## 3 Results and Discussion
### Responses of ELUE and GPP to Bio-Physical and Environmental Factors  
#### 3.2.1 Responses of ELUE and GPP to Vegetation and Physiological Factors  
NDVI affected crop ELUE significantly with a linear relationship in all the crop fields (\(p<0.01\), Figure 4), with the highest Pearson correlation coefficient (r) of 0.87 (R\({}^{2}\) = 0.76) in soybean, followed by summer maize (0.81, R\({}^{2}\) = 0.66), paddy rice (0.79, R\({}^{2}\) = 0.62) and winter wheat (0.73, R\({}^{2}\) = 0.53). In addition, it seemed that NDVI was better fitted to ELUE with an exponential function than linear function, with the R\({}^{2}\) of 0.78, 0.67, 0.63 and 0.58 in soybean, summer maize, paddy rice and winter wheat, respectively. The consistent relationship showed the potential of utilizing NDVI to estimate ELUE as well as further GPP in the agroecosystems. Similar variation patterns of ELUE with NDVI were reported in other ecosystems [4]. [PERSON] et al. (2014) examined the fraction of absorbed PAR (fAPAP) by the photosynthetic tissues in cropland sites and found that there was an exponential function relationship between NDVI and fAPAR [14]. The fAPAR increases when NDVI rises, and PAR is more effectively intercepted for carbon uptake, leading to an increase in ELUE. An ecosystem-level ELUE study showed that NDVI was quite consistent with photosynthesis dynamics and could be used as a proxy for both fAPAR and ELUE to predict GPP on a seasonal time scale [54; 55]. Moreover, positive correlation relationships were found between NDVI and GPP (\(p<0.01\), Table 3), with the r of 0.85, 0.91, 0.81 and 0.76 in paddy rice, soybean, summer maize and winter wheat, respectively. Strong seasonal and positive coupling of leaf area and photosynthesis occurred in annual crops, such as wheat [56; 57] and peatland [58], where the findings demonstrated that the higher the LAI is, the higher the GPP is. These findings revealed the fact that the vegetation factor (NDVI) can be recognized as an essential parameter in ecosystem photosynthesis [59; 24; 56]. Figure 4: The relationship between ecosystem light use efficiency (ELUE) and normalized difference vegetation-tion index (NDVI) on a daily basis on non-rainy days at the (**a**) paddy rice, (**b**) soybean, (**c**) summer maize and (**d**) winter wheat fields. The correlation coefficient (R\({}^{2}\)) and [PERSON]’s correlation coeficient (r), as well as the exponential and linear function, are also shown. The color of the cross symbol showed the level of daily gross primary production (GPP). There is a significant relationship between ELUE and g\({}_{\rm c}\) in the soybean, summer maize and wheat fields (with r of 0.68, 0.56 and 0.41 (\(p<0.01\)), respectively) but not in the rice fields (with r of 0.07) (Figure 5). Besides, GPP was also significantly positively related to g\({}_{\rm c}\) in the soybean (r = 0.68), maize (r = 0.54) and wheat (r = 0.40) fields (\(p<0.01\), Table 3). These results revealed that the physiological factor (g\({}_{\rm c}\)) can be well recognized as the control for crop photosynthesis in the typical agroecosystems, except for paddy rice. Vegetation physiological control of water and carbon fluxes between the atmosphere and vegetation canopy is exerted by stomata and the degree of control is quantified in terms of g\({}_{\rm c}\)[60]. g\({}_{\rm c}\) was conducted using an inversion of the Penman-Monteith equation as described in Section 2.2. The Penman-Monteith equation, which was termed as a \"big-leaf\" model to estimate ET, can generally obtain satisfying simulation results only in a closed canopy [61; 62], when vegetation transpiration was dominant in the composition of evapotranspiration.