agricultural water management 86 (2006) 140–149

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Macroscopic approaches to root water uptake as a function ofwater and salinity stressTodd H. Skaggs *, Martinus Th. van Genuchten, Peter J. Shouse, James A. Poss
George E. Brown, Jr. Salinity Laboratory, USDA, ARS, 450 West Big Springs Road, Riverside, CA 92507, USA

article info

abstract

Article history:

Computer simulation models can be important tools for analyzing and managing site-

Accepted 12 June 2006

specific irrigation, soil salinization, or crop production problems. For many of these pro-

Published on line 18 July 2006

blems, computer analyses require simulations of root water uptake as a function of waterand salinity stress. We give an overview of macroscopic modeling approaches that are based

Keywords:

on the Richards equation with a sink term specifying water uptake. Various parameteriza-

Root water uptake

tions of the sink term as functions of water and salinity stress are reviewed. An example

Salt tolerance

application demonstrates the simulation of drainage for a wide range of salinity and water

Simulation models

stress conditions. The example shows that in practice it is very difficult to discriminate
among the various functional forms proposed for the sink term. Future improvements tomodels may involve the incorporation of more dynamic root functions, such as the ability ofroots to respond actively to growing conditions. As an example, we consider modelingcompensated uptake, in which plants react to stress in one section of the root zone byincreasing uptake in sections with more favorable conditions. Lastly, the challenge of
estimating uptake reduction parameters from crop salt tolerance databases is discussed.
# 2006 Elsevier B.V. All rights reserved.

1.

Introduction

Irrigation has contributed significantly to increased crop
production worldwide. Unfortunately, irrigation has contributed also to increased salinization of agricultural lands, andhas caused the destruction of agriculture in many areas (Van
Schilfgaarde, 1980, 1984, 1994). About 20–30 million ha ofirrigated land are seriously damaged by the build-up of salts
and 0.25–0.5 million ha are estimated to be lost from production every year as a result of salt build-up (FAO, 2002). The
FAO/AGL SPUSH network (http://www.fao.org/ag/agl/agll/
spush/intro.htm) estimates that 19.5% of the world’s 230 million ha of irrigated land is salt-affected. In the United States,
9% of cropland and pastureland suffers from reduced
productivity due to salinity (Ghassemi et al., 1995). Still,
despite the negative impacts, irrigation is critical to sustaining

and increasing agricultural production. While about 17% ofagricultural land worldwide is irrigated, this 17% accounts forabout 40% of the total global food harvest (FAO, 2002).
Moreover, per capita arable land has decreased over theyears, from a worldwide average of 0.38 ha in 1970 to 0.28 ha in
1990, and some analysts project a further decrease to 0.15 ha in
2050 (Ghassemi et al., 1995). Hence, increased production mustcome from increased average yields, increases that will bepossible only through high-yielding irrigated agriculture.
Effective management of salt-affected soils requires
knowledge of many coupled physicochemical processes
affecting soil conditions. Computer models such as SWAP
(van Dam et al., 1997; Kroes and van Dam, 2003) and HYDRUS1D (Šimunek et al., 2005) have become increasingly important
tools for analyzing site-specific irrigation, soil salinization, or
crop production problems. Most of these models are based on* Corresponding author. Tel.: +1 951 369 4853; fax: +1 951 342 4964.
E-mail address: tskaggs@ussl.ars.usda.gov (T.H. Skaggs).
0378-3774/$ – see front matter # 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.agwat.2006.06.005

agricultural water management 86 (2006) 140–149

the Richards equation for variably saturated water flow andthe advection–dispersion equation for solute transport. In
their simplest one-dimensional forms, these equations are


