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Evaluation of Spatial and Temporal Root Water Uptake
Patterns of a Flood-Irrigated Pecan Tree Using
the HYDRUS (2D/3D) Model
Sanjit K. Deb 1; Manoj K. Shukla 2; Jiří Šimůnek 3; and John G. Mexal 4
Abstract: Quantitative information about the spatial and temporal patterns of compensatory root water uptake (RWU) in flood-irrigatedpecan orchard is limited. We evaluated spatio-temporal compensated and uncompensated RWU patterns of mature pecan tree in a silty
clay loam orchard using the HYDRUS (2D/3D) model. HYDRUS (2D/3D) simulations, which agreed well with measured water contents
and temperatures at different soil depths and horizontal distances from the tree trunk, suggested that while both compensated and uncompensated RWU varied with soil depth they did not do so laterally because of similar spatial vertical distributions of root length density (RLD)
for the under-canopy and the tree canopy dripline locations. Considering compensated RWU resulted in an increase in actual transpiration
by 8%, and a decrease in evaporation and drainage by 5% and 50%, respectively, during a growing season. Simulated transpiration andrelative transpiration (a ratio between actual and potential transpiration) values were correlated with measured transpiration and plant-based
water stress indicators (stem and leaf water potentials), respectively. Overall, our results of the spatio-temporal compensatory RWU provide
support to use HYDRUS (2D/3D) as a tool for managing efficient water use of pecan. DOI: 10.1061/(ASCE)IR.1943-4774.0000611.
© 2013 American Society of Civil Engineers.
CE Database subject headings: Silts; Clays; Floods; Irrigation; Evaporation; Trees.
Author keywords: Carya illinoinensis; Silty clay loam soil; Root water uptake; Compensated uptake; Flood irrigation; Transpiration;
HYDRUS (2D/3D) model.

Introduction
New Mexico is a leading producer of pecans (Carya illinoinensis).
Pecan trees require large quantities of water during the growing
season, and most orchards in the region use flood irrigation to
optimize consumptive water use and production of mature pecans.
The total amount of water applied using flood irrigation to maturepecans grown at soils with different textures on the Rio Grande
floodplain in the Mesilla Valley was reported to range between
1039 and 1977 mm per season (Deb et al. 2012a, 2013). Water
availability is considered a major constraint to pecan productivity.
With the increased emphasis on water conservation in conflictwith the necessity of water availability for pecan production, much
effort has been expended over the years on evaluating the amountof water required by a flood-irrigated mature pecan orchard(e.g., Miyamoto 1983; Sammis et al. 2004; Wang et al. 2007).
The efficient use of water in flood-irrigated mature pecan orchards
1

Postdoctoral Fellow, Dept. of Plant and Environmental Sciences,
New Mexico State Univ., Las Cruces, NM 88003 (corresponding author).
E-mail: sanjit@nmsu.edu
2
Associate Professor, Dept. of Plant and Environmental Sciences,
New Mexico State Univ., Las Cruces, NM 88003. E-mail: shuklamk@
nmsu.edu
3
Professor, Dept. of Environmental Sciences, Univ. of California
Riverside, Riverside, CA 92521. E-mail: jiri.simunek@ucr.edu
4Professor, Dept. of Plant and Environmental Sciences, New Mexico
State Univ., Las Cruces, NM 88003. E-mail: jmexal@nmsu.edu
Note. This manuscript was submitted on November 8, 2012; approvedon March 4, 2013; published online on July 15, 2013. Discussion period
open until January 1, 2014; separate discussions must be submitted forindividual papers. This paper is part of the Journal of Irrigation and Drainage Engineering, Vol. 139, No. 8, August 1, 2013. © ASCE, ISSN 07339437/2013/8-599-611/$25.00.

and a better understanding of the soil-plant-atmosphere water relations have been repeatedly addressed in recent years (Deb et al.
2011a, 2012b, 2013).
Actual evapotranspiration (ET a ), i.e., actual evaporation (Ea )from the soil and actual transpiration (T a ) from plants, is affectedby root zone soil water dynamics and requires simultaneous knowledge of water flow and actual root water uptake (RWU) in soils.
Spatial distribution of actual RWU depends not only on the root
distribution but also on temporal functioning of the roots as determined by soil water availability. Therefore, efficient water management in flood-irrigated rooting systems depends on the knowledgeof spatial and temporal distributions of RWU, as well as on variations of soil water in the root zone. The understanding of spatial
and temporal RWU patterns of a mature pecan orchard is also essential for a variety of agricultural and hydrological perspectives,
including irrigation management and predictions of yield underwater-scarce conditions and of water fluxes to both the atmosphereand the groundwater. However, there remains a paucity of quantitative information about the spatio-temporal RWU patterns of aflood-irrigated mature pecan orchard.
The functioning of roots, whether they are represented microscopically or macroscopically, has received major attention in
RWU modeling. A large number of microscopic and macroscopic
approaches to model RWU have been proposed over the years andintensely discussed in the literature (e.g., Molz 1981; Feddes andRaats 2004; Green et al. 2006). The microscopic scale model,
or single-root model, studies a convergent radial flow of soil water
toward a representative individual root, which is idealized as an
infinitely long cylindrical sink of a uniform radius. The dynamics
and detailed geometry of the rooting system at this microscopic scale are difficult to measure (Vrugt et al. 2001b). In themacroscopic scale approach or a root-system model, a sink term

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representing water extraction by the root system is added to the
dynamic water flow equation, e.g., the Richards equation (Richards
1931). The first category of macroscopic models is based on
steady-state or steady-rate approximations of the single-root models, in which the water flow toward the root system is simulated
first, and the total water uptake by the plant is then taken as thesum of the water uptake from each soil layer. The models consider
root resistances and water potentials inside and at the root-soilwater interface (e.g., Gardner 1964; Hillel et al. 1976), which are
difficult to quantify (Wu et al. 1999; Yadav et al. 2009). In thesecond category of macroscopic models, root water extraction is
calculated from the plant transpiration rate, rooting depth, root
spatial distribution, and soil water potential. These models take into
account the effects of a soil moisture deficit on root water extraction
using some response functions dependent on the soil water potential (e.g., Feddes et al. 1978). The parameters in the second category of models are relatively easy to obtain and are generally
available in most vadose zone hydrological models (e.g., van Dam
et al. 1997; Fayer 2000; Šimůnek et al. 2008).
A multidimensional RWU approach allows more accurate quantification of spatial variability of the soil water regime and water
fluxes, especially for an isolated tree in large monocultures where
the process of water uptake is complex (Green and Clothier 1999;
Vrugt et al. 2001b). Because of the difficulties encountered inmeasuring spatial and temporal distributions of RWU rates directlyin the field, the influence of plant-root systems on water movement
can be better understood using variably saturated water flow simulation models, provided that accurate spatial and temporal RWU
distributions, particularly compensatory RWU (Skaggs et al. 2006;Šimůnek and Hopmans 2009), are considered. Compensated water
uptake, in which plants may respond to nonuniform water stressin the root zone, is a mechanism by which a reduced water uptake
in a water-stressed part of the rhizosphere is balanced by anenhanced uptake from another less water-stressed region of theroot zone (Jarvis 1989; Šimůnek and Hopmans 2009). HYDRUS(2D/3D) (Šimůnek et al. 2011) is such a numerical model, which
simultaneously solves both two- and three-dimensional water flow
in homogeneous or heterogeneous soils and both compensated anduncompensated RWU by plants. The model can be utilized to study
the interaction between pecan T a rates and soil water availability.
This may provide further insight into how the interaction between
soil and roots determines compensated and uncompensated RWU
patterns of a flood-irrigated mature pecan tree.
The spatial and temporal distributions of RWU have beenmostly reported for microirrigated rooting systems, particularly insprinkler- and dripper-irrigated orchards (e.g., Vrugt et al. 2001a, b;
Koumanov et al. 2006). However, no information is available on
the spatial and temporal RWU pattern in a flood-irrigated pecanorchard. In an earlier study on a sandy loam mature pecan orchard,
Deb et al. (2011a) simulated the vertical distribution of uncompensated and compensated RWU at an under-canopy location using the
HYDRUS-1D model (Šimůnek et al. 2008). These simulations
showed that the soil water stress compensation allocated relatively
more transpiration to the deeper, less water-stressed depths of theroot zone. However, limited to one-dimension, conclusions drawn
from this study have raised further questions regarding the spatial
and temporal distribution of compensatory RWU in a floodirrigated mature pecan. The scarcity of information is equally true
for pecan orchards in fields with different soil textures in southern
New Mexico, particularly in orchards with clayey soil characterized
by a much higher water-holding capacity than the sandy loam
orchard reported in Deb et al. (2011a). Therefore, the objective of
this study was to evaluate spatial and temporal compensated anduncompensated RWU patterns of a flood-irrigated mature pecan
tree in a silty clay loam orchard using HYDRUS (2D/3D).

