# Mathematical Modeling to Estimate Photosynthesis: A State of the Art
## 3 Discussion
It also presents the percentage of the number of times a certain variable is used to build the mathematical model, reinforcing the idea that it is not possible to standardize the units of photosynthesis estimation. According to Figure 5, light (photosynthetically active radiation (PAR) \(\mu\)mol m\({}^{-2}\) s\({}^{-1}\); average amount of incident energy per unit area per unit time on a surface (Irradiance) \(W/\)m\({}^{2}\)) is the most used variable for estimating photosynthesis in mathematical models since it is required in 25% of the models, followed by ambient temperature with 14%. In general, the advantage of involving biochemical variables in the models is that photosynthesis is more reliable, since they are directly related to the photosynthetic process. However, since the information on the biochemical variables is obtained by a completely invasive process, and the type of equation to be implemented requires digital elements of a better quality, the implementation price is quite high. On the other hand, involving physical variables is less invasive since it depends on the method used for the measurement, as is the case of the leaf's area index and leaf's temperature variables. Finally, agroecological variables are those found in the atmosphere; these variables are completely non-invasive. Figure 4: Input variables used in the reviewed mathematical models, classified by biochemical, physical, and agroecological type. Another relevant finding is that there are other important variables for estimating photosynthesis that have not been used in previous models since they interfere in this metabolic process thus opening a niche of opportunity for future models, variables such as, minerals, processed sap (glucose), relative humidity of the air and relative humidity of the leaf. Table 4 shows the statistics of the number of input variables used in the mathematical models. It is emphasized that 31% of the models require only 2 input variables, and 5% used 7 input variables for the estimation of photosynthesis. Thus, it is shown that it is not necessary to measure all the possible input variables to obtain a photosynthesis output value. In addition, Table 4 also shows that statistics on the number of input variables used by each mathematical model are observed according to their classification. Based on this Table, it was concluded that black box models tend to use only 2 input variables; although the estimation process is unknown, the expected result is not affected since there are even white box models that also use only two input variables to estimate the photosynthesis. These statistics confirm once again that regardless of the number of input variables and the type of modeling, it does not influence the expected photosynthesis estimation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Mathematical Models**} \\ \hline
**Number of Input** & **White Box** & **Black Box** & **Gray Box Models** & **Percentage Equivalent to the Number** \\
**Variables** & **Models** & **Models** & **Models** & **of Input Variables Used by Models** \\ \hline
7 & 8\% & - & - & 5\% \\
5 & 15\% & 20\% & - & 13\% \\
4 & 23\% & 20\% & 50\% & 28\% \\
3 & 31\% & - & 13\% & 23\% \\
2 & 23\% & 60\% & 38\% & 31\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Reported input variables in mathematical models for estimating photosynthesis. The table shows the representation of the percentage equivalent to the number of input variables used by the reviewed mathematical models for white, black, or gray box models. Figure 5: Input variables used by the mathematical models to estimate photosynthesis; invasiveness based on their measurement; as well as the equivalent percentage to the number of times that the models use these variables. [PERSON] [125] established that photosynthesis is perhaps the most studied physiological process in plant science since it supports plant productivity.