Post on 08-Jan-2023
A simple model for chickpea growth and yield
A. Soltani*, K. Ghassemi-Golezani, F.R. Khooie, M. Moghaddam
Department of Agronomy, Faculty of Agriculture, University of Tabriz, Tabriz, Iran
Accepted 18 February 1999
Abstract
Chickpea (Cicer arietinum L.) is a major crop in cool and cold semi-arid environments of Iran, where yield is limited by
climatic factors, water availability and genotype. A robust crop model can assist in evaluation of biophysical limitations in
crop yield. The objective of this study was, therefore, to develop a simple mechanistic model for chickpea to be used in
assessing production limitations. The model simulates crop phenology, development of leaves as a function of temperature,
accumulation of crop biomass as a function of intercepted radiation, dry matter accumulation of grains as a function of time
and temperature, and soil water balance. Phenology, leaf growth and senescence and biomass production were made sensitive
to soil water content. The model uses a daily time step and readily available weather and soil information. The model was
tested using independent data from a range of Iran's environmental conditions. In most cases, simulated grain yield were
similar to observed yield and ranged from 0.4 to 3.25 t/ha. The root mean square error was 0.24 t/ha. The agreement between
simulated and observed grain yields showed the robustness of the model in predicting chickpea growth and yield for both
irrigated and rainfed conditions. It was concluded that the model can be used in simulation studies of potential yield and
production limitations. # 1999 Elsevier Science B.V. All rights reserved.
Keywords: Chickpea; Crop modeling; Crop physiology; Grain yield; Simulation; Water balance
1. Introduction
Chickpea is one of the major pulse crops throughout
the world. It is cultivated on a large scale in arid and
semiarid environments, and has considerable impor-
tance as food, feed and fodder (Singh, 1997). In Iran
the climate of the chickpea producing area is largely
cool and cold semi-arid with a high variability in
rainfall. Chickpea cultivars used in Iran have been
subjected to little breeding work, and consequently,
chickpea yield in Iran is limited by climatic factors,
water availability and genotype.
Biophysical limitations in crop yield at any location
can be assessed by coupling a crop simulation model
to long-term sequences of weather data and generating
probability distributions of simulated yield. Simple
models that are easy to interpret and use have been
developed and utilized successfully for examining
yield potential and yield limitations. A simple and
robust crop model for soybean was developed by
Sinclair (1986) using a phenomenological and phy-
siological framework. This modeling approach has
been generalized and used to examine yield potential
and production risks in other species, such as cowpea
and black-gram (Sinclair et al., 1987), spring wheat
(Amir and Sinclair, 1991), maize (Muchow and
Field Crops Research 62 (1999) 213±224
*Corresponding author.
0378-4290/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 9 0 ( 9 9 ) 0 0 0 1 7 - 9
Sinclair, 1991), sorghum (Hammer and Muchow,
1994), and peanut (Hammer et al., 1995). This is an
alternative approach to complex models that include a
large number of assumptions and parameters and
require large amounts of information about the soil/
crop system. The complexities in specifying inputs
and in interpreting how the model works make it
dif®cult to use in examining yield potential and pro-
duction risks. The recently developed chickpea model
of Singh and Virmani (1996) can be considered as a
complex model.
The objective of this study was to develop a simple
mechanistic model of chickpea growth and yield.
Objectives for the model are to examine yield poten-
tial and production limitations. To do this, we started
with a simple modeling framework and adapted
it for the chickpea. The model describes phenology,
crop leaf area dynamic, biomass production and
yield formation of the crop from sowing to physiolo-
gical maturity. Since the responses of leaf growth
and transpiration (photosynthesis) rate to soil drying
are important components of the model an experi-
ment was conducted to develop the necessary relation-
ships.
2. Model development
Functional relations were derived for model com-
ponents from experimental data collected in ®eld
studies in Iran (Table 1) and from a glasshouse experi-
ment conducted as a part of this study. For the ®eld
experiments, data which were affected by diseases,
pests, or nutrients de®ciencies were not used in devel-
oping relationships for the model. Most of the data
were available for local cultivars Jam (kabuli type) and
Kaka (desi type). When it was required, statistical
analysis was performed using SAS (SAS, 1989).
Shiraz and Gorgan have mild winters so chickpea is
sown in autumn, but since other locations presented in
Table 1 have cold winters chickpea is sown in spring.
In Iran major chickpea producing areas have cold
winters. Table 2 shows monthly means of maximum
and minimum temperatures and rainfall for Tabriz and
Gorgan.
