Extending generalized Horton laws to test embedding algorithms for topologic river networks

Mantilla, Ricardo; Gupta, Vijay; Troutman, Brent M.

doi:10.1016/j.geomorph.2012.01.002

Cited by 10 publications

(5 citation statements)

References 36 publications

(56 reference statements)

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“…Moussa [22] proposed new indices independent of threshold area that have similar properties to the Horton-Strahler ratios. Mantilla et al [23] extended generalized Horton's laws to test embedding algorithms for topological river networks. Later, many scholars applied Horton's law to other fields.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Irrigation Canal System Characteristics in Heilongjiang Province and the Influence on Irrigation Water Use Efficiency

Sun

et al. 2018

Water

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Irrigation water use efficiency is a primary evaluation index that links economic production development with the efficient use of water resources. Canal water conveyance is an important part of irrigation, and the distribution characteristics of canal systems have an important influence on irrigation water use efficiency. In this paper, 75 irrigated districts in Heilongjiang Province in 2015 were selected as the study objects. The main, branch, lateral, and sublateral canals were graded into first-, second-, third-, and fourth-order classes, respectively. The irrigation districts were divided into three classes, that is, four-order, three-order, and two-order, according to the canal orders that the irrigation districts contained. The canal system framework was described by Horton's law. The fractal dimension of the canal system was calculated based on the bifurcation ratio and length ratio of the canals. The relationships between fractal dimensions and irrigation water use efficiency were evaluated. The results showed that the irrigation water use efficiency of the four-order and three-order irrigation districts initially increased and then decreased with increases in the fractal dimension (D). In the irrigation districts, an irrigation water use efficiency of more than 10 × 10 3 hm 2 and less than 0.67 × 10 3 hm 2 was proportional to the increase in the fractal dimension, whereas the opposite result was found for districts with (0.67-10) × 10 3 hm 2 . The irrigation water use efficiency of the four-order and two-order irrigation districts with less than 3.3 × 10 3 hm 2 had the greatest potential to increase the water use efficiency. Therefore, canal system reconstruction suggestions for different irrigation districts were provided. The results have important theoretical significance and practical value for the improvement of irrigation construction and the promotion of irrigation water efficiency planning.

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Section: Introductionmentioning

confidence: 99%

Analysis of Irrigation Canal System Characteristics in Heilongjiang Province and the Influence on Irrigation Water Use Efficiency

Sun

et al. 2018

Water

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“…For certain vascular morphologies, Takahashi [ 31 ] determined that the D F values and the branching exponents ( x ) were equal (see Hughes [ 20 ] for succinct re-verification of the relation). The H-ML is obeyed in many branched biological structures [ 8 , 15 – 17 , 20 , 49 , 53 , 58 , 121 , 130 – 132 , 174 , 178 – 185 ]. The data acquired here compellingly show that the bronchial and vascular systems of the human lung comply with the H-ML.…”

Section: Discussionmentioning

confidence: 99%

Fractal analysis of concurrently prepared latex rubber casts of the bronchial and vascular systems of the human lung

Essay

Maina

2020

Open Biol.

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Fractal geometry (FG) is a branch of mathematics that instructively characterizes structural complexity. Branched structures are ubiquitous in both the physical and the biological realms. Fractility has therefore been termed nature's design. The fractal properties of the bronchial (airway) system, the pulmonary artery and the pulmonary vein of the human lung generates large respiratory surface area that is crammed in the lung. Also, it permits the inhaled air to intimately approximate the pulmonary capillary blood across a very thin blood–gas barrier through which gas exchange to occur by diffusion. Here, the bronchial (airway) and vascular systems were simultaneously cast with latex rubber. After corrosion, the bronchial and vascular system casts were physically separated and cleared to expose the branches. The morphogenetic (Weibel's) ordering method was used to categorize the branches on which the diameters and the lengths, as well as the angles of bifurcation, were measured. The fractal dimensions ( D F ) were determined by plotting the total branch measurements against the mean branch diameters on double logarithmic coordinates (axes). The diameter-determined D F values were 2.714 for the bronchial system, 2.882 for the pulmonary artery and 2.334 for the pulmonary vein while the respective values from lengths were 3.098, 3.916 and 4.041. The diameters yielded D F values that were consistent with the properties of fractal structures (i.e. self-similarity and space-filling). The data obtained here compellingly suggest that the design of the bronchial system, the pulmonary artery and the pulmonary vein of the human lung functionally comply with the Hess–Murray law or ‘the principle of minimum work’.

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“…In the literature, river networks have been studied from a physical, geometrical, and hydraulic point of view, introducing specific scaling laws that represent, within a given river basin, the relationships of scale invariance between topological variables (Dodds & Rothman, ; Gangodagamage et al, ; Hooshyar et al, ; Le & Kumar, ; Mantilla et al, ; Rodriguez‐Iturbe & Rinaldo, ) or between channel characteristics such as mean depth, water surface width, mean velocity, length of active wet channels, and discharge (among the most recent studies, Dodov & Foufoula‐Georgiou, ; Godsey & Kirchner, ; Hooshyar et al, ; Lawrence, ; Mersel et al, ; Nardi et al, ; Stewardson, ). In this research field, based on the contribution made by Mandelbrot (), several studies have applied fractal and multifractal analysis of river basins and networks in order to characterize many relevant geomorphologic and hydraulic‐hydrologic variables (Ariza‐Villaverde et al, , ; De Bartolo et al, , , ; De Bartolo, Primavera, et al, ; Dodds & Rothman, ; Dombradi et al, ; Ijjasz‐Vasquez et al, ; Perron et al, ; Rigon et al, ; Rinaldo et al, , ; Saa et al, ; Veneziano & Iacobellis, ; Veneziano & Niemann, ), while in very recent years, they have been extended also into the context of urban drainage basins (Gires et al, , ).…”

Section: Introductionmentioning

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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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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Extending generalized Horton laws to test embedding algorithms for topologic river networks

Cited by 10 publications

References 36 publications

Analysis of Irrigation Canal System Characteristics in Heilongjiang Province and the Influence on Irrigation Water Use Efficiency

Analysis of Irrigation Canal System Characteristics in Heilongjiang Province and the Influence on Irrigation Water Use Efficiency

Fractal analysis of concurrently prepared latex rubber casts of the bronchial and vascular systems of the human lung

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

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