# Upscaling Gross Primary Production from Leaf to Canopy for Potato Crop (_Solanum tuberosum_ L.)
## 1 Introduction  
Gross primary production (GPP) is a key ecosystem process that decreases the atmospheric carbon dioxide (CO\({}_{2}\)) concentration [1, 2, 3] CO\({}_{2}\) flux information [1] is necessary to improve the knowledge of the potential of ecosystems to grow and mitigate climate change [4, 5]. Although eddy covariance (EC) measurements provide accurate and reliable information about carbon and energy balances at the ecosystem level, flux measurements are often not available in many places [6]. Therefore, different methodologies are needed to estimate GPP based on extrapolations of chamber and biometric measurements and the canopy upscaling process using readily measurable meteorological and environmental variables [4, 7, 8]. Upscaling the GPP from leaf to canopy is challenging because of the large microenvironment [light, temperature, vapor pressure deficit (VPD)] variability within plant canopies at both the vertical and horizontal dimensions [9, 10]. A common strategy to represent carbon uptake during gross primary production (GPP) is through photosynthetic light use efficiency models based on photosynthetic light-response curves and light distribution through the canopy [1, 11, 12, 13, 14, 15, 16], assuming that light is the primary driver of vertical variationin photosynthesis [17]. Nevertheless, canopy estimates require additional features such as light distribution through the canopy, canopy structure (mean leaf angle and leaf area index), and vertical profiles of weather variables within and above the crop [9; 18]. Scaling methods vary with different complexity from the simplest one-big leaf [19; 20; 21; 22; 23], to two-big leaf models [24; 22; 25] and multilayer models [26; 27; 28; 10; 29]. The big leaf model is a representation of a canopy as a single giant leaf [18], which can be parameterized under a tractable mathematical solution at the canopy level [16]. In most plant species, the photosynthetic system is bulked in the upper layer of the canopy, and light decreases faster in horizontal canopies than in vertical ones [14]. Since the leaves in the potato canopy have a horizontal tendency [30; 31], an approach that treats vegetation as a big leaf where the canopy GPP predictions are proportional to the photosynthesis of topmost unshaded leaves [16] could be useful. However, since the canopy is arbitrarily represented by a single leaf, it treats sunlit and shaded leaves within the canopy equally. In other words, the model assumes that there is no uncertainty introduced by ignoring the shaded fraction of the canopy, which results in an overestimation of flux rates [24; 25; 16; 22]. In the multilayer model, the canopy is divided into \(n\) layers and light intensity declines with depth into the canopy as a function of the leaf area index [18; 32]. Consequently, canopy photosynthesis is calculated separately for each layer. In general, multilayer models consider variations in the light level within the canopy, leaf inclination, and other leaf aspects as well as the variation of air temperature, wind speed, humidity, and CO\({}_{2}\) concentration [13; 18; 22]. The model calculates the net photosynthetic rate (An) for each layer, using the absorptance and the respective layer's leaf area [1; 18; 22; 33]. Several researchers have attempted to evaluate the performance of different upscaling schemes with flux measurements (for wheat, shrublands, broadleaf, Amazonian, and conifer forests) [1; 34; 35; 36], and have shown that the big-leaf approach matches overestimate or underestimate EC measurements [13; 15; 36]. Other studies have demonstrated the improved accuracy of multilayer models for GPP calculations [13; 15; 36]. Potatoes are critical for the food security of people across South America, Africa, and Asia, feeding more than one billion people worldwide [37; 38].