## 3 Results and Discussion
### Experiment 5: The Effect of VIs and Their Gradient  
This experiment aims to demonstrate the effect of VIs and their gradients on the classification accuracy improvement and their capabilities to decrease the scheduled time for image acquisition. For this purpose, firstly, NDVI and EVI, as examples of VIs, are considered and temporal signatures of wheat and barley are computed and depicted in Figure 8 for training data. In Figure 8a,c, the temporal gradient of NDVI and EVI for wheat and barley are showed. These diagrams may seem very similar in appearance, but the direction and size of their variations are different from time to time. In contrast to wheat, barley yields faster and loses its chlorophyll almost three weeks earlier. Then, the temporal gradient of wheat and barley is computed and given in Figure 8b,d. Although the temporal signatures of these crops in the first stages of growth are almost the same and have high spectral similarity, as shown in Figure 8, the temporal gradient at the end of the season can provide appropriate features for better discrimination. In particular, the temporal gradient between images T6 and T7, which were acquired on 17 April and 3 May, respectively, could provide the first significant difference between these similar classes for discrimination. In other words, from 17 April to 3 May, the wheat stands at the late stage of its growth, while the barley lost chlorophyll more rapidly. In this research, because of the time series images used, the information from all plant growth stages was used as new features in the model. Since other crops in the area have a planting time, greenness peak time, and different harvest time, therefore, the spectral gradients and changes in their VIs will also be different. The proposed method performed well in distinguishing and classifying other crops. The main problem was the separation of wheat from the barley due to its similarity with the general agronomic calendar and the spectral similarity of the two crops. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**1** & \(\surd\) & - & \(\surd\) & - & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & 93.2 & 85.3 & 91.5 & 51.1 \\
**2** & \(\surd\) & - & \(\surd\) & - & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & - & 93.1 & 85.2 & 90.3 & 55.1 \\
**3** & \(\surd\) & - & \(\surd\) & - & \(\surd\) & \(\surd\) & \(\surd\) & - & 95.5 & 90.4 & 96.3 & 59.2 \\
**4** & \(\surd\) & - & \(\surd\) & - & \(\surd\) & \(\surd\) & \(\surd\) & - & - & 94.3 & 87.8 & 96 & 46.6 \\
**5** & \(\surd\) & - & \(\surd\) & - & \(\surd\) & \(\surd\) & - & - & - & 91.2 & 81.2 & 92 & 14 \\
**6** & \(\surd\) & - & \(\surd\) & - & \(\surd\) & - & - & - & - & 86.8 & 71.5 & 82.4 & 9.8 \\
**7** & \(\surd\) & - & - & - & - & \(\surd\) & - & - & - & 94.1 & 87.5 & 95.9 & 24.2 \\
**8** & \(\surd\) & - & - & - & - & - & \(\surd\) & - & - & - & 94.8 & 88.9 & 96.5 & 33.1 \\
**9** & \(\surd\) & - & - & - & - & \(\surd\) & \(\surd\) & - & - & - & 95.3 & 90.1 & 97.7 & 45.5 \\
**10** & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & - & - & - & - & - & 87.4 & 72.8 & 84.0 & 11.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The (OA) and kappa of the RF classifier using combinations of image acquisition times. In Figure 8a,b, the temporal gradient of NDVI shows that the barley greenness peak time was at T6 and, since then, the slope of the variation of the VI has been descending and, for wheat, it continues to rise until T7. The random forest distinguished between the two crops well using the same difference. After illustrating the VIs and their temporal gradients, the gradient of spectral bands and the aforementioned VIs (Table 3) along with their temporal gradients (i.e., Equations (1) and (2)) are incorporated in the RF classification. Figure 9a,b, show the results obtained for 27 combinations of image acquisition times when only spectral bands are used.