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

2017 ◽  
Vol 21 (5) ◽  
pp. 2361-2375 ◽  
Author(s):  
Auguste Gires ◽  
Ioulia Tchiguirinskaia ◽  
Daniel Schertzer ◽  
Susana Ochoa-Rodriguez ◽  
Patrick Willems ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Hydrological Models ◽  
Scale Invariant ◽  
Sewer System ◽  
Distributed Models ◽  
Urban Catchments ◽  
Distributed Hydrological Models ◽  
Dimension Characteristic

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 sub-catchments 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.

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

2016 ◽  
Author(s):  
Auguste Gires ◽  
Ioulia Tchiguirinskaia ◽  
Daniel Schertzer ◽  
Susana Ochoa Rodriguez ◽  
Patrick Willems ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Hydrological Models ◽  
Scale Invariant ◽  
Sewer System ◽  
Distributed Models ◽  
Urban Catchments ◽  
Distributed Hydrological Models ◽  
Dimension Characteristic

Abstract. Fractal analysis relies on scale invariance and the concept of fractal dimension enables to characterise 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 5 European countries. The aim was to characterise 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 sub-catchments with coefficients of imperviousness greater than a range of thresholds. It enabled to quantify how well spatial structures of imperviousness were represented in the urban hydrological models.

Fractal analysis of a new generation of HVOF sprayed coatings based on optical surface metrology

2016 ◽  
Vol 83 (6) ◽  
Author(s):  
Yibo Zou ◽  
Markus Kästner ◽  
Eduard Reithmeier
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Confocal Laser Scanning Microscope ◽  
Confocal Laser ◽  
Surface Metrology ◽  
Roughness Parameters ◽  
Scale Invariant ◽  
Sprayed Coatings

AbstractIn this article, fractal analysis combined with roughness measurement is proposed to characterize the new generations of HVOF sprayed coatings' surface textures. Two-dimensional and three-dimensional box counting algorithms are introduced to determine the fractal dimension, which is considered as a scale-invariant parameter and is able to describe chaos and complexity of the surface. For surface roughness metrology, a confocal laser scanning microscope with different lenses is used to acquire the areal topography, providing a sequence of height maps with different image resolutions. Typical areal roughness parameters are assessed based on the international standard ISO-25178. The results show that the fractal dimension is a powerful tool to depict the nature of the surface texture of the investigated coatings. Moreover, it is found that the traditional amplitude roughness parameters depend strongly on the range of the measurement field as well as the datasets' resolution, whereas the fractal dimension is rather invariant to the scales of the measured datasets. Finally, the correlation between the fractal dimension and roughness parameters is given at the end of this paper.

scholarly journals FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY

2011 ◽  
Vol 19 (1) ◽  
pp. 45 ◽  
Author(s):  
Ian Parkinson ◽  
Nick Fazzalari
Keyword(s):  
Fractal Dimension ◽  
Trabecular Bone ◽  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Box Counting ◽  
Cell Tissue ◽  
Image Analyser ◽  
Model Independent ◽  
Box Counting Method ◽  
Image Orientation

A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge). The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm) and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals), with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.

Image Reconstruction and Analysis of Three-Dimensional Fracture Surfaces Based on the Stereo Matching Method

2004 ◽  
Vol 261-263 ◽  
pp. 1593-1598
Author(s):  
M. Tanaka ◽  
Y. Kimura ◽  
A. Kayama ◽  
L. Chouanine ◽  
Reiko Kato ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Image Reconstruction ◽  
Fracture Surface ◽  
Fractal Analysis ◽  
Stereo Matching ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Matching Method ◽  
Fracture Surfaces ◽  
Box Counting Method

A computer program of the fractal analysis by the box-counting method was developed for the estimation of the fractal dimension of the three-dimensional fracture surface reconstructed by the stereo matching method. The image reconstruction and fractal analysis were then made on the fracture surfaces of materials created by different mechanisms. There was a correlation between the fractal dimension of the three-dimensional fracture surface and the fractal dimensions evaluated by other methods on ceramics and metals. The effects of microstructures on the fractal dimension were also experimentally discussed.

