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Earth System Subject Earth Surface System Synthesis

The Farquhar biochemical growth model (Farquhar et al., 1980) calculates photosynthesis as a function of demand and supply of CO_{2}. The advantage with this model is that photosynthesis is regulated not only by radiation and transpiration, but also by air humidity, leaf temperature, CO_{2} availability and leaf nitrogen content, and the plant also experience radiation saturation at high levels of radiation. To function properly, driving variables need to be given as input to the simulation at least once an hour. In this module photosynthesis, *P*, is calculated as mole carbon per leaf area per second. Thus, *P* has to be converted to g carbon per unit soil area per day, *C*_{Atm}_{→}* _{a}*, at the end of the module:

where *M _{C}* is the molar mass of carbon.

Parameters and variables used in the photosynthesis model are converted in a similar manner.

There are several viewing functions that illustrate the Farquhar photosynthesis model, e.g. Farquhar model – Carbon dioxide pressure as a function of time, Farquhar model – Photosynthesis as a function of carbon dioxide pressure in the sub-stomatal cavity, Farquhar model – Photosynthesis as a function of LAIand Farquhar model – Photosynthesis as a function of radiation.

Three types of photosynthesis are calculated: Rubisco limited photosynthesis, *P _{V}*, and RuBP limited photosynthesis,

*P _{V}*, is the Rubisco (leaf enzyme) or carboxylation limited rate of assimilation, which is a function of light, leaf nitrogen, leaf temperature and soil moisture. Photosynthesis as a function of internal CO

(5.15)

where *V _{m}* is a function of the maximum activity of Rubisco,

The CO_{2} compensation point in the absence of mitochondrial respiration, *Γ ^{*}*, is calculated as:

(5.16)

where the Q_{10} value is calculated from the leaf temperature, *T _{l}*:

(5.17)

The Michaelis-Menten constant of Rubisco for CO_{2}, *K _{c}*, is calculated as:

(5.18)

and the Michaelis-Menten constant of Rubisco for O_{2}, *K _{o}*, is calculated as:

(5.19)

*V _{m}*, is a function of the potential maximum capacity of Rubisco,

(5.20)

*P _{J}* is the RuBP regeneration limited (i.e. light-limited) rate of photosynthesis calculated as:

(5.21)

where *J _{m}* is calculated as:

(5.22)

where *ε* is the quantum efficiency, *η* is the conversion factor for biomass to carbon, *R _{s,pl}* is the absorbed short-wave radiation by the plant and

Finally, the metabolism of end product limited (TPU limited) rate of photosynthesis, *P _{S}*

(5.23)

where *p _{atm}* is the atmospheric pressure at the surface.

The maximum Rubisco capacity for the bulk canopy per leaf area, *V _{max}*, can be calculated using equations similar to Beer’s law:

(5.24)

where *V _{cmax}* is the maximum Rubisco capacity per leaf area at the top the canopy respectively,

To avoid abrupt transition from one limiting rate to another, we apply two quadratic equations on the assimilation rates that are solved for their smaller roots (Collatz et al., 1991):

(5.25)

where *β _{vj}* and

Analogously to Fick’s law of gas diffusion, the supply of CO_{2} for photosynthesis can be calculated as:

(5.26)

where *c _{a}* is the external carbon dioxide concentration,

1) Carbon concentration in the atmosphere, *c _{a}*: model input.

2) Carbon concentration in the canopy air space, *c _{b}*:

(5.27)

where *c _{b,t-1}* is the carbon concentration in the canopy air space from the previous time step,

(5.28)

where *d* is the displacement height, *a _{mol}* is the amount of gas in one cubic meter of air,

3) Carbon concentration in at the leaf surface, *c _{s}*:

(5.29)

4) Carbon concentration in the sub-stomatal cavity, *c _{i}*:

(5.30)

The functions to derive the equilibrium concentration of carbon dioxide in the sub-stomatal cavity, *c _{i}*, from the demand and the supply functions, follows the iterative procedure in the SiB2 model (Sellers et al., 1996).

The conductance from the canopy air space to the free flowing air for carbon dioxide, *g _{ac}*, is calculated from the aerodynamic resistance to water flow,

The boundary layer conductance for carbon dioxide, *g _{rc}*, is calculated from the boundary layer resistance for water flow,

where the boundary layer resistance, *r _{b}*, is given as an input to model simulations. 1.4 is the ratio of the diffusivities of CO

The stomatal conductance for carbon dioxide, *g _{sc}*, is calculated from the resistance to water flow through stomata,

where the response function for soil water stress *f(E _{ta}/E_{tp})* is multiplied with the stomatal resistance to account for stomatal closure due to plant water stress. 1.6 is the ratio of the diffusivities of CO

The resistances to water flow are measured in s m^{-1}, and thus corresponding conductance is in m s^{-1}. To convert the conductance from m s^{-1} to moles m^{-2} s^{-1}, which is the unit used in the photosynthesis equations, the following conversion is performed:

Reduction of photosynthesis due to grain development is simulated in the same way as in the light use efficiency approach, by replacing ε_{L} with *ε* in Eq.(5.13).

mimi (2019). Farquhar, Model Item, OpenGMS,
https://geomodeling.njnu.edu.cn/modelItem/72372c7c-3164-4bfa-b8dc-1cd862b5d6ef

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