2.1. Glasshouse experiment
The response of transpiration and leaf area devel-
opment to various degrees of soil drying were deter-
mined from a pot experiment similar to that conducted
on soybean by Sinclair and Ludlow (1986) and on ®eld
pea by Lecoeur and Sinclair (1996). Chickpea culti-
vars Jam and Kaka were grown in 5 l pots. For each
cultivar, 30 pots were ®lled with a potting mix. All the
pots were well-watered and supplied with a complete
nutrient solution until 8±9 leaves were fully expanded.
The soil surface was covered with 80 g of medium-
sized perlite to prevent direct soil evaporation. Water-
ing treatments identical to those described by Lecoeur
Table 1
Experiments used to derive data sets for chickpea model development or testing
Location and years Latitude Treatments References
Gorgan, 36.858N Cultivar Anonymous,
Isfahan, 32.628N Time of planting 1971±1977
Karaj, 35.938N Plant density
Mashhad, 36.278N Water
Oroomeih, 37.538N Fertilizer
Shiraz, 29.558NTabriz, 38.138NVaramin, and 35.328NYasuj 1970±1976 31.238NGorgan 1996 36.858N Cultivar (growth analysis) M.R. Rahimi, unpubl. data
Tabriz 1994 38.138N Cultivar, time of planting, plant density Mohammadi, 1995
Tabriz 1994 38.138N Plant density harvest date Tabatabaian, 1995
Tabriz 1995 38.138N Cultivar (growth analysis) F. Shekari, unpubl. data
Tabriz 1995±1996 38.138N Cultivar (grain and growth analysis) K. Ghassemi-Golezani unpubl. data
Tabriz 1995 38.138N Cultivar, plant density, water (growth analysis) Movahhedi, 1996
214 A. Soltani et al. / Field Crops Research 62 (1999) 213±224
and Sinclair (1996) were then imposed. Each pot was
weighted daily and the area of the expanding leaves
was measured. Leaf area development and transpira-
tion rates of plants in drying pots were expressed
relative to those of plants in well-watered pots.
The relative rates of both transpiration and leaf area
development were expressed as functions of fraction
transpirable soil water (FTSW). To calculate FTSW in
these experiments, total transpirable soil water was
calculated as the weight difference between the initial
weight of each pot after it had been watered and
allowed to drain, and the weight when the daily
transpiration rate decreased to less than 10% that of
well-watered plants. The FTSW was calculated each
day as a fraction of the transpirable soil water still
remained in the pot.
2.2. Model components
Relatively few conservative relationships devel-
oped from a mechanistic perspective are required in
this model to describe the development, growth and
yield of chickpea. The major processes simulated are
crop phenology, development of leaves as a function
of temperature and drought stress, accumulation of
crop biomass as a function of intercepted radiation and
radiation use ef®ciency modi®ed for temperature and
water de®cit stresses, dry-matter accumulation in
grains as a function of time, temperature and water,
and soil water balance (Sinclair, 1994).
2.2.1. Phenology
Phenological stages may be input directly or may be
predicted by the model. The starting time of linear
seed growth and the time of physiological maturity are
required for calculations in the model. Phenology of
chick-pea is controlled by temperature, day length
(before ¯owering) and water de®cit stress (Roberts et
al., 1980; Summer®eld et al., 1980; Siddique and
Sedgley, 1986; Singh, 1991; Silim and Saxena,
1993). Examination of data from experiments listed
in Table 1 using the procedures outlined by Summer-
®eld et al. (1991) and Sinclair et al. (1991) showed that
under conditions of Iran, phenology of chickpea is
mainly controlled by temperature, and the inclusion of
day length did not reduce the coef®cient of variation or
increase coef®cient of determination of prediction,
because of long day lengths during growing seasons
of chickpea. Hence, thermal time concept was used to
quantifying phenological stages, with a base tempera-
ture (Tb) of 08C (Covell et al., 1986; Ellis et al., 1986;
Siddique and Sedgley, 1986) as:
DTT � 0 if T < Tb
DTT � T ÿ Tb if T > Tb(1)
where DTT is thermal time each day (8C) and T is
average daily temperature. Thermal time (TT) was
