# Estimation of Chlorophyll Content in Wheat Based on Optimal Spectral Index
## 3 Results
### Modeling Results and Analysis  
Through the above correlation analysis, the optimal vegetation index with a good correlation with chlorophyll content was determined. The input variable of this model is the optimized spectral index with a high correlation with chlorophyll content, in which 80% of data were used for modeling, 20% of data were used for verification, and the modeling accuracy verification set models R2, RMSE, and RE are shown in Table 4.  
During the flag-picking period, combined with polynomial regression, random forest, decision tree, and artificial neural network modeling. The R2, RMSE, and RE of the polynomial regression model were 0.792, 2.632, and 3.977, respectively. Compared with random forest, decision tree, and artificial neural network, the R2 is increased by 0.472, 0.274, and 0.255, respectively. The best model validation results are shown in Figure 5a.  
The R2, RMSE, and RE of the random forest model at the flowering stage were 0.784, 3.858, and 3.064, respectively. When compared with polynomial regression, decision tree, and artificial neural network model, the R2 increased by 0.102, 0.564, and 0.310, respectively. Additionally, the RE decreased by 2.791 and 0.984 compared with the polynomial regression and artificial neural network models, respectively. The model validation results are shown in Figure 5b.  
\begin{table}
\begin{tabular}{c c} \hline
**Child-Bearing Period** & **Variable** \\ \hline flagging stage & NDVI (\(R_{679}R_{683}\) ). GCI (\(R_{683}R_{679}\)) \\ flowering period & NDVI(\(R_{407}R_{412}\)), RDVI (\(R_{981}R_{989}\)) \\ \(\text{pustulation period}\) & NDVI (\(R_{857}R_{720}\) ), RVI (\(R_{857}R_{934}\) ), GCI (\(R_{857}R_{724}\)) \\ maturity & NDVI (\(R_{989}R_{996}\) ). GCI (\(R_{989}R_{996}\)) \\ \hline \end{tabular}
\end{table}
Table 3: Selection of independent variables at different growth stages.  
During the filling period, the R\({}^{2}\), RMSE, and RE of the random forest model were 0.677, 4.651, and 3.829, respectively. The values were 0.061 higher than the R\({}^{2}\) of artificial neural networks, and RE decreased by 4.414, 0.520, and 1.088 for multinomial regression, decision trees, and artificial neural networks, respectively. The model validation results are shown in Figure 5c.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Child-Bearing** \\ **Period** \\ \end{tabular} } & \multirow{2}{*}{**Modeling**} & \multicolumn{2}{c}{**Modeling Set**} & \multicolumn{2}{c}{**Validation Set**} \\ \cline{3-6}  & & **R\({}^{2}\)** & **R\({}^{2}\)** & **RMSE** & **RE** \\ \hline \multirow{4}{*}{flagging stage} & PR & 0.353 & 0.792 & 2.632 & 3.977 \\  & RF & 0.810 & 0.320 & 4.027 & 3.512 \\  & DT & 0.705 & 0.518 & 3.913 & 3.268 \\  & ANN & 0.526 & 0.537 & 2.060 & 2.948 \\ \hline \multirow{4}{*}{flowering period} & PR & 0.376 & 0.682 & 3.236 & 5.855 \\  & RF & 0.906 & 0.784 & 3.858 & 3.064 \\  & DT & 0.908 & 0.220 & 2.477 & 1.837 \\  & ANN & 0.659 & 0.474 & 2.526 & 4.048 \\ \hline \multirow{4}{*}{pustulation period} & PR & 0.674 & 0.668 & 4.288 & 8.243 \\  & RF & 0.872 & 0.677 & 4.651 & 3.829 \\  & DT & 0.794 & 0.376 & 5.803 & 4.331 \\  & ANN & 0.706 & 0.616 & 2.846 & 4.917 \\ \hline \multirow{4}{*}{maturity} & PR & 0.401 & 0.371 & 8.376 & 10.764 \\  & RF & 0.838 & 0.249 & 8.926 & 7.589 \\ \cline{1-1}  & DT & 0.447 & 0.683 & 8.662 & 6.070 \\ \cline{1-1}  & ANN & 0.847 & 0.773 & 7.230 & 9.785 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Wheat model results.  
Figure 5: The best model validation results of the key growth periods.  
At the maturity stage, the R\({}^{2}\), RMSE, and RE of the artificial neural network model for estimating chlorophyll content were 0.773, 7.230, and 9.785, respectively. The R\({}^{2}\) of polynomial regression, random forest, and decision tree increased by 0.402, 0.524, and 0.09, respectively, while the RMSE decreased by 1.146, 1.696, and 1.432, respectively. The model validation results are depicted in Figure 5d.