@u
@
@h
¼
KðhÞ
 KðhÞ  S
@t @z
@z


@ðuRcÞ
@@c¼
uD  qc  f
@t
@z
@z

(1)
(2)

head, root characteristics, and meteorological conditions suchas evaporative demand. Several approximations have beenused for S in the macroscopic approach. A popular early
approach assumed that uptake rate is proportional to thedifference between the soil water pressure head, h, and an
effective root water or plant pressure head (or potential), hr,
leading to the general form:SðzÞ ¼ bðzÞðh  hr Þ

respectively, where u is the volumetric water content, h the soil
water pressure head (L), t the time (T), z the depth (L), K thehydraulic conductivity (L T1), R a retardation factor accounting for sorption or exchange, c the solute concentration of theliquid phase (M L3), D the solute dispersion coefficient(L2 T1), q the Darcy–Buckingham volumetric water flux(LT1), and S (T1) and f (M L3 T1) are sinks or sources forwater and solutes, respectively. In this paper, S and f areassociated exclusively with root uptake processes.
While models based on Eqs. (1) and (2) are critical tools in
irrigation and drainage studies, the equations pose challenges
because of (i) the many highly nonlinear processes involved,
including water and energy exchange between the biosphereand the atmosphere; (ii) issues of scale, especially for studies
at larger field and watershed scales; (iii) lack of data on the
many parameters required in the model. Proper parameterization of root water uptake as a function of water and salinity
stress remains one of those challenges.
A large number of microscopic and macroscopic
approaches to modeling water uptake have been proposedover the years. Comprehensive reviews from a mostlyhydrological perspective include Molz (1981), Hopmans andBristow (2002), Wang and Smith (2004), and Feddes and Raats(2004). The microscopic approach generally involves descriptions of radial flow to, and uptake by, individual roots (Hillel
et al., 1975; Raats, in press). In contrast, modeling uptake witha sink term in the Richards equation (Eq. (1)) is a typicalmacroscopic approach that averages uptake over a large
number of roots. The approach ignores or implicitly averages
pore-scale variations in the pressure head or solute concentration in the immediate vicinity of individual roots.
This paper is limited to the macroscopic approach.
Specifically, we review relatively standard macroscopic
approaches to modeling root water uptake in the presenceof water and salinity stress, provide an example application
involving a lysimeter study, briefly raise the issue ofcompensatory uptake, and discuss some practical issues
concerning the use of salt tolerance databases to determine
uptake reduction parameters. Elsewhere in this issue, Greenet al. (this issue) provide an overview of root uptake that iscomplimentary to our discussion, focusing on new technologies for measuring plant water use and observing compensatory uptake, and on the use of modeling to develop better
irrigation policies for allocating water.

2.
General model for the root water uptaketerm
The root water uptake term S in Eq. (1) should in general be afunction of the soil water pressure head, the osmotic pressure

141

(3)

in which b is a function that has been hypothesized in various
studies to depend on depth (z), the local average soil waterpressure head (h), the soil water content (u), the soil hydraulicconductivity (K(h)), soil and plant (xylem) resistances to root
water uptake, and/or the root distribution versus depth (e.g.,
Hillel et al., 1976; Molz, 1981). One version of Eq. (3) that has
been used in many numerical simulations is (Whisler et al.,
1968; Bresler et al., 1982):SðzÞ ¼ bðzÞKðhÞðh  hr Þ

(4)in which b is now a depth dependent proportionality constant, often referred to as the root effectiveness function (L2).
Some studies (e.g., Feddes et al., 1974) have used a term
corresponding to 1/b(z) rather than b(z) in Eq. (4), while othersaccounted for gravity by substituting the hydraulic head forthe pressure head (e.g., Gardner, 1964). Although b(z) is essentially an empirical parameter that somehow integrates thephysics of flow at and across the soil–root interface, in practice b(z) has been assumed to reflect the relative root distribution in the soil profile, and as such has been equated to thenormalized root density function with units of root length perunit volume of soil (Whisler et al., 1968). Most studies
assumed that hr in Eq. (2) or (3) is constant over the root zone.
The value of hr generally depends on specific soil, plant, andclimatic conditions, and cannot become less than some critical value, hcr, commonly taken to be the permanent wilting
point (150 m). Once S is calculated as part of a numericalsolution of Eqs. (1) and (4), the transpiration rate, Ta, may be
calculated with

Ta ¼

Z

S dz

(5)

LR

where LR is the depth of the root zone.
Eq. (3) describes water uptake as a function of water stressonly. Bresler et al. (1982), among others, accounted for salinity
stress by adding the osmotic head, p, directly to the pressurehead:SðzÞ ¼ bðzÞKðhÞðh þ p  hr Þ

