# Mathematical Modeling to Estimate Photosynthesis: A State of the Art
## 3 Discussion
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Equation** & **Author** & **Mechanistic Mathematical Models** \\ \hline (23) & [PERSON] [102] & \(A_{n}=(C_{a}-C_{s})(g_{b}/1.4)=(C_{s}-C_{i})(g_{b}/1.6)\) \\  & [PERSON] [102] & \(A_{n}=(C_{a}-C_{s})(g_{b}/1.4)(F_{AOS})=(C_{s}-C_{i})(g_{b}/1.6)(F_{AOS})\) \\  & \(F_{AOS}=1.0421-0.2399*ClO,ClO=\sum\left(\frac{C_{0}}{S_{s}}\right)[O_{3}]\) \\ (24) & [PERSON] [103] & \(P(t)=\frac{k_{x}+m^{*}\cdot a^{*}(t)}{k_{x}+m^{*}\cdot a^{*}(t)}=\frac{p_{x}+m ^{*}\cdot a^{*}(t)}{k_{x}+m^{*}\cdot a^{*}(t)}\) \\  & \(P_{nl}=P_{gmax}\left(1-exp\left(\frac{-\alpha_{0}\cdot Up}{P_{gmax}}\right) \right)-R_{d}\) \\ (25) & [PERSON] [104] & \(P_{nlmax}=\frac{p_{\mathrm{cO}_{3}}+P_{gmax}-(\sqrt{p_{\mathrm{cO}_{3}}+P_{ gmax}})^{2}-\left(4\cdot p_{\mathrm{cO}_{3}},P_{gmin}\right)}{A_{n}=a_{0}\cdot ln \left(\frac{LMA}{VDRDINCE}+a_{1}\right)}\) \\ (26) & [PERSON] [105] & \(\left(1-exp\left(\frac{-(b_{V}DPD+b_{1})\cdot PAR}{(4b_{1}(\sqrt{p_{\mathrm{cO }}})+4b_{4})}\right)\right)-R_{d}\) \\  & \(PAR_{i}=PAR_{i}exp\left(-k_{i}\cdot\frac{LMA_{i}}{sin(p)}\right)\) \\  & \(K=f(d_{0}\psi+d_{1}CLA+d_{2})\cdot RDINCE^{(\phi_{0}+CLA+\varepsilon_{1})}\) \\  & **Empirical mathematical models** \\ (27) & [PERSON] \& [PERSON] [106] & \(P_{g}=\frac{b_{0}}{a(1-a)\cdot k}[1-e^{-K(1-a)F(2)}]-\) \\  & \(\frac{b_{0}(1-m)}{a_{0}^{2}b(1-a)\cdot k}*ln\left(\frac{-1-m)+a_{0}kK-(1-a) \cdot v(t)}{(1-m)+a_{0}kK-(1-a)\cdot v(t)}\) \\ (28) & [PERSON] [107] & \(P_{ij}=P_{max}(t)[PAR_{ij}/\left(I_{R}+PAR_{g}\right)]\) \\  & Primienta de la Torre & \(B=a+bD+c(D^{2}+H),B=a+bD+cD^{2}+d(HD^{2}),\) \\ (29) & [108] & \(B=a+bD^{2}+c(HD^{2}),B=a+bD+cH,B=a+D^{2}+Hc\) \\  & \(P_{n}=\alpha_{0}+a_{1}I+a_{2}\ T+a_{3}C+a_{4}\ VPD\) \\  & & (Linear model (G-model)) \\  & \(P_{n}=\beta_{0}+\beta_{1}I+\beta_{2}\) & \(T+\beta_{3}C+\beta_{4}\ VPD+\beta_{5}I\cdot T+\beta_{6}I\cdot C+\beta_{7}I \cdot VDP+\beta_{8}T\cdot C\) \\  & & \(+\beta_{9}T\cdot VDP+\beta_{10}\cdot VPD\) \\  & (Linear interaction model (I-model)) \\ (30) & Romdhonah [109] & \(P_{n}=\gamma_{0}+\gamma_{1}I+\gamma_{2}\ T+\gamma_{3}C+\gamma_{4}\ VPD+\gamma_{5}\ I^{2}+\gamma_{6}\ T^{2}+\gamma_{7}\ C^{2}+\gamma_{8}\ VPDI^{2}\) \\  & & (Linear squared model (S-model)) \\  & & \(P_{n}=\delta_{0}+\delta_{1}I+\delta_{2}\) & \(T+\delta_{5}C+\delta_{4}\ VPD+\delta_{5}I\cdot T+\delta_{6}I\cdot C+\delta_{7}I \cdot VDP+\delta_{8}T\cdot C\) \\  & & \(+\delta_{9}T\cdot VDP+\delta_{10}\cdot C\cdot VDP+\delta_{11}\ T^{2}+\delta_{12}\ T^{2}+\delta_{13}\ C^{2}\) \\  & & \(+\delta_{14}\ VPDI^{2}\) \\  & & (Linear interaction-squared model (IS-model)) \\ (31) & [PERSON] [110] & \(P_{n}=P_{mmar}\cdot f\ (PPPD)\cdot f\ (T_{a})\cdot f\ (VPD)\cdot f\ (SWC)\cdot f\ (T_{s})\cdot f\ (age)-R_{d}\) \\  & **Gray box mathematical models** \\ (32) & [PERSON] [111] & \(P_{i,d}^{2}=F_{x,i,d}\big{(}1-exp\big{(}-\epsilon_{d\cdot}R_{a,d}/F_{x,i,d} \big{)}\big{)}\) \\ (33) & [PERSON] [112] & \(F_{i,d}=F_{x,f}f_{1}(T_{i,d}),\epsilon_{i,d}=\epsilon_{x}f_{2}(T_{i,d})\) \\  & & Functions \(f_{1}\) and \(f_{2}\) differ by crop, and by crop history \\ (34) & [PERSON] [113] & \(P_{i,d}=F_{x,i,d}\) \\ (35) & [PERSON] [114] & \(RO2=R_{Q2}(lav)\cdot RO_{Q2}(T)\cdot RO_{Q2}(pth)\cdot RO_{Q2}\left(DO_{2} \right)\) \\ (36) & [PERSON] [115] & \(PO2=PO2(I)\cdot\overline{PO2}\ (T)\cdot PO2(pth)\cdot PO2\left(DO2\right)\) \\ (37) & [PERSON] [116] & \(p=\theta\cdot\sigma\cdot\Phi_{p}\cdot I\) \\ (38) & [PERSON] [117] & \(A_{n}=(a_{0}\cdot ln\ \ \ \left(\frac{LMA}{VDRDINCE}\ \right)+a_{1})\cdot\left[1-exp\left[-\frac{(a_{0}\cdot VPD+a_{0}) \cdot PAR}{(4b_{1}\left(\frac{LMA}{VDRDINCE}+a_{1}\right)}\right]\right]\) \\ (39) & [PERSON] [118] & \(PO2=PO2(I)\cdot\overline{PO2}\ (T)\cdot\overline{PO2(pth)\cdot PO2\left(DO2\right)}-RO2(I)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._the number of plants (samples); the validation method used for the modeling; and the coefficient of determination (R2).