Simulating daily field crop canopy photosynthesis: an integrated software package

Additional keywords: CO₂ partial pressure, dry matter accumulation, modeling, modelling, radiation, temperature effects.

The next advance in field crop productivity will likely need to come from improving crop use efficiency of resources (e.g. radiation, CO₂, water and nitrogen), aspects of which are closely linked with overall crop photosynthetic efficiency (Long et al. 2015). For this, there is an emerging agenda focussed on genetic manipulation of the biochemical pathway of photosynthesis aiming to enhance photosynthesis for improved crop yield (Evans 2013; Long et al. 2015). However, progress is limited by the lack of connection between biochemical/leaf-level photosynthetic manipulation and crop performance, which is influenced by interactions between (photosynthetic) genetic controls, plant growth and development processes, and environmental effects. Crop models that can incorporate the interactions and integrate across scales of biological organisation might be the tool needed to accelerate progress in photosynthetic enhancement (Wu et al. 2016).

In many crop models that are used for seasonal simulation of crop growth, development and yield, daily biomass accumulation (which is determined by canopy photosynthesis) is a key driver of crop growth that has been used to simulate source-limited plant growth. Canopy photosynthesis modelling began with empirical models of leaf photosynthetic light response (PLR), which were upscaled and integrated to simulate diurnal canopy photosynthesis (Monsi and Saeki 1953; Hammer et al. 2009). There are multiple approaches for such upscaling, which focussed on modelling the heterogeneous light environment within the canopy. These can be classified into models with ‘simplified’ canopy representation, such as multi-layer models (each layer partitioned into sunlit and shade leaf fractions) (Duncan et al. 1967), single-layer big-leaf models (Sellers et al. 1992; Sands 1995) or (single-layer) sun–shade leaves models (Hammer and Wright 1994; de Pury and Farquhar 1997). Another type of approach is detailed models, such as static 3D and dynamic 3D (Vos et al. 2010) canopy architecture models. The respective (dis)advantages of these models have been discussed (Wu et al. 2016) and many have supported the simplicity and robustness of the sun–shade leaves approach. This approach can use either single or multiple layers with canopy leaf area index in each layer(s) partitioned into sunlit and shade leaf fractions. Another widely used type of canopy photosynthesis simulation, which avoids the need for photosynthesis modelling and upscaling, is to utilise a simple empirical linear relationship between daily crop (aboveground) biomass increment and intercepted solar radiation (or radiation use efficiency, RUE) (Sinclair and Muchow 1999). Theoretical derivations have shown consistencies between the PLR and RUE approaches to modelling (Hammer and Wright 1994). Both types underpin source-limited plant growth simulation, which can be connected with crop models that incorporate both source- and sink-limited crop growth (Hammer et al. 2010). For example, the APSIM crop models (Hammer et al. 2009) provide important effects that can regulate canopy photosynthesis via crop nitrogen status, which influences photosynthetic capacity. This is an effective and robust framework for connecting photosynthesis with crop growth, development and yield simulation (Wu et al. 2016).

Given the focus of photosynthetic enhancement at the biochemical level for field crop improvement, the PLR and RUE types of canopy photosynthesis modelling may not be adequate despite their apparent success in crop models. Their responses to variations at the biochemical level and to environment are difficult to predict due to the aggregated nature of the models. To overcome the limitations, canopy models based on more mechanistic photosynthesis models (e.g. C₃ and C₄ photosynthesis models; von Caemmerer 2000) have emerged (de Pury and Farquhar 1997) and have been incorporated into vegetation growth models (e.g. BioCro, http://biocro.r-forge.r-project.org/, accessed 16 October 2017; Ecosys, http://ecosys.ualberta.ca/, accessed 16 October 2017; GECROS, Yin and van Laar (2005); and WIMOVAC, Humphries and Long (1995)). Most of these have utilised the simple and robust sun–shade leaves approach. However, there are only a limited number of such canopy photosynthesis models being applied in crop models (Yin and Struik 2008). Despite a limited number, these examples of modelling work demonstrated the value of using biochemical based canopy photosynthesis models to expand the biological functionality of crop models, which could potentially aid progress in photosynthetic enhancement for field crop improvement.

Besides the eventual target of incorporating diurnal canopy photosynthesis into field crop performance prediction, there is also a need for developing a standalone diurnal canopy photosynthesis simulator. This is likely to stimulate and guide different approaches to leaf-level photosynthesis research and reinforces thinking at the canopy level. For example, correlating Rubsico carboxylation rate with leaf nitrogen content would be useful for simulation of instantaneous canopy photosynthetic rate (de Pury and Farquhar 1997). More examples of relationships between photosynthetic and plant attributes have also emerged (Braune et al. 2009). As discussed above, there are existing examples of canopy models; however, they have been developed as integrated modules in more extensive vegetation growth models. A standalone diurnal canopy photosynthesis simulator that informs canopy CO₂ assimilation/biomass accumulation in terms of photosynthetic attributes and diurnal environment would be a desirable tool. Such a tool can be utilised to aid the wider community of photosynthesis experimentalists to understand consequences at a higher level over a longer simulation period, as well as providing a valuable teaching tool.

The rationale of extending crop modelling and aiding progress in photosynthesis research warrant the development for a standalone tool of diurnal canopy photosynthesis simulation. It will need to incorporate the biochemical models of photosynthesis as well as respond to diurnal environment effects for simulating canopy CO₂ assimilation/biomass accumulation of a field crop over a day. To develop such a tool, three objectives have been identified:

1. develop a standalone C₃ and C₄ Diurnal Canopy Photosynthesis Simulator (DCaPS) for both C₃ and C₄ photosynthesis based on the concept of a cross-scale modelling framework that facilitates connection with crop growth and development dynamics (Wu et al. 2016),

2. present model rationality tests by simulating responses to key environmental factors (i.e. light, CO₂ and temperature), canopy nitrogen status (i.e. specific leaf nitrogen and its profile through the canopy), and canopy attributes and architecture (i.e. canopy leaf area index and leaf angle), and

3. develop DCaPS into an interactive web-based application that can be accessed using internet browsers on any major platform for simulating likely canopy-level consequences of photosynthetic changes.

The implications of the DCaPS package for crop modelling and it applications for photosynthetic manipulation are also discussed.

