scholarly journals Urban Sewers Evolve Similarly to River Networks

Eos ◽  
2017 ◽  
Author(s):  
Sarah Stanley
Keyword(s):  
River Networks ◽  
River Systems ◽  
Drainage Networks

Like river systems, engineered drainage networks become increasingly fractal as they grow.

scholarly journals Automated Detection of Instability-Inducing Channel Geometry Transitions in Saint-Venant Simulation of Large-Scale River Networks

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2236
Author(s):  
Cheng-Wei Yu ◽  
Ben R. Hodges ◽  
Frank Liu
Keyword(s):  
Large Scale ◽  
Open Channel ◽  
Search Algorithm ◽  
Shallow Water Equation ◽  
Stable Solution ◽  
River Networks ◽  
River Systems ◽  
Channel Network ◽  
Channel Geometry ◽  
Venant Equation

A new sweep-search algorithm (SSA) is developed and tested to identify the channel geometry transitions responsible for numerical convergence failure in a Saint-Venant equation (SVE) simulation of a large-scale open-channel network. Numerical instabilities are known to occur at “sharp” transitions in discrete geometry, but the identification of problem locations has been a matter of modeler’s art and a roadblock to implementing large-scale SVE simulations. The new method implements techniques from graph theory applied to a steady-state 1D shallow-water equation solver to recursively examine the numerical stability of each flowpath through the channel network. The SSA is validated with a short river reach and tested by the simulation of ten complete river systems of the Texas–Gulf Coast region by using the extreme hydrological conditions recorded during hurricane Harvey. The SSA successfully identified the problematic channel sections in all tested river systems. Subsequent modification of the problem sections allowed stable solution by an unsteady SVE numerical solver. The new SSA approach permits automated and consistent identification of problem channel geometry in large open-channel network data sets, which is necessary to effectively apply the fully dynamic Saint-Venant equations to large-scale river networks or for city-wide stormwater networks.

Investigating the Response of Tectonic Loading in the Himalayas on the Peripheral Forebulge through Drainage Network Analysis

2021 ◽  
Author(s):  
Parv Kasana ◽  
Vimal Singh ◽  
Rahul Devrani
Keyword(s):  
Dynamic Equilibrium ◽  
Ganga River ◽  
Indian Plate ◽  
River Networks ◽  
Drainage Network ◽  
River Systems ◽  
Himalayan Orogeny ◽  
Narmada River ◽  
Indian Lithosphere ◽  
Tectonic Loading

<p>Drainage divide migration is a conspicuous natural process through which a landscape evolves. In response to a forced climatic and tectonic disturbance, susceptible river networks transfer the transient signals to the entire river basin, which results in an incision or aggradation. The Himalayan orogeny and subduction of the Indian plate have resulted in an upward flexure in the Indian lithosphere known as a peripheral forebulge. A forebulge can flexurally uplift and migrate following the variation in tectonic load. The emergence of the central Indian plateau is a consequence of the upwarping of the Indian lithosphere (Bilham et al. 2003).  In this work, we are trying to assess the drainage network dynamics between the Narmada and Ganga river systems, which drain the uplifted central Indian plateau. We have calculated the Chi(χ) metrics, steepness index (Ksn), knickpoints for the channels in the study area. We have generated Topographic swath profiles to analyze the topographic variations on the plateau. It has been observed from the results that the rivers in the study area lack dynamic equilibrium, and river capturing is an evident response to the perturbations. Our analysis shows that the Narmada River tributaries are gaining drainage area and aggressing Northwards by capturing adjacent Ganga river tributaries. The field observations show a variation in the surface slope and presence of knickpoints (waterfalls) along the "aggressor" drainages. We propose a model to show a correlation between the tectonic loading of Himalayas, movement of forebulge, and its feedback to the river systems present on the forebulge.</p>

scholarly journals Bifurcation dynamics of natural drainage networks

2013 ◽  
Vol 371 (2004) ◽  
pp. 20120365 ◽  
Author(s):  
Alexander P. Petroff ◽  
Olivier Devauchelle ◽  
Hansjörg Seybold ◽  
Daniel H. Rothman
Keyword(s):  
Mathematical Problem ◽  
Basic Feature ◽  
River Networks ◽  
Network Growth ◽  
Local Shape ◽  
Harmonic Field ◽  
Interface Growth ◽  
Drainage Networks ◽  
Logarithmic Spirals ◽  
Scale Network

As water erodes a landscape, streams form and channellize the surficial flow. In time, streams become highly ramified networks that can extend over a continent. Here, we combine physical reasoning, mathematical analysis and field observations to understand a basic feature of network growth: the bifurcation of a growing stream. We suggest a deterministic bifurcation rule arising from a relationship between the position of the tip in the network and the local shape of the water table. Next, we show that, when a stream bifurcates, competition between the stream and branches selects a special bifurcation angle α =2 π /5. We confirm this prediction by measuring several thousand bifurcation angles in a kilometre-scale network fed by groundwater. In addition to providing insight into the growth of river networks, this result presents river networks as a physical manifestation of a classical mathematical problem: interface growth in a harmonic field. In the final sections, we combine these results to develop and explore a one-parameter model of network growth. The model predicts the development of logarithmic spirals. We find similar features in the kilometre-scale network.

