CO2‐response function of radiation use efficiency in rice for climate change scenarios

The objective of this work was to evaluate a generalized response function to the atmospheric CO2 concentration [f(CO2)] by the radiation use efficiency (RUE) in rice. Experimental data on RUE at different CO2 concentrations were collected from rice trials performed in several locations around the world. RUE data were then normalized, so that all RUE at current CO2 concentration were equal to 1. The response function was obtained by fitting normalized RUE versus CO2 concentration to a Morgan-Mercer-Flodin (MMF) function, and by using Marquardt's method to estimate the model coefficients. Goodness of fit was measured by the standard deviation of the estimated coefficients, the coefficient of determination (R2), and the root mean square error (RMSE). The f(CO2) describes a nonlinear sigmoidal response of RUE in rice, in function of the atmospheric CO2 concentration, which has an ecophysiological background, and, therefore, renders a robust function that can be easily coupled to rice simulation models, besides covering the range of CO2 emissions for the next generation of climate scenarios for the 21st century.


Introduction
After the 2009 Copenhagen Summit, which included the 15 th Conference of the Parts (COP 15) to the United Nations Framework Convention on Climate Change and the 5 th Meeting of the Parts (MOP 5) to the Kyoto Protocol, little or no progress has been achieved for the reduction of global CO 2 emissions in the coming decades, therefore, a new generation of climate scenarios has been proposed to guide the projections of temperature increase for the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC), scheduled to be released in 2014 (Moss et al., 2010;O'Neill & Schweizer, 2011).The new climate projections will be based on four CO 2 emission scenarios, named "representative concentration pathways" -RCP, selected by a new Integrated Assessment Modeling Consortium, with radiative forcing pathways based on possible trajectories of CO 2 concentration over the 21 st century, as follows: RCP2.6, increase up to 490 ppmv CO 2 until 2020-2030 and, then, declines, so that the radiative Pesq.agropec.bras., Brasília, v.47, n.7, p.879-885 , jul. 2012 forcing is 2.6 W m -2 at 2100; RCP4.5, increase up to 650 ppmv CO 2 , radiative forcing of 4.5 W m -2 until 2100, and stabilizing afterwards; RCP6.0, increase up to 850 ppmv CO 2, radiative forcing of 6.0 W m -2 until 2100, and stabilizing afterwards; RCP8.5, increase superior to 1,370 ppmv CO 2 , radiative forcing higher than 8.5 W m -2 up to 2100, and continuing to rise after 2100 (Moss et al., 2010).
Plants respond to atmospheric CO 2 mostly by increasing photosynthesis rate, which has the potential to increase agricultural crops growth and yield (Streck, 2005).Rice (Oryza sativa L.) is the staple food of about half of the world population, and Brazil is the largest rice producer outside Asia, with about 2.8 million hectars grown annually (United States Department of Agriculture, 2011).Traditionally, the effect of CO 2 on agricultural crops, including rice, has been simulated in climate change studies using the "current/elevated CO 2 " approach, i.e., crop models are run at current CO 2 (usually 350-360 ppmv) and, then, run again at an elevated CO 2 concentration scenario (usually doubled CO 2 -700 ppmv) (Matthews et al., 1997;Streck & Alberto, 2006;Walter et al., 2010).The four new RCP-based groups of climate scenarios demand a redesign of this traditional approach, for simulating the CO 2 effects on crops by using a CO 2 -response function in simulation models.
Crop simulation models vary in complexity from simple empirical statistic-based models (Pedro Júnior et al., 1995;Klering et al., 2008) to very complex process-based models (Hasegawa & Horie, 1996;Mall & Aggarwal, 2002;Bouman & Laar, 2006;Confalonieri et al., 2009).Models with intermediate levels of complexity combine advantages from the former (simplicity) and from the latter (mechanisms) by using general and robust response functions for describing plant processes on a canopy level, which requires less and more easily-measured coefficients and inputs.For rice, the InfoCrop is a recent process-based model with intermediate complexity (Aggarwal et al., 2006), which gave similar or better simulations of rice yield in India than Oryza, a more complex process-based model (Krishnan et al., 2007).
A robust canopy-based approach is the radiation use efficiency (RUE), which is widely used in crop simulation models, including InfoCrop, as a surrogate for biochemical and leaf-based approaches to describe the complex photosynthesis process.RUE is defined as the amount of crop dry matter produced per unit of solar radiation intercepted or absorbed by the crop canopy (Sinclair & Muchow, 1999).Common values of RUE in rice vary from 1.32 to 2.95 g MJ -1 of intercepted photosyntheticaly active radiation (PAR) (Weerakoon et al., 2000;Mall & Aggarwal, 2002).