calculated by accumulating DTT after sowing. Taba-
tabaian (1995), Ghassemi-Golezani (unpubl. data) and
Rahimi (unpubl. data) examined changes of grain
weight after ¯owering. We ®tted a broken-linear
Table 2
Monthly means of maximum (TMAX) and minimum (TMIN) temperatures and rainfall (RAIN) for Tabriz and Gorgan
Month Tabriz Gorgan
TMAX (8C) TMIN (8C) RAIN (mm) TMAX (8C) TMIN (8C) RAIN (mm)
January 7.7 ÿ6.3 23.5 12.2 2.8 46.2
February 8.4 ÿ4.5 21.7 12.0 2.8 60.7
March 11.2 0.2 41.2 14.6 5.3 70.6
April 16.9 6.0 50.3 21.7 9.9 42.1
May 22.2 10.6 44.0 26.2 14.4 38.5
June 28.4 15.2 18.9 31.4 19.6 16.8
July 32.7 19.5 3.7 32.4 22.8 10.8
August 32.2 19.1 3.5 31.7 22.4 36.8
September 28.2 14.4 8.5 29.7 18.9 33.5
October 20.2 8.1 23.6 24.6 12.8 46.3
November 12.7 2.2 29.3 18.9 8.4 52.5
December 8.2 ÿ3.0 26.9 13.6 4.1 56.0
19.1 6.8 295.1 22.4 12.0 510.8
A. Soltani et al. / Field Crops Research 62 (1999) 213±224 215
model to their data using PROC NLIN (method DUD)
of SAS (SAS, 1989). The broken-linear model con-
sists of two intersecting lines, a sloping line for an
assumed linear seed growth and a horizontal line
which represents seed weight at maturity. The starting
time of grain growth was determined by extrapolating
the ®tted line (sloping) back to time axis (zero grain
growth), and the time of physiological maturity was
taken as the intersection time of the broken-linear
model, i.e., ®rst time when grain reaches its maximum
weight. Then, thermal times for the start of linear
growth of grain and physiological maturity were
calculated as 1350 and 2100 for Jam and 1300 and
2000 for Kaka, respectively. Drought stress in chick-
pea hastens development, which is proportional to the
amount of stress experienced by the crop (Singh,
1991; Silim and Saxena, 1993). We assumed that
water-de®cit stress has no effect on phenological
development when it is not limiting for dry matter
production (i.e. RT � 1). Thereafter, increasing water
de®cit stress, accelerates phenological development,
but not more than 50% of that determined by tem-
perature. Eq. (3) describes such a response and was
used to quantify the hastening of phenological devel-
opment as soil water became limiting:
DTT � DTT�WSCFDS (2)
WSCFDS � 1:5ÿ 0:5� RT (3)
where WSCFDS is water stress correction factor for
development and senescense and RT is relative tran-
spiration as de®ned by Eq. (11). Eq. (3) signi®cantly
improved model predictions under rainfed conditions.
More experiments, however, are necessary to re®ne
this equation.
2.2.2. Crop leaf area
Prediction of leaf area index (LAI) was required to
estimate interception of radiation and biomass pro-
duction. It was calculated as the product of green leaf
area per plant (GPLA) and plant density. GPLA was
calculated as the difference between total plant leaf
area (TPLA) and senescent plant leaf area (SPLA)
using procedures outlined by Chapman et al. (1993)
and Hammer and Muchow (1994) (Eqs. (4)±(6);
Fig. 1):
GPLA � TPLAÿ SPLA (4)
Fig. 1. Predicted change in green leaf area per plant (GPLA, dashed line) of chickpea calculated from relationships between TPLA (solid
line), SPLA (dotted line) and TT from sowing. MXTPLA for this example is 1015 (cv. Jam), other parameters as presented in the text. (This
example calculated from the data of Movahhedi, 1996).
216 A. Soltani et al. / Field Crops Research 62 (1999) 213±224
TPLA � MXTPLA
�1� EXP�ÿA1� �TTÿ B1��� (5)
SPLA � MXTPLA
�1� EXP�ÿA2� �TTÿ B2��� (6)
where MXTPLA is maximum total plant leaf area
(cm2), and A1, B1, A2, and B2 are ®tted coef®cients.
Examining the data of Table 1 resulted in 0.0082, 900,
0.0119 and 1700 values for A1, B1, A2 and B2,
respectively for cultivars Jam, Kaka, Pyrooz, and
Koorosh. The value of MXTPLA was more variable
between cultivars, but the parameter is linearly related
to thermal time between sowing and maturity of
cultivars (data not shown). The effect of plant density
(PD) on TPLA was considered via a density multiplier
(PDFAC), which derived from plant density experi-
ments of Table 1 (Fig. 2):
PDFAC � EXP�0:31ÿ 0:0117� PD� (7)
The value of MXTPLA is decreased at plant densities
greater than 26.5 plants mÿ2.
