## Materials and Methods
### NDVI and Its Derivative Parameters  
NDVI and its derivative parameters are spectral characteristic parameters composed of four bands: blue, green, red, and near-infrared. The correlation between vegetation indices and the leaf area index is not same with varying degrees. For example, [PERSON] et al. [5] obtained the derivative normalized NI (D524, D805) formed by the combination of 524 nm and 805 nm, which has the best correlation with LAI. [PERSON] et al. [1] calculated that 692/858 nm was the combination of the NDVI band with the highest determination coefficient of wheat coverage. Additionally, the vegetation index calculated by the other band combination can be ignored in the correlation analysis. [PERSON] et al. [3] worked out the mean values of the composition band of VNDVI (Visible NDVI) and got the vegetation index values by putting these mean values into formulas. This idea reduced the complexity of calculation and enhanced the anti-interference ability of these parameters to some extent, but neglected a large amount of feature information of the spectral data. In this study, A\({}_{\text{VNDVI}}\) (Accumulative Visible NDVI), a new type of derivative parameters of NDVI, was constructed through leading the band combination calculation into VNDVI [3] and accumulating the results. The parameters take account of vegetation spectral information contained in red, blue, and green wavebands. Thus, the stability of the response characteristics is enhanced by the accumulative calculation of spectral information, and the fitting performance of the inversion models is improved because of the complementary information of the hyperspectral bands. The calculation formula is as follows:  
\[\text{A}_{\text{VNDVI}}=\sum_{\text{r=1}}^{\text{r=2}}\sum_{\text{r=1}}^{\text {r=2}}\frac{\text{NIR}_{\text{m}}-\text{VIS}_{\text{n}}}{\text{NIR}_{\text {m}}+\text{VIS}_{\text{n}}} \tag{1}\]  
where NIR\({}_{\text{m}}\) represents the spectral reflectances of near infrared; VIS\({}_{\text{n}}\) represents the spectral reflectances of visible bands, containing blue, green, and red wavebands; \([r_{m1},r_{m2}]\) and \([r_{n1},r_{n2}]\) represent the reflectances in the near infrared and visible band range respectively; and \([m1,\,m2]\) and \([n1,\,n2]\) denote the range of the near infrared and visible waveband. The specific calculation formulas of vegetation indices are shown in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline
**Index** & **Calculation Formula** & **Reference** & **Comment** \\ \hline NDVI & NDVI = \(\frac{\text{NIR}-\text{RED}}{\text{NIR}+\text{RED}}\) & [PERSON] et al. [21] & normalized vegetation index \\ \hline GNDVI & GNDVI = \(\frac{\text{NIR}-\text{Green}}{\text{NIR}+\text{Green}}\) & [PERSON] et al. [9] & Green normalized vegetation index \\ \hline BNDVI & BNDVI = \(\frac{\text{NIR}-\text{Blue}}{\text{NIR}+\text{Blue}}\) & [PERSON] et al. [3] & Blue normalized vegetation index \\ \hline GRNDVI & GRNDVI = \(\frac{\text{NIR}-\text{(Green+Red)}}{\text{NIR}+\text{(Green+Red)}}\) & [PERSON] et al. [3] & Green and Red normalized vegetation index \\ \hline GBNDVI & GBNDVI = \(\frac{\text{NIR}-\text{(Green+Blue)}}{\text{NIR}+\text{(Green+Blue)}}\) & [PERSON] et al. [3] & Green and Blue normalized vegetation index \\ \hline RBNDVI & RBNDVI = \(\frac{\text{NIR}-\text{(Red+Blue)}}{\text{NIR}+\text{(Red+Blue)}}\) & [PERSON] et al. [3] & Red and Blue normalized vegetation index \\ \hline A\({}_{\text{NDVI}}\) & \(\text{A}_{\text{NDVI}}=\sum_{\text{r=1}}^{\text{r=2}}\frac{\text{r=2}}{\text{NIR }_{\text{m}}-\text{Red}_{\text{n}}}\frac{\text{NIR}_{\text{m}}-\text{Red}_{ \text{n}}}{\text{NIR}_{\text{m}}+\text{Red}_{\text{n}}}\) & this paper & accumulative normalized vegetation index \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of NDVI and its derivative parameters. The series of Landsat satellites are one of the main sources of observation data for remote sensing technology research and application.