FRACTAL ANALYSIS OF DENDRITIC ARBORISATION PATTERNS OF STALKED AND ISLET NEURONS IN SUBSTANTIA GELATINOSA OF DIFFERENT SPECIES

Fractals ◽  
2007 ◽  
Vol 15 (01) ◽  
pp. 1-7 ◽  
Author(s):  
NEBOJŠA T. MILOŠEVIĆ ◽  
DUŠAN RISTANOVIĆ ◽  
JOVAN B. STANKOVIĆ ◽  
RADMILA GUDOVIĆ
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Islet Cells ◽  
Fractal Dimensions ◽  
Substantia Gelatinosa ◽  
Neuronal Populations ◽  
Box Counting ◽  
Morphological Descriptor ◽  
The Mean ◽  
Box Counting Method

Through analysis of the morphology of dendritic arborisation of neurons from the substantia gelatinosa of dorsal horns from four different species, we have established that two types of cells (stalked and islet) are always present. The aim of the study was to perform the intra- and/or inter-species comparison of these two neuronal populations by fractal analysis, as well as to clarify the importance of the fractal dimension as an objective and usable morphological parameter. Fractal analysis was carried out adopting the box-counting method. We have shown that the mean fractal dimensions for the stalked cells are significantly different between species. The same is true for the mean fractal dimensions of the islet cells. Still, no significant differences were found for the fractal dimensions of the stalked and islet cells within a particular species. The human species has shown as the only exception where fractal dimensions of these two types of cells differ significantly. This study shows once more that the fractal dimension is a useful and sensitive morphological descriptor of neuronal structures and differences between them.

Fractal analysis of leaf shapes

1986 ◽  
Vol 16 (1) ◽  
pp. 124-127 ◽  
Author(s):  
J. Vlcek ◽  
E. Cheung
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Sugar Maple ◽  
Shape Change ◽  
Leaf Shape ◽  
Fractal Dimensions ◽  
Imaging Method ◽  
Analysis Program ◽  
White Oak ◽  
Starting Position

An application of fractal mathematics to the analysis of leaf shapes is presented. Six leaves randomly selected from nine tree species were used in the study. A video imaging method together with microcomputer-based image processing was used to generate leaf outlines. A fractal analysis program was written to calculate the fractal dimensions of the leaves. Recalling a leaf outline from a diskette and specifying both the starting position on it (e.g., the beginning of the petiole) and six step lengths (explained later), the program then generates the fractal dimension according to the theory described. The results show that the fractal dimension is sensitive to leaf shape variations within a species. For example, two types of ginkgo leaves (one with and one without a notch in the middle of the leaf outline) showed distinctly different fractal values. Similar sensitivity to shape change was observed among the leaves of white oak, red oak, and sugar maple where such variables as width to length ratio and the degree of jaggedness of the leaf caused a departure of the fractal value from the average.

scholarly journals A physically-based distributed karst hydrological model (QMG model-V1.0) for flood simulations

2021 ◽  
Author(s):  
Ji Li ◽  
Daoxian Yuan ◽  
Fuxi Zhang ◽  
Yongjun Jiang ◽  
Jiao Liu ◽  
...  
Keyword(s):  
Hydrological Model ◽  
Complex Model ◽  
Hydrological Models ◽  
Runoff Generation ◽  
Average Value ◽  
Distributed Models ◽  
Physically Based ◽  
Flood Simulations ◽  
Distributed Hydrological Models ◽  
Hydrogeological Data

Abstract. Karst trough valleys are prone to flooding, primarily because of the unique hydrogeological features of karst landform, which are conducive to the spread of rapid runoff. Hydrological models that represent the complicated hydrological processes in karst regions are effective for predicting karst flooding, but their application has been hampered by their complex model structures and associated parameter set, especially so for distributed hydrological models, which require large amounts of hydrogeological data. Distributed hydrological models for predicting the Karst flooding is highly dependent on distributed structrues modeling, complicated boundary parameters setting, and tremendous hydrogeological data processing that is both time and computational power consuming. Proposed here is a distributed physically-based karst hydrological model, known as the QMG (Qingmuguan) model. The structural design of this model is relatively simple, and it is generally divided into surface and underground double-layered structures. The parameters that represent the structural functions of each layer have clear physical meanings, and the parameters are less than those of the current distributed models. This allows modeling in karst areas with only a small amount of necessary hydrogeological data. 18 flood processes across the karst underground river in the Qingmuguan karst trough valley are simulated by the QMG model, and the simulated values agree well with observations, for which the average value of Nash–Sutcliffe coefficient was 0.92. A sensitivity analysis shows that the infiltration coefficient, permeability coefficient, and rock porosity are the parameters that require the most attention in model calibration and optimization. The improved predictability of karst flooding by the proposed QMG model promotes a better mechanistic depicting of runoff generation and confluence in karst trough valleys.

