Soil & Tillage Research 194 (2019) 104342

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Soil & Tillage Research
journal homepage: www.elsevier.com/locate/still

Assessing salinity leaching efficiency in three soils by the HYDRUS-1D and-2D simulations

T

Ting Yanga, Jirka Šimůneka, Minghao Mob, Blake Mccullough-Sandenc, Hossein Shahrokhniaa,⁎
Setrag Cherchiana, Laosheng Wua,a

Department of Environmental Sciences, University of California, Riverside, CA 92521, USA
Jiangxi Institute of soil and Water Conservation, Nanchang, 330029, Chinac
University of California Cooperative Extension, Kern County, Bakersfield, CA 93307, USAb

ARTICLE INFOABSTRACT

Keywords:
Salinity
Leaching fraction
Root water uptake
HYDRUS-1DHYDRUS-2D
Evapotranspiration

Salinity leaching is necessary to sustain agricultural production in irrigated croplands. Improving salinity
leaching efficiency not only conserves water but also reduces groundwater contamination. Current leachingrequirement (LR) calculations are based on steady-state and one-dimensional (1D) approaches, and consequently, this LR concept may not be applicable to drip irrigation (approximately 2D), which is becoming morecommon due to its higher water use efficiency. The aims of this study were to assess the salinity leaching fraction(LF) in clay, loam, and sand soils under 1D (to mimic sprinkler irrigation) and 2D (to mimic drip irrigation)transient conditions with a numerical model (HYDRUS). Water applications used the actual irrigation scheme inan almond orchard located in central California without considering precipitation. Model simulations showedthat soil salinity at the lower boundary (depth of 150 cm) reached steady-state in 10 years in HYDRUS-1D
simulations. The leaching fractions calculated from the ratio of drainage-water depth to irrigation-water depth(LFw = Ddw/Diw) and irrigation-water salinity to drainage-water salinity (LFEC = ECiw/ECdw) from HYDRUS-1D
were similar among different textured soils. However, they were much higher under drip irrigation (2D) thanunder sprinkler irrigation (1D) when the same amount of water was applied, and LFEC values were much greaterthan the LFw values under 2D simulations. Salt balance (SB) and leaching efficiency (LE) indicated that sprinkler
irrigation (1D) is more effective for salinity leaching than drip irrigation (2D). To improve salinity leachingefficiency, further evaluation of LRs under drip irrigation is needed.

1. Introduction
The level and distribution of salinity in irrigated cropland soils are
the result of time-dependent interactions of rainfall, irrigation, evapotranspiration, leaching, and drainage. These interactions involve crop
growth and yield, root water extraction, soil salinity, irrigation, saltloading, leaching, and drainage are complicated and are not fully understood or quantified (Corwin et al., 2007). In irrigated soils, salts willremain behind and concentrate on the crop root zone because crops
take up nearly pure water for transpiration. Thus, periodic leaching isrequired to move excessive salts downward to minimize crop yield reduction (Letey et al., 2011).
The ratio of the water depth that drains beyond the root zone relative to the depth of applied irrigation water is defined as a leaching
fraction (LF). The minimum LF that will adequately leach salts out of
the root zone to prevent soil salinity from exceeding a specified value⁎

over a growing season, for the water of a particular quality, is defined as
the leaching requirement (LR) (U.S. Salinity Lab, 1954). A soil profilethat has been irrigated over a long period will reach steady-state conditions with regard to salt accumulation and distribution, and the LF
can be estimated using the ratio of the electrical conductivities of irrigation water (ECiw, dS/m) and drainage water (ECdw, dS/m), LF =ECiw/ECdw (dS/m) or the ratio of drainage water depth (Ddw) to irrigation water depth (Diw) (Letey and Feng, 2007).
In recent years, the appropriateness of the traditional method related to the steady-state assumption has been discussed. A comprehensive evaluation of steady-state approaches and transient model
evaluations indicated that there exist substantial differences among
different methods in estimating LRs (Letey et al., 2011). Hoffman(1985) also compared 5 different steady-state LR calculation methods
using the field and plot experimental data based on the mass balance ofboth water and salts, and found that the highest correlation coefficient

Corresponding author.
E-mail address: laowu@ucr.edu (L. Wu).

https://doi.org/10.1016/j.still.2019.104342
Received 13 February 2019; Received in revised form 12 July 2019; Accepted 17 July 20190167-1987/ © 2019 Elsevier B.V. All rights reserved.