(6)thus implying simple additivity of water and salinity contributions to plant stress. Again, Eq. (6) may be modified toaccount for the effects of gravity by substituting the hydraulic head for the pressure head (e.g., Childs and Hanks, 1975).
Eqs. (4) and (6) have been shown to work very well for nonsaline or mildly saline conditions, but not necessarily formore saline situations. For example, Cardon and Letey(1992a,b) showed that Eq. (6) may lead to unreasonable142

agricultural water management 86 (2006) 140–149

shifts between optimal and zero transpiration as compared
to experimental data. Because of the dominance of thehydraulic conductivity term, Eq. (6) failed to predict significant decreases in transpiration under highly saline conditions.
As an alternative to Eq. (4), Feddes et al. (1978) and Belmans
et al. (1983) suggested a much simpler root extraction termthat depends only on the pressure head and a maximum or
potential transpiration rate:SðzÞ ¼ bðzÞaðhÞTp

(8)

where Sp (T1) is the potential uptake rate. A large number offunctions for b(z) have been proposed and used, including
constant, linearly decreasing, trapezoidal, and exponentialfunctions. We refer the reader to Hoffman and Van Genuchten(1983) and Hao et al. (2005) for details.
In the sections below we discuss various functional forms
for the water stress response function (Section 3.1), equivalent
formulations for salinity stress (Section 3.2), and possible waysof combining water and salinity stress using these functions(Section 3.3).

3.
Uptake reduction models for water andsalinity stressEq. (7) defines a very general equation for the effects of drought
stress on water uptake. Similar forms can be postulated forsalinity stress (or for any other variable such as nutrient
stress), i.e.:SðzÞ ¼ bðzÞaðpÞTp

(9)

One important question is how to combine water and salinity
stress. That question is discussed in Section 3.3. We focus firston reduction functions for water stress (Section 3.1) and salinity stress (Section 3.2) separately.
Many of the functional forms that have been proposed for
uptake reduction are patterned after whole-plant water use
and salt stress relationships. This correspondence is motivated by the often assumed relationship (De Wit, 1958;
Doorenbos and Kassam, 1979):
Y
Ta
¼
¼a
Y p Tp8100;
ECe  A
>
>
>
100
<
Y
þA

AÞ;
A
< ECe 
100

BðEC
e
ð%Þ ¼
B
>
Yp
>
100
>
: 0;
ECe >
þA
B

(11)

and the S-shaped salinity yield response curve (van Genuchten and Hoffman, 1984):(7)

where b(z) is the normalized root density distribution (L1),
Tp the potential transpiration rate (L3 L2 T1), and a(h) is adimensionless water stress response function, sometimes
called the uptake reduction function (0  a  1). Notethat under conditions of no stress, a = 1 and Eq. (7) reducestoSp ðzÞ ¼ bðzÞTp

crop yield response to soil salinity (Maas and Hoffman,
1977):

Y1¼
 
Yp 1 þ C p

In Eqs. (11) and (12), ECe (dS m1) is the root-zone-averaged
saturation extract electrical conductivity, A (dS m1) and B(% m dS1) the empirical parameters called the threshold salinity and slope parameters, respectively, C the average rootzone salt concentration, and p and C50 are the empiricalparameters, the latter corresponding to the salt concentration
at which yield is reduced by half. The exponent p was found tobe approximately 3 when Eq. (12) was applied to a large
number of crop salt tolerance data sets (van Genuchten,
1987; van Genuchten and Gupta, 1993). Eq. (12) has beensuccessfully fitted to salt tolerance data for many crops (vanGenuchten and Gupta, 1993; Steppuhn et al., 2005a, b).

3.1.

