CROP ECOLOGY, MANAGEMENT & QUALITY
Root-Zone Salinity: I. Selecting a Product–Yield Index
and Response Function for Crop Tolerance

Reproduced from Crop Science. Published by Crop Science Society of America. All copyrights reserved.

H. Steppuhn,* M. Th. van Genuchten, and C. M. Grieve
ABSTRACTmeasurable agricultural product defines the magnitudeof crop tolerance or resistance to salinity. Salinity generally slows the rate of crop growth, resulting in plants
with smaller leaves, shorter stature, and reduced economic yield (Shannon et al., 1994). The degree to which
growth is curtailed by salinity differs with crop species
and variety (Shannon and Grieve, 1999).
In this study, we briefly review the factors that affectthe response of crops to root-zone salinity, summarize
and evaluate a number of models that have or could be
used for the crop salt tolerance response function, andpropose a Salinity Tolerance Index that provides a relative ranking of crops according to their tolerance to rootzone salinity.

Six empirical functions were compared for describing the productyields of agricultural crops grown while subject to increasing levelsof root-zone salinity. The four nonlinear functions fit the test datafrom a spring wheat (Triticum aestivum L. , cv. Biggar) experimentconducted in Canada’s Salt Tolerance Testing Facility closer than the
two linear functions. Although each of the four nonlinear declining
functions could reasonably describe the data, the modified compounddiscount equation recorded the lowest root mean square error andthe highest R2 value. Additional response data using the nonlinear
discount function obtained from 33 separate trials averaged 11%
closer in statistical fit and 45% lower in statistical error than the best
linear function. The discount function {Yr ⫽ 1/(1 ⫹ [(C/C50)exp(sC50)]}
follows a sigmoidal form and relates relative yield (Yr) to a measureof root-zone salinity (C ) such as the solute concentration with anelectrical conductivity of an equivalent saturated soil paste extract(ECe). This function features two parameters, the salinity level producing 50% of the nonsaline crop yield (C50) and the absolute value ofthe general decline in relative yield with salinity at and near C50, thesteepness constant (s ). These parameters combine to form a singlevalue, salinity-tolerance index (ST-Index) consisting of the 50% reduction in crop yield (C50) plus the tendency to maintain some productyield as the crop is subjected to increasing salinity levels approaching
C50, i.e., ST-Index ⫽ C50 ⫹ s(C50). The ST-Index for the Biggar wheat
registered 6.44. Approximations for C50 and s can be derived fromthe threshold salinity (Ct) and declining slope (b ) parameters of thethreshold-slope linear response function [Yr ⫽ 1 ⫺ b(C ⫺ Ct)]. Procedures for converting Ct to C50 and b to s offer linkages between theselinear and nonlinear response function parameters, and are further
explored in this paper’s companion. The resulting ST-Index-values
equal 6.56, 9.43, and 5.67 for sample field (corn, Zea mays L.), forage(alfalfa, Medicago sativa L. and falcata L.), and vegetable (radish,Raphanus sativus L.) crops, respectively.

CROP YIELD RESPONSE TO SALINITY
Ayers and Westcot (1985) define a salinity problem
as a condition where the salts in solution within the crop
root zone accumulate in concentrations which decrease
crop yield. Although all dissolved solids and gasses contribute ions to the total concentration, these authors,
writing for FAO, list the most common excess constituents as calcium, magnesium, sodium, carbonate, bicarbonate, chloride, sulfate, nitrate, ammonium, phosphate,potassium, boron, and various trace elements. Solutes
in aqueous solutions decrease osmotic potential, which
affects plant water uptake (Wadleigh and Ayers, 1945;
Munns and Termaat, 1986; Jacoby, 1999; Katerji et al.,1997). Osmotic effects contribute to reduced growthrate, changes in leaf color, and developmental characteristics, such as root/shoot ratio and maturity rate. In addition, ion toxicities or nutritional deficiencies may arise
as a result of the excessive presence of specific ions and/or
a competition among specific cations or anions (Bernstein, 1974; Torres-Bernal et al., 1974; Shannon andGrieve, 1999). Ionic effects are often manifested by leaf
and meristem damage or as symptoms typical of nutritional disorders. For example, Na or Cl ions may accumulate in plant leaf tissue and cause necrotic tips and/or
margins (Bernstein et al., 1956; 1969). Salinity-induced
nutritional deficiencies present symptoms generally similar to those that occur in the absence of salinity. Often
cited is the presence of sulfate and large Na/Ca ratios
in root-zone solutions which were thought to lead tosymptoms of calcium deficiency (Maas and Hoffman,
1977; Janzen and Chang, 1987, 1988). More commonly,Laboratory and field tests to identify decreases incrop yield in response to increasing root-zone salinity have been conducted for many years and are listed
by Francois and Maas (1978, 1985) and Ulery et al.
(1998), among others. The inherent ability of crop plants
to withstand the effects of elevated solute concentrations in their root-zone solutions and still produce a

H. Steppuhn, Semiarid Prairie Agricultural Research Centre, Agriculture and Agri-Food Canada, Box 1030, Swift Current, SK, Canada
S9H 3X2; M.Th. van Genuchten, Soil Physics/Pesticide Unit, George
E. Brown, Jr. Salinity Laboratory, Agricultural Research Service,
U.S. Department of Agriculture, Riverside, CA; C.M. Grieve, Plant
Sciences Group, George E. Brown, Jr. Salinity Laboratory, Agricultural Research Service, U.S. Department of Agriculture, Riverside, CA.
Received 8 Sep. 2003. *Corresponding author (SteppuhnH@agr.gc.ca).

Abbreviations: ECe, electrical conductivity of saturated soil paste extract; ECi, electrical conductivity of the irrigated water; ECs, electricalconductivity of test solution; FAO, Food and Agriculture Organization, United Nations; ST-Index, salinity tolerance index.

