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Published online 27 April 2005
Published in Agron J 97:722-733 (2005)
DOI: 10.2134/agronj2004.0171
© 2005 American Society of Agronomy
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Agronomic Modeling

Development of a Leaf-Level Canopy Assimilation Model for CERES-Maize

J. I. Lizasoa,*, W. D. Batchelorb, K. J. Bootea and M. E. Westgatec

a Agronomy Dep., Univ. of Florida, Gainesville, FL 32611-0500
b Dep. of Agricultural and Biological Engineering, 100 Howell Hall, Mississippi State Univ., Mississippi State, MS 39762
c Dep. of Agronomy, Iowa State Univ., Ames IA 50011

* Corresponding author (jlizaso{at}ufl.edu)

Received for publication June 23, 2004.

   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Calculating crop growth rate as the product of intercepted light and radiation use efficiency may yield inaccurate predictions under stress conditions. A more mechanistic simulation of photosynthesis and respiration may be required to improve model accuracy under stresses. We developed a leaf-level photosynthesis and respiration model for maize (Zea mays L.) and linked it to CERES-Maize. The new model has three components that simulate light absorption, instantaneous leaf gross assimilation, and canopy respiration. Daily solar radiation was fractioned into hourly direct and diffuse components, and transformed into hourly photosynthetically active radiation (PAR). Extinction coefficients for direct and diffuse PAR were calculated, and a hedgerow approach followed to restrict the calculation of leaf area index (LAI), light interception, and photosynthesis to the fraction of ground shaded by the canopy. Light absorption was calculated for sunlit and shaded fractions of LAI. Instantaneous gross assimilation per leaf considered the effects of light intensity, leaf age, and air temperature, and was integrated for daylight hours and green leaf area. Maintenance and growth components of respiration are computed separately. The new model was linked to CERES-Maize and provided reasonable estimates of instantaneous leaf gross assimilation as well as daily trends of canopy gross assimilation and respiration. It also conforms to the standards of CERES-Maize, thus requiring only a minimum set of daily weather inputs (solar radiation, maximum and minimum temperature, and rainfall). The model supports the simulation of leaf-level processes such as hail damage, mechanical damage, herbivory, leaf pathologies, detasseling, and others.

Abbreviations: GDD, growing degree day • IPAR, light intercepted by the canopy • LAI, leaf area index • PAR, photosynthetically active radiation • PARd, diffuse PAR • PGR, daily rates of crop growth • PPFD, photosynthetic photon flux density • PS, plant spacing within the row • RS, row spacing • RUE, radiation use efficiency • SOC, standard overcast sky • UOC, uniform overcast sky


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
CERES-MAIZE (Jones and Kiniry, 1986) and other crop simulation models calculate daily rates of crop growth (PGR, g plant–1 d–1) as the product of the light intercepted by the canopy (IPAR, MJ plant–1 d–1) and the radiation use efficiency (RUE, g MJ–1):

[1]
This simple approach proposed by Monteith (1977) has proved to be useful to predict crop growth and yield, particularly under environmental conditions favorable for crop growth. When stresses affect crop growth, the radiation use efficiency is reduced with stress factors and adjustment parameters of various types.

This simple approach has limits. Photosynthesis and respiration, the main processes determining crop growth, respond differently to environmental conditions. For instance, photosynthetic rate in maize increases with temperature, to a maximum around 35°C, then decreases at higher temperatures (Oberhuber and Edwards, 1993; Naidu et al., 2003). The rate of dark respiration, however, continues to increase with temperature (Oberhuber and Edwards, 1993). On the other hand, there are many environmental factors such as light, CO2, temperature, and leaf water and N status, known to interact with photosynthesis. At low light intensity, the optimum temperature for photosynthesis is substantially lower than at saturating light intensity (Oberhuber and Edwards, 1993). Recently Loomis and Amthor (1999) have argued for an end to the RUE era in crop simulation models and its substitution by photosynthesis and respiration submodels. A more mechanistic simulation of these processes would open new opportunities to improve the accuracy of model predictions. The objective of this work was to develop such photosynthesis and respiration submodels and link them to CERES-Maize. The new model conforms to the standards of CERES-Maize, thus requiring only a minimum set of daily weather inputs (solar radiation, maximum and minimum temperature, and rainfall). This restriction constrained our choices to simulate photosynthesis, but should greatly improve model applicability worldwide among current and future CERES-Maize users. In this initial approach we focused on simulating correctly potential plant growth as measured under conditions where soil water and N are not limiting. Our future efforts will target the development of energy balance and stomatal conductance modules that will make possible to compute leaf-level C, water, and N balances.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Model Development
We developed a photosynthesis-respiration model to substitute for Eq. [1] and calculate PGR as the net result of the daily rates of gross assimilation and respiration. The PGR calculated in this way was linked to CERES and partitioned to growth in the same way as the version 3.5 of the model. The new model is referred to as CERES-PR. Table 1 shows a summary of the new variables used in CERES-PR. In spite of the inherent complexity suggested by the large number of variables in Table 1, our model provided robust simulations under a wide range of conditions as will be shown in a companion paper (Lizaso et al., 2005).