There is a lack of a response function to atmospheric CO 2 concentration, when RUE is used as the driving variable for increasing crop dry matter production in rice simulation models, which constituted the rationale for this study.Anticipating the upcoming IPCC 2014 AR5, the objective of this work was to evaluate a generalized response function to the atmospheric CO 2 concentration [f(CO 2 )] by the RUE in rice, which can easily be coupled to process-based rice simulation models.

Materials and Methods
A widely used approach in crop simulation models is to describe the effects of environmental variables such as solar radiation, temperature and photoperiod, on crop growth and development with adimensional response functions which vary from zero to one (Streck et al., 2003(Streck et al., , 2007;;Setiyono et al., 2007Setiyono et al., , 2010)).The underlying hypothesis in the present study was that a similar approach can be used for developing a f(CO 2 ).
Literature data on the response of RUE to CO 2 in rice are usually from Open Top Chambers (OTC) and from Free-Air CO 2 Enrichment (FACE) experiments, in which a current and an elevated CO 2 levels are set.These approaches make it difficult to hypothesize upon the general shape of a f(CO 2 ).From a biochemical perspective, however, CO 2 is the substrate for photosynthesis, and leaf photosynthesis rate is expected to increase steadily in the range from 350-400 to 800-1000 ppmv CO 2 in C 3 plants, like rice, because the current CO 2 concentration (390 ppmv) in the atmosphere is insufficient to saturate the ribulose 1.5-bisphosphate carboxylase/oxygenase (Rubisco), the enzyme responsible for primary carboxylation in the metabolic process that drives photosynthesis (Bowes, 1991;Streck, 2005).An increase in the availability of CO 2 suppresses photorespiration in C 3 plants because it increases carboxylation and decreases the oxygenase activity of Rubisco (Streck, 2005).But at the canopy level, the response to CO 2 may not follow the same shape mainly because some leaves (those located within and in the lower portion of the canopy) are in the shade and may be senescent.Shaded and senescent leaves have very low photosynthesis efficiency because of high respiration rates and low leaf nitrogen content (Kitagima et al., 2002).Therefore, we selected a flexible response function -the Morgan-Mercer-Flodin (MMF) function (Morgan et al., 1975) -, for describing the response of RUE to CO 2 in rice.The general form of the MMF function is: in which: Y is the response (dependent) variable; X is the explanatory (independent) variable; a is the intercept when X = 0; c is the asymptote, as X approaches infinity; n is a shape coefficient; and b is interpreted as b = (X 0.5 ) n , with X 0.5 being the value of X, when Y is half of the maximum response.The MMF is a very flexible function because users can set the intercept and the asymptote -two coefficients which define the range of the response variable -, and because it can take several shapes, varying from a rectangular hyperbole for n = 1 to a step-function for n = infinite and sigmoidal curves for 1<n<infinite, only by changing the shape coefficient (Streck et al., 2003).
For the f(CO 2 ), X is the atmospheric CO 2 concentration, and Y is the normalized RUE response.By normalized RUE, we mean that the RUE values 1 at current atmospheric CO 2 concentration.Therefore, the lower limit of the range of RUE response is 1 at current CO 2 concentrations and, thus, the coefficient a in equation ( 1) was set to be equal to 1.The other three coefficients (b, c, n) of the equation (1) were estimated as follows.
Published data on RUE at several atmospheric CO 2 concentrations, from different rice trials conducted in OTC, FACE, and numerical experiments conducted with different cultivars under different conditions and in distinct locations were used.These data were collected from a thorough literature search on trials which tested the effect of CO 2 concentration on RUE in rice and which were published in international main stream journals.The source and some details of these trials are presented in Table 1.RUE data were normalized by dividing RUE at elevated CO 2 concentration treatments by RUE at the current CO 2 concentration treatment, and assuming that all current CO 2 treatments were 1.The CO 2 concentration from the whole data sets varied from 330 ppmv to 990 ppmv (Table 1), which covers the CO 2 concentrations of the RCP2.6,RCP4.5 and RCP6.0 emission scenarios by the year 2100 and the RCP8.5 emission scenario up to about the year 2070, which should guide the AR5 of the 2014 IPCC (Moss et al., 2010).
Normalized RUE versus CO 2 concentrations were then fitted to equation (1), by setting a = 1, and coefficients b, c and n were estimated with the PROC NLIN procedure (SAS Institute, 2001), with the Marquardt´s method for minimizing the square error of the fit.Goodness of fit was measured by the standard deviation of the estimates of the coefficients b, c and n, the coefficient of determination (R 2 ), and the root mean square error (RMSE) (Streck et al., 2003).