Leaf area development is restricted when soil
water becomes limiting. The response to soil drying
was obtained from the glasshouse experiment pre-
sented in Fig. 3, which shows the relationship between
relative leaf growth(RL) and FTSW. The logistic
function (Eq. (8)) was used to quantify the reduction
in leaf area development as soil water became limit-
ing:
RL � 2
�1� EXP�ÿ6:5� �FTSWÿ 0:058��� ÿ 1
(8)
Also, the effect of water limitation on leaf area
senescence was quanti®ed using a multiplier
(WSCFDS; Eq. (3)), which multiplied to dSPLA/dt.
2.2.3. Daily biomass production
Daily increase in total above ground biomass (DBP)
is required to predict grain yield (Eqs. (12)±(16)). It
was estimated (Eq. (9)) as the product of incident solar
radiation (SR, MJ/m2/day), the fraction of that radia-
tion intercepted by the crop (FINT) and the ef®ciency
with which the intercepted radiation was used to
produce biomass (RUE, g/MJ). The quantity FINT
was determined (Eq. (10)) from an exponential func-
tion of crop LAI:
DBP � SR� FINT� RUE (9)
FINT � 1ÿ EXP�ÿK � LAI� (10)
where K is the extinction coef®cient of the canopy.
Fig. 2. Effect of plant density on relative MXTPLA. Symbols show different experiments. (Calculated from the data of Mohammadi, 1995;
Tabatabaian, 1995; Movahhedi, 1996).
A. Soltani et al. / Field Crops Research 62 (1999) 213±224 217
Hughes et al. (1987) reported that K was 0.61 for a
line with prostrate growth habit and 0.47 for a line with
erect growth habit. In this model K was set at 0.5 for
semi-erect local cultivars. The value of RUE was set at
0.95 g/MJ, which was observed by Hughes et al.
(1987) for chickpea and also calculated using Sinclair
(1991) method with a light ef®ciency of 5 mgCO2/kJ
(Ehleringer and Bjorkman, 1977) and a light-saturated
leaf CO2 assimilation rate of 0.8 mgCO2/m2/s (cali-
brated using crop growth rate data of Movahhedi,
1996). When grains began to grow, a RUE value of
0.70 was used to allow for effect of mobilization of
leaf N to grain (Sinclair and de Wit, 1976). The cool
temperatures to which the chickpea is subjected would
inhibit photosynthetic activity. The value of RUE was
modi®ed by the average daily temperature according
to the response of dry matter production to tempera-
ture (Saxena, 1984; Khana-Chopra and Sinha, 1987).
This effect was incorporated by multiplying RUE by a
scaling factor that had a value of 1 at 158C, but
declined linearly to 0 at 08C. A similar approach
was used by Chapman et al. (1993) and Hammer
and Muchow (1994) in their sun¯ower and sorghum
models. During the growing season of chickpea in Iran
high temperatures that may limit the photosynthesis of
chickpea (above 348C, Singh and Virmani, 1996)
rarely occur. Thus, the effect of high temperature
on RUE was ignored.
The photosynthesis rate also falls due to stomatal
closure associated with water limitation. The response
to soil drying was obtained from the glasshouse
experiment presented in Fig. 4, showing the relation-
ship between relative transpiration (RT) and FTSW.
The logistic function that quanti®es the response
(Eq. (11)) was used to reduce RUE as soil water
became limiting:
RT � 2
�1� EXP�ÿ7:5� FTSW�� ÿ 1 (11)
2.2.4. Grain yield
During grain ®lling, grain dry matter (GDM) may
be considered as the product of total above ground
vegetative dry matter (VDM) and harvest index (HI).
Speath and Sinclair (1985) reported that the HI of
soybean increased linearly with time throughout grain
®lling. Grain growth can then be de®ned as a function
of the rate of HI increase(DHI) and the date of onset of
the increase in HI. This approach implicitly combines
the contribution of current and stored assimilate to
grain. In the case of chickpea, progression in HI during
grain growth has not been reported, but calculation of
Fig. 3. Relative leaf growth rate (RL) versus FTSW for chickpea plants in pots filled with potting mix.
