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A semimechanistic model predicting the growth and production of the bioenergy crop Miscanthus×giganteus: description, parameterization and validation

Authors

  • FERNANDO E. MIGUEZ,

    1. Department of Crop Sciences, University of Illinois at Urbana-Champaign, 1102 S, Goodwin Ave., Urbana, IL 61801, USA,
    2. Energy Biosciences Institute, Institute for Genomic Biology, 1206 West Gregory Drive, MC-195, Urbana, IL 61801, USA,
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  • XINGUANG ZHU,

    1. Department of Plant Biology, University of Illinois at Urbana-Champaign, 1201 W, Gregory Drive, 379 Madigan Lab., Urbana, IL 61801, USA,
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    • 1Current address: Plant Systems Biology Group, CAS-MPG Partner Institute of Computational Biology, 342 Yue Yang Road, Shanghai 200031, China

  • STEPHEN HUMPHRIES,

    1. ADAS, Woodthorne Wergs Road, Wolverhampton WV6 8TQ, UK
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  • GERMÁN A. BOLLERO,

    1. Department of Crop Sciences, University of Illinois at Urbana-Champaign, 1102 S, Goodwin Ave., Urbana, IL 61801, USA,
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  • STEPHEN P. LONG

    1. Department of Crop Sciences, University of Illinois at Urbana-Champaign, 1102 S, Goodwin Ave., Urbana, IL 61801, USA,
    2. Energy Biosciences Institute, Institute for Genomic Biology, 1206 West Gregory Drive, MC-195, Urbana, IL 61801, USA,
    3. Department of Plant Biology, University of Illinois at Urbana-Champaign, 1201 W, Gregory Drive, 379 Madigan Lab., Urbana, IL 61801, USA,
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Fernando E. Miguez, Department of Crop Sciences University of Illinois at Urbana-Champaign. 1102 S. Goodwin Ave., Urbana, IL 61801, USA, e-mail: miguez@illinois.edu

Abstract

Biomass based bioenergy is promoted as a major sustainable energy source which can simultaneously decrease net greenhouse gas emissions. Miscanthus×giganteus (M.×giganteus), a C4 perennial grass with high nitrogen, water, and light use efficiencies, is regarded as a promising energy crop for biomass production. Mathematical models which can accurately predict M.×giganteus biomass production potential under different conditions are critical to evaluate the feasibility of its production in different environments. Although previous models based on light-conversion efficiency have been shown to provide good predictions of yield, they cannot easily be used in assessing the value of physiological trait improvement or ecosystem processes. Here, we described in detail the physical and physiological processes of a previously published generic mechanistic eco-physiological model, WIMOVAC, adapted and parameterized for M.×giganteus. Parameterized for one location in England, the model was able to realistically predict daily field diurnal photosynthesis and seasonal biomass at a range of other sites from European studies. The model provides a framework that will allow incorporation of further mechanistic information as it is developed for this new crop.

Introduction

The recent interest on the potential of biofuels (Koonin, 2006; Ragauskas et al., 2006; U.S.DOE, 2006) to supply energy security, reduce carbon dioxide emissions and support agriculture, demands that the most productive, efficient and environmentally responsible cropping systems are used (Heaton et al., 2008). At present ethanol constitutes 99% of the biofuels in the United States and it is mainly derived from maize (Zea mays L.) (Farrell et al., 2006). Although the use of maize-derived ethanol is expected to increase, cellulosic ethanol will be needed in order to meet the longer-term renewable energy mandate (U.S.DOE, 2006). In addition, when harvesting biomass crops nearly all aboveground plant components can be used for cellulosic ethanol production which can enable much larger quantities of biofuel production compared with grain-derived ethanol (Lewandowski et al., 2000). Miscanthus×giganteus, Greef et Deux. Hodkinson et Renvoize, (Hodkinson & Renvoize, 2001), hereinafter referred to as M.×giganteus, is a C4 perennial grass with high yield potential (Heaton et al., 2004, 2008), efficient conversion of radiation to biomass (Beale & Long, 1997), efficient use of nitrogen (N) and water (Beale & Long, 1995), which has been extensively researched in Europe (Lewandowski et al., 2000). However, at the moment M.×giganteus is not commercially produced at large scale in the United States, being limited mostly to experimental plots. Thus, there is a need for the development and parameterization of process-based crop models that can provide reliable predictions of carbon assimilation, growth and yield. Further, it is currently an unimproved crop with significant opportunities for yield improvement via selection, breeding and genetic engineering. A semimechanistic model would provide a framework in which to evaluate potential traits for improvement, ahead of a lengthy breeding program.