Materials and Methods
Field Site
Field measurements required for the numerical modeling weremade over two seasons (March 2009 to December 2010) in amature, closed-canopy pecan orchard, located at the New Mexico
State University Leyendecker Plant Science Research Center(LPSRC), 14.5 km south of Las Cruces, New Mexico. A detailed
description of this orchard can be found in Deb et al. (2012a, b,2013). The experimental region is semiarid, and the study area
is dominated by the Harkey-Glendale soil association. A 1.0-ha
orchard consisted of seven rows of 30-year-old “Western Schley”
pecan trees in a rectangular pattern (7 × 8 m) with 29 trees ineach row. An experimental plot, 50 × 15 m, consisting of 18 trees
in six rows, was located in the middle of the orchard and separated
by raised berms.
A single tree in the experimental plot, instrumented with time
domain reflectometry (TDR) and soil temperature sensors, wasconsidered in this study. The CS616 TDR sensors (Campbell
Scientific, Inc., Logan, UT) were horizontally installed at soil
depths of 5, 10, 20, 40, 60, and 80 cm at different distances of
100 (underneath the canopy), 350 (underneath the tree canopy dripline), and 440 cm (just outside of the tree canopy dripline) awayfrom the trunk of a selected pecan tree to continuously monitor thevolumetric soil water content (θ) (cm3 cm−3 ). For evaluating watercontents below 80 cm, we installed two additional TDR sensors at
depths of 120 and 160 cm immediately outside of the tree canopy
dripline. Sensor data were recorded every 10 min using a CR10X
datalogger connected to an AM16/32B multiplexer (Campbell
Scientific, Inc., Logan, UT). All TDR sensors were calibrated
in situ against gravimetric water content and bulk density data
(Deb et al. 2013). We expected that soil temperatures at different
distances of 100, 350, and 440 cm from the trunk of the selectedpecan tree would be similar in this closed-canopy experimental
plot. Therefore, temperature sensors (TMC6-HD, Onset Computer
Corp., Bourne, MA) were installed at soil depths of 5, 10, 20, and40 cm at a distance of 100 cm away from the tree trunk and connected to HOBO H8 4-channel dataloggers (Onset Computer
Corp., Bourne, MA) to record soil temperature every 20 min.
The orchard was flood-irrigated using both surface water andgroundwater. Six irrigations were applied to the orchard in boththe 2009 and 2010 growing seasons. A flow meter was installed
to measure both the flow rate and the volume of irrigation water.
During an irrigation event, water was applied uniformly across thewidth of the orchard until the entire orchard was flooded and theberm at the lower end of the orchard prevented tail water fromleaving the experimental area. The irrigation water was ponded on
the soil surface of the experimental plot, which caused soil watercontent at the depths of 0–40 cm to remain at near saturation for∼22–26 h as indicated by TDR sensor responses at these depths(data not shown). Weather data obtained from the LPSRC weather
station, which is in close proximity to the experimental site,
included hourly rainfall, maximum and minimum daily air temperatures, solar radiation, wind speed and direction, and relative
humidity measured 2 m above the ground. The experimental site
received 302 and 221 mm of rainfall from the day of the year
(DOY) 60 to DOY 365 (March 1 to December 31) in 2009 and2010, respectively.

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Numerical Simulation
We assumed that the RWU around a pecan tree of this closedcanopy orchard was axisymmetrical. Therefore, the axisymmetricalform of the Richards equation could be used to solve the water flow
problem. HYDRUS (2D/3D) was used to simulate water flow, heattransport, and RWU processes in an isotropic variably-saturated
flow domain. Details on HYDRUS (2D/3D) can be found inŠimůnek et al. (2011). Neglecting the effects of the air phaseon water flow, the axisymmetric Richards equation, describing
variably-saturated water flow in the axisymmetric flow domain, is∂θ 1 ∂
∂ψ
∂
∂ψ
∂K
¼
rK
þ
K
−
− Sðψ; r; zÞ
ð1Þ
∂t r ∂r∂r∂z∂z∂z
where t = time (d); r = radial coordinate (cm); z = vertical coordinate (positive upward) (cm); ψ = pressure head (cm); Sðψ; r; zÞ =RWU as a sink term (cm3 cm−3 d−1 ); and K = unsaturated hydraulicconductivity function (cm d−1 ). The soil water retention curve
and the unsaturated hydraulic conductivity function were estimated using the van Genuchten-Mualem constitutive relationships(van Genuchten 1980; Mualem 1976)θs −θrθr þ ½1þðjαψ<0n mv ψj ÞθðψÞ ¼
ð2Þ
ψ≥0
θs
m 2

