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Test of leaf-area development in CERES-Maize: a correction
Field Crops Research, 27 ( 1991 ) 159-167
159
Elsevier Science Publishers B.V., Amsterdam
Test of leaf-area development in CERES-Maize: a correction P.S. Carberry CS1RO Division of Tropical Cropsand Pastures, PrivateBag, Aitkenvale, Qld. 4814, Australia (Accepted 14 May 1990)
ABSTRACT Carberry, P.S., 1991. Test of leaf-area development in CERES-Maize: a correction. Field Crops Res., 27: 159-167. Routines controlling development of leaf area in the CERES-Maize model have been misinterpreted in recent papers, owing to an inaccuracy in parameter definition in the published documentation of the model. This paper provides the correct description of functions for leaf-area development in CERES-Maize, and tests the performance of these functions. Given the correct definitions of the variables CUMPH, as the cumulative number of visible leaf tips, and XN as the next leaf which will emerge on the plant, CERES-Maize simulates leaf-area expansion per plant as a function of the number of emerged leaf tips. A test of the leaf-canopy routines in CERES-Maize indicated that constants, used in the functions describing both rate of appearance of leaf tips and rate of leaf-area expansion per plant, needed calibration for predicting leaf-area development of the tropically adapted hybrid maize Dekalb XL82.
INTRODUCTION
CERES-Maize is a crop simulation model which simulates the growth, development and grain-yield of a maize (Zea mays L. ) crop, given climatic and cultural inputs. Detailed descriptions of the biological and physical relationships used in CERES-Maize (Jones and Kiniry, 1986 ), and the ready availability of this software and its documentation, have resulted in wide application of the model (de Vos and Mallet, 1987; Hodges et al., 1987; Keating et al., 1988; Carberry et al., 1989; Liu et al., 1989). Carberry et al. (1989) and Muchow and Carberry (1989) have tested and calibrated the leaf-area development functions in CERES-Maize against data collected for a tropically adapted maize cultivar in a semi-arid tropical region. However, recent discussions with the principal developer of CERES-Maize, J.T. Ritchie, have identified an error in parameter definition in the User's Guide (Jones and Kiniry, 1986 ) which can result in misinterpretation of the method by which CERES-Maize simulates leaf-area development. 0378-4290/91/$03.50
© 1991 Elsevier Science Publishers B.V. All rights reserved.
160
P.S. CARBERRY
Based on definitions from Jones and Kiniry ( 1986 ), Carberry et al. ( 1989 ) interpreted the development of leaf area by CERES-Maize as the summation, on a given day, of the lamina area of all leaves that have reached full expansion. In fact, CERES-Maize simulates, not the area of individual leaves but, on a total-plant basis, cumulative leaf area as a function of the appearance of individual leaf tips (J.T. Ritchie, personal communication, 1989). This difference in interpretation is significant, not only in method but also for the mechanistic level at which the model operates, i.e., individual leaf versus whole plant. Ironically, the simulation of leaf-canopy development using individual leaves has shown considerable merit, not only for maize (Carberry et al., 1989; Muchow and Carberry, 1989) but also for sorghum (Muchow and Carberry, 1990). The objectives of this paper are to provide the correct description of functions for leaf-area development in CERES-Maize, and to test the performance of these functions using the same experimental crops that were used for previous tests of the model (Carberry et al., 1989). MATERIALS AND METHODS
Simulation ofleaf-area development From Jones et al. (1986), CERES-Maize calculates, for each day, the cumulative number of fully expanded leaves (CUMPH) from daily thermal time (DTT), such that: CUMPH = CUMPH + D T T / ( 3 8 . 9 .
PC)
(
1)
where: PC = 0.66 + 0.068, CUMPH for CUMPH< 5 and PC = 1.0 for CUMPH> 5.
(2)
Therefore, rate of leaf appearance equals 38.9°C d leaf -1 for leaves greater than 5, but is faster for the first 4 leaves (determined by the variable PC). In the model, half of the first leaf is visible at emergence (CUMPH=0.5). The fraction of a leaf that emerges on a day (TI) is calculated as TI = D T T / ( 3 8 . 9 .