Previous semimechanistic models based on light conversion efficiency and temperature thresholds for leaf growth have been shown effective for simulating M.×giganteus yields (Clifton-Brown et al., 2000, 2004; Price et al., 2004). These models strongly depend on a parameter which describes the efficiency of the crop in converting radiation to biomass (radiation use efficiency, RUE). Although in these models RUE has been treated as a constant, Clifton-Brown et al. (2000, 2004) reported that the value of ec for M.×giganteus ranged from 2.4 to 4.2 g MJ−1 PAR. These authors recognized that the model depends strongly on RUE and that a more mechanistic model would be more appropriate (Clifton-Brown et al., 2001). These models are appealing due to their simplicity but by their design they cannot provide insights into the physiological basis of RUE variation, or growth and the physiology of water use (Demetriades-Shah et al., 1992; Reddy, 1995; Loomis & Amthor, 1999).

WIMOVAC is a generic plant production model, based on the key physiological and micrometeorological processes underlying plant production (Humphries & Long, 1995). Here, we describe the model as adapted to the specific crop, M.×giganteus. The model was parameterized from laboratory physiological measurements and shown to effectively predict diurnal photosynthesis in the field. Biomass partitioning was parameterized from measurements made at one site in England. Finally, we demonstrate the ability of the model to predict biomass accumulation and yield for the same genotype at sites distinct from that used for parameterization.

Description of the model

Macroclimate

The macroclimate data (i.e. light, temperature, relative humidity, rainfall, and wind speed) were obtained from records made at each trial location. Day, time, and latitude were used to determine the solar declination and solar zenith angle. Given the solar constant and atmospheric transmittance, the direct and diffuse solar radiation above canopy were predicted (Norman, 1980) Eqns (A1)–(A5). The air temperature was simulated as a function of daily mean temperature Eqn (A6), range Eqn (A7) and excursion Eqns (A8) and (A9). The parameter hr in Eqn (A8) was determined experimentally and allowed a time offset between the maximum incident solar radiation and the maximum temperature of simulated days that reflects the localized heat capacity of the surroundings. The model assumed that all rainfall was incident upon the soil surface and wind speed was determined experimentally (2 m above the canopy).

Leaf level photosynthesis

Leaf CO2 uptake rate (A) was predicted from the steady-state model of Collatz et al. (1992) Eqns (A10)–(A14). To mimic decrease in stomatal conductance (gs) with water stress, a linear relationship was assumed between reduction in gsEqns (A15)–(A18) and the decrease of leaf water potential.

Canopy level photosynthesis

The proportion of a canopy that was sunlit and shaded at any point in time was determined based on Norman (1980) and Forseth & Norman (1991). The leaf area of sunlit and shaded leaves and the mean irradiance of these two populations were calculated dynamically Eqns (A20)–(A26). Sunlit leaves were assumed to receive direct (Idir) and diffuse (Idiff) solar radiation Eqn (A23) while shaded leaves received diffuse and scattered (Iscat) light from other leaves in the canopy Eqn (A24). Total canopy photosynthesis was the sum of the photosynthesis at both the sunlit and shaded leaves, calculated by the equation for leaf CO2 uptake rate Eqn (A27). The canopy was divided into 10 layers and the proportion of sun and shade leaves, and their radiative conditions computed for each, following the above principles Eqns (A20)–(A34). This multilayer approach is essential in modeling the canopy of M.×giganteus since it can exceed 3 m in canopy height (Cosentino et al., 2007). In most natural canopies, leaves assume a range of orientations in which they may be predominantly horizontal (planophile), vertical (erectophile) or an intermediate mixture. A single parameter, χ (the ratio of the horizontal projection of the ellipsoid to the vertical) was used to describe the shape of the distribution and calculate the canopy extinction coefficient [k, Eqn (A19)].

