Journal of Hydrology 587 (2020) 124940

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Journal of Hydrology
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Research papers

A macroscopic soil-water transport model to simulate root water uptake inthe presence of water and disease stress

T

Srinivasa Rao Peddintia,⁎, B.V.N.P. Kambhammettua, Ranjith S Ladb, Jiří Šimůnekc, R.M. Gadeb,
J. AdinarayanadaDepartment of Civil Engineering, Indian Institute of Technology Hyderabad, Telangana, India
Department of Plant Pathology, Dr. Panjabrao Deshmukh Krishi Vidyapeeth, Akola, Maharashtra, Indiac
Department of Environmental Sciences, University of California Riverside, Riverside, CA 92521, USAdCenter of Studies in Resource Engineering, Indian Institute of Technology Bombay, Powai, Indiab

ARTICLE INFOABSTRACTThis manuscript was handled by Corrado
Corradini, Editor-in-Chief, with the assistanceof Weiping Chen, Associate Editor

Macroscopic modeling approaches based on the solution of the Richards equation with root water uptake (RWU)
as a sink term can help in understanding soil-water-plant interactions within the rhizosphere. However, thesemodels currently cannot capture the differences in RWU attributed to variations in plant health. Errors in simulating RWU from unhealthy plants are significant when disease-causing fungus inhibits water uptake rather
than other usually considered plant stresses. We developed RWU reduction functions to simulate plant transpiration under combined water and disease stress conditions using linear and non-linear response models. The
developed functions were implemented in the numerical model HYDRUS (2D/3D) to simulate water uptake froma root system in a radially symmetrical flow domain. Field experiments were conducted in the Vidarbha region ofcentral India for one crop cycle on four citrus trees with varying disease intensities (healthy to severely diseased). The proposed model was rigorously tested by comparing its results with measured soil water contents
and plant transpiration fluxes under various water and disease limiting conditions. Error in simulating RWU
fluxes from unhealthy trees by ignoring the disease stress factor was found to be significant (15% for slightly
diseased to 26% for the severely diseased tree). Parameters of the spatial root distribution and the disease stressresponse functions were optimized for each scenario using a genetic algorithm approach. Our results indicatethat calibration targets to validate uptake reduction functions should be chosen cautiously based on thedominant stress experienced by the plant root system.

Keywords:
Root water uptake
Water stress
Disease stressCitrusHYDRUS
central India

1. Introduction
The plant root system is a primary pathway for the exchange ofwater and energy between the soil environment and the atmosphere(Zheng and Wang, 2015). The morphology, spatial distribution, andwater uptake mechanism of the root system controls several hydrological fluxes, including evapotranspiration, soil moisture, and drainage(Canadell et al., 1996). Accurate quantification of root water uptake(RWU) and characterization of its temporal variability can help in optimizing irrigation schedules and improving crop productivity for sustainable development (Schröder et al., 2009). The assessment of RWU
can also help in understanding the movement of nutrients and otherchemicals in the vadose zone for solute transport studies (Somma et al.,
1998; Vrugt et al., 2001b). Several variably-saturated water flow
models that simulate soil-water-plant interactions within the⁎rhizosphere, including SWAP (Kroes et al., 2000) and HYDRUS(Šimůnek et al., 2008, 2016) can analyze the role of site-specific irrigation and management practices on crop production (Skaggs et al.,2006). However, these models work on the assumption that the plant ishealthy and do not impose any stress on RWU resulting from the disease
severity.
Based on the representation of complex structure and geometry ofroots in the soil-water flow equation, RWU from the vadose zone can bemodeled using two approaches, i.e., microscopic and macroscopic. In
the microscopic approach, the geometry of individual roots is approximated by an infinitely long cylinder of uniform radius and waterabsorbent properties (e.g., Gardner, 1960; Philip, 1957). The soil-waterflow equation is then analytically solved in a radial domain with theflow into the root driven by a product of the water potential gradientand the soil hydraulic conductivity (Šimůnek and Hopmans, 2009).

Corresponding author at: Department of Land, Air, and Water Resources, University of California Davis, CA 95616, USA.
E-mail address: ce14resch01007@iith.ac.in (S.R. Peddinti).

https://doi.org/10.1016/j.jhydrol.2020.124940
Received 17 November 2019; Received in revised form 5 March 2020; Accepted 7 April 2020
Available online 11 April 20200022-1694/ © 2020 Elsevier B.V. All rights reserved.

Journal of Hydrology 587 (2020) 124940

S.R. Peddinti, et al.

However, this method considers steady-state conditions that rarely exist
in field situations (Feddes and Raats, 2004; Yadav et al., 2009). Also,
this method requires detailed knowledge of the geometry of the rootsystem, which is difficult to measure and hence limits its application tosimple root systems (Deb et al., 2013; Vrugt et al., 2001b). In themacroscopic approach, the Richards equation is numerically solved
with RWU represented by an empirical sink term, averaged over thesystem of roots (Vrugt et al., 2001b):

t

=

[K (h

z)]

