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Published online 3 January 2006
Published in Agron J 98:34-42 (2006)
DOI: 10.2134/agronj2004-0298
© 2006 American Society of Agronomy
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Crop Models

Evaluating the CROPGRO–Soybean Model Ability to Simulate Photosynthesis Response to Carbon Dioxide Levels

G. Alagarswamya,*, K. J. Bootea, L. H. Allen, Jr.b and J. W. Jonesc

a Dep. of Agronomy, Univ. of Florida, Gainesville, FL 32611-0500
b USDA-ARS and Dep. of Agronomy, Univ. of Florida, Gainesville, FL 32611-0965
c Dep. of Agricultural and Biological Engineering, Univ. of Florida, Gainesville, FL 32611-0570. Florida Agric. Exp. Stn. Journal Ser. no. R-10598

* Corresponding author (alagarsw{at}msu.edu)

Received for publication December 6, 2004.

   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS and DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Atmospheric carbon dioxide concentration [CO2] will increase in the future and will affect global climate and ecosystem productivity. Crop models used in past assessments of climate change effect on ecosystem productivity have not been adequately tested for the ability to simulate ecosystem responses to [CO2]. Our objective was to evaluate the ability of the default CROPGRO–Soybean model to predict the responses of net leaf photosynthesis (A) and canopy photosynthesis (Acan) to photosynthetic photon flux (PPF) at different [CO2]. We also compared the default leaf photosynthesis equations in CROPGRO with the full Farquhar equations for ability to predict the response of A to [CO2]. Simulated and observed A and Acan were light saturated at 800 µmol m–2 s–1 PPF at ambient [CO2] but did not light saturate at PPF >1100 µmol m–2 s–1 at elevated [CO2]. Observed and simulated A responded asymptotically to increasing intercellular [CO2]. The CROPGRO default photosynthesis equations and the Farquhar equations simulated A equally well at all [CO2]. Doubled [CO2] increased simulated A by 52% and Acan by 42%; these values are close to the increases of 39 to 48% for A and 59% for Acan reported in the literature. Root mean square errors for simulated A and Acan were low, and Willmott's index of agreement ranged from 0.86 to 0.99, confirming that the CROPGRO model with default photosynthesis equations can be used to evaluate potential effects of [CO2] on soybean photosynthesis and productivity.

Abbreviations: LAI, leaf area index • MSE, mean squared error • MSEs, systematic mean squared error • MSEu, unsystematic mean squared error • PPF, photosynthetic photon flux • QE, quantum efficiency • RuBP, ribulose 1,5 bisphosphate • RMSE, root mean squared error


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS and DISCUSSION
 CONCLUSIONS
 REFERENCES
 
INCREASE OF carbon dioxide concentration [CO2] in the atmosphere will change future global climate via increased temperature and altered precipitation patterns, which affect ecosystem productivity. Carbon dioxide concentration steadily increased from 280 µmol CO2 mol–1 during the preindustrial period (around the year 1750) to about 375 µmol CO2 mol–1 in the year 2000. Projections of [CO2] in the year 2100 will range from 540 to 970 µmol CO2 mol–1 of air, depending on emission scenarios (Houghton et al., 2001). The projected rise in [CO2] will influence plant processes at various hierarchic levels from short-term effects on net leaf photosynthesis (A) to long-term effects on primary productivity of terrestrial ecosystems.

Approaches to predict the effects of climate change on primary productivity often involve the use of mechanistic ecosystem simulation models coupled to climate change predictions from atmospheric general circulation models. Crop simulation models have been used to assess the productivity responses of various crops to anticipated future changes in [CO2] and temperature (Adams et al., 1990; Wang et al., 1992; Easterling et al., 1993; Wall et al., 1994; Matthews et al., 1995). Using the SOYGRO model V5.42 (Jones et al., 1989) with empiric adjustments to simulate effects of [CO2] on biomass accumulation, Peart et al. (1989) evaluated the impact of [CO2] on potential soybean production. The CROPGRO model (Boote et al., 1998) is more mechanistic than the SOYGRO model. Leaf photosynthesis simulation in CROPGRO is an adaptation of the equations of Farquhar et al. (1980) in an hourly leaf-level to canopy assimilation scaling approach with hedge-row light interception. The goal of this paper is to evaluate the CROPGRO model for its ability to simulate soybean leaf and canopy assimilation response to [CO2].