KðψÞ ¼ K s Sle ½1 − ð1 − S1=m
e Þ 

ð3Þ

where θr and θs = residual and saturated soil water contents(cm3 cm−3 ), respectively; αv = reciprocal of the air-entry ψ (cm−1 );m ¼ 1 − 1=n (n > 1); n = pore-size distribution index (unitless);
Se = effective saturation (unitless) given by Se ¼ ðθðψÞ − θr Þ=ðθs − θr Þ; l = pore-connectivity parameter (unitless); and K s =saturated hydraulic conductivity (cm d−1 ). The effects of temperature on soil hydraulic properties (i.e., the soil water retention
curve and soil hydraulic conductivity) were taken into account.
In HYDRUS (2D/3D), using the capillary theory, the influenceof temperature on ψ is quantitatively predicted from the influenceof temperature on surface tension (Philip and de Vries 1957). The
temperature dependence of KðψÞ is predicted from the influence oftemperature on the viscosity and density of water (Constantz 1982).
Neglecting the effects of water vapor diffusion, the governing
equation describing the two-dimensional heat transport (i.e., due to
conduction and convection with flowing water) in the axisymmetricdomain is described by∂T 1 ∂∂T∂∂T
1∂
Cp ðθÞ
¼
rλðθÞ
þ
λðθÞ
− Cw
ðrqTÞ
∂t
r ∂r
∂r
∂z
∂z
r ∂r
∂qT
− Cw
− Cw ST
ð4Þ
∂zwhere T = temperature (°C); λðθÞ = apparent thermal conductivityof the soil (J cm−1 d−1 °C−1 ); CP and CW (≈4.2 J cm−3 °C−1 ) =volumetric heat capacities (J cm−3 °C−1 ) of the soil and liquid,
respectively (de Vries 1963); q = flux density of liquid water(cm d−1 ); and the term Cw ST = a sink of energy associated withRWU (J cm−3 d−1 ). The λðθÞ in Eq. (4), expressed as a linear
function of the velocity, combines the thermal conductivity ofthe porous medium (solid plus water) (λ0 ) in the absence offlow and the macrodispersivity (de Marsily 1986; Šimůnek andSuarez 1993a). The apparent thermal conductivity λðθÞ is given by(Šimůnek and Suarez 1993b)
λij ðθÞ ¼ β T Cw jqjδ ij þ ðβ L − β T ÞCwqj qi
þ λ0 ðθÞδ ij
jqj

ð5Þ

where subscripts i and j = space direction indices; δ ij (unitless) =Kronecker delta function (δ ij ¼ 1 if i ¼ j and δ ij ¼ 0 if i ≠ j); andβ L and β T = longitudinal and traverse thermal dispersivities (cm),respectively. The thermal conductivity λ0 (J cm−1 d−1 °C−1 ) is described by the equation of Chung and Horton (1987)
λ0 ðθÞ ¼ b1 þ b2 θ þ b3 θ0.5

ð6Þ

where b1 , b2 , and b3 = empirical parameters (J cm−1 d−1 °C−1 ).
The average electrical conductivity of the soil profile(0–100 cm), determined in the 1∶2 soil∶water suspension at soil
depths of 0–20, 20–40, 40–60, 60–80, and 80–100 cm at the endof the 2009 and 2010 growing seasons, was <0.5 dS m−1 . Therefore, the RWU reduction model of Feddes et al. (1978) without theosmotic stress was considered for Sðψ; r; zÞ in Eq. (1)Sðψ; r; zÞ ¼ αðψ; r; zÞ × Sp ðr; zÞ ¼ αðψ; r; zÞ × bðr; zÞ × T p × L
ð7Þ
where the water stress response function αðψ; r; zÞ = dimensionlessfunction of ψ (0 ≤ α ≤ 1) (Feddes et al. 1978); Sp ðr; zÞ =potential water uptake (cm3 cm−3 d−1 ); bðr; zÞ = normalized water
uptake distribution (cm−2 ); T p = potential transpiration rate
(cm d−1 ); and L (cm) = surface length associated with transpiration.
For αðψ; r; zÞ, Feddes et al. (1978) proposed a piece-wise linear
reduction function parameterized by four critical values of ψ(i.e., ψ4 < ψ3 < ψ2 < ψ1 )8>
ðψ − ψ4 Þ=ðψ3 − ψ4 Þ;
>
>
>
>
< 1;
αðψ; r; zÞ ¼
> ðψ − ψ1 Þ=ðψ2 − ψ1 Þ;
>
>
>
>
: 0;

ψ3 > ψ > ψ4
ψ2 ≥ ψ ≥ ψ3

ð8Þ

ψ1 > ψ > ψ2
ψ ≤ ψ4orψ ≥ ψ1

Water uptake above ψ1 (oxygen deficiency point, i.e., wetter
than some arbitrary “anaerobiosis point”) and below ψ4 (wilting
point) is assumed to be zero. Water uptake is maximal between ψ2and ψ3 (reduction point). Between ψ1 and ψ2 and between ψ3 andψ4 , a linear variation is assumed. The value of ψ3 depends on thewater demand of the atmosphere, and the true ψ3 is interpolated
from low and high values of ψ3 and T p .
The Sðψ; r; zÞ with compensation in Eq. (7), implemented in
HYDRUS (2D/3D), was developed by Šimůnek and Hopmans(2009). Following Jarvis (1989), Šimůnek and Hopmans (2009)
introduced a critical value of the water stress index (ωc ). The ωcrepresents a threshold value above which RWU, reduced in waterstressed parts of the root zone, is fully compensated by enhanced
extraction from other less water-stressed parts. In HYDRUS(2D/3D), depending on the value of ωc , the Sðψ; r; zÞ represents
either compensated (0.0 < ωc < 1.0) or uncompensated (ωc ¼ 1.0)
RWU. We refer the reader to Šimůnek and Hopmans (2009) for
details. The bðr; zÞ describes the spatial variation of the Sp ðr; zÞover the root zone and is obtained by normalizing any arbitrarily
measured or prescribed root distribution function. Normalizing theuptake distribution ensures that bðr; zÞ integrates to unity overthe flow domain.
HYDRUS (2D/3D) uses the Galerkin finite element method tosolve Eqs. (1) and (4), and details can be found in Šimůnek et al.
(2011). Fig. 1 shows the considered radially symmetric transportdomain with applied boundary conditions. The transport domain,which is 100 cm deep and 450 cm long in the radial direction, wasdiscretized into finite elements using a grid spacing of 2 cm in theradial and 1 cm in the vertical direction. The transport domain was

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Fig. 1. Axisymmetric flow domain of a flood-irrigated mature pecan
tree with considered water flow boundary conditions and spatial root
distribution (not drawn to scale)

discretized into 45,000 triangular 2D elements and 22,826 nodes.
In general, the soil texture of the orchard was silty clay loam down
to a 100-cm soil depth (Deb et al. 2012a, 2013), and thus the soil
domain was assumed to be a homogeneous. Observation nodes
were located at depths of 5, 10, 20, 40, 60, and 80 cm to coincidewith TDR sensor measurements at three radial distances of 100 cm,
400 cm, and 440 cm from the tree trunk.
An atmospheric boundary condition, i.e., the daily potential
evaporation (Ep ) and transpiration (T p ), and irrigation and rainfall
rates were used as the upper water flow boundary condition. For
this boundary condition, water evaporates at Ep as long as ψ at thesurface remains above a threshold value (ψcrit ) of −15,000 cm (Debet al. 2011a). No flux was allowed through the vertical sides of thetransport domain due to symmetry. A free drainage boundary condition was set at the bottom boundary because the water table at thisorchard is generally located more than 2.5 m below the soil surface
and, therefore, does not influence the root zone soil water dynamics(Deb et al. 2012a). First-type (Dirichlet-type) boundary conditions
with specified time-variable temperatures at the soil surface and thebottom were considered for heat transport. Initial conditions were
provided by specifying the top and bottom water contents averaged
from measured values at 5 and 80 cm and soil temperatures measured at 5 and 40 cm depths and assuming a linear distribution withdepth for the 100-cm soil profile.
Measurements and HYDRUS (2D/3D) Parameterization
Soil physical properties down to a 100-cm soil depth at the experimental site were reported in Deb et al. (2012a, 2013). Briefly,
the soil texture at the experimental site is silty clay loam, with anaverage bulk density of 1.5 Mg m−3 . The value of K s ranged from
0.24 to 41 cm d−1 within the root zone (0–80 cm soil depth), withan average value of 10.03 cm d−1 . Soil water retention was determined using the pressure chamber method at ψ of 0, −300, −500,−1,000, −3,000, −5,000, −10,000, and −15,000 cm H2 O. The
initial values of parameters θr , θs , αv and n were estimated byfitting the van Genuchten (1980) soil water retention model[Eq. (2)] to the measured drainage curve data using the RETC code(van Genuchten et al. 1991) [Fig. 2(a)]. The initial value of parameter l was assumed to be 0.5 (Mualem 1976).
The core soil samples (three replicates × three tree locations)were collected down to the depth of 40 cm to determine λ0 ðθÞ,the volumetric heat capacity, and the thermal diffusivity using
the KD2 Thermal Properties Analyzer (Decagon Devices, Inc.,

