Table 1.
List of parameters in the berry growth module and carbon allocation module
| Parameters | Definitions | Values | Unit | Sourcesa | |
|---|---|---|---|---|---|
| Cabernet Sauvignon | Sangiovese | ||||
| Berry growth module | |||||
| Berry surface area | |||||
| γ | Empirical coefficient | 4.152 | 4.463 | cm2 g−1 | Experiment |
| η | Empirical coefficient | 0.707 | 0.604 | Dimensionless | Experiment |
| Berry surface transpiration | |||||
| ρmin | Minimum berry surface conductance to water vapour | 55.4 | 25.8 | cm h−1 | Experiment |
| ρ0 | Scaling factor | 503 | 682 | Dimensionless | Experiment |
| k ρ | Exponential decay rate | –4.97 | –1.67 | cm g−1 h−1 | Experiment |
| H f | Relative humidity of air space in fruit | 0.996 | Dimensionless | Fishman and Genard (1998) | |
| Phloem hydraulic conductance | |||||
| L p,min | Minimal phloem hydraulic conductance | 3.5e-2 | g cm−2 MPa−1 h−1 | Exploration | |
| L p,max | Maximal phloem hydraulic conductance | 0.15 | 0.7 | g cm−2 MPa−1 h−1 | Calibration |
| FM*Lp | Fresh mass at the inflection point | 0.95 | 1.33 | g | Calibration |
| k Lp | Proportional to the slope at inflection point of Lp | 9 | 7.4 | g−1 | Calibration |
| Composite membrane area | |||||
| αx | Coefficient for converting fruit surface area to membrane area | 3.5e-3 | Dimensionless | Calibration | |
| Berry volume growth | |||||
| ϕ | Cell wall extensibility coefficient in Lockhart’s equation | 0.1 | MPa−1 h−1 | Fishman and Génard (1998) | |
| Y | Turgor pressure threshold for growth | 0.05 | MPa | Matthews et al. (2009); Castellarin et al. (2016) | |
| Sugar uptake—mass flow | |||||
| σp | Reflection coefficient for sugar for entering the composite membrane | 0.9 | Dimensionless | Fishman and Génard (1998) | |
| Sugar uptake—active uptake | |||||
| V max,berry | Maximal rate of active sugar uptake per unit of dry mass | 8e-3 | 2.8e-3 | gSucrose (gDW)−1 h−1 | Calibration |
| K M,berry | Michaelis constant for active transport | 0.08 | gSucrose gH2O−1 |
Milner et al. (1995); Fishman and Génard (1998) |
|
| C*f | Sugar concentration at the inflection point | 0.13 | 0.15 | gHexose gH2O−1 | Calibration |
| K Cf | Proportional to slope at the inflection point of Ua | 35 | gH2O ghexose−1 | Calibration | |
| Sugar partition | |||||
| k ss | Fraction of increase in dry matter allocated into soluble sugar at each time step | 0.9 | 1.0 | Dimensionless | Experiment |
| q m berry | Maintenance respiration coefficient for berry | 5.9e-5 | gC gC−1 h−1 | Dai et al. (2010) | |
| Q g berry | Growth respiration coefficient for berry | 0.02 | gC gC−1 | Dai et al. (2010) | |
| Constants | |||||
| V w | Molal volume of water | 18 | cm3 mol−1 | ||
| D w | Water density | 1 | g cm−3 | ||
| R | Gas constant | 8.3 | cm3 MPa mol−1 K−1 | ||
| Carbon allocation module | |||||
| Carbon loading by leaf | |||||
| V max,leaf | Maximal rate of carbon loading per square meter of leaf per hour | 1.0 | gC m−2 h−1 | Baldazzi et al. (2013) | |
| K M,leaf | Michaelis constant for carbon loading by leaf | 0.05 | gNSC gFM−1 | Exploration; Zufferey (2000); Quereix et al. (2001) |
|
| Carbon loading by internode, cordon, and trunk | |||||
| V max,stem | Maximal rate of carbon loading per gram of stem per hour | 1.0e-4 | gC gFM−1 h−1 | Exploration; Grechi et al. (2007) | |
| K M,stem | Michaelis constant for carbon loading by stem | 0.05 | gNSC gFM−1 | Baldazzi et al. (2013) | |
| Carbon unloading by internode, cordon, and trunk | |||||
| k leakage | Rate of carbon unloading per gram of stem per hour | 3.5e-3 | gC gFM−1 h−1 | Exploration; Baldazzi et al. (2013); Rossouw et al. (2017) |
|
| Carbon unloading by root | |||||
| V max,root | Maximal rate of carbon unloading per gram of roots per hour | 5e-4 | gC gFM−1 h−1 | Exploration; Barillot et al. (2016); Rossouw et al., (2017) | |
| K M,root | Michaelis constant for carbon unloading by roots | 0.084 | gNSC gH2O−1 | Barillot et al. (2016) | |
| Maintenance coefficient | |||||
| Maintenance respiration coefficient | 4e-5 | gC gC−1 h−1 | Cieslak et al. (2011) | ||
| Maintenance respiration coefficient | 2e-5 | gC gC−1 h−1 | Vivin et al. (2002) | ||
| Maintenance respiration coefficient | 2e-4 | gC gC−1 h−1 | Cieslak et al. (2011) | ||
| Root turnover coefficient | 2e-5 | gC gC−1 h−1 | Buwalda (1993) | ||
| Q10 | Temperature ratio of maintenance respiration | 2.03 | Dimensionless | Thornley and Cannell (2000) | |
| Growth coefficient | |||||
| Growth respiration coefficient | 0.2 | gC gC−1 | Vivin et al. (2003) | ||
| Carbon loading and unloading cost | |||||
| q p | Cost for either carbon loading to phloem or unloading from phloem | 0.03 | gC gC−1 | Thornley and Cannell (2000) | |
a Parameters were estimated in four complementary methods: (i) directly estimated from experimental data described above (experiment); (ii) directly taken from the literature; (iii) taken from the literature first but then adapted for grapevine based on the trends published in the literature or in our data collection (exploration); and (iv) taken from the literature first but then calibrated for our data through numerical optimization (calibration). The data sets of Dai et al. (2009) and Bobeica et al. (2015) were used for calibration.