The leaf photosynthesis model of Farquhar et al. (1980) has been widely used to simulate response of A to [CO2]. This model assumes that A is limited by the slower of two processes, namely the maximum rate of Rubisco-catalyzed carboxylation (Rubisco-limited) and the Ribulose 1,5 bisphosphate (RuBP) regeneration rate controlled by electron transport rate (RuBP-limited). The Farquhar model requires Rubisco enzyme kinetic parameters. Some of the kinetic parameters of the Rubisco enzyme, such as Michaelis constants for oxygen (Ko) and for CO2 (Kc) and CO2 compensation point in the absence of dark respiration ({Gamma}*), are constant across species of C3 plants. However, other required parameters that depend on the Rubisco enzyme concentration, such as maximum RuBP-saturated rate of carboxylation (Vc,max), maximum RuBP-saturated rate of oxygenation (Vo,max), and dark respiration rate (Rd), vary even within individual plants because they are conditioned by growing conditions. This makes application of the Farquhar model in mechanistic crop simulation models difficult.

The CROPGRO model uses a modified Farquhar and von Caemmerer (1982) approach in which only the RuBP-limited part is used to simulate responses of A to [CO2]. Unlike the leaf photosynthesis model of Farquhar et al. (1980) and Farquhar and von Caemmerer (1982), CROPGRO's default leaf photosynthesis equations do not require Kc, Ko, Vc,max, or the maximum rate of electron transport (Jmax) to simulate A. Rather, the approach in CROPGRO defines light-saturated leaf photosynthetic rate (Amax) at reference values of CO2, O2, temperature, reference specific leaf weight (SLWREF), and leaf nitrogen (N) concentration. It uses an asymptotic exponential light response equation to simulate A, where quantum efficiency (QE) and Amax are dependent on [CO2], O2, and temperature (Boote and Pickering, 1994). Models of photosynthesis at a canopy ecosystem level require not only equations describing CO2 fluxes at leaf level but also some method of scaling photosynthesis from leaf to canopy level. CROPGRO simulates hourly Acan using a hedge-row light interception model and leaf-level photosynthesis parameters (Boote and Pickering 1994; Pickering et al., 1995). Briefly, the model computes absorption of direct and diffuse irradiance by sunlit and shaded leaf classes as a function of canopy height, width, leaf area index (LAI), leaf angle, row direction, latitude, day of year, and time of day. The Acan is the sum of sunlit and shaded leaf photosynthetic rates over their respective LAI classes.

Before applying the CROPGRO model in future assessments of climate change effects, its ability to predict [CO2] effects on A and Acan should be evaluated using results from controlled-environment studies. Our objectives were to evaluate the CROPGRO–Soybean model for predictions of (i) response of A to PPF at 330 (ambient) and 660 (elevated) µmol CO2 mol–1, (ii) response of A to sub- to supra-ambient [CO2], (iii) response of Acan to PPF at sub- and supra-ambient [CO2], and (iv) to compare the simulation of A response to intercellular [CO2] (Ci) with CROPGRO's default photosynthesis equations compared with the full Farquhar equations. To evaluate model performance, we followed the statistical model testing procedures of Willmott (1981) and Willmott et al. (1985).


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS and DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Description of Data Sets Used in Model Evaluation
Data published by Valle et al. (1985) were used to test the simulated response of A to PPF at ambient and elevated [CO2]. Data published by Harley et al. (1985), Valle et al. (1985), Sims et al. (1998), and Griffin and Luo (1999) were used to test the model's ability to simulate the response of A to Ci. We used Acan data of Campbell et al. (1990) for soybean canopies grown at six sub- to supra-ambient [CO2] to simulate Acan response to PPF. The experimental protocols describing growth conditions, age of plants, and photosynthesis measurement conditions are given in Table 1. Data from Harley et al. (1985) contained two sets of experiments. In one of the experiments, the light levels during A measurements were high (PPF > 2000 µmol m–2 s–1) compared with growth-light level, and we designated this experiment as a high-light experiment. In another experiment, the light level during A measurement was low and same as growth intensity (PPF = 800 µmol m–2 s–1), and we designated this as a low-light experiment.


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  		Table 1. Experimental protocols for growing plants and measuring CO2 assimilation rate in various data sets used in the model evaluation.