The instantaneous transpiration for each leaf class within the canopy was calculated following the approach of Penman–Monteith (Monteith, 1973) and using the stomatal conductance for each layer and sunlit/shaded leaf class following Collatz et al. (1992) Eqns (A36) and (A37). Transpiration values of both sunlit and shaded leaves at all layers were then summed to give total canopy water loss. The transpiration and leaf temperature were calculated iteratively considering the interaction between energy balance, photosynthesis and conductance at the leaf surface Eqn (A23) and (A24). Total canopy assimilation, transpiration and conductance were obtained by integrating over individual leaf classes Eqns (A27)–(A37).

Growth, partitioning and allocation

Carbon allocation was determined by dry biomass partitioning coefficients which depend on phenological stages. These phenological stages were controlled by thermal periods defined by the sum of average daily temperatures from the start of the growing season. In this way the fraction of available carbon was allocated to each of the plant structural pools, i.e. leaf, stem, structural root, fine root, and rhizome at the current stage Eqn (A52)–(A60). Thus, by varying these coefficients (−1 to 1), the dynamic source/sink demands of the plant during development were modelled. The total carbon available for growth during a given developmental stage was the total of net photosynthetic assimilation and leaf/storage root remobilization Eqn (A53). The new leaf area, stem or root length was simulated based on allocated carbon resources for each tissue and the specific leaf area, specific stem length, and specific root length, respectively, Eqns (A61)–(A64). New leaf growth was assumed to occur uniformly with respect to height in the canopy. Additionally, new stem growth was associated with an increase in canopy height and new root growth with an increase in root density at a specific soil depth.

Respiration

Respiration (Rtotal), following Penning de Vries (1972), was calculated by assuming that growth respiration was a constant fraction of gross photosynthesis. However, the respiratory cost of maintaining plant structures varied depending on the tissue type and temperature [Eqn (A65); Spain & Keen, 1992].

Soil-plant water relations, surface evaporation, soil heat flux and temperature

An analytical plant water uptake model derived by Campbell (1991) was used to predict water potentials in soil and plant system. This model considered the soil profile as a series of discrete layer slices, each with a characteristic root density, soil water potential and associated resistance. Water would move up or down the profile according to soil conductance to water flow and water potential differences between adjacent slices. Water was assumed to move from the soil, through the plant, to the evaporating surface in the substomatal cavities in response to gradients in water potential. The soil water potential, leaf water potential, transpiration, and stomatal conductance are interdependent and therefore were calculated simultaneously using an iterative process Eqns (A66)–(A76).

The evapo-transpiration model of Penman (1948) and Monteith (1973) were used to predict soil evaporation Eqns (A66)–(A76). This formulation included a soil boundary layer conductance term to give actual rather than potential evaporation and shows the expected reduction in evaporation rate associated with increasing canopy leaf area. The conductive heat transfer and water flux in soil followed simple diffusion, as in Chung & Horton (1987). Boundary conditions, latent and sensible heat fluxes were calculated using an energy balance approach through an iterative procedure Eqns (A77)–(A80).

Parameterization of WIMOVAC for M.×giganteus

The C4 photosynthesis parameters (Table 1) were obtained from Collatz et al. (1992) and validated using data from Naidu et al. (2003) and Beale et al. (1996). Several studies have shown that M.×giganteus is able to attain high photosynthetic potential at low temperatures (Beale & Long, 1995; Beale et al., 1996; Naidu et al., 2003). The default values in Collatz et al. (1992) provided a satisfactory fit (R2=0.99) when this model was used to predict the temperature response studied in Naidu et al. (2003) as shown in Fig. 1.

Table 1.   Parameters in Collatz et al. (1992) photosynthesis model
Parameter descriptionValue
Initial slope of photosynthetic CO2 response (kp, mol m−2 s−1)0.7
Maximum Rubisco capacity (Vmax, μmol m−2 s−1)39
Initial slope of photosynthetic light response (α, mol mol−1)0.04
Leaf respiration rate (Rd, μmol m−2 s−1)0.8
Curvature parameter (θ). Gives gradual transition between light limited and carboxylation limited flux0.83
Curvature parameter (β). Analogous to θ. Describes the co-limitation between flux determined by Rubisco and light and CO2 limited flux0.93
Figure 1.

