## 4 Results
### Validation of the Modified Ratio Vegetation Index (MRVI)  
The existing VIs for monitoring the crop N content or C\({}_{\text{ab}}\) were collected from previous literatures (Table 3) [(43; 47; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69)]. Based on the MODIS reflectance at the blue, green, red, and NIR bands, which were transformed from the field spectral reflectance in exp1, the VIs were calculated and are listed in Table 3. The relationships between the VIs and leaf C\({}_{\text{ab}}\) in exp1 were discussed using the linear regression analysis. The VI was the \(x\)-axis and the C\({}_{\text{ab}}\) was the \(y\)-axis. The accuracy of VI was evaluated using a correlation coefficient (R\({}^{2}\)) and the root mean square error (RMSE). If the R\({}^{2}\) was higher and RMSE was lower, the VI was recognized to be more accurate for detecting the C\({}_{\text{ab}}\) of winter wheat. As shown in Table 3, the results showed that the MRVI obtained the best estimation accuracy with an increased correlation coefficient of 0.62 and it decreased the RMSE of 8.34 \(\text{\mu}\)g/cm\({}^{2}\). The improved results were followed by RVI2, a newly built index (\(\rho_{\text{NIR}}\)/\(\rho_{\text{blue}}\)); MSR\({}_{\text{3}}\) and SIPI, with correlation coefficients of 0.59, 0.54, 0.52 and 0.52, respectively, corresponding to RMSEs of 8.66, 9.08, 9.27, and 9.35 \(\text{\mu}\)g/cm\({}^{2}\), respectively. Except for normalized difference vegetation index  
Figure 4: Relationship between the leaf C\({}_{\text{ab}}\) and leaf total nitrogen content (TN) of winter wheat in exp1 at Yucheng Station. Figure 5: The winter wheat canopy reflectance and leaf C\({}_{\text{ab}}\) with different N rates during the winter wheat growth period in exp1 at Yucheng Station, as follows: the measured canopy spectral reflectance on (**a**) 4 April 2011; (**b**) 12 April 2011; (**c**) 30 April 2011; and (**d**) 11 May 2011, and (**e**) was the measured leaf C\({}_{\text{ab}}\). (green-blue) (NDVIg-b) and plant senescence reflectance index (PSRI), the correlation coefficients of C\({}_{\text{ab}}\) and VIs were significant (\(p<0.05\)). The MRVI improved the estimation accuracy of the leaf C\({}_{\text{ab}}\) of the winter wheat in comparison with other indexes. The verified five indexes with the higher R\({}^{2}\) and lower RMSE in exp1, that is, MRVI, RVI2, \(\rho_{\text{NIR}}/\rho_{\text{blue}}\), MSR, and SIPI, were calculated for each winter wheat pixel (1 km) in Hengshui City in 2017. The relationships between the situ leaf C\({}_{\text{ab}}\) and the calculated indexes of the corresponding pixel were analyzed using the linear regression in exp2 and the accuracy of the index was validated using the R\({}^{2}\). There were six pure pixels and eleven mixed pixels at the experimental plots of exp2. The analyzed results of the leaf C\({}_{\text{ab}}\) and VIs for the pure pixels and all of the pixels of exp2, are shown in Figures 7 and 8, respectively. Figure 7 shows the relationships between the leaf C\({}_{\text{ab}}\) and the five indexes (MRVI, RVI2, \(\rho_{\text{NIR}}/\rho_{\text{blue}}\), MSR, and SIPI) in the pure winter wheat pixels of exp2, at Hengshui City. Figure 8 shows the relationships between the leaf C\({}_{\text{ab}}\) and the five indexes in all of the winter wheat pixels of exp2 (pure pixels and mixed pixels). As shown in Figures 7 and 8, during the winter wheat growth period of Hengshui City, the top leaf C\({}_{\text{ab}}\) was well estimated by MRVI, with higher correlation coefficients, which were both significant (\(p<0.01\)).