Agricultural Water Management 195 (2018) 1–10

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

Research Paper

Soil and irrigation heterogeneity effects on drainage amount andconcentration in lysimeters: A numerical study
Iael Raij a , Alon Ben-Gal b , Naftali Lazarovitch a,∗aWyler Department of Dryland Agriculture, French Associates Institute for Agriculture and Biotechnology of Drylands, The Jacob Blaustein Institutes for
Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion, IsraelbInstitute of Soil, Water and Environmental Sciences, Agricultural Research Organization, Gilat Research Center, Israela r t i c l e

i n f oArticle history:
Received 25 June 2017
Received in revised form
18 September 2017
Accepted 22 September 2017
Keywords:
Variability
Salinity
Lysimeter ﬂuxes
Leaching fractiona b s t r a c t
Water and solute ﬂuxes measured from lysimeters located in the ﬁeld can be used to estimate evapotranspiration, for irrigation scheduling and in solute leaching management. System-imposed heterogeneities
are expected to affect the variability of the measured ﬂuxes, and therefore the uncertainty of data obtainedusing lysimeters. In this study, local heterogeneities in soil hydraulic conductivity and dripper discharge
rate were studied and their effect on drainage amount and concentration assessed. Three-dimensional
simulations were performed with HYDRUS (2D/3D) with 100 simulations per treatment. The effect of
three levels of soil and irrigation heterogeneities was studied for lysimeters of two different sizes (1 m2
and 0.5 m2 ). Additionally, three leaching fraction levels and water uptake reduction due to solute stresswere evaluated. Coefﬁcient of variations of the drainage amount and solute concentrations were evaluated for the different scenarios. Irrigation heterogeneity caused higher variability in drainage amountwhile soil heterogeneity caused higher variability in drainage concentration. The larger the lysimeter, or
the higher the leaching fraction, the lower the variability for both drainage concentration and amount.
Combined soil and irrigation heterogeneities produced no synergistic effect, suggesting that the variability measured in lysimeters was governed by the factor that caused the highest variability. Whenwater uptake reduction due to salinity was considered, the same trends were observed. The results fromthis study can help to decide if to use either drainage concentration or amount values, for saline water
irrigation management using lysimeters, according to the soil or irrigation heterogeneity levels.
© 2017 Elsevier B.V. All rights reserved.

1. Introduction
Lysimeters are widely used for closing water balances by monitoring drainage amount and water storage in the soil proﬁle.
Lysimeters are also used as management tools for fertigation
scheduling (Ruiz-Peñalver et al., 2015) and salt leaching (Tripler
et al., 2012) by monitoring drainage solute concentration and loads.
Systems of lysimeters are a good compromise between point measurements with sensors in the soil or plant (water content andsalinity, sap ﬂow, etc) and large scale measurements of ET based onnear or remote sensing (energy balance, vegetation indices, Bowen
ratio, scintillometers, etc) (Skaggs et al., 2012, 2013). When properly calibrated and well representative of the surrounding ﬁeld,
in situ lysimeters have been shown to be easy to operate and per-∗ Corresponding author.
E-mail address: lazarovi@bgu.ac.il (N. Lazarovitch).
https://doi.org/10.1016/j.agwat.2017.09.012
0378-3774/© 2017 Elsevier B.V. All rights reserved.

form with relatively small measurement errors (Allen et al., 2011),
compared to alternative methods.
The accuracy of lysimeters is often deﬁned as the resolution
and precision of the scale or load cell used in the setup (Howell
et al., 1991). However, the overall accuracy of water and solutebalances measured using lysimeters will depend on the representativeness of the lysimeter in comparison to the ﬁeld (Evett et al.,2012). This representativeness is deﬁned mainly, but not exclusively, by the similarity of the plants inside and outside of thelysimeter and it is inﬂuenced by: edge effects, boundary conditions, soil properties, fetch and lysimeter surface area (Allen et al.,2011; Evett et al., 2015). In addition, the uncertainty of output values measured in a lysimeter will be affected by heterogeneities
imposed by the system such as micro-meteorological conditions,plant response, irrigation method and soil hydraulic properties.
Heterogeneous atmospheric conditions in greenhouses was the
motivation for a rotating lysimeter system proposed by Lazarovitch
et al. (2006a). Recently, Hagenau et al. (2015) demonstrated how

