# Mathematical Modeling to Estimate Photosynthesis: A State of the Art
## 2 Techniques  
Over the years, various mathematical models have been developed and introduced for photosynthesis estimation. The review of these models is based on an exhaustive search and analysis of the reported literature, it focuses on their mathematical formulation, validation, input variables, as well as the type of cultivation at the leaf, plant, or canopy level. As a result, an updated list of the most relevant mathematical evaluation models was obtained, and possible areas of opportunity was detected. The research was conducted in the main databases (Science Direct, Web of Science, IEEE, Google Scholar, Scielo, ResearchGate), scientific organizations such as the American Society of Agricultural and Biological Engineers ASABE, and specialized journals such as Bioresource Technology Reports, Ecological Modeling, Metabolic Engineering, Biotechnology and Bioengineering, Environmental and Experimental Botany, Bioresource Technology, Journal of American Society Hortaliza Science, Aquatic Botany, European Journal of Agronomy, Agricultural Systems, Wageningen Journal of Life, Journal of Plankton Research, Limnology and Oceanography, Biological Theory, Agricultural and Forest Meteorology, Computers and electronics in agriculture, Journal of Theoretical Biology, Annals of Botany, Photosynthesis Research, Experimental Marine Biology and Ecology, Marine Biology, Progress in Oceanography, and Plant Cell and Environment, among others. The research approach adopted for this study was comparing mathematical models to estimate photosynthesis with a variety of input variables developed over time. This approach allows us to contribute to the knowledge of the different existing methodologies for estimating photosynthesis. The selection criteria were:  
1. The models had to estimate gross photosynthesis, net photosynthesis, photosynthetic rate, biomass, or carbon assimilation. [PERSON] & [PERSON] [50] reviewed the photosynthesis background and the associated terminology; they showed that different definitions and names are used for photosynthesis in literature. Then, as the understanding of photosynthesis has deepened, the terminologies and definitions of photosynthesis have also evolved [51]. In this work, Gross photosynthesis is defined as the total energy that plants fix during the photosynthesis process, while net photosynthesis is the total fixation of CO\({}_{2}\)[52]. The photosynthetic rate refers to the amount of CO\({}_{2}\) absorbed by a plant per unit of leaf area and unit of time. Biomass results from the net accumulation of assimilated CO\({}_{2}\) throughout the growth cycle [53]. Lastly, carbon assimilation is the amount of CO\({}_{2}\) stored in the plant. These terms are related to photosynthesis since plants can capture CO\({}_{2}\) from the atmosphere and metabolize it through the photosynthetic process to obtain sugars and other compounds that are required for the normal development of their life cycle [26; 54]. Then, the series of definitions described above refers to the estimation of photosynthesis. 2. The articles had to have a validation method to check if the different models used in the existing literature yielded similar results among other accredited models or with a photosynthesis measurement device on the market. This is important because one of the steps for modeling development is validation [55; 56]. Validation is defined as the comparison of the model predictions with the observed values of the actual process to determine if the model fits its purpose; the validation results are a necessary step in the acceptance of the model [57; 58; 59]. Validation can also be defined as a demonstration that a model has acceptable predictive accuracy in that domain within a specific application. The quantitative precision of the predictions is often referred to as the \"validity\" of the model. Generally, it refers to the ability of a model to accurately predict the results of a particular experimental or observational scenario [44].