 
Net Leaf Photosynthesis Simulation
For these simulations, we used the default unmodified code and equations of the CROPGRO model (V4.0), where A is simulated using an asymptotic exponential light-response equation:

[1]
where A is the net rate of CO2 uptake per unit leaf area (µmol m–2 s–1), Amax is the light-saturated A (defined at 30°C, 350 µmol CO2 mol–1, 21% O2, leaf nitrogen [N] concentration of 55 g kg–1, and SLWREF of 35.0 g m–2 leaf area); and QE is the quantum efficiency of the leaf, which is referenced at the same conditions. Beginning with the 1994 release of the CROPGRO model, temperature and CO2 effects on QE and Amax have been modeled using a modification of the Farquhar and von Caemmerer (1982) method as described in Eq. [37], [38], and [41] of Boote and Pickering (1994) and as described by Pickering et al. (1995). For simulating A, we used the following default soybean model input parameters: Amax = 1.00 mg CO2 m–2 s–1 (22.7 µmol CO2 m–2 s–1) defined at SLWREF = 35.0 g m–2, and leaf nitrogen (N) concentration = 55 g kg–1. Specific leaf weight (SLW) and leaf N concentration normally vary during model simulations due to climatic and management conditions. Thus, actual single-leaf Amax was modeled as a linear function of SLW and as a quadratic function of leaf N concentration. The rationale for the effect of SLW on Amax was that thick leaves have more chloroplasts and a higher mass of photosynthetic enzymes and thereby have enhanced photosynthetic capacity per unit leaf area. Hence, SLW and leaf N concentration were model state variables that influenced Amax. To simulate the leaf conditions for the specific days of tested experiments, we input into the model the SLW, leaf N concentration, LAI, hourly PPF, temperature, and [CO2] for any day and output the hourly means of instantaneous gross A and Acan. The SLW data for the Valle et al. (1985) data set were taken from a comparable study by Allen et al. (1988). The SLW data were not available from Harley et al. (1985) but were derived by running the crop model for the growth temperature and PPF conditions up to the specific day when photosynthesis was measured. The SLW and leaf N inputs for testing simulations of Sims et al. (1998) were taken from a comparable study by Luo et al. (1998), and SLW and leaf N data for testing simulations of Griffin and Luo (1999) were taken from the study by Griffin and Luo (1999).

Dark Respiration Rate
The CROPGRO model simulates gross leaf A and Acan and separately computes growth and maintenance respiration of each tissue type. Thus, the model does not normally compute net A. However, to compare with published data on net A, we took the outputs of simulated gross A and subtracted the observed Rd. Sims et al. (1998) and Griffin and Luo (1999) measured net A and Rd. Harley et al. (1985) measured Rd as a function of leaf temperatures (TLEAF) varying from 15 to 45°C. We fitted a nonlinear relationship to the data.

[2]

For the Harley et al. (1985) data, simulated net A was derived by subtracting Rd calculated with Eq. [2] from the modeled gross photosynthesis. For the Valle et al. (1985) data, Rd values for ambient and elevated [CO2] were obtained from graphs as the y intercept where the PPF was zero. For the Campbell et al. (1990) data, we used the modeled total canopy respiration (including growth and maintenance components) for the specific day when Acan was measured. Total modeled respiration was interpolated for the observed temperature using canopy Rd and air temperature relationships developed by Pan (1996). Net Acan was derived by subtracting the interpolated Rd from modeled gross Acan.

Comparison of CROPGRO's Default Photosynthesis Equations with Farquhar Photosynthesis Equations
We compared CROPGRO's default photosynthesis equations with the full Farquhar equations for their ability to predict A response to Ci. We used A vs. Ci (A/Ci) data published by Sims et al. (1998), Griffin and Luo (1999), and Harley et al. (1985) for model comparison. The parameters Kc, Ko, Vc,max, Jmax, and Rd required for the Farquhar equations were taken from these publications. The Vc,max values were 48.7 and 49.2 µmol m–2 s–1 for soybean grown at ambient and elevated [CO2], respectively, in the Griffin and Luo (1999) data set and 83.6 µmol m–2 s–1 for the Sims et al. (1998) data set. The Jmax values were 131.3 and 139.6 µmol m–2 s–1 for soybean grown at ambient and elevated CO2, respectively, in the Griffin and Luo (1999) data set and 184.8 µmol m–2 s–1 for soybean in the Sims et al. (1998) data set.

