False Composite Color

A false composite color was created by combining the green, red, and near infrared channels, the last being understood as the most suitable for discriminating vegetation cover [40]. The composite color of the images provides the ability to select the training areas necessary to perform supervised classifications based on visual interpretation of the images supported by GPS data [41,42].

### Determination of the Urban, Peri-Urban, and Rural Zones of the Port-au-Prince Agglomeration

To characterize the spatiotemporal dynamics of the different zones of the urban–rural gradient, the land cover was defined in urban, peri-urban, and rural zones according to the decision tree of the definitions of the zones present in the urban–rural gradient [11]. This decision tree, based on morphological characteristics, was preferred owing to its rapidity of execution, simplicity, and closeness to the ground reality, where there is a heterogeneous mix of land cover [6,43]. It should be noted that the urban zone is characterized by the dominance and continuity of the built-up area, which is otherwise dense. The peri-urban zone is characterized by the dominance of a discontinuous and less dense built-up area, while the dominance of vegetation indicates a rural zone [6,11].

The aforementioned decision tree was applied to map the different land cover (urban, peri-urban and rural) on each of the composite Landsat images by a supervised classification employing the maximum likelihood algorithm. This algorithm uses training sites to calculate the probability of each pixel belonging to one of the classes [44]. It should be noted that the urban zone is characterized by the dominance and continuity of the built-up area, which is otherwise dense. The peri-urban zone is characterized by the dominance of discontinuous and less dense built-up area, while the dominance of vegetation indicates a rural zone [6,11]. Thus, the training samples used for this classification were delineated through 219 fixed points acquired with a Garmin 66s GPS (accuracy 3 m) during November and December 2020. The classification accuracy was assessed using the Kappa coefficient

and the overall accuracy, based on the confusion matrix generated with 387 validation points. The Kappa coefficient provides a more accurate estimate (which takes into account well-classified pixels) of the quality of the classification. The overall classification accuracy represents the average of the percentages of correctly classified pixels. The percentage of landscape, which indicates the relative abundance of each urban–rural gradient zone, was calculated.

Qualification of the Port-au-Prince Agglomeration's Municipalities in Urban, Peri-Urban, and Rural Zones

Subsequently, the morphological status of the municipalities along the urban–rural gradient of the Port-au-Prince agglomeration was defined according to the proportions of the different zones (urban, peri-urban, and rural) resulting from the supervised classification of the urban–rural gradient zones from the Landsat image of 2021. If the proportion of the built-up area dominates the landscape, a distinction is drawn between the urban and the peri-urban: if the urban dominates, the area is urban and if the peri-urban dominates, the area is peri-urban. If the co-dominance of urban and peri-urban is less than rural, the area is recognized as rural. Finally, if the co-dominance of urban and peri-urban is higher than rural, the area is considered peri-urban [43].

Classification and Assessment of Land Cover Changes along the Urban–Rural Gradient Zones

Based on knowledge of morphological status, the municipalities of the Port-au-Prince agglomeration were grouped into urban, peri-urban, and rural zones. In each group of municipalities, the land cover dynamics from 1986 to 2021 were assessed based on a second supervised classification. For this reason, the following land cover types were defined: builtup and bare soil (built-up area, bare ground, road), field (mono- or multi-crop agricultural areas, agroforestry systems), woody vegetation (wooded savannah, forest, mangrove) and grassy vegetation (grass, young fallow land, pastures). A total of 206 fixed points and plots obtained from these different land cover types were used in the definition of training samples for supervised classification, based on the maximum likelihood algorithm [45]. Finally, a confusion matrix generated from 497 ground points was employed to verify the classification accuracy, based on the Kappa coefficient and the overall accuracy—two appropriate indices for verifying the reliability of a supervised classification [46].

To assess the impact of peri-urbanization on land cover changes along the urban–rural gradient, the proportion of land cover types in each type of municipality (urban, peri-urban, and rural) was calculated based on the patch area. This index often indicates human impact on landscape morphology [47]. It may provide information on the fragmentation of a land cover type between two periods, particularly through its decrease (Equation (1)).

Rate of land cover change (Rc):

$$\text{(Rc)} = \frac{(\text{UA}\_{\text{i}+\text{n}} - \text{UA}\_{\text{i}})}{\text{UA}\_{\text{i}}} \tag{1}$$

where UAi is the extent occupied by a class in the initial year of a period, n is the interval between two evaluated years, and UAi+n is the extent occupied by the same class in year i+n[48].