Published in Crop Sci. 45:209–220 (2005).
© Crop Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

209

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CROP SCIENCE, VOL. 45, JANUARY–FEBRUARY 2005

nutritional effects tend to work in conjunction with specific ion toxicity but vary in their degree of manifestationin different crops (Curtin et al., 1993; Grattan and Grieve,1999).
Salinity is commonly measured in units of electrical conductivity at 25⬚C and an electrode spacing of 10 mm.
Representative soil samples are obtained from the rootzone to which deionized water is added to derive saturatedpaste extracts following standard procedures (Rhoades,
1982). The electrical conductivity (ECe) of these extracts
provides a consistent, repeatable, and widely acceptedsalinity standard (U.S. Salinity Laboratory Staff, 1954).
An advantage of using ECe as a salinity measure is thatit relates to saturated field soil water conditions. Other
measures of root-zone salinity include solute concentration (Cs) and osmotic potential (⌿o) of the soil extracts.
For many soil extracts,
ECe ≈ 640 (Cs)[1]and ⌿o ≈ ⫺36.47 (ECe)[2]where ECe, Cs, and ⌿o are respectively expressed in decisiemens per meter (dS/m), parts per million (ppm), andkilopascals (kPa) (U.S. Salinity Laboratory Staff, 1954).
Experience has also shown that the electrolyte concentration resulting from the saturated soil-paste-extract
procedure equals approximately one-half that of the soil
pore water at field capacity (Ayers and Westcot, 1985).
The relative effects of specific ions in root-zone solutions compared with decreased osmotic potential resulting
from elevated solute concentrations has been debatedat length. Palmer (1937) noted that adding Na2SO4 topotted soils was more injurious to cereals than adding
MgSO4, but less than when NaCl was added. Magistad
et al. (1943) found little, if any, significant differencesin the yields of garden beets, wax beans, or carrots
when the chloride and sulfate salt concentrations wereconverted to osmotic pressures and compared. The UnitedStates Salinity Laboratory Staff (1954) agreed with Magistad et al. (1943) but with the corollary that deviations
from direct osmotic-yield relationships were caused by
specific-ion effects.
One of the concerns with salinity-tolerance response
functions relates to anion dominance of the test solutions, i.e., between chloride and sulfate ion concentrations. Warne et al. (1990) measured better growth for
Chenopodium rubrum L. plants subjected to Cl solutions as compared with plants grown in SO4–dominatedsystems. In contrast, Boursier and Läuchli (1990), Wu
and Huang (1991), Mor and Manchanda (1992), andCurtin et al. (1993), respectively, observed that, at moderate sulfate salinity, crop growth of sorghum [Sorghum
bicolor (L.) Moench], tall fescue (Festuca arundinacea
Schreber), table pea (Pisum sativum L.), and Kochia scoparia (L.) Schrad. was generally less limiting than undercomparable chloride salinity. More recently, Grieve andSuarez (1997) and Grieve et al. (1999, 2001b) demonstrated the feasibility of applying sulfate-based irrigation water to Portulaca oleracea L. (a halophyte), wheat,and nine leafy vegetable crops and still realize satisfactory yields. Maas (1990) cited the work of Bernstein(1962) in suggesting that upward salt-tolerance adjustments of 1 to 3 dS/m are appropriate where calcium
sulfate salinity dominates soil solutions to apply cropyield data obtained at the same ECe in chloride-dominated response tests.
Crops have been tested for salt tolerance in both fieldand greenhouse experiments in soil and sand cultures.
Yaron et al. (1972) studied regression procedures for
estimating the yield of field-grown crops in response tosoil water content and salinity. Using grapefruit (Citrus ⫻paradisi Macfad.) and peanut (Arachis hypogaea L.)
data, they identified many of the difficulties associatedwith correlating yield with salinity when soil water contents vary. Typically, randomly arrayed field plots orlarge tanks containing the crops under investigation are
separately salinized artificially with an irrigated solution
whose solute concentration equates to one of a range
of increasing salinities. In the field, within soil, the timerequired for complete mixing and diffusion of the irrigated test solutions with the initial soil solutions throughout the root zone can require days or weeks or longer
as compared to minutes or hours for greenhouse sandcultures. Field tests with soil provide greater opportunity for evapotranspiration or rainfall to concentrate or
dilute the in situ, dissolved salts, especially following
infrequent applications of saline test solutions. Unlessgrowing conditions carefully duplicate those of the target growing season, greenhouse testing can also causeskewed responses. In addition, soil-based, salt-tolerance
testing may have to contend with preferential flow andwith spatial and temporal salinity transients in the rootzones. Unless irrigated with large leaching fractions, thesoil may act as either an ion source or sink. Variationsin the actual solute concentration of the solutions acting
on the roots of test crops, especially in field trials, cancause considerable variations in the resulting crop yields.
Besides changes in solute concentrations, many othercrop–environment interactions may cause variations insalinity-yield relationships, such as those involving temperature, radiation, humidity, atmospheric pollutants,
wind, soil water content, and fertility (Shannon et al.,1994). The combination of high temperatures and low
humidity may decrease crop salt tolerance, especially ifsoil water reserves are limited (Bernstein, 1974). Hoffman et al. (1978) observed that pinto bean grown in acool, humid environment tolerated higher salt levels
than those predicted from published data. Drought often combines with salinity adding to the difficulties facedby crop plants (Bresler et al., 1982; Katerji et al., 1992;
Feng et al., 2003a, 2003b). Testing for crop salt tolerance involves separating the simultaneous effects of any
water deficits from those resulting from the salinity.
Root-zone fertility and aeration in the absence or presence of salinity contribute eminently to the productivityof crop plants. Doughty and Stalwick (1940), Lunin et al.
(1961a, 1963), Ravikovitch and Porath (1967), Ravikovitch and Yoles (1971), Bernstein (1974), and Peters(1983) are among many who reported salinity–fertility
interactions affecting interpretations of salt-tolerance
data. If the yield response to increasing root-zone salinity encounters nutrient or oxygen deficits, a thresholdReproduced from Crop Science. Published by Crop Science Society of America. All copyrights reserved.

