## 3 Results and Discussion
### Experiment 5: The Effect of VIs and Their Gradient
In addition to spectral bands, the effect of incorporating VIs and their spectral gradients obtained by Equations (1) and (2) are given in Figure 9a,b, in terms of OA and kappa coefficients. As demonstrated in Figure 9, by utilizing the temporal gradient of spectral bands and VIs, along with their gradients, the OA and kappa values are improved up to 5% and 9%, respectively. The results of all of the various combinations of images are shown in Figure 9a,b. In the first case, only the T7 image was used and the overall accuracy and kappa coefficient were 92% and 82.9%, respectively. If any of the images are used, the results will be weaker until 17 April. For example, the results of using the T6 image for overall accuracy and the kappa coefficient were 79.9% and 58%, respectively. In the case in which only two images of time series images were used, T1 and T7 images had better results. In the case in which three images were used, T1, T6, and T7 had the best results. In addition to reducing the calculation time, as well as using the minimum number of images, this combination also provides the highest producer's accuracy for barley (Table 9). Figure 8: The NDVI and EVI indices and their temporal gradient for: (**a**) NDVI; (**b**) temporal gradient of NDVI; (**c**) EVI; and (**d**) the temporal gradient of EVI, during the growing season. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c} \hline \hline
**Parameter** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** \\
**VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** & **VIs** \\ \hline
**1** & \(\surd\) & - & \(\surd\) & - & \(\surd\) & - & - & - & - & - & - & - & 86.8 & 71.5 & 82.4 & 9.8 & 95.9 & 24 & 264.5 \\
**2** & \(\surd\) & - & \(\surd\) & - & \(\surd\) & - & - & - & - & - & \(\surd\) & - & 88.1 & 73.9 & 83.9 & 10.9 & 96.7 & 51 & 270.8 \\
**3** & \(\surd\) & - & \(\surd\) & - & \(\surd\) & - & - & - & - & - & \(\surd\) & 89.9 & 78.1 & 86.8 & 13.0 & 98.5 & 102 & 275.7 \\
**4** & \(\surd\) & - & - & - & - & \(\surd\) & - & - & - & - & - & 95.3 & 90.1 & 97.7 & **45.5** & 99.0 & 24 & 264.5 \\
**5** & \(\surd\) & - & - & - & \(\surd\) & - & - & - & \(\surd\) & - & 96.4 & 92.3 & 98.2 & 49.3 & 100 & 51 & 270.8 \\
**6** & \(\surd\) & - & - & - & \(\surd\) & - & - & - & \(\surd\) & 99.3 & 98.4 & 99.4 & **92.5** & 99.9 & 102 & 275.7 \\
**7** & \(\surd\) & \(\surd\) & \(\surd\) & - & - & - & - & - & \(\surd\) & 90.5 & 79.8 & 90.2 & 13.8 & 98.2 & 170 & 280.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The overall accuracy (OA), kappa, and producer’s accuracy (PA) of appropriate acquisition times of images with their VIs and the gradient by the RF classifier. Figure 9: The classification results when only spectral bands are used versus spectral bands, along with VIs and their gradients are used: (**a**) overall accuracy (OA); and (**b**) kappa coefficient. As shown in Table 9 when only spectral bands are used, there are 24 features. This number is 51 when only VIs are used. If gradient of VIs and gradient of spectral bands are added, the number of features increase to 102. Processing time column in Table 9 shows that the addition of new features imposes a low-cost computation. From 27 combinations, three combinations which incorporate the minimum acceptable number of images such that differentiate classes of case 1 early in the season are selected for comparison. In this experiment, classification was first done using only a spectral band data of images. Then vegetation indices were added to the model alone as a new feature, and it was observed that, by creating these features, the overall accuracy and kappa coefficient were improved by 1.3% and 2.4%, respectively.