Evaluation of Model Performance
We compared simulated and observed A and Acan using a linear regression approach in conjunction with the deviation-based statistical measures and dimensionless index of agreement (D) as suggested by Willmott (1981) and Willmott et al. (1985). In this method, we used observed and simulated A in response to various levels of PPF and Ci and hourly mean values of observed and simulated Acan (from 0700 to 1700 h). The deviation-based statistical parameters (root mean squared error [RMSE] and its systematic [RMSEs] and unsystematic [RMSEu] components and Willmott's index of agreement [D index]) were used to compare how well modeled A and Acan compared with the observed values. Because there was no calibration of the model, the results reported in this study can be considered a validation of model performance in predicting A and Acan.


   RESULTS and DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS and DISCUSSION
CONCLUSIONS
 REFERENCES
 
Response of Net Leaf Photosynthesis to Photosynthetic Photon Flux at Ambient and Elevated Carbon Dioxide Concentration
The rate of regeneration of CO2 acceptor RuBP is dependent on the concentrations of the high-energy nucleotides ATP and reduced NADPH, both of which depend on photochemical energy supply and rates of whole-chain electron transport. Thus, it was essential to evaluate the model capability to simulate the response of A to photochemical energy supply, which is controlled by PPF. Observed and simulated A increased as PPF increased and were light saturated at 800 µmol m–2 s–1 PPF at ambient [CO2] (330 µmol mol–1). At high light (PPF > 1100 µmol m–2 s–1), simulated A was 21.7 µmol m–2 s–1, closely matching the observed A of 21.4 ± 3.1 µmol m–2 s–1 (mean ± SD of four leaves) (Fig. 1 ). At elevated [CO2] (660 µmol mol–1), simulated A was 33.1 µmol m–2 s–1, but the observed A was 41.4 ± 8.4 µmol m–2 s–1 (mean ± SD of four leaves), indicating that model underpredicted observed A. Grant (1989, 1992) had previously used data from Valle et al. (1985) to test a leaf photosynthesis model that contained the full Farquhar and von Caemmerer (1982) leaf photosynthesis equations. Grant (1989) tested the response of A to irradiance and showed that the simulated light-response curves closely matched the observed curve of Valle et al. (1985) at ambient [CO2], whereas the model underpredicted the response of A to irradiance at elevated [CO2] above 400 µmol m–2 s–1 PPF. Grant's model underpredicted A by 24% at PPF >1100 µmol m–2 s–1. In a second paper, Grant (1992) again showed that the leaf photosynthesis model underpredicted A by 14% at elevated [CO2] compared with the data of Valle et al. (1985). The CROPGRO model simulations of response of A to PPF were similar to the results reported by Grant (1989, 1992). Our results, taken together with Grant's simulations, indicate that it is likely that the observed A by Valle et al. (1985) at elevated [CO2] are very high, and two different simulation models were not able to reproduce these high leaf photosynthetic rates. Our underprediction by 20% is in the same range as the 14 to 24% underpredictions that Grant reported. It is possible that CO2 leakage from the leaf chamber system associated with steeper gradient from elevated [CO2] to ambient could have contributed to greater observed A.



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  		Fig. 1. Simulated soybean net leaf photosynthesis (A) response to PPF. Symbols are for measured data for eight different leaflets (adapted from Valle et al., 1985), and curves are for simulations using default CROPGRO photosynthetic equations. Open symbols and solid line are for ambient [CO2] (330 µmolmol–1); solid symbols and dashed line are for elevated [CO2] (660 µmol mol–1).

 
Simulated and observed A agreed closely at ambient [CO2] (Table 2). The RMSE was 15% of the observed mean A, indicating that the model captured most of the variation in observed A. The proportion of unsystematic mean squared error (MSEu) (equivalent to RMSEu2) to MSE (equivalent to RMSE2) was high (87%), and the proportion of systematic mean squared error (MSEs) (equivalent to RMSEs2) to MSE was only 13%. Low values of MSE, values of MSEu approaching MSE, and values of MSEs approaching zero are measures of a "good model." The D index was 0.97, reflecting the degree to which the observed A was accurately estimated by the model at ambient [CO2]. Unlike simulation of A in ambient [CO2], RMSE was 25% of the observed mean A at elevated [CO2]. The proportion MSEs to MSE was high (84%), indicating that the model did not predict well at high [CO2], although the D index was 0.93.


