# Upscaling Gross Primary Production from Leaf to Canopy for Potato Crop (_Solanum tuberosum_ L.)
## 3 Results
### GPP Up Scaling  
The measured EC GPP shows a progressive increase from 28 DPP until a maximum GPP (500 kg C ha\({}^{-1}\) day\({}^{-1}\)) occurred at 88 DPP. From 90 to 138 DPP, the daily GPP decreased progressively until a minimum value of 200 kg C ha\({}^{-1}\) day\({}^{-1}\). Multilayer (ML) models correctly reproduce the behavior of potato GPP over time as well as the magnitude of the maximum values that occur around 90 DPP. In the ML Michaelis-Mentem (Smith) model [47], the GPP was underestimated between 36 and 66 DPP (measured GPP was up to 170% higher) and between 87 and 117 DPP (measured GPP was 50% higher). The multilayer model-based Mitscherlich (Webb) function [49] underestimates the GPP during most of the cycle. The greatest differences were in the period between 28 and 65 DPP and 95 to 117 DPP. The Big-leaf (BL) Michaelis-Mentem ([PERSON]) model [47] underestimates the GPP mainly between 28-70 DPP. After this period, however, GPP values were close to the measured GPP. The maximum GPP reached is 50% greater than the one measured with the EC tower. However, BL models overestimated GPP, mainly during the maximum LAI phase (80-90 DPP) (Figure 6). The modeled and measured GPP showed variations of the half-hourly GPP mean throughout the day and across growth stages (Figure 7). In the tubeterization stage, GPP measured rates increased progressively throughout the day, reaching a maximum of 1.30 \(\pm\) 0.19 mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\) between 9 to 13 h. In this stage, the ML Michaelis-Menten ([PERSON]) model [47] predicted the measured values more closely than the other models. In the vegetative and tuber bulking stages, half-hourly GPP maximums (0.83 \(\pm\) 0.37 mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\) and 0.96 \(\pm\) 0.18 mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\), respectively) were also found between 9 and 13 h. Again, the GPP predicted by the ML Michaelis-Menten ([PERSON]) model [47] was closer to the measured values. The BL Michaelis-Menten (Baly) model [46] overestimates the half-hourly GPP in all stages (Figure 7). Figure 5: Parameters of light-saturated gross photosynthetic rate (\(A_{gmax}\)) and quantum yield of assimilation (\(\Phi\)) for the topmost unshaded leaves ((c,f), respectively), middle stratum leaves((b,e), respectively), and the bottommost shaded leaves ((a,d), respectively) of potato (_Solanum Tuberosum_ L. Var. Diacol capiro) calculated by the rectangular hyperbola Michaelis—Menten type function, [PERSON] [47] and [PERSON] [46], and by an exponential Mitscherlich function [49]. Figure 8 shows day-to-day variations of GPP measured (obtained by the eddy covariance technique) versus the big-leaf and multilayer models. In general, the correlation coefficient r showed that the modeled and measured GPP values had a strong linear correlation. The RMSE value was higher for BL models than ML models, indicating a lower performance and hence less accuracy for BL models. Most of the ML GPP modeled vs. GPP measured data are closely distributed around the 1:1 line. This greater closeness of the multilayer models' scatter plot of the predicted value to the 1:1 line indicates a better accuracy than BL models (Figure 8a,b). The ML Michaelis-Menten ([PERSON]) [47] based model had the highest accuracy due to its lowest RMSE (0.131) obtained, followed by the multilayer model based on the Mitscherlich ([PERSON]) [49] function (RMSE = 0.155). Likewise, the daily variability in GPP is more accurately captured by the ML Michaelis-Menten ([PERSON]) [47] model due to the linear regression showing the smallest deviation from the 1:1 line (Figure 8b). Figure 6: Daily gross primary production (GPP) estimated with the scaling up Big-Leaf—BL (red, blue solid lines) and Multilayer—ML (green, black solid lines) models and Eddy Covariance—EC measurements (open circles), Vs. days post planting (DPP).