PC)
(3)
Under optimal water conditions, the daily growth of leaf area per plant (PLAG) is calculated as a function of TI and the number of the oldest expanding leaf (XN), where: XN = C U M P H + 1
(4)
This function calculates PLAG for different values of XN (Table 1 ); thus, for XN less than 4.0:
TEST OF LEAF-AREA DEVELOPMENT IN CERES-MAIZE: A CORRECTION
PLAG= 3.0. XN*TI
161
(5)
Total plant leaf area (PLA) is calculated by adding PLAG to the previous day's value of PEA. The value of PLAG is modified under severe water stress, or when assimilate production is insufficient to maintain its potential value (e.g., at high plant densities, because of lack of assimilate supply). As CUMPH is defined in the original documentation as the number of fully expanded leaves (Jones et al., 1986), the rate of 38.9°C d leaf -I was interpreted as the rate of appearance of fully expanded leaves, defined as the appearance of leaf ligules. Also, as the number of emerged leaf tips (LN) always equals XN (i.e. CUMPH + 1 ), then only one leaf is being expanded at any one time by CERES-Maize. If, for instance, one whole leaf is expanded on a day (TI = 1 ), the increment in area (PLAG) that is added to total plant leaf area ( P E A ) must represent the fully expanded lamina area of the expanding leaf (XN). Therefore, given the definitions from Jones and Kiniry ( 1986 ), CERESMaize was interpreted as simulating the rate of appearance of fully expanded leaves and the leaf area of individual leaves. However, the above definitions of CUMPH and XN are erroneous (J.T. Ritchie, personal communication, 1989 ). CUMPH is correctly defined as the cumulative number of leaf tips that have emerged. The correct definition of XN is the newest emerging leaf ( X N = CUMPH + 1 ) and, as such, LN represents its integer value. These correct definitions result in a different interpretation of the functions that describe leaf-area development in CERES-Maize. CERES-Maize thus simulates the appearance of successive leaf tips, and leaf area per plant is simulated as a function of the number of leaf tips that have emerged by a given day. The differential equation of the relationships between total plant leaf area (PEA) TABLE 1 Equations describing leaf-area expansion per plant (PLAG) as functions Of XN for (a) CERES-Maize and (b) fitted regressions to data for the three sowings ( Fig. 3 ) Leaf number (a) CERES-Maize 1-3 4-11 12-(TLNOa--4) > (TLNO-- 3)
(b) Fitted regressions 1-3 4-13 14-(TLNO--2) > (TLNO-- 1 )
Function
PLAG -----3.0. XN PLAG-- 3 . 5 . XN* XN PLAG ~---5 9 5 . 0
PLAG= 595.0/( XN + 5 -- TLNO ) PLAG= 5.55.XN PLAG = 0 . 2 6 1 * X N * X N * X N
PLAG=611.5 PLAG= 611.5-- 104.3. (XN+2--TLNO)
aTLNO is defined as the total number of leaves that the plant produces.
162
P.S.CARBERRY
and XN is approximated in the model by the discontinuous functions describing PLAG in Table 1.
FieM experimentation Data used in this analysis are from the same experiments as described in the analyses of Muchow and Carberry (1989). To summarise, maize was grown under non-limiting nitrogen conditions at Katherine Research Station, Northern Territory, Australia (latitude 14 ° 28'S, longitude 132 ° 18'E, alt. 108 m) at three sowing dates, 10 October 1984, 6 February 1985 and 20 August 1985. There were four replicates at each sowing date. Cultural details were similar for all sowings; and these are fully described by Muchow ( 1989 ). The maize hybrid Dekalb XL82 was grown at 70 000 plants h a - 1under highinput conditions (240 kg N h a - l ; 30 kg P h a - l ) , and weeds, insects and diseases were controlled. The crops were fully irrigated to restore water to field capacity in the soil profile after four rain-free days. Lamina areas of individual leaves were recorded at each sampling date using five representative plants. After thinning ( 10-15 days after sowing), leaf 5 from the base of the plant was tagged. The length and breadth of all leaves, the number of fully expanded leaves and the number of fully expanded green leaves (senescence < 50% area) were recorded for each plant. The area of each leaf was recorded once the leaf tip was visible above the whorl of the preceding leaf. Subsequently, these data were recorded twice weekly until silking. The lamina area of both fully expanded and expanding leaves was calculated as length, breadth. 0.75 (McKee, 1964). The mean area of each leaf was calculated as the mean of those leaves present at each position on the stem, and the mean area per plant was calculated from the five representative plants.