 Observed and simulated assimilation of M.×giganteus. The open circles are observed data from Naidu et al. (2003) and the solid line is simulated using the Collatz et al. (1992) model in WIMOVAC (R2=0.99).

The length of the growing season was assumed to span from the last frost in the spring until the first frost in the fall (Price et al., 2004). Phenological stages followed typical phases in grasses (Cao & Moss, 1997), including emergence, juvenile stage, floral apex initiation, panicle emergence, anthesis, and end of cycle. Contrary to grain crops, the modeling of the reproductive organ development in M.×giganteus is of negligible importance. Flowering was predicted to start around 3500 °Cd (degree days; with a base temperature of 0 °C) and the end of the season was around 4000 °Cd (Table 3). At the moment a mechanistic model of leaf senescence is not available, mainly because the relationship between environmental factors which trigger the onset of leaf senescence at different locations has not been elucidated. In addition, there are limited data available on the decay of harvestable biomass after peak yield, which are needed to parameterize a leaf senescence and biomass decay model (Hastings et al., 2009). The leaf was assumed to start senescing at 2000 °Cd in the United Kingdom and 4000 °Cd in southern Italy based on two experiments (Beale & Long, 1997; Cosentino et al., 2007), with intermediate values for other locations using a simple linear interpolation based on latitude (i.e. senescence thermal time=latitude ×−86.7+6507). It was further assumed that 60% of the mass of a leaf is reabsorbed during its senescence. Leaf area index (LAI, m2 leaf m−2 soil) was simulated by assuming a constant specific leaf area (Spleaf) Eqn (A63) of 65 g m−2 and the canopy was simulated using 10 layers.

Table 3.    M.×giganteus phenological stages and dry biomass partitioning coefficients. These coefficients are obtained from the calculations in Table 2 and assumptions regarding dry biomass partitioning to roots which were not measured on the Beale & Long (1997) study. Thermal period is the interval for each phenological stage in thermal time units; the first number is the start of the period and the second is the end
StageThermal Period
(°Cd)
LeafStemRhizomeRoot
Emergence0–5250.330.37−0.10.3
Juvenile525–12260.140.85−0.080.01
Induction1226–19270.010.630.350.01
Post-induction1927–35000.010.630.350.01
Flowering3500–36000.010.630.350.01
Post-flowering3600–40000.010.630.350.01

Initial values for coefficients for dry biomass partitioning were determined empirically from the measurements of Beale & Long (1997) with a mature (third year) M.×giganteus plots in SE England (Table 2). However, this experiment did not provide the complete information needed to estimate the dry biomass partitioning coefficients (Table 2). Additional data from Beale & Long (1995) suggested that initially carbohydrates are partitioned in equal proportions to root, leaf and stem components. With this additional information, the dry biomass partitioning coefficients were obtained (Table 3). This parameterization showed an acceptable agreement between model simulations and observed dry biomass (Fig. 2) in Beale & Long (1997). This model was then tested, without further parameter adjustment, against data for the same genotype at eight study sites elsewhere in Europe (van der Werf et al., 1992; Schwarz et al., 1994; Danalatos et al., 1996, 1998, 2007; Jorgensen, 1996; Foti et al., 1996; Clifton-Brown et al., 2000). The weather conditions at each location, daily solar radiation, temperature and relative humidity, were obtained either from the individual studies, where reported, or from the World Meteorological Organization (World Meteorological Organization, 2007).

Table 2.   Prior information regarding M.×giganteus dry biomass partitioning at different days during the growing season (DOY, day of the year) from Beale & Long (1997)
DOYDry biomass
(Mg ha−1)
Difference (Mg ha−1)Proportion
RhizomeStemLeafRhizomeStemLeafRhizomeStemLeaf
1157.200   
1576.443.6−0.843.6 0.530.47
1955.614.75.4−0.810.71.8 0.860.14
2309.021.14.23.46.4−1.20.350.65 
26410.424.23.21.43.1−1.00.310.69 
3079.424.21.5−1.00−1.7   
35010.323.100.9−1.1−1.5   
Figure 2.