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I. Raij et al. / Agricultural Water Management 195 (2018) 1–10

Table 1
Scenarios of lysimeter area, heterogeneity and leaching fraction levels and water or osmotic stresses.
Heterogeneity level
Scenario #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22

Lysimeter size m2
0.5
0.5
0.5
1
1
1
0.5
0.5
0.5
1
1
1
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5

Drippers discharge rate CV
–
–
–
–
–
–
0.02
0.044
0.09
0.02
0.044
0.09
0.044
0.044
0.044
–
–
0.044
0.044
–
–
0.044

Soil hydraulic conductivity CV
0.25
0.5
1
0.25
0.5
1
–
–
–
–
–
–
0.5
–
–
0.5
0.5
–
–
0.5
0.5
0.5

two identical lysimeters were effected signiﬁcantly by slightly different surrounding conditions in the ﬁeld.
It is well known that soil heterogeneity will affect the results ofmeasurements (Weihermüller et al., 2006). However, understanding the effect of the type or magnitude of the heterogeneity on
water ﬂow and solute transport at different scales still remains achallenge. In general, increased soil heterogeneity causes increased
solute dispersion and spreading due to variability in pore watervelocity (Mousavi Nezhad et al., 2011; Russo, 1998). Abdou andFlury (2004) studied the effect of different spatially structured soil
heterogeneities on water ﬂow and solute transport in free-drainage(h = 0 cm at the lower boundary condition) lysimeters and foundthat breakthrough of a non-reactive solute was faster in the ﬁeld
in comparison to lysimeters for vertically structured soils. Theseprevious studies, however, do not explain how different levels ofsoil heterogeneity affect the uncertainty or variability of the results
measured in the lysimeters themselves.
Irrigation uniformity has been widely studied (Guan et al., 2013;
Lazarovitch et al., 2006b; Li, 1998; Or and Hanks, 1992; Pang et al.,
1997; Russo, 1986; Solomon, 1984; Warrick and Gardner, 1983;
Wu and Barragan, 2000; Zhao et al., 2012). Most studies focus on
the effect of the water application uniformity on yield or soil watercontent and look for an optimum between irrigation water amountand uniformity. For sprinkler irrigation systems, soil water content
uniformity was shown to be higher than the imposed irrigation uniformity (Li, 1998). Similarly, crop yield was found to have higher
uniformity than the irrigation imposed uniformity for drip irrigatedcorn (Or and Hanks, 1992). It is possible to compensate for low
uniformity by increasing the irrigation amount (Letey et al., 1984),
but this will translate into lower water use efﬁciency, economicallosses, groundwater pollution, waterlogging or salinity problems.
It is therefore advisable that uniformity due to its repercussions oncrops, water management, and the environment, play a role in irrigation system design (Wu and Barragan, 2000). In addition, dripper
clogging can be a major issue affecting irrigation uniformity withinor between seasons (Bounoua et al., 2016).
The primary objective of this study was to investigate the inﬂuence of local heterogeneities in soil hydraulic conductivity andirrigation discharge rate, individually and combined, on the variability of drainage amount and solute concentration obtained fromlysimeters. Additional objectives included quantiﬁcation of theeffects of lysimeter size, leaching fraction, and ET reduction due

Leaching fraction
0.43
0.43
0.43
0.43
0.43
0.43
0.43
0.43
0.43
0.43
0.43
0.43
0.43
0.2
0.33
0.2
0.33
0.2
0.43
0.2
0.43
0.43