Data analysis Thermal time was calculated with the algorithms of CERES-Maize, using base, optimum and maximum temperatures of 8, 34 and 44°C, respectively (Jones et al., 1986 ). Relationships between leaf-area development, thermal time and leaf number were fitted by least-squares regression. The logistic equation:
Y = M / ( I +exp( - k . ( X - m ) ) )
(6)
where M is the asymptote, and k and m are constants, was fitted to observed total leaf area per plant (Y) versus the number of leaf tips (X), which were predicted from the linear regression of leaf tips against thermal time. Predicted rather than observed number of leaf tips was used in equation 6 as the independent variable, because considerable leaf-area expansion occurred after the observed appearance of the final leaf tip. As there were insufficient ob-
TEST O F LEAF-AREA D E V E L O P M E N T I N CERES-MAIZE: A C O R R E C T I O N
163
served data to fit the discontinuous differential equations o f CERES-Maize (Table 1 ) for rate o f leaf area expansion (PL,4G), PL,4G was determined for cv. Dekalb XL82 from the predicted fits to the logistic regression for each sowing. RESULTS AND DISCUSSION For hybrid maize Dekalb XL82, the observed rate of appearance o f leaf tips was 48.3°C d leaf -~ (Fig. 1), considerably slower than that assumed in CERES-Maize (38.9 ° C d leaf- ~). The assumption of a constant rate of leaf tip appearance among cultivars, although appropriate among some groups of hybrids (Kiniry and Ritchie, 1981 ), was not supported in a study by Tollenaar et al. (1984), who concluded that genotypic variability occurred in leaf appearance in maize. The rate of leaf appearance for Dekalb XL82 was slower than that for any o f the cultivars studied by Kiniry and Ritchie ( 1981 ) or by Tollenaar ¢t al. ( 1984 ). The relationship between observed leaf area per plant (without losses due to senescence ) and predicted n u m b e r o f leaf tips for each o f the three sowings is presented in Fig. 2. The logistic equation adequately fitted the observed data, although there were few observations for low values o f PEA. Differences between sowings were mainly in the m a x i m u m value o f PEA, which was related to the differences in final leaf number. Mean m a x i m u m leaf numbers in the October, February and August sowings were 18.2, 17.5 and 19.2 leaves, respectively ( M u c h o w and Carberry, 1989 ). As shown in Fig. 2, observed PEA increased as the predicted n u m b e r of leaf tips increased above the final leaf-tip n u m b e r observed in each o f the three 20
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Fig. l. Relationship between the number of leaf tips and thermal time from emergence as observed in the October (©), February ( A ) and August ( • ) sowings,and as predicted by CERESMaize ( - - - ). Each point is the mean of observations on 20 plants. The fitted regression line for observed data ( - - ) is Y=2.44+0.020?X, r2=0.95.
164
P.S. CARBERRY 7000 6000
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Number of leaf tips Fig. 2. Relationship between observed total leaf area per plant (PLA; without losses due to senescence) and number of leaf tips (X) predicted from equation in Fig. 1 for the October ( • ) , February ( A ) and August (11) sowings. Each point is the mean of observations on 20 plants. The fitted functions for October, February and August sowings are: (--), PLA=5879/( 1 +exp( --0.440, ( X - 14.15) ) ) r2=0.99; ( .......... ), PEA=5521/(1 +exp(--0.470, ( X - 13.89))) r2=0.99; ( ), PEA=6464/( 1 +exp( - 0 . 3 8 6 , ( X - 14.67) ) ) r2=0.99.
sowings. The use of number of leaf tips as the independent variable in CERESMaize in calculating PLA necessitates the continued prediction of leaf appearance past the limits of observed data. Using the relationship between the appearance of leaves and thermal time (Fig. 1 ), more realistic asymptotic values of leaf area per plant can be achieved by increasing PLA as a function of thermal time after emergence (Muchow and Carberry, 1989). The differential of the logistic function for leaf area per plant and leaf number represents the rate of leaf-area expansion per leaf-appearance interval. In comparison with data from three experimental sowings (Fig. 3), the functions which describe leaf-area expansion in CERES-Maize (Table 1 (a)) overpredict the early rate of expansion and underpredict subsequent development. Not only were coefficients of the functions different for the observed data but, in the range 4-14 leaves, PLAG was better fitted to a cubic function of XN, whereas for the final three leaves, a linear function was the most appropriate (Table 1 (b)). The combined effects of a faster rate of leaf appearance (Fig. 1 ) and the greater rate of early leaf area expansion (Fig. 3) generally resulted in large overpredictions of PLA by CERES-Maize on a given day for all three sowings (Fig. 4). Although timings were not synchronised, maximum leaf areas per plant were little different from those observed. This result explains the adequate predictions of leaf-area index at silking made by the model (Carberry et al., 1989 ). The estimated maximum PLA was attained much earlier than that observed and, because date of silking in CERES-Maize corresponds to end of leaf growth (Jones et al., 1986 ), predicted phenological dates for these
TEST O F LEAF-AREA D E V E L O P M E N T IN CERES-MAIZE: A C O R R E C T I O N
165
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Number of leaf tips Fig. 3. Relationship between leaf area expansion per plant (PLAO)and number of emerged leaf tips for the October ((2)), February ( A ) and August ( • ) sowings and the predictions of CERESMaize: ( - - ) , October; ( ...... ), February; ( - - - ), August; Table 1. Each point is the mean of observations on 20 plants. 8000
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Thermal time from emergence ( °C d) Fig. 4. Comparison of the development of total leaf area per plant (PLA; without losses due to senescence) as observed in the October ( © ) , February (ZX) and August ( • ) sowings, and as predicted by CERES-Maize ( - - - ) and the functions developed in Fig. 1 and Fig. 3 ( - - ) . Each point is the mean of observations on 20 plants.