Water stress response functions

Feddes and Raats (2004) reviewed various functional forms fora that have been proposed over the years. We mention here
two general model types that have been used most often:
piecewise linear functions and continuous smooth functions.
To describe water stress, Feddes et al. (1978) proposed apiecewise linear reduction function parameterized by four
critical values of the water pressure head, h4 < h3 < h2 < h1:8h  h4>>>> h3  h4 ;><1;aðhÞ ¼h  h1>>;>>>: h2  h1
0;

where Y is the yield and Yp is the potential yield (i.e., themaximum yield that would be obtained under optimal
growing conditions). Pertinent examples of whole-plant
response functions include the threshold–slope model ofh3 > h > h4
h2  h  h3

(13)h1 > h > h2h  h4 or h  h1

Fig. 1a shows a plot of Eq. (13). Note that in this model water
uptake is reduced at high and low water contents. Uptake is at
the potential rate when the pressure head is h3  h  h2, drops
off linearly when h > h2 or h < h3, and becomes zero whenh  h4 or h  h1. In general, the value of h3 is expected to be afunction of evaporative demand.
van Genuchten (1987) proposed an alternative smooth, Sshaped reduction function to account for water stress:aðhÞ ¼

(10)

(12)

C50

1þ

1
  p1hh50(14)where h50 and p1 are adjustable parameters (Fig. 1b). Eq. (14)was motivated by a study (van Genuchten and Hoffman,
1984) that found that an S-shaped function (Eq. (12))
described salt tolerance yield reduction data better that
other functions, including the threshold–slope model ofagricultural water management 86 (2006) 140–149

143

Similarly, in correspondence to Eq. (12), a smooth function
may be postulated for the effects of salinity stress on local root
water uptake:aðpÞ ¼
1þ

1
  p2

(16)

p
p50

where p2 and p50 are the adjustable parameters, the latterbeing the osmotic pressure head where uptake is halved.

3.3.

Combined water and salinity stress

A major challenge is how to combine the effects of water andsalinity stress. Uptake reductions due to a combination ofwater and salinity stresses could be modeled by assuming thatthe stresses are somehow additive or multiplicative. A
generalized model for additive stresses is obtained byassuming that water uptake occurs in response to someweighted sum of the soil water pressure and osmotic heads:
aðh; pÞ ¼

Fig. 1 – Plots of (a) the Feddes et al. (1978) water stress
uptake reduction function (Eq. (13)), and (b) the S-shaped
function of van Genuchten (1987) (Eq. (14)).

Maas and Hoffman (1977). van Genuchten (1987) reasoned
that if water and salinity stress are assumed to have similareffects on yield, and hence on transpiration, then the Sshaped function should also be applicable to water stressresponse data.

3.2.

1
h
i p2
2p
1 þ a1 hþa
p50

(17)

with simple additivity resulting when a1 = a2 = 1. Althoughadditivity has been inferred from a number of laboratory
and field experiments (e.g., Wadleigh, 1946; Meiri and Shalhevet, 1973; Childs and Hanks, 1975; du Plessis, 1985; Bresler andHoffman, 1986), its general applicability remains uncertain(Shalhevet and Hsiao, 1986), especially for field conditions
subject to relatively wide ranges in pressure heads (wetting/drying cycles).
Linear or weighted additivity is only one of several
possibilities for combining the effects of water and salinity
stress. Another approach presumes that water and salinity
effects are multiplicative. In the general case this leads to(18)aðh; pÞ ¼ aðhÞaðpÞ

where a(h) and a(p) can be any of the functions in Sections 3.1
and 3.2. For example, if Eqs. (14) and (16) are used, this gives

Salinity stress response functions

Consistent with the Maas and Hoffman (1977) model for crop
salt tolerance (Eq. (11)), the effects of salinity stress on root
water uptake can be described using the piecewise linear(threshold–slope) function:
8
1;
ap0
>
>
>
1
<
1
þ
bðp

aÞ;
a
>p>a 
aðpÞ ¼
b
>
>
1
>
: 0;
pa
b

(15)

where a and b are the adjustable parameters, often referred toas the salinity threshold and slope, respectively, thus mirroring the terminology used for the Maas–Hoffman parameters A
and B. Note, however, that the parameter sets are not thesame: A and B parameterize total yield reductions as a function of average root zone salinity, whereas a and b parameterize local reductions in the root water uptake rate as a functionof osmotic head.

aðh; pÞ ¼
1þ

1
  p1hh50

1þ

1
  p2

(19)

p
p50

where h50, p50, p1 and p2 are the presumably crop, soil, andclimate-specific parameters.

4.

