## 4 Discussion  
In this study, four ML methods were used to predict the maize GPP of three sites in Nebraska (i.e., the NE1, NE2, and NE3 sites) and one site in Minnesota (i.e., the RO1 site). Previous ML models simply took processed meteorological data and remote sensing data as model inputs, without the consideration of influences from phenology and leaf physiology on photosynthesis. The novelty of this study is integrating maize phenology (represented by NMP) and leaf photosynthetic rate factor determined by phenology (represented by \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **RMSE** & **URMSE** \\ \hline \multirow{2}{*}{RF} & A0 & 2.837 & 2.771 \\  & A3 & 2.654 & 2.213 \\ \hline \multirow{2}{*}{SVM} & A0 & 2.556 & 2.502 \\  & A3 & 2.656 & 2.280 \\ \hline \multirow{2}{*}{CNN} & A0 & 2.629 & 2.627 \\  & A2 & 2.539 & 2.417 \\ \hline \multirow{2}{*}{ELM} & A0 & 2.549 & 2.472 \\  & A2 & 2.571 & 2.168 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The comparison of RMSE and URMSE for ML methods introducing SLN and NMP or not introducing them in RO1 site. The unit is gC-m\({}^{-2}\)-day\({}^{-1}\). Figure 8: GPP estimation results of SVM, CNN, and ELM in RO1 site. The red line is the fitting line between estimated GPP (GPPm) and ground-measured GPP (GPPg), and the dashed line is the 1:1 line. SLN) into the model inputs. The selection of appropriate input variables plays a key role in GPP prediction [89]. The contribution rate of selected variables and the importance of SLN and NMP are further verified by ranking the importance of input factors in the RF method. SSR is the most important contribution factor (43.3%) to GPP, and it is the main energy source of organisms. There is a direct relationship between photosynthesis and SSR. The physiological process and photosynthesis of maize are regulated by the light and thermal effects brought by radiation [90]. The contribution rate of NDVI is 21.8%, and it is the most commonly used feature factor, which can reflect the plant canopy dynamics. The greater the amount of green vegetation, the more infrared light it absorbs, leading to a rise in NDVI [91]. Unexpectedly, the contribution of SLN and NMP factors exceeded that of air temperature, suggesting that they also had a significant impact on GPP estimates. Three kinds of temperature also have a certain proportion, reflecting the characteristics of the climate of the site. In addition, by regulating the physiological process of vegetation, temperature makes it form a phenological process for maize to a large extent. Therefore, there is a certain correlation between temperature and phenological factor (NMP). But by using data from three NE sites in Nebraska, the four ML methods all prove that the positive effect of NMP on the model (A3) can compensate for the decrease in accuracy caused by information overlap. Therefore, it is feasible to consider the three temperature and NMP factors simultaneously. The role of SLN and NMP were further validated from site to site in Nebraska using the RF method. The division of the training set and test set was determined by the respective data volume and water stress differences of the three sites, and the optimal input variable combination of Section 3.2.2 was used. SLN and NMP both maintained their positive impact on the model, but to different degrees, depending on the specific soil and water information at each site. When the other three ML methods (SVM, CNN, and ELM) were applied to GPP prediction for all three sites in Nebraska, good results were also obtained (NSE > 0.95 and RMSE < 2 gC\(\cdot\)m\({}^{-2}\).day\({}^{-1}\)), and the estimation accuracy of all methods was similar. Specifically, after considering SLN and NMP, the accuracy of all models improved. But when SLN and NMP were considered at the same time, SVM and RF had the greatest improvement, while for CNN and ELM, only when SLN or NMP was considered separately. CNN uses a more complex model and weight sharing in its algorithm, which can learn complex problems quickly.