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between measured and predicted values was 0.67, indicating that noneof the methods was completely satisfactory. Gonçalves et al. (2006)
analyzed transient water flow and solute transport in three soil lysimeters irrigated with waters of different ECs over a period of 4 years
using the HYDRUS-1D model (Šimůnek et al., 2008, 2016) with major
ion chemistry subroutines from UNSATCHEM, indicating that HYDRUS1D with UNSATCHEM can successfully simulate the water regime, as
well as the effects of different irrigation water on the geochemistry of
the test soil. LRs based on steady-state, one-dimensional (1D) and waterbalance approaches often overestimate those observed values underfield conditions (Oster et al., 2012). Another question is related to thefact that surface and sprinkler irrigated fields have been largely converted to drip or micro-spray systems for regions in California, South
Africa, Israel, and some other areas. Consequently, the 1D water balance approach for calculating field-scale LFs is considered to be inappropriate for drip irrigation (Ayars et al., 1999; Dhawan, 2000;
Benouniche et al., 2016).
The temporal pattern of soil water and salinity in cropland soils is
often transient instead of steady-state. It appears that a single LR value
is not sufficient for describing inherently transient and non-uniform
systems. Many studies have investigated the movement and distributionof water and salts in soils under drip irrigation. Nightingale et al.
(1991) estimated the apparent LFs for drip irrigation in a silt/clay loam
soil using chloride concentrations under three water application rates at
50%, 100%, 150% of crop evapotranspiration rates (ETc). They estimated that the LFs in the 1-m space drip line system was 0.05, 0.22, and0.36, respectively, for 50% ETc, 100% ETc and 150% ETc, and was 0.06
to 0.34, respectively, in the 1.6 m space drip line system for the 100%
and 150% of ETc treatments. It was observed that the LFs decreased
with distance from the drip line for the 100% and 150% of the ETctreatment, and increasing the water volume to 100% and 150% of ETc
moved the zone of salt accumulation farther from the drip line.
Hanson et al. (2008) defined the localized leaching fraction (LLF) as
the actual leaching fraction representative of the local irrigated root
domain near the drip line. They found that higher salinity accumulatedon the edges of the wetted zone, and localized salt leaching around/
below the drip line occurred even under deficit irrigation. Raij et al.
(2016) used drip-irrigated lysimeter to calibrate the HYDRUS 2D/3D
coupled with UNSATCHEM module and evaluated LFs using drainage
water fluxes, chloride concentrations and overall salinity of the drainage water. Their results showed that, over the long term, LFs calculated from electrical conductivity (EC) were affected by the pressure
head at the lower boundary conditions of the soil profile, while LFs
calculated from chloride concentrations and drainage fluxes were notaffected.
The evaluation of LFs whether using steady-state or transient models
is still a controversial topic (Corwin et al., 2007; Letey and Feng, 2007;
Dudley et al., 2008; Letey et al., 2011). There has been wide interest in
the concept of LFs under both steady-state and transient state. Nevertheless, application of the traditional LF approach to new irrigation
systems such as drip irrigation can lead to erroneous conclusions, which
would directly affect irrigation decision making. Improving leachingefficiency can minimize salt accumulation in the root zone and sustain
crop production with less water. However, few studies have been
published to consider the effects of multidimensionality of flow andsolute patterns, root water uptake, and soil texture on LF calculationand leaching efficiency, especially at the field scale.
The objectives of this study were to use the HYDRUS-1D and
HYDRUS-2D models to (1) predict salinity leaching in three soils ofdifferent textures (clay, loam, and sand) under sprinkler (1D) and drip(2D) irrigation based on the actual irrigation scheme of an almondorchard in central California, (2) reveal differences in soil water andsalinity distributions in the three test soils with two different root water
uptake functions and their associated LFs under drip (2D) and sprinkler(1D) irrigation systems, and (3) evaluate leaching efficiency under
different soil types, irrigation methods, and root water uptake

functions.
2. Materials and methods
2.1. Water flow modeling
To simulate water flow, the Richards equation [Eq. (1)] subject toappropriate initial and boundary conditions is numerically solved inboth HYDRUS-1D and HYDRUS-2D models using the Galerkin finite
element method based on the mass conservative iterative scheme proposed by Celia et al. (1990):

t

=

h
x

K (h )

x

+

z

K (h)

h
z

K (h )z

S (h )
3

(1)

−3

where
is the volumetric water content (cm cm ), h is the matricpressure head (cm H2O), K(h) is the soil unsaturated hydraulic conductivity (cm day-1), x is the horizontal coordinate (cm), z is the verticalcoordinate (cm), and S(h) is the root water uptake term (cm3 cm−3 day1).
The relationship between and h is represented in the HYDRUS
models using the following equation (van Genuchten, 1980v):(h ) =sr|h|) n]m[1 + (

+

r

(2)
3

−3

where θs is the saturated volumetric water content (cm cm ), θr is theresidual volumetric water content (cm3 cm−3), α, n, and m are empirical parameters (m = 1-1/n).
The unsaturated hydraulic conductivity K(h) is defined as a functionof h (van Genuchten, 1980):

K (h) = Ks Se0.5 [1

(1

(3)

Se1/ m ) m]2−1

where Ks is the saturated hydraulic conductivity (cm day ), and Se is
the effective saturation.
The root water uptake model is based on the sink term in the
Richards equation, S(h), representing the volume of water removed
from a unit volume of soil per unit time due to plant water uptake(Feddes et al., 1978):(4)

S (h) = (h) Sp−1where Sp is the potential water uptake rate (day ), which is reduced
using the water stress response function β(h) that is a prescribed dimensionless function of the soil water pressure head (0 < β < 1). To
simplify the analysis of the leaching performance under different dimensions, the osmotic stress was not considered in this study.
In a 1D system, the potential root water uptake Sp is described by
Feddes et al.(1978):b (z ) Tp

Sp (z ) =Zm0b (z ) dz(5)−1

where b(z) is a function (cm ) describing the root distribution withdepth, Tp is the potential transpiration rate (cm day−1), and Zm is the
maximum rooting depth (cm). The 1D root-depth distribution model
was proposed by Vrugt et al. (2001), based on the model by Raats(1974):*ze (pz / Zm ) | z z |zmb (z ) = 1(6)where pz and z* are empirical parameters.
In an axially symmetrical system, the two-dimensional (2D) root
water uptake model is used (Vrugt et al., 2001):

Xm b (x , z ) Tp

Sp (x , z ) =

Xm
0

zm
0

b (x , z ) dxdz

(7)where Xm is the maximum root radius (cm). The root spatial distribution in 2D2

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T. Yang, et al.

zZmb (x , z ) = 1

1

x
e
Xm

Table 1
Hydraulic parameters of the three soils representing different textures.