An application

In practice, it is difficult to determine which of the reduction
functions (those noted here as well as others, reviewed forexample by Feddes and Raats (2004)) best describes root water
uptake. The detailed root zone and transpiration data needed
to discriminate the models are difficult to obtain and rarely
available. We illustrate this using data from a recent
experiment (Skaggs et al., 2006a, 2006b) conducted in alysimeter facility consisting of 24 volumetric lysimeters, eachmeasuring 81.5 cm wide  202.5 cm long  85 cm deep. The
lysimeters were filled with river sand (96% sand, 3% silt, 1%

144

agricultural water management 86 (2006) 140–149

involved a combination of salinity and drought stresses; thesame irrigation waters were used, but the lysimeters were
irrigated with a prescribed fraction ( f = 0.5, 0.75, 1.0, or 1.25) ofwater consumed in two well-watered ‘‘control’’ lysimeters.
Thus, lysimeters with f < 1 received less water than was being
consumed in the control, whereas lysimeters with f  1
received water equal to or in excess of that amount. During
both phases the lysimeters were irrigated every other day.
Drainage was measured nearly continuously throughout theexperiment.
Skaggs et al. (2006b) simulated the experiment using
HYDRUS-1D (Šimunek et al., 2005) with a reduction functionthat combined Eqs. (14) and (15) into a multiplicative model:
aðh; pÞ ¼
Fig. 2 – Comparison of the threshold–slope salinity stress
reduction function used by Skaggs et al. (2006b) (solid line)
and the S-shaped function (dashed line) used in thesimulations presented in Figs. 3 and 4.

clay) to a depth of 80 cm. Twelve of the lysimeters wereplanted with ‘Salado’ alfalfa (Medicago sativa) and 12 with ‘Jose’tall wheatgrass (Agropyron elongatum). The crops were established over several months using low salinity irrigation water.
Experimental treatments started on 2 May 2002 (day of year122) and proceeded in two phases. During the first phase (DOY
122–237) only salinity stress was imposed, with all lysimeters
being abundantly irrigated with waters ranging in salinityfrom 2.5 to 28 dS m1. The second phase (DOY 247–297)1þ

1
  p1 ½1 þ bðp  aÞ
h
h50

(20)

Using a trial-and-error fitting procedure, Skaggs et al. (2006b)
obtained values for h50, p1, a, and b which resulted in thesimulated drainage being in very good agreement with themeasured drainage. However, due to complications arisingfrom the coarseness of the sandy soil, they found that themodeling results were mostly insensitive to the form of thewater stress component of the reduction factor, and thus wereunable to evaluate the performance of the S-shaped water
stress response function and the assumed multiplicativeinteraction.
We have now re-analyzed their alfalfa drainage data to showthat a comparable fit to the data could have been obtained using
the S-shaped function for the salinity reduction (i.e., Eq. (16))
instead of the threshold–slope model in Eq. (20). Skaggs et al.

Fig. 3 – Comparison of simulated cumulative drainage with that measured during the ‘‘Phase 1’’ experiments of Skaggs et al.
(2006a, 2006b). Text in each plot indicates the irrigation water salinity (ECiw) and the lysimeter number. Irrigation timings
are shown on the bottom of each plot and the irrigation depth is indicated on the axes on the right side of each plot.

agricultural water management 86 (2006) 140–149(2006b) used the values a = 25 m and b = 0.004 m1 in thethreshold model. For the S-shaped model we used p2 = 3 (thevalue recommended by Šimunek et al. (2005) based on the
aforementioned p = 3 value obtained by van Genuchten (1987))
and p50 = 150 m (the value of p corresponding to a = 0.5 in thethreshold model used by Skaggs et al. (2006b)). As shown in
Fig. 2, the threshold model used by Skaggs et al. (2006b) and the
S-shaped model used here nearly coincide.
Figs. 3 and 4 present plots of cumulative drainage
simulated using the S-shaped function as well as the drainage

145

measured by Skaggs et al. (2006a). The agreement between thedata and simulations shown in Figs. 3 and 4 is essentially thesame as reported by Skaggs et al. (2006b) for the thresholdmodel (results not shown here), with both approaches (i.e.,
Eqs. (19) and (20)) producing a close match with the data.
The Skaggs et al. (2006a) experiment was not ideal for
identifying the full uptake reduction function since the coarse
soil texture was ill-suited for studying the drought response.
Still, the experiment did allow for a good examination of thesalinity response function. However, the drainage data were

Fig. 4 – Comparison of simulated cumulative drainage with that measured during the ‘‘Phase 2’’ experiments of Skaggs et al.
(2006a, 2006b). Text in each plot indicates the irrigation water salinity (ECiw), the target irrigation depth f, and the lysimeter
number (see text for an explanation of f). Irrigation timings are shown on the bottom of each plot and the irrigation depth isindicated on the axes on the right side of each plot.