STEPPUHN ET AL.: SELECTING A FUNCTION AND INDEX FOR CROP SALINITY TOLERANCE

211

limit for maximum productivity typically results (Maasand Hoffman, 1977). Shallow water tables or very frequentirrigation can cause poor soil aeration, and thereby, negatively affect the testing of crops for their tolerance ofsalinity, as exemplified in tomato and wheat (Aubertin
et al., 1968; Aceves-N et al., 1975).
Plant ontogeny or growth stage also affects crop tolerance of salinity. For example, turnip (Brassica rapa L.)
is most salt tolerant at germination, but more sensitive
as a seedling than at harvest (Francois, 1984). In general,
the earlier and longer that crop plants must cope withroot-zone salinity, the greater the reduction in vegetative growth (Lunin et al., 1961b, 1962, 1963; Kaddah
and Ghowail, 1964; Francois et al., 1994; Katerji et al.,1998). A common practice in testing crop plants fortheir salinity tolerance is to delay salinization of rootzones until after the plants have been established (Maasand Grattan, 1999). Delaying salinization from sowing
to establishment causes variation in crop yields (Lunin
et al., 1962; Steppuhn et al., 1996). In wheat, delaying
salinization beyond emergence increases the number ofprimordia, the final leaf number, and likely the grain
weight (Grieve et al., 2001a). Even the same variety can
respond differently depending on the interactions ofphenology and the initiation of the root-zone salinity(Shannon and Noble, 1990).
Genetic, physiological, and ecological crop differences combine to determine how a crop will respond tosalinity. Wheat, for example, varies in tolerance among
many of its varieties, cultivars, and strains (Torres-Bernal and Bingham, 1973; van Hoorn et al., 1993; Steppuhn
and Wall, 1997). At the same time, plants grown fromlarger seeds, at least for two wheat cultivars, tend toshow better salinity tolerance than plants from smaller
seeds (Grieve and Francois, 1992). Ecologically, crop
yields in saline environments vary in their response toplant density. In wheat, widely spaced crop plants tend
to show the effects of saline root-zones more thanclosely spaced plants (L.E. Francois, personal communication; Steppuhn, 1997). The distinction between testingfor salt tolerance among agricultural crops rather thanamong agricultural plants guides the discussion and work
presented herein.
Most lists of the relative salinity tolerance among
agricultural crops are based on comparisons of parameters in specific salinity–yield functional relationships(van den Berg, 1950; U.S. Salinity Laboratory Staff,
1954; Allison, 1964; Bernstein, 1974; Maas and Hoffman,
1977; Bresler et al., 1982; Maas, 1986; Francois andMaas, 1994; Maas and Grattan, 1999). The parameters inthese functions have come to serve as indices for salinity
tolerance. The objective of this study was to compare
various yield functions to suggest a general response andindex, which, though empirical, most closely reflects thegeneral response of agricultural crops to root-zone salinity.

environment, soil fertility, pest damage, and many otherfactors besides salinity. Yields also vary because thecommodities produced from plant crops originate froma diverse array of plant components: leaves, stems, flowers, fruits, seeds, roots, tubers, and other tissues. To
compare the tolerance of crops to root-zone salinity,yields are usually standardized and expressed on a relative basis. The usual procedure for converting absolute
yield (Y) to relative yield (Yr) employs a scaling divisor(Ym) based on the production where salinity has very
little or no influence on yield (Maas, 1990). Such adivisor normalizes the data set, and almost always equals
the maximum yield resulting from the response test. A
Yr value is determined for each cultivar in each test by

RESPONSE FUNCTIONS

Bi-Exponential Function

Crops produce a wide array of agricultural commodities and do so with efficiencies measured by crop yield.
Yields vary depending on crop species, cultivar, ambientvan Genuchten (1983) included a more general exponential response function for analyzing crop salt-tolerance data,

Yr ⫽ Y/Ym[3]

Various empirical equations have been applied or suggested for describing Yr as a function of a variable, whichreflects the average root-zone salinity (C). Measuresused for C have included Cs, ⌿o, ECe, and ECi, where ECi
equals the electrical conductivity of the irrigation water.

Simple Linear Function
Early analyses of crop yield responses to salinity commonly followed a simple linear relationship of the form
Yr ⫽ a ⫺ b(C)[4]

Researchers restrictively applied a fitted linear function
over the range of the salinities tested, or they simply
showed the plotted response points without a fitted
function (Palmer, 1937; Magistad et al., 1943; Ayers etal., 1943; Wadleigh and Ayers, 1945; Batchelder et al.,
1963; Holm, 1983). Rarely, if ever, were the regression
coefficients a and b identified as representing any biophysical characteristics of the response.

Modified Weibull Function
The statistical Weibull cumulative probability distribution exponentially relates one variable to another andincreases in value from zero to one as the independent
variable ranges from its upper to its lower values (Weibull, 1951). Used as a response function to root-zone
salinity, the Weibull distribution has been modified andexpressed in terms of the proportionate Yr yield remaining at any C as follows:
Yr ⫽ exp[a(C b)][5]where the regression coefficient a is always negativeand defines the intensity of the relationship, and theconstant b reflects the shape of the response curve.
Neither a nor b specify any distinct biophysical characteristic. The modified Weibull function has served as
an analog for the response of crop growth or yield toenvironmental toxicity and solute excess (Rawlings andCure, 1985; Taylor et al., 1991; Jalil et al., 1994a, 1994b).

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Reproduced from Crop Science. Published by Crop Science Society of America. All copyrights reserved.