S (x , y , z , t )a diseased tree consumes less water than a healthy tree. It is difficult tomodify existing abiotic stress functions to account for both abiotic andbiotic stresses, as the inter-dependence of these stresses can result indifferent RWU patterns (Atkinson and Urwin, 2012; Fujita et al., 2006).
The effect of soil-borne diseases on the uptake mechanism was never
explored from the hydrological perspective, hence questioning the applicability of existing models to simulate RWU from disease-affected
trees (Peddinti et al., 2018). In the co-existence of multiple uptake reduction factors of varying strengths, it is crucial to dynamically quantify appropriate stresses that a plant experiences so that effective
management strategies can be implemented. Peddinti et al. (2018)highlighted the role of plant health in simulating RWU from disease
citrus trees. However, they failed to develop stress response functions
that consider plant health conditions for the use with numerical models
and irrigation scheduling.
The Vidarbha region in Maharashtra, India, is the leading producerof mandarin oranges (Citrus reticulate), accounting for 40% of thecountry’s citrus production with a yield of 6 t ha−1, far below the nation’s average (Peddinti et al., 2018). The low citrus production in Vidarbha is primarily attributed to improper management activities that
result in the formation and propagation of a water mold disease called‘root rot’ (Phytophthora spp.). Under favorable conditions (high soil
moisture and cold temperature), the disease-causing fungus produces alarge number of motile zoospores that move towards the roots. Thesezoospores contact the root system, then encyst, germinate, and enter
the root tip, resulting in the rot of the entire rootlet (Savita and Nagpal,2012). These root pathogens can damage the tree by decreasing the root
density, and water and nutrient uptake (Duniway, 1971). It is almost
impossible to identify early-stage symptoms of this disease, which originates in the rhizosphere (Jagtap et al., 2012). Late-stage impressionsof a disease-affected tree are seen at the surface with symptoms including leafless branches, yellow foliage, shoot dieback, reduced fruit
size and yield, thin canopy, and reduced water and nutrient uptake(Zekri and Rouse, 2007). The disease intensity can be estimated bymeasuring the population density of Phytophthora spp. in the soil surrounding the root zone and is expressed on a scale of 0 (healthy) to 4
(severely diseased) (Gade et al., 2006; Gade and Koche, 2012). The
disease intensity has a strong negative correlation with biomass andcrop yield (Choudhari et al., 2018). A disease-affected tree inhibits
RWU, resulting in higher soil water contents, a condition favorable forfurther growth of disease-causing fungus. In order to evaluate alternate
irrigation and management practices for citrus trees of different healthconditions, it is imperative to accurately represent RWU from diseaseaffected trees using numerical tools.
The objectives of this research are: i) to formulate linear and nonlinear disease stress response functions and implement them in a numerical model to simulate RWU from citrus trees, ii) to evaluate theapplicability of disease stress response functions in the presence andabsence of water stress conditions, and iii) to derive optimal root distribution and disease sensing parameters for use with numerical models
and the operational management of citrus trees.

(1)
3

−3

where θ is the volumetric water content (cm cm ), K is the unsaturated hydraulic conductivity tensor (cm s−1), h is the soil water
matric potential (the pressure head) (cm), and S is an empirical sink
representing RWU (cm3cm−3s−1). The macroscopic approach is widelyused in numerical models since it requires easy to measure and/or estimate parameters, including the soil water potential, plant transpiration, and root density (Wang et al., 2015). The sink term S in Eq. (1)defines the volume of water removed by RWU from a unit volume ofsoil per time. This can be represented using: i) water transfer models
that are based on the water pressure head gradient at the soil-root interface and a depth-dependent root density function (e.g., Feddes et al.,
1974; Gardner, 1964; Molz, 1981) or ii) transpiration based models that
depend on the atmospheric demand and a spatially varied root distribution function (e.g., Belmans et al., 1983; Šimůnek et al., 1994; Wu
and Cosgrove, 2000; Zuo et al., 2004). In the former case, the root
density function is primarily dependent on soil hydraulic properties,
whereas in the latter case, it represents root morphology and architecture in the spatial domain (Skaggs et al., 2006). Owing to a simple
representation and reliable estimation of the atmospheric demand frommeteorological parameters, the transpiration based RWU functions arecommonly adopted (Gardner, 1960) and have the form:Sp (x , y, z, t ) = (x , y, z ) Tpot Lt(2)where Sp is the potential RWU that could occur from a water-unlimited,saline-free, and healthy root system, (x , y, z ) is a normalized root
density distribution function (cm−3), Tpot is potential transpiration (cms−1) that depends on meteorological conditions and leaf properties (vanden Berg et al., 2002), and Lt is the surface area associated with transpiration (cm2). Several empirical equations were proposed in the literature to model (x , y, z ) (e.g., Feddes and Zaradny, 1978; Hao et al.,2005; Vrugt et al., 2001b; Wu and Cosgrove, 2000). These functions
largely differ in terms of representing the shape (linear, exponential, ortrapezoidal) and scale parameters of the root system. Actual RWU
under prevailing agrometeorological conditions can be obtained as:

Sa (x , y, z, t ) = (h ,) Sp (x , y , z , t )(3)where Sa is actual RWU occurring from a natural root system, and (h,Φ) is a dimensionless stress response function (0 ≤ (h, Φ) ≤ 1) representing the stress factors that reduce potential RWU due to nonoptimal conditions that exist during crop growth, such as:a) the water stress, α(h), that reduces RWU due to sub-optimal soil
water pressure head (h), and can be modeled using either a piece-wiselinear reduction function (Feddes and Zaradny, 1978) or a continuous
S-shape reduction function (van Genuchten and Jury, 1987), and b) thesalinity stress, α(Φ), that reduces RWU due to the osmotic head (Φ), andcan be modeled considering the relation between the whole-plant water
use and yield loss (van Genuchten and Hoffman, 1984; Maas andHoffman, 1977)
Almost all water uptake reduction functions proposed in the literature are based on abiotic (drought, salinity, nutrient) stresses encountered by a plant. However, the plant water consumption can also
be hampered by biotic (bacteria, viruses, fungi) stresses, which primarily reduce the ability of roots to absorb water by lowering the cropwater consumption and associated yield (Rejeb et al., 2014). For thesame irrigation and water management conditions, it is well known that