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  		Table 1. Definition and units of variables used by CERES-PR.

 
The model takes advantage of the detailed description of individual leaf growth, aging, and senescence provided by a new leaf area model recently linked to CERES-Maize (Lizaso et al., 2003a). CERES-PR has three main components for simulating light absorption, gross assimilation, and respiration. First the daily input solar radiation is fractioned into hourly components, separated in direct and diffuse fractions, and transformed into hourly intensities of photosynthetically active radiation (PAR). Extinction coefficients for direct and diffuse PAR are calculated. Following a hedgerow approach (Boote and Pickering, 1994), LAI, light interception, and photosynthesis are restricted to the fraction of ground shaded by the canopy. Leaf area index is separated into sunlit and shaded fractions and light absorption is calculated for each component. Next, instantaneous leaf gross assimilation is calculated and integrated over the green leaf area and day hours. Respiration is computed per unit area of land and maintenance and growth components are estimated separately.

Light Absorption
The detailed description of the light profiles within the canopy was modified from that used in CROPGRO (Boote et al., 1998).

Hourly Direct and Diffuse PAR
The model has an internal hourly loop that converts daily input values of solar radiation (R, MJ m–2 d–1) into instantaneous values in hourly steps (J m–2 s–1) (Eq. [6] in Spitters et al., 1986). A portion of the incoming beam of solar radiation is scattered by gas molecules, particulates, and small droplets as it passes through the atmosphere, thus creating diffuse radiation. Incident hourly values of R are fractioned into direct and diffuse components using a single sigmoidal equation that simplifies the multiple-function proposed by Spitters et al. (1986):

[2]
where Rd/R is the fraction of diffuse radiation in R, and R0 is the extraterrestrial irradiance (MJ m–2 d–1) calculated as a function of the solar constant and the solar elevation. Rd/R is constrained to a maximum value of 1. Under clear skies the diffuse radiation is anisotropic due to the predominant forward direction of the light scattered by microscopic aerosol particles (Mie scattering). Thus, the direct radiation is larger and the diffuse component is smaller at sky elevations closer to the sun. Hourly Rd/R values are reduced to account for this circumsolar effect as a function of solar elevation angle (Eq. [9], Spitters et al., 1986) and then the fraction of diffuse PAR (PARd/PAR) is calculated (Eq. [10], Spitters et al., 1986).

CERES assumes that 50% of the daily solar radiation (R) is within the wavelengths of PAR. We found that this assumption overestimates daily PAR and proposed a relationship that improves the estimation of PAR from solar radiation (Lizaso et al., 2003b):

[3]
where PAR and R have units of MJ m–2 d–1. Equation [3] gives values of PAR/R of 0.43 for R > 10 MJ m–2 d–1, increasing to 0.51 for R = 1 MJ m–2 d–1. These values are similar to the 0.45 value of Monteith (1965) and Meek et al. (1984). Hourly values of PAR are calculated assuming that the same ratio of PAR to R calculated with Eq. [3] for daily values holds for hourly values:

[4]
where RHOUR is the hour-step instantaneous solar radiation (J m–2 s–1), PARHOUR is the hour-step instantaneous PAR (µmol m–2 s–1), and {eta} has a value of 4.6 µmol J–1 and converts flux units of energy into photosynthetic photon flux density (PPFD) according to McCree (1981). The PARHOUR is separated into direct (PARHOUR,D) and diffuse components (PARHOUR,d) using the fraction of diffuse PAR calculated previously (Eq. [10], Spiters et al., 1986).

Extinction Coefficients
The PARHOUR (Eq. [4]) is transmitted through the canopy following the Bouguer-Lambert-Beer Law in which the degree of attenuation is dictated by the extinction coefficient and the number of leaf layers (LAI). The extinction coefficient is the ratio of the area of shadow projected by leaf blades in a horizontal surface to the surface area of leaf blades (Monteith, 1973). The area of projection (i.e., shadow) changes through the day with the sun position in the sky and depends on the curvature of leaves. The effect of the distribution of leaf area angles in the canopy is simulated by assuming that the ratio of shadow to leaf area can be approximated by calculating the ratio of shadow to area of known geometric solids, such as cylinders, cones, and spheres (Monteith, 1973). Campbell (1986) extended the theoretical treatment of spherical leaf angle distribution developed by Goudriaan (1977) to calculate the extinction coefficient into a more general spheroidal leaf angle distribution. The extinction coefficient of black leaves (i.e., assuming they do not exhibit transmission nor reflection) for direct radiation k(ß) is calculated according to Campbell (Campbell, 1986, 1990):

[5]
where ß is the solar elevation angle (degrees) and x is a parameter defining the spheroidal leaf angle distribution calculated as the ratio of horizontal to vertical axis of the spheroid. When x = 1 the leaf angle distribution is spherical; x values > 1 indicates a flattened (oblate) spheroid with larger concentration of leaf surface at low angles (prostrate-leaf canopy); x values between 0 and 1 indicates an elongated (prolate) spheroid with increasing area of leaves at high angles (erect-leaf canopy). When an x value of 1.0 was used for maize (Antunes et al., 2001) k(ß) decreased from 1.0 at 30° down to 0.5 at 90°.