The Diurnal Canopy Photosynthesis Simulator (DCaPS) calculates diurnal (period from sunrise to sunset) canopy CO₂ assimilation and daily (24 h) biomass increment for a crop under well watered conditions. A schematic diagram of the model is provided in Fig. 1, model detail in the next section, and a comprehensive description and list of model equations and parameters in Tables 1, 2 and the appendices. Daily values of incident solar radiation, air temperature (T_a) and air vapour pressure deficit (VPD_a), commonly used in crop models, were used to derive instantaneous values at the start of each hour over the diurnal period. A single-layer sunlit and shade leaf modelling approach was used. Canopy leaf area index (LAI_can) was partitioned into sunlit and shade leaf fractions using the sun–shade leaves modelling approach (Hammer and Wright 1994; de Pury and Farquhar 1997) to calculate the amount of photosynthetically active radiation (PAR) absorbed by each fraction. T_a was assumed as a proxy for leaf temperature (T_l), which affects photosynthetic physiology. The canopy profile of leaf nitrogen on a leaf area basis (specific leaf nitrogen, SLN) was input and used to calculate the maximum rate of Rubisco carboxylation (V_cmax), the maximum rate of electron transport (J_max) and the maximum phosphoenolpyruvate (PEP) carboxylase activity (V_pmax) (de Pury and Farquhar 1997), which are parameters of the C₃ and C₄ photosynthesis models (Farquhar et al. 1980; von Caemmerer 2000) used in DCaPS. The photosynthesis models were coupled with a CO₂ diffusion model to calculate C_c and CO₂ assimilation rate. Photosynthesis of both the sunlit and shade leaf fractions of the canopy were calculated, summed for the canopy, integrated hourly, and summed over the diurnal period to calculate total diurnal canopy photosynthesis, which was taken as the daily sum. This was converted to daily total biomass increment (BIO_total,DAY) assuming a conversion ratio (B), which combines factors allowing for biochemical conversion and maintenance respiration (Sinclair and Horie 1989). A fraction of BIO_total,DAY was partitioned to root and the remaining amount was taken as the daily aboveground canopy (shoot) biomass increment (BIO_shoot,DAY).

Fig. 1.  Schematic of the Diurnal Canopy Photosynthesis Simulator (DCaPS). Model inputs are categorised into environment, canopy attributes and architecture, canopy nitrogen status, CO₂ diffusion, photosynthetic and temperature response parameters. Model outputs are diurnal environment variables, diurnal canopy photosynthesis and daily aboveground canopy biomass increment. The two-way arrow between the CO₂ diffusion model and the biochemical models indicates that the models are coupled and solved simultaneously for the chloroplastic CO₂ partial pressure (C_c) and photosynthesis. Parameters in bold font are driven by specific leaf nitrogen (SLN). Abbreviations: RATIO, atmospheric transmission ratio for incident solar radiation; VPD_a, air vapour pressure deficit; PAR, photosynthetic active radiation; SLN_av, canopy-average specific leaf nitrogen; SLN_{ratio_top}, ratio of SLN at the top of canopy to SLN_av; T_l, leaf temperature; g_m, mesophyll conductance for CO₂; g_bs, bundle-sheath conductance for CO₂; O_l, O₂ partial pressure inside leaves. The SLN canopy profile is used to calculate parameters in bold font. Comprehensive lists of the photosynthetic parameters are given in Tables 1, 2.

Table 1.  Description of symbols used in the Diurnal Canopy Photosynthesis Simulator (DCaPS)

Table 2.  C₃ and C₄ temperature response parameters used in Eqns 1 and 2
Note: values marked with ‘A’ were variable (see Table 1); n.a., not applicable

In both the C₃ and C₄ photosynthesis models (not replicated here, but see Appendix 1 and 2, available as Supplementary Material to this paper), the potential electron transport rates (J, μmol e^– m^–2 s^–1) of sunlit and shade leaf fractions are driven by absorbed PAR using a non-rectangular hyperbolic function (von Caemmerer 2000). Absorbed PAR for each of the sunlit and shade leaf fractions varies diurnally and its calculation requires diurnal total incident solar radiation, LAI_can, canopy architecture (in the form of canopy-average leaf angle), and optical properties (reflectance and transmittance) of leaves. Separation of absorbed PAR for the sunlit and shade leaf fractions of the canopy is a necessary detail to avoid errors in over estimation of photosynthetic rate (de Pury and Farquhar 1997).

The calculation of diurnal absorbed PAR depends on the radiation environment (Hammer and Wright 1994). First, diurnal extra-terrestrial radiation (S_o, MJ m^–2 ground day^–1) was calculated from latitude (Lat, radians) and day of year (DAY) (Eqn A5, see Supplementary Material). Then diurnal total incident solar radiation on the ground (S_g, MJ m^–2 ground s^–1) was calculated by multiplying S_o and the atmospheric transmission ratio (RATIO) (Eqn A4). S_g was then distributed sinusoidally over the diurnal period to derive instantaneous values for incident radiation (I_o MJ m^–2 ground s^–1) (Eqn A3). I_o consists of direct (I_dir, MJ m^–2 ground s^–1) and diffuse (I_dif, MJ m^–2 ground s^–1) radiation components. Diffuse radiation represents 17% of solar insolation (S_o) for any Lat, DAY and RATIO (Eqn A1). The diurnal pattern of atmospheric transmission of I_dir is more complex, so was simply obtained by the difference between I_o and I_dif (Eqn A2). This approach allows the proportion of I_dir and I_dif to vary across a diurnal period giving, for example, higher proportion of I_dif in early and later hours of the diurnal period and higher proportion of I_dif if RATIO is low due to cloud cover.

The derived I_dir and I_dif (total incident solar radiation) from above were used to estimate direct and diffuse PAR (I_{dir_PAR} and I_{dif_PAR} respectively). It was assumed that 50% of the energy in I_dir and I_dif was PAR, which was converted to photosynthetic photon flux density by multiplying by 4.56 and 4.25 μmol PAR (J PAR)^–1 respectively (Eqns A21 and A22). Units for I_{dir_PAR} and I_{dif_PAR} are μmol PAR m^–2 ground s^–1.