Water or osmotic stress
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water + osmotic
Water + osmotic
Water + osmotic
Water + osmotic
Water + osmotic

to salinity on the generated variabilities of drainage amount andconcentration.
2. Methods
2.1. Heterogeneity analyses
The effect of heterogeneity stemming from soil hydraulic conductivity and dripper discharge rate on drainage amount andchloride concentration was studied. One hundred numerical simulations were performed for each scenario that consisted of adifferent combination of: soil hydraulic conductivity or dripper discharge rate heterogeneity, lysimeter size, leaching fraction leveland salinity stress. A summary of the 22 unique scenarios is presented in Table 1. Irrigation and soil heterogeneity levels (3 foreach) are expressed as the coefﬁcient of variation (CV) values used
to generate each simulation (Sections 2.3 and 2.4). Lysimeter size,
expressed as surface areas (0.5 m2 and 1 m2 ) was chosen so as tobe relevant when different drippers discharge heterogeneity levels
were applied. Further explanation on how the irrigation heterogeneity was applied is found in Section 2.3. Drainage results were
evaluated every 4 days in order to reduce the noise consequential
to daily variability in ET (Fig. 2). A total of 2200 simulations wererun, each with an average running time of 8.5 h. Some of the simulations were run on an Intel Core i7-6700 CPU 3.4 GHz with16 GBof memory while others on an Intel Core i5-4570 CPU 3.2 GHz with
8 GB of memory.
2.2. Numerical simulations
Lysimeters with two surface areas (1 m × 1 m and 0.5 m × 1 m)
and a depth of 0.6 m were simulated using HYDRUS (2D/3D)(Šimůnek et al., 2016). This model represents the most used andmost accessible simulation tool for three dimensional water ﬂow
and solute transport in soils (Dudley et al., 2008). The 1 m2 lysimeters were deﬁned by 18 equally spaced horizontal planes anddiscretized using an unstructured ﬁnite element mesh, resulting ina total of 18,078 nodes and 52,224 three-dimensional tetrahedral
elements (Fig. 1). The 0.5 m2 lysimeters were deﬁned by 21 equally
spaced horizontal planes with a ﬁnite element mesh having 14,156
nodes and 40,080 three-dimensional tetrahedral elements. The soil
hydraulic and transport properties were as deﬁned in Raij et al.

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Table 2
Hydraulic and transport parameters of the loamy sand soil.a
Soil parameter

Units

Value

r
s
␣
n
l
KS
b
L
T

(cm3 cm−3 )(cm3 cm−3 )(cm−1 )(−)(−)
(cm day−1 )(g cm−3 )
(cm)
(cm)

0.004
0.36
0.016
3.43
0.5
145.44
1.5
1.7
0.17

a
 r , residual water content;  s , saturated water content; ␣ and n, empirical shapeparameters; l, tortuosity factor; KS , saturated hydraulic conductivity; b, bulk density, L and T ,g longitudinal and transverse dispersivities, respectively.

Table 3
Root water uptake parameters.aWater stress response function parameters

Fig. 1. Three dimensional ﬁnite element mesh domain in HYDRUS (2D/3D) for the
1 m2 lysimeter. Areas with different shades of pink are those with different variable
ﬂux boundary condition (Q1 –Q4 ) and blue areas are those with a seepage face ofh = −30 cm boundary condition. (For interpretation of the references to colour inthis ﬁgure legend, the reader is referred to the web version of this article.)(2016) for a loamy sand soil (Table 2). Raij et al. (2016) calibrated the
HYDRUS (2D/3D) model with major ion transport in drip irrigatedlysimeters with the same boundary conditions as those simulated
in this study. Vertical root distribution was deﬁned according to themodel of Vrugt et al. (2001), with maximum rooting depth of 50 cm,
depth of maximum intensity of 10 cm and the shape parameter Pz
set as 2. Horizontal root distribution was homogeneous.
Sigmoidal response functions were used in order to simulate
both water and osmotic stresses (van Genuchten, 1987). Whenboth stresses were included in the simulation, their effect was
assumed to be multiplicative (van Genuchten, 1987). The parameters deﬁning the sigmoidal shaped functions are deﬁned in Table 3
as calculated in Groenveld (2010) for similar conditions. Compensated root water uptake was considered by setting the critical stressindex to 0.8 (Šimůnek and Hopmans, 2009). All simulations were

