Investigating metropolitan change through mathematical morphology and a dynamic factor analysis of structural and functional land-use indicators.

We presented an operational rationale grounded on complex system thinking to quantify structural and functional landscape transformations along three stages representative of post-war metropolitan development in Rome, Italy (urbanisation with population/settlement densification, 1949-1974; suburbanisation with medium-density settlement expansion, 1974-1999; counter-urbanisation with settlement sprawl, 1999-2016). A mathematical morphology approach assessing the geometric form of land patches and a multi-way factor analysis (MFA) of landscape metrics were used to investigate the joint evolution of urban form and land-use functions over time. The empirical results of the MFA delineated the multivariate relationship between nine land-use classes (with distinctive socioeconomic functions) and seven morphological types (reflecting different landscape structures) according to four observation times (1949, 1974, 1999, 2016). Taken as an intrinsic attribute of complex landscape systems experiencing intense transformations, an estimation of the 'rapidity-of-change' in the form-functions relationship at a given development stage was derived from MFA outcomes separately for urbanisation, suburbanisation, and counter-urbanisation. A simplified form-functions relationship, reflecting the spatial polarisation in compact settlements and rural (low-density) landscapes, was observed with compact urbanisation. By stimulating urban sprawl into fringe farmland, suburbanisation resulted in patchy and heterogeneous rural landscapes. Counter-urbanization was associated with the fragmentation of built-up settlements leading to a chaotic mosaic of land structures that mixes urban and rural traits. Rapidity-of-change in form-function relationships was greater during suburbanisation than urbanisation and counter-urbanisation. It reflects the intrinsic pressure of economic growth in contemporary cities.