prunus domestica). Important nut crops
are almonds (Prunus amygdalus), filberts (Corylus avellana), pecans (Carya illinoensis) andwalnuts (Juglans regia). All these crops are grown mainly in temperate zones [79]. Irrigationis critical to the efficiency of deciduous trees because most of them can consume large
amounts of water when evaporative demand is high. Therefore, improving irrigationwater use in deciduous and nut trees is also essential due to water scarcity and the risk ofgroundwater contamination from leachate from irrigated fields [80].
6.1. HYDRUS 2D/3D Model Performance in Deciduous Fruit Trees and Nut Trees
Twelve studies were found in the literature using the HYDRUS 2D/3D model tosimulate water dynamics under deciduous trees (Table 3). The first simulation of drip
irrigation in a deciduous tree was also the first simulation conducted on trees using the
HYDRUS 2D/3D model and was conducted on jujube trees by Yao et al. [81]. In deciduous

Water 2023, 15, 741

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trees (apple trees) were also the first studies to simulate drip irrigation in perennial crops
using the 3D model of the HYDRUS 2D/3D package [82,83].
In the first study by Yao et al. [81], the goodness of fit between simulated and measured
values of volumetric soil water content was evaluated by using the root-mean-absolute error(RMAE). The results show that the RMAE values for water dynamics in all soil layers below
the drip tube indicate that the model can perform well throughout the growing season.
Subsequently, many studies of -drip-irrigated deciduous trees successfully simulatedchanges in soil water content at various distances from the emitter, times and soil depths
using HYDRUS 2D. Phogat et al. [9], Phogat et al. [84] and Phogat et al. [85] matched
the simulated soil water content well with the weekly measured neutron probe values
for both pulsing and continuous irrigation treatments in an almond orchard. Measured
mean soil water salinity (ECsw) also agreed well with predicted values, for both pulsedand continuous drip systems. In the study by Phogat et al. [84], they also observed thatthe root-mean-squared error (RMSE) value between the weekly measured and simulated
moisture content decreased throughout the domain when only a soil depth of 30 cm wasconsidered, where root density is highest in almonds. This indicates a good predictionof seasonal soil moisture distribution and plant water uptake. Yang et al. [86] calibrated
and validated the HYDRUS 2D model using soil water content and transpiration data.
Simulation results for both calibration and validation showed that average simulated soil
water values (within water volume) matched those measured once, especially during theirrigation period. In addition, simulated transpiration matched the measured data quite
well in both years. According to Janssens et al. [87], soil water potential (Ψsoil) can also
be successfully simulated using HYDRUS 2D. Only when the observed Ψsoil increased
above −20 kPa did the observed Ψsoil not match the calculated one, possibly due to thelimitations of the Watermark sensors in measuring the soil water potential in the wet range,
above −20 kPa. This suggests that positioning the sensors near the irrigation drippers
should be avoided, as mentioned in a previous chapter.
Xi et al. [88] and Nazari et al. [89] showed that HYDRUS-2D also provided a good estimate of soil water content under subsurface drip irrigation in a P. tomentosa plantation andin an apple orchard, respectively. In addition, Xi et al. [88] agree with Phogat et al. [84] thatthe top layer of 30 cm provides more robust simulations of water content and consequently
better predictions of tree growth responses to soil water.
Domínguez-Niño [82,83] were the first to use HYDRUS 3D to simulate soil water
dynamics in drip-irrigated trees. They pointed out that for the simulation of an orchard, it
is more interesting to use HYDRUS-3D than HYDRUS-2D because it solves the transport
problems on all three axes simultaneously and provides more realistic calculations of thesoil water distribution around the dripper. Special attention was paid to the source of thesoil hydraulic parameters. Simulations parameterized with the ROSETTA approach werecompared with others parameterized with the HYPROP + WP4C approach. ROSETTA isa software package that evaluates pedotransfer functions that use neural network models to predict soil hydraulic parameters from soil texture and related data for the van
Genuchten–Mualem model [51]. The results showed that the best agreement with soil moisture measurements was obtained with simulations parameterized with HYPROP + WP4C.
6.1.1. Findings Regarding the Design of Drip Irrigation Systems
Most of the studies in deciduous fruit trees and nut trees using the HYDRUS 2D/3Dmodel were conducted under surface drip irrigation with one or two irrigation lines,
although no comparison was made between irrigation systems and designs. Two of
the studies on deciduous trees examined soil wetting patterns under subsurface drip
irrigation [87,88]. According to many irrigation studies, compared to surface drip irrigation(DI), subsurface drip irrigation improves the delivery of water and nutrients directly to theroot zone while significantly reducing water losses through evaporation [39,90,91]. Nazari
et al. [89] try to determine the optimal location of emitters (radial and deep) in an irrigatedapple orchard using the HYDRUS 2D model. Their results show that for maximum use of