[(pz / Zm ) | z * z| + (px / Xm ) | x * x |](8)

where Zm and Xm are the maximum rooting depth and length in z and x
directions, respectively, z and x are the distances from the origin of thetree in the z and x directions, respectively, and pz, z*, px, and x* areempirical parameters.
Potential transpiration Tp and evaporation Ep fluxes can be calculated from potential evapotranspiration using Beer’s law that partitions
the solar radiation component of the energy budget via interception by
the canopy (Ritchie, 1972) as follows:

Tp = ET0 (1Clay soil
Loam soil
Sand soil

where ET0, Tp, and Ep are reference evapotranspiration, potential
transpiration, and potential evaporation fluxes (cm/day), respectively;
LAI is leaf area index (-), and k is a constant governing the radiation
extinction by the canopy (-) as a function of sun angle, the distributionof plants, and the arrangement of leaves (between 0.35-0.75). For almond trees in this study, k was taken as 0.463, and LAI was 0–3.351(Zarate-Valdez et al., 2012).
2.2. Solute transport model
The convection dispersion equation (CDE) representing nonsorbing, conservative solute transport is numerically solved in both
HYDRUS-1D and -2D as follows:
For HYDRUS-1D:

( C)
=
t
z

D

C
z

z

(qw C )

(11)

For HYDRUS-2D:

( C)
=
t
x

D

C
+
x
z

D

C
z

z

(qw C )

(12)–3

where C is the solute concentration (g cm ), θ is the volumetric watercontent (cm3 cm−3), D is the dispersion coefficient (cm2 day-1), qw is
water flux (cm day-1). The dispersion coefficient is defined as (ignoring
molecular diffusion):

D=

|v|

Alpha [1/cm]

n [-]Ks [cm/day]

l [-]

0.068
0.048
0.045

0.38
0.51
0.43

0.018
0.09
0.1

1.04
1.14
1.24

28.8
225.27
300

0.5
0.5
0.5

2.3.2. Initial and time-variable boundary conditions
HYDRUS-1D simulations were used to mimic sprinkler irrigation.
The vertical soil profile was discretized into 101 equidistant finite
elements in HYDRUS-1D simulations. The initial soil water pressure
head was set to a uniform value of -100 cm throughout the soil profiles.
The initial soil solute concentrations were specified in terms of ECsw,
which was set to 0 dS/m at the beginning of the simulations. The same
initial conditions were applied in HYDRUS-2D to simulate drip irrigation, where the soil profiles were discretized using triangular finite
elements with grid sizes of about 3.3 cm near the drippers and 10 cm
elsewhere (Fig. 1).
The surface boundary condition used the variable flux boundary
condition of the once a week water application rate, evaporation (E)and transpiration (T) rates, and EC of the applied irrigation water.
Variable flux upper boundary conditions were specified using theweekly irrigation data of an almond orchard in the Kern County, CA.
The average annual precipitation in the area is about 16 cm, but it was
not considered for the simulations. The reference evapotranspiration
fluxes (ET0) were calculated using the Penman-Monteith equation fromthe local meteorological data (Allen et al., 1998). The crop potential
transpiration and evaporation fluxes were then calculated from Eqs. (9)and (10).
The lower boundary condition used the free drainage boundary
condition (Fig. 1). The solute transport bottom boundary condition was
set as the third-type (or Cauchy, mixed, or solute flux). The seasonalchange of the crop evapotranspiration (ETc = kc×ET0) and irrigation
scheme are shown in Fig. 2. The annual irrigation depth was 141.8 cm,
and the ETc was 126.2 cm/yr, so that the ratio of Diw/ETc was 1.12.

(10)

Ep = ET0 e kLAI

Qs [-]The same hydraulic parameters and field irrigation scheme wereused both in the HYDRUS-1D and HYDRUS-2D models to predict water
movement and salinity leaching in the three soils (Table 1).

(9)

e kLAI )Qr [-](13)

2.3.3. Root distribution and root-water uptake
The almond root depth was set to 122 cm (4 ft, based on field observations, constant over time) for 1D simulations. The depth of maximum root density was 50 cm and the shape parameter of Pz was 1. For
2D simulations, the root depth was set to 122 cm (4 ft), the width of theroot zone was set to 152.4 cm (5 ft), the radius of the maximum intensity was 76.2 cm, and the shape parameters of Pz and Px were 1(Fig. 1). The soil water pressure head parameters in the Feddes et al.
(1978) model were set as follows: h1 = -10, h2 = -25, h3 = -500, and h4= -8000 cm. For simplicity, no salinity stress and no active solute uptake were considered in this study.