scholarly journals Bi-Fractal Characterization of the Pore Network of Tight Sandstone

2021 ◽  
Vol 9 ◽  
Author(s):  
Zezhang Song ◽  
Junyi Zhao ◽  
Yuanyin Zhang ◽  
Dailin Yang ◽  
Yunlong Wang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Thin Section ◽  
Fractal Analysis ◽  
Pore Space ◽  
Fractal Dimensions ◽  
Pore Network ◽  
Physical Analysis ◽  
Tight Sandstone ◽  
Gas Bearing

Fluid seepage performance and accumulation in tight sandstone is a critical research topic for in-depth exploration and development, closely related to the heterogeneity of the pore network. The fractal characterization is one of the most compelling and direct ways for quantitative investigation of heterogeneity. However, only one kind of fractal is used in most studies, and the differences and relations between different fractal dimensions are rarely discussed. This paper chose one of the most representative tight sandstone formations in China, the second member of the Xujiahe Formation, as the research object. First, based on physical analysis and XRD analysis, we carried out a qualitative investigation on pore structure utilizing thin-section and scanning electron microscopy. Then, detailed pore structure parameters were obtained using high-pressure mercury intrusion (HPMI). Lastly, we combined two-dimensional fractal analysis on thin-section images and three-dimensional fractal analysis on HPMI data to characterize the pore network heterogeneity quantitatively. The Xu2 tight sandstone is mainly medium- to fine-grained lithic feldspathic sandstone or feldspathic lithic sandstone with low porosity and permeability. Also, the Xujiahe tight sandstone is mainly composed of quartz, feldspar, and clay. The pore types of Xu2 tight sandstones are primarily intergranular pores, micro-fractures, and intra- and intergranular dissolution pores. Moreover, most of the micro-fractures in gas-bearing formation are open-ended, while most are filled by clay minerals in the dry formation. The r50 (median pore radius) is the most sensitive parameter to seepage capability (permeability) and gas-bearing status. The 2D fractal dimension (Ds) of gas-bearing samples is significantly larger than that of dry samples, while the 3D fractal dimension (D1, D2) of gas-bearing samples is lower than that of dry samples. There is a strong negative correlation between D2 and gas-bearing status, permeability, quartz content, and r50, but a positive correlation between Ds and these parameters. D2 represents the heterogeneity of pore space, while the Ds indicates the development of the pore network. Tectonic movements that generate micro-fractures and clay cementation that blocks the seepage channels are the two main controlling factors on fractal dimensions. Combining 2D and 3D fractal analysis could give a more in-depth investigation of pore structure.

scholarly journals A hydrography upscaling method for scale invariant parametrization of distributed hydrological models

2020 ◽  
Author(s):  
Dirk Eilander ◽  
Willem van Verseveld ◽  
Dai Yamazaki ◽  
Albrecht Weerts ◽  
Hessel C. Winsemius ◽  
...  
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Flow Direction ◽  
Hydrological Models ◽  
Scale Invariant ◽  
Distributed Hydrological Models ◽  
Relationship Of ◽  
Improved Accuracy ◽  
Basin Boundaries ◽  
Made In

Abstract. Distributed hydrological models rely on hydrography data such as flow direction, river length, slope and width. For large-scale applications, many of these models still rely on a few flow-direction datasets, which are often manually derived. We propose the Iterative Hydrography Upscaling (IHU) method to upscale high-resolution flow direction data to the typically coarser resolutions of distributed hydrological models. The IHU aims to preserve the upstream-downstream relationship of river structure, including basin boundaries, river meanders and confluences, in the D8 format, which is commonly used to describe river networks in models. Additionally, it derives sub-grid river attributes such as drainage area, river length, slope and width. We derived the multi-resolution MERIT Hydro IHU dataset at resolutions of 30 arcsec (~1 km), 5 arcmin (~10 km) and 15 arcmin (~30 km) by applying IHU to the recently published 3 arcsec MERIT Hydro data. Results indicate improved accuracy of IHU at all resolutions studied compared to other often applied methods. Furthermore, we show that using IHU-derived hydrography data minimizes the errors made in timing and magnitude of simulated peak discharge throughout the Rhine basin compared to simulations at the native data resolutions. As the method is fully automated, it can be applied to other high-resolution hydrography datasets to increase the accuracy and enhance the uptake of new datasets in distributed hydrological models in the future.

Sign in / Sign up

Export Citation Format

Share Document