## 2 Materials and Methods
### Data Analysis
The RMSE provides an estimate of modelling errors expressed in the original measurement units, and the rRMSE normalizes the RMSE according to the mean, allowing the comparison of models in which errors are measured in different units [101]. \[\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{n}\left(\hat{y}_{i}-y_{i}\ \right)^{2}}{n}} \tag{5}\]  
\[\text{rRMSE}=\frac{\text{RMSE}}{\overline{y}}\ \times 100 \tag{6}\]  
\[\text{Bias}=\ \frac{\sum_{i=1}^{n}\left(\hat{y}_{i}-y_{i}\ \right)}{n} \tag{7}\]  
Figure 3: Histogram of residual RPV cost function for the two study sites: (**a**) The Lowveld and (**b**)iSimangaliso study site. The COST function values are unit less. The dashed black line shows the threshold used to discard samples of expected poor quality. \[\text{rBias}=\ \frac{\text{Bias}}{\overline{y}}\times 100 \tag{8}\]  
where \(\hat{y}_{i}\) is the MISR estimated mean tree height or canopy cover, \(y_{i}\) is the LiDAR measured mean tree height or canopy cover, \(n\) is the number of observations and \(\overline{y}\) is the mean LiDAR measured tree height or canopy cover. An analysis of variance (ANOVA) was used to test for any statistical significance between the models by comparing the critical F-value and the F-statistics. It was reported with the subscript of F as the first and second degrees of freedom which gave us the critical F value. A number of scenarios were investigated to address the objectives of the study. The scenarios were based on different combinations of MISR-HR multi-spectral and multi-angular datasets, as well as the RPV anisotropic parameters. All the Lowveld samples were categorized as savanna vegetation. In the iSimangaliso St-Lucia site, the 2013-2014 Land Cover map mentioned in Section 3.4 was used to separate samples into indigenous forests and plantation forests. We analyzed the following scenarios:  
* Scenario 0: The baseline reference scenario was set up to establish the expected performance of a RF model using a traditional approach based on the red and NIR spectral bands similar to that provided by the nadir-viewing instruments such as the MODIS instrument. These two MISR-HR datasets bands (at 275 m) have a similar pixel size to that of MODIS dataset (i.e., 250 m). * Scenario 1: The first scenario considered all four spectral bands from the An (nadir) camera. This scenario was carried out to establish whether adding more spectral bands from the nadir-pointing cameras improves the predictive capacity of the RF model. * Scenario 2: This second scenario sought to evaluate if angular data is superior to spectral data for the retrieval of the forest parameters, or vice versa. We developed a set of four models; each including all view angles for a single spectral band (i.e., one RF model for each of the MISR bands and involving all 9 cameras). * Scenario 3: The third scenario assessed the RF model performance constrained by data in each view angle separately. It consisted of eight models including all spectral bands for each individual forward and aft viewing angle (i.e., off-nadir camera: Af, Bf, Cf, Df, Aa, Ba, Ca and Da). * Scenario 4: The fourth scenario was carried out to ascertain whether the combined use of all MISR angular and spectral data (i.e., the 36 MISR-HR BRF data channels) improves the forest structural parameter retrievals compared to any of the previous scenarios and if it does by how much. * Scenario 5: The fifth scenario assessed if the anisotropic BRF parameters provide additional benefits compared to the raw MISR-HR BRF data (scenario 4). Here, we tested four models, three models which assessed the performance of each individual RPV model parameter (\(\rho_{0},k,\Theta\)) considering all spectral bands, and one additional model combining all three RPV parameters for all spectral bands.