Water 2023, 15, 741

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available water by plant roots, it is better to install emitters at a distance (60 cm and 50 cm)
from the tree trunk.
Another important parameter in the design of a modern irrigation system in thecontext of smart agriculture is accurate monitoring. The optimal position of the sensors
must show significant variation and should be sensitive to irrigation. To ensure reliable
monitoring, several publications on drip irrigation simulation using the HYDRUS 2D/3Dmodel investigate the position of the measuring devices (e.g., tensiometers and sensors)
in deciduous trees, especially with respect to the drippers. No similar studies have been
published for olive and citrus trees. Only Autovino et al. [22] mentioned drip-irrigated olive
trees in their study and that the detection of soil water status requires the correct positioningof the measurement sensors to determine the soil water content values representative of
the whole root zone. Janssens et al. [87] used the HYDRUS 2D model in their study to
calculate soil water potential in an irrigated pear orchard to evaluate the extent to whichΨsoil observations obtained with soil water potential sensors in irrigated pear orchards
can be related to numerical calculations of Ψsoil distribution. The results of this study
suggest that sensor positioning near the irrigation drippers should be avoided to prevent
overestimation of Ψsoil and inaccurate irrigation scheduling. On the other hand, Yanget al. [86] recommended that sensors should be placed at a depth of 10 cm and at a distanceof about 15 cm from the dripper for surface drip irrigation. Their study was conducted in
P. tomentosa plantations using the HYDRUS 2D model. Their objective was to determine
the appropriate location of soil–water potential (SWP) sensors for a representative SWP.
Populus tomentosa plantations are not fruit or nut trees, but irrigation is a critical factor
for tree growth. In this study, different locations of tensiometers around the dripper andthe tree were investigated combining field experiments and numerical simulations whileconsidering indices of soil water, root distribution, tree growth, plant physiology andirrigation scenarios. Two other studies conducted in an apple orchard by DomínguezNiño et al. [82] and Domínguez-Niño et al. [83] concluded that the recommended sensor
locations could be a combination of sensors near the vertical of the drip and other sensors
in the middle between adjacent drippers, both at a 30 cm depth. The results of the lasttwo studies are more robust because the HYDRUS 3D model was used. The HYDRUS 3D
model provides more realistic calculations of soil water distribution around the dripper
in the orchard compared to HYDRUS 2D because it solves the transport problems on
all three axes simultaneously. For example, a 3D representation allows consideration ofneighboring drippers distributed along an irrigation dripline and at greater distances fromneighboring driplines. A recent study conducted in a pistachio orchard aimed to determine
the optimal measurement position for soil apparent electrical conductivity (ECa) using
an electromagnetic sensor (EMI) to monitor soil salinity (ECe). Two case studies were
simulated using HYDRUS 2D, one with high initial soil salinity and low salinity irrigationwater, and one with low initial soil salinity and high salinity irrigation water. The analysesof these two case studies show that a reliable EMI measurement distance from the dripline
was about 100 cm in the case of low salinity irrigation in saline soils and close to thedripline in the case of high salinity irrigation [92]. The results obtained from these studies
are specific to the case studies considered. The optimal location for measurement may
differ for different soils, crops and/or irrigation scenarios.
6.1.2. Findings Regarding Irrigation Strategies
As with olive, avocado and citrus, research on irrigation strategies/treatment is as
important as research on irrigation systems and designs to optimize productivity andminimize losses of limited irrigation water. Phogat et al. [84] were the first to conduct
HYDRUS-2D simulations on field data recorded for a deciduous tree (almond tree) to
evaluate daily variations in water fluxes under normal and stress conditions. The treatments
studied for the almond tree were a) full irrigation (100% ETc) by pulsed irrigation (FIp),b) sustained deficit irrigation (65% ETc) by pulsed irrigation (SDIp) and c) full irrigation(100% ETc) by continuous irrigation (FIc). The results obtained by the above HYDRUS-