The PAR absorbed by either sunlit or shade leaves fractions (I_{abs_sun} and I_{abs_sh}, both with units of μmol PAR m^–2 s^–1) was calculated using the equations of de Pury and Farquhar (1997). This incorporated I_{dir_PAR} and I_{dif_PAR}, optical properties of leaves, such as reflectance and transmittance to PAR, LAI_can, and the proportion of intercepted radiation (dependent on canopy-average leaf angle and LAI_can). It was assumed that the sunlit leaf fraction received I_{dir_PAR}, I_{dif_PAR} and scattered radiation (caused by reflectance and transmittance of leaves), while the shade leaf fraction received only I_{dif_PAR} and scattered radiation. Detailed equations and calculation procedures are given by Eqns A19–A32 in Appendix 1. In the current model, diurnal variations in leaf reflectance and transmittance are not considered. However, as a first approximation, it can be input into DCaPS for each diurnal simulation.

Air vapour pressure deficit (VPD_a, kPa) was calculated as the difference between the saturated vapour pressure at air temperature (SVP_a) and that at dew-point temperature (SVP_d) (Eqns A16–A18). The minimum temperature (T_a,min; more below) for the day was assumed as the dew-point temperature, which has been shown to give robust estimates of VPD_a (Lobell et al. 2015). Accordingly, VPD_a varies diurnally with air temperature.

Specific leaf nitrogen (SLN, g N m^–2 leaf) influences key photosynthetic physiological parameters. Using the mathematical development by de Pury and Farquhar (1997), vertical variation through the canopy can be explicitly incorporated; the approach integrates the profile to give a total for the single-layer canopy, which is then partitioned into sunlit and shade leaves. Distribution of SLN in the canopy was assumed to follow an exponential decay with canopy depth (Eqn A34). The decay function was specified by SLN at the top layer of the canopy (SLN_o, g N m^–2 leaf) and the average SLN for the canopy (SLN_av, g N m^–2 leaf). To incorporate the effects of SLN on photosynthetic physiology, this model assumed that at the reference temperature of 25°C, the maximum rate of Rubisco carboxylation (V_cmax), the maximum rate of electron transport (J_max), leaf day respiration (R_d), and the maximum PEP carboxylase activity (V_pmax) were all zero below a minimum SLN and increased linearly with slope of χ_V, χ_J, χ_R and χ_P, respectively, above that threshold value (Eqns A37–A40). The minimum SLN values were 0.35 and 0.2 g N m^–2 (leaf) for C₃ and C₄ respectively (Table 1).

Estimation of air temperature (T_a, °C) is needed as it significantly influences leaf temperature (T_l, °C). A model of daily T_a (over the 24 h) was used (Eqn A15). Even though the majority of daylight hours can be modelled by the diurnal function of the model, the night time function is sometimes applicable for the early hours of the diurnal period. The diurnal period was modelled with a sine function and an exponential decay function was used during the night. The amplitude of the daily T_a fluctuation was specified by the maximum (T_a,max, °C) and minimum (T_a,min, °C) air temperature of the day. The phase shift of the sine function was determined by the lag coefficient for the maximum temperature (x_lag), the night-time temperature coefficient (y_lag), and the lag of minimum temperature from the time of sunrise (z_lag) (Eqn A15). It was assumed here that T_l is approximated by T_a for both sunlit and shade leaf fractions. This is a reasonable assumption over a wide range of temperature under well watered conditions.

The response of photosynthesis to T_l was modelled through responses of the C₃ and C₄ photosynthesis model parameters to T_l (i.e. K_c, K_o, V_omax/V_cmax, V_cmax, J_max and R_d for C₃ plus K_p and V_pmax for C₄; Table 1). There is a growing availability of these temperature responses, in particular, for model species. The most comprehensive dataset for the C₃ Nicotiana tabacum L. have been used effectively for simulating temperature responses of leaf photosynthesis (Bernacchi et al. 2002). Temperature responses of K_c, K_o and V_omax/V_cmax are usually assumed to be similar among C₃ species (von Caemmerer 2013), so here we used parameters from N. tabacum for C₃ crop species. It was reported that K_c of Triticum aestivum L. is significantly different to N. tabacum (Sharwood et al. 2016), but whether or not this has significant implications for diurnal canopy photosynthesis will require sensitivity analysis when other wheat parameters also become available. Parameter availability for C₄ crop species is not as comprehensive so here we used parameters for the C₄ model species Setaria viridis (L.) P.Beauv. (Boyd et al. 2015). These default values can be readily changed as parameters of C₄ crop species become better known.

Temperature responses of K_c, K_o, V_cmax, R_d, K_p and V_pmax were modelled using an exponential type function (Eqn 1, adapted from Sharkey et al. (2007)), whereas J_max, due to its apparent optimum in temperature response (Farquhar et al. 1980), was modelled via a normal distribution function (Eqn 2, adapted from June et al. (2004)). V_cmax/V_omax and its temperature response were not available from Bernacchi et al. (2002), where K_c and K_o were reported, but can be back calculated from K_c, K_o and Γ_* with Eqns A52 and A53 (assuming a chloroplastic oxygen partial pressure (O_c) of 210000 μbar). Its temperature response can be modelled with Eqn 1. In summary, temperature responses of the C₃ and C₄ photosynthesis model parameters to T_l were modelled with Eqn 1 or 2 with parameter values given in Table 2.

Expression of the exponential type function used to describe temperature response of certain photosynthesis model parameters (adapted from Sharkey et al. (2007)):

where P₂₅ is the modelled value of parameter at 25°C, c and b are empirical constants, which are balanced to give the factor after P₂₅ unity at 25°C. Expression of the normal distribution function (adapted from June et al. (2004)):

where T_opt is the optimum temperature and Ω is the difference in temperature from T_opt at which P falls to e^–1 (0.37).

