## 3 Results and Discussion
### Experiment 5: The Effect of VIs and Their Gradient
In the next step, in addition to the vegetation indices, the TGVI was added to the model as new features and it was observed that the overall accuracy and kappa coefficient were improved by 1.8% and 4.2%, respectively. In other words, the production of these new features increased the overall accuracy and kappa coefficient by 3.1% and 6.6% on average, respectively, compared to the conventional methods used to date. Most importantly, the barley producer's accuracy, which has been reported in the other researches so far [4; 26] and in the case of using only the spectral bands of images, showed a maximum around 70%, but using the proposed method and, in the case of using the optimized images, the separation capacity of barley from wheat and other crops was increased by 45.5%, reaching 92.5%. Figure 10 shows the classification map of the time series images of the studied area according to the optimal conditions in row 6 from Table 7.  
In contrast to Comb. 4, in Comb. 3 the TGVI and TGBS do not improve the PA of barley significantly. This is due to the similarity between wheat and barley in the early stages of growth. Therefore, the results demonstrated that the appropriate model is Comb. 6, which utilizes only one image from the first stage of the growing season and two images from the seasonal change point of wheat and barley. It is worth noting that compared to Comb. 3, the scheduled time decreases to 07-MAR-15 in Comb. 7 and yields better results in terms of OA and kappa when the temporal resolution increases to one week (i.e., two images of path 163 are used). In the random forest, in order to estimate the importance of the \(m\)th variable of tree k, by eliminating the relevant variable, the decrease of the degree of accuracy of the results is examined. Figure 10: The classification map of a part of study area. In other words, the greater the lack of a feature, the lower the mean accuracy, which indicates a high importance of that feature in decision-making. In this experiment, all 10 images with all produced features are included in all models and, for all the features, the variable importance was calculated. In Figure 11, 24 features with the highest effect have been shown. This means the feature of the \(i\)th image, and T\({}_{i}\)T\({}_{j}\) means the difference between the two \(i\)th and \(j\)th images. The results indicate that the TGVI of the two T6 and T7, and then TGVI between the T1 and T6 have the highest importance. In other words, T1, T6, and T7 images have the highest importance among the time series images. Another important point is that all of the important features shown in the Figure 11 are due to temporal gradients of VIs and their spectral gradients. Our results showed that using these new features will improve the performance of the model and the accuracy of the results. In addition, the ability to detect wheat from barley increases. Also, results showed that among the VIs and their gradients, the difference between the vegetation indexes STVI3, the subsequent EVI and MSAVI are the most important features. Additionally, overall accuracy and the kappa coefficient obtained from experiments 3-4, using different combinations of time series images and the analysis of variable importance in the random forest, showed that images at times T1, T6, and T7 have the highest importance in the time series images.