Yr ⫽ exp[aC ⫺ b(C 2)][6]

in which the empirical constants a and b again lack any
biophysical identity and can be evaluated by nonlinear
regression. van Genuchten and Hoffman (1984), Steppuhn et al. (1996), and Wang et al. (2002) used the biexponential function to describe the yield-responses of
perennial ryegrass (Lolium perenne L.), wheat, and elephant grass (Pennisetum purpureum Schum.), respectively.

Modified Gompertz Function

their work is that it demonstrated the use of mathematical response functions and associated parameters toevaluate and compare the salinity tolerance of crops.
Feinerman and Yaron (1982) extended the thresholdslope response function to include the effects of soil
moisture with all other factors assumed constant.

Modified Discount Function
The compound discount equation can be modified
into a sigmoidal-shaped response function,
Yr ⫽ 1/[1 ⫹ (C/C50)exp(sC )]50

According to Lapp and Skoropad (1976) actuaries formany years used a form of an equation proposed byGompertz (1825) to predict human mortality. In various
forms, the same equation has been applied in botany
to model germination (Tipton, 1984), emergence (Ganet al., 1992), and growth (Baker et al., 1975). Steppuhn
et al. (1998) compared the emergence of two Russian
wild ryegrass cultivars from saline seedbeds with theGompertz function. In the following form, it can also
serve as a crop-yield salinity response function:
Yr ⫽ 1 ⫺ exp[a exp(bC)][7]

where empirical constants a and b are always negative,
lack any biophysical identity, and can be evaluated by
nonlinear regression.

Three-Piece Linear (Threshold-Slope) Function
After reviewing the yield responses measured in alarge number of root-zone salinity experiments conducted worldwide, Maas and Hoffman (1977) introduced a two-piece linear model for the response of agricultural crops to increasing salinity. This resulted intheir now classic threshold-slope concept. In its mostgeneral form, this model can be written as a three-piece
response function (van Genuchten, 1983):
Yr ⫽ 10 ⬍ C ⬍ Ct

Yr ⫽ 1 ⫺ b(C ⫺ Ct)

Ct ⬍ C ⬍ C 0

Yr ⫽ 0C ⬎ C0[8]

where b is the absolute value of the declining slope in
Yr with C; Ct is the maximum value of salinity withouta yield reduction (the threshold C); C0 is the lowest
value of C, where Yr ⫽ 0. The empirical constants, b
and Ct, are usually evaluated by regression and/or visualinspection. Maas and Hoffman (1977) introduced theirmodel as a two-piece expedient, ignoring the third segment, the yield response beyond Co. They also defined
the “threshold salinity” Ct and the “slope” b, as characteristics that are uniquely specific to each crop, but gave
no biophysical reasons for the existence of these characteristics. Maas and Hoffman (1977) also manually fitted
the threshold-slope function to data for some 60 crops
using experimental salt-tolerance field data reported in
the literature. They included reports from experiments
in which crops were grown while subjected to two or
more levels of salinity plus a nonsaline control. For
25 yr, their threshold-slope values have served as first
approximations of crop salinity tolerance. The value of[9]where C50 defines C at Yr ⫽ 0.5, and s represents the response curve steepness. The steepness parameter equals
the average absolute value of the slope (dYr/dC) of theequation through C50 and its steepest segments on eitherside of C50, evaluated in our study from Yr ⫽ 0.3 to 0.7.
The argument sC50 of the exponent in Eq. [9] contributes
to a symmetrical concave-convex yield response with
the inflection point at C50 and is analogous to the productbCt of the threshold-slope model (Eq. [8]). Both s andb indicate unit decreases in relative product yield withunit increases in root-zone salinity. As in the thresholdslope function, the modified discount function features
parameters (s and C50) with identifiable biophysicalcharacteristics.
van Genuchten (1983) was the first to apply a formof the modified discount function to yield data of agricultural crops growing subjected to increasing rootzone salinity; he used the empirical constant p as the
exponent instead of exp(sC50):
Yr ⫽ 1/[1 ⫹ (C/C50)p][10]

In this form of the discount equation, p is a shapeparameter without biophysical identity, which has been
evaluated from 1 through 9 (van Genuchten and Gupta,
1993). In all reported applications of this form of thefunction, the value of p has always exceeded 1.0 (vanGenuchten and Hoffman, 1984; van Genuchten and
Gupta, 1993; Steppuhn, 1993; Steppuhn et al., 1996).
This is related to the property of Eq. [10] that its slope
at zero salinity (C ⫽ 0) is zero for p values greater than
1, finite (⫺1/C50) when p ⫽ 1, and ⫺∞ when p ⬍ 1, thelatter case being unrealistic from a practical view.

SALINITY TOLERANCE INDEX
Before 1977, the concept of using an index to rate thesalinity tolerance of agricultural crops was consistently
followed (Ayers et al., 1951; U.S. Salinity Laboratory
Staff, 1954; Brown and Hayward, 1956). The practice
was to simply use C50, derived directly from experimental data, as the index. The introduction of the thresholdslope function to assess the yield response of agricultural
crops to increasing levels of root-zone salinity provided
two functional parameters (b and Ct) with which toindex relative salt tolerance (Maas and Hoffman, 1977).
These parameters served as dual indices resulting invarious lists of the relative salinity tolerance among
agricultural crops (Maas and Hoffman, 1977; Bresler etReproduced from Crop Science. Published by Crop Science Society of America. All copyrights reserved.