Water 2023, 15, 741

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2D simulation showed that the efficiency of water uptake was significantly higher undersustained deficit irrigation (SDIp), while the additional water supply under full irrigation(FIp and FIc) resulted in water losses due to drainage. In addition, they observed thatsimulated salinity distribution was higher under SDIp, but well below the threshold forsalinity in almond cultivation. The tolerance of almonds to water stress is also reflected inwater productivity values. Similar conclusions were reached by Janssens et al. [87] who
applied two Sustained Deficit Irrigation treatments in a drip-irrigated pear orchard, one at
80% of ETc and one at 50% of ETc. They observed that at an irrigation rate of 80% ETc, thewet area of the soil extended to the entire irrigated side of the tree to a depth of 70 cm, incontrast to irrigation at a rate of 50% ETc where the wetting front remained concentrated
around the drippers. When applying water stress treatments, attention must be paid to tree
growth and productivity in addition to environmental impacts (water and nutrient losses
due to drainage). According to Xi et al. [88], soil water availability is directly related to tree
growth and productivity. In their study, two treatments were applied: a rainfed control
treatment in which no irrigation occurred and a treatment in which trees were irrigatedwhen the average soil water potential (SWP) reached −25 kPa at a depth of 20 cm fromthe dripper. In both treatments, water availability in the soil increased with depth and wassignificantly higher in the treatment with 25 kPa irrigation than in the treatment without
irrigation, but this difference was very small in the soil below a depth of 90 cm. Despite thehigh water availability at a 90 cm depth, the trees still suffered from growth loss when thesoil was dry at the surface.
Phogat et al. [9], Phogat et al. [84] and Phogat et al. [85] used the finite element
numerical model HYDRUS 2D to evaluate the effects of pulsed irrigation on water balanceand salinity distribution in the soil. Pulsing irrigation is the application of daily irrigation
in a phase of one hour of irrigation and one hour of break. The results of the first study [85]show that pulsed irrigation with a higher discharge rate (3.87 l/h) resulted in a similarwater and salinity distribution in the soil compared to continuous irrigation with a low
discharge rate (2 l/h). They also observed that simulated seasonal water uptake wasslightly higher with pulsed irrigation, but soil storage was slightly higher with continuous
irrigation. Studies like this are important in accurately calculatinig the leaching fraction
required to flush salts from the root zone. More specifically, in their extensive researchon the design of a drip irrigation system for almond trees, Phogat et al. [9] concluded
that: a) soil texture, initial water content and duration of irrigation are important factors
in the movement and distribution of water and solutes within the soil profile; b) pulsing
has little effect on the leaching percentage and salt removal in coarse textured soils; c) it
is possible to control the wetted volume of a soil by an appropriate combination of drip
discharge and timing of irrigation and d) initial flushing of salts from the plant root zone
can be achieved in surface drip irrigation with continuous heavy irrigations early in theirrigation season, regardless of the method used. However, it is not clear from these studies
what the long-term effects of pulsed irrigation are. Therefore, in the same almond orchard,
Phogat et al. [84] used HYDRUS 2D/3D on field data recorded over one growing season.
Regarding the design of the irrigation system, they reached the same conclusions as in theprevious studies. That is, high discharge rate pulsed irrigation could be a viable alternative
to slow discharge continuous irrigation in soils with a coarse texture. This study attempted
to further investigate the effects of pulse irrigation on water uptake, drainage and waterproductivity by combining it with deficit irrigation strategies. The results of this study wereanalyzed in detail in a previous paragraph. Nazari et al. [89] also concluded that dripper
discharge and duration of irrigation are very important parameters for irrigation strategies.
Their results show that by reducing the emitter discharge and increasing the irrigation
duration (while maintaining the same water volume), the root water uptake increases.
The irrigation rate was also studied by Hardie et al. [93]. This study was also conducted
on an irrigated apple orchard, where a low irrigation rate treatment was irrigated for
45 min, while the high irrigation rate treatment was irrigated for 90 min. Modeling showedthat irrigation tended to wet the soil near the surface between emitters at both rates. In