where λ is the dispersivity (cm), and v is obtained from the numericalsolution of the water flow model (the water flux qw (cm day−1) divided
by θ)
2.3. Model parameters and input data
2.3.1. Irrigation salinity and soil hydraulic properties
The electrical conductivity (EC) of irrigation water (ECiw) in theorchard ranged from 0.9 to 1.1 dS/m during the experimental period.
Undisturbed soil core samples were collected in the field to measure
hydraulic properties of the clay soil from Holtville, loam soil from Kern
County and sand soil from Irvine, CA. The soil water retention curves of
the three test soils (drying) were determined in the laboratory using thepressure plate apparatus for pressures of 0.01, 0.03, 0.10, 0.50, and1.50 MPa (Klute, 1986). Another set of undisturbed soil-core samples
was used to determine the saturated hydraulic conductivities (Ks) using
the constant-head method (Klute and Dirksen, 1986), as well as the soil
bulk densities. Other parameters, such as the residual water content (θr)
are empirical parameter, (α and n) in Eq. (2) were optimized using both
the water retention and hydraulic conductivity data. The hydraulicparameters for the three soils used in the numerical simulations in thisstudy are listed in Table 1. Solute transport parameters used the default
values provided by the HYDRUS model. For simplicity, the soil profile
was considered as a uniform soil layer between depths of 0 and 150 cm.

2.4. Leaching efficiency evaluation
Leaching fraction (LF) is a measure of the proportion of the watersupposedly dedicated to leaching salts from the root zone. Root water
uptake leads to a corresponding increase in soil salt concentrations(salinity) as the leaching fraction (LF) decreases with depth (Ayers andWestcot, 1985). The effect of LF on soil salinity (measured using soil
water electrical conductivity, ECsw) is more evident at the bottom of theroot zone. LFs can be calculated annually and independently for water
fluxes (LFw) and EC (LFEC) for each soil type (Ayers and Westcot, 1994):

LFw =
3

Ddw
Diw

(14)

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T. Yang, et al.

Fig. 1. The HYDRUS-2D model setup showing the FE-Mesh, boundary conditions for water flow, and two-dimensional root water uptake in the soil profile.

LFEC =ECiw
ECdw

A salt-balance evaluation involves measuring the depth and salinityof irrigation water diverted into the soil and the depth and salinity ofdrainage discharged from the soil. The salt-balance (SB) is then calculated from the cumulative data by the equation (Wilcox and Resch,1963):(15)

where ECiw is the EC of irrigation water, ECdw is the EC of drainage
water at the bottom of the root zone (dS/m), and Diw and Ddw are thedepths of irrigation water and drainage water (cm), respectively.
The traditional approach to estimate the LF is based on an assumption that the salt concentration of the soil solution at any point in
the soil profile (1D) is constant at all times (steady-state). Steady-state
does not actually exist in the field, but if a given irrigation regime isfollowed for an extended period of time, the salt concentration below
the root zone will be constant with time; such conditions can be taken
as quasi-steady-state (Letey et al., 2011; Tripler et al., 2012). Under
quasi-steady-state, LF below the root zone can be calculated by assuming no appreciable contribution of salts from the dissolution of soil
minerals or salts, or loss of soluble salts by the precipitation process andcrop removal, and uniform areal application of water in the field, where
LFw equals to LFEC.

SB = Ddw ECdw

Diw ECiw = Diw ECiw

LFw
LFEC

1

(16)

where SB can be expressed with the ratio of LFw/LFEC. When
LFw > LFEC, then SB > 0, which means drainage water carries more
salts than salts applied from irrigation water; when LFw = LFEC, SB = 0,
which means steady-state, the amount of salts in drainage equals theamount of applied salts from irrigation; and when LFw < LFEC, SB < 0,drainage water can only remove part of salts from the total amount of
input salts by irrigation water.
Leaching efficiency can be determined from the ratio of the collected drained salt mass to the applied salt mass (Grismer, 1990), which

Fig. 2. Seasonal variation of crop evapotranspiration (ETc) and irrigation scheme.
4

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T. Yang, et al.

Fig. 3. The salinity distribution along the soil profile at different time simulated using HYDRUS-1D for (a)-clay soil, (b)-loam soil and (c)-sand soil.

can be expressed by LFw and LFEC:

LE =Ddw ECdw
LFw=
Diw ECiw
LFEC

depth and location, which agrees with the observation by Hanson et al.
(2008).
The water balances at the 10th year of simulations for the three soils
using HYDRUS-1D and -2D simulation are shown in Table 2. Based on
the yearly applied water and crop potential evapotranspiration rates,
the traditional LF is 0.11 (LF = (Diw - ETc)/ Diw = 0.11), and it is expected that steady-state would be reached for both water and solutes(Letey et al., 2011; Tripler et al., 2012). The time series (daily andyearly) of LFw for the three soils calculated from both HYDRUS-1D and-2D simulated values of Ddw/Diw (LFw) in Eq. (14) are shown in Fig. 4.

(17)

3. Results and discussion
3.1. Comparison of LFw under one- and two- dimensional simulations
To evaluate the traditional LF values, the HYDRUS-1D and -2Dmodels were used to simulate soil salinity leaching using meteorological data at the almond orchard in Kern County, CA and measured
hydraulic parameters of three soils representing different textures for aperiod of 10 years (3660 days) to ensure the ECsw at the bottom of theroot zone in the three test soils reached approximately steady state. The
annual soil water salinity profiles (ECsw) for the clay, loam, and sandsoils from HYDRUS-1D simulations are shown in Fig. 3. Soil salinity
distributions in the clay soil profile in years 1 to 10 are shown in Fig. 3a.
The initial condition (time = 0) when ECsw = 0 is not shown. As thesimulation time increased, the EC of drainage water at the bottom of thesoil profile (ECdw) continued to increase until it reached the highest
value, and then it became nearly constant with time. Similar trends
were also observed in the loam and sand soils (Figs. 3b and c, respectively). In contrast, salinity distribution in drip-irrigated soils based on
HYDRUS-2D simulations was not uniform, and it varied with time,

