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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