Water 2023, 15, 741

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addition, there was no significant difference in nitrate concentration after irrigation at boththe high and low irrigation rates. One treatment that has also been studied in drip-irrigateddeciduous trees using the HYDRUS 2D model, is saline irrigation [92]. Two case studies
were simulated: (a) low salinity soil irrigated with high salinity irrigation water and (b)high salinity soil irrigated with low salinity water. The two different treatments wereapplied to determine the optimal location for the electromagnetic sensor (EMI) for soil
salinity measurements, which was analyzed in a previous chapter.
6.2. Summary of HYDRUS 2D/3D Application in Deciduous Fruit Trees and Nut Trees
In the HYDRUS 2D/3D studies on deciduous fruit trees and nut trees, different
irrigation systems and irrigation schemes are used. Most of them use surface drip irrigation
with one or two irrigation laterals, while two studies investigate soil-wetting patterns undersubsurface drip irrigation (Table 4). Although no comparison was made between irrigation
systems and designs, one study of apples with subsurface drip irrigation attempted todetermine the optimum distance to install emitters from the tree trunk. One factor in
irrigation system design that has been considered only for deciduous trees is the optimal
location of monitoring sensors. Conclusions from the studies are not clear on the monitoring
position, as some studies argue that sensors should not be near the drippers, while othersargue the opposite. However, there are also studies that suggest a combination of positions
for the sensors, and this is probably the safest for accurate monitoring. As for deficit
irrigation, the conclusions for deciduous trees are similar to those for citrus and olive
trees. Compared to full irrigation treatment, where water uptake efficiency is higher, water
losses through drainage are lower and salinity distribution is higher. There are different
conclusions for the influence of irrigation frequency, especially for irrigation. Pulsing
irrigation with a high discharge rate could be a viable alternative to continuous irrigation
with slow discharge to control the wetted volume of a soil. In addition, the rate of irrigation
treatment (e.g., reducing the emitter discharge and increasing the duration of irrigation)
can affect root water uptake but has does not significantly affect nitrate concentrations. It
should also be emphasized that only drip-irrigated deciduous trees were simulated withthe 3D model. Furthermore, the application of fertigation and the evaluation of the fate ofnitrates in the soil were only performed in one study, in an apple orchard.
Table 4. Summary of HYDRUS 2D/3D simulations in deciduous trees.
Research
ReportYao et al. [81]CropjujubeSoil Type(soil depth 0–60):
loam

Irrigation
System 1

Irrigation
Treatment 2

HYDRUS
2D/3D

Simulation
Processes

DI-2 drip lines-

2D

Water flow
Root uptake(soil depth 60–100):
clay loam
Phogat et al.
[85]

almond(homogenous soil depth
0–150):
sand

DI-2 drip lines

Ip vs. Ic

2D

Water flow
Root uptake
Salinity dynamics

Phogat et al. [9]almond(homogenous soil depth
0–150): sandDI-2 drip lines

Ip vs. Ic

2D

Water flow
Root uptake
Salinity dynamics

almond(homogenous soil depth
0–150): sand

2D

Water flow
Root uptake
Salinity dynamics

FIp: 100% Etc
Phogat et al.
[84]

DI-2 drip lines

SDIp: 65% Etc
FIc: 100% Etc

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Table 4. Cont.
Research
ReportCrop

Soil Type

Irrigation
System 1

Janssens et al.
[87]

pear

(homogenous soil depth):
silt loam

DI-1 drip line

Xi et al. [88]P. tomentosa
plantation(soil depth 0–120):silt(soil depth >120):silt loam

apple(soil depth 30–50):
sandy loam
(soil depth 50–70):
light clay

HYDRUS
2D/3D

Simulation
Processes

2D

Water flow
Root uptake

SDI: 80% ETc
SDI: 50% ETc

SubDI-3 drip
lines/tree belt

(soil depth 0–30):
sandy loam
Hardie et al.
[93]