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  		Table 2. Mean ± SD of net leaf photosynthesis and results of regression analysis Pi = a x Oi + b, where Oi are observed (Valle et al., 1985) and Pi are simulated leaf photosynthesis by the default CROPGRO equations for two [CO2]. Also shown are Willmott's index of agreement, root mean square error, and the systematic and unsystematic components of the root mean square error.

 
The model predicted that doubled [CO2] from 330 to 660 µmol mol–1 increased simulated A (at PPF >1100 µmol m–2 s–1) by 52%, similar to values of most published studies. The simulated doubled [CO2] effect on A for soybean was similar to the 48% increase reported by Vu et al. (1997), the 39% increase reported by Ainsworth et al. (2002), and the 45% increase reported by Booker et al. (2005). In contrast, Valle et al. (1985) reported an increase of 93% due to doubling of [CO2]. The simulated quantum efficiency by the CROPGRO model at 330 and 660 µmol CO2 mol–1 was 0.050 and 0.064 µmol CO2 mol–1 quanta, respectively, which compares well with values reported by Ehleringer and Björkman (1977).

Response of Leaf Photosynthesis to Intercellular Carbon Dioxide Concentration
The primary source of biochemical limitation to A depends generally on the Ci. It is therefore important to evaluate CROPGRO model predictions of A/Ci response. We compared simulated A/Ci curves to observed A/Ci data from Valle et al. (1985), Harley et al. (1985), Sims et al. (1998), and Griffin and Luo (1999). Observed and simulated A responded asymptotically to increases in Ci in all data sets with an initial steep slope at subambient [Ci], where A is generally limited by Rubisco activity (Fig. 2 ). Simulated and observed A/Ci curves exhibited a gradual saturation as Ci increased above ambient [Ci] and approached the RuBP-regeneration limited part of the A/Ci response curve. This response of A to Ci is expected because increased [CO2] provides more substrate for carboxylation and overcomes the competitive inhibition of Rubisco enzyme by oxygen. The simulated A/Ci curves showed similar responses as reported by Griffin and Luo (1999), Valle et al. (1985), and Sims et al. (1998) (Fig. 2a–d). In contrast, the model underpredicted A at all Ci levels above ambient [CO2] in the data sets from Harley et al. (1985) (Fig. 2e–f). In their high light level experiment, the observed A at 1200 µmol mol–1 Ci was 60 µmol m–2 s–1, whereas the model predicted 34 µmol m–2 s–1. One reason for this anomaly could be that very high light levels were used during A measurement (PPF >2000 µmol m–2 s–1), whereas the plants were grown at low light levels (PPF {approx}800 µmol m–2 s–1 (Table 1). In a low light experiment by Harley et al. (1985), the observed A was 32.3 µmol m–2 s–1 (at 560 µmol mol–1 Ci and PPF {approx}800 µmol photon m–2 s–1), compared with 50.6 µmol m–2 s–1 (at 580 µmol mol–1 Ci and PPF >2000 µmol photon m–2 s–1) measured by Harley et al. (1985) in the high light level experiment. The simulated A was 24.6 µmol m–2 s–1 at 600 µmol mol–1 Ci and PPF of 800 µmol photon m–2 s–1.



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  		Fig. 2. Simulated net leaf photosynthesis (A) of soybean as a function of intercellular [CO2] (Ci). Symbols are for measured data (mean ± SD, adapted from references), and curves are for simulations using default CROPGRO photosynthetic equations. Panels (a) and (b) are from Griffin and Luo (1999) for plants grown in 350 and 700 µmol CO2 mol–1, respectively; panel (c) is from Valle et al. (1985); panel (d) is from Sims et al. (1998); panel (e) and (f) are from the high- and low-light experiments, respectively, of Harley et al. (1985). Arrows indicate the intercellular [CO2] equivalent to ambient [CO2].