2. Materials and methods
2.1. Experimental setup and data acquisition
Factorial field-scale experiments were conducted on four matured
citrus trees of varying health conditions located in the Nagziri village ofMaharashtra, India (latitude: 21° 27′ 5″ N, longitude: 78° 9′ 12″ E,
elevation: 460 m asl). Agrometeorological conditions at the experimental site were discussed in Peddinti et al. (2018). The selection oftrees was made based on the visual disease symptoms at the surface(Gade and Koche, 2012). These include a healthy tree with no yellowing (T1), a tree with 10–25% yellowing of leaves with oozing lesionsof 1 cm2 area (T2), a tree with 25–50% yellowing of leaves with oozing
lesions of 2.5 cm2 area (T3), and a tree with more than 50% yellowing
2

Journal of Hydrology 587 (2020) 124940
Oozing lesion developed above
5 cm2 area with bark splitting
70
1.63

4

Oozing lesion developed above
2.5 cm2 area
120
3.62

2–3

Oozing lesion developed above
1 cm2 area
140
4.97

1–2

None
160
5.32

0

Disease Symptoms
Disease Level(Scale)Yield atHarvest (kg)LAI (m2
m−2)

0.04

2.22

17

Undisturbed soil samples were collected in cylindrical cores (height:
13 cm, diameter: 10 cm) from a representative depth of 30 cm surrounding each experimental plot. These samples were used to estimate
soil physical and electrical properties in the laboratory under controlled
conditions (Table 1). Texturally, the soil is classified as vertisol, having
high expansive clay content and water-holding capacity with a swell
index of 55% (Virmani et al., 1982). Soil suctions and moisture contents
during the drying phase were estimated using dew point potentiometerand gravimetric methods, respectively. The van Genuchten-Mualem
model (van Genuchten, 1980) shape parameters α and n were estimatedusing the RETC code (van Genuchten et al., 1991) that considers theconstitutive relationships given by:

12.7

12.0

1.66

1.61

1.36

17
2.34
0.05

11.5
1.65

1.38

17
2.43
0.04

13.6
1.67

1.52

17
2.46
0.03

Ks (cmd−1)

1.47

Age (yr)C (-)
b (S m−1)

2.2. Laboratory estimation of soil propertiesn (–)

a (S m−1)of leaves with oozing lesions of 5 cm2 area (T4). Phenological anddisease characteristics of the experimental trees are presented inTable 1.
Electrical resistivity tomography (ERT) was proven to be an effective method to monitor soil moisture profiles at a high spatial resolution
within the root zone of orange trees (Cassiani et al., 2015). A squaregrid of 2.8 m by 2.8 m having 40 surface electrodes ( x = 0.4 m,
y = 0.7 m) with an orange tree located at the center was laid tomonitor root zone water contents (Fig. 1). The reliability of ERT toestimate soil water contents was tested using gravimetric measurements
at selective depths. Plant transpiration was measured using SFM1 sap
flow meters (ICT International, Armidale, NSW, Australia) that wereplaced in the tree trunk at the height of 0.5 m above the ground in four
citrus trees (Fig. 1). The sap flow meter utilizes a heat-ratio method tomeasure high, low, and reverse sap flows using a set of three 35 mm
stainless steel needles placed at 5 mm spacing. Sap flows were monitored at 15 min interval and accumulated over each day. The hydraulicgradient across the root zone was estimated using tensiometers placedalong the vertical axis (Fig. 1), and drainage fluxes across the bottom
boundary were estimated using Darcy’s law (Whitaker, 1986).

s

( )=

r + [1 + (|rn mv | )]α (cm−1)

0.013

0.016

0.011

0.009

0.51

0.53

0.49

0.54

−3

0.09
1.82

0

(4)

(5)

=a c+bis the electrical conductivity of a soil sample,
where (Sm(cm3cm 3) is the soil volumetric water content, with a (Sm 1), b (Sm 1)
and c ( ) being the best-fit parameters. A comprehensive description
and methodology for laboratory estimation of pedo-physical and pedoelectrical relations can be found in Peddinti et al. (2018). Inoculum
dynamics for the four trees (T1 through T4) were observed at weeklyintervals to characterize disease intensity. Soil cores from four cornersof each tree, located at 75 cm distance from the trunk, were pooled tomake the composite soil. About 10 cm3 of soil from the homogeneous
sample was added to 90 ml of 0.025 percent agar, and 1 ml of the slurry
was plated on Phytophthora selective medium (Tsao and Stephen,1977). Plates were then incubated at 27 °C for three days and Phytophthora colonies were counted using a microscope and reported as apropagule count per cc of soil, PC (Gade and Koche, 2012).
1)

58.4
T4 (Severely diseased citrus tree)
0–30
25.3
16.3

0.11
1.66
T3 (Moderately diseased citrus tree)
0–30
15.6
24.3
60.1

0.08
1.73
54.5
T2 (Slightly diseased citrus tree)
0–30
17.5
28

0.07
1.69
57
21
T1 (Healthy citrus tree)
0–30
22

<0

where r and s are the residual and saturated soil water contents(cm3cm 3) respectively; v is the reciprocal of air entry (cm 1) ; n is a1pore-size distribution index (−) with m = 1 n (−). The non-linear
relation between electrical resistivity and soil moisture was developed
following ASTM guidelines (ASTM G57-06, 2012). A simplified form of
Waxman and Smits (1968) was fitted to the data using the constitutive
relation given by:

)

3
s (cm
cm−3)

s

3

r (cm cm

Bulk density(g cm−3)
Clay (%)
Silt (%)
Sand (%)
Soil depth(cm)

Table 1
Physical, hydraulic, and electrical properties of the soils as well as phenological and disease characteristics of citrus trees of the study area ( r is the residual soil water content, s is the saturated soil water content(cm3cm−3), α and n are van Genuchten (1980) fitting parameters, Ks is the saturated hydraulic conductivity (cm d−1), and a (S m−1), b (S m−1), c are the Waxman and Smith (1968) model fitting parameters.

S.R. Peddinti, et al.

2.3. Root water uptake model
For isolated trees such as citrus in large monocultures, the process of3

Journal of Hydrology 587 (2020) 124940

S.R. Peddinti, et al.