Results and Discussion
Normalized RUE, published in the literature, varied from 1 at 330-370 ppmv to 1.44 at 990 ppmv, i.e., RUE increase as CO 2 increase.This feature is consistent with the response of increase in photosynthesis with CO 2 fertilization in C 3 plants (Streck, 2005).The estimates of the coefficients of the MMF function (equation 1) with the fitting procedure were: a = 1; b = 3.096x10 23 , standard error = 1.188x10 24 ; c = 1.4382; standard error = 0.0147; and n = 8.378, standard error = 0.6017.The probability (p-value) of all three coefficients were highly significant (p<0.01), the coefficient of determination was high (R 2 = 0.999), and the root mean square error was low (RMSE = 0.012).The MMF function was appropriate to describe the response of RUE to the atmospheric CO 2 concentration in rice.Therefore, the f(CO 2 ) response function of RUE in rice is: (2).
From equation (2): the coefficient X 0.5 , which represents the CO 2 concentration, when the response of RUE is half of the maximum response, is 637 ppmv; the coefficient c is the maximum increase in the attained, RUE due to the increase in CO 2 concentration; and the coefficient n = 8.378 gives a sigmoidal shape to the curve.A value of 1.4382 for the asymptote (coefficient c in equation 2) means that the maximum increase in RUE, due to elevated CO 2 , was 44% greater than the RUE at current CO 2 .
The sigmoidal response indicates that RUE in rice increases slowly, in the range from 350 to 500 ppmv of CO 2 , then it has a quasi-linear (the highest rate) increase from about 500 to 750 ppmv and, again, shows a slow increase in RUE from about 750 to 950 ppmv, leveling off at CO 2 concentrations greater than 950 ppmv (Figure 1).
The sigmoidal response of RUE to an increase in atmospheric CO 2 concentration, obtained in the present study (equation 2, Figure 1), differed from the overall response of leaf photosynthesis to CO 2 commonly reported in C 3 plants, which follows a rectangular hyperbole-type shape response (Sage et al., 1989;Streck, 2005).The main difference between the sigmoidal response and rectangular hyperbole response to CO 2 was from about 350 to 700 ppmv.In this range, Rubisco carboxilation activity is promptly increased with the increase in atmospheric CO 2 , resulting in a linear increase in the rate of leaf photosynthesis.This biochemical response has been used as a general background, for assuming that plant growth increases linearly from current to elevated CO 2 concentrations in crop simulation models (Matthews et al., 1997;Walter et al., 2010).Although by this linear approach, in the range from 350 to 700 ppmv, CO 2 gives the right response of RUE at the upper-end portion of the CO 2 response range (around 700 ppmv), it greatly overestimates the response of RUE on a crop canopy level at 500-600 ppmv (Figure 1), which is a CO 2 concentration range expected in the upcoming 20-40 years (Moss et al., 2010).
To explain the lower response of RUE, in comparison to leaf photosynthesis rate from 500-600 ppmv of CO 2 , a hypothesis is that only sunlit leaves in the top of the canopy could fully take advantage of CO 2 fertilization.Throughout the growing season, there are many leaves which are shaded and senescent, in the half lower part of the canopy, and the photosynthetic efficiency of these leaves is lower than the photosynthesis of sunlit ones (Kitagima et al., 2002).Therefore, because RUE is a more robust ecophysiological parameter than photosynthesis rate of individual leaves, our approach to develop a f(CO 2 ) response function is more appropriate for assessing the response of crop canopies to increased atmospheric CO 2 .
The saturation of RUE response to CO 2 concentrations approaching 1000 ppmv (Figure 1) is consistent with the saturation of leaf photosynthesis in C 3 plants at 800-1000 ppmv (Sage et al., 1989;Streck, 2005).At low and intermediate atmospheric CO 2 concentrations, photosynthesis is limited by the carboxylation capacity of Rubisco, while at high CO 2 concentrations leaf photosynthesis is limited by the regeneration capacity of Rubisco in the Calvin cycle (Chen et al., 2005).
A further limitation for plants, including rice, to respond positively to elevated atmospheric CO 2 concentration that has been extensively claimed as the probable acclimation of leaf photosynthesis to CO 2 fertilization (Chen et al., 2005;Streck, 2005).The acclimation of leaf photosynthesis in rice has been attributed to limitations in both Rubisco carboxylation and Rubisco regeneration (Chen et al., 2005).The reduction of Rubisco carboxylation and regeneration is related to the increase of soluble sugar contents (hexoses or nonstructural carbohydrates) in the leaves of plants grown at elevated CO 2 concentrations (Chen et al., 2005).In addition, in rice plants exposed to high CO 2 concentration for long periods (throughout the growing period), there is a lower concentration of Rubisco inside cells, which reduces the photosynthetic rate at plant level (Chen et al., 2005).However, the results of OTC and FACE, used for defining the f(CO 2 ) in the present study (Table 1), are from long-term experiments (plants were grown under elevated CO 2 throughout their entire growing period), which indicates that the acclimation of photosynthesis to elevated CO 2 at leaf level did not offset the fertilization effect at canopy level, and that there was an overall positive effect of elevated CO 2 on crop growth.