 
The observed and simulated A clustered along the 1:1 line in Valle et al. (1985), Sims et al. (1998), and Griffin and Luo (1999) data sets (Fig. 3a –d). The size of RMSE as the percentage of the observed mean A ranged from 5 to 21%. The D indices were all high, explaining most of the variations in the observed A. In contrast, the model underpredicted A in the high light experiment of the Harley et al. (1985) data set (D = 0.67), where the light environment for plant growth and A measurement were greatly different. In this data set, A values fell below 1:1 when observed A was above 20 µmol m–2 s–1 (Fig. 3e). The size of RMSE compared with the observed mean A was 44%, and the D index was low, indicating that the model did not explain most of the variations in observed A. However, in a low light experiment (Harley et al., 1985) where the light environment for plant growth and A measurement were the same, the simulated A values were closer to the 1:1 line (Fig. 3f), the ratio of RMSE to observed mean A was 27%, and the D index was high. Considering the high D indices and low variance (RMSE was 5–27% of mean) for five of the six data sets used for model evaluation, our analysis indicated that the CROPGRO default photosynthetic equations reasonably simulate the A/Ci curves. The underprediction of A in one experiment by Harley et al. (1985) was an exception, and CO2 leakage could have caused higher A, especially under high light (PPF > 2000 µmol m–2 s–1).



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  		Fig. 3. Comparison of observed (data adapted from references) and simulated net leaf photosynthesis using default CROPGRO photosynthetic equations. (a) Griffin and Luo (1999) for plants grown in 350 µmol CO2 mol–1; (b) Griffin and Luo (1999) for plants grown in 700 µmol CO2 mol–1; (c) Valle et al. (1985); (d) Sims et al. (1998); (e) Harley et al. (1985) (at high light, PPF > 2000 µmol photon m–2 s–1); and (f) Harley et al. (1985) (at low light, PPF {approx}800 µmol m–2 s–1). Solid lines show linear regression, and dashed lines show the 1:1 line.

 
The current leaf photosynthesis equations in the CROPGRO model accurately simulated the response of A to [CO2] because they reproduced the A/Ci curves and the average doubled [CO2] effect on A that have been reported in the literature. Doubling [CO2] from ambient increased simulated Asat by 41, 38, and 36% (mean 38%) in comparison to the observed Asat increase of 61, 35, and 31% (mean 41%) in the Harley et al. (1985), Sims et al. (1998), and Griffin and Luo (1999) data sets, respectively. This simulated response of A to the doubling of [CO2] compares well with the 39% average increase reported with doubling of [CO2] summarized from 78 studies in the meta-analysis of soybean by Ainsworth et al. (2002), with the 49% increase reported by Vu et al. (1997) when [CO2] was increased from 350 to 700 µmol CO2 mol–1, with the 45% increase reported by Booker et al. (2005), and with the 52% increase due to [CO2] doubling reported for various crops (Cure and Acock, 1986).

Comparison of CROPGRO's Default Photosynthesis Equations to Farquhar Photosynthesis Equations
The CROPGRO default photosynthesis equations and the Farquhar photosynthesis equations predicted A/Ci response reasonably well in Griffin and Luo data sets (Fig. 4a , b). CROPGRO predicted A/Ci response well for the Sims et al. (1998) data set, but the Farquhar equations did not, and the Farquhar equations underpredicted A/Ci response at all levels of Ci (Fig. 4c). Sims et al. (1998) derived the Vc,max using kinetic parameters Kc and Ko. The derivation of Vc,max value strongly depends on the use of correct Kc and Ko values. The parameter Jmax was linearly related to Vc,max in 109 crop species (Wullschleger, 1993) and in soybean (Griffin and Luo, 1999). Sims et al. (1998) reported 83.6 and 184.8 µmol m–2 s–1 for Vc,max and Jmax, respectively. However, based on the linear relationship between Vc,max and Jmax developed by Griffin and Luo (1999) for soybean, the revised value for Jmax for Sims et al. data should be 220.0 µmol m–2 s–1 rather than 184.8 µmol m–2 s–1. One reason for the lower predictions of A at all levels of Ci in Sims et al. (1998) data by the Farquhar equations could be the use of lower Jmax values. The predictions of A for Harley et al. (1985) data by both models were reasonably good at Ci levels below 200 µmol mol–1, but both underestimated A in the RuBP-limited portion of the A/Ci response curve (Fig. 4d).



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  		Fig. 4. Comparison of observed (symbols) (data adapted from references) and simulated A using the default CROPGRO photosynthetic equations (dashed lines) or the full Farquhar photosynthetic equations (solid lines). (a) Griffin and Luo (1999) for plants grown in 350, (b) Griffin and Luo (1999) for plants grown in 700 µmol CO2 mol–1, (c) Sims et al. (1998), and (d) Harley et al. (1985). Arrows indicate the intercellular [CO2] equivalent to ambient [CO2] treatments.