P50
cm
P3
[−]
PW
cm
Salinity stress response function parameters
Cl50
mg cm−3
P3[−]
Osmotic coefﬁcient−800
3-1.00E + 10
3.198
1.435
1

a

P50, the pressure head by which the root water uptake is reduced by 50%; P3,
exponent in the root water uptake response function associated either with water orsalinity stress; PW, pressure head at wilting point below which transpiration stops;
Cl50 , chloride concentration at which the root water uptake is reduced by 50%.

considered to have potential root water uptake reduction due towater stress. Five cases for the 0.5 m2 lysimeter (Table 1) were considered to have additional solute stress according to the parametersin Table 3.
Initial condition for water ﬂow in all simulations was deﬁned
as hydrostatic equilibrium with a pressure head of −30 cm at thebottom of the soil proﬁle. Initial soil solution concentration wasdeﬁned as 1.3 mg cm−3 , a value close to the steady state drainage
concentration.
Irrigation was applied in four or two circular areas, for the 1 m2
and 0.5 m2 lysimeters respectively, representing drippers, eachwith a radius of 2.5 cm deﬁned as variable ﬂux boundary conditions (Fig. 1 –1 m2 domain). Two circular drainage exits, each witha radius of 2.5 cm, were delineated at the lower boundary of theFig. 2. Modeled water ﬂuxes: average irrigation, drainage and ET in mm per day for the 1m2 lysimeter with a coefﬁcient of variation of 0.02 in the irrigation discharge rate.

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I. Raij et al. / Agricultural Water Management 195 (2018) 1–10

lysimeter. This boundary was speciﬁed as a seepage face with apressure head of −30 cm such that outﬂow occurs when the pressure head at the bottom boundary reaches −30 cm. The rest of theboundaries of the domain were designated as no ﬂow. Solute transport at both the upper and lower boundaries was assigned as a
Cauchy boundary condition.
Although this study focuses on numerical work, soil hydraulicand transport parameters, ET, leaching fraction and irrigation
quality were obtained from a ﬁeld experiment performed withlysimeters similar in their design as the ones simulated. In the preliminary ﬁeld experiment, bell pepper plants were grown in ﬁve
1 m2 weighing lysimeters ﬁlled with loamy sand soil, and daily
evapotranspiration (ET) was measured. Irrigation with brackish(EC = 3.4 ds m−1 ) water was applied daily in order to maintain aleaching fraction (LF) of 0.43 (Fig. 2). Leaching fraction was deﬁned
as volume of water draining from the lysimeter divided by volume of irrigation water. In the model, ET was considered only as
root water uptake, without separation between evaporation andtranspiration. The measured ET values were set as the potential
transpiration or root water uptake. Chloride concentration in theirrigation water was 0.8 mg cm−3 .
2.3. Modeled irrigation variability
Average dripper discharge rate was 1.6 L h−1 with a predeﬁned
variability. A normal distribution was assumed for each of three
coefﬁcient of variation (CV) levels: 0.02, 0.044 and 0.09. The middle
value, 0.044, was measured under ﬁeld conditions for 108 drippers
with an average discharge rate of 1.6 L h−1 (UniRam-RC, Netaﬁm,Israel). For each simulation, every dripper in the model, represented
as a variable ﬂux area, received a different discharge rate according
to the CV level and normal distribution (2 and 4 values for the 0.5 m2
and 1 m2 respectively).
2.4. Modeled soil variability
Knowledge of soil hydraulic properties is crucial for a proper
evaluation of physical and chemical processes within the vadosezone involved in variably saturated water ﬂow and transport ofwater-dissolved salts (Lazarovitch et al., 2007). The van GenuchtenMualem (Mualem, 1976; van Genuchten, 1980) soil hydraulicmodel was used to relate the unsaturated hydraulic conductivity
and volumetric water content to the pressure head (parameters in
Table 2). Average saturated hydraulic conductivity for loamy sandsoil was taken from Raij et al. (2016) as 145 cm day−1 . The coefﬁcient of variation of the saturated hydraulic conductivity (Eq. (1))
was set to three levels: 0.5 (expected variability (Warrick, 2003)),0.25 (low) and 1 (high).
 = CVKS

The corresponding KSn * is:KSn ∗ = KS ∗ +  ∗ Z(5)where Z is a random number from a normal distribution with amean of zero and a variance of unity.
From Eqs. (2) and (5), KSn was calculated as:
KSn = exp (KS ∗ + Z)(6)

A Gaussian sequential simulation was used in order to generate a
random ﬁeld for Z in three dimensions (SGEMS software). A random
sample was generated using an exponential model: (h) = C0 1 − exp −h 
a(7)

where ␥ is the sample variogram, a is the practical range (30 cm
used in this case), h is the lag distance [L] and C0 is the sill value(1). Finally KSn values were divided by the average KS and thevalues were imported as scaling factors (˛k in Eq. (8)) in the threedimensional mesh in HYDRUS (2D/3D). These scaling factors wereused by the model according to Eq. (8) for the simulation of theheterogeneous unsaturated hydraulic conductivity K(h). A visualization of the scaling factors of one representative simulation foreach CV value is presented in Fig. 3.
K (h) = ˛k K ∗ (h∗ )(8)2.5. Combined heterogeneities
A set of simulations was performed for the 0.5 m2 lysimeterswith combined heterogeneity of irrigation rate and heterogeneityof hydraulic conductivity (scenario 13 in Table 1). This combination was performed by using the previously generated ﬁles of the
100 simulations in which soil and irrigation heterogeneities were
evaluated individually. The ﬁles describing the time dependent
atmospheric boundary conditions (ATMOSPH.IN) and the graphic
domain information (DOMAIN.DAT) including irrigation and soil
heterogeneity information, respectively, were included in eachsimulation.
2.6. Sensitivity analysis – leaching fraction
A sensitivity analysis was performed in order to study the effectof LF on the variability of each drainage amount and concentration.
Two LFs, 0.20 and 0.33, were simulated in addition to the previously
simulated LF of 0.43 (scenarios 14–17, 2 and 8 in Table 1).
3. Results and discussion
3.1. Soil and irrigation heterogeneities(1)

Where  is standard deviation and KS is average saturated hydraulic conductivity. The randomly distributed saturated
hydraulic conductivity, KSn was represented by a log-normal distribution (Lazarovitch et al., 2006b) and therefore log-transformed:
K Sn ∗ = lnK Sn(2)where KSn * is the log-transformed randomly distributed saturated
hydraulic conductivity.
The log-transformed hydraulic conductivity KS ∗ together with
its log-transformed standard deviation ␴* was deﬁned by Warrick(2003) Eqs. (3) and (4), as:








∗2

KS = exp KS ∗ + 0.5 ∗2
 2 = exp 2KS ∗ + (3)

 ∗2 

exp 



−1

(4)

As expected, the higher the imposed irrigation or soil heterogeneity, the higher the variability of either the measured drainage
amount or concentration. While increasing heterogeneity of thesoil hydraulic conductivity brought about higher variability regarding the drainage Cl− concentration, heterogeneity in irrigation rate
produced higher variability in the drainage amounts (Figs. 4–7).
Drainage ﬂux is a result of the balance between the irrigation
amount and precipitation, ET, and water storage in the soil proﬁle.
In this study, there was no precipitation and a ﬁxed high irrigation
regime supplying excess water to insure salt leaching was maintained so that there was no ET reduction due to water stress. These
conditions drove the system to a quasi-steady state with minimal changes in soil water storage (Tripler et al., 2012). Therefore,drainage ﬂux was directly affected by the irrigation amount, controlled in this case by the irrigation heterogeneity. Variability in thequantity of drainage reached even larger values than the imposed

I. Raij et al. / Agricultural Water Management 195 (2018) 1–10

5

Fig. 3. Visualization of three representative simulations (i = 1–3) of soil hydraulic conductivity scaling factors in 1m2 lysimeters simulated for three levels of soil heterogeneity(low, medium and high).