STEPPUHN ET AL.: SELECTING A FUNCTION AND INDEX FOR CROP SALINITY TOLERANCE

al., 1982; Maas, 1986; Francois and Maas, 1999; Maas
and Grattan, 1999).
As briefly reviewed in this study, many factors influence the yield of agricultural crops besides the response
to increasing root-zone salinity. With a myriad of influences acting on the yield relationship, a single-value
index of crop tolerance to root-zone salinity would seem
sufficient for comparing the salinity tolerance of agricultural crops. If C50 were enhanced by a term, which dictates the shape of the yield response for salinity levels
approaching C50, such as the argument of the exponent
in Eq. [9], a comprehensive, single-value, Salinity Tolerance Index or ST-Index results:
ST-Index ⫽ C50 (1 ⫹ s)

[11]

where C50 and s can be computed as regression constants,
or approximated by a visual inspection of the response
data. The shape of the function for salinity levels greaterthan C50 is not included in this index.
MATERIALS AND METHODS
The crop-yield response data selected for comparing thefunctional effects to root-zone salinity on crops were obtained
from Canada’s Salt Tolerance Testing Laboratory (Steppuhn
and Wall, 1999). A spring-seeded wheat cultivar, Biggar, wastested for salinity tolerance in an environmentally controlledgreenhouse (Steppuhn and Wall, 1997). Biggar produces flourwith medium protein, medium gluten, and medium kernel
hardness for world trade (DePauw et al., 1991).
The Biggar wheat crop was grown in plastic tanks (0.85-m
diam., 1.0 m deep cylinders) containing washed silica sand(99.8% pure) having an average bulk density of 1.5 Mg m⫺3.
At saturation, the sand has a mean volumetric water content
of 31.3%. In this test, the tanks were flushed four times daily
with a modified Hoagland nutrient solution consisting of 2.0
mM Ca(NO3)2, 2.5 mM KNO3, 0.17 mM KH2PO4, 1.0 mM
MgSO4, 0.05 mM chelated Fe, 0.5 mM NH4NO3, 0.05 mM KCl,
0.023 mM H3BO4, plus trace elements including Mn, Zn, Cu,
Si, and Mo. Solutions were salinized by adding NaCl and
CaCl2 (1:1 by mass) resulting in pH values of 7.5 to 7.9. Eachirrigation continued for five minutes until the sand was completely saturated after which the solutions drained into 612-L
reservoirs for the next irrigation. Water lost by evapotranspiration was replenished weekly or more frequently when thevolume of the solution in the supply reservoir decreased by
3% or more. The electrical conductivity of each solution waschecked initially, weekly, and at harvest.
Eleven treatment solutions were prepared with solution
electrical conductivities targeted at 2, 3, 4, 6, 8, 10, 12, 16, 20,
24, and 28 dS m⫺1. The relative variability in grain yield which
likely would occur in association with each conductivity wasestimated from previous experiments. These estimates divided
by an error tolerance squared and multiplied by an appropriatet-table value squared indicated the treatment replication necessary to maintain accuracy of the planned statistical regressions. The tank arrangement followed a randomized block
design with respect to cultivars, but was modified slightly toeliminate any bias caused by taller plants blocking solar radiation associated with low sun angles. Forty-five Biggar wheat
seeds were sown per tank on 3 Feb. 1993, 40 mm deep into
the sand separated by 80 mm within rows spaced 150 mm
apart. After emergence, populations were thinned to 35 plants
per tank.
The procedure for adding salts to the irrigated solutions

213

in this test approximated that practiced by the U.S. Salinity
Laboratory (L.E. Francois, E.V. Maas, and C.M. Grieve, personal communications). Salts were added gradually, with thefirst third on Day 13 after seeding (plants emerging), the second third on Day 18 (plants showing two leaves), and thefinal third on Day 22 (three leaves showing). Daylengths were
adjusted during the growing period with 475 W sodium lamps
positioned 1.5 m above the sand surfaces to mimic a typicalfield seeding date of 1 May at latitude 50⬚N. Mean temperatures equaled 24⬚C daytime and 18⬚C nighttime. The maximum
daily ambient air temperature ranged from 22 to 26⬚C andthe minimum between 16 and 19⬚C.
The response of the wheat crop to the salinity treatments
at harvest was determined by weighing the oven-dried grain
yield. Yield measurements were averaged and related to ECederived from the electrical conductivities of the test solutions(ECi) by the conventional relationship followed by the U.S.
Salinity Laboratory (Maas, 1990),

ECe ≈ 0.5 ECi[12]This equation assumes that the solutions fill the soil pores tofield capacity and has been substantiated by Janzen and Chang(1988) and Kohut and Dudas (1994).
The optimal value of Ym is determined by substituting Y/Ym
(Eq. [3]) for Yr for each of the response functions tested andestimating Ym by linear or nonlinear least-squares regression
with the data set (van Genuchten, 1983). To ensure a common
initial basis for comparing the six response functions with theBiggar wheat data, Ym was set equal to the yield of the firstdata pair, 307.0 g m⫺2, obtained in the absence of root-zone
salinity. With Ym determined, and Yr (Y/Ym) computed, thedifferent response functions were fitted to the ECe–data totest each model obtaining the associated root mean squareerror, coefficient of determination, and parameter estimates.
Least-square fits were performed by the maximum neighborhood method of Marquardt (1963), which is based on an optimum interpolation between the Taylor series method and themethod of steepest descent (Bates and Watts, 1988; SAS,
1995).
In addition to the Biggar wheat data, the absolute or relative
yields found within 33 other studies from crops grown in increasingly saline rooting media were assessed. R2 values androot mean square errors (RMS errors) associated with applications of the threshold-slope and modified discount equations
to these additional data sets were computed and compared.

RESULTS AND DISCUSSION
The decline in crop yield for Biggar wheat in response
to increasing root-zone salinity corresponds similarly tothe declines reported for spring-sown wheats in fieldsalinity trials conducted by Holm (1983) and McKenzie(1988) during comparable daylengths and temperatures.
Grain yields produced from the wheat grown under low
salinity levels at first deviated only slightly from thenonsaline production (Table 1). As salinity increased,
its incremental effect on yield increased to a maximum
about midway or two-thirds into the response relationship. Thereafter, increasing salinity had a decreasingly
reduced influence on yield. Any one of the functionalplots resulting from the six test equations applied to theBiggar wheat test data could serve as an empirical analog of the relationship (Fig. 1–6). The three-piece linear
function was determined by selecting the first three data
pairs as points within the upper horizontal segment of214

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Reproduced from Crop Science. Published by Crop Science Society of America. All copyrights reserved.