 
The Farquhar equations were not superior to CROPGRO's equations for simulating A. Over all the data sets, the mean RMSE for predictions of A by the CROPGRO equations was 2.72, compared with 3.89 for predictions of A by the Farquhar equations (Table 3), indicating that CROPGRO's equations simulated A more closely than did the Farquhar equations. The RMSEs was the major component of RMSE for predictions of A by both models. The D indices ranged from 0.90 to 0.99 for all the data sets used in model evaluation, indicating that the CROPGRO and Farquhar equations were equally efficient in predicting A over a range of Ci.


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  		Table 3. Mean (± SD) of observed and simulated net leaf photosynthesis using the full Farquhar and von Caemmerer (1982) equations or the default CROPGRO equations. Shown also are Willmott's index of agreement and root mean square error and its systematic and unsystematic components.

 
Response of Canopy Photosynthesis to Photosynthetic Photon Flux and Carbon Dioxide Concentration
CROPGRO responses of A are integrated over sunlit and shaded leaf classes. The model simulates vertical gradients in SLW and leaf N concentration with LAI depth. The SLW and leaf N concentration are highest for upper leaves (which maximizes upper leaf response to higher irradiance) and decline progressively toward the bottom of the canopy to affect Amax with LAI depth (Boote and Pickering, 1994). Because canopy photosynthesis plays a vital role in determining the consequences of [CO2] on primary productivity, it is important to evaluate the capabilities of the CROPGRO model to predict the response of Acan to PPF at different [CO2].

Simulated and observed Acan increased with increasing PPF at all [CO2] (Fig. 5 ). Observed Acan light saturated at 800 µmol m–2 s–1 at the two lowest [CO2], but simulated Acan continued to increase at higher light for the higher [CO2] treatments (Fig. 5). Observed Acan was not light saturated even at 1300 µmol m–2 s–1 for [CO2] above 280 µmol mol–1. With the assumption of PPF transmission of 0.88, the simulations underpredicted Acan at [CO2] above 280 µmol mol–1 when the PPF was above 400 µmol m–2 s–1. The recorded PPF shown on the x axis of Fig. 5 was measured outside and above the chambers; however, the initial simulations were done assuming 88% transmission of PPF through chamber walls (transmission measured for this chamber covering material). However, simulations by Kim et al. (2004) for comparable sunlit chambers showed that on a clear day at a height of 0.5 m from soil surface the crop growing area inside sunlit chambers received 108% of ambient PPF because of reflected light from back panels and side panels of the sunlit chambers. To the extent that inside-chamber PPF is higher than what we assumed [from Kim et al. (2004) analyses], the model would be expected to underestimate Acan compared with the observed Acan, especially for larger canopies. To test the influence of possible increase in the radiation environment inside the sunlit chambers, Fig. 5 shows a comparison of simulated Acan using PPF transmission factor of 0.88 or 1.08. With an assumption of 1.08 transmission, the simulated Acan for various [CO2] was much closer to the observed Acan at all but the lowest [CO2] (Fig. 5). Furthermore, some of the remaining underprediction of Acan at higher [CO2] could be attributed to the greater fraction diffuse PPF in the chambers that the model did not predict (with higher PPF, the model predicts less diffuse PPF). The model computes fraction diffuse PPF based on actual radiation compared with the solar constant.



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  		Fig. 5. Simulated soybean net Acan as a function of PPF at six [CO2]. Symbols are from observed data at 5-min intervals (adapted from Campbell et al., 1990), and curves are from simulation by the CROPGRO model using hourly PPF between 0600 and 1700 h, with assumption of PPF transmission of 0.88 (solid lines) or PPF transmission of 1.08 (dashed lines). The PPF on the x axis is external to and above the chamber walls.

 
Moreover, using a multilayer canopy light interception model, simulations of Cecropia peltata L. (a fast-growing tropical tree species) by Allen et al. (1974) indicated that Acan increased slightly with increasing fraction diffuse PPF (up to nearly 0.60 diffuse PPF) even as total global PPF was decreasing across this range. This impact of fraction diffuse PPF on Acan is further supported by the review by Sinclair and Muchow (1999), wherein radiation use efficiency (crop biomass accumulation per unit solar radiation intercepted) was increased as fraction diffuse PPF increased.

