*3.4. Comparison of Machine Learning Algorithms for Estimating Wheat Yield Using Multisource Data*

The results presented in the previous section indicate that the best results were consistently obtained using the information from Day 1-2-3. Having determined the optimal date combination, the next objective was to determine which algorithm achieved the best results for it. For this purpose, the RMSE and rRMSE were used. To capture the variability of each algorithm more accurately, the authors trained and validated each algorithm 10 times using different partitions of three datasets (S1, S2, and S1S2), resulting in 30 RMSE and rRMSE values for each algorithm (Table 2).

**Table 2.** Mean values of RMSE, SD and rRMSE of the four algorithms (MLR, Multiple Linear Model; RF, Random Forest; SVM, Support Vector Machine; CatBoost). Three different datasets were employed: S1 using only data from S1, S2 using data only from S2 and S1S2 using data from S1 and S2.


\* Each algorithm was trained and tested with ten different partitions of each dataset (S1, S2 and S1S2).

Table 2 shows the statistics associated to the prediction error obtained after running each algorithm 10 times with each of the three datasets (S1, S2 and S12). CatBoost produced the lowest error with an RMSE of 0.41 t ha-1 and a mean rRMSE of 5.91%. The SD of the RMSE for CatBoost was 0.29, the lowest among the four models. CatBoost not only produced results that were closest to the actual data, but also had less variability in the results compared to the other algorithms. RF and SVM performed similarly, with an average RMSE of 0.69 and 0.62 t ha−1, respectively. The values of rRMSE were 9.78% and 8.92% (Table 2). The SD for both was nearly the same, 0.35 for RF and 0.34 for SVM. Finally, MLR produces the highest mean RMSE of 1.1 t ha<sup>−</sup>1, with a mean rRMSE of 15.25% and an SD of 0.77.

After determining that CatBoost was the algorithm with the lowest RMSE and rRMSE among the four evaluated algorithms, the subsequent step involved evaluating the performance of CatBoost with each dataset (S1, S2, and S1S2). To this end, CatBoost was trained and tested with each of the three datasets 10 times with different partitions of data to train and test. The results presented in Figure 6 show that the RMSE varied depending on the dataset used for yield estimation. The use of the S1S2 dataset produced the lowest error, with a mean RMSE of 0.24 t ha−1, which is an rRMSE of 3.46%. The RMSE values ranged between 0.22 and 0.26 t ha−1. The mean RMSE obtained with S2 was 0.34 t ha−<sup>1</sup> and the rRMSE was 4.86%. RMSE values ranged from 0.30 to 0.37 t ha−<sup>1</sup> (Figure 6). Finally, the highest RMSE values were obtained when using only S1 data, with a mean RMSE of 0.79 t ha−<sup>1</sup> and values ranging from 0.55 to 0.83 t ha−1. The rRMSE for the S1 dataset was 11.34%. Therefore, the use of combined S1 and S2 (S1S2) data reduced the error by 30%

compared to using S2 data alone. Figure 7 presents the comparison of the predicted values versus the real values using CatBoost with S1S2. The R2 value was 0.95.

**Figure 6.** RMSE obtained using the CatBoost algorithm with data from S1 (Sentinel-1), S2 (Sentinel-2), and the combination of both (Sentinel-1 and Sentinel-2).

**Figure 7.** Linear regression between observed and predicted wheat grain yield for the test dataset obtained using the CatBoost algorithm and the S1S2 dataset.
