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

Abstract

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.

Stochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in Fourier and wavelet space

“…This paves the way for two-dimensional reconstructions, e.g. of urban rent price fields [61,62] where it would be highly interesting to investigate local intermittency properties on the basis of the methodology outlined in [63]. In terms of a three-dimensional synthetic wind field, the model must also respect the divergence-free condition and offer the possibility for anisotropic energy spectra.…”

A Python package for the local multiscale analysis of spatial point processes (LomPy)

“…Therefore, wavelets (equations S2, S4, S5) are widely recognized as beneficial for the analysis of non-stationary signals (Lee and Yamamoto 1994) compared to, for example, sandbox coefficients (equations S1, S3). For their advantages in the context of urban analytics, see also Lengyel et al (2023b).…”

“…draws on a recently developed framework for multiscale analysis in geographical contexts (Lengyel et al 2022, 2023b; Sémécurbe et al, 2016). It perceives urban data as a marked point process, with the spatial distribution referred to as support and any attached quantity as mark .…”

“…The typical representation consists of a set of scaling exponents that characterize how certain statistical properties remain invariant under scaling. The extracted features can be used, for example, to characterize urban form (Batty and Longley, 1987; Lengyel et al, 2023b; Murcio et al, 2015; Sémécurbe et al, 2016), identify urban boundaries (Chen 2016), reveal spatial inequalities (Hu et al, 2012; Lengyel et al, 2022), or to detect self-similar and multifractal cross-correlations (Jaffard et al, 2019a, 2019b) in a multivariate setting. They can also be further integrated into spatial clustering techniques.…”

Local multifractality in urban systems—the case study of housing prices in the greater Paris region

“…Secondly, we define a local environment T > r max (r max being the largest observed ball of radius r) which is the length scale within which we compute estimations using grid locations g(x g , y g ) as focal points. The value of T is both dependent on the spatial distribution of the data as well as on the desired resolution for the analysis [59], we also refer the reader to the performance assessment part of this section. Let L(e, r) henceforth stand for both multi-resolution quantities: N(e, r) of the support and I(e, r) of the mark.…”