Table 2
Cumulative depths of irrigation, root water uptake, evaporation and drainage
water in the 10th year of simulation.
Soil types

Cum.
Irrigation
water
[cm]

Cum. Root
water
uptake[cm]

Cum.
Evaporation
[cm]

Cum.
Drainage
water
[cm]

1D

141.86141.89141.88141.82141.84141.8494.29
91.70
102.79
77.47
98.38
97.23

23.66
24.09
23.98
16.27
13.7
9.23

22.69
26.49
15.12
42.88
30.46
35.56

2D

5

clay soil
loam soil
sand soil
clay soil
loam soil
sand soil

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T. Yang, et al.

Fig. 4. Time series of leaching fractions (LFw) calculated from HYDRUS-1D (a) and -2D (b) simulations for the three test soils.

The daily data represent the dynamic nature of soil water and salinity inthe field; while the yearly averaged data provide a basis for comparison
between the LF based on a traditional steady-state model and on transient models such as HYDRUS over a crop rotation period (Corwin
et al., 2007).
The LFw of the daily time series from HYDRUS-1D decreased sharply
at the beginning of the simulations, while the yearly averaged LFw values were much smoother. Both daily and yearly LFw values approacheda constant leaching fraction at the end of the 10-year simulations,which were 0.16, 0.19 and 0.11, respectively, for the clay, loam andsand soil (Fig. 4a). The LFw for the sand soil in 1D simulation is close to
the traditional LF of 0.11. While, for the clay and loam soils, the 1D
simulated LFw values were higher than those of the traditionally estimated LFw, indicating that soil texture indeed influences the simulated
LFw values. Coarse soils normally have larger continuous pores and thus
it is easier for a coarse soil to reach quasi-steady-state.
Compared with 1D simulation, 2D simulations had higher drainage
and lower evapotranspiration (Table 2), and greater leaching below theroot zone. As shown in Fig. 4b, the daily and yearly LFw values in 2D
simulations were similar to those in 1D simulations during early timestages. However, 2D simulations resulted in very different LFw (Fig. 4b)
in Year 10, which were 0.3 for the clay, 0.22 for the loam and 0.25 forthe sand soil. These LFw values were greater than that of the traditional
LF (0.11) and those of 1D simulations (0.16, 0.19 and 0.11 respectively,
for the clay, loam and sand soil). The higher LFw from transient 2Dsimulations than that of the traditional LF as well as those of 1D simulations are attributed to the fact that drip-irrigation systems typically wet only part of the soil surface, and field-wide application of
traditional LF to drip system leads to underestimation of actual LFw(Hanson et al., 2009; Letey et al., 2011), especially for drip irrigation.
Water application and root distribution can also affect water distribution and crop water uptake in the soil profile, and consequently,
LFw. With the same amount of water application and ETc, water and salt

fluxes behaved similarly in different parts of the field in 1D simulations
that mimic sprinkler irrigation, while 2D simulations representing drip
irrigation wet only part of the soil surface, inducing differences in waterand salt movement in the wetted and dry or less wetted area (particularin the wetting edge) (Burt and Isbell, 2005). Furthermore, in 1D simulations, root distribution and water uptake only consider the verticaldirection, whereas, in 2D simulations, root distribution considers bothvertical and horizontal directions. Because drip irrigation wets only
part of the root zone, it is difficult for roots to extract water from the dry
soil, which may effectively reduce the evapotranspiration. In addition,
as the same amount of water is applied to only a small portion of thesurface area, it is not surprising to see higher leaching (higher LFw) in
2D simulations when the potential root water uptake was the same as in
1D simulations, which led to the concept of localized leaching fraction fordrip irrigation (Hanson et al., 2008).
3.2. Evaluation of LFEC under one- and two-dimensional simulations
To evaluate the salinity leaching efficiency by the same amount ofwater, the ECdw change with pore volume (dimensionless time) for thethree test soils are presented in Fig. 5. For HYDRUS-1D, the ECdw values
were 8.58, 4.89 and 5.47 dS/m for the sand, loam, and clay soil, respectively, at the pore volumes of 2.1, 3.61, 3.14 when they reachedquasi-steady-state (Fig. 5a). For HYDRUS-2D, the average ECdw values
were 3.03, 2.63 and 1.72 dS/m, respectively, at pore volumes of 4.95,
4.23 and 6.03 for the sand, loam and clay soil (Fig. 5b). In the meantime, salts appeared in the drainage water much earlier (at about 0.1
pore volume) in 2D simulations than it did in 1D simulations (at about
0.3 pore volume). The early appearance of salts in the drainage waterand lower ECdw values in 2D simulations are largely attributed to thefact that in drip irrigation, soil salts near the drip line move much
faster, and consequently more salts were leached downward by relatively larger amounts of localized drainage water near the drip lines.
6

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T. Yang, et al.

Fig. 5. Changes of electrical conductivities of the drainage waters (ECdw) in the three soils with pore volumes (representing 10 years) from HYDRUS-1D (a) andHYDRUS-2D (b) simulations.