Fig. 1. Photograph of a typical experimental set up showing the ERT grid, the sap flow meter, tensiometers, and the micro-lysimeter around a citrus tree (left) and thecorresponding schematic plan with the detailed arrangement (right).

water uptake is complex and hence requires a three-dimensional representation of the spatial root distribution (Green and Clothier, 1998).
The distribution of soil moisture following the irrigation of citrus trees
has been found to be symmetric in the X-Y plane, and hence considering
an isotropic distribution of RWU in the lateral direction is appropriate(Peddinti et al., 2018). Since the root distribution function proposed by
Vrugt et al. (2001a) can be readily tested with numerical tools such as
HYDRUS and has the scale and shape parameters that can be readily
modified, it is ideal for characterizing the root morphology and simulating RWU. Keeping these points in view, we have adopted the twodimensional axisymmetric form of the root distribution function proposed by Vrugt et al. (2001a) to model RWU of the citrus trees in the
study area:(r, z) = 1

Z
Zm

1

r
e
Rm

pz
|z
Zm

z| +

pr
|r
Rm

disease-free conditions is violated, biotic pathogens in the rhizospherecan cause an additional reduction in RWU, and the plant is said toexperience the disease stress α (PC). In reality, all these stresses cancoexist during the crop cycle; hence, their integrated effect on RWU
needs to be simulated. The combined effect of all possible uptake reduction factors can be described using either additive or multiplicative
approaches of individual stresses experienced by the plant. It is still
under debate, which approach can best describe the plant water uptake
more accurately (Fujimaki et al., 2008; Šimůnek and Hopmans, 2009).
2.4.1. Water stress response function
To account for the reduction in RWU resulting from changes in soil
moisture between irrigations, piece-wise linear and non-linear response
functions are often used (Feddes and Zaradny, 1978; van Genuchten
and Jury, 1987). The piece-wise linear model is parameterized using
four thresholds of the soil water pressure head between a permanent
wilting point and full saturation, with h4 < h3 < h2 < h1. The water
stress response function α(h) used in this study is given as (Feddes andZaradny, 1978):

r|

(6)

where (r , z ) is the shape function describing the spatial root distribution (cm−2); Zm and Rm are the maximum rooting depth (cm) andthe maximum radial distance (cm) respectively; z* and r* are the empirical parameters that control the position of the maximum uptake
intensity (cm), and pz and pr are the empirical parameters that control
the shape of the root distribution (–). These empirical parameters areconstrained to provide zero RWU at z ˃ = Zm, r ˃ = Rm, and maximum
RWU at z* and r*. Normalized RWU from the citrus root system, Sp(cm3cm−3s−1), considering the atmospheric demand, is given by:

Sp (r, z) = (r, z) × Tp × Lt

h h4,
h3 h 4(h ) =

h

h3 h2

h

h3

h1 > h > h2hh4 orh

h1

(9)

(7)
2.4.2. Disease stress response function
Peddinti et al. (2018) concluded that ignoring plant health conditions in the numerical models can result in significant deviations insimulated RWU fluxes, particularly from disease-affected trees. In thisresearch, the disease level of a citrus tree is quantified using the population density of Phytophthora spp. (i.e., propagule count, PC) per aunit volume of soil (cfu g−1) and is represented on a scale of 0 (healthy
with no yellowing) to 4 (severely affected with more than 50% yellowing and leaf fall) (Gade et al., 2006). Several researchers haveconcluded that PC changes during crop growth stages have a strong
correlation with soil moisture and yield loss (Bright et al., 2004; Gade
and Koche, 2012). We considered the yield data from 30 mature citrus
trees of the region with varying disease intensities to obtain a functional
form of the water uptake reduction function due to plant disease conditions, (PC ) (Fig. 2). Because of the differences in frequency andamount of irrigation between crop growth stages, we defined stage

Eq. (7) is applicable to estimate potential RWU from a healthy tree
subjected to stress-free conditions. In the presence of uptake reduction
stresses, actual RWU, Sa (cm3cm−3s−1) is given by:, PC ) Sp (r , z )

h2

h h1
,
h2 h1

0

2.4. Uptake reduction functions

Sa (r , z ) = (h,1h3 > h > h4(8)where Γ(h, , PC ) is the total stress experienced by the plant rootsystem, involving both biotic and abiotic components. The integrationof the above equation over the spatial domain gives cumulative actual
RWU from the root system, which is equal to actual plant transpiration,
Ta (Vrugt et al., 2001b; Šimůnek and Hopmans, 2009). Commonly usedabiotic uptake reduction factors include the water stress α(h) and thesalinity stress α(Φ), which depend on the pressure head and the osmotic
head, respectively (Fujimaki et al., 2008). When the assumption of4

Journal of Hydrology 587 (2020) 124940

S.R. Peddinti, et al.

Fig. 2. Plots of piece-wise linear (left) and S-shaped nonlinear (right) uptake reduction functions fitted to the observed data of a stage-specific propagule count (PC)of disease-causing fungus (Refer to Eqs. (10) and (11) for mathematical representation).
Table 2
Schedule of irrigation and ERT data acquisition activities performed during the experiment.
Case/Scenario

Case I

Case II

Case III

Case IV
Case V
Case VI

Date of observation

10.09.2017
11.09.2017
13.09.2017
16.09.207
26.09.2017
27.09.2017
28.09.2017
29.09.201729.10.201729.10.2017 (AI)30.10.201731.10.2017
14.11.2017
15.11.2017
16.11.2017
26.12.201727.12.2017
28.12.2017
17.02.2018
18.02.2018

Start – End Times of the ERT Survey

Start–End Times of Irrigation(Indian Standard Time)(Indian Standard Time)

