In this research, measurement of the economic impact of sprinkling on the population was done through the preliminary estimate of additional costs due to the urbanization necessary for new settlements.
The estimate of the tangible costs that local administrations must bear due to this urbanization model was then related to the SPX index or, better, to the extent of its variation. For this, a regression model was used. The investigation was conducted on some municipalities in the Basilicata region. The time interval taken as reference was from 1950 to 2013.
To analyze the dynamics of sprinkling, together with the ISTAT data relating to the distribution of the population as of 2013, the following territorial data were acquired from the Regional Technical Map and from the Geo-Topographical Database of the geoportal of the Basilicata Region:
The above-mentioned data, downloaded in vector format, were subsequently processed and compared using the support of the open-source software QGIS.
3.1. Study Area
The data provided by the National Institute of STATtistics (ISTAT) [
41] between 1950 and 2013 relating to the entire region revealed a trend of an ever-decreasing population, mainly determined by migratory flows directed to other regions and by low birth rates. This decrease contrasted with the intense construction of new residential properties, which has recorded a constant percentage increase in the reference time interval (
Figure 1).
Figure 2 shows the map of Basilicata’s municipalities classified by the degree of fragmentation and resident population in 2013 based on the results of previous research [
24]. The municipalities analyzed in this work were also identified: Potenza, Matera, Melfi, Pisticci, and Lagonegro. An attempt was made to consider one municipality for each class of fragmentation without considering the low class of fragmentation in which very small municipalities are included.
The five municipalities were chosen considering the degree of fragmentation, the resident population, and the morphological characteristics of some territories that have certainly characterized the dynamics of transformation. Potenza, Matera, Melfi, and Pisticci are the first four municipalities in the region per resident population (over 16,000 inhabitants), while Lagonegro is among the municipalities with a population range between 2000 and 6000 inhabitants. For the class of high fragmentation, two municipalities—Matera, the main town of the province, and Pisticci—were chosen. This last municipality is interesting because it is a coastal municipality whose urban transformation is concentrated far from the main center and mainly for tourism purposes. For the medium–high fragmentation class, the municipality of Melfi was chosen, which, with about 17,000 inhabitants, is the third largest municipality in terms of population. The dynamics of transformation have been widely studied in other studies [
42]. For the class of average fragmentation, it was decided to analyze the municipality of Potenza, the regional capital and first city by number of inhabitants. The municipality of Lagonegro, which falls in the medium–low fragmentation class, was chosen for its morphological characteristics, its position in the south of the region, and its transformation dynamics that are almost stable over time.
Figure 3 shows the relationship between demographic trends and changes in urbanized areas over twenty years in the municipalities studied and for all the regional territory. Each symbol represents one of the five municipalities analyzed and the regional territory. The symbols in grey represent the variation between 1989 and 1990, while those in red represent the variation between 1990 and 2013.
In analyzing the graph, it can be observed that, overall, in the face of a decrease in population, in some cases even substantial, the urbanized area continued to increase. In the case of the municipality of Lagonegro, the one with the smallest population among the municipalities analyzed, in the first decade (1989–1998) a decrease in population of 2% corresponded to an increase in artificial surface area of 25%, which continued to increase in the second decade with an increase in artificial surface area of 31% and a further decrease in population of 7%. The same happened for the municipality of Pisticci: a decrease in population corresponded to an increase in artificial surface area. In the municipality of Potenza, in the first decade, a population increase of 5% corresponded to a 24% increase in artificial surface area, while in the second decade, a 14% increase in artificial surface area corresponded to a 3% decrease in population. For the other two municipalities, Melfi and Matera, a growth of the artificial surface corresponded to a demographic increase.
As already demonstrated in previous work [
24], the increase of artificial surface area in the region in the years considered has increased without a real demand for new residences. Moreover, the increase in artificial surface area was fragmented and affected the phenomenon of sprinkling.
3.2. Sprinkling Index and Cost Estimation
The sprinkling index defined by Romano et al. [
22] was used in this research to describe the dynamics of territorial transformation. Considering buildings aggregated in complex polygons at a predetermined distance (50 m according to [
24]), and dividing the municipal territory with a grid of 1 square km, the index measures the degree of fragmentation of each analyzed cell. The grid was set casually on the examined territory. The SPX index is a purely geometric measure that found its basis on the Euclidean distance between the different geometries (aggregated buildings) present in the cell and assumes that the most compact and sustainable form of urban growth is that of a circle. The SPX index is expressed by Equation (1):
where x
i and y
i are the coordinates of the centroid of the ith polygon of the urbanized areas that fall in the examined cell, and x* and y* are the coordinates of the centroid of the aggregate larger buildings present in each cell of the grid at the instant considered; R is the radius of the circular area of dimensions like those of the sum of the urbanized areas present in each cell.
