Roughness and intermittency within metropolitan regions - Application in three French conurbations

Even though the past three decades have seen numerous crucial investigations on interurban scaling characteristics, there has been less focus on revealing multiscale properties within municipal or metropolitan structures. We demonstrate how a newly developed methodology, the Geographically Weighted Multiscale Analysis (GWMSA) stemming from the theory of multifractal systems, can be used to analyze small-scale urban environments with respect to their intermittency and roughness simultaneously. To this end, apart from the widely used sand-box method, we introduce wavelet coefficients in the multiscale analysis of urban systems. In more detail, the spatially continuous scanning of the three largest French conurbations—Paris, Marseille, and Lyon—over their territories and at length scales ranging from parcel to neighborhood level will allow to derive and compare globally and locally characteristic scaling exponents. Depending on the feature under analysis, the exponents reveal qualitatively distinct structural properties, whereby the viability of our findings is further verified on four exemplary typologies of multiscale behavior in urban systems. To introduce GWMSA, this paper focuses primarily on morphological characteristics and findings provide a compelling alternative to how we capture and define district-scale spatial organization and interdependencies within urban settlements.