The extinction coefficient of black leaves for diffuse radiation (kd) can be approximated assuming an exponential transmission (Campbell and Norman, 1998) as:

[6]
where {tau}diff is the diffuse light transmission coefficient calculated as (Campbell and Norman, 1998):

[7]
and {tau}dir(ß) is the direct light transmission coefficient (Campbell and Norman, 1998):

[8]
Equation [7] is integrated numerically in small steps for the whole hemisphere, assuming a uniform overcast sky (UOC), which is simpler and yields almost identical results (Goudriaan, 1977) than assuming standard overcast sky (SOC).

Hedgerow Approach
The crop canopy captures the direct and diffuse components of incoming PAR generated by Eq. [4]. Canopy cover is incomplete early in the season rendering some of the incoming light unavailable for photosynthesis. We followed the approach of Boote and Pickering (1994) to calculate the shadow projected by individual plants in the canopy as a function of canopy height and width, solar elevation, and row azimuth. The procedure assumes a row crop and includes the effects of incomplete-cover canopies, both between rows and within the row, calculating hourly the fraction of ground covered by the shadow (fs). Row azimuth (degrees) is a model input, and solar elevation is calculated using standard equations as a function of latitude, day of year, and time of day (Spitters et al., 1986). Canopy height (CH, m) is simulated following a sigmoidal function assuming maximum height is reached at silking:

[9]
In Eq. [9], H is the final canopy height (m) and PA is a relative-scale phenological age (0 = emergence; 1 = silking; 2 = physiological maturity) calculated according to Lizaso et al. (2003b). Canopy width (CW, m) is calculated from the horizontal projection of leaves. Stewart and Dwyer (1999) reported that maize leaf shape (i.e., length and width) is consistent and predictable. They also found a good relationship between shape and area of leaves. We developed a relationship between leaf length (l, cm) and leaf area (LA, cm2 leaf–1) for leaves that had completed 80% or more of expansion using a nonrectangular hyperbola:

[10]
Equation [10] has three parameters: initial slope, s, asymptote, lx, and curvature, c. We assumed that leaves at early stages of expansion form the whorl and thus are more erect, contributing little to setting the width of the canopy. The projection of leaves in the horizontal plane (lw, cm) is calculated as:

[11]
where {delta} is the average angle (degrees) of the leaf with the horizontal. Typically maize leaves are more horizontal at the bottom of the canopy and more erect at the top of the canopy (Whigham, 1971). Also the curvature of expanded leaf blades changes along leaf length with the highest inclination at the ligule (Antunes et al., 2001). Most maize cultivars exhibit the longest leaf around the ear. Upper leaves contribute little to determine canopy width, because they are shorter and more erect. Therefore, the projection of lower leaves determines the increase in canopy width until the maximum width (i.e., row spacing) is reached. Thus canopy width (CW, m) is calculated as:

[12]
for CW ≤ RS, being RS the row spacing (m). The model uses dynamically the longest value of lw calculated daily from leaves that have completed at least 80% of expansion.

Sunlit and Shaded Leaf Area
To describe light absorption by leaves correctly, two classes of leaf area were distinguished: sunlit and shaded fractions. Sunlit leaf area absorbs direct and diffuse PAR; shaded leaf area absorbs only diffuse PAR. The amount of sunlit leaf area is calculated as (Goudriaan, 1977; Boote and Pickering, 1994):

[13]
where fs is the fraction of ground shaded by the canopy calculated according to Boote and Pickering (1994) and k(ß) is the direct beam extinction coefficient calculated with Eq. [5]. The shaded leaf area is calculated as the difference:

[14]

Light Absorbed by Sunlit and Shaded Leaf Area
Photosynthetic photon flux density (PPFD) as calculated with Eq. [4] is absorbed by sunlit and shaded LAI following the description provided by Spitters (1986). A fraction of the direct PPFD is scattered within the canopy and converted into diffuse radiation. The scattering coefficient ({sigma}) includes transmittance and reflectance down through the canopy (Goudriaan, 1977). The reflectance of diffuse PAR ({rho}dif) from the canopy back into the sky is calculated as (Goudriaan, 1977):

[15]
And the reflectance of direct PAR ({rho}dir) as (Goudriaan, 1988):

[16]
Light absorption is calculated for each leaf from the top to the bottom of the canopy. In the next section, Eq. [17] through [38] are in a loop. At each computing step, LAI accumulates the surface area of an additional leaf, calculating the incremental sunlit and shaded leaf surface (Eq. [13] and [14]). Three light fluxes are accounted for: incident direct (beam), incident diffuse, and reflected diffuse. All absorbed light components (A) calculated in this section are as µmol m–2 s–1. Total absorbed direct PAR (AD) is calculated according to Spitters (1986) as:

