**4. Results**

The mean (sd) of the RCF for the calibration data of corn, wheat and soybean were 17.8 (9.6), 20.1 (11.2) and 19.2 (7.7)%, respectively (Figure 2). These values were 17.4 (9.4), 18.2 (10.3) and 18.6 (8.5)% for validation data, respectively. The RCF means and sd values based on the calibration and validation datasets were close to each other. The highest frequency of calibration data for corn, wheat and soybean crops was in the 10.9–18.3, 10.5–17.3 and 17.4–23.4% categories, respectively. For validation data, the highest frequency for these products was in the 12.2–18.4, 11.1–16.6 and 18.8–25.0% categories, respectively.

The efficiency of spectral indices based on reflective bands in RCF modeling was different. The efficiency of NDI5, NDI7, NDTI, NDVI, STI, DFI and BAI was higher than other indices, such as 3BI1, 3BI2, MCRC, NDSVI, SGNDI, and SRNDI (Table 2). The R2 between BAI and corn, wheat and soybean residues were 0.63, 0.66 and 0.61, respectively, which was higher than other spectral indices. The R<sup>2</sup> between the VV (VH) bands and the corn, wheat and soybean residues were 0.25 (0.29), 0.28 (0.36) and 0.20 (0.25), respectively. The efficiency of radar bands in RCF modeling was less than the spectral indices.

In the first scenario (dataset including reflective band-based spectral indices), based on calibration data, the R<sup>2</sup> (RMSE) between the actual and modeled RCF using ANN, RFR, SVR and PLSR algorithms for corn crop were 0.86 (3.13), 0.91 (2.63), 0.82 (3.92) and 0.79 (4.22%), respectively (Figure 3). These values were 0.84 (4.22), 0.88 (3.72), 0.81 (5.25) and 0.77 (5.85%) for wheat and 0.85 (3.14), 0.89 (2.73), 0.79 (3.81) and 0.75 (4.04%), respectively,

for soybean. The efficiency of RCF modeling using different machine learning algorithms based on spectral indices was different. The RFR and PLSR algorithms had the highest and lowest accuracy in forming an optimal network for RCF modeling, respectively.

**Figure 2.** Frequency distribution of RCF values of corn, wheat and soybean crops for calibration and validation data in different classes.

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**Table 2.** The R<sup>2</sup> between the effective variables and the residues for different crops.

**Figure 3.** R<sup>2</sup> and RMSE between real and modeled RCF based on calibration data.

For the validation data, the R<sup>2</sup> (RMSE) between the actual and modeled RCF based on ANN, RFR, SVR and PLSR algorithms for corn were 0.83 (3.89), 0.86 (3.25), 0.76 (4.56) and 0.75 (4.81%) (Figure 4). These values were 0.81 (4.86), 0.85 (4.22), 0.78 (5.45) and 0.74 (6.20%) for wheat and 0.81 (3.96), 0.83 (3.38), 0.76 (5.01) and 0.72 (5.65%), respectively, for soybean. The results showed that the RFR algorithm had the highest accuracy in RCF modeling. The efficiency of this algorithm in corn RCF modeling was higher than soybean and wheat.

**Figure 4.** R<sup>2</sup> and RMSE between actual and model RCF based on validation data.

The addition of radar bands to the spectral indices dataset in the corn RCF modeling, caused an increase in the accuracy of RCF estimation using machine learning algorithms (Table 3). Considering the radar bands, the RMSE of corn RCF modeling using ANN, RFR, SVR and PLSR decreased by 0.44, 0.57, 0.54 and 0.30%, respectively. The reduction rates of RMSE for wheat (soybean) were 0.71 (0.37), 0.61 (0.49), 0.55 (0.51) and 0.38 (0.64), respectively.

**Table 3.** R<sup>2</sup> (RMSE) between the actual and modeled values of the RCF based on different machine learning algorithms, considering spectral indices and radar bands as dependent variables.


The R2 between the actual and modeled RCF based on the fusion strategy at the decision level for corn, wheat and soybean crops was 0.92, 0.89 and 0.88, respectively (Figure 5). RMSE values were 1.78, 2.65 and 1.90%, respectively. The error of estimating the RCF of corn, wheat and soybean products based on the proposed strategy was reduced by 0.90, 0.96 and 0.99%, respectively, compared to the results of the best machine learning algorithm.

The RCF map of corn, wheat and soybean crops prepared based on the fusion strategy at the decision level showed that the spatial distribution of the residue varied across the study area (Figure 6). The RCF of three crops varied between 0 and 62%. The RCF of corn on farms located in the eastern parts of the study area was less than the western part. Corn fields located in the northwestern parts of the study area had the highest values of residue. The lowest values of soybean RCF were in farms located in the central parts of the study area. The number of wheat fields in the study area was less than corn and soybean fields. The number of wheat fields with low RCF was lower than wheat fields with high RCF.

**Figure 5.** R<sup>2</sup> and RMSE between the actual and modeled RCF based on the fusion strategy at the decision level for corn, wheat and soybean crops. ORCF: observed residual cover fraction; MRCF: modeled residual cover fraction.

**Figure 6.** RCF maps for different land crop in the study area.

The mean RCF for corn, wheat and soybean crops in the study area were 18.2%, 19.39% and 17.7%, respectively (Figure 7). RCF was higher in wheat fields than in corn and soybean fields. The values of the standard deviation (Sd) of the RCF for corn, wheat and soybean fields in the study area were 8.3%, 10.23% and 7.4%, respectively. The highest and lowest variation of RCF in this study area was related to wheat and soybean crops. The range of variation in the RCF amount for corn fields as greater than wheat and corn crops.

**Figure 7.** Frequency histogram and statistical parameters of the modeled RCF values of corn, wheat and soybean crops in the study area based on the proposed strategy.
