## 3 Results
### Yield Estimation Model  
In this study, vegetation indices at different growth stages and florescence spectral indices were used as independent variables, and rice yield was used as the dependent variable. Yield estimation models were established based on both vegetation indices and florescence spectral information. They were compared with the yield estimation models using vegetation indices alone, and the potential of spectral information at the flowering stage in improving yield estimation was analyzed. The yield estimation models are presented in Table 5:  
As seen in Table 6, the best single-growth stage model was constructed by NDVI(\({}_{(740,768)}\))(Booting) at the booting stage, with R\({}^{2}\) of 0.748. The introduction of FDI1(\({}_{(576,664)}\), FDI2(\({}_{(596,784)}\)) and FDI4(\({}_{(848,872)}\)) into this model effectively improved the model performance, with R\({}^{2}\) increasing from 0.748 to 0.799, increasing by 6.8%, and MAPE and RMSE decreasing by 11.8% and 10.7%, respectively. For the two-growth stage model, the involved vegetation indices were NDVI(\({}_{(740,768)}\)) (Booting) at the booting stage and DVI(\({}_{(52,864)}\))(Filling) at the filling stage. After introducing florescence spectral indices FRI1(\({}_{(624,716)}\), FRI4(\({}_{(692,720)}\)) and FDI5(\({}_{(576,608)}\), the model R\({}^{2}\) increased by 4.1%, MAPE and RMSE decreased by 16.0% and 11.3%, respectively. For the three-growth stage model, RVI(\({}_{(748,832)}\))(Heading) at the heading stage was added on the basis of the two-growth stage model and the introduction of FRI8(\({}_{(692,720)}\)) and FDI4(\({}_{(848,872)}\)) at the flowering stage increased R\({}^{2}\) by 2.7%, and decreased MAPE and RMSE by 7.8% and 4.6%, respectively. It could be seen that the performance of estimation models using vegetation indices alone were improved when two or three florescence spectral indices were included. Among the involved florescence spectral indices, FDI4(\({}_{(848,872)}\)) was used in the single-growth stage model and three-growth stage model, and FRI4(\({}_{(692,720)}\)) was introduced in the two-growth stage model and three-growth stage model. \begin{table}
\begin{tabular}{c c c c c} \hline
**Index** & **Equation** & **CC** & **Index** & **Equation** & **CC** \\ \hline FRI1 & \(\frac{\rho^{\prime}_{\tau,FTH(62)}}{\rho^{\prime}_{\tau,FTH(716)}}\) & \(-0.4852\) & FDI1 & \(\frac{\rho^{\prime}_{\tau,FTH(716)}}{\rho^{\prime}_{\tau,FTH(716)}}\) & \(-0.4671\) \\ FRI2 & \(\frac{\rho^{\prime}_{\tau,FTH(716)}}{\rho^{\prime}_{\tau,FTH(716)}}\) & \(-0.4696\) & FDI2 & \(\frac{\rho^{\prime}_{\tau,FTH(716)}}{\rho^{\prime}_{\tau,FTH(716)}}\) & \(-0.4660\) \\ FRI3 & \(\frac{\rho^{\prime}_{\tau,FTH(716)}}{\rho^{\prime}_{\tau,FTH(716)}}\) & \(0.5149\) & FDI3 & \(\frac{\rho^{\prime}_{\tau,FTH(716)}}{\rho^{\prime}_{\tau,FTH(716)}}\) & \(0.4756\) \\ FRI4 & \(\rho^{\prime}_{\tau,FTH(716)}-\rho^{\prime}_{\tau,FTH(716)}\) & \(0.5363\) & FDI4 & \(\frac{\rho^{\prime}_{\tau,FTH(716)}}{\rho^{\prime}_{\tau,FTH(716)}}\) & \(-0.4755\) \\ FRI5 & \(\frac{\rho^{\prime}_{\tau,FTH(716)}}{\rho^{\prime}_{\tau,FTH(716)}}\) & \(0.4589\) & FDI5 & \(\frac{\rho^{\prime}_{\tau,FTH(716)}}{\rho^{\prime}_{\tau,FTH(716)}}\) & \(0.4746\) \\ \hline \end{tabular} Note: CC means coefficient correlation.  
\end{table} 
Table 4: The expressions of florescence difference index (FDI) and florescence ratio index (FRI) with high correlation with rice yield.