# Mathematical Modeling to Estimate Photosynthesis: A State of the Art
Over the past century, with the increasing carbon release from landcover change and fossil fuel burning, the CO\({}_{2}\) accumulation rate on land, in the ocean and in the atmosphere has continuously increased. The increment of CO\({}_{2}\) in Earth's atmosphere is the major cause of global climate change. A major contribution to this high variability comes from GPP, as the photosynthesis process is vulnerable to droughts, heatwaves, floods, frost, and other types of disturbances. An accurate estimation of GPP will not only provide information about the ecosystem response to these extreme events but also help to predict the future carbon cycle dynamics [16]. For the agronomic sector the research about photosynthesis is useful in many aspects, such as: determining the state of crops or of certain plants; indicating crop production; helping in crop-health control; helping with the optimization of natural resources; detecting genetic alterations in plants to know how plants react to stressful situations; and serving as a predictive indicator of biomass accumulation in green plants [17; 18; 19; 20; 21; 22]. Many of the methods for inferring photosynthesis are invasive; they physically or chemically interfere with the plant, altering its natural process during measurement. Non-invasive methods do not alter the plant's natural process since there is no contact with the specimen [23; 24]. [PERSON] et al. [25] presented a review of the advantages and disadvantages of the methods used for photosynthesis estimation. Table 1 shows the classification of these methods. CO\({}_{2}\) exchange is the most used method for constructing commercial and experimental equipment [26; 27]. It is possible to measure photosynthesis at the level of individual leaves, whole plants, plant canopies, and even forests [28; 29]. \begin{table}
\begin{tabular}{p{113.8 pt} p{227.6 pt}} \hline \hline
**Methods Used for Photosynthesis Estimation** & **Description** \\ \hline \multirow{3}{*}{Destructive} & Involes cutting a whole plant or only a portion of it to estimate the photosynthetic activity based on the accumulation of dry matter in the plant, from the point of germination until it is cut [25]. \\ \cline{2-3}  & \multicolumn{1}{p{227.6 pt}}{Consists of direct measurement of oxygen (O\({}_{2}\)) pressure or carbon dioxide (CO\({}_{2}\)) in an isolated chamber with photosynthetic organisms [30].} \\ \hline \multirow{3}{*}{Electrochemical} & Uses electrochemical electrodes to measure O\({}_{2}\), CO\({}_{2}\), or pH in aqueous solutions of the sample to detect variations that depend on photosynthetic activity [30]. \\ \cline{2-3}  & \multicolumn{1}{p{227.6 pt}}{} \\ \end{tabular}
\end{table} 
Table 1: Classification of the methods used for photosynthesis estimation and their general description. As can be noticed from previous Table 1 Photosynthesis is a complex process that involves several and distinct variables; hence, it cannot be directly measured, if not through a mathematical model. Then, photosynthesis can be inferred by integrating and measuring these variables of interest. Hence, it is possible to generate a mathematical model if the contributions of the variables of interest of a physical, chemical, or biological process, among others, are known [36; 37]. It should be noted that all invasive or non-invasive methods that are used to infer photosynthesis apply some type of mathematical model. Therefore, the invasiveness or non-invasiveness when developing any method to estimate photosynthesis depends on the technique used to measure the variables of interest; for this reason, the present document focuses on studying and comparing the most relevant mathematical models reported in the literature. Authors like [PERSON] [38], [PERSON] [39], [PERSON] [25], [PERSON] [40], [PERSON] [41], [PERSON] [42], and [PERSON] [43], demonstrate the use of some photosynthesis measurement methods.