## 2 Materials and Methods
### Land Use Maps Comparison and Changes Detection  
Successive paired thematic maps of land uses were compared using the open-source software Map Comparison Kit (MCK) [37], developed by the Research Institute for Knowledge Systems (RIXS) in Maastricht, the Netherlands. To run the comparison with the MCK software, it was necessary to apply subsequent geoprocessing and conversion tools. Firstly, to ensure that the spatial extension of all the maps was exactly the same, the intersect operation was needed, which allowed for the creation of a new boundary polygon common \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Urban Growth**} & \multicolumn{2}{c}{**Metrics**} \\ \cline{2-4}
**Process** & **Acronym** & **Formulae** & **Description** \\ \hline \hline \multirow{8}{*}{Aggregation} & \multirow{3}{*}{NP} & \multirow{8}{*}{\(n_{i}\)} & NP \(\geq\) 1 \\  & & & The number of patches is a simple measure of the extent of subdivision or \\  & & & fragmentation of the patch type. \\  & & & 1 = the landscape contains only one patch of the corresponding patch type, \\  & & & when the class consists of a single patch. \\ \hline \hline \multicolumn{2}{c}{Area \(\geq\) 0} \\  & \multirow{3}{*}{AREA\_MN} & \multirow{3}{*}{\(a_{ij}\left(\frac{1}{10,000}\right)\)} & Area \(\geq\) 0 \\  & & & This is the mean of the patch size (AREA\_MN) at the class level. \\ \cline{3-5}  & & & A reduction in AREA at class level usually indicates increasing the \\ \cline{3-5}  & & & fragmentation of a land use/cover class. \\ \cline{3-5}  & & & 0 \(<\) PLAND \(\leq\) 100 \\  & PLAND & \(\frac{\sum_{i=1}^{n}a_{ij}}{\text{A}}(100)\) & The percentage of the landscape quantifies the proportional abundance of \\  & & & each patch type in the landscape. \\  & & & 0 = all patches of habitat disappeared; 100 = one habitat occupies \\  & & & all the landscape. \\ \hline \hline \multirow{8}{*}{Compaction} & \multirow{8}{*}{GYRATE\(\geq\) 0} \\  & & & GYRATE equals the mean distance between each cell in the patch and the patch type centroid. Radius of gyration is a measure of patch extent; thus, it \\ \cline{3-5}  & & \(\sum\limits_{r=1}^{n}\frac{h_{ij}}{z}\) & is effected by both patch size and patch compaction and can be considered \\ \cline{3-5}  & & & a measure of the average distance an organism can move within a patch \\ \cline{3-5}  & & & before encountering the patch boundary from a random starting point. \\ \cline{3-5}  & & & 0 = the patch consists of a single cell. The maximum values imply the \\ \cline{3-5}  & & & patch comprises the entire landscape. \\ \hline \hline \end{tabular}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{O-Limitless} \\  & & & This metric relates to the distance to the nearest patch of the same land \\  & & use/cover class. ENN equals the distance (m) to the nearest neighbouring \\  & & patch of the same type, based on shortest edge-to-edge distance. \\  & & & 0 = the distance to the nearest neighbour decreases. The upper limit is \\  & & & constrained by the extent of the landscape. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Detailed description of the set of metrics used. to all maps. The next step was the conversion of all the LU maps into TIFF raster images (rasterization), with a resolution of 20 m \(\times\) 20 m. Finally, the raster files were transformed into raster-ASCII files to be imported into the MCK software [9]. The comparison between paired maps using MCK was based on the cell-by-cell method [36]. In order to implement this basic information on the similarities/differences in maps, the more flexible Kappa statistic indicator was used [37; 38; 39]. In fact, this statistic method is able to synthesize information on the position (such as spatial correlation) and quantity of cells divided by categories for a more balanced measure of similarity. In the present work, the Kappa algorithm, based on cell-by-cell comparison, was used. It expresses the degree of similarity between two categorical datasets.