The maximum carboxylation rate at 25degC (Vcmax25) and the maximum electron
transport rate at 25degC (Jmax25), which characterize photosynthetic capacity,
are calculated as at leaf level.
The required variables Gs and Ci can be calculated from
surface.conductance and intercellular.CO2, respectively.
Gas exchange parameters are taken from Bernacchi et al. 2001 (apparent values, which
assume an infinite mesophyll conductance). Negative and very low Ci values
(the threshold is set to Ci < 80umol mol-1 at the moment) are filtered out.
Vcmax is calculated from the photosynthesis model by Farquhar et al. 1980.
If net photosynthesis is Rubisco-limited (RuBP-saturated carboxylation
rate, i.e. light has to be (near-)saturating):
$$Vcmax = (GPP * (Ci + Kc*(1.0 + Oi/Ko))) / (Ci - Gam)$$
where Kc and Ko are the Michaelis-Menten constants for CO2 and O2 (mmol mol-1),
respectively, Oi is the O2 concentration, and Gam is the photorespiratory CO2
compensation point (umol mol-1).
Under low-light conditions, the electron transport rate J is calculated from
the RuBP regeneration-limited photosynthesis rate:
$$J = (GPP * (4.0 * Ci + 8.0 * Gam) / (Ci - Gam)$$
In this function, bulk canopy photosynthesis is assumed to be Rubisco/RuBP-regeneration
limited, if incoming PPFD is above/below a specified threshold or range. These ranges
are determined by the parameters PPFD_j and PPFD_c. If, for example,
PPFD_j = c(100,400), all conditions with a PPFD between 100 and 400 are assumed
to be in the RuBP-regeneration (i.e. light-limited) photosynthesis domain. The electron
transport rate J is then only calculated for periods that meet this criterion.
Jmax is calculated from J and absorbed irradiance:
$$J = (APPFD_PSII + Jmax - sqrt((APPFD_PSII + Jmax)^2 -
4.0 * Theta * APPFD_PSII * Jmax)) / (2.0 * Theta)
$$
where APPFD_PSII is the absorbed PPFD by photosystem II (PS II),
and Theta is a curvature parameter. APPFD_PSII is calculated as
$$PPFD * alpha_canopy * 0.85 * beta$$
where alpha_canopy is canopy-scale absorptance, 0.85 is a correction factor,
and beta is the fraction of photons absorbed by PS II (assumed 0.5).
alpha_canopy accounts for non-absorbing components of the ecosystem such as
stems or soil, and is very likely ecosystem-specific. This parameter is relatively
sensitive for the determination of Jmax25 at some sites.
Vcmax and Jmax at canopy level are assumed to follow the same temperature response
as at leaf level. Hence, the respective parameter k at 25degC (k25) is calculated as
(see e.g. Kattge & Knorr 2007):
$$k25 = k /
( exp(Ha * (Temp - Tref) / (Tref * Rgas * Temp)) *
(1 + exp((Tref * dS - Hd) / (Tref * Rgas))) /
(1 + exp((Temp * dS - Hd) / (Temp * Rgas)))
)
$$
where Ha is the activation energy (kJ mol-1), Hd is the deactivation energy (kJ mol-1),
and dS is the entropy term (kJ mol-1 K-1) of the respective parameter. Tref is set
to 298.15 K.
For C4 photosynthesis, the simplified model by von Caemmerer 2000 is used.
For light-saturated photosynthesis, Vcmax is given by:
$$Vcmax = GPP$$
Note that in addition to the range PPFD_c, the range Ci_C4
discards all periods with low Ci, in which photosynthesis is likely to
be CO2-limited (see von Caemmerer 2000 for details).
In the light-limited case, J is calculated as:
$$J = 3 * GPPj / (1 - 0.5) $$
The calculation of Jmax25 and Vcmax25 is identical to C3 photosynthesis
as described above.