# Mathematical Modeling to Estimate Photosynthesis: A State of the Art
## Abbreviations
\begin{tabular}{l l} \(K_{1}\) [\(RuBP\)] & Carbon fixed by photosynthesis Equation (7) \\ \(K_{2}\) [\(RuBP\)]\({}^{2}\) & Carbon used by photorespiration Equation (7) \\ \(K_{S}\) [\(TP\)] & Carbon used by dark respiration Equation (7) \\ \(K_{a}\) & PPFD extinction on chlorophyll Equation (11) \\ \(K_{c}\) & Michaelis constant for carboxylation Equations (1), (9), (10), (18) and (22) \\ \(K_{m}C\) & Rubisco constant for CO\({}_{2}\) Equation (19) \\ \(K_{m}O\) & Rubisco constant for O\({}_{2}\) Equation (19) \\ \(K_{o}\) & [PERSON] constant for oxygenation Equations (1), (9), (10), (18) and (22) \\ \(KO_{3}\) & Leaf resistance ratio for O\({}_{3}\) Equation (23) \\ \(k_{p}\), \(k_{s}\) & Constan Equations (14) and (24) \\ \(L\) & Foliar area index Equation (20) \\ \(LAI\) & Foliar area index Equation (6) \\ \(LFmax\) & Maximum leaf photosynthesis rate Equation (6) \\ \(LMA\) & Leaf's mass per area Equations (26) and (38) \\ \(m\) & Leaf light transmission coefficient Equations (6), (20) and (27) \\ \(m_{sat}\) & Rate of light saturated carboxylation Equation (11) \\ \(Np\) & Leaf nitrogen content Equation (11) \\ \(n_{sat}\) & Leaf nitrogen content Equation (11) \\ \(O\) & Oxygen from the atmosphere Equations (9) and (18), \\ \(O\) & Oxygen in the leaf Equations (1), (10), (12), (13), (17), (19), (22) and (24) \\ \(O(O)\) & O\({}_{2}\) partial pressures Equation (10) \\ \(O_{3}\) & Oxygen in the leaf Equation (23) \\ \(O_{bs}\) & O\({}_{2}\) concentration in the bundle-sheath cell Equations (9) and (19) \\ \(P\) & Photosynthetic rate Equations (8), (13), (14), (15), (17), (24) and (37) \\ \(p^{*}\) & Photosynthesis rate without photoinhibition Equation (4) \\ \(P(T)\) & Photosynthesis reduction factor Equation (20) \\ \(PAR\) & Radiation Equations (26), (34) and (38) \\ \(PAR_{t}\) & PAR incident on top of crown Equation (26) \\ \(PAR_{pp}\) & PAR intensity reaching the epidermis of the leaf Equation (28) \\ \(PCARB\) & Potential biomass accumulation per plant Equation (34) \\ \(P_{g}\) & Total gross photosynthesis Equations (6), (20) and (27) \\ \(P_{gmax}\) & Maximum gross photosynthesis Equation (25) \\ \(PGRED(T)\) & Function to modify \(P_{g}\), below suboptimal temperatures Equation (6) \\ \(pH\) & Degree of acidity or alkalinity of the plant Equations (35), (36) and (39) \\ \(P_{ij}\) & Photosynthesis Equation (28) \\ \(P\,l_{g}\) & Photosynthetic rate Equation (21) \\ \(PLTOP\) & Plant density per unit area Equation (34) \\ \(Pm\) & Maximum photosynthesis rate Equation (14) \\ \(P_{m}\) (\(O\)) & Oxygen release rate Equation (24) \\ \(Pm\) (\(T\), \(a\)) & Maximum net photosynthesis rate per unit of leaf area over all PPFD levels, \\ \(P_{m}\) (\(T\), \(C\), \(N\)) & Temperature and ages Equation (5) \\ \(P_{m}\) (\(T\), \(C\), \(N\)) & Photosynthetic value with saturation of \(l_{j}\) Equation (21) \\ \(P_{mmax}\) & Maximum photosynthetic rate Equations (2) and (3); Specific velocity \\ \(P_{mmax}\) & coefficient for photosynthesis calculated by a saturated speed-dependent \\ \(hyperbolic\) function of light and is a function of temperature Equations (17) and (28) \\ \(P_{mm}\) & Maximum endogenous photosynthesis capacity Equation (25) \\ \(P_{n}\) & Net photosynthetic rate Equations (2), (7), (16), (30) and (31) \\ \(P_{nCO2}\) & Net photosynthesis rate limited by CO\({}_{2}\) Equation (25) \\ \(P_{nl}\) & Photosynthesis rate Equation (25) \\ \(P_{nImax}\) & Maximum net photosynthesis Equation (25) \\ \(P_{mmx}\) & Maximum net photosynthesis Equation (31) \\ \(PO2\) & Net photosynthesis rate Equations (36) and (39) \\ \(PO2\) (\(DO2\)) & Net photosynthesis rate in function of dissolved oxygen concentration \\ \(PO2\) (\(I\)) & Equations (36) and (39) \\ \(PO2\) (\(pH\)) & Net photosynthesis rate in function of irradiance Equations (36) and (39) \\ \(PO2\)(\(T\)) & Net photosynthesis rate in function of temperature Equations (36) and (39) \\ \(PO2\)\({}_{2}^{B}\) & Rate of gross photosynthesis Equation (32) \\ \end{tabular}