The ECsw distributions in the profiles of the three test soils at the end of
the 10-year simulation period are shown in Fig. 6. ECsw near the drip
lines (emitters) was low so osmotic stress was not considered as in thisstudy. Fig. 6 clearly showed that sprinkler irrigation (1D) was more
effective in leaching salts out of the crop root zone than drip irrigation(2D), and more salts moved below the root zone in the sand soil than in
the clay and loam soils.
Under transient-state, the salt concentration continually changes aswater is added, drained, and extracted by roots. According to previous
studies, soil salinity distribution is sensitive to root water extraction
patterns (Gardner, 1983; Rhoades, 1999) and a large amount of water is
extracted from the upper part of the root zone where soil salinity (LFw)
is low (Letey et al., 2011). To assess the root distribution effect on water
uptake and salinity leaching, the time series (daily and yearly) of simulated LFEC for the three soils from both HYDRUS-1D and -2D using
Eq. (14) are shown in Fig. 7. The yearly LFEC calculated from 1D simulations decreased with time and then became nearly constant values(0.18, 0.20, and 0.12, respectively, for the clay, loam, and sand soils).
In the 10th year, the LFEC values for the three test soils calculated fromthe simulations were very close to their respective LFw for each soil typefrom HYDRUS-1D simulations (Table 3).
It is well recognized that water and solute fluxes under 1D transientstate conditions can approach quasi-steady state below the root zone
after a long period of leaching (Letey and Feng, 2007; Letey et al.,2011). However, the behaviors of water and salinity leaching underdrip irrigation (2D, transient) in the three soils were different fromthose under 1D. Under 2D transient conditions, the daily water and salt
fluxes never reached quasi-steady state, and the LFEC values at the endof the 10-year simulations were 0.58, 0.38 and 0.33, respectively, in theclay, loam, and sand soils, which were much greater than those from 1D
simulations, especially for the clay soil.
Furthermore, the LFEC values were greater than the LFw values in all
the three soils, even though they were both based on the data fromHYDRUS-2D simulations. Apparently, the equality between LFw and

LFEC after a long period of leaching cannot be applied to drip irrigation(2D transient condition).
The higher LFEC in 2D simulations can be explained by the transverse dispersion phenomenon as well as by lower ET (more drainage),which results in lower ECdw than that in 1D simulations. The relationship between LFEC and the parameter Disp.T (dispersion in the transverse direction) for the sand soil is depicted in Fig. 8. When Disp.T is
between 2–10 cm, there is no significant difference in LFEC (roughlyaround 0.35 for the three of them). However, when Disp.T is 0 cm, the
LFEC is higher than the LFEC values for Disp.T = 2–10 cm in the sand soil
for the initial 3 years; after that, it decreased sharply and became lower
than the LFEC values for Disp.T = 2–10 cm. At the end of the 10-year
simulation, the LFEC reached 0.12 for Disp.T = 0, which is closest to theresults of LFEC of the sand soil in 1D simulation and it is an indicationthat Disp.T, not lower ET, is the major factor for the higher LFEC in 2D
simulations.
In addition, drip irrigation can cause edge effects through accumulate salts near the wetting edge. Thus, proportionally large water
application and drainage near the drip lines (2D) effectively reduce thetotal salinity leaching, even when the same amount of water as that ofsprinkler irrigation (1D) is applied, leading to a higher value of LFEC in
drip irrigation than in sprinkler irrigation.
Furthermore, root uptake patterns and chemical factors such as
precipitation and dissolution of calcite and gypsum in the root zone cancause an increase or decrease in ECsw in the root zone (Raviv and Lieth,
2007). Rainfall (Isidoro and Grattan, 2011) and drainage boundary
conditions (Raij et al., 2016) can also influence the soil salinity distribution, as well as LF. Thus, LF under drip irrigation varies with soil
water content, soil salinity, root distribution, and distance from anddepth to the drip line.
3.3. Salt balance (SB) and leaching efficiency (LE) under 1D and 2D
It is well known that micro-irrigation has higher water use
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Fig. 6. Contour maps of ECsw at the end of 10-year simulations by HYDRUS-1D (Left) and HYDRUS-2D (Right) for the clay a, d), loam (b, e) and sand (c, f) soils. The
three locations of 0 cm (Drip line), 91.4 cm and 182.9 cm from the drip line resemble the soil sampling sites.

efficiency than flood irrigation. However, evaluating leaching efficiency in micro-irrigation systems still remains a challenge. The relative
leaching efficiency proposed by Burt and Isbell (2005) for micro-irrigation systems, expressed by the ratio of the salt reduction to theequivalent leaching depth curve, indicates that the amount of salt removed per unit depth of leaching water decreases as more leachingwater is applied.
As illustrated earlier, a positive SB represents a net removal of salts
in the soil. Based on the HYDRUS-1D simulations, the calculated SB
values were -10.1, -4.5 and -9.8 mg (SB < 0, indicating net increase insoil salinity), respectively, accounting for 11.1%, 4.9% and 10.8% of
the total applied salts (90.75 mg cm−2 yr-1 land surface) for the clay,
loam and sand soil in the 10th year. This means drainage water carried
90–95% of the salts in the irrigation water out of the root zone under
1D conditions.
For 2D simulations, the SB values were -43.8, -38.2 and -19.2 mg(SB < 0), respectively, for the clay, loam and sand soils, which implies

that 48% (clay), 42% (loam) and 21% (sand) of the total input salts(90.75 mg) remained in the soils. The large SB values from 2D simulations are mainly the results of concentrated leaching under or near the
drip lines where ECdw is relatively low in the drainage water. Leachingunder drip irrigation is not as effective as that of sprinkler irrigation(1D), because the edges of the wetted area are not fully leached.
Based on the definition of leaching efficiency (LE) [Eq. (17)], when
LE is greater than 1, the SB is positive (removal of salts in drainage
water is greater than that of irrigation input). In 1D simulations, LE was
88.9%, 95% and 92%, respectively, for the clay, loam and sand soils;
while in 2D simulations, LE was 51.7%, 57.9% and 78.8% for the clay,
loam and sand soils, which is considerably lower than the LE values in
1D.
4. Conclusion
Analyses of leaching fractions (LF) and leaching efficiency (LE) by
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T. Yang, et al.