146

agricultural water management 86 (2006) 140–149

not sufficient to discriminate between the S-shaped and thethreshold–slope models—either model could describe the data
equally well. In general, we suspect that drainage data ortranspiration data (or a surrogate such as yield data) alone will
not permit discriminating among different functional forms
for reduction functions such as those considered here, as wellas others containing additional parameters (e.g., Homaee
et al., 2002a; Dudley and Shani, 2003; Feddes and Raats, 2004).
Additional detailed root zone data might allow for discrimination; Green et al. (this issue) discuss measurement technologies that may provide such data. However, our view is thatmost of the proposed reduction models can be calibrated to
produce essentially the same simulation results, at least
within the limits of experimental observation.
Finally, we emphasize that the reduction function
approach used in hydrologically oriented uptake models as
reviewed here has a limited plant physiological basis. For
example, it is known that plant response to salinity stress
may not be constant over time: osmotic effects tend to
dominate initially, whereas over the long term the accumulation of ions may become more important (Munns, 2002). Thislatter effect, plus other temporal components of plant
response, is not accounted for in the type of models
considered here. On balance, we think that further refinement of the functional forms of the reduction functions is notwarranted at this time, and recommend the use of the twoparameter S-shaped models (Eqs. (14) and (16)) which provide
sufficient flexibility without the introduction of unwarranted
complexity.

5.

Compensated water uptake

One area of research that may improve hydrologically oriented
models of root water uptake involves the development of sinkterms which incorporate a wider range of dynamic root andplant function. As biological organisms, plants and roots may
respond in various ways to environmental stresses. Of interest
are root functions that could be represented without having tomodel plant physiology in detail. One example is compensatedwater uptake in which plants may respond to non-uniform
stress conditions by increasing water uptake from sections of
the root zone with more favorable conditions (Taylor andKlepper, 1978; Hasegawa and Yoshida, 1982; Jarvis, 1989).
Compensatory water uptake is potentially an important
aspect of irrigation and drainage practices that impose
nonuniform water stress in the root zone. These practices
include deficit irrigation (e.g., English and Raja, 1996; Leib et al.,2006), partial root zone drying (e.g., Kang et al., 2002; Stikic
et al., 2003), and deficit irrigation in combination with shallow
groundwater management (e.g., Ayars et al., 1999; Shouse
et al., 2006). Since these practices rely on the ability of a crop to
respond to stress, including compensatory uptake in modelsof root water uptake would clearly aid in the analysis anddesign of such practices.
Several modeling approaches are possible for compensatory water uptake (e.g., Li et al., 2001; Braud et al., 2005). We
briefly review here the approach of Jarvis (1989), as modified byŠimunek et al. (2005) in HYDRUS-1D. Jarvis (1989) formulated
the following in terms of the soil water content, whereasŠimunek et al. (2005) used the soil water pressure head as thecontrolling variable.
First recall that for the models in Section 3.1, the actual
transpiration rate Ta is given by
Ta ¼ TpZ

a½hðzÞbðzÞ dz

(21)

LR

where as before Tp is the potential transpiration rate, a thewater stress reduction factor, and b(z) is the normalized root
density distribution. To formulate a compensatory uptake
model, define v to bev

Z

a½hðzÞbðzÞ dz

(22)

LR

Note that 0  v  1. The functional v is called the weighted
stress index and provides a measure of total plant stress, with
v = 1 indicating no stress throughout the soil root zone.
The transpiration rate for compensatory water uptake is
now given by
Ta
¼
Tp