[17]
In Eq. [17], fs increases the effective LAI for incomplete canopies. A proportion of the direct PAR is leaf-scattered and becomes diffuse. The component of AD which is not scattered (AD,D) is:

[18]
and thus the scattered component is the difference:

[19]
Direct light absorbed by sunlit and shaded leaf surfaces is calculated next. Total absorbed direct light in sunlit leaf area is:

[20]
ASLD is split into direct (ASLD,D) and leaf-scattered (ASLD,d) components:

[21]

[22]
The fraction of the leaf-scattered light (AD,d, Eq. [19]) that is not absorbed by the sunlit leaf area is assumed to be absorbed as diffuse light by the shaded leaf area:

[23]
The absorption of diffuse light from the sky is calculated next. The model takes into account the effect of incomplete canopies by calculating a view factor, fv, (i.e., fraction of sky seen by plants) from row spacing (RS), plant spacing within the row (PS), canopy height (CH), and canopy width (CW). The algorithms were developed by Goudriaan (1977) and were extended by Boote and Pickering (1994) to account for gaps between plants within the row early in the season. The total absorbed diffuse radiation (Ad) is computed as:

[24]
Diffuse light captured by sunlit (ASLd) and shaded (ASHd) components of leaf area is calculated:

[25]

[26]
Light reflected from the soil generates an upward flux of diffuse light available for photosynthesis. Light reflected from the soil (PARHOUR,r) is calculated from the soil albedo and the light flux reaching the soil:

[27]
where {rho}soil is the reflectance (albedo) of soil to PAR, PARHOUR is the total flux of incoming PAR calculated with Eq. [4], and PARHOUR,INT is the amount of PARHOUR intercepted by the canopy. PARHOUR,INT is the sum of the absorbed direct and diffuse light plus the canopy reflected direct and diffuse light:

[28]
Absorption of light from the soil-reflected diffuse flux is calculated similar to Eq. 24:

[29]
Shaded- and sunlit-absorbed fractions of Ar are calculated as:

[30]

[31]
Light absorbed down through the canopy is accumulated next for sunlit (CUMASL) and shaded (CUMASH) leaf area:

[32]

[33]
Equation [32] accumulates diffuse light (ADIFSL) and direct light absorbed in sunlit leaf area. The diffuse light absorbed in shaded leaf area is:

[34]
The final step is to disaggregate cumulative values of leaf area and absorbed light for sunlit and shaded components. Since LAI was accumulated in reverse-number order (i.e., top to bottom) LAIsun and LAIshd are:

[35]

[36]
where l is leaf number as they appear in the whorl (i.e., bottom to top). The PPFD (µmol m–2 s–1) absorbed at each leaf level by sunlit and shaded LAI:

[37]

[38]
As explained before, Eq. [17] through [38] are within a per-leaf loop that calculates surface leaf area and hourly absorbed light of sunlit and shaded components.

Photosynthesis
The detailed description within the canopy of both the light environment and the individual leaf development are integrated to calculate instantaneous gross assimilation per leaf. Assimilation is calculated as a function of light intensity, temperature, and leaf age. Each leaf is assumed to assimilate CO2 following a distinctive light response curve that is affected by leaf development and air temperature. Light response curves follow a nonrectangular hyperbola function (Thornley and Johnson, 1990):

[39]
where Ag is the gross assimilation rate (µmol CO2 m–2 of leaf s–1), and APAR is the absorbed PPFD (µmol quanta m–2 of leaf s–1) as calculated with Eq. [37] for sunlit area of each leaf, or with Eq. [38] for the corresponding shaded area. Equation [39] has three parameters: {phi} is the quantum efficiency of CO2 assimilation [µmol CO2 (µmol quanta)–1] and corresponds to the initial slope of the curve; Asat is the saturated assimilation rate (µmol CO2 m–2 of leaf s–1) when APAR is not limiting the process and corresponds to the asymptote of the curve; {theta} is the ratio of the diffusion resistance to the total resistance to CO2 assimilation and is a unit less curvature parameter. The lower root of Eq. [39] is the physiologically meaningful solution (0 < {theta} < 1) used in the model:

[40]

Leaf Age Effect
Leaves are assumed to be photosynthetically active when they exhibit a green surface area of at least 5% of the maximum surface area per leaf. Stirling et al. (1994) reported the general pattern of variation of light response curve parameters with leaf age at constant temperature (20°C): Asat and {theta} changed while {phi} remained constant. Boedhram (1998) reported similar seasonal trend of parameters. However, evidence in the literature (McCree, 1972; Ku and Edwards, 1978; Moreno-Sotomayor et al., 2002) suggests that {phi} decreases in old leaves. An internal algorithm allows the model to keep track of each leaf age by separating leaf expansion from leaf maturity and senescence. During leaf expansion the current expanded leaf area is compared with the maximum leaf area to ascertain relative leaf age (r). When leaf expansion is completed Asat is assumed to peak (Stirling et al., 1994; Boedhram, 1998). The thermal time elapsed after leaf expansion is completed is compared with the thermal time required to reach 50% senescence (i.e., leaf longevity) to determine relative leaf age (r). The value of Asat is calculated using two sigmoidal functions; one yields larger values with increasing leaf age during leaf expansion; the other yields decreasing values afterward as the leaf grows older:

[41]
Equation [41] is a relative function (0 – 1) with vertical offset (a0) scaled to calculate the species maximum assimilation rate at 30°C (Ax, µmol CO2 m–2 s–1). Parameter au is the upper end of the sigmoid, ka is a curvature parameter, r is the current relative leaf age, and ra50 the relative age when 50% of au is reached. For Ax we used a value of 57 µmol CO2 m–2 s–1 (Wong et al., 1985; Earl and Tollenaar, 1998; Choudhury, 2001).