 Observed and simulated M.×giganteus dry biomass partitioning for data from Beale & Long (1997) through the growing season (DOY, day of the year).

Results and discussion

The predicted photosynthetic CO2 uptakes of M.×giganteus at different temperatures correlated well with controlled environment laboratory measurements (Naidu et al., 2003) (Fig. 1). Furthermore, the field diurnal CO2 uptake of Beale et al. (1996) was closely simulated for most measurement days during the growing season, except the first measurement day, June 1, where the model overpredicted CO2 uptake (Fig. 3). This can possibly be attributed to the low temperatures preceding this date, which normally occur in the early growing season in United Kingdom (Beale et al., 1996). Controlled environment studies have shown that growth at mean daytime temperatures below 12 °C decreases photosynthetic capacity (Beale et al., 1996; Farage et al., 2006). The effect of low temperatures on leaf photosynthesis through photoinhibition is a critical factor for both future development of models for biomass crops as well as a target for breeding efforts, since the ability to photosynthesize at lower temperatures could increase the length of the growing season and the period of maximum growth rate.

Figure 3.

 Observed (open circles) and simulated (closed circles) diurnal carbon dioxide assimilation of M.×giganteus. ‘Hour’ is the hour of the day when the measurements were taken. The observed data was taken from Beale et al. (1996).

Simulated yields also closely followed observed yields throughout the growing season for all M.×giganteus studies across a wide range of locations in western Europe (Fig. 4). Not only were final yields predicted well, at most locations, but also growth in terms of shoot biomass accumulation across the growing season. The close agreement between simulated and observed data was observed in studies ranging from Ireland to Greece, suggesting that the model was able to account for the variability in environmental conditions. The largest discrepancy was seen in a study conducted in Catania, Sicily (‘Italy 93 and Italy 94’, Fig. 4) (Foti et al., 1996), where M.×giganteus showed peak yield much later in the growing season than predicted by the model and than observed at other sites (Foti et al., 1996; Cosentino et al., 2007). Some reasons for the disagreement can be discarded: (1) genotype differences; all plants were cloned from the same source; (2) temperatures; these were similar to those in Greece where this was not evident (Danalatos et al., 2007; Cosentino et al., 2007). Severe drought which occurred in Catania, but not in Greece, might be responsible for the delayed development. Indeed, irrigation in the second growing season accelerated M.×giganteus flowering in Catania (Cosentino et al., 2007). This indicates that the model may fail to capture the effects of water stress on the duration of phenological stages and it is an area where future model development will improve accuracy by allowing more flexibility in the response of C allocation in response to environmental factors. In addition, it is expected that this is a major source of genotypic variability since there are notable differences within the Miscanthus genus in their response to water stress (Clifton-Brown & Lewandowski, 2000) with M. sinensis being a more conservative user of water through a lower leaf area and stomatal conductance than M.×giganteus and thus better suited for drier environments.

Figure 4.

 Observed (open circles, blue) and predicted (closed circles, black) M.×giganteus above ground dry biomass in multiple year and location experiments in Europe as a function of thermal time. Each panel has first the name of the location where the experiment was conducted followed by the last two digits of the year. Austria91 (Schwarz et al., 1994), Denmark90 (Jorgensen, 1996), Greece01, 02 (Danalatos et al., 2007), Greece93, 94, 95 (Dalianis et al., 1994; Danalatos et al., 1996, 1998), Ireland94, 95 (Clifton-Brown et al., 2000), Italy93, 94 (Foti et al., 1996), Netherlands91 (van der Werf et al., 1992).

Compilation of all the predicted with their parallel observed biomass samplings for all sites (Fig. 5) suggested that, with current parameterization, shoot (Fig. 5), stem mass (Fig. 6) and leaf area index (Fig. 7) were slightly overpredicted. The tendency toward overprediction can potentially be contributed to several factors: (1) the impact of nutrient deficiencies and weed competition on biomass accumulation were not incorporated in the current model; (2) at some northern locations high light intensities and low temperatures can cause photo-damage and reduce growth (Long et al., 1983); (3) limitations in the model structure and parameterization of the model. As more experiments are conducted on M.×giganteus and more growth data are available, better parameterization will be possible. In addition, there is also a need for better algorithms for parameter estimation in crop models which will allow to get point estimates as well as a measure of the uncertainty in the parameters of interest (Wallach et al., 2001; Miguez, 2008).