Air CO₂ (C_a, μbar) has to diffuse into leaves to reach the carboxylating site of Rubisco inside the chloroplasts for photosynthesis. The best practice for expressing CO₂ levels is in partial pressure (Sharkey et al. 2007). To convert from the usual unit of ppm to μbar, it was multiplied by the air pressure (e.g. at sea level, CO₂ of 400 ppm is (400 × 10^–6 × 1013 250 μbar = 405.3 μbar). Leaf boundary-layer and stomatal conductance have significant effects on the drawdown of intercellular airspace CO₂ partial pressure (C_i) relative to C_a (Leuning 1995) and mesophyll conductance has significant effects on the drawdown of CO₂ partial pressure at the carboxylating site of Rubisco (C_c) relative to C_i (Flexas et al. 2012). Diffusional conductance, the reciprocal of resistance, of these three components (i.e. leaf boundary-layer (g_lb), stomatal (g_s) and mesophyll (g_m) conductance) are incorporated in C_c estimation (Eqn A47) based on Fick’s first law of diffusion. To model crop canopies, the turbulent resistance through the canopy boundary layer, which would affect CO₂ partial pressure, air temperature and vapour pressure deficit (relative to those above the canopy), needs to be considered (Leuning et al. 1995). However, in their modelling work, Leuning et al. (1995) showed simulated canopy photosynthesis reproduced features in data so the omission of the turbulent resistance is a reasonable approximation.

However, there are uncertainties in the estimation of g_lb and g_s. The model that is commonly used for g_lb estimation relies on leaf width and local wind speed (Goudriaan and van Laar 1994), which cannot be assigned a priori. Numerous types of leaf stomatal conductance (g_s) models have been developed over the years (Damour et al. 2010). Two particular types are widely used. These are the empirical multiplicative models of environmental influences such as light, C_a and VPD_a (e.g. the Jarvis model; Jarvis (1976)) and the semi-empirical models relating g_s to photosynthesis with VPD_a (e.g. the BWB model (abbreviated using authors’ names); Ball et al. (1987)), whereas more mechanistic models with plant physiology considerations based on abscisic acid or hydraulic control have also been developed (Damour et al. 2010). The limitation of the multiplicative type models is the lack of interactions between plant physiology and among the environmental factors; while the models relating g_s to photosynthesis rely on empirical parameters, which cannot be assigned a priori. These empirical coefficients can vary greatly between C₃ species (Li et al. 2012) and so cannot be generalised for C₃ crop species, whereas the coefficients are rarely reported for C₄ crop species. Given that there are limited data available to calibrate the empirical coefficients of the Jarvis or the BWB models for C₃ and especially C₄ crop species, an alternative approach to estimate C_i is to use the ratio of C_i/C_a, which is based on stomatal optimisation theory in that stomata respond to maintain a constant C_i under a given C_a to maximise CO₂ assimilation. This ratio (~0.7 for C₃ and ~0.4 for C₄) has been found to be stable with C_a between 100 μbar and 400 μbar in combination with any PPFD between 250 μmol m^–2 s^–1 and 2000 μmol m^–2 s^–1 (Wong et al. 1979); further, C_i/C_a does not appear to change under elevated C_a (Ainsworth and Long 2005). The consistency in C_i/C_a in a wide range of conditions makes it an efficient and robust modelling approach. It is not clear how C_i/C_a would respond to PPFD lower than 250 μmol m^–2 s^–1, but such conditions only apply to the very early and late hours in a diurnal period, which amount to less than ~5% of diurnal canopy photosynthesis and so any changes under such conditions would have limited effect on diurnal total estimation. However, like g_s, C_i/C_a is influenced by VPD_a. It was found to decrease linearly with VPD_a in various species including C₃ Oryza sativa and C₄ Zea mays (Zhang and Nobel 1996). C_i/C_a response to VPD_a can be given by:

where a and b are empirical constants. For C₃ they are –0.12 and 0.90, respectively; for C₄, they are –0.19 and 0.84 respectively. At VPD_a between 1 to 2 kPa, Eqn 3 gives ~0.7 and 0.5 for C₃ and C₄, respectively, which are similar to those reported by Wong et al. (1979). Here, we used the simpler C_i/C_a ratio approach for C_c estimation (Eqn A49), which avoided the need for g_lb and g_s.

The importance of mesophyll conductance (g_m) has been recognised only recently. g_m in model C₃ species is known to vary with temperature and there is evidence that g_m may also respond to the other key environmental factors (e.g. irradiance and CO₂), but this variation is not yet completely certain (Pons et al. 2009). So here we included only the effect of temperature and modelled this by using the normal distribution function (Eqn 2). At the reference temperature (i.e. 25°C) g_m (per leaf area) in C₃ wheat is assumed to be 0.55 mol CO₂ m^–2 s^–1 bar^–1. No values for C₄ species have been reported, so the C₃ value was used as a default value.

Diurnal canopy CO₂ assimilation, daily respiration and conversion losses, and allowance for root biomass were used to calculate daily aboveground canopy (shoot) biomass increment (BIO_shoot,DAY). This model assumes that photosynthesis during the diurnal period results in carbon assimilation for the entire day so we use the symbol A_can,DAY. A_can,DAY was calculated by summing the CO2 assimilation of the sunlit (A_sun) and shaded (A_sh) leaf fractions of the canopy at the start of each hour over the diurnal period, integrated hourly and summed over the diurnal period (Eqn A73). Using the C₃ and C₄ photosynthesis models, leaf respiration during the diurnal period can be implicitly accounted for at the leaf level with the parameter R_d (Eqns A51, A54, A55 and A59). However, this lacks consideration of respiration from other plant organs and during the night period. A common approach is to omit the leaf-level R_d (by setting χ_R to zero) and consider respiration at the plant level on a daily basis, which can be accounted for within a conversion ratio (B) that combines factors allowing for biochemical conversion of CO₂ to biomass and CO₂ loss due to maintenance respiration (Sinclair and Horie 1989). This approach is consistent with the conservative respiration : photosynthesis ratio approach (Gifford 2003), by which plant respiration is taken as a fraction of total canopy photosynthesis. The conversion ratio, B, is 0.41 g biomass (g CO₂)^–1 for cereal crops such as rice and maize (Sinclair and Horie 1989). Therefore, daily whole-plant biomass increment (BIO_total,DAY) was calculated by multiplying A_can,DAY with the molecular weight of CO₂ (= 44 g (mol CO₂)^–1) and B. To calculate shoot biomass increment (BIO_shoot,DAY), BIO_total,DAY is multiplied by the fraction of aboveground (shoot) biomass to total biomass (shoot + root), denoted by P_shoot (Eqn A74). In effect, this simulates partitioning of a fraction of BIO_total,DAY to root. Here, P_shoot is given a default of 1 assuming a mature canopy around flowering. The RUE for the day (RUE_DAY, g biomass MJ^–1) was then calculated by dividing BIO_shoot,DAY by the total amount of intercepted solar radiation (Eqns A75 and A76 respectively).