Table 1. Average absolute (Y ) and relative (Yr) spring wheat
grain yields (cv. Biggar) in response to irrigation with salinized solutions.
Target ECi†

Actual ECi

2‡
3
4
6
8
10
12
16
20
24
28

dS m⫺1
1.96
3.11
4.20
6.24
8.12
10.60
12.08
16.34
19.94
24.20
27.60

ECe†

Y

Yr

0.98
1.55
2.10
3.12
4.06
5.30
6.04
8.17
9.97
12.10
13.80

g m⫺ 2
307.0
306.9
282.9
234.9
225.4
170.0
111.0
82.6
64.5
19.9
15.0

1.0
0.999
0.921
0.765
0.734
0.554
0.362
0.269
0.210
0.065
0.049

† ECi, electrical conductivity of the average irrigated test solution;
ECe, approximate equivalent electrical conductivity of saturated soilpaste extract.
‡ Nutrients (1 dS m⫺1) plus background salinity of the hydroponic test
water (1 dS m⫺1), considered nonsaline.

Fig. 2. Modified Weibull response function, Yr ⫽ exp[a(Cb)], applied
to the Biggar spring wheat data.

Fig. 1. Simple linear response function, Yr ⫽ a ⫺ b(C ), applied to
the Biggar spring wheat data.

the function. Other data-pair selections would havegiven different results.
The R2 values from regression analyses using the six
functions ranked from a low of 0.941 for the simple
linear to a high of 0.988 for the modified discount relationship (Table 2). RMS errors ranged from a low of
0.0433 for the discount equation to a high of 0.0940
for the simple linear relationship. On the basis of thestatistics in Table 2, the modified discount function isslightly better than the other nonlinear functions andconsiderably better than the linear models. In addition,
the discount-based function features empirically derived
parameters which represent the biophysical characteristics of mid-yield salinity (C50) and generalize unit decline
in yield with salinity (s). These discount parametersrespectively dictate the position of the functional curve
and the general steepness of the decline along the increasing scale of root-zone salinity. Only the thresholdslope model also features constants which identify biophysical parameters, threshold salinity (Ct), and linear
decline in yield with salinity (b).
Additional R2 and RMS error values, calculated forFig. 3. Bi-exponential response function, Yr ⫽ exp[aC ⫺ b(C2)], applied to the Biggar spring wheat data.

33 other data sets (17 different crops) further demonstrate the greater utility of the modified discount function compared to the threshold-slope function (Table 3).
Thirty-two out of 33 R2 values and 30 out of 33 RMS
errors favor the discount equation. Arithmetic averages
from the 33 comparisons for the threshold-slope linear
model R2 and RMS error equal 0.815 and 0.1276, respectively. For the discount nonlinear model, the averages
equal 0.904 and 0.0705, respectively. The modified-discount response function represents an improvement to
the linear relationship, decreasing the average error by
45% and increasing the model-fit by an 11% average.
The literature offers no theoretical rationale for the
existence of a Ct. Taylor et al. (1991) even argue against
it, stating, “There is no a priori reason to expect therelationship between yield and exposure to a metal ion
to be discontinuous.” It is true that plant species have
evolved various salt-tolerance mechanisms to cope withsaline root zones (Yeo and Flowers, 1984). AcceptanceReproduced from Crop Science. Published by Crop Science Society of America. All copyrights reserved.

STEPPUHN ET AL.: SELECTING A FUNCTION AND INDEX FOR CROP SALINITY TOLERANCE

Fig. 4. Modified Gompertz response function, Yr ⫽ 1 ⫺ exp[a exp(bC)],
applied to the Biggar spring wheat data.

Fig. 5. Three-piece linear (threshold slope) response function; Yr ⫽1.0, Yr ⫽ 1 ⫺ b(C ⫺ Ct), Yr ⫽ 0.0, applied to the Biggar springwheat data.

of the threshold concept in crop-yield response requires
acceptance of the thermodynamic premise that plants
with such mechanisms develop and operate at a constant
growth capacity regardless of the magnitude of the rootzone salt concentration (Soo, 1962). That is, the biological energy utilized to grow and operate salt-tolerance
mechanisms up to Ct is constant and unrelated to crop
yield. A continuous, though small and increasing, cropyield decline at pre-Ct salinity levels would seem tosupport more plausible thermodynamic logic.

215

Fig. 6. Modified discount response function, Yr ⫽ 1/[1 ⫹ (C/C50)exp(sC50)],
applied to the Biggar spring wheat data.

Relating Yr to C/C50 by the modified discount function(Eq. [9]), wherein s, the steepness component, is fixedin values from 0.001 through 0.22 and C50 ⫽ 10 dS m⫺1,
results in an array of response curves with a common
point at C/C50 ⫽ 1.0 (Fig. 7). The change in Yr with aunit change in C/C50 for different values of s is not linear.
Figure 8 shows changes in relative yield as a functionof relative salinity for four unit changes in parameters. The plots in Fig. 8 indicate that a maximum changeof 15% in Yr is associated with a C/C50 value near 0.35
as s varies from 0.001 to 0.069. This maximum change
in Yr decreases with increases in s and with shifts tohigher C/C50 values. If s is constant, an increasing valueof C50 results in relative crop yields (Yr) which differ
depending on the value of C. Three plots of the differences in Yr for three changes in C plotted with increasing
C50 and s ⫽ 0.11 reveal that percentage differences inrelative yield do not exceed 11% of a unit difference inroot-zone salinity and that percentages decrease as C
increases (Fig. 9).
Acceptance of the continuous, discount response
function for crop yield with increasing root-zone salinity
also accepts the threshold-slope function as an approximation. This implies that the parameters of the twofunctions are related and can be derived from relationships based on each other. For example, if Ct and b are
known for any crop, it should be possible to estimate
C50 and s from them. Various methods for deriving C50
and s from Ct and b are explored, and the best procedures for the conversions are selected in the companion