A similar double-sigmoidal approach was used to calculate the curvature parameter {theta}, but in this case an extended plateau is simulated through most of the life span of the leaf. Therefore, parameter {theta} is calculated as:

[42]
where qu is the upper end of the sigmoid, kq is a parameter controlling the slope of the function, and rq50 the relative age when 50% of qu is reached.

The quantum efficiency parameter ({phi}) has a value of 0.06 µmol CO2 (µmol quanta)–1 (Ku and Edwards, 1978; Ehleringer and Pearcy, 1983) during leaf expansion and the first half of the life cycle of the mature leaf. Thereafter it decreases sigmoidally according to:

[43]
where f0 is the vertical offset of the function and controls the lowest value of {phi} when senescence approaches, fu is the upper end of the sigmoid, kf is a curvature parameter controlling the slope, and rf50 is the relative age when 50% of fu is reached.

Temperature Effect
The effect of temperature on light response curve parameters was derived from published data (Oberhuber and Edwards, 1993; Edwards and Baker, 1993). Oberhuber and Edwards (1993) measured maize leaf assimilation at a range of temperatures (15–40°C) and at two light intensities, 300 and 1100 µmol quanta m–2 s–1. We reconstructed the light response curves for each temperature, from which relative curve parameters (i.e., relative to parameters at 30°C) were derived. These calculations assume that the quantum efficiency parameter ({phi}) remains constant within the range 15 to 40°C (Ku and Edwards, 1978; Ehleringer and Pearcy, 1983). Below 15°C, {phi} decreases due to chilling damage (Stirling et al., 1991; Long, 1999). Above 40°C, {phi} also decreases (Ehleringer and Pearcy, 1983) due to thermal damage of proteins. The convexity parameter ({theta}) also remains constant within the range 15 to 40°C (Thornley and Johnson, 1990) with slight increases at temperatures above and below this range. The Asat parameter increases with temperature and reaches a maximum between 35 and 40°C (Oberhuber and Edwards, 1993). The functions describing the relative effect of temperature on light response curve parameters (pt) are polynomials of the third order:

[44]
where a, b, c, and d are empirical parameters and t is the hourly air temperature. The light response curve parameter corrected by temperature (Pt) is calculated:

[45]
where P30 is either {phi}, Asat, or {theta}, as calculated with Eq. [43], [41], or [42], and pt is the corresponding relative temperature effect as calculated with Eq. [44].

Gross Assimilation
Next, leaf gross assimilation is calculated hourly using Eq. [40] first for the sunlit fraction of each leaf (Asun, µmol CO2 m–2 of leaf s–1) and then for the shadow fraction (Asha, µmol CO2 m–2 of leaf s–1) using the light absorbed calculated with Eq. [37] and [38], respectively, and the temperature-adjusted parameters calculated with Eq. [45]. The canopy instantaneous gross assimilation (Acan, µmol CO2 m–2 of land area s–1) integrates the contributions of sunlit and shadow portions of each leaf:

[46]
Canopy instantaneous gross assimilation is converted into hourly g of CO2 and integrated daily as (Aday, g CO2 m–2 of ground d–1):

[47]
and the result is expressed in units of glucose (Adayg, g glucose m–2 of land area d–1):

[48]
Equation [48] assumes that 6 mol of CO2 (44 g mol–1) are reduced to produce 1 mol of glucose (180 g mol–1).

Respiration
We followed the approach of Wilkerson et al. (1983) to calculate plant tissue respiratory costs. The procedure differentiates maintenance from growth respiration.

Maintenance Respiration
In a recent review of respiration paradigms, Amthor (2000) distinguishes two main components of maintenance respiration, namely turnover of cellular components and intracellular ion-gradient maintenance. We calculate maintenance respiration (Rm, g glucose m–2 of land area d–1) by adding the contributions of the two components mentioned by Amthor (2000):

[49]
where Ra [g glucose respired (g glucose assimilated)–1 d–1] is the unit respiratory cost of cellular components turnover, Adayg is the daily gross assimilation (g glucose m–2 d–1) calculated with Eq. [48], Rb [g glucose respired (g DW)–1 d–1] is the unit respiratory cost of maintenance of membranes and ion-gradients, and B (g m–2) is the effective biomass demanding respiratory maintenance. The first component in Eq. [49] represents the respiratory cost associated with turnover of enzymes and lipids. It is a function of the gross assimilation rate primarily because this is a good approximation for amount and activity of photosynthetically active tissue. The second component in Eq. [49] (RbB) represents the energy demand for the maintenance of cell membranes and ion gradients, and is a function of biomass (Wilkerson et al., 1983). The effective biomass B in Eq. [49] is calculated as:

[50]
where Rwt, Lwt, Swt, Ewt, and Gwt are the dry weight (g m–2) of roots, leaves, stems, reproductive organs (ear) and grain, respectively. Equation [50] assumes that the 20% content of lignin in stems is a structural component that does not demand respiratory maintenance; it also assumes that reserves stored in the grain (79.5% starch and 4.5% oil) are not subjected to respiratory maintenance.

