Equations following Buckley and Diaz-Espejo (2015):
Rubisco-limited assimilation rate:
$$W_\mathrm{carbox} = V_\mathrm{c,max} C_\mathrm{chl} / (C_\mathrm{chl} + K_\mathrm{m})$$
where:
$$K_\mathrm{m} = K_\mathrm{C} (1 + O / K_\mathrm{O})$$
RuBP regeneration-limited assimilation rate:
$$W_\mathrm{regen} = J C_\mathrm{chl} / (4 C_\mathrm{chl} + 8 \Gamma*)$$
where \(J\) is a function of PPFD, obtained by solving the equation:
$$0 = \theta_J J ^ 2 - J (J_\mathrm{max} + \phi_J PPFD) + J_\mathrm{max} \phi_J PPFD$$
TPU-limited assimilation rate:
$$W_\mathrm{tpu} = 3 V_\mathrm{tpu} C_\mathrm{chl} / (C_\mathrm{chl} - \Gamma*)$$
Symbol | R | Description | Units | Default |
\(C_\mathrm{chl}\) | C_chl | chloroplastic CO2 concentration | Pa | input |
\(\Gamma*\) | gamma_star | chloroplastic CO2 compensation point (T_leaf) | Pa | calculated |
\(J_\mathrm{max}\) | J_max | potential electron transport (T_leaf) | \(\mu\)mol CO2 / (m\(^2\) s) | calculated |
\(K_\mathrm{C}\) | K_C | Michaelis constant for carboxylation (T_leaf) | \(\mu\)mol / mol | calculated |
\(K_\mathrm{O}\) | K_O | Michaelis constant for oxygenation (T_leaf) | \(\mu\)mol / mol | calculated |
\(O\) | O | atmospheric O2 concentration | kPa | 21.27565 |
\(\phi_J\) | phi_J | initial slope of the response of J to PPFD | none | 0.331 |
PPFD | PPFD | photosynthetic photon flux density | umol quanta / (m^2 s) | 1500 |
\(R_\mathrm{d}\) | R_d | nonphotorespiratory CO2 release (T_leaf) | \(\mu\)mol CO2 / (m\(^2\) s) | calculated |
\(\theta_J\) | theta_J | curvature factor for light-response curve | none | 0.825 |
\(V_\mathrm{c,max}\) | V_cmax | maximum rate of carboxylation (T_leaf) | \(\mu\)mol CO2 / (m\(^2\) s) | calculated |
\(V_\mathrm{tpu}\) | V_tpu | rate of triose phosphate utilization (T_leaf) | \(\mu\)mol CO2 / (m\(^2\) s) | calculated |