With the 1.08 transmission assumption, the simulated and observed Acan clustered close but somewhat below the 1:1 line in all [CO2] except at 160 and 220 µmol mol–1 (Fig. 6 ). The D index values ranged from 0.96 to 0.99 in all but the lowest [CO2], reflecting the degree to which the simulated Acan compares with the observed. The RMSE expressed as a percentage of observed mean Acan ranged from 8 to 16% in all but the lowest [CO2], giving a good overall measure of model performance and complementing the D index. A full statistical comparison in Table 4 shows the general improvement in the model predictions (lower RMSE, especially lower RMSEs, and higher D index) when PPF transmission of 1.08 is assumed compared with 0.88. The decomposition of RMSE indicated a generally higher systematic error (RMSES) than random error (RMSEU), especially for the 0.88 transmission assumption. The substantial decrease in RMSES associated with switch from 0.88 to 1.08 transmission factor is the type of error that could be associated with failure to account for the reflected radiation from the side and back walls of the chambers. Even with the 1.08 transmission assumption, the model still slightly underpredicts, as evidenced by the slopes being less than unity, but increasing the fraction diffuse PPF would also improve this situation. Considering the high D index and low ratio of RMSE compared with the observed mean Acan (ratios of 8–16%), our analysis indicates acceptable agreement between the observed and simulated Acan at sub- and supraoptimal [CO2] by the CROPGRO model.



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  		Fig. 6. Comparison of observed (adapted from Campbell et al., 1990) and simulated net Acan by the CROPGRO model at six [CO2], assuming PPF transmission of 1.08. Linear regression using hourly observed and simulated Acan values from 0700 to 1700 h (solid lines) and 1:1 line (dashed lines).

 

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  		Table 4. Mean ± SD of 11 hourly observed (Campbell et al., 1990) and simulated net canopy photosynthesis from CROPGRO model for six CO2 concentrations. Simulations of net canopy photosynthesis were done with transmission factors of 0.88 and 1.08 of photosynthetic photon flux external to and above the chambers. Also shown are the root mean square error, its systematic and unsystematic components, and Willmott's index of agreement for both simulations.

 
Doubling of [CO2] from the ambient (330 µmol CO2 mol–1) increased simulated Acan (at 1350 µmol m–2 s–1 PPF) by 42% and observed Acan by 36%. The effect of doubling [CO2] on simulated Acan in this study is similar to the 59% increase (range of 40–87%, using 95% confidence interval) summarized in the soybean meta-analysis (Ainsworth et al., 2002).


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS and DISCUSSION
 CONCLUSIONS
REFERENCES
 
We used leaf and canopy photosynthesis data obtained from environmentally controlled [CO2] enrichment experiments on soybean to test the ability of the unmodified CROPGRO soybean model to accurately simulate responses of A and Acan to PPF and the response of A to Ci. Simulated A closely matched observed A (Valle et al., 1985) at all PPF levels at ambient [CO2], but the model underpredicted A on high PPF at elevated [CO2]. Two other modeling studies have reported similar underprediction of A at elevated [CO2] for this particular data set.

Simulated A/Ci curves were similar to the observed curves in most cases. Comparison of observed and simulated A, Acan, and A/Ci curves indicated a high D, varying from 0.93 to 0.99, and deviation-based RMSE were small compared with the respective observed mean A and Acan. Simulated and observed Acan light saturated at 800 µmol m–2 s–1 PPF below 280 µmol mol–1 [CO2] but did not light saturate even at 1300 µmol m–2 s–1 PPF above 280 µmol mol–1 [CO2]. The simulation of effects of doubling [CO2] on A and Acan were comparable to increases summarized in the soybean meta-analysis (Ainsworth et al., 2002). Even though the CROPGRO model uses a simplification based on the RUBP-limiting equations of Farquhar and von Caemmerer (1982), our comparison using common data sets indicated that the CROPGRO default photosynthesis equations and the Farquhar photosynthesis equations were equally effective in simulating A over a range of Ci. This model evaluation study indicated that the CROPGRO model with default photosynthesis equations adequately simulated the response of A and Acan to PPF and the response of A to [Ci]. Simulated doubled [CO2] effects on A and Acan matched closely to the values reported in the literature.


   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.


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





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