Since both components in Eq. [49] are temperature-dependent, the second-degree polynomial provided by McCree (1974) is used to estimate Ra and Rb:

[51]

[52]
where THOUR is the hourly air temperature (°C). Parameters rp and rg are the hourly g of glucose respired at 30°C, per g of glucose assimilated, and per g of dry weight, respectively. Current values of rp and rg in CROPGRO represent 20 yr of calibration for soybean [Glycine max (L.) Merr.] (Wilkerson et al., 1983; Boote et al., 1998). Therefore, our approach was to define rp and rg for maize using the parameters in CROPGRO as a benchmark. Yamaguchi (1978) evaluated seasonal photosynthesis and respiration of maize and soybean. When total seasonal respiration is expressed per unit of total dry weight [g glucose (g DW)–1], maize respiration rate is 45% of the soybean respiration rate. Thus, we scaled parameter rg accordingly and then calibrated parameter rp to yield a similar seasonal ratio of respiration to gross photosynthesis as the ratio measured in maize by Yamaguchi (1978). Resulting parameters rp and rg were 0.0026 and 0.000158, respectively.

Growth Respiration
Growth respiration follows Penning de Vries and colleagues approach (Penning de Vries and van Laar, 1982; Penning de Vries et al., 1989). The procedure calculates a respiratory cost [g of glucose (g component)–1] associated with the transport and biosynthesis of five organic components (carbohydrates, proteins, lipids, lignins, organic acids) and with the transport of minerals required for tissue growth (Table 10 in Penning de Vries et al., 1989). The growth respiratory demand for each organ is weighted according to its composition. For instance, the respiratory cost for leaves [RCL, g glucose (g leaf growth)–1] is:

[53]
where Car, Pro, Lip, Lig, Oac, and Min are the fraction composition of carbohydrates, proteins, lipids, lignins, organic acids, and minerals (ash) in leaves (Car + Pro + Lip + Lig + Oac + Min = 1). Next a weighted growth respiratory demand is calculated for the whole plant (RDG, g glucose [g biomass growth]–1):

[54]
where RCR, RCL, RCS, RCE, and RCG are the respiratory cost calculated for roots, leaves, stems, reproductive organs, and grain [g glucose (g organ growth)–1], and GRR, GRL, GRS, GRE, and GRG are the growth rate of roots, leaves, stems, reproductive organs, and grain (g m–2).

Growth Rate
The daily potential growth rate (PGRP, g plant–1 d–1) is calculated as:

[55]
where Adayg is calculated with Eq. [48], Rm with Eq. [49], RDg with Eq. [54] and PD is the plant population density (plant m–2); PGRP, calculated with Eq. [55], is used by the new model instead the PGR, calculated with Eq. [1] by the original CERES.

Model Calibration
Several published data sets were used to calibrate CERES-PR. The canopy height algorithm (Eq. [9]) was calibrated using previous detailed measurements (Lizaso, 1993). Canopy height was measured in field-grown plants under near optimal conditions, as the distance from the ground up to the point at which the edges of the uppermost expanding leaf first separated from each other, or, when visible, up to the collar of the flag leaf. To calibrate canopy width, we used simultaneous field measurements of leaf area and light interception (Westgate et al., 1997). Pioneer 3790, a dent-type hybrid of 95 d relative maturity, was planted in 1986 in Morris, MN, at 7.2 plants m–2 in rows spaced 76 cm. Leaf area was measured destructively every 7 to 10 d after emergence. Light interception was evaluated with the same time interval around 1200 h and by placing the 1-m line quantum sensor (LI-191SB, LICOR, Lincoln, NE) perpendicular and between rows, thus capturing the gap between canopy units.

To calibrate the effect of leaf age on the light response curve parameters, we used the same data set that previously provided information to calibrate the detailed description of leaf area (Lizaso et al., 2003a). Temperature effects on light response curve parameters were developed from published information (Oberhuber and Edwards, 1993; Edwards and Baker, 1993) under conditions close to optimum for plant growth.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Canopy Growth
To implement the hedgerow approach, we developed algorithms to simulate the growth of maize canopy height and width through the season. The model benefits from the adequate simulation of canopy growth since both variables are used to compute hourly light absorption by leaves from solar elevation and the shadow projected by canopy units. Figure 1 shows the progression of canopy height through the season as simulated with CERES-PR. Since the algorithm (Eq. [9]) uses a relative phenological scale previously developed and incorporated into CERES-Maize (Lizaso et al., 2003b), we also included the simulation of LAI for the same experiment, showing the accurate prediction of leaf area surface matching maximum leaf expansion at silking.