datasets were consequently underestimated (Carberry et al., 1989 ). The inclusion of the observed rate of leaf appearance in CERES-Maize (48.3 °C d leaf- l into equations 1 and 3 ), and the revised functions for PLAG (Table l ) resulted in significant improvements in the simulations of PEA for the three sowings (Fig. 4). The slight error in the revised simulations resulted from inappropriate values calculated for PC [equation 2 ], which resulted in slight delays in the appearance of the first four leaf tips. Carberry et al. (1989) and Muchow and Carberry (1989) interpreted the leaf-growth functions described in the model documentation of Jones and Kiniry (1986) as simulating the appearance and expansion of individual
166
P.S.CARBERRY
leaves. Carberry et al. (1989) revised the leaf functions as part of a number of modifications to CERES-Maize which resulted in better model predictions in northern Australia. Muchow and Carberry (1989) employed the framework suggested by CERES-Maize to analyse the environmental control of phenology and leaf growth in a tropically adapted maize. The revelation of the disparate methods of simulating leaf-area development does not invalidate these results. In fact, the simulation of leaf-area development through the appearance and expansion of individual leaves not only proved successful for maize grown at Katherine, N.T., but also for maize grown in Kenya (Wafula and Keating, personal communication, 1990) and for sorghum (Muchow and Carberry, 1990). The key to the success of the individual-leaf method lies in the function which was developed to predict the area of individual leaves based solely on the prediction of final leaf number (Muchow and Carberry, 1990). As a consequence, the approach based on processes at the individual-leaf level remains valid as a method for simulating crop canopy development. CONCLUSIONS This paper serves the purpose of correcting the erroneous parameter descriptions from Jones and Kiniry (1986), and the resulting misinterpretations, in CERES-Maize made by Carberry et al. (1989) and Muchow and Carberry ( 1989 ), concerning leaf canopy development. Thus, CERES-Maize simulates the expansion of leaf area on an individual plant basis and not, as previously reported, on the basis of the expansion of individual leaves. Validation of the leaf canopy routines in CERES-Maize indicated that the functions describing both rate of appearance of leaf tips and rate of leaf area expansion per plant were not appropriate, without prior calibration, for predicting leaf-area development of the tropically adapted maize hybrid Dekalb XL82. The earlier conclusions that CERES-Maize required genetic parameterization of the leaf-growth functions (Carberry et al., 1989; Muchow and Carberry, 1989) therefore remain valid. ACKNOWLEDGEMENTS I thank J.T. Ritchie for identifying the problem that this paper addresses, and R.C. Muchow for making available the experimental data to conduct these analyses. REFERENCES Carberry, P.S., Muchow,R.C. and McCown,R.L., 1989. Testingthe CERES-Maizesimulation model in a semi-aridtropical environment.Field Crops Res., 20:297-315.
TEST OF LEAF-AREA DEVELOPMENT 1N CERES-MAIZE: A CORRECTION
167
de Vos, R.N. and Mallett, J.B., 1987. Preliminary evaluation of two maize (Zea mays L. ) growthsimulation models. S. Afr. J. Plant Soil, 4: 131-136. Hodges, T., Botner, D., Sakamoto, C. and Haug, J., 1987. Using the CERES-Maize model to estimate production for the U.S. Cornbelt. Agric. For. Meteorol., 40: 293-303. Jones, C.A. and K_iniry, J.R. (Editors), 1986. CERES-Maize: A Simulation Model of Maize Growth and Development. Texas A&M University Press, College Station, 194 pp. Jones, C.A., Ritchie, J.T., Kiniry, J.R. and Godwin, D.C., 1986. Subroutine structure. In: C.A. Jones and J.R. Kiniry (Editors), CERES-Maize: A Simulation Model of Maize Growth and Development. Texas A&M University Press, College Station, pp. 49-111. Keating, B.A., Wafula, B.M. and McCown, R.L., 1988. Simulation of plant density effects on maize yield as influenced by water and nitrogen limitations. In: S.K. Sinha, P.V. Sane, S.C. Bhargava and P.K. Agrawal (Editors), Proc. Int. Congress of Plant Physiology, 15-20 February 1988, Soc. Plant Physiology and Biochemistry, New Delhi, India, pp. 547-559. Kiniry, J.R. and Ritchie, J.T., 1981. Rates of leaf primordia and tip appearance of different maize genotypes in the field. Am. Soc. Agron. Abstr., 12. Liu, W.T.H., Botner, D.M. and Sakamoto, C.M., 1989. Application of CERES-Maize to yield prediction of a Brazilian maize hybrid. Agric. For. Meteorol., 45:299-312. McKee, G.W., 1964. A coefficient for computing leaf area in hybrid corn. Agron. J., 56: 240241. Muchow, R.C., 1989. Comparative productivity of maize, sorghum and pearl millet in a semiarid tropical environment I. Effect of sowing date on yield potential. Field Crops Res., 20: 191-205. Muchow, R.C. and Carberry, P.S., 1989. Environmental control of phenology and leaf growth in a tropically-adapted maize. Field Crops Res., 20:221-236. Muchow, R.C. and Carberry, P.S., 1990. Phenology and leaf area development in a tropical grain sorghum. Field Crops Res., 23:221-237. Tollenaar, M., Muldoon, J.F. and Daynard, T.B., 1984. Differences in rates of leaf appearance among maize hybrids and phases of development. Can. J. Plant Sci., 64: 759-763.
159
Elsevier Science Publishers B.V., Amsterdam
Test of leaf-area development in CERES-Maize: a correction P.S. Carberry CS1RO Division of Tropical Cropsand Pastures, PrivateBag, Aitkenvale, Qld. 4814, Australia (Accepted 14 May 1990)
ABSTRACT Carberry, P.S., 1991. Test of leaf-area development in CERES-Maize: a correction. Field Crops Res., 27: 159-167. Routines controlling development of leaf area in the CERES-Maize model have been misinterpreted in recent papers, owing to an inaccuracy in parameter definition in the published documentation of the model. This paper provides the correct description of functions for leaf-area development in CERES-Maize, and tests the performance of these functions. Given the correct definitions of the variables CUMPH, as the cumulative number of visible leaf tips, and XN as the next leaf which will emerge on the plant, CERES-Maize simulates leaf-area expansion per plant as a function of the number of emerged leaf tips. A test of the leaf-canopy routines in CERES-Maize indicated that constants, used in the functions describing both rate of appearance of leaf tips and rate of leaf-area expansion per plant, needed calibration for predicting leaf-area development of the tropically adapted hybrid maize Dekalb XL82.
INTRODUCTION
CERES-Maize is a crop simulation model which simulates the growth, development and grain-yield of a maize (Zea mays L. ) crop, given climatic and cultural inputs. Detailed descriptions of the biological and physical relationships used in CERES-Maize (Jones and Kiniry, 1986 ), and the ready availability of this software and its documentation, have resulted in wide application of the model (de Vos and Mallet, 1987; Hodges et al., 1987; Keating et al., 1988; Carberry et al., 1989; Liu et al., 1989). Carberry et al. (1989) and Muchow and Carberry (1989) have tested and calibrated the leaf-area development functions in CERES-Maize against data collected for a tropically adapted maize cultivar in a semi-arid tropical region. However, recent discussions with the principal developer of CERES-Maize, J.T. Ritchie, have identified an error in parameter definition in the User's Guide (Jones and Kiniry, 1986 ) which can result in misinterpretation of the method by which CERES-Maize simulates leaf-area development. 0378-4290/91/$03.50
© 1991 Elsevier Science Publishers B.V. All rights reserved.
160
P.S. CARBERRY
Based on definitions from Jones and Kiniry ( 1986 ), Carberry et al. ( 1989 ) interpreted the development of leaf area by CERES-Maize as the summation, on a given day, of the lamina area of all leaves that have reached full expansion. In fact, CERES-Maize simulates, not the area of individual leaves but, on a total-plant basis, cumulative leaf area as a function of the appearance of individual leaf tips (J.T. Ritchie, personal communication, 1989). This difference in interpretation is significant, not only in method but also for the mechanistic level at which the model operates, i.e., individual leaf versus whole plant. Ironically, the simulation of leaf-canopy development using individual leaves has shown considerable merit, not only for maize (Carberry et al., 1989; Muchow and Carberry, 1989) but also for sorghum (Muchow and Carberry, 1990). The objectives of this paper are to provide the correct description of functions for leaf-area development in CERES-Maize, and to test the performance of these functions using the same experimental crops that were used for previous tests of the model (Carberry et al., 1989). MATERIALS AND METHODS
Simulation ofleaf-area development From Jones et al. (1986), CERES-Maize calculates, for each day, the cumulative number of fully expanded leaves (CUMPH) from daily thermal time (DTT), such that: CUMPH = CUMPH + D T T / ( 3 8 . 9 .
PC)
(
1)
where: PC = 0.66 + 0.068, CUMPH for CUMPH< 5 and PC = 1.0 for CUMPH> 5.
(2)
Therefore, rate of leaf appearance equals 38.9°C d leaf -1 for leaves greater than 5, but is faster for the first 4 leaves (determined by the variable PC). In the model, half of the first leaf is visible at emergence (CUMPH=0.5). The fraction of a leaf that emerges on a day (TI) is calculated as TI = D T T / ( 3 8 . 9 .
PC)
(3)
Under optimal water conditions, the daily growth of leaf area per plant (PLAG) is calculated as a function of TI and the number of the oldest expanding leaf (XN), where: XN = C U M P H + 1
(4)
This function calculates PLAG for different values of XN (Table 1 ); thus, for XN less than 4.0:
TEST OF LEAF-AREA DEVELOPMENT IN CERES-MAIZE: A CORRECTION
PLAG= 3.0. XN*TI
161
(5)
Total plant leaf area (PLA) is calculated by adding PLAG to the previous day's value of PEA. The value of PLAG is modified under severe water stress, or when assimilate production is insufficient to maintain its potential value (e.g., at high plant densities, because of lack of assimilate supply). As CUMPH is defined in the original documentation as the number of fully expanded leaves (Jones et al., 1986), the rate of 38.9°C d leaf -I was interpreted as the rate of appearance of fully expanded leaves, defined as the appearance of leaf ligules. Also, as the number of emerged leaf tips (LN) always equals XN (i.e. CUMPH + 1 ), then only one leaf is being expanded at any one time by CERES-Maize. If, for instance, one whole leaf is expanded on a day (TI = 1 ), the increment in area (PLAG) that is added to total plant leaf area ( P E A ) must represent the fully expanded lamina area of the expanding leaf (XN). Therefore, given the definitions from Jones and Kiniry ( 1986 ), CERESMaize was interpreted as simulating the rate of appearance of fully expanded leaves and the leaf area of individual leaves. However, the above definitions of CUMPH and XN are erroneous (J.T. Ritchie, personal communication, 1989 ). CUMPH is correctly defined as the cumulative number of leaf tips that have emerged. The correct definition of XN is the newest emerging leaf ( X N = CUMPH + 1 ) and, as such, LN represents its integer value. These correct definitions result in a different interpretation of the functions that describe leaf-area development in CERES-Maize. CERES-Maize thus simulates the appearance of successive leaf tips, and leaf area per plant is simulated as a function of the number of leaf tips that have emerged by a given day. The differential equation of the relationships between total plant leaf area (PEA) TABLE 1 Equations describing leaf-area expansion per plant (PLAG) as functions Of XN for (a) CERES-Maize and (b) fitted regressions to data for the three sowings ( Fig. 3 ) Leaf number (a) CERES-Maize 1-3 4-11 12-(TLNOa--4) > (TLNO-- 3)
(b) Fitted regressions 1-3 4-13 14-(TLNO--2) > (TLNO-- 1 )
Function
PLAG -----3.0. XN PLAG-- 3 . 5 . XN* XN PLAG ~---5 9 5 . 0
PLAG= 595.0/( XN + 5 -- TLNO ) PLAG= 5.55.XN PLAG = 0 . 2 6 1 * X N * X N * X N
PLAG=611.5 PLAG= 611.5-- 104.3. (XN+2--TLNO)
aTLNO is defined as the total number of leaves that the plant produces.
162
P.S.CARBERRY
and XN is approximated in the model by the discontinuous functions describing PLAG in Table 1.
FieM experimentation Data used in this analysis are from the same experiments as described in the analyses of Muchow and Carberry (1989). To summarise, maize was grown under non-limiting nitrogen conditions at Katherine Research Station, Northern Territory, Australia (latitude 14 ° 28'S, longitude 132 ° 18'E, alt. 108 m) at three sowing dates, 10 October 1984, 6 February 1985 and 20 August 1985. There were four replicates at each sowing date. Cultural details were similar for all sowings; and these are fully described by Muchow ( 1989 ). The maize hybrid Dekalb XL82 was grown at 70 000 plants h a - 1under highinput conditions (240 kg N h a - l ; 30 kg P h a - l ) , and weeds, insects and diseases were controlled. The crops were fully irrigated to restore water to field capacity in the soil profile after four rain-free days. Lamina areas of individual leaves were recorded at each sampling date using five representative plants. After thinning ( 10-15 days after sowing), leaf 5 from the base of the plant was tagged. The length and breadth of all leaves, the number of fully expanded leaves and the number of fully expanded green leaves (senescence < 50% area) were recorded for each plant. The area of each leaf was recorded once the leaf tip was visible above the whorl of the preceding leaf. Subsequently, these data were recorded twice weekly until silking. The lamina area of both fully expanded and expanding leaves was calculated as length, breadth. 0.75 (McKee, 1964). The mean area of each leaf was calculated as the mean of those leaves present at each position on the stem, and the mean area per plant was calculated from the five representative plants.
Data analysis Thermal time was calculated with the algorithms of CERES-Maize, using base, optimum and maximum temperatures of 8, 34 and 44°C, respectively (Jones et al., 1986 ). Relationships between leaf-area development, thermal time and leaf number were fitted by least-squares regression. The logistic equation:
Y = M / ( I +exp( - k . ( X - m ) ) )
(6)
where M is the asymptote, and k and m are constants, was fitted to observed total leaf area per plant (Y) versus the number of leaf tips (X), which were predicted from the linear regression of leaf tips against thermal time. Predicted rather than observed number of leaf tips was used in equation 6 as the independent variable, because considerable leaf-area expansion occurred after the observed appearance of the final leaf tip. As there were insufficient ob-
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served data to fit the discontinuous differential equations o f CERES-Maize (Table 1 ) for rate o f leaf area expansion (PL,4G), PL,4G was determined for cv. Dekalb XL82 from the predicted fits to the logistic regression for each sowing. RESULTS AND DISCUSSION For hybrid maize Dekalb XL82, the observed rate of appearance o f leaf tips was 48.3°C d leaf -~ (Fig. 1), considerably slower than that assumed in CERES-Maize (38.9 ° C d leaf- ~). The assumption of a constant rate of leaf tip appearance among cultivars, although appropriate among some groups of hybrids (Kiniry and Ritchie, 1981 ), was not supported in a study by Tollenaar et al. (1984), who concluded that genotypic variability occurred in leaf appearance in maize. The rate of leaf appearance for Dekalb XL82 was slower than that for any o f the cultivars studied by Kiniry and Ritchie ( 1981 ) or by Tollenaar ¢t al. ( 1984 ). The relationship between observed leaf area per plant (without losses due to senescence ) and predicted n u m b e r o f leaf tips for each o f the three sowings is presented in Fig. 2. The logistic equation adequately fitted the observed data, although there were few observations for low values o f PEA. Differences between sowings were mainly in the m a x i m u m value o f PEA, which was related to the differences in final leaf number. Mean m a x i m u m leaf numbers in the October, February and August sowings were 18.2, 17.5 and 19.2 leaves, respectively ( M u c h o w and Carberry, 1989 ). As shown in Fig. 2, observed PEA increased as the predicted n u m b e r of leaf tips increased above the final leaf-tip n u m b e r observed in each o f the three 20
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sowings. The use of number of leaf tips as the independent variable in CERESMaize in calculating PLA necessitates the continued prediction of leaf appearance past the limits of observed data. Using the relationship between the appearance of leaves and thermal time (Fig. 1 ), more realistic asymptotic values of leaf area per plant can be achieved by increasing PLA as a function of thermal time after emergence (Muchow and Carberry, 1989). The differential of the logistic function for leaf area per plant and leaf number represents the rate of leaf-area expansion per leaf-appearance interval. In comparison with data from three experimental sowings (Fig. 3), the functions which describe leaf-area expansion in CERES-Maize (Table 1 (a)) overpredict the early rate of expansion and underpredict subsequent development. Not only were coefficients of the functions different for the observed data but, in the range 4-14 leaves, PLAG was better fitted to a cubic function of XN, whereas for the final three leaves, a linear function was the most appropriate (Table 1 (b)). The combined effects of a faster rate of leaf appearance (Fig. 1 ) and the greater rate of early leaf area expansion (Fig. 3) generally resulted in large overpredictions of PLA by CERES-Maize on a given day for all three sowings (Fig. 4). Although timings were not synchronised, maximum leaf areas per plant were little different from those observed. This result explains the adequate predictions of leaf-area index at silking made by the model (Carberry et al., 1989 ). The estimated maximum PLA was attained much earlier than that observed and, because date of silking in CERES-Maize corresponds to end of leaf growth (Jones et al., 1986 ), predicted phenological dates for these
TEST O F LEAF-AREA D E V E L O P M E N T IN CERES-MAIZE: A C O R R E C T I O N
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datasets were consequently underestimated (Carberry et al., 1989 ). The inclusion of the observed rate of leaf appearance in CERES-Maize (48.3 °C d leaf- l into equations 1 and 3 ), and the revised functions for PLAG (Table l ) resulted in significant improvements in the simulations of PEA for the three sowings (Fig. 4). The slight error in the revised simulations resulted from inappropriate values calculated for PC [equation 2 ], which resulted in slight delays in the appearance of the first four leaf tips. Carberry et al. (1989) and Muchow and Carberry (1989) interpreted the leaf-growth functions described in the model documentation of Jones and Kiniry (1986) as simulating the appearance and expansion of individual