Fig. 2. (a) Water retention curve measured on core samples (θ =volumetric water content and ψ = pressure head), and the van
Genuchten (1980) model [Eq. (2)] is fitted to the measured drainage
curve using RETC (van Genuchten et al. 1991) (θr ¼ 0.1 cm3 cm−3 ,θs ¼ 0.52 cm3 cm−3 , αv ¼ 0.0093 cm−1 , and n ¼ 1.44); (b) the thermal conductivity (λ0 ) as a function of the volumetric water content (θ),
and the nonlinear thermal conductivity equation given by Chung andHorton (1987) [Eq. (6)] is fitted to the measured λ0 -θ relationship(values of regression parameters b1 , b2 , and b3 are 0.048, −1.76, and2.37 Wm−1 °C−1 , respectively)

Pullman, WA) at ψ of 0, −300, −500, −1,000, −3,000, −5,000,−10,000, and −15,000 cm H2 O. The nonlinear thermal conductivity equation of Chung and Horton (1987) [Eq. (6)] was fitted tothe measured λ0 -θ data, and initial values of regression parameters(b1 , b2 , and b3 ) were determined [Fig. 2(b)].
During both growing seasons, 2009 and 2010, soil cores werecollected down to a 100-cm soil depth (in 10-cm increments) at
distances up to 450 cm away from the trunk of three pecan trees
to determine the rooting depth and root length density (RLD)(cm root cm−3 soil) distributions for the under-canopy, tree canopy
dripline, and just outside of the tree canopy dripline locations.
Descriptions of soil core sampling, root extraction procedures, andanalysis of RLD can be found in Deb et al. (2013). No roots wereobserved below 80 cm soil depth (Fig. 1). Similar spatial vertical
distributions of RLD for the under-canopy and the tree canopy dripline locations were observed during both growing seasons, 2009
and 2010. The total RLD was higher at shallow depths (0–40 cm)
than at the deeper depths (40–80 cm) at all radial distances in thisflood-irrigated pecan orchard. For bðr; zÞ in Eq. (7), a linear root
distribution varying between 1.0 (at the soil surface) and 0 (below
the depth of 80 cm) was specified.
For αðψ; r; zÞ, the functional form of RWU parameters given
by Feddes et al. (1978) with compensation was used for the
HYDRUS (2D/3D) simulations. Deb et al. (2011a) evaluatedvertical compensated RWU profiles at different values of ωc underwater-stressed conditions and concluded that the increased compensation from deeper depths was not consistent for lower valuesof ωc ð0.1 < ωc < 0.5Þ. Therefore, we used a value of ωc ¼ 0.5 forthe soil water stress compensation. Moreover, trial simulations,conducted to evaluate compensated RWU using the critical water
stress index (ωc ) below 0.5 (0.1 < ωc < 0.5), gave similar results
or a negligible increase in RWU compared to simulations using
ωc of 0.5. Following the recommendation of Deb et al. (2011a),
critical ψ values [Eq. (8)] for the RWU stress function were takenfrom the HYDRUS (2D/3D) database for a deciduous fruit.
HYDRUS (2D/3D) requires daily potential soil evaporation(Ep ) and plant transpiration (T p ) input separately for the atmospheric boundary, i.e., each separately entered into a single atmospheric input. We first estimated daily reference evapotranspiration

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(ET 0 ) using the FAO-56 Penman-Monteith equation (Allen et al.
1998) based on the weather data. The estimated ET 0 was thenmultiplied by a crop coefficient (K c ) to estimate pecan evapotranspiration (ET c ). K c was estimated using the following equations forflood-irrigated mature pecan (Sammis et al. 2004):
K C ¼ −3.866 × 10−12 × GDD4i þ 1.11 × 10−8 × GDD3i− 1.08 × 10−5 × GDD2i þ 4.31 × 10−3 × GDDi

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þ 3.34 × 10−1

ð9Þ
GDDi ¼ T avg − T bð10Þ

where GDDi = growing degree day value for day i (T avg > T b , else
GDD ¼ 0) (°C day); T avg = average of daily maximum and minimum air temperatures (°C); and T b = crop-specific base air temperature of 15.5°C for pecan (Sammis et al. 2004; Deb et al. 2012a).
Previous studies used Ritchie’s formula (Ritchie 1972) (e.g., Vrugt
et al. 2001a, b) and/or leaf area index (LAI) (e.g., Droogers 2000)
to separate ET c into Ep and T p for orchard trees. For partitioning
ET c between Ep and T p , we calculated Ep using Ritchie’s formula(Ritchie 1972) as
Ep ¼ ET c e−κ×LAI

ð11Þ

where κ = constant governing the radiation extinction by the
canopy as a function of the sun angle, the distribution of plants,
and the arrangement of leaves. T p was then obtained by subtracting
Ep from ET c (Fig. 3). The leaf area index in Eq. (11) was measured
on a monthly basis using a LAI-2000 instrument (LI-COR Biosciences, Lincoln, NE) (Deb et al. 2012a). The κ in Eq. (11)was estimated for an ellipsoidal leaf orientation using an equation
given by Campbell and Norman (1998). As suggested by Deb
et al. (2011a), a spherical leaf angle distribution, which had larger
vertical area than horizontal and leaves of all inclinations, was considered in the canopy.

achieved using the Gauss-Marquardt-Levenberg method. PEST
is a model-independent nonlinear parameter estimator, characterized by an ability to interface with any model through that model’s
input and output files, thus requiring no alterations to the HYDRUS(2D/3D) model. The calibration process was initiated using measured water flow and heat transport parameters. At the beginning of
the model calibration process, we adjusted model parameters in asequential manner, beginning with water flow parameters and ending with heat transport parameters. Note that we used combined
water flow, heat transport, and compensatory RWU processes during the parameter optimization. Selected water flow parameters[i.e., θr , θs , αv , n, l, and K s in Eqs. (2) and (3)] and heat transportparameters [i.e., volume fraction of solid phase, volumetric heat
capacities of the solid phase and organic matter, and coefficients
b1 , b2 and b3 in Eq. (6)] were optimized using measured watercontent and soil temperature data at measurement soil depths at
different radial distances from the tree trunk. Finally, we simultaneously optimized both water flow and heat transport parameters(Table 1). As suggested by Deb et al. (2011a), the ranges of the apriori parameter distribution were derived based on the fits of measured soil water retention data and directly measured λ0 .
The HYDRUS (2D/3D) was validated (compensatory RWU
with a ωc value of 0.5) using the measured and optimized waterflow and heat transport parameters for a 306-day period from
DOY 60 through DOY 365 (March 1 to December 31) 2010. Once
validated, we also used the validated HYDRUS (2D/3D) model
to evaluate the spatial and temporal pattern of uncompensated
RWU (RWU option with a value of ωc ¼ 1.0) for the same period.
During the HYDRUS (2D/3D) calibration and validation, model
predictions of daily average water contents at depths of 5, 10, 20,
40, 60, and 80 cm and soil temperatures at depths of 5, 10, 20, and40 cm were statistically compared to measured values using theroot mean square error (RMSE), the mean bias error (ME) (Shenet al. 1998), and an index of agreement (d) (Willmott 1981), which
are defined as:ﬃ
rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
PN2
i¼1 ðPi − Oi Þ
RMSE ¼N

HYDRUS (2D/3D) Calibration and Validation
The HYDRUS (2D/3D) calibration (compensatory RWU option
with a ωc value of 0.5) was performed for a 255-day period from
DOY 91 through DOY 365 (April 1 to December 31) 2009. The
PEST (parameter estimation) optimization package of Doherty(2004) was used, in which the inverse parameter optimization is

ME ¼

d ¼ 1.0 − PN

ð12Þ

PN

i¼1 ðPi − Oi Þ

ð13Þ

N

PN

i¼1 ðPi − Oi Þ

2i¼1 ðjPi − Oavg j þ jOi − Oavg jÞ

2

ð14Þ

where N = number of paired measured and simulated values;
Pi = ith simulated value; Oi = ith measured value; and Oavg =average of measured values. The value of RMSE reflects a magnitude of the mean difference between measured and simulated results. The value of ME indicates a systematic error or bias in themodel prediction, i.e., positive and negative values of ME indicate atendency for an overprediction or underprediction, respectively.
The value of d ranges from 0 (i.e., no agreement) to 1 (i.e., a perfect
fit between simulated and measured values).
Fig. 3. Potential pecan evapotranspiration (ET c ), soil evaporation (Ep ),and transpiration (T p ) during the growing periods from day of the year
(DOY) 91 to 365 (April 1 to December 31) of 2009 (the model calibration year) and from DOY 60 to DOY 365 (March 1 to December 31)
of 2010 (the model validation year), used as boundary conditions at thesoil surface in the HYDRUS (2D/3D) model

Measurements of Transpiration and Plant Water Status
We further evaluated HYDRUS (2D/3D) predictions by comparing
simulated actual transpiration (T a ) with measured transpiration(T leaf ) and simulated daily soil stress conditions, expressed as therelative transpiration (T a =T p ), with measured plant-based water

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Table 1. PEST-Optimized Water Flow and Heat Transport Parameters of the HYDRUS (2D/3D) Model during Calibration

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HYDRUS (2D/3D) model parameters
Water flow parameters:
Saturated soil water content (θs , cm3 cm−3 ) (van Genuchten 1980)
Residual soil water content (θr , cm3 cm−3 ) (van Genuchten 1980)
αv (cm−1 ) in the soil water retention function (van Genuchten 1980)n (unitless) in the soil water retention function (van Genuchten 1980)
Tortuosity parameter l (unitless) in the conductivity function (Mualem 1976)
Saturated hydraulic conductivity (K s , cm d−1 )Heat transport parameters:
Volume fraction of solid phase (θn , cm3 cm−3 )a (de Vries 1963)
Volumetric heat capacity of the solid phase (Cn , J cm−3 °C−1 ) (de Vries 1963)
Volumetric heat capacity of the organic matter (C0 , J cm−3 °C−1 )a (de Vries 1963)
Coefficient b1 in the thermal conductivity function (W m−1 °C−1 ) (Chung and Horton 1987)
Coefficient b2 in the thermal conductivity function (W m−1 °C−1 ) (Chung and Horton 1987)
Coefficient b3 in the thermal conductivity function (W m−1 °C−1 ) (Chung and Horton 1987)aParameter range of a priori
parameter distribution

Optimized
parameter value

0.4–0.52
0.09–0.13
0.008–0.09
1.4–2.0
0.5–0.7
0.3–25

0.48
0.10
0.008
1.44
0.65
10.2

0.48–0.60
1.65–2.20
2.37–3.00
0.43–0.57−0.97 to −1.80
2.20–2.64

0.5
1.78
2.51
0.47
−1.75
2.34

Literature value.

stress indicators including midday stem (ψstem ) and leaf (ψleaf )water potentials.
Transpiration rate (T leaf ) (i.e., evaporation from a dry canopy)(μg cm−2 s−1 ) was measured from DOY 152 to DOY 273 (June 1
to September 30) 2010 with a steady-state porometer LI-1600(LI-COR Biosciences, Lincoln, NE). The porometer consists ofa cuvette with a broadleaf aperture (2 cm2 ), which permits measurements of water loss by transpiration. It measures the flow rateof dry air (<2% relative humidity) necessary to maintain a constantrelative humidity (zeroed to ambient relative humidity) inside thecuvette that has been clamped onto a transpiring leaf. Measurements of T leaf during the afternoon (between 1400 h and 1500 h)
were taken on five mature, well-exposed leaves for three tree
canopy layers, representing lower (at a tree height of 2.5 m fromthe soil surface), mid- (at 4.6 m), and upper canopy (at 7.6 m). Care
was also taken that all leaves were completely dry before any readings were taken. Measured T leaf rates were converted to “cm d−1 ”,
applying the density of evaporated water (1 g cm−3 ).
Midday (between 1400 h and 1500 h) ψstem (for nontranspiring
or bagged leaves close to stem) and ψleaf (for nonbagged leaves)
were determined from DOY 152 to DOY 273, 2010 at each of thelower, mid-, and upper canopy layers. Measurements of ψstem andψleaf were made twice a week (every third and sixth day after irrigation) on three selected trees using a pressure chamber (model
1000, PMS Instrument Company, Albany, OR). Details aboutψstem and ψleaf measurements were described by Deb et al. (2012b).

Results and Discussion
HYDRUS (2D/3D)’s Performance during the Calibration
and Validation
Comparisons between measured and simulated daily mean watercontents at four depths (5, 10, 20, and 40 cm) at a radial distanceof 100 cm from the tree trunk during the calibration period (DOY
91 though DOY 365, 2009) and at different radial distances of 100,
400, and 440 cm during the validation period (DOY 60 though
DOY 365, 2010) are shown in Figs. 4(a) and 5, respectively. Therewas generally a close agreement between measured and simulated
water contents for both the calibration and validation periods.
Statistics of RMSE, ME, and the index of agreement (d) of simulated and measured θ values, presented in Figs. 4(a) and 5, arecomparable with previous modeling studies for flood-irrigatedpecan (Deb et al. 2011a, 2012a). For example, RMSE varied

between 0.02 and 0.04 cm3 cm−3 , ME between −0.003 and−0.02 cm3 cm−3 , and d between 0.84 and 0.89 during the calibration period [Fig. 4(a)]. Similar discrepancies between simulated
and measured θ values were reported by Deb et al. (2011a).
During the validation period, RMSE varied between 0.034 and0.06 cm3 cm−3 , ME between −0.007 and 0.06 cm3 cm−3 , and d
between 0.82 and 0.89 for different soil depths and radial distancesfrom the tree trunk (Fig. 5), which represents a good correspondence of the validated model (Deb et al. 2011a, 2012a).
The HYDRUS (2D/3D) predicted both the sharp increase in
the water content following irrigation and the gradual decreases
during dry-down. However, immediately after an irrigation event,the model predicted higher peak values of θ at depths of 10, 20, and40 cm, especially during the validation period (Fig. 5), which could
be explained by the soil water retention behavior [Fig. 2(a)].
On average, the majority of ME values (Figs. 4(a) and 5) indicatedthat the model slightly underpredicted θ at most measurement
depths. Small differences between simulated and measured θ may
be partially explained by measurement errors, which are inevitable
under field conditions (Deb et al. 2011a, b, 2012a).
Temporal variations in simulated daily mean soil temperatures
for four measurement depths during the calibration and validation periods were consistent with field measurements [Figs. 4(b)and (6)]. For example, RMSE varied between 1.8 and 2.4°C, ME
between −0.42 and 1.3°C, and d between 0.93 and 0.98 during thevalidation period (Fig. 6). Similar discrepancies between simulated
and measured soil temperatures were reported in previous modelingstudies (Deb et al. 2011a, b), which led us to judge the accuracy of
HYDRUS (2D/3D) predictions to be good. Differences between
simulated and measured soil temperatures may be partially attributed to the specified initial conditions. Due to the lack of directly
measured data below the 40-cm soil depth, initial conditions were
simplified, and provided by specifying the top and bottom soil
temperatures measured at 5 and 40 cm and assuming a linear distribution with depth. The accuracy of measured and optimized soil
heat parameters (Table 1) and the effects of specified surface andbottom heat transport boundary conditions are also possible reasonsfor the deviations between measured and simulated soil temperatures (Deb et al. 2011a, b).
Spatial and Temporal Root Water Uptake PatternFig. 7 illustrates two-dimensional plots of simulated ψ, θ, and RWUwith (ωc ¼ 0.5) and without (ωc ¼ 1.0) compensation at DOY 180
and DOY 198 after an irrigation event at 1200 h on DOY 174

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Fig. 4. Comparisons between simulated and measured daily average (a) volumetric water contents and (b) soil temperatures at soil depths of 5, 10, 20,
and 40 cm at a distance of 100 cm from the trunk of the pecan tree during the HYDRUS (2D/3D) calibration period from day of the year (DOY) 91 to
DOY 365 (April 1 to December 31) 2009. RMSE, ME, and d are the root mean square error, the mean bias error, and the index of agreement[Eqs. (12)–(14)], respectively, between measured and simulated water contents (a) and soil temperatures (b)during the HYDRUS (2D/3D) validation year 2010. Contour plots
for both days were presented at 1430 h because the highest water
stress in mature pecans was generally observed in midafternoon(between 1400 and 1500 h) (Deb et al. 2012b). It is clear fromcontour plots shown in Fig. 7 that both compensated and uncompensated RWU varied with the soil depth but not with distance fromthe tree trunk under both wet [Fig. 7(a)] and relatively dry soil
[Fig. 7(b)] conditions. This is largely attributed to similar vertical
distributions of RLD at different radial distances from the tree
trunk underneath the canopy and the tree canopy dripline locations(Fig. 1), in accordance with previously reported data during the2009 growing season (Deb et al. 2013). Furthermore, in thisflood-irrigated closed-canopy pecan orchard, Deb et al. (2013)
observed that the soil water depletion pattern within the 0–80-cm
soil depth varied only depthwise at the under-canopy and outsideof the tree canopy dripline locations. Similar observation thatthe soil water depletion was independent of the horizontal distancein the closed-spaced pecan orchard was also reported byMiyamoto (1983).
The magnitude and pattern of compensated and uncompensated
RWU rates were similar 6 days after the irrigation was applied
on DOY 174, i.e., at 1430 h on DOY 180, [Fig. 7(a)], and followed
the spatially similar vertical distributions of RLD (Fig. 1). The roots
extracted water at a higher rate from the upper part of the soil
profile (0–40-cm depth) and gradually less from the deeper
depths down to 80 cm. The soil profile was slightly drier when
the compensated RWU was considered, compared with theuncompensated RWU. For example, θ (or ψ) varied between
0.33 cm3 cm−3 (−329 cm) and 0.35 cm3 cm−3 (−234 cm), and between 0.35 cm3 cm−3 (−252 cm) and 0.38 cm3 cm−3 (−187 cm)
for compensated and uncompensated, respectively [Fig. 7(a)].
However, ψ and θ profiles for the compensated RWU are likely
to be more representative since calibration was performed withthis option [Fig. 4(a)].

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Fig. 5. Comparisons between simulated and measured daily average volumetric water contents at soil depths of 5, 10, 20, and 40 at a distance of(a) 100 cm; (b) 400 cm; (c) 440 cm from the trunk of the pecan tree during the HYDRUS (2D/3D) validation period from day of the year (DOY) 60 to
DOY 365 (March 1 to December 31) 2010. RMSE, ME, and d are the root mean square error, the mean bias error, and the index of agreement[Eqs. (12)–(14)], respectively, between measured and simulated water contents

Due to soil drying, both compensated and uncompensated
RWU rates generally decreased 25 days after the irrigation on
DOY 174 (at 1430 h on DOY 198) [Fig. 7(b)]. RWU increased
to a depth of 50 cm as θ values in the upper part of the soil profile(above the depth of 30 and 20 cm for compensated and uncompensated profiles, respectively) decreased (θ < 0.16 cm3 cm−3 ),while remaining higher at deeper depths (below the depth of
30 or 20 cm, respectively). Another noteworthy phenomenon isthat θ remained relatively high even 25 days after irrigation(Fig. 7), which could be explained by the clayey texture in thisorchard. A much lower soil hydraulic conductivity, much higher
field capacity, and water-holding capacity resulted in a muchslower redistribution of water after irrigation in this silty clay
loam soil. Similarly, higher daily average water contents at
different soil depths underneath the canopy (radial distances of
100 cm and 400 cm) and outside of the tree canopy dripline(at 440 cm) were observed during the entire growing season(Figs. 4 and 5).

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occurred had the pecan root zone had significant variations in RLD
both vertically and spatially underneath the canopy and outside of
the tree canopy dripline, as well as for nonuniform water applications, such as for microirrigation systems as reported by Koumanovet al. (2006).

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Temporal Variation in Actual Transpiration

Fig. 6. Comparisons between simulated and measured daily averagesoil temperatures at soil depths of 5, 10, 20, and 40 at a distance of
100 cm from the trunk of pecan tree during the HYDRUS (2D/3D)
validation period from day of the year (DOY) 60 to DOY 365(March 1 to December 31) 2010. RMSE, ME, and d are the root
mean square error, the mean bias error, and the index of agreement[Eqs. (12)–(14)], respectively, between measured and simulated soil
temperatures

RWU compensation produced slightly higher RWU rates[Fig. 7(b)]. The compensated RWU pattern differed substantiallyfrom the uncompensated on DOY 198 under relatively dry soil conditions. It is possible to distinguish the soil depth where soil water
becomes critical for the most efficient RWU by a mature pecan.
Even after depletion of water in the top 20 cm, uncompensated
RWU was spatially distributed within the upper parts of the rootzone (0–50-cm depth). While the upper 30 cm of the soil profile
were depleted of water, the depth distribution of compensated
RWU was not only governed by the status of soil water but also
spatially concentrated in the most densely rooted soil zone or soil
layers (30–50 cm).
For evaluating temporal pattern of RWU in the soil profile, Fig. 8
further depicts depth distributions of ψ, θ, and RWU values on different days (i.e., DOY 180, 187, 194, and 198) after the irrigation
event on DOY 174 at a radial distance of 100 cm from the tree
trunk. Compensated RWU gradually decreased within the upper
depths (above 20 cm), and the peak RWU occurred within the depthof 30–50 cm on DOY 198 prior to the subsequent irrigation eventon DOY 200 (Fig. 5). In the lower part of the root zone (50–80-cm
soil depth) with lower RLD, both compensated and uncompensated
RWU rates remained markedly lower and significant variations inθ were not observed between successive irrigation events (Figs. 7
and 8). The spatial occurrence of the highest RLD at soil depths of
30–50 cm would be expected to enhance the ability of pecans tocope with the soil water stress [Fig. 7(b)]. However, had the mostdensely rooted layer (i.e., the highest RLD) been too shallow(above 20 cm), severe pecan stress due to the water depletion in
the upper 20 cm could have caused significant yield loss. Underboth wet (nonstressed) and dry (water-stressed) soil conditions, thesoil depth (0–50 cm) with higher RLD was the primary RWU
uptake layer, and thus water conditions within this layer are more
important than the maximum rooting depth of 80 cm (i.e., the effective soil volume for RWU by pecans) to help maintain a certain
rate of RWU by pecans. Similar spatial RWU patterns may not have

The simulated actual transpiration of a mature pecan and soil
evaporation with and without compensation during the HYDRUS(2D/3D) validation year 2010 are shown in Fig. 9(a). During theperiod from DOY 60 to DOY 365, T a was the main contributor
to actual evapotranspiration, and the values of compensated anduncompensated T a varied from 0.06 to 0.80 cm d−1 and from0.04 to 0.70 cm d−1 , respectively. Temporal trends of both compensated and uncompensated Ea rates were almost identical, withmuch smaller values varying from 0.001 to 0.33 cm d−1 [Fig. 9(a)].
Soil evaporation occurred only after wetting the surface soil by
irrigation or rainfall since the canopy of this closed-canopy orchard
helped reduce soil evaporation losses by shading the soil surface
and enhancing drying of the soil surface primarily by root water
extraction. As shown in Fig. 9(a), a sharp increase in both compensated and uncompensated T a , particularly from DOY 147 (May 27)
to DOY 262 (September 19), was caused by an increase in LAI.
Monthly average LAIs varied from 2.0 to 3.4 during this period.
The most plausible explanation for sharp drops in simulated T a
immediately after a flood irrigation event is a reduction in RWU
as a result of hypoxia under flooded conditions and could be explained by water uptake above critical pressure head ψ1 in Eq. (8).
Both uncompensated and compensated cumulative values of T a
and bottom water flux are depicted in Fig. 9(b). Cumulative valuesof compensated T a remained high and close to potential values,
resulting in an 8% increase compared to uncompensated T a during
a 306-day model validation period from DOY 60 to DOY 365,
2010. Deb et al. (2011a) reported that the compensated T a rates
were 15% higher than the uncompensated rates in a flood-irrigatedsandy loam mature pecan orchard. It has been reported that theenhanced compensated RWU takes place only after there has beena substantial depletion of water or distribution of water stress acrossthe soil profile (Šimůnek and Hopmans 2009; Deb et al. 2011a).
As mentioned earlier, except for a moderate depletion of water
within the soil depth above 30 cm, the soil water-holding capacityof the silty clay loam orchard was enough to avoid the severe water
stress during the growing season. This explains the relatively lower
increase in compensated T a in our study. As shown in Fig. 9(c),similar temporal trends were observed for the average root zonepressure head (ψRZ ) with and without compensation. Water stressincreased in the compensated root zone between successive irrigations, suggesting the enhanced compensatory RWU.
The cumulative bottom drainage was almost 50% less undercompensated RWU conditions than without compensation at theend of the 2010 growing season [Fig. 9(b)]. Similarly, cumulative
Ea was about 5.1% less during this period for RWU with compensation. Deb et al. (2012a) evaluated deep percolation below a
100-cm vertical soil profile after each irrigation event during the
2009–2010 growing seasons and reported that ∼32–36% of theapplied water percolated below the root zone in this pecan orchard.
From this perspective, simulations with compensatory RWU in ourstudy provided support for using HYDRUS (2D/3D) as a tool toaddress the water management issue of minimizing water loss via
deep percolation.
As shown in Fig. 9(b), the simulated cumulative actual evapotranspiration (ET a ) (per unit area of the axisymmetric domain)(Fig. 1) at the end of the 2010 growing season (DOY 60 through

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Fig. 7. Spatial distributions of simulated pressure heads (ψ), soil water contents (θ), and root water uptakes (RWU) with (ωc ¼ 0.5) and without(ωc ¼ 1.0) compensation after an irrigation event at 1200 h on DOY 174 during the HYDRUS (2D/3D) validation year 2010: (a) at 1430 h on day ofyear (DOY) 180 (June 29); (b) at 1430 h on DOY 198 (July 17)

DOY 365) was between 124 cm (compensated) and 118 cm(uncompensated). Comparatively, the compensated seasonal ET awas close to the simulated seasonal potential evapotranspiration(ET c ) of 128 cm. These seasonal ET a and ET c predicted by
HYDRUS (2D/3D) were reasonable when compared with theseasonal ET c values reported in previous studies. For example,
Miyamoto (1983) estimated the consumptive use of a mature pecanorchard to be 131 cm for the growing season of April throughOctober. Sammis et al. (2004) reported that the total seasonal ET cof a 30-year-old mature flood-irrigated pecan, measured with theeddy covariance (OPEC) system, ranged from 117 to 126 cm forthe growing season of April through November. Samani et al.
(2009) estimated the pecan seasonal ET c using remote sensing, andthe maximum seasonal ET c was 109.5 cm for the growing seasonof April through October.

We compared daily averages of the simulated compensated anduncompensated T a rates predicted by HYDRUS (2D/3D) with themeasured transpiration (T leaf ) for a period from DOY 152 to DOY
273 (June 1 to September 30, 2010) [Fig. 10(a)]. When the measured T leaf was regressed against the simulated compensated anduncompensated T a during DOY 152 through DOY 273, both compensated (R2 ¼ 0.70) and uncompensated (R2 ¼ 0.60) T a weresignificantly (P ≤ 0.05) correlated with T leaf . However, measured
transpiration rates were consistently higher than those predicted by
HYDRUS (2D/3D). Relatively higher transpiration rates might relate in part to measurement errors, which were also reported in several studies (e.g., Inoue et al. 1990; Ansley et al. 1994). Air in theporometer cuvette was drier than ambient air, and it was difficult to
avoid the porometer leaf chamber warming during afternoon (between 1400 h and 1500 h) readings, particularly at mid- (at 4.6-m

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Fig. 8. Depth distributions of simulated (a) pressure heads (ψ); (b) soil water contents (θ); (c) root water uptakes (RWU) with (ωc ¼ 0.5) and without(ωc ¼ 1.0) compensation on different days between two successive irrigation events on day of the year (DOY) 174 (June 23) and DOY 200 (July 19)
during the HYDRUS (2D/3D) validation year 2010

tree heights) and upper canopy (at 7.6 m) layers where the porometer was continually exposed to ambient conditions. The maximum pecan water stress (i.e., diurnal minimum of ψstem andψleaf ) and the higher evaporative demand expressed as the midday

atmospheric vapor pressure deficit (VPD) occurred between 1400 h
and 1500 h (Deb et al. 2012b), which might also result in a
relatively higher T leaf . On the contrary, simulated data [shown in
Fig. 10(a)] were mean values of T a rates that varied during the day.
Comparison of HYDRUS (2D/3D) Simulation with Plant
Water Status