218 A. Soltani et al. / Field Crops Research 62 (1999) 213±224
HI from published data indicates that a linear response
also exists in chickpea (Saxena, 1984; Khana-Chopra
and Sinha, 1987; Saxena, 1987; Singh, 1991; Singh
and Virmani, 1996). Field data of Rahimi (unpubl.
data, Table 1) during grain growth provided direct
evidence for the linear increase in HI during seed
growth (Fig. 5). The rate of increase in HI was
0.01 dayÿ1 for the cultivars Jam and Kaka.
Grain growth for each day(GGR) is calculated as:
HI�t� � HI�t ÿ 1� � DHI (12)
GGR � VDM�t ÿ 1� � HI�t�1ÿ HI�t� ÿ GDM�t ÿ 1�
(13)
where VDM(tÿ1) is VDM on day tÿ1. Therefore, the
values of GDM and VDM on day t are given by:
GDM�t� � GDM�t ÿ 1� � GGR (14)
VDM�t� � VDM�t ÿ 1� � DBPÿ �GGR� GCF�(15)
TDM�t� � VDM�t� � GDM�t� (16)
where DBP is the daily biomass production(g/m2/day)
and GCF is grain conversion factor which allow for the
energy content difference between the two types of
tissue (VDM and GDM). We assumed GCF equal to 1
for chickpea due to similar chemical composition of
grain and vegetative tissues. Grain growth rate is
calculated with an hourly time step which eliminates
the numerical oscillations observed with the daily time
step (Sinclair, 1986).
Under conditions of severe water limitation during
grain ®lling HI ceased to increase (Siddique and
Sedgley, 1986; references presented in Table 1). This
effect was modelled by stopping the linear increase in
HI if FTSW was below 0.1 and HI exceeded 0.2 in
similar manner to that set out for sun¯ower by Chap-
man et al. (1993), for sorghum by Hammer and
Muchow (1994). This allowed for maximum mobili-
zation of stored assimilate in the absence of signi®cant
current assimilation capacity.
2.2.5. Water balance
Soil water content is required to calculate the degree
of water limitation experienced by the crop (FTSW),
which affects biomass accumulation, leaf area produc-
tion and senescence and phenological development.
Hence, a soil water balance similar to that described
by Amir and Sinclair (1991) was used. This soil water
balance accounted for additions from in®ltration (I)
and losses from soil evaporation (E), transpiration (T)
Fig. 4. RT versus FTSW for chickpea plants in pots filled with potting mix.
A. Soltani et al. / Field Crops Research 62 (1999) 213±224 219
and drainage (D):
ATSW�t� � ATSW�t ÿ 1� � I ÿ E ÿ T ÿ D (17)
I � PRÿ R (18)
FTSW � ATSW
TTSW(19)
where ATSW is actual transpirable soil water, PR is
rainfall, R is run-off and TTSW is total transpirable
soil water.
TTSW in the pro®le was calculated from the effec-
tive depth of water extraction and the volumetric
fraction of extractable soil water, both of which must
be input to model. Amount of ATSW stored in the
pro®le at sowing must also be speci®ed. Daily in®l-
tration is added to ATSW until TTSW is exceed by
4 mm. Any water input beyond this limit is assumed
lost as drainage.
In®ltration was calculated from daily rainfall less
any run-off. We estimated run-off using the curve
number technique (Knisel, 1980). Curve numbers
are assigned to various soils depending on their texture
and condition and then modi®ed to take account of
standing crop cover and soil water content.
Soil evaporation was calculated using the two-stage
model as implemented in the spring wheat model
developed by Amir and Sinclair (1991). Stage I eva-
poration occurred when water was present in the top
200 mm of soil and FTSW for the total pro®le was
greater than 0.5. Evaporation rate was calculated from
the modi®ed Penman equation (Amir and Sinclair,
1991) and was based on the solar radiation which
penetrates the crop canopy. Stage II evaporation
occurred when the water in the top layer was
exhausted or the FTSW for the total soil pro®le was
less than 0.5. In Stage II, the potential rate of soil
evaporation was also calculated from a modi®ed Pen-
man equation, but it was decreased substantially as a
function of the square root of time since the start of
Stage II. The calculation of soil evaporation returned
to Stage I only when rain or irrigation of greater than
10 mm occurred.