Figure 5.

 Observed vs. simulated M.×giganteus above ground dry biomass in multiple year and location experiments in Europe (R2=0.84). The line is the 1 : 1 relationship. Points closer to the line reflect a higher agreement between observed and predicted.

Figure 6.

 Observed (circles) and simulated (lines) dry biomass of M.×giganteus in multiple year and location experiments in Europe. The solid lines are the stem and the dashed lines are the leaf dry biomass. See Fig. 4 for details.

Figure 7.

 Observed (open circles, blue) and simulated (closed circles, black) leaf area index (LAI) of M.×giganteus in multiple year and location experiments in Europe. See Fig. 4 for details.

Features and limitations of using a semimechanistic crop model

WIMOVAC is characterized by its emphasis on process-based description of physiological processes. This immediately results in a model with more detail and, in general, with greater data requirements for its parameterization for a given crop. This greater data requirement can be seen as a limitation, but it also highlights the need for additional research in basic aspects of M.×giganteus physiology (Jorgensen & Schwarz, 2000). In this study dry biomass partitioning was parameterized with studies conducted in the United Kingdom, but substantially uncertainty remains regarding the modification of the partitioning coefficients under different environments (locations and/or years). However, the model was able to simulate the dynamics of dry biomass accumulation during the growing season in different environments (Fig. 4) and these dynamics are needed for accurate modeling of nutrient, carbon and water cycles, which are critical for determining the potential for carbon sequestration and the nutrient and water requirements of a biofuel crop such as M.×giganteus. An important aspect in biomass crops simulations and M.×giganteus in particular is the trade-off between early and late harvest (Miguez et al., 2008) which depends greatly on its end use (Lewandowski & Heinz, 2003). Modelling yield losses due to leaf senescence, nutrient translocation to the rhizomes and stem and leaf drop remains a challenge since these physiological processes are not well understood, but nevertheless are of great importance in producing accurate estimates of harvestable biomass. In addition, a model which incorporates yield losses should possibly account for severe weather which can greatly reduce harvestable biomass (Lewandowski et al., 2003).

Comparison of WIMOVAC with other models used for M.×giganteus

Other models have been proposed for modeling M.×giganteus (Clifton-brown et al., 2004; Price et al., 2004; Hastings et al., 2009) and these models have been successful at capturing the potential for growing this crop in different regions. The main difference between WIMOVAC and these models is the emphasis on physiological details, which increases the number of parameters and the amount and quality of data needed to parameterize the model. As a result the quality and the detail of the simulations also increase. For example, in this manuscript we showed how the model was able to capture hourly leaf-level photosynthesis (Fig. 3) which becomes relevant when the objective of the simulation is to predict the effect of future climate scenarios (increase temperature, CO2 and vapour pressure deficit) on the performance of biomass crops. Currently, WIMOVAC does not model moisture content in the biomass or rhizome and shoot death due to cold temperatures or extended periods of water stress as it has been recently incorporated in MISCANFOR (Hastings et al., 2009). A combination of information derived from field studies and process-based description of physiological process incorporated in WIMOVAC is needed in order to improve simulations of growth and productivity of biomass crops such as M.×giganteus.

Conclusions

In summary, we adapted WIMOVAC for the biomass crop M.×giganteus and demonstrated that it can closely predict field diurnal CO2 uptake of M.×giganteus and biomass accumulation patterns through the growing season at different sites in Europe. The current model and parameterization tended to overpredict leaf area index and biomass accumulation. As a mechanistically rich model, this provides a vehicle for numerical experiments that may allow optimization of field experiments and long-term breeding and selection. For example, would yield benefit from a decreased or increased LAI or from a larger or smaller proportional investment in rhizome mass? At the same time it provides a framework for predicting yields outside the current range of experience in Europe and a means to assess the benefit of addition of physiological traits found in other M.×giganteus germplasm.

Acknowledgements

We would like to acknowledge Clive Beale and Sotiris Archontoulis for providing data from their publications.

