Photosynthesis Model

Appendix

Photosynthesis model

Outline of the model was as follows.An(I,TL, Narea), net photosynthetic rate at certain I(μmol m-2 s-1), leaf temperature (TL, °C), and Narea is expressed as:

(Eqn.A1)

where Ag(I,TL, Narea) and Rd(I,TL, Narea) are the gross photosynthetic rate and the leaf day respiration rate at TL, I, and Narea, respectively.

Light photosynthesis curve was expressed as:

(Eqn.A2)

where Ag(I,25, Narea) was gross photosynthetic rate at 25°C, Amax is the light-saturated rate of gross photosynthesis, φ is the initial slope of the curve, and θ is the convexity of the curve. Amax and Rd(I,25, Narea) were expressed as a function of Narea, and φ and θ were constant number. Temperature dependency of photosynthetic rate and respiration rate were modelled followingSugiura andTateno (2011). Temperature dependency of Ag(I,TL, Narea) was simply expressed as a function of TL and as an quadric approximation formula where Ag(I,25, Narea) was relativized to 1 as a standard value:

(Eqn.A3)

where the constants were constant values obtained from the photosynthesis measurements.

The temperature dependency of dark respiration rate,Rn(I,TL, Narea)is described as (Hikosaka et al. 2006):

(Eqn.A4)

where Rn(I,TL, Narea) and Rn(I,25, Narea) are values of Rn at TL and 25ºC, respectively. R is the gas constant (0.0083 J K-1mol-1) and ΔHa is the activation energy of Rn (66.405 kJ mol-1) (Farquhar et al. 1980).We also considered the Kok effect and estimated Rdusing therelationship with Rn (Atkin et al. 2000; Oguchi et al. 2008):

(when I > 0 µmol m-2 s-1)(Eqn. A5)

(when I = 0 µmol m-2 s-1)(Eqn. A6)

We used a TL estimating formula which we developed in previous study (Sugiura and Tateno 2011).TLwas measured by a thermocouple (Type T6 ft Beaded Thermocouple Sensor, Onset Computer, Pocasset, MA, USA) and the estimating formula was determined by multiple regression analysis:

(r2 = 0.96)(Eqn. A7)

where Ta is air temperature (ºC), and P3min (mol m-2) is the integratedvalue of I for the last 3 minutes.

TLin the night was set to Ta because these values were nearly the same in the night.

Then, seasonal change in Narea was approximated as a quadric function of DOY for each branch. Leaf photosynthesis was assumed to start at DOY of the first leaf sampling and to cease at DOY of the last leaf sampling in each year. By considering the Amax-Narealinear relationship and the Amax-Rdlinear relationship, seasonal change in light-photosynthesis curve for each leaf can be reproduced. Then, area-based amount of assimilated CO2 (or respired CO2) every minute was calculatedby substituting I, Ta, and TL into the equations (eqn.A1 to A7). Amount of net assimilated glucose (NAGLeaf, g C6H12O6) at the leaves foreach growth period was then calculated by converting CO2(µmol) to glucose (g C6H12O6), integrating them in each growth period, and multiplyingLAfor each branch.

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