Default environmental parameters were set for C₃ wheat (winter crop) and C₄ sorghum (summer crop), with a canopy leaf area index (LAI_can) = 6, growing in the southern hemisphere spring (DAY = 298) and summer (DAY = 15), respectively, at locations with Lat = –35° and –27.5° respectively. Clear sky with atmospheric transmission ratio (RATIO) of 0.75 was assumed unless otherwise stated. The average maximum and minimum air temperatures at these times of year were 21 and 7°C for Lat = –35° and 30 and 15°C for Lat = –27.5°.

Diurnal patterns of net C₃ and C₄ canopy photosynthesis for a range of canopy LAI (LAI_can) and canopy-average leaf inclination relative to the horizontal (β) were simulated as a qualitative test of the DCaPS. The C₄ simulations (Fig. 2c, d) were consistent in the diurnal pattern and magnitude with those reported by Duncan et al. (1967) and Hammer et al. (2009), who found that the canopy with erect leaves (β = 80°) continued to increase canopy photosynthetic rate beyond LAI_can = 4 at high LAI_can (= 8) due to better light distribution throughout the canopy. There was ~40% increase in midday canopy photosynthetic rate at LAI_can = 8 compared with LAI_can = 4, which was comparable to that simulated by Duncan et al. (1967) and Hammer et al. (2009). In the canopy with less erect leaves (β = 40°), there was little increase in canopy photosynthetic rate with increase in LAI_can beyond 4. In terms of the magnitude, the simulated canopy photosynthetic rate at LAI_can = 4 (Fig. 2c, d) was comparable to that observed in a similar size maize canopy (~70 μmol CO₂ m^–2 s^–1) by Grant et al. (1989). The simulation also indicated that for a canopy with low LAI_can (= 2), less erect leaves (β = 40°) offered greater PAR absorption by both sunlit and shade leaf fractions consistent with greater radiation interception as found by Hammer et al. (2009). Even though the sunlit LAI (LAI_sun) can be reduced up to 30% with less erect leaves, its photosynthetic rate was not affected due to associated increase in absorbed PAR. For the case of the shade leaf fraction, the increase in both the absorbed PAR and shade LAI (LAI_sh) significantly increased shade leaf A_j,sh. These consequences for the two leaf fractions translate to a greater canopy photosynthesis with less erect leaves at low LAI_can. The effects of leaf erectness were mostly analogous for the C₃ simulations (Fig. 2a, b). However, the greater radiation interception offered by less erect leaves at low LAI_can did not translate to greater canopy photosynthesis. Unlike C₄, reduction in LAI_sun significantly reduced the Rubisco-limited photosynthetic rate (A_c,sun) resulting in reduced photosynthetic rate in the sunlit leaf fraction. This more than offset the increase (because of increase in both the absorbed PAR and LAI_sh) in A_j,sh. So in the case of C₃, Rubisco limitation can reduce photosynthetic rate of small (low LAI_can) canopies with less erect leaves.

Fig. 2.  Diurnal net C₃ (upper panels) and C₄ (lower panels) canopy photosynthesis with various combinations of canopy attributes: leaf area index (LAI_can) of 2, 4 or 8 and canopy-average leaf inclination relative to the horizontal (β) of 40° (a, c) or 80° (b, d). In all four panels, the lower, middle and top curves show results for LAI_can of 2, 4 and 8 respectively. Default values of other model parameters are given in Tables 1, 2.

A simulation of net C₃ and C₄ diurnal canopy photosynthesis (A_can,DAY) for a range of air CO₂ partial pressures (C_a) and temperatures (T_a) was undertaken as a qualitative test. Based on various large-scale free-air CO₂ enrichment (FACE) studies, elevating C_a to 475–600 μbar (or an average of 540 μbar) increased C₃ A_can,DAY by an average of 28% relative to C_a = 360 μbar (Ainsworth and Long 2005). This increase was reproduced when T_{a_min} and T_{a_max} were set to 14 and 28°C, respectively, simulating hot days for winter wheat crops (Fig. 3). Ainsworth and Long (2005) noted that when the large-scale free-air CO₂ enrichment (FACE) studies were categorised by temperature, the relative increase in light saturated photosynthesis was lower (an average of 19%) at lower temperatures (<25°C). Simulation results for average days with T_{a_min} and T_{a_max} of 7 and 21°C, respectively, is consistent with this CO₂ response at lower temperatures (Fig. 3). The increase in A_can,DAY can be as high as 50% at C_a = 1000 μbar. This result is discussed further below in regards to daily radiation use efficiency. In the case of C₄ canopy photosynthesis, the response of net A_can,DAY to C_a and temperature was significantly less, which is consistent with the finding that C₄ maize photosynthesis is not significantly affected by elevated C_a (Leakey et al. 2006). This simulation suggested that canopy photosynthesis of C₃ crops can significantly benefit from elevated CO₂, while C₄ crops do not.

Fig. 3.  Relative net C₃ (dashed curves) and C₄ (solid curves) daily canopy photosynthesis (A_can,DAY) and radiation use efficiency on a daily basis (RUE_DAY) in response to air CO₂ and temperature. A_can,DAY or RUE_DAY curves were normalised to their respective values at an air CO₂ partial pressure (C_a) = 360 μbar respectively. Days were categorised as hot (14−28°C), average (7−21°C) or cold (0−14°C) for winter wheat crops; temperatures were not assigned to C₄ curves due to their small response to C_a. The triangle indicates a 28% increase in A_can,DAY at an average C_a of 540 μbar on hot days, relative to that at C_a = 360 μbar; the circle indicates a 19% increase in relative A_can,DAY increase on average days at the same average C_a. These relative increases were taken from work by Ainsworth and Long (2005). Default values of other model parameters are given in Tables 1, 2.