(

1;
v
;
ve

vc < v  1
v < vc(23)

where 0 < vc  1. According to this formulation, transpiration
occurs at the potential rate (Ta = Tp) when the total stress isrelatively low (i.e., when v is greater than some critical valuevc). To obtain the potential rate, uptake is increased throughout the root zone by a factor of 1/v. Although on a relative basis
uptake is increased uniformly throughout the root zone, inabsolute terms the biggest increase occurs in those parts of theroot zone where stress is low and/or the root density is high(i.e., where S(z) = a[h(z)] b(z) is large). Conversely, the increaseis negligible in sections where S(z) is very small. Root water
uptake from stressed parts of the root zone is hence fullycompensated by uptake from other parts. When stress ishigher and v < vc, compensation is only partial, with uptake
increased throughout the root zone by a factor of 1/vc.
Unfortunately, little is known about the parameter vc.
Jarvis (1989) analyzed oat, spring rape, and mustard crop datafrom a field experiment in Sweden and obtained a seemingly
very low value of vc = 0.1, implying fully compensated uptake
except at very high levels of stress. The compensated uptake
model also appears to have conceptual limitations. For
example, let us assume momentarily that a[h(z)] is given by
Eq. (14), the root distribution is uniform with depth (b(z) = 1/LR),and the soil is initially at field capacity, uniformly wetted in theroot zone. In that case h(z) = h and, from Eq. (22), v = a(h). As theroots extract water from the soil, the soil would dry down
uniformly, thus decreasing the value of a(h). As long asa(h) > vc, uptake would remain at potential levels and above
the rate specified by a(h), with uptake being increased
uniformly throughout the root zone by a factor of 1/a. Later
when a(h) decreased below vc, uptake would fall below
potential levels, although uptake throughout the root zone
would still be greater by a factor of 1/vc than the rate specified
by a(h). However, both of these increases in uptake above thelevel specified by a(h) do not mimic compensatory uptake, andboth seem to contradict the meaning of a(h). What, afterall,agricultural water management 86 (2006) 140–149

does a(h) stand for if it does not describe the reduction in
uptake that occurs in this example? So while the model iscapable of exhibiting compensatory behavior for certain typesof stress conditions, it does not seem to be a completely
satisfactory solution to the compensatory uptake problem
either.

6.
Estimation of uptake parameters fromdatabases
Uptake reduction functions such as those given in Figs. 1 and 2
are generally very difficult to determine experimentally. We
noted earlier that the various forms for the uptake reduction
functions are similar to, and sometimes based on, forms thathave been observed for whole-plant responses to stress.
Because of this similarity, it has been anticipated (e.g., vanGenuchten, 1987; van Dam et al., 1997) that uptake reduction
parameters for different crops could be derived from literaturestudies of whole plant response. For example, Kroes and vanDam (2003, Appendix 3) provide a database of high and low h3
parameters for the water stress reduction function given by
Eq. (13), based on whole-plant observations compiled by
Taylor and Ashcroft (1972).
An abundance of data exists for whole-plant salt tolerance
as a function of root-zone-average salinity. Salt tolerance data
may be found in Maas and Hoffman (1977), Maas (1990), andSteppuhn et al. (2005b), among other publications. In addition
to using salt tolerance data to derive salinity uptake reduction
parameters, van Genuchten (1987) noted the intriguing
possibility of also deriving information about water stressparameters. If one assumes that water and salinity stresseffects on the transpiration rate are approximately similar,
then crop salt tolerance data could possibly be used toindirectly derive information about the water stress response
function parameters. Eq. (17) is noteworthy in this regard as it
expresses the combined drought and salinity uptake reductionin terms of the salinity reduction parameters p50 and p2. Thus,if p50 and p2 were estimated from salt tolerance data, theuptake reduction due to water stress could be subsequently
simulated with Eq. (17). Although Munns (2002) notes that at
early times plant responses to water and salinity stresses arein fact similar, the appropriateness of water stress parameters
obtained in this way is yet to be tested.
In any event, there are a number of potential problems thatshould be kept in mind when using plant salt tolerance data toderive parameter values for the salinity, water, and combined
uptake reduction functions. One difficulty concerns the natureand quality of plant salt tolerance information, which mostoften has been reported in terms of the A and B parameters in
Eq. (11). Maas and Hoffman (1977) themselves noted that‘‘These data serve only as a guideline to relative tolerancesamong crops. Absolute tolerances vary, depending on climate,soil conditions, and cultural practices’’. Additionally, theexperimental data from which the tabulations of A and B
were derived were very often not sufficient to determine salt
tolerance parameters with great precision (e.g., van Genuchten and Gupta, 1993). Confidence intervals for A and B are
typically not reported. Hence, while thousands of publicationsof crop salt tolerance studies have been compiled and indexed