The SPX can have a range of values from 0 to +∞: the higher the index value, the higher the degree of fragmentation of the territory. An SPX equal to zero represents an urban transformation that has occurred in an unfragmented and, therefore, compact way. It expresses the presence in a grid cell of a single aggregate that can occupy the whole cell, with a surface of 1 square km in this case, or has smaller dimensions.
The SPX index has been calculated for 1950 and 2013 for each cell of the considered municipality, and the gap between them was measured.
Figure 4 shows an example of the discretization of the territory of one of the municipalities analyzed and the values of the SPX index relating to each square of the grid.
In order to describe the transformation dynamics of the territory, the SPX index was divided into six classes of fragmentation from “not fragmented” to “high fragmentation”. The fragmentation classes are shown in
Table 1.
Comparing the SPX indices measured in 1950 and 2013 made it possible to detect the evolution of the phenomenon within each square of the grid.
Figure 5 and
Figure 6 show two examples that highlight the variation of the SPX index over time. The buildings in the two time phases analyzed (1950 and 2013) and the aggregates built around them are represented.
Figure 5 shows an example of a decrease in the SPX due to the increase in the size of the main aggregate present in 1950 following the construction of new buildings close to the existing ones. We define this urban transformation dynamic as compaction dynamics.
Figure 6 shows the opposite situation, which is an increase in the SPX index. In the cell from 1950 to 2013, the size of the existing aggregates increased, but new buildings were also built far away from them. This transformation dynamic is exactly that of sprinkling.
A sample of 57 cells belonging to the five municipalities was selected. These had undergone the greatest territorial transformations, i.e., the SPX index changed from 1950 to 2013. Of these cells, only those in which the SPX index increased were analyzed. An increase in the index corresponds, in fact, to an increase in fragmentation. The index increased for 15 cells, and the analyses carried out on these cells are illustrated below. To better clarify the choice, the regression analysis was also carried out on the meshes with negative ΔSPX (42) demonstrating in this case, as expected, that there is no statistically significant relationship between the variables taken into consideration.
In the regression model, the cost of linear infrastructures (roads, underground services, public lighting, etc.) per unit volume of building (cubic meters) was taken as a dependent variable, while the following were considered as independent predictors or variables:
the variation in sprinkling, defined by the difference,
the mean square deviation, S, of the elevation values (X) measured every 5 square meters within the reference mesh,
Index S is representative of the orographic complexity of the mesh. Meshes with strong variations in altitude have higher values of this parameter compared to almost flat meshes.
The idea behind the choice of this second predictive variable is that the orographic conformation of the single mesh affects the cost of infrastructure. A geomorphological conformation with greater elevation differences entails a certainly more complex road network layout, which obviously is reflected in the costs of this infrastructure.
To estimate the construction costs of the road infrastructure, all road sections within each mesh were identified, and for each of them, the type was identified and the length defined.
The length of each road section was determined approximately by placing it equal to its semiperimeter. Given the lack of information relating to the year of construction of the roads, by a comparison between the map of the residential buildings surveyed in 1950 and 2013 and a subsequent overlap with the road cartography, it was assumed that urban and local roads outside the inhabited centers (in 1950), different from those which were the main routes, had been built precisely in this interval to allow accessibility to the new construction. It was also hypothesized that any roads dating back to the year 1950 or earlier, serving buildings outside the existing urban perimeters, were mostly configured as sheep tracks made of clay. Therefore, although already existing, they have been considered in calculating the new infrastructures generated by sprinkling. As mentioned, extra-urban roads (main and secondary) and highways were excluded from the calculation.
For the definitions of the physical and geometric characteristics of the road superstructures of each type, the indications provided by the Road Paving Catalog drawn up by the CNR (National Research Center) were used. This catalog assigns the thicknesses to the different layers of the pavement according to the number of passages of commercial vehicles, the climatic conditions, and the type of substrate (which expresses their bearing capacity). Finally, quantities were determined to define the construction costs of the road sections, which defined the costs per linear meter for the different categories of roads (as described by the Highway Code), based on the items reported in the price list of the Basilicata region.
To estimate the average costs of water and sewage networks and public lighting systems, price lists known in the literature were used that define a detailed reference of parametric prices for various urbanization works.
Subsequently, the volumes of residential buildings built after 1950 were measured, calculating the product of the height per building area. Finally, the cost of urbanization was weighed on the volumes present in each mesh of the grid, and the costs per unit of volume were estimated.