A simulation of C₃ and C₄ daily canopy radiation use efficiency (RUE_DAY) for a range of air CO₂ partial pressures (C_a) and air temperatures (T_a) was also undertaken as a qualitative test. Elevated C_a is known to increase the net photosynthetic rate of C₃ plants resulting in increased biomass accumulation and RUE (Kimball et al. 2002) and there is also an enhanced effect on RUE at higher T_a (Reyenga et al. 1999). The general consensus is that RUE of C₃ crops increases almost linearly from C_a of 300 to 660 μbar, reaches ~30% increase at double the ambient C_a and plateaus at ~50% beyond C_a of 1000 μbar (Lobell et al. 2015). O’Leary et al. (2015) found a ~22% increase in wheat crop biomass in response to elevated C_a from 365 to 550 μmol mol^–1. These known responses of C₃ RUE were reproduced with the model for winter wheat crops experiencing average to hot temperatures (Fig. 3). The response relative of RUE_DAY to C_a and temperature reflect that of net A_can,DAY because of the linear relationship between RUE_DAY and A_can,DAY (Eqns A74 and A75). In the case of the C₄ canopy, elevated C_a had only a small effect on the simulated RUE_DAY (Fig. 3), which was consistent with a lack of response to C_a observed in C₄ sorghum. This simulation suggested that elevated CO₂ can significantly benefit canopy biomass accumulation of C₃ crops, but not C₄ crops.

A simulation of C₃ and C₄ daily canopy radiation use efficiency (RUE_DAY) for a range of average air temperature was undertaken as a qualitative test. Air temperature (T_a) varies diurnally between the daily maximum (T_a,max) and minimum (T_a,min) temperature and the diurnal pattern can be modelled with Eqn A15. A 15°C difference between T_a,max and T_a,min was assumed and a range of temperature used so that temperatures ranging from 0−35°C for C₃ and 10−40°C for C₄ were included. When plotted against average daily temperature the simulated RUE_DAY was relatively insensitive between average temperatures of 14−23°C for C₃ and 21−28°C for C₄ (Fig. 4). This is consistent with known insensitivities of crop biomass accumulation and RUE to temperatures around optimal values (Yan and Hunt 1999). These temperature ranges for C₃ and C₄ responses were associated with the response of leaf photosynthesis to temperature, which is also insensitive within a broad range (e.g. C₃, rice and wheat (Nagai and Makino 2009); C₄, various grasses (Ludlow 1981), maize (response curve was derived from picking a typical C_i (e.g. 150 μbar) in A/C_i curves measured at different temperature in Massad et al. (2007)). Further, RUE under optimum growth conditions has been reported as 1.2–1.5 g MJ^–1 for wheat (Fischer et al. 2014) and 1.2–1.4 g MJ^–1 for dwarf sorghum (George-Jaeggli et al. 2013). The simulated maximum RUE_DAY for C₃ and C₄ corresponded with these reported ranges (Fig. 4).

Fig. 4.  Radiation use efficiency on a daily basis of C₃ (dashed curve) and C₄ (solid curve) canopy in response to temperature. RUE_DAY is plotted against average daily air temperature, which is calculated by averaging the daily maximum (T_a,max) and minimum (T_a,min) air temperatures; T_a,max = T_a,min + 15 with T_a,min = 0−20°C for C₃ and 10−25°C for C₄. Solid curve 1 was simulated for a dwarf hybrid sorghum with the slope of the linear relationship between the maximum rate of Rubisco carboxylation (χ_Vc), maximum rate of electron transport (χ_J), maximum PEP carboxylase activity (χ_VP) and specific leaf nitrogen of 0.5, 2.4 and 1.0 μmol CO₂ (mmol N)^–1 s^–1, respectively; solid curve 2 was simulated for maize and tall hybrid sorghum with χ_Vc, χ_J and χ_VP of 1.0, 4.0 and 2.0 μmol CO₂ (mmol N)^–1 s^–1 respectively. Default values of other model parameters are given in Tables 1, 2.

The comparison here between C₃ wheat and C₄ dwarf sorghum RUE does not reveal differences in magnitude between C₃ and C₄ crops, where the latter is typically higher. RUE of some tall hybrid sorghum varieties (George-Jaeggli et al. 2013) and maize (Sinclair and Muchow 1999) was found to be as high as 1.6–1.8 g MJ^–1, or possibly even higher (2.0–2.2 g MJ^–1) during the rapid stem elongation and maximum biomass accumulation phase (Olson et al. 2012). The typical high C₄ RUE could be ascribed to higher photosynthetic rate (Hammer et al. 2010) and/or differences in canopy architecture, which may affect diurnal canopy photosynthesis (Fig. 2). These scenarios (and their combinations) can be simulated with the model. As a demonstration of this capability, we have assumed the first case by increasing the slope of the linear relationship between the maximum rate of Rubisco carboxylation (χ_Vc), maximum rate of electron transport (χ_J), maximum PEP carboxylase activity (χ_VP) and specific leaf nitrogen; these gave greater V_cmax, J_max and V_pmax, respectively, and simulated the typical high RUE in C₄ crops (Fig. 4).

A simulation of C₃ and C₄ RUE_DAY for a range of canopy-average specific leaf nitrogen (SLN_av) with varying direct : diffuse radiation was undertaken as a qualitative test. Direct : diffuse radiation was varied by changing the atmospheric transmission ratio (RATIO) in a similar manner to the simulation study by Hammer and Wright (1994). High values (RATIO = 0.75) reflect clear sky with high transmission of direct radiation and a low fraction of diffuse radiation. Massignam (2003) found that RUE of the C₃ crop sunflower responded asymptotically to SLN_av with RUE of ~1 and 1.5 g MJ^–1 at SLN_av of 1.5 and 2 g N m^–2 respectively. This was closely predicted by the model with clear sky conditions (Fig. 5a). Muchow and Sinclair (1994) found that RUE of field-grown dwarf sorghum responded asymptotically to SLN_av, but did not approach the asymptote because sorghum SLN_av maximised at 1.3 g N m^–2 giving RUE of 1.26 g MJ^–1. This was also closely predicted by the model with clear sky conditions (Fig. 5b). The simulated RUE_DAY response of typical dwarf sorghum was not significantly different from that for wheat, but when the model was parameterised for the greater photosynthetic rate of the tall hybrid sorghums, the response was higher at all SLN_av (Fig. 5b). These responses were comparable to that of maize crops (RUE of ~1.5 and 2 g MJ^–1 at SLN_av of 1 and 2 g N m^–2 respectively) (Massignam 2003). In general, direct radiation level was higher with higher RATIO, while the absolute level of diffuse radiation was insensitive to RATIO, leading to a greater fraction of diffuse at low RATIO (cloudy days). Simulated results of increasing diffuse radiation fraction on C₃ species (Fig. 5a) were consistent with Tubiello et al. (1997), who found a significant increase (~40%) in wheat RUE when grown under high diffuse radiation conditions due to the fact that diffuse radiation penetrates deeper into the crop canopy and increases photosynthetic rate of the lower leaves. Hammer and Wright (1994) used a simpler canopy photosynthesis model to show that decreases in RATIO caused RUE to increase. This response of RUE_DAY to RATIO was reproduced (Fig. 5). Although both C₃ and C₄ types responded similarly to the increased fraction of diffuse radiation, the standard C₄ types achieved higher RUE_DAY at much lower SLN_av as a result of their greater photosynthetic rate (Fig. 5b). This is consistent with the comparison of responses reported by Sinclair and Horie (1989).