Fig. 9. Temporal variations in (a) actual transpiration (T a ) and evaporation (Ea ) rates; (b) cumulative potential transpiration (T p ), cumulative
actual transpiration and evaporation, and cumulative bottom water flux
(outflow); (c) average root zone pressure heads (ψRZ ) for compensated(ωc ¼ 0.5) and uncompensated (ωc ¼ 1.0) root water uptake (RWU)
simulations during the HYDRUS (2D/3D) validation period fromday of the year (DOY) 60 to DOY 365 (March 1 to December 31) 2010

The variations in simulated relative transpiration (T a =T p ) values
with and without compensation were consistent with measured plant-based water stress indicators midday ψleaf and ψstem[Fig. 10(b)]. Again, the soil water stress compensation could keep
the simulated T a =T p at a relatively high level to cope with the potential demand of a pecan tree during the growing period. ψstem wasa more stable indicator, as the lower values of ψleaf compared toψstem [Fig. 10(b)] were the result of both T leaf effects on the water
potential and desiccation of the leaf following excision during
measurement (Deb et al. 2012b). In earlier studies on this orchard,both ψstem and ψleaf were significantly correlated with variations inboth θ at soil depths down to 40 cm and midday VPD (Deb et al.
2012b). Values of T a , and in particular, values of compensated T a ,were relatively close to T p during early periods after irrigation.
However, during soil drying, particularly after the depletion ofwater from the depth of 0–30 cm, the compensated T a =T p dropped
to a minimum value of 0.42 compared to the uncompensated minimum T a =T p of 0.24 during DOY 200 through DOY 238 (July 19
to August 26). This was likely a result of the fact that, during thislonger (37d) irrigation interval, the RWU rate may have been highand water available in the root zone did not respond to the T p
demand. This might also be related to the lower soil hydraulicconductivity at the soil-root interface due to the higher clay content
of the soil. The decrease in T a =T p could be clearly explainedby correspondingly sharp decreases in both ψstem and ψleaf . For
instance, ψstem varied from −0.64 MPa (nonstressed conditions) to−1.70 MPa (water-stressed conditions) during DOY 200 throughDOY 238 [Fig. 10(b)].
Because of much lower magnitudes of soil water depletion
within the root zone at this silty clay loam pecan orchard, Deb
et al. (2013) recommended that the measured plant water stressindicator ψstem be used for determining the irrigation date. However, measurements of both ψstem and ψleaf using the pressurechamber method are expensive and time consuming, and destructive sampling of stems is required (Deb et al. 2012b). It is also

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Fig. 10. (a) Simulated compensated (ωc ¼ 0.5) and uncompensated (ωc ¼ 1.0) actual transpiration rates (T a ) versus the measured transpiration(T leaf ); (b) simulated relative transpiration (ratio between actual and potential (T p ) transpiration), and the midday stem water potential (ψstem )and the midday leaf water potential (ψleaf ) during the period from day of the year (DOY) 152 to DOY 273 (June 1 to September 30) 2010.
T leaf , ψstem , and ψleaf values represent mean of the nine measurements, which were made on three trees at three pecan canopy layers, i.e., lower
canopy (a tree height of 2.5 m above the soil surface), mid-canopy (at 4.6 m), and upper canopy (at 7.6 m)

difficult to sample multiple trees regularly, especially in a commercial pecan orchard. Alternatively, simulated soil stress conditions
predicted by HYDRUS (2D/3D), which are closely related to pecan
water stresses (ψstem and ψleaf ) [Fig. 10(b)], further validate theuse of HYDRUS (2D/3D) as a tool for the evaluation of pecan
water stress.
Overall, as shown in Fig. 10, as well as in Figs. 4–9 discussed
earlier, spatial and temporal distributions of a simulated compensatory RWU of a mature pecan tree suggested that HYDRUS(2D/3D) can be used for managing the efficient water use of floodirrigated mature pecans while optimizing the pecan production.
However, relatively higher plant water stress indicated by ψstemand ψleaf for the clayey soils that could hold more water in the rootzone between irrigation events lead us to recommend further studies considering the influence of the root resistivity on compensatory
RWU by a flood-irrigated mature pecan tree.

Conclusions
HYDRUS (2D/3D) model simulations were found to agree withmeasured soil water contents and soil temperatures at different soil
depths and horizontal distances away from a flood-irrigated maturepecan in a silty clay loam orchard during both calibration (2009)and validation (2010) periods. The RLDs have similar vertical distributions at different distances from the tree: underneath the canopy, tree canopy dripline, and outside of the tree canopy dripline.
Similarly to RLD, both compensated and uncompensated RWU
patterns of a flood-irrigated pecan varied with soil depth but notwith distance from the tree trunk. Both compensated and uncompensated RWU rates were similar during early periods after irrigation. However, the compensated RWU always remained higher in
response to the root zone water-stressed conditions, resulting in an
increase in compensated actual transpiration (T a ) by 8% and adecrease in actual evaporation (Ea ) by 5%, and in bottom drainage
by 50% during the 2010 growing season. Spatio-temporal compensatory RWU in this silty clay loam soil, where soil water remained
higher throughout the entire root zone between irrigation events,
indicated that distribution of roots (the highest RLD within a depthof 30–50 cm) and water content availability within these depths
were the most critical factors for maintaining peak RWU rates

under dry (water-stressed) soil conditions. Under both wet (nonstressed) and dry soil conditions, the 0–50-cm soil depth withhigher RLD was the primary RWU uptake layer, and thus waterconditions within this layer were more important than the maximum rooting depth of 80 cm to maintain a certain rate of RWU.
Compensated T a rates predicted by HYDRUS (2D/3D) were correlated with measured transpiration rates under wet and dry soil
conditions. The soil water stress compensation could keep thesimulated relative transpiration (ratio between T a and T p ) at a
relatively high level to cope with the potential demand of a pecan
tree during the growing period. Compensatory T a =T p was moreconsistent with temporal variations in the pecan water stress indicated by both midday stem and leaf water potentials over several
irrigation cycles. Overall, our results of the spatio-temporal compensatory RWU simulations provide support for using HYDRUS(2D/3D) as a tool for managing the efficient water use of a floodirrigated pecan. Similar work with the consideration of the influence of the root resistivity on compensatory RWU patterns is
recommended to improve the understanding of model predictions.

Acknowledgments
We thank New Mexico State University Agricultural Experiment
Station for support and the Specialty Crop Research Initiative (SCRI), USDA-NIFA for funding this research. We thankDr. Rolston St. Hilaire, Department of Plant and Environmental
Sciences, New Mexico State University, for providing LAI data
and the LI-1600 porometer. Our thanks are to Mr. Ramakrishna
R. Gopal for his help with PEST, and Dr. Parmodh Sharma and
Dr. Pradip Adhikari with field sampling. We also thank Dr. Laurie
Abbott, Department of Animal and Range Sciences, New Mexico
State University, for allowing us to use plant root washing facilities.

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