Scrutinizing the Statistical Distribution of a Composite Index of Soil Degradation as a Measure of Early Desertification Risk in Advanced Economies

Using descriptive and inferential techniques together with simplified metrics derived from the ecological discipline, we offer a long-term investigation of the Environmental Sensitive Area Index (ESAI) as a proxy of land degradation vulnerability in Italy. This assessment was specifically carried out on a decadal scale from 1960 to 2020 at the province (NUTS-3 sensu Eurostat) level and benefited from a short-term forecast for 2030, based on four simplified assumptions grounded on a purely deterministic (‘what … if’) approach. The spatial distribution of the ESAI was investigated at each observation year (1960, 1970, 1980, 1990, 2000, 2010, 2020, 2030) calculating descriptive statistics (central tendency, variability, and distribution shape), deviation from normality, and the increase (or decrease) in diversification in the index scores. Based on nearly 300 thousand observations all over Italy, provinces were considered representative spatial units because they include a relatively broad number of ESAI measures. Assuming a large sample size as a pre-requisite for the stable distribution of the most relevant moments of any statistical distribution—because of the convergence law underlying the central limit theorem—we found that the ESAI scores have increased significantly over time in both central values (i.e., means or medians) and variability across the central tendency (i.e., coefficient of variation). Additionally, ecological metrics reflecting diversification trends in the vulnerability scores delineated a latent shift toward a less diversified (statistical) distribution with a concentration of the observed values toward the highest ESAI scores—possibly reflecting a net increase in the level of soil degradation, at least in some areas. Multiple exploratory techniques (namely, a Principal Component Analysis and a two-way hierarchical clustering) were run on the two-way (data) matrix including distributional metrics (by columns) and temporal observations (by rows). The empirical findings of these techniques delineate the consolidation of worse predisposing conditions to soil degradation in recent times, as reflected in a sudden increase in the ESAI scores—both average and maximum values. These trends underline latent environmental dynamics leading to an early desertification risk, thus representing a valid predictive tool both in the present conditions and in future scenarios. A comprehensive scrutiny of past, present, and future trends in the ESAI scores