Fixed-mass multifractal analysis of river networks and braided channels

Bartolo, Samuele De; Primavera, Leonardo; Gaudio, Roberto; D’Ippolito, Antonino; Veltri, Massimo

doi:10.1103/physreve.74.026101

Cited by 20 publications

(19 citation statements)

References 27 publications

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“…It is important to highlight that the interpretation of the results provided so far is in perfect agreement with the results obtained by De Bartolo, Primavera, et al (), in the context of the characterization of multifractal spectra related to streams of different Horton‐Strahler orders, the network for which has been extracted from digitized maps on a 1:25,000 scale.…”

Section: Resultssupporting

confidence: 86%

“…Besides these traditional approaches, the multifractal measures have been characterized by considering the distribution of points defining the geometry of a generic set on a fractal or multifractal support (see, e.g., Harte, ; Olsen, ). Following these ideas, De Bartolo et al () and De Bartolo, Primavera, et al () applied multifractal techniques to analyze the geometry of the river networks. These studies demonstrated that the characterization of fluvial structures by net − points and specifically their measure (see next section) can be considered as a fluvial geomorphological magnitude like the other ones mentioned previously.…”

Section: Methodsmentioning

confidence: 99%

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Hydraulic Characterization of River Networks Based on Flow Patterns Simulated by 2‐D Shallow Water Modeling: Scaling Properties, Multifractal Interpretation, and Perspectives for Channel Heads Detection

Costabile

Costanzo

Bartolo

et al. 2019

Water Resources Research

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This paper is focused on the contribution that the two‐dimensional Shallow Water Equations could provide in respect to the fields of research devoted to the river networks analysis. The novelty introduced in this work is represented, in particular, by the hydraulic characterization of the river drainage networks, starting from flow patterns simulated by the two‐dimensional Shallow Water Equations on high‐resolution digital elevation model (DEM) through the analysis of water depths flowing down the hillslopes, channelized in both the main river and in all the tributaries or stored in small depressions. The first finding of this research is the determination of scaling laws that describe the relations between the water depth threshold, used to identify the network cells, and a dimensionless area, related to the total area of the network cells themselves. The observed bimodal scaling behavior has been considered as representative of the flow patterns belonging to the channel networks (CN) and hillslope plus channel networks (HCN), the physical and geomorphological interpretation of which has been provided from a multifractal point of view. In particular, the analysis of the multifractal spectra highlights significant variations in the multifractal signatures, between the CN and the HCN structures, leading to the proposal of a novel criterion for channels heads detection that has provided encouraging predictions of field observations.

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Section: Resultssupporting

confidence: 86%

Section: Methodsmentioning

confidence: 99%

Hydraulic Characterization of River Networks Based on Flow Patterns Simulated by 2‐D Shallow Water Modeling: Scaling Properties, Multifractal Interpretation, and Perspectives for Channel Heads Detection

Costabile

Costanzo

Bartolo

et al. 2019

Water Resources Research

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“…The investigation includes analysis of the sewer network geometry and distribution of imperviousness derived from available GIS data, including the way in which it is represented in operational semi-distributed hydrodynamic urban drainage models. In order to be able to use the same technique to analyse both sewer networks and maps of distributed imperviousness, we use fractal tools on them, and not multifractal ones such as the one found in De Bartolo et al (2004Bartolo et al ( , 2006 for river networks. Multifractals will be used in the characterization of the representation of imperviousness in models.…”

Section: Introductionmentioning

confidence: 99%

Fractal analysis of urban catchments and their representation in semi-distributed models: imperviousness and sewer system

Gires

Tchiguirinskaia

Schertzer

et al. 2017

Hydrol. Earth Syst. Sci.

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Abstract. Fractal analysis relies on scale invariance and the concept of fractal dimension enables one to characterize and quantify the space filled by a geometrical set exhibiting complex and tortuous patterns. Fractal tools have been widely used in hydrology but seldom in the specific context of urban hydrology. In this paper, fractal tools are used to analyse surface and sewer data from 10 urban or peri-urban catchments located in five European countries. The aim was to characterize urban catchment properties accounting for the complexity and inhomogeneity typical of urban water systems. Sewer system density and imperviousness (roads or buildings), represented in rasterized maps of 2 m × 2 m pixels, were analysed to quantify their fractal dimension, characteristic of scaling invariance. The results showed that both sewer density and imperviousness exhibit scale-invariant features and can be characterized with the help of fractal dimensions ranging from 1.6 to 2, depending on the catchment. In a given area consistent results were found for the two geometrical features, yielding a robust and innovative way of quantifying the level of urbanization. The representation of imperviousness in operational semi-distributed hydrological models for these catchments was also investigated by computing fractal dimensions of the geometrical sets made up of the subcatchments with coefficients of imperviousness greater than a range of thresholds. It enables one to quantify how well spatial structures of imperviousness were represented in the urban hydrological models.

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“…Other multifractal studies include those of DeBartolo et al . () on river networks and braided channels, Roy and Padhi () on earthquakes in Iran, García‐Marín et al . () on validating a rainfall model, and Movahed and Hermanis () and Zhang et al .…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of apparent multifractality of samples from processes subordinated to truncated fBm

Guadagnini

Neuman

Riva

2011

Hydrological Processes

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Abstract:We investigate numerically apparent multi-fractal behavior of samples from synthetically generated processes subordinated to truncated fractional Brownian motion (tfBm) on finite domains. We are motivated by the recognition that many earth and environmental (including hydrological) variables appear to be self-affine (monofractal) or multifractal with Gaussian or heavy-tailed distributions. The literature considers self-affine and multifractal types of scaling to be fundamentally different, the first arising from additive and the second from multiplicative random fields or processes. It has been demonstrated theoretically by one of us that square or absolute increments of samples from Gaussian/Lévy processes subordinated to tfBm exhibit apparent/ spurious multifractality at intermediate ranges of separation lags, with breakdown in power-law scaling at small and large lags as is commonly exhibited by real data. A preliminary numerical demonstration of apparent multifractality by the same author was limited to Gaussian fields having nearest neighbor autocorrelations and led to rather noisy results. Here, we adopt a new generation scheme that allows us to investigate apparent multifractal behaviors of samples taken from a broad range of processes including Gaussian with and without symmetric Lévy and log-normal (as well as potentially other) subordinators. Our results shed new light on the nature of apparent multifractality, which has wide implications vis-a-vis the scaling of many hydrological as well as other earth and environmental variables.

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Fixed-mass multifractal analysis of river networks and braided channels

Cited by 20 publications

References 27 publications

Hydraulic Characterization of River Networks Based on Flow Patterns Simulated by 2‐D Shallow Water Modeling: Scaling Properties, Multifractal Interpretation, and Perspectives for Channel Heads Detection

Hydraulic Characterization of River Networks Based on Flow Patterns Simulated by 2‐D Shallow Water Modeling: Scaling Properties, Multifractal Interpretation, and Perspectives for Channel Heads Detection

Fractal analysis of urban catchments and their representation in semi-distributed models: imperviousness and sewer system

Numerical investigation of apparent multifractality of samples from processes subordinated to truncated fBm

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