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  		Fig. 1. Measured and simulated canopy height and leaf area index of maize cultivar GL 420, 5.6 plants m–2, on 1991. Original data from Lizaso (1993).

 
The simulation of canopy width is based on the expansion of leaves. We assumed that the projection of leaves on a horizontal plane provides a good estimation of canopy width. Only leaves that have expanded at least 80% of their final surface area are included in the calculation. Before this level of expansion, leaves are associated with the whorl and are more vertically oriented. We found a strong relationship (r2 = 0.987) between leaf area and leaf length using data from several cultivars (Fig. 2). This is consistent with previous reports showing a fairly predictable leaf shape for maize (Stewart and Dwyer, 1999). Calculated leaf length and an average inclination angle are used to compute the leaf projection (Eq. [11]). Figure 3 shows the seasonal measurements and CERES-PR simulated fraction of intercepted PAR at noon. Simulations were run for various average inclination angles of leaves. When the leaf angle was 45°, simulated canopy closure occurred too early in the season and fraction of intercepted PAR grew faster than measured values. When using a leaf angle of 75°, complete canopy closure never occurred, and the fraction of intercepted PAR remained low for whole season. A leaf angle of 64° provided the best simulation of light interception, resulting in a fraction of intercepted PAR closest to the measured values (RMSE = 0.04).



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  		Fig. 2. Relationship between leaf length and leaf area for individual leaves that have completed at least 80% of expansion.

 


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  		Fig. 3. Field measured and model simulated fraction of intercepted PAR. Measurements were done around 1200 h in north–south oriented rows (Westgate et al., 1997). Simulations were done at 1200 h with various average angles of expanded leaves ({delta}, Eq. [11]). Optimum {delta} (minimum RMSE) was 64°. Vertical lines are standard errors.

 
Leaf Age
The model simulates effects of leaf age on leaf assimilation by linking the changes in the light response curve parameters to the current green leaf area simulated for each leaf. Since water and N stresses can reduce leaf longevity and accelerate leaf senescence, we assume that leaf age is dynamically associated to environmental factors summarized daily by the current status of the green leaf surface area of each leaf. Figure 4 shows the simulated surface area of leaf 13 and the corresponding evolution of the light response curve parameters on a thermal time scale. The model assumes optimum temperature of 30°C and no water or N limitation. The parameters follow the general trend with age reported by Stirling et al. (1994) and Boedhram (1998). Stirling et al. (1994) measured light response curves at 20°C in leaf discs taken from a segment of the fourth leaf of field-grown plants. The main difference between our simulated parameters and those measured by Stirling et al. (1994) is the trend in quantum efficiency ({phi}) that they found to be constant under their experimental conditions. However, reports from the literature using intact attached leaves in a controlled environment (Ku and Edwards, 1978), or in field conditions (McCree, 1972; Moreno-Sotomayor et al., 2002), suggest a decrease in quantum efficiency in old leaves probably associated with declining leaf N content. Currently, CERES-Maize does not simulate N concentrations per leaf. When this component is developed and incorporated into the model, levels of leaf N in each leaf could be used to control the reduction of Asat and quantum efficiency as senescence approaches.



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  		Fig. 4. Effect of leaf age on light response curve parameters: green leaf area simulated for the specified leaf and corresponding light response curve parameters.

 
Using the parameters depicted in Fig. 4, CERES-PR simulated the effect of leaf age on instantaneous gross assimilation (Fig. 5). Leaf age is indicated by the thermal time accumulated after emergence. The simulated photosynthetic rate increases as the leaf expands, reaching the maximum Asat when leaf expansion is completed (725 GDD8 after emergence). A subsequent decline in Asat (Fig. 4) decreased photosynthetic rates as the leaf aged, until the beginning of leaf senescence when the three parameters decreased resulting in a rapid drop in the photosynthetic capacity of the leaf (Fig. 5).



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  		Fig. 5. Photosynthetic light response curves simulated for the specified leaf at selected thermal times after emergence (GDD8).

 
Leaf Temperature
The effect of temperature on leaf photosynthesis of C4 plants is much less understood than the corresponding effect for C3 plants (Naidu et al., 2003). We chose to use available measurements instead of theoretical conventions (e.g., Thornley and Johnson, 1990). Measured leaf assimilation at two light intensities through a range of leaf temperatures (Oberhuber and Edwards, 1993; Edwards and Baker, 1993) provided the basis to derive the relative temperature functions depicted in Fig. 6a. The parameters of the polynomials fitted to the measurements (Eq. [44]) are provided in Table 2. Consistent with C4 photosynthesis theory, the initial slope ({phi}) of the light response curves is constant except at the lowest (15°C) and highest (45°C) temperatures in the range simulated. The curvature parameter ({theta}) is also constant (Thornley and Johnson, 1990).