CV of the irrigation rates (Fig. 7-A). Water content and velocities
in the proﬁle were affected by the heterogeneity of K(h), but did
not affect water uptake, or alter the water balance. Therefore, variability of the drainage amount when soil heterogeneity was applied
remained low (Fig. 5 – A). Despite the consideration of a 4-day average for the calculation of drainage amount CV, a high variability of
the CV values was observed (Fig. 5 – A) due to the strong variability
in drainage amount (Fig. 2).
The ﬁxed irrigation-to-ET ratio insured equilibrium of thedrainage water chloride concentration so that heterogeneity inirrigation quantity caused only a small variability in the drainage
concentration. Conversely, heterogeneity of K(h) caused higher
variability of the drainage concentration due to increased or
reduced solute dispersion and spreading as pore water velocity wasvaried (Mousavi Nezhad et al., 2011; Russo, 1998; Weihermüller
et al., 2006).
Variability in drainage ﬂux or concentration decreased whenlysimeter surface area increased; the larger the lysimeter, thesmaller the resulting CV (Figs. 5 and 7). This was found for concentration of Cl− in drainage when either heterogeneity of irrigation
rate or K(h) were applied (Figs. 5 and 7 – B). Variability of drainage
volume was found to increase with increased surface area only

when heterogeneity of irrigation rate was applied (Fig. 7 – A) andwas not consistently affected by heterogeneity of K(h) (Fig. 5 – A).
There was a gradual decrease in the ratio of the variability between
the lysimeters with different surface areas as the imposed irrigation heterogeneity increased for both drainage amount (1.49, 1.40
and 1.36 for irrigation rate CVs of 0.02, 0.044 and 0.09, respectively,
Fig. 7 – A) and for chloride concentration (1.08, 1.05 and 1.01 for
CVs of 0.02, 0.044 and 0.09, respectively, Fig. 7 – B). These data
show that, as heterogeneity in irrigation rate increased, the relative gained beneﬁt from increasing the lysimeter size decreased. No
such effect was observed regarding heterogeneity of soil hydraulicconductivity.

3.2. Combined heterogeneities
A set of 100 simulations for each of the 1 and 0.5 m2 lysimeters was performed for cases of simultaneous dripper discharge
rate and K(h) heterogeneities. The variability of drainage volume
that resulted from the combined heterogeneities, for both lysimeter
dimensions, was very similar to that obtained when only irrigation heterogeneity was simulated (Fig. 8 – A). In a similar manner,the variability in drainage Cl− concentration of the combined het-6

I. Raij et al. / Agricultural Water Management 195 (2018) 1–10

Fig. 4. Averages and 96% conﬁdence intervals for simulated drainage amount and Cl− concentration for 1 m2 (pink) and 0.5 m2 (blue) lysimeters for three levels of heterogeneityof soil hydraulic conductivity (K(h)). Conﬁdence intervals for drainage amounts were very small and therefore almost not visible in the ﬁgure. CV values indicate those used
for the generation of spatial heterogeneity of K(h). (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.)

