## 2 Materials and Methods
### Land Cover Classification
#### 2.3.7 Validation  
To validate the map, we created a confusion matrix and calculated Cohen's Kappa [69; 70; 71]. We also calculated the receiver operating characteristic (ROC) area under the curve (AUC) for our land-cover methods, which is sometimes used to demonstrate the accuracy of machine learning methods [72]. However, this metric assumes that grid contents are homogenous. Given that we are dealing with high-resolution data and land cover classes that are often not discrete, we also assessed the accuracy of our maps by calculating the root mean square error (\(RMSE\)) and a correlation coefficient (\(R^{2}\)) like land cover classification studies that use high-resolution images [73; 74; 75; 76].  
First, we generated a grid of \(60\times 60\) m squares. We randomly selected 15 squares on each island that overlapped areas where we had high-resolution images and control points but that did not overlap with the areas chosen for training the algorithm. This way, we maintained independent data sources for the geometry of the classified images and our reference polygons [69]. We created two versions of these areas, one to serve as the reference polygons and the other to serve as the prediction. We intersected the prediction polygons with the classified maps to extract the information corresponding to those areas. For the reference polygons, we cut them into sections that visually matched the high-resolution UAV images and the GPS control points, and we manually classified them.  
To characterize the effectiveness of our classification for estimating land cover fractions, we calculated the percentages of the polygons that were occupied by the different classes, and obtained a root mean square error (\(RMSE\)) and a correlation coefficient (\(R^{2}\)) for each island and for each class \(c\) using Equations (2) and (3) [73; 74; 75; 76], respectively:  
\[RMSE(c)=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\bigl{(}\hat{f}_{i,c}-f_{i,c}\bigr{)}^ {2}}, \tag{2}\]  
\[R^{2}{}_{c}=\frac{\sum_{i=1}^{N}\bigl{(}\hat{f}_{i,c}-\overline{f}_{c}\bigr{)} ^{2}}{\sum_{i=1}^{N}\bigl{(}\hat{f}_{i,c}-\overline{f_{c}}\bigr{)}^{2}} \tag{3}\]  
where \(\hat{f}_{i,c}\) is the predicted land cover fraction of class \(c\) for sample \(i\), \(f_{i,c}\) is the true land cover fraction of class \(c\) for sample \(i\), \(\overline{f_{c}}\) is the mean class \(c\) land cover fraction of the samples, and N is the total number of samples. If the predicted cover perfectly matched the reference cover, we would expect an \(R^{2}\) value of 1 and an \(RMSE\) of 0 for that class. The island-wide results were obtained by summing simultaneously over samples and classes in Equations (2) and (3).  
The AUC is a performance metric that estimates how well a model is able to distinguish between classes, typically ranging between 1 (perfect classification) and 0.5 (no predictive capability); values less than 0.5 are characteristic of a classifier that is anticorrelated with the true categories [77; 78]. The AUC only characterizes binary predictors, so we calculated the AUC values for each land cover category versus all other categories, using the same 60 reference polygons to evaluate our classification. An AUC value of 0.7 is usually determined as the threshold for usefulness in an application, while scores \(>\)0.9 denote high performance and are the most useful for classification [79].