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  		Fig. 6. Relative effect of temperature (Eq. [44]) on light response curve parameters, and simulated leaf assimilation curves at selected temperatures when leaf expansion is completed (original data from Oberhuber and Edwards, 1993). Parameters are: Asat, saturated assimilation rate (µmol CO2 m–2 leaf s–1); {phi}, quantum efficiency of CO2 assimilation [µmol CO2 (µmol quanta)–1]; {theta}, curvature (unitless). Dashed lines correspond to 40 and 45°C.

 

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  		Table 2. Coefficients of Eq. [44] used to estimate hourly temperature effect on light response curve parameters and determination coefficients. Original data from Oberhuber and Edwards (1993) and Edwards and Baker (1993).

 
Using the relative temperatures of Fig. 6a we simulated assimilation curves within the range of temperatures 15 to 45°C assuming complete leaf expansion. Light response curve parameters when the leaf completes expansion are: {phi} = 0.06 µmol CO2 (µmol quanta)–1; Asat = 57 µmol CO2 m–2 s–1; {theta} = 0.9. The simulated assimilation curves depicted in Fig. 6b predicted a decrease of 58% in leaf assimilation at light-saturated conditions when the temperature drops from 35 to 15°C. Naidu et al. (2003) reported a reduction of 59% in assimilation of light-saturated maize leaves for the same temperatures.

Plant Growth
Figure 7 provides an example of the seasonal simulation of the photosynthesis and respiration processes by CERES-PR. When the crop had the maximum leaf surface area around silking, both photosynthetic and respiration rates peaked around 68 and 27 g glucose m–2 d–1 for a ratio R/Ag of 0.39. The seasonal trends depicted in Fig. 7 are in good agreement with previous reports showing seasonal profiles of photosynthesis and respiration (e.g., Andre et al., 1978; Pearson et al., 1984; Dong et al., 1993). Dong et al. (1993) used field chambers to measure rates of canopy photosynthesis and respiration through the growing season. At silking, the R/Ag ratio was 0.36 similar to our simulated 0.39.



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  		Fig. 7. Simulated seasonal progression of canopy gross assimilation and respiration with CERES-PR for hybrid Pioneer 3790, planted in Morris, MN, in 1986 at 5.4 plants m–2.

 
CERES-Maize has been calibrated over the years for many environmental conditions yielding reasonable predictions, particularly under nonstress situations as those depicted in Fig. 8. When we compared the daily potential growth rate predictions of CERES-Maize with our CERES-PR, both models followed a similar trend (Fig. 8), although CERES-PR predicted larger growth early in the season. However, CERES-PR was able to simulate more closely the seasonal expansion and senescence of leaf area, particularly during the grain filling. More detailed testing of CERES-PR and the sensitivity analysis is provided in a companion paper (Lizaso et al., 2005).



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  		Fig. 8. Simulated seasonal progression of potential growth rate and measured and simulated leaf area index and aboveground biomass as predicted with CERES-Maize and with CERES-PR for hybrid Pioneer 3790, planted in Morris, MN, in 1986 at 5.4 plants m–2.

 

   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
The objective of the present work was to substitute the current calculation of the daily growth rate in CERES-Maize with a more mechanistic leaf level photosynthesis and respiration submodels. This substitution will open opportunities for further model improvement and increased accuracy, especially under stress conditions. To accomplish our objective we developed a model with three main components simulating leaf light absorption, instantaneous leaf gross assimilation, and daily canopy respiration. CERES-PR is unique compared with previous models of leaf photosynthesis (e.g., SUCROS) because it simulates individual values of leaf surface area, leaf age, and leaf assimilation for each leaf. It also requires only a minimum set of daily weather inputs (i.e., no wind speed, air humidity). The daily potential growth rate calculated with our model uses water and N stress factors in the same way that the current CERES model does. It uses also the current relative response to ambient CO2 levels, but this could be modified in the future.

Our model provides a much needed ability to separate the photosynthetic gross assimilation from the associated respiratory cost, allowing the independent simulation of both processes as affected by environmental factors. We incorporated the effects of leaf age, light intensity, and temperature. Our next target is to develop and incorporate a stomatal conductance model allowing for simultaneous simulation of C assimilation and water transpiration at the leaf level. This will involve hourly energy balance and CO2 effects on stomatal conductance (and photosynthesis) addressed concurrently. The challenge is doing so without requiring additional daily weather inputs (solar radiation, maximum and minimum temperature, and rainfall).


   ACKNOWLEDGMENTS
 
This research was supported by the Biological and Environmental Research Program (BER), U.S. Department of Energy, through the Great Plains Regional Center of the National Institute for Global Environmental Change (NIGEC) under Cooperative Agreement no. DE-FC03-90ER61010. The data to calibrate our temperature functions was kindly provided by Dr. Gerald E. Edwards from Washington State University. Thanks also go to Armen Kemanian from Washington State University, who provided excellent suggestions to implement the calculation of extinction coefficients according to Campbell (1986). Heartily thanks to Ricardo Ramirez, who taught me the principles of corn physiology.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES