1 simulating daily field crop canopy photosynthesis: an ......85 1994). both types underpin...

Simulating daily field crop canopy photosynthesis: an integrated software package 1

Short running title: Diurnal canopy photosynthesis simulator (DCaPS) 2

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Alex Wu1*, Al Doherty1, Graham Farquhar2, Graeme L. Hammer1 4

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1 Centre for Plant Science, Queensland Alliance for Agriculture and Food Innovation, The 6

University of Queensland, Brisbane, QLD 4072, Australia 7

2 Research School of Biology, Australian National University, Canberra, ACT 2601, Australia 8

9

* Correspondence: 10

Dr. Alex Wu 11

[email protected] 12

The University of Queensland 13

Queensland Alliance for Agriculture and Food Innovation 14

Centre for Plant Science and ARC Centre of Excellence for Translational Photosynthesis 15

306 Carmody Road, 16

Brisbane, QLD 4072, Australia 17

Tel: +61 7 3346 2780 18

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Summary Text 22

In the near future, global demand for agricultural product is predicted to surpass our production 23

capacity and enhancing plant photosynthesis may be a solution for crop yield improvement. To 24

accelerate enhancement, we need to know which target(s) should be manipulated for greatest 25

impact, therefore, a modelling tool is developed. The tool will be able to improve our 26

understanding of photosynthetic manipulation impacts on crop biomass accumulation, which 27

ultimately affects crop yield. 28

29

Abstract 30

Photosynthetic manipulation is seen as a promising avenue for advancing field crop 31

productivity. However, progress is constrained by the lack of connection between leaf-level 32

photosynthetic manipulation and crop performance. Here we develop a model of diurnal 33

canopy photosynthesis for well-watered conditions by using biochemical models of C3 and C4 34

photosynthesis upscaled to the canopy level using the simple and robust sun-shade leaves 35

representation of the canopy. The canopy model was integrated over the time course of the day 36

for diurnal canopy photosynthesis simulation. Rationality analysis of the model showed that it 37

simulated the expected responses in diurnal canopy photosynthesis and daily biomass 38

accumulation to key environmental factors (i.e. radiation, temperature and CO2), canopy 39

attributes (e.g. leaf area index and leaf angle) and canopy nitrogen status (i.e. specific leaf 40

nitrogen and its profile through the canopy). This Diurnal Canopy Photosynthesis Simulator 41

(DCaPS) was developed into a web-based application (www.dcaps.net.au) to enhance usability 42

of the model. Applications of the DCaPS package for assessing likely canopy-level 43

consequences of changes in photosynthetic properties and its implications for connecting 44

photosynthesis with crop growth and development modelling are discussed. 45

46

Key words 47

Canopy photosynthesis, CO2 partial pressure, Temperature effects, Dry matter accumulation, 48

Radiation, Modelling 49

50

Introduction 51

The next advance in field crop productivity will likely need to come from improving crop use 52

efficiency of resources (e.g. radiation, CO2, water and nitrogen), aspects of which are closely 53

linked with overall crop photosynthetic efficiency (Long et al. 2015). For this, there is an 54

emerging agenda focused on genetic manipulation of the biochemical pathway of 55

photosynthesis aiming to enhance photosynthesis for improved crop yield (Evans 2013; Long 56

et al. 2015). However, progress is limited by the lack of connection between 57

biochemical/leaf-level photosynthetic manipulation and crop performance, which is 58

influenced by interactions between (photosynthetic) genetic controls, plant growth and 59

development processes, and environmental effects. Crop models that can incorporate the 60

interactions and integrate across scales of biological organisation might be the tool needed to 61

accelerate progress in photosynthetic enhancement (Wu et al. 2016). 62

63

In many crop models, used for seasonal simulation of crop growth, development and yield, 64

daily biomass accumulation, which is determined by canopy photosynthesis, is a key driver 65

of crop growth that has been used to simulate source-limited plant growth. Canopy 66

photosynthesis modelling began with empirical models of leaf photosynthetic light response 67

(PLR), which were upscaled and integrated to simulate diurnal canopy photosynthesis (Monsi 68

and Saeki 1953; Hammer et al. 2009). There are multiple approaches for such upscaling, 69

which focused on modelling the heterogeneous light environment within the canopy. These 70

can be classified into models with “simplified” canopy representation, such as multi-layer 71

models (each layer partitioned into sunlit and shade leaf fractions) (Duncan et al. 1967), 72

single-layer big-leaf models (Sellers et al. 1992; Sands 1995) or (single-layer) sun-shade 73

leaves models (Hammer and Wright 1994; de Pury and Farquhar 1997). Another type of 74

approach is detailed models, such as static 3D and dynamic 3D (Vos et al. 2010) canopy 75

architecture models. The respective (dis)advantages of these models have been discussed 76

(Wu et al. 2016) and many have supported the simplicity and robustness of the sun-shade 77

leaves approach. This approach can use either single or multiple layers with canopy leaf area 78

index in each layer(s) partitioned into sunlit and shade leaf fractions. Another widely used 79

type of canopy photosynthesis simulation, which avoids the need for photosynthesis 80

modelling and upscaling, is to utilise a simple empirical linear relationship between crop 81

(above-ground) biomass accumulation and intercepted solar radiation (or Radiation Use 82

Efficiency, RUE) (Sinclair and Muchow 1999). Theoretical derivations have shown 83

consistencies between the PLR and RUE approaches to modelling (Hammer and Wright 84

1994). Both types underpin source-limited plant growth simulation, which can be connected 85

with crop models that incorporate both source- and sink-limited crop growth (Hammer et al. 86

2010). For example, the APSIM crop models (Hammer et al. 2009) provide important effects 87

that can regulate canopy photosynthesis via crop nitrogen status, which influences 88

photosynthetic capacity. This is an effective and robust framework for connecting 89

photosynthesis with crop growth, development and yield simulation (Wu et al. 2016). 90

91

Given the focus of photosynthetic enhancement at the biochemical level for field crop 92

improvement, the PLR and RUE types of canopy photosynthesis modelling may not be 93

adequate despite their apparent success in crop models. Their responses to variations at the 94

biochemical level and to environment are difficult to predict due to the aggregated nature of 95

the models. To overcome the limitations, canopy models based on more mechanistic 96

photosynthesis models [e.g. C3 and C4 photosynthesis models; von Caemmerer (2000)] have 97

emerged (de Pury and Farquhar 1997) and have been incorporated into vegetation growth 98

models [e.g. BioCro: biocro.r-forge.r-project.org; Ecosys: ecosys.ualberta.ca; GECROS: Yin 99

and van Laar (2005); WIMOVAC: Humphries and Long (1995)]. Most of them have utilised 100

the simple and robust sun-shade leaves approach. However, there are only a limited number 101

of such canopy photosynthesis models being applied in crop models (Yin and Struik 2008). 102

Despite a limited number, these examples of modelling work demonstrated the value of using 103

biochemical based canopy photosynthesis models to expand the biological functionality of 104

crop models, which could potentially aid progress in photosynthetic enhancement for field 105

crop improvement. 106

107

Besides the eventual target of incorporating diurnal canopy photosynthesis into field crop 108

performance prediction, there is also a need for developing a standalone diurnal canopy 109

photosynthesis simulator. This is likely to stimulate and guide different approaches to leaf-110

level photosynthesis research and reinforces thinking at the canopy level. For example, 111

correlating Rubsico carboxylation rate with leaf nitrogen content would be useful for 112

simulation of instantaneous canopy photosynthetic rate (de Pury and Farquhar 1997). More 113

examples of relationships between photosynthetic and plant attributes have also emerged 114

(Braune et al. 2009). As discussed above, there are existing examples of canopy models, 115

however they have been developed as integrated modules in more extensive vegetation 116

growth models. A standalone diurnal canopy photosynthesis simulator that informs canopy 117

CO2 assimilation/biomass accumulation in terms of photosynthetic attributes and diurnal 118

environment would be a desirable tool. Such a tool can be utilised to aid the wider 119

community of photosynthesis experimentalists to understand consequences at a higher level 120

over a longer simulation period, as well as providing a valuable teaching tool. 121