T1

T2

T3

T4

T1

09:00–09:20
13:35–14:00
12:00–12:25
09:30–09:55
10:30–11:00
18:00–18:30
10:00–10:30
11:30–12:00
11:45–12:15
17:15–17:45
10:00–10:30
09:45–10:15
15:30–16:00
13:30–14:00
09:00–09:30
11:00–11:25
16:00–16:30
08:00–08:30
16:00–16:30
11:00–11:30

09:30–09:50
14:40–15:00
10:15–10:45
10:45–11:15
16:15–16:45
17:30–17:50
12:00–12:30
10:30–11:00
10:00–10:30
16:45–17:05
10:45–11:10
10:30–11:00
16:15–16:45
11:30–11:50
11:30–12:00
11:30–12:00
13:00–13:30
10:30–11:00
16:30–17:00
11:30–12:00

11:00–11:20
13:05–13:25
11:00–11:25
09:50–10:20
17:00–17:30
16:30–17:00
13:00–13:30
09:45–10:15
11:00–11:30
15:45–16:05
11:45–12:15
09:00–09:30
15:00–15:25
12:45–13:15
10:00–10:30
10:20–10:40
16:45–17:15
08:45–09:15
17:30–18:00
12:15–12:45

11:30–11:50
15:15–15:40
09:45–10:15
11:30–12:00
12:00–12:30
15:40–16:10
11:00–11:30
09:00–09:30
13:00–13:30
16:10–16:30
12:45–13:15
08:30–08:55
17:00–17:30
12:00–12:25
12:15–12:45
12:30–12:55
15:15–15:45
09:30–10:00
18:15–18:50
13:00–13:30

Rain (2 mm) on 12.09.207

specific parameters while formulating the disease stress response
function. For the observed citrus trees, the range in PC is highest during
the growth stage (20–35), followed by the flowering stage (9–20), andthe harvest stage (4–15). Increased frequency and irrigation amounts

T2

T3

T4

Irrigation on 27.09.2017 at 15:00

Irrigation on 29.10.2017 at 14:00

Irrigation on 15.11.2017 at 11:00
Irrigation on 26.12.2017 at 12:00
Irrigation on 17.02.2018 at 19:00

during the growth stage has resulted in swampy environment and highsoil moisture, a condition favorable for further growth of diseasecausing bacteria. First, we proposed a segmented linear function of theform:
5Journal of Hydrology 587 (2020) 124940

S.R. Peddinti, et al.

Fig. 3. Three-dimensional volumetric watercontent distributions measured using ERT
around four experimental trees (from healthy(T1) to severely diseased (T4)) before irrigation(top row) and after irrigation (bottom row). The
high soil water content around the severely illtree (T4) reflects the low water uptake produced by the plant. Irrigation was given on 2709-2017.

Fig. 4. An axisymmetric flow domain used in HYDRUS (2D/3D) for numerical simulations of RWU in experimental plots with water and disease stress function.

respectively, and is the slope of the linear function (note that can beevaluated directly from PCmin , PCmax , and min ). Similarly, a nonlinear
or S-shaped continuous smooth function is postulated to simulate theeffects of plant health on RWU:

Table 3
Parameters of the optimal root distribution for citrus trees of varying healthconditions considering the root distribution function proposed by Vrugt et al.
(2001b).
Tree

Zm (cm)Rm (cm)z (cm)r (cm)pz (–)pr (–)

T1
T2
T3
T4

47.51
43.22
39.19
35.88

162.11151.58146.67129.98

38.52
36.73
32.33
26.81

108.73101.18
92.47
87.55

3.44
3.44
3.44
3.44

3.32
3.32
3.32
3.32

(PC ) =

(PC

1
PCmin) ×min

PC < PCmin
PCmin < PC < PCmax
PC > PCmax

( )

PC p3
PC50

(11)

where PC50 and p3 are the empirical parameters, with PC50 representing
the soil PC at which (PC ) becomes 0.5.

Note: Parameter ranges considered during optimization process are as follows:z m (0–100 cm); Rm (0–250 cm); z (1–100 cm); r (1–250 cm).

(PC ) = 1

1

1+

2.4.3. Combined water and disease stress
We assume that the two stress functions ‘disease’ and ‘water’ aresolely caused by changes in PC and water potential, respectively, andare independent of each other. Even though PC has an indirect relationship with the soil water potential, this relationship is yet unexplored, and hence difficult to implement with Eq. (9). Since the soil
water potential is explicitly included in the water stress function, thisassumption seems to be meaningful. In reality, plants show different
degrees of sensitivity to water and disease stress conditions (Rejeb(10)

where min is the lowest possible uptake factor that is possible from adisease-affected tree, PCmin and PCmax are the minimum and maximum
thresholds for PC that results in unit and min uptake factors,
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Fig. 5. Comparison of simulated and ERT-measured water contents in four experimental plots (from healthy (T1) to severely diseased (T4)). Black dots (●) represent
soil water contents following irrigation (no water stress), and open circles (o) represent soil water contents a long time after irrigation (severe water stress).
Fig. 6. Time evolution of daily planttranspiration (cm d−1) from experimental
trees of varying health conditions (fromhealthy (T1) to severely diseased (T4))
considering ‘piece-wise linear’ (top) and‘S-shaped nonlinear’ (bottom) uptake reduction functions. Dots (•) showing thedaily variations of the observed transpiration fluxes for four trees. (Here DOY:
Day of the year L: Linear model, NL: Nonlinear/S-shaped model, O: Observed
transpiration rates at daily scale).

et al., 2014). We assumed that the effects of water and disease stress on
the uptake reduction are independent and hence their integrated effect(h, PC ) can be obtained using a multiplication rule (Skaggs et al.,2006; Šimůnek and Hopmans, 2009):(h, PC ) =

(h )

(PC )

2.4.4. Numerical implementation
The proposed linear and non-linear disease stress response functions(Eqs. (10) and (11)) were implemented in HYDRUS (2D/3D) (Šimůnek
et al., 2016, 2008) to simulate either individual or simultaneous effectsof water and disease stresses on RWU. Both static (Zm, Rm , pz , pr , z , r )and dynamic (PCmin, PCmax , min,or PC50, p3 ) parameters of the RWU
function were varied during model calibration to minimize the discrepancy between measured and simulated soil water contents as well
as plant transpiration fluxes.

