# Forage Biomass Estimation Using Sentinel-2 Imagery at High Latitudes
## 3 Results
### Multivariate Regressions  
Table 5 shows the results from the PLSR, SVR and RFR models. Overall, calibration accuracies were high, with mean \(NSE\) and \(RMSE\) ranging from 0.81 to 0.95 and 0.19 to 0.39 t ha\({}^{-1}\), respectively. However, for the validation, the accuracies decreased. Mean \(NSE\) ranged from 0.34 to 0.61, and mean \(RMSE\) increased to 0.58 to 0.75 t ha\({}^{-1}\). Evaluation underlined obvious model differences, as RFR performed better than PLSR and SVR (mean \(NSE\) and \(RMSE\) value of 0.86 and 0.26 t ha\({}^{-1}\)).  
For both calibration and validation, the SVR and RFR performed better than PLSR. The accuracy of SVR was slightly higher than RFR due to the relatively higher mean \(NSE\), but RFR performed more stably for calibration since standard deviation (\(SD\)) values were lower. When considering the evaluation dataset, RFR showed a better performance than PLSR and SVR, with higher \(NSE\) and less spread of values.  
Based on the calculations of the variable importance measures (%IncMSE and Inc-NodePurity) shown in Figure 4, the bands of near infrared (NIR) and red-edge and the related VIs (e.g., REDVI1, REDVI 2, NDRE1, TCI, CIre1) are the most important for the RFR analysis.  
Figure 5 shows the effect of running the model 300 times on the \(NSE\) of calibration, validation and evaluation. SVR and RFR show similar median values of validation \(NSE\) but the values were lower comparing to calibration, yet the majority of \(NSE\) values distributed from 0.4 to 0.8 suggest relatively comparable accuracies for SVR and RFR. In addition, the variation in \(NSE\) values intuitively indicates that RFR was more stable, especially for model calibration and evaluation, which is confirmed by the results shown in Table 5 (lower \(SD\) values for RF calibration).  
Figure 6 shows scatterplots of observed versus RFR-estimated \(DMY\), using a model with a calibration \(NSE\) value of 0.92 (Table 5), which was the average value of randomizing the samples and running the model 300 times (Table 5). The corresponding \(NSE\) values for validation and evaluation of the selected RFR model were 0.62 and 0.84, respectively. The distributions of scatterplot points showed that the effect from the BC on the selected RFR model was mild.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Indicator**} & \multicolumn{4}{c}{**Calibration (\(n=49\))**} & \multicolumn{4}{c}{**Validation (\(n=16\))**} & \multicolumn{4}{c}{**Evaluation (\(n=9\))**} \\  & **PLSR** & **RFR** & **SVR** & **PLSR** & **RFR** & **SVR** & **PLSR** & **RFR** & **SVR** \\ \hline \(NSE\) & 0.81 \(\pm\) 0.17 & 0.92 \(\pm\) 0.01 & 0.95 \(\pm\) 0.04 & 0.34 \(\pm\) 0.41 & 0.55 \(\pm\) 0.22 & 0.61 \(\pm\) 0.21 & 0.35 \(\pm\) 1.11 & 0.86 \(\pm\) 0.04 & 0.61 \(\pm\) 0.26 \\ \(RMSE\) & 0.39 \(\pm\) 0.17 & 0.27 \(\pm\) 0.03 & 0.19 \(\pm\) 0.11 & 0.75 \(\pm\) 0.21 & 0.63 \(\pm\) 0.17 & 0.58 \(\pm\) 0.17 & 0.49 \(\pm\) 0.31 & 0.26 \(\pm\) 0.03 & 0.43 \(\pm\) 0.14 \\ \hline \end{tabular}
\end{table}
Table 5: Statistical analysis results for the multivariate regressions, using methods from partial least square regression (PLSR), random forest regression (RFR) and support vector regression (SVR). The values show the statistical distribution (mean \(\pm\) standard deviation) of \(NSE\) and \(RMSE\) from running the model 300 times.  
Figure 4: Importance of predictor variables (individual bands and vegetation indices) according to the random forest regression analysis in explaining the dry matter yield (_DMY_). Descriptions of the individual bands and indices are given in Table 4.  
Figure 5: Variation in Nash–Sutcliffe efficiency (_NSE_) of running the models 300 times using partial least square regression (PLSR), random forest regression (RFR) and support vector machine-based regression (SVR). The horizontal lines in the boxplot show the first quartile, median and third quartile of _NSE_ values.