## 4 Results and Discussion
### Construction of Standard Summer Maize EVI Time Series Curve in the Study Area  
#### 4.2.1 Estimation of Summer Maize Phenology  
The summer maize phenology is divided into eight key stages, which are souring, seedling emergence, trefoil, seven-leaf, jointing, tasseling, milk-ripe, and maturation. The phenology of summer maize in different regions varies due to the different natural environments. In this study, employing the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **Data** & **Parameters** & **Data** & **Parameters** & **Data** \\ \hline \(a_{1}\) & 0.282 & \(a_{2}\) & 0.321 & \(a_{3}\) & 0.341 \\ \(b_{1}\) & 217.8 & \(b_{2}\) & 254.7 & \(b_{3}\) & 204.7 \\ \(c_{1}\) & 20.87 & \(c_{2}\) & 23.17 & \(c_{3}\) & 61.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulated enhanced vegetation index (EVI) function parameters of summer maize in reference area. Figure 6: Moderate Resolution Imaging Spectroradiometer (MODIS) EVI time series curve of summer maize in the reference area. multiple linear stepwise regression method, the phenological observation data and the corresponding meteorological data of 32 agrometeorological stations were analyzed, and the multiple linear regression equations between summer maize phenology and natural environmental factors were constructed. The specific formulas are as follows:  
\[Y_{1}=1.24X_{1}-0.0026X_{4}+0.0087X_{5}+29.27 \tag{6}\]  
\[Y_{2}=1.07X_{1}+0.68X_{2}+23.60 \tag{7}\]  
\[Y_{3}=1.12X_{1}+0.58X_{2}-0.0030X_{4}+40.51 \tag{8}\]  
\[Y_{4}=1.17X_{1}-0.0054X_{4}+77.97 \tag{9}\]  
\[Y_{5}=1.20X_{1}-0.0049X_{4}+85.79 \tag{10}\]  
\[Y_{6}=1.06X_{1}-0.0059X_{4}+123.9 \tag{11}\]  
\[Y_{7}=1.34X_{1}-0.54X_{3}-0.0124~{}X_{4}+155.36 \tag{12}\]  
\[Y_{8}=0.64X_{1}+1.04X_{2}-0.0112X_{4}+207.9 \tag{13}\]  
where \(Y_{1}\), \(Y_{2}\), \(Y_{3}\), \(Y_{4}\), \(Y_{5}\), \(Y_{6}\), \(Y_{7}\), and \(Y_{8}\) are the analog DOY of the sowing, seedling emergence, trefoil, seven-leaf, jointing, tasseling, milk-ripe, and maturation stages, respectively; \(X_{1}\) is the longitude, \(X_{2}\) is the latitude, \(X_{3}\) is the annual average temperature, \(X_{4}\) is the annual precipitation, and \(X_{5}\) is the \(\geq\)10 \({}^{\circ}\)C accumulated temperature. The phenology observation data in 2007, 2009, 2011, and 2012 were used to verify the analog values of summer maize phenology that were calculated by the multiple linear regression equations (Equations (6) to (13)) at 32 agro-meteorological stations, respectively. The correlation coefficient (R) values were between 0.559 and 0.790 (Figure 7), which showed that the correlation between the simulated phenology and the actual phenology of summer maize was significant. It was illustrated that the summer maize phenology simulated by multiple linear regression equations were reliable in the current study. According to the multiple linear regression equations, the simulated results of summer maize phenology in the study area were calculated and are shown in Figure 6:0 Generally, the eight growth stages of summer maize in Hunaghuaihai Plain showed a trend of delaying from the southwest to northeast. The differences in seedling emergence, seven-leaf, and joint stages were the smallest, and the DOY discrepancy among the regions was about 16 days in the study area, whereas the difference in the maturation phase of summer maize was largest, up to about 32 days. The occurrence of this event may be related to the climate with high temperature in summer and a larger temperature difference between North and South in winter in Huanghaihai Plain [64,65]. Based on the summer maize phenology of Ruzhou City (Table 1) and the simulated phenology of summer maize in the study area, the lag at each pixel from the sowing stage to maturation stage of maize was roughly calculated using the following equations. The corresponding values of \(i\) and \(s\) are shown in Figure 6:1  
Figure 6:2 Correlation between actual summer maize phenology and simulated summer maize phenology with environmental factors in Huanghuaihai Plain in 2012.