Irrigation
Treatment 2

T25

2D

No irrigation

1D

Water flow
Root uptake

low rate
DI-1 drip line
and fertigation

2D

Water flow
Root uptake
Nitrate dynamics

high rate(soil depth >70):
medium clay

Yang et al. [86]P. tomentosa
plantation

DomínguezNiño et al.
[82]

apple

DomínguezNiño et al.
[83]

apple

Nazari et al.
[89]

apple

Bughici et al.
[92]

pistachio(soil depth 0–140):
sandy loam

DI-2 drip lines

T20

2D

Water flow
Root uptake(soil depth 0–60):
loam

DI-1 drip line

FI: 100% ETc

3DWater flow
Root uptake(soil depth 0–60):
loam

DI-1 drip line

FI: 100% ETc

3DWater flow
Root uptake

SubDI-2 drip
lines

different
discharge andduration

2D

Water flow
Root uptake

2D

Water flow
Root uptake
Salinity dynamics((soil depth 140–300):
silt loam(soil depth 0–30):
loam(soil depth 30–120):sandy loam
(homogenous soil depth):clay loam

DI-1 drip line

high salinity
low salinity

Notes: 1 SubDI: Subsurface Drip Irrigation; DI: Drip Irrigation. 2 FI: Full Irrigation; RDI: Regular Deficit Irrigation;
SDI: Sustained Deficit Irrigation; Ip: Pulsed Irrigation; Ic: Continuous Irrigation; Tn: a treatment in which thetrees were irrigated when the average soil water potential at 20 cm depth from the dripper reached − n kPa.

7. Conclusions and Future Challenges
Reliable information on the wetted area of soil under drip irrigation helps researchersand farmers determine the optimal irrigation design (emitter flow, distances from thetrunk, number of laterals, etc.) and optimal strategy/treatment (deficit or full irrigation,rate, frequency and timing of application) for effective use of water and fertilizer. Thus,
there is a need for a simple and inexpensive yet robust calculation and visualization ofwater and solute transport patterns to support irrigation design and management. The
HYDRUS 2D/3D model has proven to be able to predict soil water dynamics, root uptake
and salinity/nitrate dynamics well to a good extent in orchards under surface or subsurface
drip irrigation conditions.

Water 2023, 15, 741

19 of 23

Despite the widespread use of drip irrigation and fertigation systems in tree crops,
there are relatively few studies that use the 2D/3D model HYDRUS to simulate water
dynamics, root uptake and solute transport in drip-irrigated trees. Twenty-two papers
were found in the literature, of which only three involve subsurface drip irrigation and therest involve surface drip irrigation. The irrigation schemes in these studies consist of one
two or more laterals per tree row, while only one study (conducted in a lysimeter) uses thescheme of a concentric dripline around the trunk. In addition, from the studies discussed
in this paper, only four examine the fate of nitrate in the soil after fertilization and only
two are based on field measurements of nitrate from the soil solution. An estimation of
nitrate dynamics within and outside the plant root zone is necessary to fully assess theefficiency of irrigation systems. In addition, although there are studies on the effects ofirrigation with wastewater, there is no study that considers the salinity dynamics in the soil.
Therefore, there is a need for further research that will assess more irrigation schemes in
the field and will investigate the fate of nitrates and the salinity distribution in soil under
different tree crops, different tree crops, soil types and climatic conditions. Such studies
would help improve irrigation and fertigation designs and strategies for perennial crops
irrigated with drip irrigation systems and lead to more efficient and less environmentally
damaging cropping practices.
Another challenge is the simulation under drip-irrigated trees in three-dimensional
domains. To date, only two studies have attempted to simulate soil water dynamics undertrees using HYDRUS 3D, with a particular focus on estimating soil hydraulic parameters.
This means that there is a wide field for studies on simulating the three-dimensional
movement of water, heat and solutes under different tree crops.
HYDRUS, like all the hydrological models, has shortcomings due to the simplificationof surface and subsurface processes. Hydrological models require several input parameterswhich may not be available or may be of a large cost to acquire. Thus, in all the HYDRUS
2D/3D studies, many parameters had to be estimated either using optimization algorithms
or during model calibration. Moreover, further improvements are needed in the accuracy
and computational efficiency of the numerical solutions of the governing equations tofacilitate larger-scale applications. There is a gap between physically based models at small
spatial scales and landscape approaches. This is a significant challenge that needs to be
overcome for HYDRUS models to be useful for decision makers.
Author Contributions: Methodology and conceptualization: G.M. and N.N.K.; Data curation andwriting-original draft preparation: G.M.; Writing–review and editing: N.N.K. and G.P.K.; Supervision:
N.N.K. and G.P.K. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable here.
Conflicts of Interest: The authors declare no conflict of interest.

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