Fig. 5. Drainage amount (A) and Cl− concentration (B) variability (CV values) along the season for three heterogeneity levels of soil hydraulic conductivity and two lysimetersizes.

erogeneities was very similar to that obtained when only K(h)heterogeneity was simulated (Fig. 8 – B). The fact that the CVof the results approximated the highest CV value obtained when
considering each source of heterogeneity separately indicates thatsimultaneous heterogeneities did not cause a synergistic effect anddid not add variation (Fig. 8 – A and B). Warrick and Gardner (1983),
similarly found that soil and irrigation variability were not additive in their effects on yield. These results can be useful if there isknowledge of the factors causing heterogeneity in the ﬁeld, allowing investment of energy to reduce only the factor which mostinﬂuences heterogeneity and according to the type of data thatwants to be collected from the lysimeter.

3.3. Sensitivity analysis of the leaching fraction
Variabilities in drainage amount and Cl− concentration were
tested for three LFs in the 0.5 m2 lysimeter. There was no root water
uptake reduction due to matric stress, such that average actual LFs
were constant along the season. Small changes in actual LF fromday to day (data not shown) were related to the response time
between irrigation and drainage and the daily ET variability (Fig. 2).
An increase in LF decreased the effect of soil and irrigation heterogeneity on drainage Cl− concentration variability (Fig. 9 – B). For thevariability of drainage amount, a change in LF had inﬂuence only
when heterogeneity of the irrigation rate was considered (Fig. 9 –A).
The variability of the drainage amount as a function of heterogeneity in irrigation rate was higher for the smaller LF. However,I. Raij et al. / Agricultural Water Management 195 (2018) 1–10

7

Fig. 6. Averages and 96% conﬁdence intervals for simulated drainage amount and Cl− concentrations for 1 m2 (pink) and 0.5 m2 (blue) lysimeters for three heterogeneitylevels of dripper discharge. CV values are those used for the normal distribution function of the dripper discharge rate. (For interpretation of the references to colour in thisﬁgure legend, the reader is referred to the web version of this article.)

Fig. 7. Drainage amount (A) and Cl− concentration (B) variability (CV values) along the season for three levels of heterogeneity of dripper discharge rate and two lysimetersizes.

the standard deviation of the drainage amount was lower for thesmaller LF. This was due to the large differences in average drainage
amount as a consequence of the different LFs.
These results support the classic approach of increasing irrigation amount in order to overcome the negative effects of low
irrigation uniformity on yield (Letey et al., 1984). When irrigating with brackish water, there is a basic need to irrigate in excess
in order to prevent salt accumulation. Such practice could therefore eliminate any effect of irrigation uniformity on yield as in the
study presented by Zhao et al. (2012) where different irrigation
uniformity levels did not affected drip irrigated cabbage growth,yield or quality. In addition, variability in soil water content may belower than irrigation imposed variability due to water movement
and redistribution in sprinkler irrigation (Li, 1998), causing consequential lower variability of water availability sensed by plants.
For the hypothetical crop in the present work, and under the speci-

ﬁed conditions, no root water uptake reduction was simulated andtherefore no yield reduction was predicted. Different levels andtypes of heterogeneity did not produce any variability or uncertainty in the hypothetical yield (a function of ET). However, thefocus of this numerical exercise was to understand the uncertainty
from lysimeter data, regarding water and solute balances, and not
to evaluate yield or its variability.
3.4. Osmotic stress
Five cases were chosen in order to understand the behaviorof variability for a salt sensitive crop under conditions leading to
reduced root water uptake in the smaller lysimeters. The ﬁve cases
included low and high LFs with soil or irrigation heterogeneity andlow LF with combined soil and irrigation heterogeneity (Table 1).
Overall CVs were lower for simulations where root water uptake

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I. Raij et al. / Agricultural Water Management 195 (2018) 1–10

Fig. 8. Variability (CV) of drainage amount (A) and Cl− concentration (B) resulting from heterogeneities due to soil hydraulic conductivity (red), irrigation rate (blue) andcombination of the two (green) in 0.5 m2 lysimeters. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of thisarticle.)Fig. 9. Variability (CV) of drainage amount (A) and Cl− concentration (B) in 0.5 m2 lysimeters for heterogeneities resulting from soil hydraulic conductivity (CV 0.5, red) andirrigation rate (CV 0.044blue) at three irrigation levels: leaching fraction (LF) of 0.20, 0.33 and 0.43. (For interpretation of the references to colour in this ﬁgure legend, thereader is referred to the web version of this article.)