Fig. 7. Time series of leaching fractions (LFEC) based on irrigation water EC (ECiw) and drainage water EC (ECdw) simulated by HYDRUS-1D (a) and HYDRUS-2D (b)for the three soils.

Our results indicate that in 1D simulations salinity leaching reachedquasi-steady-state at the end of 10-year simulations, and the LFw values
were close to LFEC values for each of the three soils representing different textures based on the simulated drainage water depths and ECs.
While in 2D simulations, the daily water and solute fluxes never attained such “steady-state” condition, but the annual average of LFs
approached quasi-steady-state in the 10th year, although the LFw values
did not equal to the LFEC values in each of the three test soils.
Under transient-state, leaching efficiencies (LE) were 88.9%, 95%,
and 92%, respectively, based on HYDRUS-1D simulations; and LE calculated from HYDRUS-2D were 51.7%, 57.9% and 78.8%, respectively,
for the clay, loam and sand soil. Thus, we conclude that considering theoverall efficiency of salt leaching out of the root zone, sprinkler irrigation (1D) is more effective than drip irrigation systems (2D), and in
drip irrigation systems the current LR guideline is not appropriate.
The main purpose of the study was to compare the LFs estimatedfrom 1D and 2D simulations with the traditional LF (1D steady-state),thus we employed HYDRUS-1D and -2D to estimate salinity leaching
without more complex modeling approaches. Our future work will

Table 3
Leaching fractions (LF) of the three test soils based on HYDRUS-1D and -2D
simulations.

1D
2D

LFw
LFEC
LFw
LFEC

Clay soil

Loam soil

Sand soil

0.16
0.18
0.30
0.58

0.19
0.20
0.22
0.38

0.11
0.12
0.25
0.33

steady-state, one-dimensional (1D) and two dimensional (2D) transientmodels are valuable in developing salinity management guidelines in
irrigated cropland. Real steady-state condition rarely exists in the field,
and new irrigation systems such as drip and micro-irrigation further
violate the assumption of LFw = LFEC under 1D and steady-state conditions. This study used the HYDRUS-1D and -2D models to simulate
water and salinity dynamics with the same irrigation scheme in threesoils of different textures. The calculated LFs based on model simulations were then compared with the traditional LFs.

Fig. 8. Change of leaching fraction based on electrical conductivities (LFEC) with transverse dispersivity (Disp. T) in the sandy soil based on HYDRUS-2D simulations.
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T. Yang, et al.

further evaluate how ion interactions and crop salinity stress may affect
LF estimation.

Hoffman, G.J., 1985. Drainage required to manage salinity. J. Irrig. Drain. Eng. 111 (3),
199–206.
Isidoro, D., Grattan, S.R., 2011. Predicting soil salinity in response to different irrigation
practices, soil types and rainfall scenarios. Irrig. Sci. 29 (3), 197–211.
Klute, A., 1986. Water Retention: Laboratory Methods. Methods of Soil Analysis: Part 1Physical and Mineralogical Methods. (Methodsofsoilan1). pp. 635–662.
Klute, A., Dirksen, C., 1986. Hydraulic conductivity and diffusivity: laboratory methods.
Methods of soil analysis: part 1-physical and mineralogical methods. Winsconsin, US:
Am. Soc. Agron. 687–734.
Letey, J., Feng, G.L., 2007. Dynamic versus steady-state approaches to evaluate irrigation
management of saline waters. Agric. Water Manage. 91 (1-3), 1–10.
Letey, J., Hoffman, G.J., Hopmans, J.W., Grattan, S.R., Suarez, D., Corwin, D.L., Oster,J.D., Wu, L., Amrhein, C., 2011. Evaluation of soil salinity leaching requirement
guidelines. Agric. Water Manage. 98 (4), 502–506.
Nightingale, H.I., Hoffman, G.J., Rolston, D.E., Biggar, J.W., 1991. Trickle irrigation rates
and soil salinity distribution in an almond (Prunus amygdalus) orchard. Agric. Water
Manage. 19 (3), 271–283.
Oster, J.D., Letey, J., Vaughan, P., Wu, L., Qadir, M., 2012. Comparison of transient statemodels that include salinity and matric stress effects on plant yield. Agric. Water
Manage. 103, 167–175.
Raats, P.A.C., 1974. Steady flows of Water and Salt in uniform soil profiles with plantroots 1. Soil Sci. Soc. Am. J. 38 (5), 717–722.
Raij, I., Šimůnek, J., Ben-Gal, A., Lazarovitch, N., 2016. Water flow and multicomponent
solute transport in drip-irrigated lysimeters. Water Resour. Res. 52 (8), 6557–6574.
Raviv, M., Lieth, J.H., 2007. Soilless Culture: Theory and Practice. Elsevier.
Rhoades, J.D., 1999. Use of saline drainage water for irrigation. Am. Soc. Agron. Crop Sci.
Soc. Am., Soil Sci. Soc. Am.
Ritchie, J.T., 1972. Model for predicting evaporation from a row crop with incomplete
cover. Water Resour. Res. 8 (5), 1204–1213.
Šimůnek, J., van Genuchten, M.T., Šejna, M., 2008. Development and applications of the
HYDRUS and STANMOD software packages and related codes. Vadose Zone J. 7 (2),587–600.
Šimůnek, J., van Genuchten, M.Th., Šejna, M., 2016. Recent developments and applications of the HYDRUS computer software packages. Vadose Zone J. 15 (7), 25. https://doi.org/10.2136/vzj2016.04.0033.
Tripler, E., Shani, U., Ben-Gal, A., Mualem, Y., 2012. Apparent steady state conditions inhigh resolution weighing-drainage lysimeters containing date palms grown under
different salinities. Agric. Water Manage. 107, 66–73.
U.S. Salinity laboratory Staff, 1954. Diagnoses and Improvement of Saline and Alkali
Soils. U.S. Dep. Agriculture, Handbook 60. U.S. Government Printing Office,Washington, DC p. 160.
van Genuchten, M.T., 1980v. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils 1. Soil Sci. Soc. Am. J. 44 (5), 892–898.
Vrugt, J.A., Wijk, M.V., Hopmans, J.W., Šimůnek, J., 2001. One-, two-, and three-dimensional root water uptake functions for transient modeling. Water Resour. Res. 37(10), 2457–2470.
Wilcox, L.V., Resch, W.F., 1963. Salt Balance and Leaching Requirements in IrrigatedLands. USDA, pp. 1290 Tech. Bul.
Zarate-Valdez, J.L., Whiting, M.L., Lampinen, B.D., Metcalf, S., Ustin, S.L., Brown, P.H.,
2012. Prediction of leaf area index in almonds by vegetation indexes. Comput.
Electron. Agric. 85, 24–32.