122

The rationale of extending crop modelling and aiding progress in photosynthesis research 123

warrant the development for a standalone tool of diurnal canopy photosynthesis simulation. It 124

will need to incorporate the biochemical models of photosynthesis as well as respond to 125

diurnal environment effects for simulating canopy CO2 assimilation/biomass accumulation of 126

a field crop over a day. To develop such a tool, three objectives have been identified: 127

(1) develop a standalone C3 and C4 diurnal canopy photosynthesis simulator (DCaPS) for 128

both C3 and C4 photosynthesis based on the concept of a cross-scale modelling 129

framework that facilitates connection with crop growth and development dynamics 130

(Wu et al. 2016) 131

(2) present model rationality tests by simulating responses to key environmental factors 132

(i.e. light, CO2 and temperature), canopy nitrogen status (i.e. specific leaf nitrogen and 133

its profile through the canopy), and canopy attributes and architecture (i.e canopy leaf 134

area index and leaf angle); 135

(3) develop DCaPS into an interactive web-based application that can be accessed using 136

internet browsers on any major platform for simulating likely canopy-level 137

consequences of photosynthetic changes. 138

The implications of the DCaPS package for crop modelling and it applications for 139

photosynthetic manipulation are also discussed. 140

141

Model overview 142

The Diurnal Canopy Photosynthesis Simulator (DCaPS) calculates diurnal (period from 143

sunrise to sunset) canopy CO2 assimilation and daily (24h) biomass increment for a crop 144

under well-watered conditions. A schematic diagram of the model is provided in Figure 1, 145

model detail in the next section, and a comprehensive description and list of model equations 146

and parameters in Tables 1, 2 and the appendices. Daily values of incident solar radiation, air 147

temperature (Ta) and air vapour pressure deficit (VPDa), commonly used in crop models, were 148

used to derive instantaneous values at the start of each hour over the diurnal period. A single-149

layer sunlit and shade leaf modelling approach was used. Canopy leaf area index (LAIcan) was 150

partitioned into sunlit and shade leaf fractions using the sun-shade leaves modelling approach 151

(Hammer and Wright 1994; de Pury and Farquhar 1997) to calculate the amount of PAR 152

absorbed by each fraction. Ta was assumed as a proxy for leaf temperature (Tl), which affects 153

photosynthetic physiology. The canopy profile of leaf nitrogen on a leaf area basis (specific 154

leaf nitrogen, SLN) was input and used to calculate the maximum rate of Rubisco 155

carboxylation (Vcmax), the maximum rate of electron transport (Jmax) and the maximum 156

phosphoenolpyruvate (PEP) carboxylase activity (Vpmax) (de Pury and Farquhar 1997), which 157

are parameters of the C3 and C4 photosynthesis models (Farquhar et al. 1980; von Caemmerer 158

2000) used in DCaPS. The photosynthesis models were coupled with a CO2 diffusion model 159

to calculate Cc and CO2 assimilation rate. Photosynthesis of both the sunlit and shade leaf 160

fractions of the canopy were calculated, summed for the canopy, integrated hourly, and 161

summed over the diurnal period to calculate total diurnal canopy photosynthesis, which was 162

taken as the daily sum. This was converted to daily total biomass increment (BIOtotal,DAY) 163

assuming a conversion ratio (B), which combines factors allowing for biochemical 164

conversion and maintenance respiration (Sinclair and Horie 1989). A fraction of BIOtotal,DAY 165

was partitioned to root and the remaining amount was taken as the daily above-ground 166

canopy (shoot) biomass increment (BIOshoot,DAY). 167

168

Model detail 169

Absorbed photosynthetic active radiation (PAR) 170

In both the C3 and C4 photosynthesis models (not replicated here, but detailed in Appendix A), 171

the potential electron transport rates (J, μmol e- m-2 s-1) of sunlit and shade leaf fractions are 172

driven by absorbed photosynthetic active radiation (PAR) using a non-rectangular hyperbolic 173

function (von Caemmerer 2000). Absorbed PAR for each of the sunlit and shade leaf fractions 174

varies diurnally and its calculation requires diurnal total incident solar radiation, LAIcan, canopy 175

architecture (in the form of canopy-average leaf angle), and optical properties (reflectance and 176

transmittance) of leaves. Separation of absorbed PAR for the sunlit and shade leaf fractions of 177

the canopy is a necessary detail to avoid errors in over estimation of photosynthetic rate (de 178

Pury and Farquhar 1997). 179

180

The calculation of diurnal absorbed PAR depends on the radiation environment (Hammer and 181

Wright 1994). Firstly, diurnal extra-terrestrial radiation (So, MJ m-2 ground day-1) was 182

calculated from latitude (Lat, radians) and day of year (DAY) (Eqn A5). Then diurnal total 183

incident solar radiation on the ground (Sg, MJ m-2 ground s-1) was calculated by multiplying So 184

and the atmospheric transmission ratio (RATIO) (Eqn A4). Sg was then distributed sinusoidally 185

over the diurnal period to derive instantaneous values for incident radiation (Io MJ m-2 ground 186

s-1) (Eqn A3). Io consists of direct (Idir, MJ m-2 ground s-1) and diffuse (Idif, MJ m-2 ground s-1) 187

radiation components. Diffuse radiation represents 17% of solar insolation (So) for any Lat, 188

DAY and RATIO (Eqn A1). The diurnal pattern of atmospheric transmission of Idir is more 189

complex, so was simply obtained by the difference between Io and Idif (Eqn A2). This approach 190

allows the proportion of Idir and Idif to vary across a diurnal period giving, for example, higher 191

proportion of Idif in early and later hours of the diurnal period and higher proportion of Idif if 192

RATIO is low due to cloud cover. 193

194

The derived Idir and Idif (total incident solar radiation) from above were used to estimate direct 195

and diffuse PAR (Idir_PAR and Idif_PAR, respectively). It was assumed that 50% of the energy in 196

Idir and Idif was PAR, which was converted to photosynthetic photon flux density by multiplying 197

by 4.56 and 4.25 μmol PAR (J PAR)-1, respectively (Eqns A21 and A22). Units for Idir_PAR and 198

Idif_PAR are μmol PAR m-2 ground s-1. 199

200

The PAR absorbed by either sunlit or shade leaves fractions (Iabs_sun and Iabs_sh, both with units 201

of μmol PAR m-2 s-1) was calculated using the equations of de Pury and Farquhar (1997). This 202

incorporated Idir_PAR and Idif_PAR, optical properties of leaves, such as reflectance and 203

transmittance to PAR, LAIcan, and the proportion of intercepted radiation (dependent on 204

canopy-average leaf angle and LAIcan). It was assumed that the sunlit leaf fraction received 205

Idir_PAR, Idif_PAR and scattered radiation (caused by reflectance and transmittance of leaves), 206

while the shade leaf fraction received only Idif_PAR and scattered radiation. Detailed equations 207

and calculation procedures are given by Eqns A19–A32 in Appendix A. In the current model, 208

diurnal variations in leaf reflectance and transmittance are not considered. However, as a first 209

approximation, it can be input into DCaPS for each diurnal simulation. 210

211

Air vapour pressure deficit (VPDa) 212

Air vapour pressure deficit (VPDa, kPa) was calculated as the difference between the saturated 213

vapour pressure at air temperature (SVPa) and that at dew-point temperature (SVPd) (Eqns A16–214

A18). The minimum temperature (Ta,min; more below) for the day was assumed as the dew-215

point temperature, which has been shown to give robust estimates of VPDa (Lobell et al. 2015). 216

Accordingly, VPDa varies diurnally with air temperature. 217

218

Specific leaf nitrogen (SLN) and photosynthetic physiology 219

Specific leaf nitrogen (SLN, g N m-2 leaf) influences key photosynthetic physiological 220

parameters. Using the mathematical development by de Pury and Farquhar (1997), vertical 221

variation through the canopy can be explicitly incorporated; the approach integrates the profile 222

to give a total for the single-layer canopy, which is then partitioned into sunlit and shade leaves. 223

Distribution of SLN in the canopy was assumed to follow an exponential decay with canopy 224

depth (Eqn A34). The decay function was specified by SLN at the top layer of the canopy 225

(SLNo, g N m-2 leaf) and the average SLN for the canopy (SLNav, g N m-2 leaf). To incorporate 226

the effects of SLN on photosynthetic physiology, this model assumed that at the reference 227

temperature of 25°C, the maximum rate of Rubisco carboxylation (Vcmax), the maximum rate 228

of electron transport (Jmax), leaf day respiration (Rd), and the maximum PEP carboxylase 229

activity (Vpmax) were all zero below a minimum SLN and increased linearly with slope of χV, 230

χJ, χR and χP, respectively, above that threshold value (Eqns A37–A40). The minimum SLN 231

values were 0.35 and 0.2 g N m-2 (leaf) for C3 and C4, respectively (Table 1). 232

233

Leaf temperature (Tl) 234

Estimation of air temperature (Ta, °C) is needed as it significantly influences leaf temperature 235

(Tl, °C). A model of daily Ta (over the 24h) was used (Eqn A15). Even though the majority of 236

daylight hours can be modelled by the diurnal function of the model, the night time function is 237

sometimes applicable for the early hours of the diurnal period. The diurnal period was modelled 238

with a sine function and an exponential decay function was used during the night. The 239

amplitude of the daily Ta fluctuation was specified by the maximum (Ta,max, °C) and minimum 240

(Ta,min, °C) air temperature of the day. The phase shift of the sine function was determined by 241

the lag coefficient for the maximum temperature (xlag), the night-time temperature coefficient 242

(ylag), and the lag of minimum temperature from the time of sunrise (zlag) (Eqn A15). It was 243

assumed here that Tl is approximated by Ta for both sunlit and shade leaf fractions. This is a 244

reasonable assumption over a wide range of temperature under well-watered conditions. 245

246

The response of photosynthesis to Tl was modelled through responses of the C3 and C4 247

photosynthesis model parameters to Tl (i.e. Kc, Ko, Vomax/Vcmax, Vcmax, Jmax and Rd for C3 plus 248

Kp and Vpmax for C4; Table 1). There is a growing availability of these temperature responses, 249

in particular, for model species. The most comprehensive data set for the C3 Nicotiana 250

tabacum have been used effectively for simulating temperature responses of leaf 251

photosynthesis (Bernacchi et al. 2002). Temperature responses of Kc, Ko and Vomax/Vcmax are 252

usually assumed to be similar among C3 species (von Caemmerer 2013), so here we used 253

parameters from Nicotiana tabacum for C3 crop species. It was reported that Kc of Triticum 254

aestivum is significantly different to Nicotiana tabacum (Sharwood et al. 2016), but whether 255

or not this has significant implications for diurnal canopy photosynthesis will require 256

sensitivity analysis when other wheat parameters also become available. Parameter 257

availability for C4 crop species is not as comprehensive so here we used parameters for the C4 258

model species Setaria viridis (Boyd et al. 2015). These default values can be readily changed 259

as parameters of C4 crop species become better known. 260

261

Temperature responses of Kc, Ko, Vcmax, Rd, Kp and Vpmax were modelled using an exponential 262

type function [Eqn 1, adapted from Sharkey et al. (2007)], whereas Jmax, due to its apparent 263

optimum in temperature response (Farquhar et al. 1980), was modelled via a normal 264

distribution function [Eqn 2, adapted from June et al. (2004)]. Vcmax/Vomax and its temperature 265

response were not available from Bernacchi et al. (2002), where Kc and Ko were reported, but 266

can be back calculated from Kc, Ko and * with Eqns A52 and A53 (assuming a chloroplastic 267

oxygen partial pressure (Oc) of 210000 bar). Its temperature response can be modelled with 268

Eqn 1. In summary, temperature responses of the C3 and C4 photosynthesis model parameters 269

to Tl were modelled with Eqn 1 or 2 with parameter values given in Table 2. 270

271

Expression of the exponential type function used to describe temperature response of certain 272

photosynthesis model parameters [adapted from Sharkey et al. (2007)]: 273

𝑃 = 𝑃25𝑒(𝑐−𝑏 (𝑇l+273)⁄ ) Eqn 1 274

where P25 is the modelled value of parameter at 25°C, c and b are empirical constants, which 275

are balanced to give the factor after P25 unity at 25°C. Expression of the normal distribution 276

function [adapted from June et al. (2004)]: 277

𝑃 = 𝑃25𝑒−(

𝑇l−𝑇opt

Ω)

2

+(25−𝑇opt

Ω)

2

Eqn 2 278

where Topt is the optimum temperature and is the difference in temperature from Topt at which 279

P falls to e-1 (0.37). 280

Chloroplastic CO2 partial pressure (Cc) 281

Air CO2 (Ca, μbar) has to diffuse into leaves to reach the carboxylating site of Rubisco inside 282

the chloroplasts for photosynthesis. The best practice for expressing CO2 levels is in partial 283

pressure (Sharkey et al. 2007). To convert from the usual unit of ppm to μbar, it was 284

multiplied by the air pressure (e.g., at sea level, CO2 of 400 ppm is (400×10−6)×285

1013250 μbar = 405.3 μbar). Leaf boundary-layer and stomatal conductance have 286

significant effects on the drawdown of intercellular airspace CO2 partial pressure (Ci) relative 287

to Ca (Leuning 1995) and mesophyll conductance has significant effects on the drawdown of 288

CO2 partial pressure at the carboxylating site of Rubisco (Cc) relative to Ci (Flexas et al. 289

2012). Diffusional conductance, the reciprocal of resistance, of these three components [i.e. 290

leaf boundary-layer (glb), stomatal (gs) and mesophyll (gm) conductance] are incorporated in 291

Cc estimation (Eqn A47) based on Fick’s first law of diffusion. To model crop canopies, the 292

turbulent resistance through the canopy boundary layer, which would affect CO2 partial 293

pressure, air temperature and vapour pressure deficit (relative to those above the canopy), 294

needs to be considered (Leuning et al. 1995). However, in their modelling work, Leuning et 295

al. (1995) showed simulated canopy photosynthesis reproduced features in data so the 296

omission of the turbulent resistance is a reasonable approximation. 297

298

However, there are uncertainties in the estimation of glb and gs. The model that is commonly 299

used for glb estimation relies on leaf width and local wind speed (Goudriaan and van Laar 300

1994), which cannot be assigned a priori. Numerous types of leaf stomatal conductance (gs) 301

models have been developed over the years (Damour et al. 2010). Two particular types are 302

widely used. These are the empirical multiplicative models of environmental influences such 303

as light, Ca and VPDa [e.g. the Jarvis model; Jarvis (1976)] and the semi-empirical models 304

relating gs to photosynthesis with VPDa [e.g. the BWB model (abbreviated using authors’ 305

names); Ball et al. (1987)], while more mechanistic models with plant physiology 306

considerations based on abscisic acid or hydraulic control have also been developed (Damour 307

et al. 2010). The limitation of the multiplicative type models is the lack of interactions 308

between plant physiology and among the environmental factors; while the models relating gs 309

to photosynthesis rely on empirical parameters, which cannot be assigned a priori. These 310

empirical coefficients can vary greatly between C3 species (Li et al. 2012) and so cannot be 311

generalised for C3 crop species, while the coefficients are rarely reported for C4 crop species. 312

Given that there are limited data available to calibrate the empirical coefficients of the Jarvis 313

or the BWB models for C3 and especially C4 crop species, an alternative approach to estimate 314

Ci is to use the ratio of Ci/Ca, which is based on stomatal optimization theory in that stomata 315

respond to maintain a constant Ci under a given Ca to maximize CO2 assimilation. This ratio 316

(~0.7 for C3 and ~0.4 for C4) has been found to be stable with Ca between 100 μbar and 400 317

μbar in combination with any PPFD between 250 μmol m-2 s-1 and 2000 μmol m-2 s-1 (Wong 318

et al. 1979); further, Ci/Ca does not appear to change under elevated Ca (Ainsworth and Long 319

2005). The consistency in Ci/Ca in a wide range of conditions makes it an efficient and robust 320

modelling approach. It is not clear how Ci/Ca would respond to PPFD lower than 250 μmol 321

m-2 s-1, but such conditions only apply to the very early and late hours in a diurnal period, 322

which amount to less than ca. 5% of diurnal canopy photosynthesis and so any changes under 323

such conditions would have limited effect on diurnal total estimation. However, like gs, Ci/Ca 324

is influenced by VPDa. It was found to decrease linearly with VPDa in various species 325

including C3 Oryza sativa and C4 Zea mays (Zhang and Nobel 1996). Ci/Ca response to VPDa 326

can be given by: 327

𝐶𝑖 𝐶𝑎⁄ = 𝑎𝑉𝑃𝐷a + 𝑏 Eqn 3 328

where a and b are empirical constants. For C3 they are -0.12 and 0.90, respectively; for C4, 329

they are -0.19 and 0.84, respectively. At VPDa between 1 to 2 kPa, Eqn 3 gives ~0.7 and 0.5 330

for C3 and C4, respectively, which are similar to those reported by Wong et al. (1979). Here, 331

we used the simpler Ci/Ca ratio approach for Cc estimation (Eqn A49), which avoided the 332

need for glb and gs. 333

334

The importance of mesophyll conductance (gm) has been recognised only recently. gm in model 335

C3 species is known to vary with temperature and there is evidence that gm may also respond 336

to the other key environmental factors (e.g. irradiance and CO2), but this variation is not yet 337

completely certain (Pons et al. 2009). So here we included only the effect of temperature and 338

modelled this by using the normal distribution function (Eqn 2). At the reference temperature 339

(i.e. 25°C) gm (per leaf area) in C3 wheat is assumed to be 0.55 mol CO2 m-2 s-1 bar-1. No values 340

for C4 species have been reported, so the C3 value was used as a default value. 341

342

Diurnal canopy photosynthesis, daily respiration, root and canopy biomass 343

accumulation, and RUE 344

Diurnal canopy CO2 assimilation, daily respiration and conversion losses, and allowance for 345

root biomass were used to calculate daily above-ground canopy (shoot) biomass increment 346

(BIOshoot,DAY). This model assumes that photosynthesis during the diurnal period results in 347

carbon assimilation for the entire day so we use the symbol Acan,DAY. Acan,DAY was calculated 348

by summing the CO2 assimilation of the sunlit (Asun) and shaded (Ash) leaf fractions of the 349

canopy at the start of each hour over the diurnal period, integrated hourly and summed over 350

the diurnal period (Eqn A73). Using the C3 and C4 photosynthesis models, leaf respiration 351

during the diurnal period can be implicitly accounted for at the leaf level with the parameter Rd 352

(Eqns A51, A54, A55 and A59). However, this lacks consideration of respiration from other 353

plant organs and during the night period. A common approach is to omit the leaf-level Rd (by 354

setting χR to zero) and consider respiration at the plant level on a daily basis, which can be 355

accounted for within a conversion ratio (B) that combines factors allowing for biochemical 356

conversion of CO2 to biomass and CO2 loss due to maintenance respiration (Sinclair and Horie 357

1989). This approach is consistent with the conservative respiration:photosynthesis ratio 358

approach (Gifford 2003), by which plant respiration is taken as a fraction of total canopy 359

photosynthesis. The conversion ratio, B, is 0.41 g biomass (g CO2)-1 for cereal crops such as 360

rice and maize (Sinclair and Horie 1989). Therefore, daily whole-plant biomass increment 361

(BIOtotal,DAY) was calculated by multiplying Acan,DAY with the molecular weight of CO2 (= 44 g 362

(mol CO2)-1) and B. To calculate shoot biomass increment (BIOshoot,DAY), BIOtotal,DAY is 363

multiplied by the fraction of above-ground (shoot) biomass to total biomass (shoot + root), 364

denoted by Pshoot (Eqn A74). In effect, this simulates partitioning of a fraction of BIOtotal,DAY 365

to root. Here, Pshoot is given a default of 1 assuming a mature canopy around flowering. 366

Radiation Use Efficiency for the day (RUEDAY, g biomass MJ-1) was then calculated by 367

dividing BIOshoot,DAY by the total amount of intercepted solar radiation (Eqns A75 and A76, 368

respectively). 369

370

Model rationality analysis 371

Environmental parameters 372

Default environmental parameters were set for C3 wheat (winter crop) and C4 sorghum 373

(summer crop), with a canopy leaf area index (LAIcan) = 6, growing in the southern hemisphere 374

spring (DAY = 298) and summer (DAY = 15), respectively, at locations with Lat = -35° and -375

27.5°, respectively. Clear sky with atmospheric transmission ratio (RATIO) of 0.75 was 376

assumed unless otherwise stated. The average maximum and minimum air temperatures at 377

these times of year were 21 and 7°C for Lat = -35° and 30 and 15°C for Lat = -27.5°. 378

379

Diurnal canopy photosynthesis in relation to canopy architecture 380

Diurnal patterns of net C3 and C4 canopy photosynthesis for a range of canopy LAI (LAIcan) 381

and canopy-average leaf inclination relative to the horizontal (β) were simulated as a qualitative 382

test of the Diurnal Canopy Photosynthesis Simulator (DCaPS). The C4 simulations (Figure 2C 383

and D) were consistent in the diurnal pattern and magnitude with those reported by Duncan et 384

al. (1967) and Hammer et al. (2009), who found that the canopy with erect leaves (β = 80°) 385

continued to increase canopy photosynthetic rate beyond LAIcan = 4 at high LAIcan (= 8) due to 386

better light distribution throughout the canopy. There was ca. 40% increase in midday canopy 387

photosynthetic rate at LAIcan = 8 compared to LAIcan = 4, which was comparable to that 388

simulated by Duncan et al. (1967) and Hammer et al. (2009). In the canopy with less erect 389

leaves (β = 40°), there was little increase in canopy photosynthetic rate with increase in LAIcan 390

beyond 4. In terms of the magnitude, the simulated canopy photosynthetic rate at LAIcan = 4 391

(Figure 2C and D) was comparable to that observed in a similar size maize canopy (~70 μmol 392

CO2 m-2 s-1) by Grant et al. (1989). The simulation also indicated that for a canopy with low 393

LAIcan (= 2), less erect leaves (β = 40°) offered greater PAR absorption by both sunlit and shade 394

leaf fractions consistent with greater radiation interception as found by Hammer et al. (2009). 395

Even though the sunlit LAI (LAIsun) can be reduced up to 30% with less erect leaves, its 396

photosynthetic rate was not affected due to associated increase in absorbed PAR. For the case 397

of the shade leaf fraction, the increase in both the absorbed PAR and shade LAI (LAIsh) 398

significantly increased shade leaf Aj,sh. These consequences for the two leaf fractions translate 399

to a greater canopy photosynthesis with less erect leaves at low LAIcan. The effects of leaf 400

erectness were mostly analogous for the C3 simulations (Figure 2A and B). However, the 401

greater radiation interception offered by less erect leaves at low LAIcan did not translate to 402

greater canopy photosynthesis. Unlike C4, reduction in LAIsun significantly reduced the 403

Rubisco-limited photosynthetic rate (Ac,sun) resulting in reduced photosynthetic rate in the 404

sunlit leaf fraction. This more than offset the increase (because of increase in both the absorbed 405

PAR and LAIsh) in Aj,sh. So in the case of C3, Rubisco limitation can reduce photosynthetic rate 406

of small (low LAIcan) canopies with less erect leaves. 407

408

Diurnal canopy photosynthesis in relation to CO2 with varying temperature 409

A simulation of net C3 and C4 diurnal canopy photosynthesis (Acan,DAY) for a range of air CO2 410

partial pressures (Ca) and temperatures (Ta) was undertaken as a qualitative test. Based on 411

various large-scale free-air CO2 enrichment (FACE) studies, elevating Ca to 475–600 μbar (or 412

an average of 540 μbar) increased C3 Acan,DAY by an average of 28% relative to Ca = 360 μbar 413

(Ainsworth and Long 2005). This increase was reproduced when Ta_min and Ta_max were set to 414

14 and 28°C, respectively, simulating hot days for winter wheat crops (Figure 3). Ainsworth 415

and Long (2005) noted that when the large-scale free-air CO2 enrichment (FACE) studies were 416

categorised by temperature, the relative increase in light saturated photosynthesis was lower 417

(an average of 19%) at lower temperatures (< 25°C). Simulation results for average days with 418

Ta_min and Ta_max of 7 and 21°C, respectively, is consistent with this CO2 response at lower 419

temperatures (Figure 3). Increase in Acan,DAY can be as high as 50% at Ca = 1000 μbar. This 420

result is discussed further below in regards to daily radiation use efficiency. In the case of C4 421

canopy photosynthesis, the response of net Acan,DAY to Ca and temperature was significantly 422

less, which is consistent with the finding that C4 maize photosynthesis is not significantly 423

affected by elevated Ca (Leakey et al. 2006). This simulation suggested that canopy 424

photosynthesis of C3 crops can significantly benefit from elevated CO2, while C4 crops do not. 425

426

RUEDAY in relation to CO2 with varying temperature 427

A simulation of C3 and C4 daily canopy Radiation Use Efficiency (RUEDAY) for a range of air 428

CO2 partial pressures (Ca) and air temperatures (Ta) was also undertaken as a qualitative test. 429

Elevated Ca is known to increase the net photosynthetic rate of C3 plants resulting in increased 430

biomass accumulation and RUE (Kimball et al. 2002) and there is also an enhanced effect on 431

RUE at higher Ta (Reyenga et al. 1999). The general consensus is that RUE of C3 crops 432

increases almost linearly from Ca of 300 to 660 μbar, reaches ca. 30% increase at double the 433

ambient Ca and plateaus at ca. 50% beyond Ca of 1000 μbar (Lobell et al. 2015). O'Leary et al. 434

(2015) found a ca. 22% increase in wheat crop biomass in response to elevated Ca from 365 to 435

550 μmol mol-1. These known responses of C3 RUE were reproduced with the model for winter 436

wheat crops experiencing average to hot temperatures (Figure 3). The response relative of 437

RUEDAY to Ca and temperature reflect that of net Acan,DAY because of the linear relationship 438

between RUEDAY and Acan,DAY (Eqns A74 and A75). In the case of the C4 canopy, elevated Ca 439

had only a small effect on the simulated RUEDAY (Figure 3), which was consistent with a lack 440

of response to Ca observed in C4 sorghum. This simulation suggested that elevated CO2 can 441

significantly benefit canopy biomass accumulation of C3 crops, but not C4 crops. 442

443

RUEDAY in relation to average temperature 444

A simulation of C3 and C4 daily canopy Radiation Use Efficiency (RUEDAY) for a range of 445

average air temperature was undertaken as a qualitative test. Air temperature (Ta) varies 446

diurnally between the daily maximum (Ta,max) and minimum (Ta,min) temperature and the 447

diurnal pattern can be modelled with Eqn A15. A 15°C difference between Ta,max and Ta,min was 448

assumed and a range of temperature used so that temperatures ranging from 0–35°C for C3 and 449

10–40°C for C4 were included. When plotted against average daily temperature the simulated 450

RUEDAY was relatively insensitive between average temperatures of 14–23°C for C3 and 21–451

28°C for C4 (Figure 4). This is consistent with known insensitivities of crop biomass 452

accumulation and RUE to temperatures around optimal values (Yan and Hunt 1999). These 453

temperature ranges for C3 and C4 responses were associated with the response of leaf 454

photosynthesis to temperature, which is also insensitive within a broad range [e.g. C3: rice and 455

wheat (Nagai and Makino 2009); C4: various grasses (Ludlow 1981), maize (response curve 456

was derived from picking a typical Ci (e.g. 150 μbar) in A/Ci curves measured at different 457

temperature in Massad et al. (2007)]. Further, RUE under optimum growth conditions has been 458

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 459

(George-Jaeggli et al. 2013). The simulated maximum RUEDAY for C3 and C4 corresponded 460

with these reported ranges (Figure 4). 461

462

The comparison here between C3 wheat and C4 dwarf sorghum RUE does not reveal differences 463

in magnitude between C3 and C4 crops, where the latter is typically higher. RUE of some tall 464

hybrid sorghum varieties (George-Jaeggli et al. 2013) and maize (Sinclair and Muchow 1999) 465

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 466

rapid stem elongation and maximum biomass accumulation phase (Olson et al. 2012). The 467

typical high C4 RUE could be ascribed to higher photosynthetic rate (Hammer et al. 2010) 468

and/or differences in canopy architecture, which may affect diurnal canopy photosynthesis 469

(Figure 2). These scenarios (and their combinations) can be simulated with the model. As a 470

demonstration of this capability, we have assumed the first case by increasing the slope of the 471

linear relationship between the maximum rate of Rubisco carboxylation (χVc), maximum rate 472

of electron transport (χJ), maximum PEP carboxylase activity (χVP) and specific leaf nitrogen; 473

these gave greater Vcmax, Jmax and Vpmax, respectively, and simulated the typical high RUE in 474

C4 crops (Figure 4). 475

476

RUEDAY in relation to SLNav with varying direct:diffuse radiation 477

A simulation of C3 and C4 RUEDAY for a range of canopy-average specific leaf nitrogen (SLNav) 478

with varying direct:diffuse radiation was undertaken as a qualitative test. Direct:diffuse 479

radiation was varied by changing the atmospheric transmission ratio (RATIO) in a similar 480

manner to the simulation study of Hammer and Wright (1994). High values (RATIO = 0.75) 481

reflect clear sky with high transmission of direct radiation and a low fraction of diffuse 482

radiation. Massignam (2003) found that RUE of the C3 crop sunflower responded 483

asymptotically to SLNav with RUE of ca. 1 and 1.5 g MJ-1 at SLNav of 1.5 and 2 g N m-2, 484

respectively. This was closely predicted by the model with clear sky conditions (Figure 5A). 485

Muchow and Sinclair (1994) found that RUE of field-grown dwarf sorghum responded 486

asymptotically to SLNav, but did not approach the asymptote because sorghum SLNav 487

maximised at 1.3 g N m-2 giving RUE of 1.26 g MJ-1. This was also closely predicted by the 488

model with clear sky conditions (Figure 5B). The simulated RUEDAY response of typical dwarf 489

sorghum was not significantly different from that for wheat, but when the model was 490

parameterised for the greater photosynthetic rate of the tall hybrid sorghums, the response was 491

higher at all SLNav (Figure 5B). These responses were comparable to that of maize crops (RUE 492

of ca. 1.5 and 2 g MJ-1 at SLNav of 1 and 2 g N m-2, respectively) (Massignam 2003). In general, 493

direct radiation level was higher with higher RATIO, while the absolute level of diffuse 494

radiation was insensitive to RATIO, leading to a greater fraction of diffuse at low RATIO 495

(cloudy days). Simulated results of increasing diffuse radiation fraction on C3 species (Figure 496

5A) were consistent with Tubiello et al. (1997), who found a significant increase (~40%) in 497

wheat RUE when grown under high diffuse radiation conditions due to the fact that diffuse 498

radiation penetrates deeper into the crop canopy and increases photosynthetic rate of the lower 499

leaves. Hammer and Wright (1994) used a simpler canopy photosynthesis model to show that 500

decreases in RATIO caused RUE to increase. This response of RUEDAY to RATIO was 501

reproduced (Figure 5). While both C3 and C4 types responded similarly to the increased fraction 502

of diffuse radiation, the standard C4 types achieved higher RUEDAY at much lower SLNav as a 503

result of their greater photosynthetic rate (Figure 5B). This is consistent with the comparison 504

of responses reported by Sinclair and Horie (1989). 505

506

507

Applications for photosynthesis manipulation – a tool for assessing consequences of 508

photosynthetic changes 509

The Diurnal Canopy Photosynthesis Simulator (DCaPS) enables simulation of likely canopy-510

level consequences of photosynthetic manipulation and canopy structural attributes in C3 and 511

C4 field crops. It integrates many non-linear responses of leaf photosynthesis to environment 512

and processes involved in upscaling to the canopy level (see Model Detail). 513

514

Considerable effort has been invested to develop DCaPS into an interactive web-based 515

application (www.dcaps.net.au), which can be run with internet browsers on any major 516

platform without prior installation of DCaPS (DCaPS v1.0 source code is available at 517

https://github.com/QAAFI/DCaPS.git). This web-based application is conveniently available 518

for experimentalists working on photosynthetic research and/or as a teaching tool. DCaPS 519

can be parameterised for a range of environments, canopy attributes, and photosynthetic 520

physiology. The online application reports diurnal patterns of environmental variables, 521

diurnal canopy photosynthesis and daily canopy biomass increment. 522

523

Here we present two examples of using DCaPS to simulate consequences of changing 524

photosynthetic attributes in both C3 and C4. These are simplified examples to demonstrate the 525

capacity of DCaPS to capture complex dynamic interactions between photosynthetic 526

physiology and diurnal variations in environment, which are not mechanistically included in, 527

for example, the RUE type of canopy photosynthesis models. Users need to be aware of 528

possible concomitant changes associated with changing model parameters. However, 529

knowledge generated from exercising this model could inform photosynthetic manipulation 530

efforts for assisting field crop improvement. 531

532

Relative CO2/O2 specificity of Rubisco 533

Increasing the relative CO2/O2 specificity of Rubisco (Sc/o) is a strategy for increasing CO2 534

assimilation in isolated leaves (Evans 2013). There are likely concomitant changes associated 535

with changing Sc/o (Evans 2013). However, in this simulation, we have minimised complexity 536

by assuming all other parameters are kept at default values (Table 1 and 2). 537

538

Using DCaPS, it was estimated that a significant (25%) increase in Sc/o, could increase C3 and 539

C4 diurnal canopy photosynthetic rate (Acan,DAY) by ca. 6.0% and 2.5%, respectively, 540

assuming all other parameters were kept at default values (Tables 1 and 2). While Sc/o was set 541

to increase by 25%, much of the enhancement was not translated to increase in 542

photosynthetic rate as Rubisco-limited photosynthesis is less sensitive to changes in Sc/o than 543

electron transport limited photosynthesis. In addition, differential effects on sunlit and shaded 544

leaves associated with the canopy light environment contributed to this overall outcome when 545

integrated to the canopy level. Figure 6A-F shows the changes to instantaneous 546

photosynthesis of the sunlit and shade leaf fractions throughout the day. 547

548

In the case of C3, Rubisco-limited (Ac,sun) and electron-transport-limited (Aj,sun) 549

photosynthetic rates of the sunlit leaf fraction increased by an average of 2.6 and 7.2% over 550

the diurnal cycle, respectively (Figure 6B). However, between 11 am and 3 pm, when the 551

canopy had a high photosynthetic rate, the sunlit leaf fraction was Rubisco (Ac,sun) limited. 552

This interplay between Ac and Aj limitation throughout the day resulted in only 5.5% increase 553

as opposed to the potential 7.2%. On the other hand, the shade leaf fraction increased by 554

7.7% over the diurnal cycle [all contributed by effects on electron-transport-limited rate (Aj)] 555

(Figure 6C). Altogether, compared to a potential 7.2% increase in Acan,DAY, Ac limitation 556

around noon reduced the potential increase in Acan,DAY to 6.0%. 557

558

C4 canopy photosynthesis was less responsive to changes in Sc/o than C3, which was 559

consistent with the notion that increasing Sc/o in C4 plants has less effect on photosynthesis as 560

they have evolved CO2-concentrating mechanisms for enhanced photosynthesis. In the case 561

of C4 canopy photosynthesis, there was no interplay between Rubisco and electron transport 562

limitations with all effects related to the latter (i.e. Aj) (Figure6 E and F), and totalling to a 563

2.5% increase in Acan,DAY. 564

565

Rubisco activity and electron-transport rate 566

There is evidence that Rubisco activity and electron transport capacity can vary among species, 567

can respond to the prevailing environment, and be bioengineered [reviewed by Evans (2013)]. 568

Putative changes in Rubisco activity and electron transport capacity can be implemented in the 569

C3 and C4 photosynthesis models of DCaPS through changing the slope of the linear 570

relationship between the maximum rate of Rubisco carboxylation (χVc), the maximum rate of 571

electron transport (χJ) and specific leaf nitrogen; giving greater Vcmax and Jmax, respectively. 572

Here we examine diurnal canopy photosynthesis consequences of such variations. 573

574

The simulation of consequences on diurnal canopy photosynthesis of changes in Vcmax and 575

Jmax for C3 and C4 types are presented in Figure 6G-N. Acan,DAY did not respond to increase in 576

Vcmax for C3 types because both the sunlit and shade leaf fractions were mostly electron 577

transport (Aj) limited in the reference scenario (Figure 6G) and any increase in Rubisco 578

activity (Ac) was not useful (Figure 6H). However, increasing Jmax could increase Acan,DAY by 579

4.5%, which was attributed to higher electron-transport limited photosynthetic rate of the 580

sunlit leaf fraction (Aj,sun) during early and late hours of the day (Figure 6I). The largest effect 581

was when Vcmax and Jmax were both increased by 20%, which gave a 9.5% increase in 582

Acan,DAY. This shifted the whole diurnal photosynthetic rate higher (Figure 6J). It was 583

apparent that the sunlit fraction of the canopy was more sensitive to these changes and 584

contributed most to the higher canopy photosynthesis. 585

586

For C4 canopy photosynthesis, there was less interplay between Rubisco- and electron-587

transport-limited photosynthetic rate. C4 canopy photosynthesis was always electron-588

transport limited (Figure 6K). Hence, increase in Rubisco activity (Vcmax) had little or no 589

effect on Acan,DAY (Figure 6L). However, a 20% increase in maximum rate of electron 590

transport (Jmax) increased Acan,DAY significantly (6%) (Figure 6M) and increasing both Jmax 591

and Vcmax simultaneously, increased Acan,DAY by 8% (Figure 6N). 592

593

Implications for crop performance prediction – connecting biochemical photosynthesis 594

models with crop models for seasonal simulations 595

Many crop models incorporate canopy photosynthesis as a key driver for crop growth for 596

seasonal simulation. In some of these models, under well-watered conditions, canopy CO2 597

assimilation/biomass accumulation is based on the empirical Radiation Use Efficiency (RUE) 598

approach, while others incorporate more detailed models of photosynthetic light response 599

(PLR). Depending on the detail required for canopy photosynthesis simulation, either type of 600

model can be used. However, the intrinsic empirical nature of these approaches makes it 601

difficult to realistically model responses to manipulation of photosynthetic processes and 602

environmental effects and so that often simple empirical indices are invoked to generate 603

possible effects (Wu et al. 2016). 604

605

In this study, we have shown that the Diurnal Canopy Photosynthesis Simulator (DCaPS) can 606

rationally simulate canopy photosynthetic rate responses to photosynthetic physiology, key 607

environmental factors and crop status (e.g. light, Ca, Ta and SLNav). This provides confidence 608

in incorporating DCaPS into crop growth and development models to drive above-ground 609

canopy biomass accumulation in seasonal simulations. The capacity to connect with 610

photosynthetic attributes makes DCaPS a valuable tool to improve the biological 611

functionality of crop models in terms of above-ground canopy biomass accumulation under 612

well-watered conditions. 613

614

At first inspection, it may seem unduly complicated to introduce DCaPS into a crop model 615

due to the parameterisation requirements at the biochemical/leaf level (Table 1). However, 616

many are related to a small subset of key parameters, while others (e.g. temperature response 617

parameters, Table 2) can be assigned a priori depending on the application of DCaPS. For 618

example, the parameter values for kinetic properties of Rubisco (i.e. Kc, Ko, Vcmax/Vomax) and 619

their temperature responses are relatively conserved within C3 species (von Caemmerer 620

2013). This means parameter values obtained from extensively studied model species, such as 621

Arabidopsis and tobacco, can be used for C3 crop species. Further, more comprehensive 622

parameter values for C3 (Braune et al. 2009) and C4 (von Caemmerer 2000; Massad et al. 623

2007) crop species are also emerging. This leaves a small set of parameters (four and five 624

parameters for C3 and C4, respectively) to be assigned as indicated in Table 1. 625

626

To facilitate connection with crop growth and development simulation models, DCaPS, 627

which operates on a daily timescale, needs to be connected with environmental and crop 628

canopy attribute data that vary throughout the growing season. These data, already used and 629

output by some crop models, can be input on a daily frequency into DCaPS at the start of 630

each daily simulation. Recall that DCaPS incorporates four key environmental parameters 631

(radiation, Ta, VPDa, Ca) and the three parameters for canopy attributes (LAIcan, β (canopy-632

average leaf inclination relative to the horizontal) and SLNav). Radiation, Ta, VPDa, LAIcan and 633

SLNav can be connected with daily values supplied by crop models such as APSIM (Hammer 634

et al. 2009; Hammer et al. 2010). This leaves Ca and β to be assigned. It would be reasonable 635

to assume Ca as a constant, while β can be reasonably estimated if a spherical leaf-angle 636

distribution is assumed for field crops [Eqn A26]. The design of DCaPS, which accepts daily 637

values of environmental parameters and crop attributes allows convenient connection with 638

crop models for seasonal simulation. 639

640

Acknowledgements 641

The authors acknowledge helpful discussions with Dr. Erik van Oosterom in relation to the 642

model schematic, Prof. John Evans and Prof. Susanne von Caemmerer in relation to the C3 and 643

C4 photosynthesis models as well as providing useful references, Dr. Enli Wang in relation to 644

temperature response of leaf photosynthesis as well as providing useful references, and the 645

National eResearch Collaboration Tools and Resources (NECTAR) for providing a free web 646

server for hosting dcaps.net.au. 647

648

Conflict of interest statement 649

The authors declare that the research was conducted in the absence of any commercial or 650

financial relationships that could be construed as a potential conflict of interest. 651

652

Tables 653

Table 1. Description of symbols used in the Diurnal Canopy Photosynthesis Simulator 654

(DCaPS). 655

Symbol Description Units Note Value and

reference Equation

Daily Canopy Summary

Acan,inst Instantaneous canopy CO2 assimilation μmol CO2 m-2 ground s-1 A73

Acan,DAY Diurnal canopy CO2 assimilation μmol CO2 m-2 ground day-1 A73

B

Conversion ratio combines factors allowing for

biochemical conversion and maintenance

respiration

g biomass (g CO2)-1 A

0.41 (wheat and

sorghum)

(Sinclair and

Horie 1989)

A74

BIOtotal,DAY Daily total biomass increment g biomass m-2 ground day-1 A74

Pshoot Fraction of above-ground (shoot) biomass to

the total (shoot + root)

g shoot biomass (g total

biomass)-1 A A74

BIOshoot,DAY Daily above-ground canopy (shoot) biomass

increment g biomass m-2 ground day-1 E A74

kDAY Canopy solar radiation extinction coefficient on

daily basis A78

RADDAY Total daily intercepted solar radiation MJ m-2 ground day-1 A76

RUEDAY Radiation use efficiency on daily basis g biomass MJ-1 A75

Environmental Parameters

So Total daily extra-terrestrial solar radiation MJ m-2 ground day-1 A5

Sg Total daily incident solar radiation MJ m-2 ground day-1 A4

RATIO Atmospheric transmission ratio A,D A4

sc Solar constant J m-2 ground s-1 A 1360 A5

Lat Latitude in radians (negative in the southern

hemisphere) radians A A5

Rl Radius vector radians A6

Dl Solar declination radians A8

Wl° Sunset hour-angle ° A7

Ll Day length hr A10

DAY Day of year A,D

tfrac t as a fraction of Ll A12

tsunrise Time of sunrise hr A13

tsunset Time of sunset hr A14

αsun Angle of solar elevation radians or degree A9

Ta Air temperature ºC A15

Ta,max Maximum Ta of DAY ºC A,D A15

Ta,min Minimum Ta of DAY ºC A,D A15

m Amount of time since time of minimum

temperature hr A15

n Amount of time since tsunset hr A15

xlag Lag coefficient for the maximum temperature

from tsunrise A

1.8 (Parton and

Logan 1981) A15

ylag Lag coefficient for the night-time temperature

from tsunrise A

2.2 (Parton and

Logan 1981) A15

zlag Lag coefficient for the minimum temperature

from tsunrise A

1

(parameterised

with hourly

temperature

data at Gatton,

Australia)

A15

VPDa Air vapour pressure deficit kPa A16

Ca Air CO2 partial pressure μbar A 400

Oa Air O2 partial pressure μbar A 210000

Io Total incident solar radiation MJ m-2 ground s-1 A3

Idir Incident direct radiation MJ m-2 ground s-1 A2

Idif Incident diffuse radiation MJ m-2 ground s-1 A1

Io_PAR Total incident photosynthetic active radiation μmol PAR m-2 ground s-1 Idir,PAR + Idif,PAR

Idir_PAR Direct incident photosynthetic active radiation μmol PAR m-2 ground s-1 A21

Idif_PAR Diffuse incident photosynthetic active radiation μmol PAR m-2 ground s-1 A22

Iabs,can Absorbed PAR by the canopy μmol PAR m-2 ground s-1 A23

Iabs,sun Absorbed PAR by the sunlit fraction of the

canopy μmol PAR m-2 ground s-1 A31

Iabs,sh Absorbed PAR by the shaded fraction of the

canopy μmol PAR m-2 ground s-1 A32

Canopy Attribute and Architecture Parameters

LAIcan Canopy leaf area index m2 leaf m-2 ground A,D A20

LAIsun LAI of the sunlit leaf fraction m2 leaf m-2 ground A19

LAIsh LAI of the shade leaf fraction m2 leaf m-2 ground A20

L Cumulative LAI from the top of canopy m2 leaf m-2 ground

kb' Direct and scattered direct PAR extinction

coefficient A24

kd' Diffuse and scattered diffuse PAR extinction

coefficient A24

kb Direct radiation extinction coefficient D A25

kd Diffuse PAR extinction coefficient A

0.78 (de Pury

and Farquhar

1997)

σ Leaf-level scattering coefficient for PAR A

0.15 (de Pury

and Farquhar

1997)

ρcb Canopy-level reflection coefficient for direct

PAR A29

ρcd Canopy-level reflection coefficient for diffuse

PAR A

0.036 (de Pury

and Farquhar

1997)

G Leaf shadow projection coefficient A27

β Canopy-average leaf inclination relative to the

horizontal radians A

60° (spherical

leaf angle

distribution) (de

Pury and

Farquhar 1997)

A27

Tl Leaf temperature °C A Ta 1, 2

Canopy Nitrogen Status Parameters

SLNav Specific leaf nitrogen averaged over the whole

canopy g N m-2 leaf A,D

1.45 (wheat)

(de Pury and

Farquhar 1997),

1.36 (sorghum)

(van Oosterom

et al. 2010)

A33

SLNratio_top Ratio of SLNo to SLNav g N m-2 leaf A,D

1.32 (wheat)

(de Pury and

Farquhar 1997),

1.30 (sorghum)

(van Oosterom

et al. 2010)

A33

SLNo SLN at the top of canopy g N m-2 leaf A33

N(L) SLN at L mmol N m-2 leaf A34

No SLN at the top of canopy mmol N m-2 leaf A33

Nb Base SLN at or below which leaf

photosynthesis = 0 mmol N m-2 leaf A

25 (wheat) (de

Pury and

Farquhar 1997),

14 (sorghum)

(Sinclair and

Horie 1989)

A34

kn Coefficient of nitrogen allocation through

canopy A36

Photosynthesis Parameters

χV Slope of linear relationship between Vmax per

leaf are at 25°C and N μmol CO2 mmol-1 N s-1 B

1.16 (de Pury

and Farquhar

1997) (wheat),

0.35 (sorghum)

(Massad et al.

2007)

A37

χJ Slope of linear relationship between Jmax per

leaf are at 25°C and N μmol CO2 mmol-1 N s-1 B

2.4 (wheat) (de

Pury and

Farquhar 1997),

2.4 (sorghum)

(Massad et al.

2007)

A38

χR Slope of linear relationship between Rd per leaf

are at 25°C and N μmol CO2 mmol-1 N s-1 B

0.01χV (wheat)

(de Pury and

Farquhar 1997),

0 (sorghum)

(Massad et al.

2007)

A39

χP Slope of linear relationship between Vpmax per

leaf are at 25°C and N μmol CO2 mmol-1 N s-1 B,C4

1.1 (sorghum)

(Massad et al.

2007)

A40

Vcmax Maximum rate of Rubisco carboxylation μmol CO2 m-2 ground s-1 Table 2

Jmax Maximum rate of electron transport μmol CO2 m-2 ground s-1 Table 2

Rd Leaf day respiration μmol CO2 m-2 ground s-1 Table 2

Rm Mesophyll mitochondrial respiration μmol CO2 m-2 ground s-1 C4

0.5Rd (von

Caemmerer

2000)

Kc Michaelis-Menten constant of Rubisco for CO2 μbar Table 2

Ko Michaelis-Menten constant of Rubisco for O2 μbar Table 2

Ac RuBP-saturated (or Rubisco-limited) net CO2

assimilation rate μmol m-2 ground s-1

Aj RuBP-regeneration-limited (or electron-

transport-limited) net CO2 assimilation rate μmol m-2 ground s-1

Γ* CO2 compensation point in the absence of Rd μbar A52

γ* Half the reciprocal of Sc/o 0.5/Sc/o

Sc/o Relative CO2/O2 specificity of Rubisco bar bar-1 A53

Vcmax/Vomax

Ratio of maximum rate of Rubisco

carboxylation to maximum rate of Rubisco

oxygenation

Table 2 A53

J Potential electron transport rate μmol e- m-2 ground s-1 A46

θ Empirical curvature factor A 0.7 (de Pury and

Farquhar 1997) A46

f Spectral correction factor A

0.15 (de Pury

and Farquhar

1997)

A46

I2 PAR absorbed by Photosystem II μmol PAR m-2 ground s-1 A45

α Fraction of PSII activity in the bundle sheath C4 0.1 (Yin and

Struik 2009) A56

Vp Rate of PEP carboxylation μmol CO2 m-2 ground s-1 C4 A58

Vpmax Maximum PEP carboxylase activity μmol CO2 m-2 ground s-1 C4 Table 2

Kp Michaelis-Menten constant of PEP carboxylase

for CO2 μbar C4 Table 2

Vpr,l PEP regeneration rate per leaf area μmol CO2 m-2 leaf s-1 A,C4

80 (von

Caemmerer

2000)

Vpr PEP regeneration rate μmol CO2 m-2 ground s-1 C4 A58

Jt Potential electron transport rate (symbol for C4) μmol e- m-2 ground s-1 C4 A46

x Fraction of electron transport partitioned to

mesophyll chloroplasts A,C4

0.4 (von

Caemmerer

2000)

A59

CO2 Diffusion Parameters

Ci Intercellular airspace CO2 partial pressure μbar

Cm Mesophyll CO2 partial pressure μbar C4 A57, A60

Cc Chloroplastic CO2 partial pressure at the site of

Rubisco carboxylation μbar A51, A54

Cs Bundle-sheath CO2 partial pressure μbar C4 A55, A59

Ol O2 partial pressure inside C3 and C4 leaves μbar Oa

Oc Chloroplastic O2 partial pressure at the site of

Rubisco carboxylation μbar Ol

Om Mesophyll O2 partial pressure μbar C4 Ol A56

Os Bundle-sheath O2 partial pressure μbar C4 A56

a Slope of linear relationship between Ci/Ca and

VPDa kPa-1

-0.12 (C3), -0.19

(C4) (Zhang and

Nobel 1996)

3

b Intercept of linear relationship between Ci/Ca

and VPDa

0.9 (C3), 0.84

(C4) (Zhang and

Nobel 1996)

3

Ci/Ca Ratio of Ci to Ca A 3

gm Mesophyll conductance for CO2 mol CO2 m-2 ground s-1 bar-1 B Table 2 A47

gbs Bundle-sheath conductance for CO2 mol CO2 m-2 ground s-1 bar-1 C4

0.003 (von

Caemmerer

2000)

A56

A: DCaPS input parameters that could be assigned a priori; B: DCaPS input parameters that 656

require calibration for different crop species; D: connector with crop models; C4: parameters 657

specific to the C4 photosynthesis model; E: DCaPS output to crop models; blank in the note 658

column means symbol is a calculated variable. 659

660

661

Table 2. C3 and C4 temperature response parameters used in equations 1 and 2. 662

C3 C4

Parameter Units P25 c (dimensionless) b (K) P25 c (dimensionless) b (K)

Kc μbar 272.41 32.71 9741.41 12104 25.94 7721.94

Ko μbar 1658001 9.61 2853.01 2920004 4.24 1262.94

Vcmax/Vomax - 4.61 13.21 3945.71 5.44 9.14 2719.54

Vcmax μmol m-2 s-1 A 26.42 7857.82 A 31.54 9381.84

Rd μmol m-2 s-1 A 18.72 5579.72 - - -

Kp μbar - - - 139 14.64 4366.14

Vpmax μmol m-2 s-1 - - - A 38.24 11402.44

P25 Topt (ºC) Ω (K) P25 Topt (ºC) Ω (K)

Jmax μmol m-2 s-1 A 28.83 15.53 A 32.65 15.35

gm μmol m-2 s-1 bar-1 0.55 34.31 20.81 0.55 34.31 20.81

A: variable. -: not applicable (see text). References: 1 (Bernacchi et al. 2002), 2 (Bernacchi et 663

al. 2001), 3 (Farquhar et al. 1980), 4 (Boyd et al. 2015), 5 (Massad et al. 2007). 664

665

666

Figures and figure legends 667

Figure 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

above-ground 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 (Cc) and photosynthesis.

Symbols: RATIO, atmospheric transmission ratio for incident solar radiation; VPDa, air

vapour pressure deficit; PAR, photosynthetic active radiation; SLNav, canopy-average

specific leaf nitrogen; SLNratio_top, ratio of SLN at the top of canopy to SLNav; Tl, leaf

temperature; gm, mesophyll conductance for CO2; gbs, bundle-sheath conductance for CO2;

Ol, 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 and 2.

668

669

Figure 2. Diurnal net C3 (upper panels) and C4 (lower panels) canopy photosynthesis with

various combinations of canopy attributes: leaf area index (LAIcan) of 2, 4 or 8 and canopy-

average leaf inclination relative to the horizontal (β) of 40° (A and C) or 80° (B and D). In

all four panels, the lower, middle and top curves show results for LAIcan of 2, 4 and 8,

respectively. Default values of other model parameters are given in Tables 1 and 2.

670

671

Figure 3. Relative net C3 (dashed curves) and C4 (solid curves) daily canopy photosynthesis

(Acan,DAY) and Radiation Use Efficiency on a daily basis (RUEDAY) in response to air CO2

and temperature. Acan,DAY or RUEDAY curves were normalised to their respective values at an

air CO2 partial pressure (Ca) = 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 Ca. The triangle indicates a 28% increase

in Acan,DAY at an average Ca of 540 μbar on hot days, relative to that at Ca = 360 μbar; the

circle indicates a 19% increase in relative Acan,DAY increase on average days at the same

average Ca. These relative increases were taken from (Ainsworth and Long 2005). Default

values of other model parameters are given in Tables 1 and 2.

672

673

Figure 4. Radiation Use Efficiency on a daily basis of C3 (dashed curve) and C4 (solid

curve) canopy in response to temperature. RUEDAY is plotted against average daily air

temperature, which is calculated by averaging the daily maximum (Ta,max) and minimum

(Ta,min) air temperatures; Ta,max = Ta,min + 15 with Ta,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 (χVc), maximum rate of

electron transport (χJ), maximum PEP carboxylase activity (χVP) 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 χVc, χJ and χVP 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 and 2.

674

675

Figure 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. RUEDAY is plotted against canopy-average

specific leaf nitrogen (SLNav). 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 panel B as well. Dotted curves in panel B show

simulated RUEDAY for a standard C4 crop (e.g. maize) with χV, χJ and χP 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 and 2.

676

677

Figure 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 (Sc/o). A and D: reference net

Ainst at default Sc/o; B and E: % changes in net Ainst for the sunlit leaf fraction of the canopy;

C and F: % changes in net Ainst for the shade leaf fraction. The bottom two rows (C3 and

C4, respectively) show changes in diurnal canopy photosynthesis with various Rubisco

activity (Vcmax) and/or electron transport capacity (Jmax). G and K: reference net Ainst with

default values; H and L: Vcmax increased by 20%; I and M; Jmax increased by 20%; J and

N: Vcmax and Jmax both increased by 20%. Solid and dotted curves show values for the

sunlit (Asun) and shade (Ash) leaf fractions of the canopy, respectively; grey and black

colour coding are for Rubisco-limited (Ac) and electron-transport limited (Aj)

photosynthetic rate, respectively. The Ac,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).

Filled areas indicate CO2 assimilation rate or its % change in the sunlit leaf fraction and

patterned areas indicate the same for the shade leaf fraction. For each leaf fraction,

photosynthetic rate is given by the minimum of Ac and Aj. Note that diurnal canopy

photosynthesis (Acan,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.

678

679

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