## 5 Discussion
### The Advantages of Leaf Age as \(V_{m25}\) Predictor  
Annual plants complete their entire life cycle within one growing season. Starting from seeds, they progress through stages of germination, growth, flowering, fruiting, and ultimately die, all within a single year. In contrast, perennials continue to grow and reproduce for several years or more. Compared to perennial plants, using annual plants as research subjects eliminates the need to consider interannual influences and allows for easier identification of their developmental stages. This simplification makes it more straightforward to study the relationship between leaf age and \(\mathrm{V_{m25}}\).  
Our Two-stage linear model takes the advantage of leaf age and effectively captures the \(\mathrm{V_{m25}}\) seasonal variation with the crop growth processes. Maize, being annual plants, undergo significant changes in photosynthetic capacity throughout their growth cycle due to various physiological characteristics. Typically, \(\mathrm{V_{m25}}\) exhibits only one peak value during the entire crop growth period [33]. This uniqueness of the crop is the basis for our proposed model. In our model, the basic assumption is that the photosynthetic capacity increases during leaf development, reaching a maximum in spring or early summer, stabilizing or  
Figure 10: The daily GPP estimation discrepancy of BESS (blue lines), BESS_P (green lines) and BESS_TL (red lines). The center lines are the multi-year averages, and the edges of the shadow area are mean \(\pm\) standard deviation.  
gradually decreasing in summer, and further decreasing during senescence [6; 84]. Comparably, our model, in which V\({}_{\text{m25}}\) is quantified with leaf age, can perform well due to the strong correlation between V\({}_{\text{m25}}\) and leaf age (Figure 2). Now, it is understandable that the performance of the existing empirical relationships established between V\({}_{\text{m25}}\) and other variables, such as N\({}_{\text{Leaf}}\), Chll, and photoperiod, is basically determined by the similarity of that variable to the leaf age [7; 8; 40; 85]. Also, the photosynthetic capacity and environmental factors are often mismatched [57].  
For the estimation of V\({}_{\text{m25}}\), our Two-stage linear model outperforms both the original BESS model and BESS_P. The main difference between the original BESS model and BESS_P is the PeakV\({}_{\text{m25}}\): PeakV\({}_{\text{m25}}\) in the original BESS model is fixed, whereas the PeakV\({}_{\text{m25}}\) in the BESS_P is the same as the PeakV\({}_{\text{m25}}\) in our Two-stage linear model. Thus, solely improving the PeakV\({}_{\text{m25}}\) cannot solve the problem. In the original BESS model and BESS_P, LAI is used to seasonalize V\({}_{\text{m25}}\)[56]. However, it is proven that the correlation between V\({}_{\text{m25}}\) and LAI is not as strong as leaf age in the later half stage of crop growth (Figure 2) because the leaves turn yellow and senesce with the senescence of crops, but the change in LAI is not significant. Furthermore, the BESS model coupled with the Two-stage linear model (BESS_TL) has significantly improved the simulation of GPP. Across the five maize sites, BESS_TL only underestimated GPP by an average of 0.85%. In contrast, the original BESS model underestimated GPP by an average of 12.60%, and the BESS_P model overestimated GPP by an average of 20.73%. The superior performance of our Two-stage linear model underscores the importance of considering PeakV\({}_{\text{m25}}\) and leaf age in accurately modeling V\({}_{\text{m25}}\).