# Upscaling Gross Primary Production from Leaf to Canopy for Potato Crop (_Solanum tuberosum_ L.)
## 4 Discussion
Therefore, each stratum contributed in a different way to the total assimilation of the canopy and this contribution changes during the crop growth cycle. The upscaling performance depends on the choice of the photosynthetic light-response curves (An-I curves). In the present study, the modeling of the GPP was achieved based on functions that describe and interpret the photosynthetic light responses of leaves. This interpretation works based on primary parameters such as light-saturated net photosynthetic rate (\(A_{gmax}\)) and quantum yield of assimilation (\(\Phi\)). For C3 species, the theoretical quantum yield is around 0.1250 \(\upmu\)mol (CO\({}_{2}\)) \(\upmu\)mol(photon)\({}^{-1}\)[50; 53; 54] and the maximum value of \(A_{gmax}\) ranges from 42 to 59 \(\upmu\)mol (CO\({}_{2}\)) m\({}^{-2}\) s\({}^{-1}\)[55]. Although, the functions used for upscaling had below typical C3 \(A_{gmax}\) values, the parameters deduced by the classical Michaelis-Menten (Baly) function were larger (32 \(\upmu\)mol (CO\({}_{2}\)) m\({}^{-2}\) s\({}^{-1}\) and 0.15 \(\upmu\)mol (CO\({}_{2}\)) \(\upmu\)mol (photon)\({}^{-1}\)), in comparison to maximum values for Michaelis-Menten (Smith) (25,6 \(\upmu\)mol (CO\({}_{2}\)) m\({}^{-2}\) s\({}^{-1}\) and 0.08 \(\upmu\)mol (CO\({}_{2}\)) \(\upmu\)mol (photon)\({}^{-1}\)) and for Webb (26.2 \(\upmu\)mol (CO\({}_{2}\)) m\({}^{-2}\) s\({}^{-1}\) and 0.098 \(\upmu\)mol (CO\({}_{2}\)) \(\upmu\)mol (photon)\({}^{-1}\)). The above indicates that the Baly-based upscaling model overestimated the GPP due to its higher values in the photosynthetic capacity parameters. The Michaelis-Menten (Baly) function, which tends to overestimate the rate of photosynthesis at low and high irradiances, fails to reproduce the decline of photosynthesis at the photoinhibitory region [56; 57; 58] and overestimates Agmax and quantum yield of assimilation (\(\Phi\)), which has also been reported in Amazon forest species [59]. There are inherent limitations of An-I curves to capture the photosynthetic responses of the canopy, mainly for the upper leaves that were never fully light-saturated even under direct sunlight (Figure 2). However, the GPP calculated based on the parameters deduced from Michaelis-Menten ([PERSON]) [47] and Mitscherlich ([PERSON]) [49] in both big-leaf and multilayer approaches was closer to the measured GPP because they saturated at a lower PPFD than the classical Michaelis-Menten ([PERSON]) equation. In this regard, authors such as [13; 60; 61] indicate that the modeling of the GPP from the Mitscherlich exponential function led to more realistic saturation assimilation values. Among the several processes that need to be described in up scaling models, canopy light absorption is essential since it drives the energy available for photosynthesis. Especially in potatoes, the planophile leaves generate a pronounced light gradient with a possible large effect on total GPP that can be estimated using the analytical solution proposed in this work, which is based on light relations in the canopy using simplified models of photosynthesis.