*3.5. Contribution of the Variables to the Defintive Algorithm*

Figure 8 shows the 10 variables that made the greatest contribution to the CatBoost model, explaining 43.05% of the total variability. Of the 45 variables used (13 VIs and two backscatter variables for each day), the VV polarization variable (VV\_Day2) derived from S1 and corresponding to April 20 (Day 2; GS39-49) contributed most to the model, with 6.69% of the explained variability. The second highest contributor was the GRVI\_Day2 variable, which explained 5.47% of the variability. This variable, derived from S2, corresponds to April 23. The VH\_Day1 variable, as shown in Figure 8, explained 2.99% of the total variability.

**Figure 8.** The 10 variables from S1 and S2 that most contributed to the model.

The analysis of the variables derived from S2 revealed a predominance of those obtained on Day 2 (April 20, GS39-49). However, there was also a representation of those from Day 3 (June 5, GS69-75), such as RVI. It is notable that the CVI variable is the only VI represented on two different days. With respect to the variables derived from S1, those corresponding to Day 2 explained more variability. However, in contrast to those derived from S2, in the case of S1 Day 1 (GS30) variables explained more variability than Day 3 (GS69-75) variables. Although the acquisition date is deemed more pertinent, polarization holds significance due to the greater explanatory power of the VV variables compared to the VH variables.

#### *3.6. The Ability of CatBoost to Predict Yield of Entire Plots Using Data from Other Plots*

In this section, the study aimed to evaluate the ability of CatBoost to predict the yield of an entire plot using information from other plots. Figure 9 shows that the mean %MAE was 4.38, which is below the acceptable error of 10%. However, plots G1 and G20 exceeded the 10% MAE threshold (Figure 9). To visually represent the difference between the actual and predicted yield values, G15 was selected.

Each dataset (measured and estimated yield data) was classified into two different classes using the ISODATA algorithm, which automatically set the optimal threshold for classification. The threshold for the measured data was set at 5.17 t ha−1, while for the estimated data, it was set at 5.23 t ha−1. To compare the agreement between the two classified maps, the accuracy and KI metrics were used. The accuracy was found to be 91.4%, while the KI was 0.77 (Figure 10). The accuracy and KI metrics show that the two classified maps are similar, indicating that the estimated map has retained the spatial variability of the original data. For G15 plot, the model predicted an average yield error of 0.190 t ha<sup>−</sup>1, which is less than the maximum established error.

**Figure 10.** On the left, the classified wheat yield map of plot G15 (6.97 ha). On the right, classified wheat yield map based on the yield data estimated using the CatBoost algorithm with the S1S2 dataset for Days 1–3. The areas with low production are depicted in red, whereas those with high production are shown in blue. The accuracy and KI metrics were used to compare the two maps.

#### **4. Discussion**

*4.1. Inclusion of Sentinel-1 and Sentinel-2 in the Yield Estimation Model*

In this study, an analysis was conducted to examine the impact of incorporating multiple variables derived from S2 bands (VIs) and S1 backscatter information with VV and VH polarization obtained from various dates on yield prediction. The results revealed a consistent pattern in which the most favorable outcomes were consistently achieved when utilizing data from all three specified dates that corresponded to the GS30, GS39-49, and GS69-75 phenological stages.

In this study, the results obtained from VIs were consistent with those reported in prior research by Hunt et al. [29], since the inclusion of data from various dates improved model accuracy. In their study, the RF model was tested using VIs obtained from December to July, and the best results were obtained when using the VIs from all months together. According to the literature, the best grain yield estimation results are typically obtained after the end of the stem elongation phase (>GS39) [91,92], with the strongest relationship occurring during the anthesis or milky grain phase [93]. However, the analysis of VI information using data from only one day revealed that the optimal results were obtained using data corresponding to Day 2 (GS39-49) (Figure 3), which corresponds to the period from the end of stem elongation until the first awns' visible growth stage (24 April). This correlation was slightly higher than that achieved with data from Day 3 when wheat is between

complete anthesis and medium milk phase GS69-75 (5 June). Despite the moderate to high collinearity among the VIs on the three dates (Figure 3), the results presented in Section 3.1 suggest that it is beneficial to use all the indices and multiple dates to obtain the best results. Furthermore, it is evident that the use of any model is superior to the use of only one index when predicting wheat yield.

Hunt et al. [29] found that the greatest improvement in the model occurred between December and April for wheat fields in the UK, with the improvement thereafter being less significant. In this study, the mean correlation coefficient between VI and yield on Day 1 (GS30) was 0.36, while on Day 2 (GS39-49), it increased to 0.78 (Figure 3). Additionally, other authors such as Segarra et al. [35] have reported that the best results (R2 = 0.89) were obtained with the leaf area index (LAI) corresponding to the stem elongation/heading stage, and the results with VIs were similar (R2 = 0.88). This is not surprising since LAI and some VIs are related [69]. Correlation between grain yield and VIs and LAI at this phase is logical since the phases encompassing stem elongation to ear growth phases are crucial in the vegetative growth of wheat [94] and greatly determine the final grain yield. The models demonstrated a high degree of efficiency in their ability to estimate yield at the end of April (GS39-49). Although it may be late to make decisions that improve yield in rainfed conditions, it could be useful for the planning of future fertilizer decisions within the framework of precision fertilization.

Analysis of the S1 backscatter information revealed that the best results were obtained using data from Day 2, corresponding to 20 April. However, in contrast to the results obtained with S2, the data from Day 1 explained more variability than Day 3 data (as seen in Figure 5). Previous research has reported a positive correlation between wheat yield and the backscattering coefficient from S1 [95]. This correlation can be attributed to the fact that backscattering is sensitive to changes in crop growth, biomass, and soil water content, all crucial factors in determining wheat yield [96]. In the early growth stages, stronger correlations were reported when backscatter information was used [96]. During these stages, the crop is more sensitive to variations in water and nutrient availability [97], and variations in backscattering can indicate crop health and potential yield. Furthermore, the correlation between the backscattering coefficient and wheat yield is more robust in areas where wheat is grown in monoculture. This is because the crop canopy in monoculture is more homogenous, and the backscattering signal can be more directly linked to crop growth and yield.

For the three S1 images, the VV polarization was found to contribute more to the model, in contrast to the results reported by Mandal et al. [98] who found higher correlations with VH polarization. The reason behind this is that VH polarization is more sensitive to changes in surface roughness, which is an indicator of crop growth, whereas VV polarization captures better changes in soil water content and soil moisture [99]. This seems to indicate that soil water content in the crop early stages affects the final yield in a relevant way. It is noteworthy that the correlation between backscattering and wheat yield is not simple, thus it is understandable that a higher R<sup>2</sup> value was obtained when using S2 data than S1 (Figures 4 and 5).