Table 2. Parameters and statistical results from regression analyses of six functions relating relative Biggar wheat yields (Yr) to rootzone salinity (C ⫽ ECe).
Function
Simple Linear
Weibull
Bi-Exponential
Gompertz
Threshold-Slope
Discount

Equation

R2

RMSE

Parameter values

Yr ⫽ a ⫺ b(C )Yr ⫽ exp[a(Cb)]Yr ⫽ exp[aC ⫺ b(C2)]
Yr ⫽ 1 ⫺ exp[a exp(bC)]
Yr ⫽ 1 ⫺ b(C ⫺ Ct)
Yr ⫽ 1/[1 ⫹ (C/C50)exp(sC50)]

0.941
0.984
0.982
0.985
0.966
0.988

0.09398
0.05058
0.053100.048390.07715
0.04328(units omitted)a ⫽ 1.0350
b ⫽ 0.0811
a ⫽ ⫺0.0289
b ⫽ 1.8226
a ⫽ ⫺0.0092
b ⫽ 0.0193
a ⫽ ⫺5.0256
b ⫽ ⫺0.3515
Ct ⫽ 1.5730
b ⫽ 0.1306
C50 ⫽ 5.442
s ⫽ 0.1838

216

CROP SCIENCE, VOL. 45, JANUARY–FEBRUARY 2005

Table 3. Resulting coefficient-of-determination (R2) and root-mean-square-error (RMSE) values derived from threshold-slope andmodified-discount response functions for product yields with increasing root-zone salinity in tested agricultural crops.
ECe
Test crop

Reproduced from Crop Science. Published by Crop Science Society of America. All copyrights reserved.

Cultivar
Alfalfa (Medicago sativa L.; M. falcata L.)
BeaverRangelander
Calif. common
Barley (Hordeum vulgare L.)
Bonanza
Bonanza
BridgeBridgeHarrington
Harrington
Canola (Brassica napus L.)
Hyola 401‡
Hyola 401§
InVigor2573§
Quantum‡
Carrot (Daucus carota L.)
Early French
Foxtail, meadow (Alopecurus pratensis L.)
unknown
Harding-grass (Phalaris tuberosa L.)
Stenoptera
Rye, fall (Secale cereale L.)
Bonel
Ryegrass, perennial (Lolium perenne L.)
unknown
Sorghum [Sorghum bicolor (L.) Moench]NK-265
Sugarbeet (Beta vulgaris L.)
unknown
Tomato [Lycopersicon lycopersicum (L.) Karsten]
unknown
Turnip (Brassica rapa L.)
Purple-top
Wheat, durum (Triticum turgidum L. var. durum Desf.)
Kyle
Wheat, spring (Triticum aestivum L.)
Neepawa
BiggarKatepwa
Fielder
Wheatgrass, green (Elymus hoffmannii Jensen & Asay)
Saltlander§
Saltlander‡
Wheatgrass (Elymus hoffmannii Jensen & Asay)
NewHy
Wheatgrass, tall [⫽Thinopyron ponticum (Podp.)
Liu & Wang]
Orbit§
Orbit‡

Response function(dS m⫺1)

Threshold-slope
2

Discount

RMSE

R

2

RMSE

Min–Max

N

R

Data source

0.7–14
0.7–14
2–18

8
8
4

0.930
0.866
0.957

0.11870.16290.0626

0.972
0.997
0.964

0.07460.02330.0577

Steppuhn et al., 1999
Steppuhn et al., 1999
Brown and Hayward, 1956

0.75–19
0.75–18
0.75–19
0.75–18
0.75–19
0.5–16

15
12
15
12
15
7

0.867
0.924
0.944
0.935
0.832
0.944

0.11360.10530.07580.09880.0996
0.0992

0.972
0.968
0.975
0.938
0.951
0.976

0.05220.06850.0504
0.09680.05380.0650†STTL, 1990
Steppuhn, 1993
STTL, 1990
Steppuhn, 1993
STTL, 1990
Steppuhn et al., 2004

0.5–16
0.75–14
0.75–14
0.5–16

7
7
7
7

0.911
0.946
0.894
0.946

0.14180.09500.14620.1023

0.955
0.950
0.988
0.938

0.10100.09210.04970.1096

Steppuhn et al., 2002
Steppuhn et al., 2002
Steppuhn et al., 2002
Steppuhn et al., 2002

0.625–7.5

12

0.795

0.16690.978

0.0546

Magistad et al., 1943; Osawa, 1965

1–14.58

0.958

0.07180.997

0.0188

Brown and Bernstein, 1953

0.8–13.78

0.895

0.08820.970

0.0472

Brown and Bernstein, 1953

5.8–15.9

6

0.527

0.16530.604

0.1448

Francois et al., 1989

1–13.780.742

0.14080.774

0.1293

Brown and Bernstein, 1953

3–12.412

0.905

0.12020.972

0.0670Francois et al., 1984

0.95–10.3

7

0.615

0.10180.665

0.1030Bower et al., 1954

1–14

6

0.808

0.16460.982

0.0499Osawa, 1965

0.9–8.3

4

0.989

0.03600.998

0.0139Francois, 1984

1–9

10

0.781

0.180

0.965

0.040

Steppuhn et al., 1996

1–14
1–14
1–14
1–14

12
12
10
10

0.775
0.692
0.754
0.717

0.100
0.170
0.200
0.230

0.953
0.934
0.890
0.730

0.040
0.060
0.100
0.260

Steppuhn et al., 1996
Steppuhn et al., 1996
Steppuhn et al., 1996
Steppuhn et al., 1996

