## 4 Discussion
### Factors Affecting the Accuracy of the Regression Models  
Our results indicate that soybean plant density can be estimated using PlanetScope imagery and climate data with acceptable accuracy. Overall, RF regression models outperformed PLS regression models (Table 3). Random forest has been reported as a superior  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Test Field**} & \multicolumn{3}{c}{**RMSE (plant m\({}^{-2}\))**} \\ \cline{2-4}  & **SR + NDVI-PLS** & **NDVI + Climate-RF** & **10 VarImp-RF** \\ \hline Field 2 & 1.60 & **1.38** & 1.49 \\ Field 3 & 2.46 & 2.43 & **2.28** \\ Field 8 & 3.06 & 1.90 & **1.82** \\ Field 9 & 1.49 & 1.39 & **1.38** \\ Field 11 & 1.84 & 1.93 & **1.74** \\ \hline \hline \end{tabular} The best models for each field are marked in bold.  
\end{table}
Table 4: RMSE values for individual fields using three different regression model (SR + NDVI-PLS; NDVI + Climate-RF; 10 VarImp-RF).  
Figure 11: Residual maps for **(a)** SR + NDVI-PLS; **(b)** NDVI + Climate-RF; and **(c)** 10 VarImp-RF models compared to actual plant density data derived from YOLOv3 model.  
regression model to PLS regression [32; 35; 36], which is consistent with our results. As indicated by the \(r^{2}\) and RMSE values in the RF models, the NDVI + Climate-RF and SR + NDVI were likely to have the best performance. The model performance significantly decreased when predicting the test data set as compared to training data set (Table 3). Data distribution differences between each observation field used in the training and test data set might have caused the different output accuracy of the models. In our data sets, each field had a unique data distribution, from low to high values of plant density, and the majority of the field had a low variance. Thus, data variance between the training and test fields might have become unbalanced. The details about descriptive statistics for each observation field is presented in Table S2. Completely random data split might be a solution to improve model performance. However, completely random data split might not be the appropriate way in our case, because we must examine not only the overall prediction accuracy but also the effect of observation year and within-field prediction accuracy.  
The different predictor combinations in the regression model development affected the accuracy of the estimation. The NDVI data used in the regression models might lead to underestimated plant densities in high population values. Previous studies [55; 56] reported that there were underestimated trends in estimating biomass using NDVI but only seen in high values of biomass. The NDVI had limitations in losing the sensitivity of the plant canopy when the leaf area index was greater than 3 m\({}^{2}\) m\({}^{-2}\)[57], which corresponds to a high plant density. According to [PERSON] and [PERSON] [58], this phenomenon is called NDVI saturation, which subsequently contributed to a reduced accuracy in estimating plant-related variables. Concerning another predictor, climate variables also contributed to the inconsistent output of the regression model, especially in PLS analysis (Figure 6d-f). This inconsistency might be due to the other environmental or edaphic factors that we did not consider in our models, even though the same pattern did not appear on the RF models, possibly due to the better capability of non-linear relationships.