(12)

where Γ(h, PC) ranges from 1 (healthy, water-unlimited) to 0 (severe
disease, water-stress) and is always less than or equal to (h) and(PC ) .

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Table 4
Parameters of the optimal disease stress reduction functions (piece-wise linear and S-shaped nonlinear) for citrus trees of varying health conditions.
Stage

T2

T3

S-Shaped

Flowering
GrowthHarvestingLinearT4

S-Shaped

PC50 (cfu
g−1)

p3 (–)

PCmin (cfug−1)

PCmax (cfu
g−1)

19.55
32.21
13.65

7.78
13.23
4.88

11.42
23.77
9.42

21.55
36.28
14.62

(–)
0.25
0.22
0.25

Linear

S-Shaped

PC50 (cfu
g−1)

p3 (–)

PCmin (cfug−1)

PCmax (cfu
g−1)

17.67
30.51
12.32

8.11
12.37
6.18

12.62
24.12
8.56

20.33
35.2
14.82

(–)
0.26
0.25
0.22

Linear

PC50 (cfu
g−1)

p3 (–)

PCmin (cfug−1)

PCmax (cfu
g−1)

18.78
31.49
11.92

7.02
11.33
5.22

14.22
23.1
8

21.4
34.9
13

Note: Parameter ranges considered during optimization process are as follows: PC50 (0–100 cfu g−1); p3 (0–50); PCmin (1–100 cfu g−1); PCmax (1–100 cfu g−1);

(–)
0.28
0.26
0.24

(0–5).

Fig. 7. Scatter plots between observed and HYDRUS (2D/3D) simulated (considering linear and non-linear response models) transpiration fluxes (cm d−1) from theexperimental citrus trees of varying health conditions (from healthy (T1) to severely diseased (T4)).

2.5. Model calibration and performance evaluation

Optimization was performed using a genetic algorithm (GA) to reveal the optimal set of the most sensitive parameters (Vrugt et al.,2001b). GAs were developed based on the evolution theory, inspired bynatural selection and genetics, and aimed to solve complex optimization problems. The root distribution and disease stress response function parameters were optimized by calibrating the model against soil
water contents and plant transpiration fluxes, respectively. Since theinverse module of HYDRUS (2D/3D) is not set to optimize these parameters, the GA toolbox in MATLAB was coupled with the forward
computational module of HYDRUS (2D/3D) to perform the calibration.
The GA was run with 1000 initial parameter sets, a penalty factor of 10,
a population size of 1000, a crossover fraction of 0.5, and a mutation
rate of 0.05 during optimization. Two-point cross over and uniform
mutation functions were used with the GA solver (Goldberg andHolland, 1988). Eight Markov chain runs with a set of 1000 generations
were utilized to minimize the errors in HYDRUS (2D/3D) simulated
water contents. Model performance was evaluated using the statisticalindices that include the root mean square error (RMSE), and coefficient

The proposed model was calibrated for different water (pre and post
irrigation) and disease limiting conditions (T1 to T4) using the spatial
distribution of water contents and whole-plant transpiration fluxes. A
global sensitivity analysis was performed using the Sobol's method(Sobol, 2001) to reveal critical parameters of each function and to determine the contribution of the uncertainty of each parameter to theuncertainty of the model output. The first-order (Si ) and total-ordersensitivity (Sti ) indices were approximated by a numerical Monte Carloestimation proposed by Saltelli et al. (2010). The static root distribution
parameters and the stage-specific disease stress function parameters
were transformed into their defined parameter intervals based on thespecified minimum and maximum values. Parameter limits on therooting depth and radial distance were observed from the ERT profiles,
whereas the other root distribution parameters were taken from theliterature. A total of 1000 parameter sets were considered to develop
the first-order and total-order sensitivity indices.
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S.R. Peddinti, et al.

reflectometry (TDR) probes placed at four depths (15, 30, 45, and60 cm below the ground level) were used to correlate with ERT measurements. ERT derived soil moisture data was in agreement with TDR
observations (R2 = 0.65, RMSE = 0.03 cm3 cm−3, error range: 0.04 to
0.08, n = 21) and hence were considered as observed soil water contents for use with HYDRUS (2D/3D) calibration.
It can be observed that irrespective of the health condition, soil
moisture profiles are visibly distinct between pre- and post-irrigation
scenarios. Since no lithological anomalies were reported, these changes
in soil water contents can be attributed to the root zone activity(Cassiani et al., 2015; Peddinti et al., 2018). Before irrigation (water
stress conditions), the soil moisture front that separates the active rootzone from the bottom soil layers is clearly visible from the ERT profiles(Fig. 3). The depth of the soil moisture front was decreasing from 47 cm
for a healthy matured tree (T1) to 35 cm for a severely diseased citrus
tree (T4). As the disease intensity progresses (from T1 to T4), the rootzone is observed to be attenuating in radial and depth directions. For
the same applied irrigation water and evaporation losses, relatively
high soil water contents under a diseased tree following irrigation (nowater stress condition) were observed due to less RWU. Low photosynthetic activity of diseased trees due to a reduction in LAI andchlorophyll contents could be an additional cause. Even though healthy
and unhealthy trees have recorded similar temporal moisture patterns,
their values differed significantly. ERT results led to the conclusion that
ignoring the health condition of a tree in the numerical model can resultin high RWU from diseased trees (due to the absence of the water
stress), which is in contrary to the field measurements.

