## 2 Materials and Methods
### Data Analysis  
Canopy structural properties derived from LiDAR data (H\({}_{\text{mean}}\) and CC), as well as MISR-HR BRFs and RPV products, were extracted using a regular 275 m spatial grid matching the MSIR-HR pixels. Only MISR pixels with full corresponding LiDAR coverage were considered. LiDAR and MISR-HR pixels which included 30% or more urban areas or cultivated fields were discarded using the 2013-2014 South African National Land-Cover (LC) map [84]. In addition, samples were filtered out when RPV values were retrieved with a high cost function value. The cost function value is the mathematical criterion that is minimized during the RPV model inversion procedure, and high values indicate poor data quality [53]. The differences in cost function values between the two sites most likely would result from varying environmental conditions which occurred during the two MISR orbits acquired one a year apart. Samples (i.e., MISR-HR data at pixel level) were removed from the two study sites when the cost value was larger than 40, across all the three RPV parameters and for all the bands. This threshold was selected through the assessment of the cost value histograms (Figure 3), considering published materials on the subject [85], and the necessary trade-off between a conservative threshold value for ensuring high RPV retrieval quality and maintaining a sufficient number of samples in the iSimangaliso Saint-Lucia site. The threshold used led to the removal of 131 pixels out of 6281 pixels for the Lowveld and 1000 pixels out of 2194 in iSimangaliso Saint-Lucia. We used the non-parametric Breiman-Cutler Random Forest (RF) algorithm [86] to model the relationship between structural LiDAR data and MISR data. Parametric models (e.g., multi-linear regression models) lack the capability to adequately characterize forest complexity and suffer from various limitations, such as the assumption of linearity, sensitivity to overfitting, or multicollinearity [87; 88]. Non-parametric models, Support Vector Machines [89], Artificial Neural Network [90] and Random Forest [91; 92], have gained popularity due to their ability to model complex non-linear and multidimensional data [93; 94]. RF is generally more robust to outliers and flexible in modelling relationships for large data sets with a large number of explanatory variables [91; 95; 96]. The Breiman-Cutler RF algorithm is built from bootstrap aggregation (bagging) and randomly selected subsets of explanatory variables, which create an ensemble classifier. RF regressions are easier to implement than optimally pruned decision trees, as they only require two user-defined inputs: 'ntree' which is the number of RF trees built in the forest and'mtry' which is the number of possible splitting variables for each of the nodes [95; 97]. The'mtry' was set to the square root of the number of variables [98] (i.e., MISR predictor variables for a given scenario). The 'ntree' was optimized by testing decreasing numbers of trees in steps of 100, starting with the default value of 500, and assessing the minimum mean square error (MSE) [98; 99]. This resulted in varying tree sizes per model, determined by the MSE. The models were implemented with the open source R software environment for statistical computing and graphics [100]. Training and test data were created via a 60/40% random split of the complete dataset and of the individual forest vegetation type. The performance of the models was assessed using the coefficient of determination (R\({}^{2}\)), the root mean squared error (RMSE) (Equation (5)), the relative root mean square error (rRMSE) (Equation (6)), the bias (Bias) (Equation (7)), and the relative bias (rBias) (Equation (8)). RMSE and rRMSE were used as estimates of error or accuracy. The rRMSE and rBias were expressed in percentages in the Equations (6) and (8) respectively.