was reduced due to relatively high drainage amounts and higher
drainage Cl− concentrations (Fig. 10 – A and B). The same trends
observed in the simulations with no osmotic stress were repeatedin these simulations (Fig. 10): 1) Heterogeneity in soil hydraulicconductivity yielded higher variability in drainage concentration
while heterogeneity in irrigation rate caused higher variability indrainage amount; 2) When considering both sources of heterogeneity simultaneously, no synergistic effect was observed, CVsof both drainage volume and concentration were very similar to
those produced by either heterogeneity of irrigation rate or soil
K(h) alone; 3) Higher irrigation levels produced lower variabilities
in both drainage amount and concentration. Actual LFs increased
along the season due to root water uptake reduction. Final LF values
were 0.38 and 0.37 for simulations with target LF of 0.20 (soil K(h)and irrigation rate respectively) and 0.51 for all the simulations
with target LF of 0.43. Variability (CV values) of actual root water
uptake (after reduction due to solute stress) was generally low
with maximum values, at day 200, of 0.02 for heterogeneity due
to soil K(h) and 0.01 for heterogeneity due to irrigation rate, forboth irrigation levels (data not shown).

4. Conclusions
When relying on lysimeter data for irrigation managementwith low quality water, either drainage amount or concentration
can be used. The drainage amount allows estimation of ET while
the drainage solute concentration or EC (electrical conductivity)
provides capability to calculate actual LF. The results from thenumerical experiments performed in this study can add conﬁdence
to decision making using either drainage amount or concentrationaccording to the variability found for each. Variability was found todepend on the level of heterogeneity imposed by the system (soilhydraulic conductivity or irrigation discharge rate, in this case),leaching fraction, and/or lysimeter size. When heterogeneity of irrigation supply rate was high, the drainage Cl− concentration had alower variability, leading to the conclusion that it can be more reliable for management decisions than the highly uncertain drainage
amount. Contrarily, in a case of low heterogeneity or uncertainty ofirrigation application rate, the ET calculated with the water balanceof the lysimeter will represent a more accurate measurement thanthe LF calculated using drainage Cl− concentration. Combining heterogeneities of soil hydraulic conductivity and irrigation discharge
rate did not cause a synergistic effect; the measured variability inI. Raij et al. / Agricultural Water Management 195 (2018) 1–10

9Fig. 10. Simulations with osmotic stress in 0.5 m2 lysimeters. Variability (CV) of drainage amount (A) and Cl− concentration (B) for heterogeneity due to irrigation rate (blue)and soil hydraulic conductivity (red) at two irrigation levels (leaching fraction (LF) of 0.20 and 0.43 and for combined heterogeneities at the high irrigation level (green). (Forinterpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.)

the results was very similar to the highest value caused by eitherof the imposed heterogeneities when applied alone. Higher irrigation levels (increased LFs) decreased the variability of the drainage
concentration for both sources of heterogeneity and also decreased
the variability of drainage amount under heterogeneity due to irrigation discharge rate. Increasing the irrigation amount did notdecrease variability in drainage amount when heterogeneity wasdue to soil hydraulic conductivity. The results of these numericalexperiments are also applicable to cases of irrigation with waterhigh in salts and conditions causing reduced water uptake.
Acknowledgments
This research was partially supported by the Israel Ministry ofAgriculture and Rural Development (Eugene Kandel Knowledge
Centers) as part of the Root of the Matter – The Root Zone Knowledge Center for Leveraging Modern Agriculture, I-CORE Programof the Planning and Budgeting Committee and The Israel Science
Foundation (Grant No. 152/11). The data of this paper are available
upon request (iael@post.bgu.ac.il).
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