Fig. 8. Distribution of transpiration (RWU) fluxes during the simulation fromunhealthy citrus trees by considering and ignoring the linear disease stress response function in the HYDRUS (2D/3D) model.

of determination (R2) (Cai et al., 2018).
3. Results and discussion
3.1. Analysis of soil moisture profiles from ERT

3.2. Numerical simulations with HYDRUS (2D/3D)

Spatiotemporal patterns of the soil water content surrounding thecitrus tree were obtained by performing 3D ERT experiments before andafter each irrigation application. During each watering, citrus trees
were flood irrigated to a depth of about 35–40 mm to replicate the fieldpractices. Six irrigation applications were considered during the monitoring period (Table 2), and a typical ERT-generated soil moistureprofile is presented in Fig. 3. Before the interpretation of the results,
ERT data quality and noise reduction were ensured using reciprocal
errors and stacking (Sreeparvathy et al., 2019). Calibrated time domain

An axisymmetric form of the Richards equation for water flow underunsaturated conditions around the citrus tree, with RWU represented by
an external sink term, was numerically solved. The finite element mesh,along with the applicable boundary conditions, is shown in Fig. 4. The
generated mesh with a mesh refinement around the root zone consistedof 8884 nodes, 346 1D elements, and 17,420 2D elements. The modelrefinement is chosen to achieve a tradeoff between computational cost

Fig. 9. The spatial representation of root distribution function, β(r,z) from the experimental citrus trees of varying health conditions (healthy (T1) to severely
diseased (T4) by considering optimal root distribution parameters.
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S.R. Peddinti, et al.

and numerical convergence. The flow domain has a length of 250 cm inthe radial direction and 100 cm in the depth direction. The upperboundary of the flow domain represents the land surface subjected toatmospheric and irrigation fluxes and was assigned an atmosphericboundary condition. Since the groundwater table depth (4–6 m) is well
below the root zone, the bottom boundary was assigned a free drainage
boundary condition to allow gravitational drainage fluxes following
irrigation, which were estimated using Darcy’s equation. All remaining
boundaries were assumed to represent no-flow conditions. The upperboundary conditions were assigned using a daily time step for 110 days
(09 Sep. to 27 Dec. 2017). Daily meteorological data was obtained froman automatic weather station (AWS) located at about 30 m from theexperimental site. The reference evapotranspiration (ET0) was estimated using the FAO based Penman-Monteith equation (Allen et al.,1998) and is in the range of 2 to 8 mm/day. ET0 was further partitioned
into evaporative (E0) and transpiration (T0) demands using the methodology proposed by Ritchie (1972) and is validated using flux partitioning methodology (Peddinti and Kambhammettu, 2019). RWU is
considered as a system-dependent boundary condition and is adjusted
during the simulation depending on the state variables (water anddisease stresses). RWU is equal to potential transpiration from ahealthy, irrigated plant and is limited by the lack of soil moisture and/or plant health conditions. Two disease stress response functions (linear
and non-linear models) were incorporated into the HYDRUS (2D/3D)
code using time-varying stage-specific PC values.
Since HYDRUS (2D/3D) does not have a dedicated calibration tool
for root distribution and disease sensing parameters, it was coupledwith the GA tool in MATLAB to perform calibration and parameter
estimation. The variance-based sensitivity analysis using Sobol's algorithm was performed to reveal the contribution of individual parameters and their interactions on simulated soil water and transpiration
fluxes. The detailed results of the sensitivity analysis are available as
Supplementary Material. Model parameterization and optimization
were performed by considering model sensitive parameters. Root distribution parameters that are sensitive to soil water simulations andtheir optimal values for each experimental tree are given in Table 3. It
can be observed that the parameters defining the shape of the spatialroot distribution (pz and pr) are insensitive to model simulations. As
discussed below in Section 3.5, the (r , z ) function for different experimental trees is governed exclusively by scale parameters in thedepth and radial directions.
The ERT domain was discretized in such a way that the grid cells of
ERT and HYDRUS (2D/3D) coincide as much as possible to minimize
the interpolation errors. Model calibration was achieved by matching i)simulated soil water contents with ERT measurements and ii) simulated
whole-plant transpiration fluxes with SAP flow measurements. A good
agreement between simulated and observed soil water contents wasachieved during water limiting (pre irrigation) and water available(post irrigation) conditions (Fig. 5). Overall, HYDRUS (2D/3D) was able
to capture the soil moisture profiles for T1 (R2 = 0.71; RMSE = 0.032;
n = 230), T2 (R2 = 0.74; RMSE = 0.026; n = 230), T3 (R2 = 0.69;
RMSE = 0.039; n = 230), and T4 (R2 = 0.78; RMSE = 0.021; n = 230)
scenarios.