To complete the calculation of the soil water budget,
daily transpiration rate was determined. Tanner and
Sinclair (1983) and Sinclair (1994) showed that the
rate of crop biomass accumulation to transpiration is
equal to a transpiration ef®ciency coef®cient divided
by a daily vapor pressure de®cit. Therefore, the daily
transpiration rate (TR) was calculated directly from
the daily rate of biomass production (DBP), transpira-
tion ef®ciency coef®cient (TECOE) and vapor pres-
sure de®cit (VPD) as:
Fig. 5. Harvest index (ratio of seed biomass to total crop biomass) versus days after sowing for Jam cultivar (Rahimi, M.R., unpubl. data).
220 A. Soltani et al. / Field Crops Research 62 (1999) 213±224
TR � DBP � VPD
TECOE(20)
The TECOE for chickpea was calculated as 0.05 mbar
(5 Pa), using procedures outlined by Tanner and Sin-
clair (1983) and Sinclair (1994). The calculation of
VPD was suggested by Tanner and Sinclair (1983) to
be approximately 0.75 of the difference between
saturated vapor pressure calculated from daily max-
imum and minimum temperatures. It was assumed that
transpiration occurred preferentially from the top soil
layer and that the relative rate of transpirational water
Fig. 6. Simulated versus observed (a) LAI throughout the season, (b) final aerial biomass, (c) grain yield at maturity for experiments on Jam
and Kaka cultivars used in developing of the model relations, and (d) grain yield at maturity based on independent data. The soild line is 1 : 1
line.
A. Soltani et al. / Field Crops Research 62 (1999) 213±224 221
loss from the top layer (TR1) is de®ned by
TR1 � TR� RT1 (21)
where RT1 is RT calculated using FTSW of the
top layer. Consequently, as the top layer dries less
of the transpirational water is derived from the top
layer.
3. Model testing
The model was tested by comparing simulated
outcomes with those observed in a range of experi-
ments that covered conditions in Iran's cool and cold
semi-arid environments. Initially, the capability of the
model to simulate crop growth and yield was tested
Fig. 6 (Continued ).
222 A. Soltani et al. / Field Crops Research 62 (1999) 213±224
against the experiments used in developing some of
the relationships used to quantify component pro-
cesses in the model. Subsequently, data from fully
independent experiments were used (Anonymous,
1971, 1972, 1973, 1974, 1975, 1976, 1977; F. Shekari
(unpubl. data)). To simulate these crops the relevant
input requirements were collected. Actual maximum
and minimum temperatures, rainfall and solar radia-
tion (derived from sunshine hours) were available for
each experiment. Date of planting and plant density
were input from known values for each experiment,
and soil water attributes were derived from measure-
ments or from the known values for similar soil types.
The relevant thermal time requirements for phenolo-
gical stages, DHI and MXTPLA were speci®ed
depending on the cultivar. The general parameters
in the model (e.g. K, RUE, TECOE, etc) were set
to the values speci®ed in the text.
Model predictions for LAI, ®nal aerial biomass and
grain yield (Table 1) were similar to observed quan-
tities (Fig. 6). LAI was predicted with a regression
slope of slightly less than one (Fig. 6(a)), which
explained 87% of observed variations. The RMSE-
(root mean square error) for predictions of LAI was
0.39. The simulated-observed relationships for ®nal
aerial biomass (Fig. 6(b)) and grain yield (Fig. 6(c))
were satisfactory over much of the observed range
(RMSE biomass � 0.59 t/ha, RMSE grain yield �0.32 t/ha).
For independent data, observed grain yield varied
between 0.4 and 3.25 t/ha and simulated grain yield
between 0.3 and 3.5 t/ha. Mean observed and simu-
lated grain yields were 1.59 and 1.66 t/ha, respec-
tively. Fig. 6(d) illustrates the scatter of simulated and
observed grain yields around the 1 : 1 line. In most
cases, simulated grain yield were similar to observed
yields with a RMSE equal to 0.24 t/ha. The regression
line of simulated yields on observed yields has an
intercept not signi®cantly different from zero
(p � 0.05) and a slope of almost one. The agreement
between simulated and observed grain yields shows
the robustness of the model in predicting crop growth
and yield for Iran's cool and cold semi-arid environ-
ments.
It can be concluded that simple approach in crop
modeling outlined by Sinclair (1986, 1994) is also
applicable to chickpea. The model explained much of
variation in grain yield in the test simulation on
independent data. The inputs required are generally
available, although some coef®cients must be derived
from experimentation. The presented model is suitable
for use in simulation studies of potential yield and
production limitations. This will be presented in
another paper.
Acknowledgements
We are grateful to Dr. T.R. Sinclair, University of
Florida, USA who provided consistent support in
model development and critical comments on the
manuscript.
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