Fig. 5.  Radiation use efficiency on a daily basis for (a) C₃ and (b) C₄ canopy in response to specific leaf nitrogen and solar radiation levels. RUE_DAY is plotted against canopy-average specific leaf nitrogen (SLN_av). Curves 1 (lowest curve), 2 and 3 (highest curve) are obtained by setting RATIO to 0.75 (clear sky), 0.55 and 0.35 (heavy cloud cover), respectively, which changes the amount of incident radiation (curve 1 greatest) and the proportion that is diffuse (curve 3 greatest). This order applies to (b) as well. Dotted curves in panel (b) show simulated RUE_DAY for a standard C₄ crop (e.g. maize) with χ_V, χ_J and χ_P of 1.0, 4.0 and 2.0 μmol CO₂ (mmol N)^–1 s^–1 respectively. Default values of other model parameters are given in Tables 1, 2.

The Diurnal Canopy Photosynthesis Simulator (DCaPS) enables simulation of likely canopy-level consequences of photosynthetic manipulation and canopy structural attributes in C₃ and C₄ field crops. It integrates many non-linear responses of leaf photosynthesis to environment and processes involved in upscaling to the canopy level (see ‘Model detail’).

Considerable effort has been invested to develop DCaPS into an interactive web-based application (www.dcaps.net.au), which can be run with internet browsers on any major platform without prior installation of DCaPS (DCaPS v1.0 source code is available at https://github.com/QAAFI/DCaPS.git, accessed 16 October 2017). This web-based application is conveniently available for experimentalists working on photosynthetic research and/or as a teaching tool. DCaPS can be parameterised for a range of environments, canopy attributes and photosynthetic physiology. The online application reports diurnal patterns of environmental variables, diurnal canopy photosynthesis and daily canopy biomass increment.

Here we present two examples of using DCaPS to simulate consequences of changing photosynthetic attributes in both C₃ and C₄. These are simplified examples to demonstrate the capacity of DCaPS to capture complex dynamic interactions between photosynthetic physiology and diurnal variations in environment, which are not mechanistically included in, for example, the RUE type of canopy photosynthesis models. Users need to be aware of possible concomitant changes associated with changing model parameters. However, knowledge generated from exercising this model could inform photosynthetic manipulation efforts for assisting field crop improvement.

Increasing the relative CO₂/O₂ specificity of Rubisco (S_c/o) is a strategy for increasing CO₂ assimilation in isolated leaves (Evans 2013). There are likely concomitant changes associated with changing S_c/o (Evans 2013). However, in this simulation, we have minimised complexity by assuming all other parameters are kept at default values (Tables 1, 2).

Using DCaPS, it was estimated that a significant (25%) increase in S_c/o, could increase C₃ and C₄ diurnal canopy photosynthetic rate (A_can,DAY) by ~6.0% and 2.5%, respectively, assuming all other parameters were kept at default values (Tables 1, 2). When S_c/o was set to increase by 25%, much of the enhancement was not translated to increase in photosynthetic rate as Rubisco-limited photosynthesis is less sensitive to changes in S_c/o than electron transport limited photosynthesis. In addition, differential effects on sunlit and shaded leaves associated with the canopy light environment contributed to this overall outcome when integrated to the canopy level. Fig. 6a–f shows the changes to instantaneous photosynthesis of the sunlit and shade leaf fractions throughout the day.

Fig. 6.  Dirunal C₃ and C₄ canopy photosynthesis and photosynthetic changes. The top two rows (C₃ and C₄ respectively) show % changes in diurnal canopy photosynthesis with 25% increase in the relative CO₂/O₂ specificity of Rubisco (S_c/o). (a, d) Reference net A_inst at default S_c/o; (b, e) % changes in net A_inst for the sunlit leaf fraction of the canopy; (c, f) % changes in net A_inst for the shade leaf fraction. The bottom two rows (C₃ and C₄ respectively) show changes in diurnal canopy photosynthesis with various Rubisco activity (V_cmax) and/or electron transport capacity (J_max). (g, k) Reference net A_inst with default values; (h, l) V_cmax increased by 20%; (i, m) J_max increased by 20%; (j, n) V_cmax and J_max both increased by 20%. Solid and dotted curves show values for the sunlit (A_sun) and shade (A_sh) leaf fractions of the canopy, respectively; grey and black colour coding are for Rubisco-limited (A_c) and electron-transport limited (A_j) photosynthetic rate, respectively. The A_c,sh curve is removed from h, i, j, l, m and n except in g and k where it is plotted using the right hand ordinate (indicated by arrows). Light grey areas indicate CO₂ assimilation rate or its % change in the sunlit leaf fraction and dark grey areas indicate the same for the shade leaf fraction. For each leaf fraction, photosynthetic rate is given by the minimum of A_c and A_j. Note that diurnal canopy photosynthesis (A_can,DAY; see text) is obtained by summing the photosynthetic rate of the two leaf fractions, integrate hourly and sum over the diurnal period. Default values of other model parameters are given in Tables 1 and 2.