0.75–25
0.75–24

8
9

0.824
0.799

0.17980.1988

0.961
0.985

0.08490.0546

Steppuhn and Asay, 2004
Steppuhn and Asay, 2004

0.75–2490.700

0.18800.985

0.0414

Steppuhn and Asay, 2004

0.75–25
0.75–24

8
9

0.912
0.810

0.11630.1699

0.970
0.979

0.0677
0.0562

Steppuhn and Asay, 2004
Steppuhn and Asay, 2004

† STTL, unpublished data, Canada’s Salinity Tolerance Testing Lab.
‡ Predominately chloride salts.
§ Predominately sulfate salts.

paper (Steppuhn et al., 2005). Converted values for the
discount parameters determined in the companion paper serve as comparisons and are shown in this paper
as examples for a field, forage, and vegetable crop (Table 4).
As briefly reviewed in this study, many factors influence the yield of agricultural crops besides exposure toincreasing root-zone salinity. Consequently, the singlevalue, Salinity Tolerance Index would seem more appropriate for comparing agricultural crops than any ofthe dual parameters of any of the response functions.
The index is based on the nonlinear parameters of C50
and s (Eq. [11]). The ST-Index identifies a salinity value
equal to the 50% reduction in crop yield from that of

the nonsaline yield plus a measure of the tendency tomaintain some product yield as the crop is subjected tosalinity levels less than but approaching C50:
ST-Index ⫽ C50 ⫹ s(C50)[13]

The ST-Index for the Biggar wheat test data equals
6.44, which ranks it less tolerant of salinity than alfalfa,
more tolerant than radish, and about equal to that offield corn (Table 4). The three ST-Index values in Table 4 reflect rankings based on the ambient conditionsof the response tests for the three representative crops
and a conversion of linear to nonlinear functional parameters using the procedures detailed in the companion paper (Steppuhn et al., 2005).

217

STEPPUHN ET AL.: SELECTING A FUNCTION AND INDEX FOR CROP SALINITY TOLERANCE

Table 4. Nonlinear discount parameters and the Salinity Tolerance Index (STI) derived from linear threshold-slope parameters by the conversion methods detailed in the companion paper(Steppuhn et al., 2005).
LinearCropb†Nonlinear
C t‡

Reproduced from Crop Science. Published by Crop Science Society of America. All copyrights reserved.

(dS m⫺1)⫺1
Corn
Alfalfa
Radish

0.120
0.073
0.130

C50§
dS m⫺1

1.70
2.00
1.20

5.54
8.49
4.73

s¶

STI

(dS m⫺1)⫺1
0.183
0.111
0.198

6.56
9.43
5.67

† b, Absolute value of the linear regression slope parameter.
‡ Ct, “Threshold” salinity parameter.
§ C50, Salinity where crop yield equals 50% of the nonsaline yield.
¶ s, Absolute value of the nonlinear steepness parameter

Fig. 7. Relative crop yield from the modified discount function, Yr ⫽1/[1⫹(C/C50)exp(sC50)], with relative root-zone salinity for C50 ⫽ 10 dSm⫺1 and a wide range of values for s.

Fig. 9. Differences in relative crop yield (Yr) derived from the modified discount function with increasing C50–salinity and constant s(s ⫽ 0.11) for three sets of changes in root-zone salinity (C ) from
1 to 10, 5 to 15, and 10 to 20 dS m⫺1.

Fig. 8. Change in relative crop yield (䉭Yr) as a function of relativeroot-zone salinity (C/C50) for four unit changes in parameter (s)using the modified discount function.

serve to rate agricultural crop tolerance to rootzone salinity [ST-Index ⫽ C50 ⫹ s(C50)].
2. Of the six response functions applied to data fromthe spring-wheat cultivar Biggar, the modified-discount, sigmoidal-shape response function {Yr ⫽1/[1 ⫹ (C/C50)exp(sC )]} gave the lowest root meansquare error and the highest R2 value.
3. The modified-discount, nonlinear relationship compared to the threshold-slope linear model for product yield-salinity response data in 33 separate trials(17 crops) averaged 11% closer in statistical fit and
45% lower in statistical error.
4. From sensitivity analyses, a maximum change of
15% or less in relative yield resulted from a 100%change in s or C50 of the modified discount function.
5. The availability of nonlinear regression software
makes it unnecessary to approximate nonlinear sigmoidal response parameters with parameters derived from linear functions.
6. Various procedures for converting the linear parameters of threshold salinity (Ct) and slope (b)into the nonlinear parameters of the salinity at 50%
yield reduction (C50) and the central unit decline
in relative yield with salinity (s) are explored fora large array of agricultural crops in the companion
paper (Steppuhn et al., 2005).
50

CONCLUSIONS
Relative crop yield has evolved as the primary indicator of agricultural crop tolerance or resistance to rootzone salinity. Experimental data to evaluate the relative
tolerance of crops to salinity require yield response functions which account for the high degree of variability
associated with testing for crop yields and include responses from factors other than salinity. With an aim
to compare various yield functions to suggest a generalempirical response and index which most closely reflect
the general agricultural crop response to root-zone salinity, this study has led to the following conclusions.
1. A comparative salinity tolerance index (ST-Index),
based on the nonlinear (modified-discount) regression parameters of C50 (the salinity level associatedwith a 50% yield of the relative nonsaline, crop
production) and s (the absolute steepness of thegeneral relative yield decline with salinity), can218

CROP SCIENCE, VOL. 45, JANUARY–FEBRUARY 2005

ACKNOWLEDGMENTS
With thanks, the authors acknowledge the valuable contributions of Mr. K.G. Wall, Mr. K.W. Deobald, Dr. Y.W. Jame,
Dr. S. Yang-Steppuhn, and staff members of the George E.
Brown, Jr. Salinity Laboratory and the Semiarid Prairie Agricultural Research Centre to this research.

Reproduced from Crop Science. Published by Crop Science Society of America. All copyrights reserved.

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