Appendices

Appendix A The key equations in WIMOVAC-related to simulating M. × giganteus

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Appendix B

Table B1.   Definition of Abbreviations
TermUnitsDefinitionValue/reference
Agrossμmol mol−1Gross rate of CO2 uptake per unit leaf area
Anetμmol mol−1Net rate of CO2 uptake per unit leaf area
Acμmol mol−1Net canopy rate of CO2 uptake per unit ground area
Ac,totg m−2 yr−1Ac integrated over the course of a year
Ac,sunmol mol−1Net rate of CO2 uptake per unit area sunlit leaves
Ac,shademol m−2 s−1Net rate of CO2 uptake per unit area shaded leaves
Aμmol mol−1Predicted rate of CO2 uptake
caμmol mol−1Atmospheric CO2 concentration378 (Collatz et al., 1992)
ADimensionlessCoefficient for growth respiration0.2 (Penning de Vries, 1972)
ciμmol mol−1Intercellular concentration of CO2 in air corrected for solubility relative to 25 °C
bleafDimensionlessCoefficient for maintenance respiration for leaf0.03 (Penning de Vries, 1972)
bstemDimensionlessCoefficient for maintenance respiration for stem0.015 (Penning de Vries, 1972)
brootDimensionlessCoefficient for maintenance respiration for root0.01 (Penning de Vries, 1972)
cpJ kg−1 K−1Specific heat capacity of dry air1010
Djdday of year
dDimensionlessZero plane displacement0.77
EJ mol−1Activation energyRd=66405 Vcmax=6800
Elmmol m−2 s−1Evapo/transpiration rate at sunlit/shaded leaves in a canopy layer
Ecmmol m−2 s−1Instantaneous canopy evapo/transpiration rate
Etotmmol m−2 yr−1Ec integrated over the course of a year
eLkPaSaturated water VPD in the leaf
Fcanopym2 m−2Canopy leaf area index
Fshadem2 m−2Canopy shaded leaf area index
Fsunm2 m−2Canopy sunlit leaf area index
Fsumm2 m−2Summed leaf area index from top of canopy to layer considered in calculation
gammol m−2 s−1Leaf boundary layer conductance
gsmmol m−2 s−1Leaf stomatal conductance
gcmmol m−2 s−1Canopy conductance of CO2
G0DimensionlessStomatal slope factor3 (Collatz et al., 1992)
G1DimensionlessStomatal intercept factor0.08 (Collatz et al., 1992)
gs,sunmmol m−2 s−1The sum of stomatal conductance of sunlit leaves
gs,shademmol m−2 s−1The sum of stomatal conductance of shaded leaves
hrhHour of day
hs%Relative humidity
hcanopymHeight of canopy
hmsmWind speed measurement height2
hlayermHeight of canopy layer above ground
Iμmol m−2 s−1Photon flux
Iabsμmol m−2 s−1Photon flux absorbed by either sunlit or shaded leaves within a canopy layer
Idirμmol m−2 s−1Photon flux in direct solar beam
Idiffμmol m−2 s−1Photon flux in diffuse radiation
Itotalμmol m−2 s−1Total photon flux incident on canopy
Isμmol m−2 s−1Solar constant, photon flux in a plane perpendicular to the solar beam above the atmosphere2600
Ishortμmol m−2 s−1Short wave radiation component of incident light
Isoilμmol m−2 s−1Solar radiation incident upon soil surface
Isunμmol m−2 s−1Mean I for leaves which receive direct solar radiation, i.e. are sunlit
Ishadeμmol m−2 s−1Mean I for leaves shaded from direct solar radiation
Iscatμmol m−2 s−1Direct beam radiation scattered by surfaces within the canopy
Jaμmol m−2 s−1Total solar radiation absorbed by either sunlit or shaded leaves within a canopy layer
KDimensionlessFoliar absorption coefficient
kslopeDimensionlessInitial slope of photosynthetic light response0.04 (Collatz et al., 1992)
kleafDimensionlessPartitioning coefficient for leaf
kstemDimensionlessPartitioning coefficient for stem
ksrootDimensionlessPartitioning coefficient for storage root
kfrootDimensionlessPartitioning coefficient for fine root