147(e.g., Francois and Maas, 1978, 1984), the data have been oflimited value for many applications. Also, many salt tolerance
studies failed to control or report environmental and cultural
factors known to affect yield. Other experiments wereconducted over a range of salinities that proved to be too
narrow or too broad. All of this motivated Ulery et al. (1998) toadvocate the development of a comprehensive computerized
database of crop salt tolerance information that would permit
a more effective evaluation of past work and, ultimately, morereliable estimates of the effects of environmental factors andcultural, soil, and water management practices on crop salt
tolerance. Obtaining root water uptake information of the typediscussed in this paper would certainly fall within the realm of
possible applications of such a database.
A second difficulty is that the parameters A and B in Eq. (11)express plant salt tolerance as a function of a time and rootzone-averaged soil salinity (ECe), whereas uptake reduction
functions are parameterized in terms of the local osmotic and/or soil water pressure head. Thus, to derive uptake reductions
parameters (e.g., a and b in Eq. (15)) from reported values of A
and B, one must assume that the response to salinity stress at
any point and time in the soil root zone is the same as thetime-and-root-zone-integrated response by the entire plant or
crop. This cannot be formally correct because of nonlinear
dependencies of uptake on the pressure head or osmotic head,
and also because of potentially significant effects of compensatory uptake. It is not clear what types of errors are
introduced by equating local and global plant responses.
Furthermore, converting A and B to a and b requires convertingroot-zone-average ECe to p. In this context it should be
remembered ECe is the electrical conductivity of the saturation
extract, not the conductivity of soil water. Recent studies by
Homaee et al. (2002a,b,c) and Skaggs et al. (2006a, 2006b)
demonstrate the various approximations needed to make theconversion, and show that uptake reduction parameters
derived from salt tolerance data may in fact not produce
accurate simulations. These conversion issues are discussed
in detail by Ulery et al. (1998).

7.

Concluding remarks

In this paper we gave an overview of macroscopic modelingapproaches for root water uptake as a function of water andsalinity stress. We showed that, at least for one set of lysimeter
experiments involving a wide range of salinity and water
stress conditions, it is very difficult to discriminate amongalternative functional forms for the sink term. Future
improvements to root water uptake models may involve theincorporation of more dynamic root functions, such as theability of roots to respond actively to growing conditions. As an
example, we considered compensated water uptake in whicha plant reacts to stress in one part of the root zone byincreasing uptake in other parts with more favorable conditions. We also discussed the challenge of estimating uptake
reduction parameters from databases of whole-plant response,
especially crop salt tolerance databases. Crop salt tolerance
information is abundant in the literature but the accuracy ofmany of the data is questionable. In general, the data does notinclude information about soil and environmental factors and148

agricultural water management 86 (2006) 140–149

cultural and water management practices known to affect crop
salt tolerance and, indirectly, root water uptake. To derive
uptake reduction parameters from whole-plant response data
one must assume that the response to salinity stress at any
point and time in the soil root zone is the same as the time-androot-zone-integrated response by the entire plant or crop. This
assumption cannot be formally correct because of the nonlinear
nature of uptake processes, and neglects potentially significant
compensatory uptake mechanisms. If uptake compensation
played a role in many of the experiments used to construct plantwater stress and salt tolerance databases, then estimates of a(h,p) from those databases would tend to be too high; including
compensatory uptake in simulations would then account twice
for the same mechanism (globally, not locally). Clearly, more
research is needed in this area if we ever hope to use wholeplant response databases to parameterize uptake reduction
functions and employ simulation models as predictive toolsthat do not require extensive crop- and site-specific calibration
exercises involving inverse modeling (Hupet et al., 2003) or othermethods of adjusting parameters (Skaggs et al., 2006b).

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