In the case of C₃, Rubisco-limited (A_c,sun) and electron-transport-limited (A_j,sun) photosynthetic rates of the sunlit leaf fraction increased by an average of 2.6 and 7.2% over the diurnal cycle, respectively (Fig. 6b). However, between 11 : 00 and 15 : 00 hours, when the canopy had a high photosynthetic rate, the sunlit leaf fraction was Rubisco (A_c,sun) limited. This interplay between A_c and A_j limitation throughout the day resulted in only 5.5% increase as opposed to the potential 7.2%. On the other hand, the shade leaf fraction increased by 7.7% over the diurnal cycle (all contributed by effects on electron-transport-limited rate (A_j)) (Fig. 6c). Altogether, compared with a potential 7.2% increase in A_can,DAY, A_c limitation around noon reduced the potential increase in A_can,DAY to 6.0%.

C₄ canopy photosynthesis was less responsive to changes in S_c/o than C₃, which was consistent with the notion that increasing S_c/o in C₄ plants has less effect on photosynthesis as they have evolved CO₂-concentrating mechanisms for enhanced photosynthesis. In the case of C₄ canopy photosynthesis, there was no interplay between Rubisco and electron transport limitations with all effects related to the latter (i.e. A_j) (Fig. 6e, f), and totalling to a 2.5% increase in A_can,DAY.

There is evidence that Rubisco activity and electron transport capacity can vary among species, can respond to the prevailing environment, and be bioengineered (reviewed by Evans (2013)). Putative changes in Rubisco activity and electron transport capacity can be implemented in the C₃ and C₄ photosynthesis models of DCaPS through changing the slope of the linear relationship between the maximum rate of Rubisco carboxylation (χ_Vc), the maximum rate of electron transport (χ_J) and specific leaf nitrogen; giving greater V_cmax and J_max, respectively. Here we examine diurnal canopy photosynthesis consequences of such variations.

The simulation of consequences on diurnal canopy photosynthesis of changes in V_cmax and J_max for C₃ and C₄ types are presented in Fig. 6g–n. A_can,DAY did not respond to increase in V_cmax for C₃ types because both the sunlit and shade leaf fractions were mostly electron transport (A_j) limited in the reference scenario (Fig. 6g) and any increase in Rubisco activity (A_c) was not useful (Fig. 6h). However, increasing J_max could increase A_can,DAY by 4.5%, which was attributed to higher electron-transport limited photosynthetic rate of the sunlit leaf fraction (A_j,sun) during early and late hours of the day (Fig. 6i). The largest effect was when V_cmax and J_max were both increased by 20%, which gave a 9.5% increase in A_can,DAY. This shifted the whole diurnal photosynthetic rate higher (Fig. 6j). It was apparent that the sunlit fraction of the canopy was more sensitive to these changes and contributed most to the higher canopy photosynthesis.

For C₄ canopy photosynthesis, there was less interplay between Rubisco- and electron-transport-limited photosynthetic rate. C₄ canopy photosynthesis was always electron-transport limited (Fig. 6k). Hence, increase in Rubisco activity (V_cmax) had little or no effect on A_can,DAY (Fig. 6l). However, a 20% increase in maximum rate of electron transport (J_max) increased A_can,DAY significantly (6%) (Fig. 6m) and increasing both J_max and V_cmax simultaneously, increased A_can,DAY by 8% (Fig. 6n).

Many crop models incorporate canopy photosynthesis as a key driver for crop growth for seasonal simulation. In some of these models, under well watered conditions, canopy CO₂ assimilation/biomass accumulation is based on the empirical RUE approach, while others incorporate more detailed models of photosynthetic light response (PLR). Depending on the detail required for canopy photosynthesis simulation, either type of model can be used. However, the intrinsic empirical nature of these approaches makes it difficult to realistically model responses to manipulation of photosynthetic processes and environmental effects and so that often simple empirical indices are invoked to generate possible effects (Wu et al. 2016).

In this study, we have shown that the DCaPS can rationally simulate canopy photosynthetic rate responses to photosynthetic physiology, key environmental factors and crop status (e.g. light, C_a, T_a and SLN_av). This provides confidence in incorporating DCaPS into crop growth and development models to drive aboveground canopy biomass accumulation in seasonal simulations. The capacity to connect with photosynthetic attributes makes DCaPS a valuable tool to improve the biological functionality of crop models in terms of aboveground canopy biomass accumulation under well watered conditions.

At first inspection, it may seem unduly complicated to introduce DCaPS into a crop model due to the parameterisation requirements at the biochemical/leaf level (Table 1). However, many are related to a small subset of key parameters, while others (e.g. temperature response parameters, Table 2) can be assigned a priori depending on the application of DCaPS. For example, the parameter values for kinetic properties of Rubisco (i.e. K_c, K_o, V_cmax/V_omax) and their temperature responses are relatively conserved within C₃ species (von Caemmerer 2013). This means parameter values obtained from extensively studied model species, such as Arabidopsis and tobacco, can be used for C₃ crop species. Further, more comprehensive parameter values for C₃ (Braune et al. 2009) and C₄ (von Caemmerer 2000; Massad et al. 2007) crop species are also emerging. This leaves a small set of parameters (three and four parameters for C₃ and C₄ respectively) to be assigned as indicated in Table 1.

To facilitate connection with crop growth and development simulation models, DCaPS, which operates on a daily timescale, needs to be connected with environmental and crop canopy attribute data that vary throughout the growing season. These data, already used and output by some crop models, can be input on a daily frequency into DCaPS at the start of each daily simulation. Recall that DCaPS incorporates four key environmental parameters (radiation, T_a, VPD_a, C_a) and the three parameters for canopy attributes (LAI_can, β (canopy-average leaf inclination relative to the horizontal) and SLN_av). Radiation, T_a, VPD_a, LAI_can and SLN_av can be connected with daily values supplied by crop models such as APSIM (Hammer et al. 2009, 2010). This leaves C_a and β to be assigned. It would be reasonable to assume C_a as a constant, while β can be reasonably estimated if a spherical leaf-angle distribution is assumed for field crops (Eqn A26). The design of DCaPS, which accepts daily values of environmental parameters and crop attributes allows convenient connection with crop models for seasonal simulation.

The authors declare no conflicts of interest.