## 4 Discussion  
Sensor fusion can provide opportunities for capturing long-term monthly CW vegetation dynamics by creating spatially and temporally near-seamless observation records. The major hindrance to multi-sensor fusion is inconsistency between coincident images from each sensor and it is important to consider sensors that are compatible in terms of spectral and spatial characteristics. L8 and S2A have demonstrated potential for synergistic use that can capture the monthly dynamics of coastal areas. L8 and S2A data represent the most widely accessible moderate resolution multispectral satellite measurements. ASTER is another moderate resolution sensor that has similar spatial and spectral characteristics and was successfully used synergistically with previous generations of Landsat [80]. While multi-sensor NDVI data provide different views of earth surface, it is important to account for the sensor differences and ensure that the final products are aligned across all relevant dimensions prior to fusion. Otherwise, the uncorrected NDVI variances will introduce spurious noise into the fusion results [20]. The virtual constellation model presented here explicitly addresses this issue by adjusting each complementary sensor separately and fusing them hierarchically (S2A followed by ASTER). The current study provides a quantitative assessment of how the use of a virtual constellation, rather than relying on a single sensor, can advance the science of developing long-term, accurate, and seamless NDVI. It uses the properties of RF to model the relationship between a labeled outcome (NDVI) and the features used to predict it. Inclusion of coordinate location into the predictor set enables the model to estimate an appropriate value considering its neighboring pixels as well as a historically reasonable value for that location. Although, this renders the model specific to locations within the spatial reference system and units used here (UTM Zone 16 North, WGS 1984). Additionally, the inclusion of month only (encoded as an integer from 1 to 12) instead of both month and year enhances the model's robustness to seasonality without overfitting to annual scale non-stationarity. Another reason for the selection of RF as the prediction interface between L8 and its supplemental sensors S2A and ASTER is its ability to estimate prediction error and feature importance simultaneously with model training and testing. This information can effectively guide researchers toward feature inclusion or exclusion as well as tuning the hyperparameters of the RF (number of features to split on and maximum depth). Table 4 shows the feature importance which is indicative of how useful each feature is in the construction of each RF decision trees used in virtual constellation for this study [81]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Synthetic Cloud Cover** & \(R^{2}\) & **RMSE** & \(p\)**-Value** \\ \hline
10\% & 0.8129 & 0.009648 & \textless{}0.05 \\
20\% & 0.8146 & 0.009669 & \textless{}0.05 \\
30\% & 0.8127 & 0.009490 & \textless{}0.05 \\
40\% & 0.8356 & 0.009557 & \textless{}0.05 \\
50\% & 0.8246 & 0.009474 & \textless{}0.05 \\
60\% & 0.8179 & 0.009457 & \textless{}0.05 \\
70\% & 0.8113 & 0.009548 & \textless{}0.05 \\
80\% & 0.8403 & 0.009457 & \textless{}0.05 \\
90\% & 0.8155 & 0.009546 & \textless{}0.05 \\
100\% & 0.8193 & 0.009581 & \textless{}0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Sensitivity of virtual constellation performance to cloud cover in base image for January 2016. As shown in Table 4, the complementary sensor NDVI is the most important feature followed by position (Northing, Easting). The month contributes much less to the estimation, accounting for only 1.4 and 2.4% of the feature importance in the ASTER and S2A models, respectively. It is likely that the month adds a final layer of spatio-historical memory to the overall prediction, but perhaps it is replicating information already known to the model as a result of the complementary sensor NDVI.