# Sugarcane Yield Mapping Using High-Resolution Imagery Data and Machine Learning Technique
## 3 Results
### Accuracy Assessment  
Table 6 summarizes the relative error and the accuracy of the predictive models (MLR and RF) for different predictor variables and dataset. RF regression showed a better accuracy, according to the RMSE and R\({}^{2}\) values, for the testing dataset. Considering the test dataset, the RF regression had RMSE values ranging from 4.63 to 5.47 Mg ha\({}^{-1}\), which was lower than the MLR model (RMSE closer to 6.0 Mg ha\({}^{-1}\)). Other studies reported RF prediction as more accurate than MLR [2; 53].  
Generally, all VIs showed a similar level of accuracy for predicting sugarcane yield considering the test dataset with an RMSE of about 5.40 Mg ha\({}^{-1}\) (Table 6). The spectral bands were more effective (the highest R\({}^{2}\) and the lowest RMSE) in estimating sugarcane yield for both (RF and MLR) models. In other words, better results were found when using the spectral bands directly rather than calculating VIs (Table 6). This result should influence the computational processing of the orbital images because it is less time-consuming to determine spectral bands when compared to the normalization of the reflectance values.  
Figure 4 shows the comparison between the observed yield map of the 2018/2019 crop season (Figure 4A) and the predicted yield maps from spectral bands or using the NDRE (the best performing VI according to Table 6), based on either RF regression or MLR. These results corroborate with previous results regarding the better performance of spectral  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Season** & \(n\) & **Model** & **Range (m)** & **Sill** & **Nugget** & **RMSE (Mg ha\({}^{-1}\))** & **Calc. Grid** \\  & & & & & & **(Samples ha\({}^{-1}\))** \\ \hline
2018/2019 & 5616 & Exponential & 42.04 & 33.79 & 12.95 & 0.53 & 23 \\
2019/2020 & 5686 & Exponential & 49.30 & 23.54 & 5.19 & 1.41 & 16 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Fitted model and semi-variogram variables used to interpolate sugarcane yield data.  
bands and RF. Figure 4D,E represent MLR prediction considering NDRE and spectral bands, respectively, which showed less similarity with the real yield map (Figure 4A). Similar results were found for the 2019/2020 season (Figure 5).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Random Forest**} & \multicolumn{3}{c}{**Multiple Linear Regression**} \\ \hline
**Variables** & **Dataset** & **RMSE** & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) & **MAE** \\ \hline \multirow{3}{*}{Spectral bands} & Training & 1.95 & 0.96 & 1.42 & 6.10 & 0.48 & 4.73 \\  & Testing & 4.63 & 0.70 & 3.46 & 6.11 & 0.47 & 4.67 \\ \cline{1-1}  & Entire & 3.13 & 0.87 & 2.11 & 6.10 & 0.47 & 4.71 \\ \hline \multirow{3}{*}{GNDVI} & Training & 2.44 & 0.93 & 1.83 & 6.35 & 0.44 & 4.92 \\ \cline{1-1}  & Testing & 5.47 & 0.57 & 4.21 & 6.14 & 0.46 & 4.79 \\ \cline{1-1}  & Entire & 3.76 & 0.81 & 2.64 & 6.28 & 0.44 & 4.87 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Results of Random Forest and Multiple Linear Regression algorithms to predict the sugarcane yield.  
Figure 3: The most important variables in decreasing order according to the Mean Squared Error based on the Random Forest (RF) regression applied for the predictor variables: Spectral bands (**A**). Green Normalized Difference Vegetation Index—GNDVI (**B**). Normalized Difference Red-Edge—NDRE (**C**). Normalized Difference Vegetation Index—NDVI (**D**). Wide Dynamic Range Vegetation Index—WDRVI (**E**).  
Figure 4: Observed sugarcane yield of 2018/2019 season (**A**). Predictive yield models based on Random Forest (RF) using: NDRE (Normalized Difference Red Edge) (**B**) and spectral bands (**C**). Predictive yield models based on Multiple Linear Regression (MLR) using: NDRE (Normalized Difference Red Edge) (**D**) and spectral bands (**E**).