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leaves. Carberry et al. (1989) revised the leaf functions as part of a number of modifications to CERES-Maize which resulted in better model predictions in northern Australia. Muchow and Carberry (1989) employed the framework suggested by CERES-Maize to analyse the environmental control of phenology and leaf growth in a tropically adapted maize. The revelation of the disparate methods of simulating leaf-area development does not invalidate these results. In fact, the simulation of leaf-area development through the appearance and expansion of individual leaves not only proved successful for maize grown at Katherine, N.T., but also for maize grown in Kenya (Wafula and Keating, personal communication, 1990) and for sorghum (Muchow and Carberry, 1990). The key to the success of the individual-leaf method lies in the function which was developed to predict the area of individual leaves based solely on the prediction of final leaf number (Muchow and Carberry, 1990). As a consequence, the approach based on processes at the individual-leaf level remains valid as a method for simulating crop canopy development. CONCLUSIONS This paper serves the purpose of correcting the erroneous parameter descriptions from Jones and Kiniry (1986), and the resulting misinterpretations, in CERES-Maize made by Carberry et al. (1989) and Muchow and Carberry ( 1989 ), concerning leaf canopy development. Thus, CERES-Maize simulates the expansion of leaf area on an individual plant basis and not, as previously reported, on the basis of the expansion of individual leaves. Validation of the leaf canopy routines in CERES-Maize indicated that the functions describing both rate of appearance of leaf tips and rate of leaf area expansion per plant were not appropriate, without prior calibration, for predicting leaf-area development of the tropically adapted maize hybrid Dekalb XL82. The earlier conclusions that CERES-Maize required genetic parameterization of the leaf-growth functions (Carberry et al., 1989; Muchow and Carberry, 1989) therefore remain valid. ACKNOWLEDGEMENTS I thank J.T. Ritchie for identifying the problem that this paper addresses, and R.C. Muchow for making available the experimental data to conduct these analyses. REFERENCES Carberry, P.S., Muchow,R.C. and McCown,R.L., 1989. Testingthe CERES-Maizesimulation model in a semi-aridtropical environment.Field Crops Res., 20:297-315.
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de Vos, R.N. and Mallett, J.B., 1987. Preliminary evaluation of two maize (Zea mays L. ) growthsimulation models. S. Afr. J. Plant Soil, 4: 131-136. Hodges, T., Botner, D., Sakamoto, C. and Haug, J., 1987. Using the CERES-Maize model to estimate production for the U.S. Cornbelt. Agric. For. Meteorol., 40: 293-303. Jones, C.A. and K_iniry, J.R. (Editors), 1986. CERES-Maize: A Simulation Model of Maize Growth and Development. Texas A&M University Press, College Station, 194 pp. Jones, C.A., Ritchie, J.T., Kiniry, J.R. and Godwin, D.C., 1986. Subroutine structure. In: C.A. Jones and J.R. Kiniry (Editors), CERES-Maize: A Simulation Model of Maize Growth and Development. Texas A&M University Press, College Station, pp. 49-111. Keating, B.A., Wafula, B.M. and McCown, R.L., 1988. Simulation of plant density effects on maize yield as influenced by water and nitrogen limitations. In: S.K. Sinha, P.V. Sane, S.C. Bhargava and P.K. Agrawal (Editors), Proc. Int. Congress of Plant Physiology, 15-20 February 1988, Soc. Plant Physiology and Biochemistry, New Delhi, India, pp. 547-559. Kiniry, J.R. and Ritchie, J.T., 1981. Rates of leaf primordia and tip appearance of different maize genotypes in the field. Am. Soc. Agron. Abstr., 12. Liu, W.T.H., Botner, D.M. and Sakamoto, C.M., 1989. Application of CERES-Maize to yield prediction of a Brazilian maize hybrid. Agric. For. Meteorol., 45:299-312. McKee, G.W., 1964. A coefficient for computing leaf area in hybrid corn. Agron. J., 56: 240241. Muchow, R.C., 1989. Comparative productivity of maize, sorghum and pearl millet in a semiarid tropical environment I. Effect of sowing date on yield potential. Field Crops Res., 20: 191-205. Muchow, R.C. and Carberry, P.S., 1989. Environmental control of phenology and leaf growth in a tropically-adapted maize. Field Crops Res., 20:221-236. Muchow, R.C. and Carberry, P.S., 1990. Phenology and leaf area development in a tropical grain sorghum. Field Crops Res., 23:221-237. Tollenaar, M., Muldoon, J.F. and Daynard, T.B., 1984. Differences in rates of leaf appearance among maize hybrids and phases of development. Can. J. Plant Sci., 64: 759-763.