The photosynthesis acclimation to elevated CO 2 is the basis for a second hypothesis to explain the small increase of RUE in the range 500-600 ppmv of CO 2 of the f(CO 2 ) (Figure 1).Makino et al. (2000) reported decrease in Rubisco content, but a nonsignificant decrease in the biomass of rice plants grown at 1000 ppmv CO 2 , i.e. under CO 2 -saturated conditions.Under CO 2 -nonsaturation conditions, such as in the study by Chen et al. (2005), in which rice plants were exposed to 580 ppmv CO 2 , the acclimation of leaf photosynthesis had a greater impact on plant biomass, with a lower increase of crop biomass than at higher CO 2 (above 600 ppmv).These two hypotheses may act together, and the contribution of each one still needs to be elucidated by further studies.
The nonlinear response of RUE in rice to the increase of atmospheric CO 2 concentration (Figure 1) has important implications for its use in the upcoming CO 2 emission scenarios which will guide the IPCC 2014 AR5 (Moss et al., 2010).For the most optimist scenario (RCP2.6),which assumes a maximum CO 2 concentration of about 490 ppmv, little benefits from CO 2 fertilization is expected for rice.For the RCP4.5 scenario, which assumes a maximum CO 2 concentration of about 650 ppmv, the final CO 2 concentration falls into the linear response of Figure 1, and RUE in rice may increase by 28%.The increase by 850 ppmv, suggested in the RCP6.0, is in the third range of response in Figure 1, with an increase of about 41% in RUE.For the RCP8.5 scenario, the response of RUE reaches a maximum of about 43% and levels off, which means that, under this very pessimist scenario, benefits from CO 2 fertilization in rice are not expected after the year 2070.
The f(CO 2 ) proposed in this paper (equation 2) takes into account the effect of CO 2 on RUE and can be easily coupled to a process-based rice simulation model such as InfoCrop.Because the data used for developing the f(CO 2 ) come from different trials conducted with different cultivars, under different locations and experimental setups (Table 1), the equation ( 2) was proposed as a robust and generalized response function to be used in models to simulate the effect of elevated CO 2 concentrations on RUE, in different rice ecosystems.This is particularly important in face of the new generation of climate change scenarios which will be the basis of the AR5 in 2014.This new redesigned scenario process uses the parallel approach for representing the socio-economic, technological, demographic, policy and institutional factors, which influence gas emissions to the atmosphere, and differs from the sequential approach used by Group I of IPCC 2007 AR4 (Moss et al., 2010).Compared to the sequential approach, the parallel one shortens the time between the development of emission scenarios and the use of the resulting climate scenarios and begins with the identification of major features for scenarios Pesq.agropec.bras., Brasília, v.47, n.7, p.879-885 , jul. 2012 of radiative forcing, setting the radiative forcing trajectories during the 21 st century (Moss et al., 2010;O'Neill & Scheweizer, 2011).
From an agriculture perspective, these new IPCC-CO 2 emission scenarios are also different from the AR4 ones and introduce new challenges for simulation studies, as CO 2 concentrations during the 21 st century may stabilize before 2100 in some scenarios (RCP2.6),while they may increase in a nonlinear fashion up to reach the highest concentration by 2100 and stabilize afterwards in others (RCP4.5 and RCP6.0), or they may steadily increase beyond 2100 (RCP8.5).Therefore, developing a f(CO 2 ) response function in rice, which covers all CO 2 concentration scenarios in a dynamic fashion, will shorten the time between the release of the AR5 and the assessment of rice response to the new climate change scenarios for the coming decades.This is especially important for the rice chain in Brazil, the largest rice producer outside Asia.

Conclusion
1.The Morgan-Mercer-Flodin function is appropriate as a generalized RUE response to increasing atmospheric CO 2 concentrations in rice, describing this response in a nonlinear, sigmoidal way, with an ecophysiological background.
2. The Morgan-Mercer-Flodin function is a robust function which can be easily coupled to rice growth simulation models to cover the range of CO 2 emission scenarios during the 21 st century.

Table 1 .
Source and some details of the rice trials used to develop the CO 2 response function of radiation use efficiency (RUE).