kstrootDimensionlessPartitioning coefficient for structural root
ωleafGramLeaf biomass
ωstemGramStem biomass
ωsrootGramBiomass of storage root
ωfrootGramBiomass of fine root
ωstrootGramBiomass of structural root
Spleafg m−2Specific leaf area65
Spstemg m−1Specific stem elongation factor60
Spfrootg m−1Specific fine root elongation factor10
Spstrootg m−1Specific structural root elongation factor60
LwmLeaf width in the direction of the wind0.04
PskPaLeaf surface partial pressure of CO2
v Saturated water vapor concentration
Q10DimensionlessIs the proportional rise in a parameter for a 10oC increase in temperature2
RDimensionlessLeaf reflection coefficient for total solar radiation0.2
RJ k−1 mol−1Real gas constant8.314
Rdmol m−2 s−1Dark respiration at a given temperature
Rlcmol m−2 s−1Longwave radiation
SkPa K−1Slope of saturated water vapor pressure change with respect to temperature (look up table)
spDimensionlessSpectral imbalance
SsizemAverage size of soil particles0.04
SrDimensionlessSoil reflectance0.2
StDimensionlessSoil transmission0.01
τDimensionlessLeaf transmittance coefficient 
ThTime of day
tsnhTime of solar noon12
Tleaf °CLeaf temperature
Tair °CAmbient air temperature
Tsoil °CSoil surface temperature
T1 °CAnnual mean air temperature
T2 °CAnnual range in air temperature
T3 °CAverage daily range in air temperature
T4 °CMaximum daily range in air temperature
Um s−1Measured wind speed at known height (2m)2
ulayerm s−1Wind speed in a given canopy layer
usoilm s−1Wind speed at soil surface
Vcmaxμmol m−2 s−1Maximum rubP saturated rate of carboxylation39 (Collatz et al., 1992)
VPDkPaLeaf-air water vapor pressure deficit
zomRoughness length0.234
×DimensionlessThe ratio of horizontal:vertical projected area of leaves in the canopy segment1
αDimensionlessAtmospheric transmittance0.85
ktmol m−1Initial slope of photosynthetic CO2 response0.7 (Collatz et al., 1992)
θcurveDimensionlessCurvature parameter0.83 (Collatz et al., 1992)
δdeg.Solar declination
Ωdeg.Latitude
Θdeg.Solar zenith angle
λMJ/KgLatent heat of vapourisation (look up table)
γPa K−1psychrometer constant (look up table)
αslopemol mol−1The quantum yield of CO2 uptake determined by the initial slope of the response of A vs. Iabs0.04 (Collatz et al., 1992)
β C4 curvature parameter0.93 (Collatz et al., 1992)
Kt C4 slope factor
ψlMPaLeaf water potential
ψtMPaThreshold leaf water potential for decreasing gs
ΦNW m−2Net radiation
ψadlMPaAverage daily plant water potential
ψptMPaThreshold water potential
ZmThickness of a soil layer
ψxMPaXylem water potential
ψsiMPaSoil water potential of the ith layer
qwKg s−1Flux of water
Rsim3 kg−1 s−1Soil resistance of the ith zone
Rrim3 kg−1 s−1root resistance of the ith zone
Licm cm−3Root density of ith zone
gm s−2Gravitional constant9.8
RLm3 kg−1 s−1Leaf resistance
Edg m−2 s−1Potential soil evaporation
Epg m−2 s−1Actual soil evaporation
θ*kg m−3Actual volumetric water content
θ1kg m−3The volumetric water content for maximizing Evaporation 
θ2kg m−3The volumetric water content for wilting point
dsmSoil depth
ρwkg m−3Density of water1000
Rlc,soilmol m−2 s−1Soil longwave radiation
IsoilW m−2Solar radiation on soil
θikg m−3The volumetric water content of the ith day
ρvakPaVapor pressure deficit
HOsoilkg m−3Saturated humidity of the air at the soil surface
HSsoilkg m−3Humidity of the air at the soil surface
hsoilmWater pressure head
λW/(m  °C)Thermal conductivity for the soil surface
GsoilW m−2Soil heat flux

Ancillary