produced similar RWU patterns during the simulations, with marginallydifferent magnitudes. During the simulation, daily RWU was in therange of 0.05 to 0.46 cm/d using a linear stress function, and 0.01 to
0.34 cm/d using a nonlinear stress function (lumped over all experimental trees). The linear stress response function yielded slightly higher
RWU (0.20 ± 0.08 cm/d) in comparison to the non-linear model(0.16 ± 0.06 cm/d). Cumulative RWU from the four experimental trees(T1 through T4) using a linear stress response function were found to be
28.07, 25.48, 20.84, and 13.54 cm, respectively, and their counterparts
using a nonlinear stress response function were found to be 20.34,
19.91, 17.75, and 11.54 cm, respectively. RWU from the linear stressresponse function was in close agreement with observed transpiration
fluxes in comparison to the non-linear model.
Daily RWU fluxes simulated using a linear stress response function
from a healthy citrus tree (T1) for growth and harvest stages were0.29 ± 0.06 cm/d and 0.18 ± 0.03 cm/d, respectively, and the corresponding values from a severely diseased citrus tree (T4) were0.146 ± 0.04 cm/d and 0.08 ± 0.01 cm/d, respectively. Similarly, daily
RWU fluxes simulated using a non-linear stress response function froma healthy citrus trees (T1) for the growth and harvest stages were0.21 ± 0.04 cm and 0.12 ± 0.01 cm/d, respectively, and the corresponding values from a severely diseased citrus tree (T4) were0.13 ± 0.03 cm/d and 0.07 ± 0.01 cm/d, respectively. Temporal patterns of RWU averaged over each crop stage can be approximated by aunimodal distribution with low RWU during the flowering stage,
highest during the growth stage, followed by a decreasing trend towards the harvest. Interestingly, this pattern coincides with the PC(Fig. 2) and irrigation frequency. This indicates that plant transpirationis sensitive to the PC and applied irrigation water with varying
strengths. Hence, the application of irrigation water to disease-affected
trees during the crop growth stage is more crucial for the effective
management of citrus trees.
Parameters of the disease stress response function were optimized
for each crop growth stage using linear and nonlinear functions and arepresented in Table 4. It can be observed that differences between optimized parameters are relatively small between different experimental
plots for a given growth stage and relatively large between different
growth stages. This indicates that it is important to consider timevariable disease sensing parameters (such as PC50, p3, PCmax, PCmin,αmin) to effectively simulate RWU from diseased trees. Scatter plots ofactual transpiration (RWU) simulated using the two disease stress reduction models along with observed whole-plant transpiration fluxes
are shown in Fig. 7. Results showed that the RWU fluxes simulatedusing the piece-wise linear stress response function are clustered aroundthe 1:1 line for all scenarios (T2 through T4), even though there is somescatter and bias in the estimates. It can be observed that the magnitudeof underestimation of RWU fluxes (deviations from the 1:1 line) when
the non-linear stress response function is used diminishes towards severely disease-affected trees (T4). This indicates that for severely diseased trees, both linear and non-linear stress functions give similar
predictions close to observed RWU fluxes. In other words, the bias inestimated daily RWU fluxes is high for a slightly diseased tree (T2) andgradually diminishes as the disease severity progresses. We attribute
this change to variations in model parameters.

3.3. Evaluation of disease stress response functions

3.4. Propagation of the error in simulated RWU due to ignorance of diseasestressTo be consistent with the commonly used water and salinity stressresponse models, we developed piece-wise linear and S-shaped nonlinear disease stress response functions (Fig. 2) for use with HYDRUS(2D/3D) simulations. However, the PC of disease-causing bacteria wasobserved to change dynamically during the crop cycle and was controlled by soil water contents and crop phenology (Fig. 2). Hence, we
divided the crop cycle into three stages (flowering (DOY90-135),
growth (DOY136-287), and harvest (DOY288-365)) to define the stagespecific functional parameters. Daily plots of RWU from the experimental plots using the two models are presented in Fig. 6. Both models

To quantify the error and its magnitude in the estimated RWU fluxes
from unhealthy trees as a function of disease intensity, HYDRUS (2D/
3D) simulations were repeated without considering the disease stressresponse function. A healthy citrus tree (T1), for which the diseasestress function is not applicable, had slightly higher simulated transpiration fluxes (Fig. 8). In reality, the ubiquitous influence of low PC
from healthy trees might inhibit RWU, resulting in low observed transpiration. To match with, HYDRUS (2D/3D) adjusts its root distribution
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parameters, yet achieving significantly deviated RWU fluxes. A similar,
yet significant deviation was observed for other disease-affected trees(T2 through T4), indicating that consideration of a compensation mechanism to lower simulated RWU is essential. The error in simulated RWU from unhealthy trees when ignoring the α(PC) component (i.e., the difference in box plots of ‘without disease stress’ and‘observed transpiration’) was found to be in the range of 15 to 26%(Fig. 8). It can be observed that for diseased trees of varying intensities(T2 through T4), actual transpiration simulated by considering thedisease stress response function matched almost perfectly with theobserved values, having the same range and median values.

using plant transpiration data can accurately quantify RWU fluxes from
diseased trees.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research is carried as a part of the ITRA-Water project that was
supported by Media Lab Asia, Ministry of Communications andInformation Technology, Government of India.

3.5. Spatial distribution of RWU from citrus trees
The spatial representation of root water uptake, β(r,z), from theexperimental trees is illustrated in Fig. 9. It can be observed that thezone of maximum RWU is located in a thin soil layer that varies from
0.2 m for T4 to about 0.32 m for T1. This zone can be designated as anexternal sink region that drives soil water flow towards active roots. A
healthy citrus tree (T1) has a larger rooting depth and radius comparedto the other three diseased trees. It can be observed that the shape of theroot distribution function remains the same for all experimental trees.
This indicates that the health condition of a tree has a significant impact
on the scale parameters of the root distribution function. The close
spacing of contours for a diseased tree indicates that pathogens are
inhibiting the water uptake mechanism, thereby minimizing the spatial
extent of RWU. We also conclude that measured plant transpiration
fluxes are more useful than measured water content for calibration ofsoil–water-plant models from diseased trees.

Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.org/10.1016/j.jhydrol.2020.124940.
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3.6. Limitations of research
The proposed disease stress functions are applicable to citrus
orchards family with similar agro-climatic conditions, and hence cannot
be generalized to other plants. We assumed that the two stress functions
are independent of each other when evaluating their combined effecton RWU simulations, which may not be accurate in reality. We could
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4. Summary and conclusions
This research provides an insight into soil-water-disease interactionsof citrus trees using combined experimental and numerical studies.
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water contents in the root zone, a condition favorable to further growthof the fungus. An axisymmetric form of the Richards equation with theroot distribution function proposed by Vrugt et al. (2001a) was thennumerically solved using HYDRUS (2D/3D). The reduction in RWU due
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