Acknowledgment
This research is supported by the Division of Agriculture andNatural Resources, University of California Competitive Grants
Program.
References
Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration-guidelines
for computing crop water requirements-FAO irrigation and drainage paper 56. Fao,
Rome 300 (9), D05109.
Ayars, J.E., Phene, C.J., Hutmacher, R.B., Davis, K.R., Schoneman, R.A., Vail, S.S., Mead,
R.M., 1999. Subsurface drip irrigation of row crops: a review of 15 years of researchat the Water management research laboratory. Agric. Water Manage. 42 (1), 1–27.
Ayers, R.S., Westcot, D.W., 1985. Water Quality for Agriculture Vol. 29 Food andAgriculture Organization of the United Nations, Rome.
Ayers, R.S., Westcot, D.W., 1994. Water Quality for Agriculture. FAO Irrigation andDrainage Paper 29, Rev. 1. Food and Agricultural Organization of the United Nations,
Rome, Italy.
Benouniche, M., Errahj, M., Kuper, M., 2016. The seductive power of an innovation:
enrolling non-conventional actors in a drip irrigation community in Morocco. J. Agr.
Educ. Ext. 22 (1), 61–79.
Burt, C.M., Isbell, B., 2005. Leaching of accumulated soil salinity under drip irrigation.
Trans. ASAE 48, 2115–2121.
Celia, M.A., Bouloutas, E.T., Zarba, R.L., 1990. A general mass-conservative numericalsolution for the unsaturated flow equation. Water Resour. Res. 26 (7), 1483–1496.
Corwin, D.L., Rhoades, J.D., Šimůnek, J., 2007. Leaching requirement for soil salinity
control: steady-state versus transient models. Ag. Water Manage. 90 (3), 165–180.
Dhawan, B.D., 2000. Drip irrigation: evaluating returns. Econ. Polit.l Weekly 3775–3780.
Dudley, L.M., Ben-Gal, A., Lazarovitch, N., 2008. Drainage water reuse: biological, physical, and technological considerations for system management. J. Environ. Qual. 37,
25–35. https://doi.org/10.2134/jeq2007.0314.
Feddes, R.A., Kowalik, P.J., Zaradny, H., 1978. Simulation of Field Water use and crop
yield. Simul. Monogr. Pudoc. 189.
Gardner, W.R., 1983. Soil properties and efficient water use: an overview 1. Limitations toefficient Water use in crop production. Am. Soc. Agron. Madison, WI 45–64.
Gonçalves, M.C., Šimůnek, J., Ramos, T.B., Martins, J.C., Neves, M.J., Pires, F.P., 2006.
Multicomponent solute transport in soil lysimeters irrigated with waters of different
quality. Water Resour. Res. 42 (8).
Grismer, M., 1990. Leaching fraction, soil salinity, and drainage efficiency. Calif. Agric.
44 (6), 24–26.
Hanson, B., Hopmans, J.W., Šimůnek, J., 2008. Leaching with subsurface drip irrigation
under saline, shallow groundwater conditions. Vadose Zone J. 7 (2), 810–818.
Hanson, B., May, D., Šimůnek, J., Hopmans, J., Hutmacher, R., 2009. Drip irrigation
provides the salinity control needed for profitable irrigation of tomatoes in the San
joaquin Valley. Calif. Agric. 63 (3), 131–136.

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