Features and controlling factors of drainage networks in the Tibetan Plateau

2020 ◽  
Author(s):  
Minhui Li ◽  
Baosheng Wu ◽  
Yi Chen
Keyword(s):  
Tibetan Plateau ◽  
Yangtze River ◽  
Yellow River ◽  
Controlling Factors ◽  
River Networks ◽  
The Tibetan Plateau ◽  
Self Similarity ◽  
Drainage Networks ◽  
Yarlung Zangbo River ◽  
Yalong River

<p><span><span lang="EN-US">Tibetan Plateau is the source of many major rivers in Asia. Drainage networks of these rivers vary in shapes and features due to complex climatic and geomorphic conditions. In this study, we extracted drainage networks in the source area of Yellow River, Yangtze River and Yarlung Zangbo River from 90-m-resolution SRTM DEM. We chose 62 sub-basins in the Yellow River, 96 sub-basins in the Yangtze River and 120 sub-basins in the Yarlung Zangbo River and tested self-similarity of drainage networks in two ways. First, we tested self-similarity for traditional Horton laws. Based on Horton-Strahler order, the results indicate that rivers with low levels generally obey Horton laws while rivers with high levels show deviation. Second, we tested statistical self-similarity in the topology of river networks. Random self-similar networks (RSN) model which combines self-similarity and randomness shows topological features of river networks statistically. Real networks were decomposed into generators that produce the network. The results demonstrate that the generators of RSN model obey a geometric distribution and the parameter p, which describes the distribution of generators, ranges from 0.401 to 0.587. Self-similarity holds in a statistical sense in the selected basins in the Tibetan Plateau. Motivated by the need to understand the controlling factors of drainage networks in Tibetan Plateau, these sub-basins were divided into groups according to possible controlling factors, such as climate, tectonic and geology. Analysis shows that Horton ratios and generators of low-level rivers are affected by precipitation, but the relationship between these parameters of high-level rivers and these factors is not obvious. In order to further explore the controlling factors, we analyzed three typical rivers (Tao River, Yalong River and Lasa River) in more details. For Yalong River, Tao River and Lasa River, bifurcation ratios are 4.46, 5.00 and 4.37 while the length ratios are 2.35, 2.71 and 2.30 respectively. The Normalized Concavity Index for Tao River, Lasa River and Yalong River are -0.129, -0.082 and 0.009</span> <span lang="EN-US">respectively, indicating that the profiles of the first two rivers are concave-up and that of Yalong River is convex-up. The influence of climate is well reflected in the structure and longitudinal profiles of the drainage network in the Tibetan Plateau. Strong tectonic activities in the eastern margin of the Tibetan Plateau destroy the network of Yalong River, resulting in river capture to maintain equilibrium.</span></span></p>

scholarly journals Solving the mystery of vanishing rivers in China

2019 ◽  
Vol 6 (6) ◽  
pp. 1239-1246 ◽  
Author(s):  
Yichu Wang ◽  
Jinren Ni ◽  
Yao Yue ◽  
Jiaye Li ◽  
Alistair G L Borthwick ◽  
...  
Keyword(s):  
Mixed Mode ◽  
River Networks ◽  
Stream Order ◽  
Previous Estimate ◽  
River Systems ◽  
Natural Streams ◽  
Rivers And Lakes ◽  
Order Scheme ◽  
National Water

Abstract A major controversy was sparked worldwide by a recent national water census claiming that the number of Chinese rivers with watersheds ≥100 km2 was less than half the previous estimate of 50 000 rivers, which also stimulates debates on the potential causes and consequences. Here, we estimated the number of rivers in terms of stream-segmentation characteristics described by Horton, Strahler and Shreve stream-order rules, as well as their mixed mode for named rivers recorded in the Encyclopedia of Rivers and Lakes in China. As a result, the number of ‘vanishing rivers’ has been found to be highly relevant to statistical specifications in addition to the erroneous inclusion of pseudo-rivers primarily generated in arid or frost-thaw areas. The modified Horton stream-order scheme reasonably depicts the configuration of complete natural streams from headwater to destination, while the Strahler largely projects the fragmentation of the named river networks associated with human aggregation to the hierarchical river systems.

scholarly journals The role of lateral erosion in the evolution of nondendritic drainage networks to dendricity and the persistence of dynamic networks

2021 ◽  
Vol 118 (16) ◽  
pp. e2015770118
Author(s):  
Jeffrey S. Kwang ◽  
Abigail L. Langston ◽  
Gary Parker
Keyword(s):  
Steady State ◽  
Dynamic Networks ◽  
River Networks ◽  
Stable Configuration ◽  
Lateral Incision ◽  
Drainage Networks ◽  
Physically Based ◽  
Physically Based Models ◽  
Lateral Erosion ◽  
Two Parameters

Dendritic, i.e., tree-like, river networks are ubiquitous features on Earth’s landscapes; however, how and why river networks organize themselves into this form are incompletely understood. A branching pattern has been argued to be an optimal state. Therefore, we should expect models of river evolution to drastically reorganize (suboptimal) purely nondendritic networks into (more optimal) dendritic networks. To date, current physically based models of river basin evolution are incapable of achieving this result without substantial allogenic forcing. Here, we present a model that does indeed accomplish massive drainage reorganization. The key feature in our model is basin-wide lateral incision of bedrock channels. The addition of this submodel allows for channels to laterally migrate, which generates river capture events and drainage migration. An important factor in the model that dictates the rate and frequency of drainage network reorganization is the ratio of two parameters, the lateral and vertical rock erodibility constants. In addition, our model is unique from others because its simulations approach a dynamic steady state. At a dynamic steady state, drainage networks persistently reorganize instead of approaching a stable configuration. Our model results suggest that lateral bedrock incision processes can drive major drainage reorganization and explain apparent long-lived transience in landscapes on Earth.

scholarly journals Brief communication: Possible explanation of the values of Hack's drainage basin, river length scaling exponent

2016 ◽  
Vol 23 (2) ◽  
pp. 91-93 ◽  
Author(s):  
Allen G. Hunt
Keyword(s):  
Percolation Theory ◽  
Theoretical Basis ◽  
Drainage Basin ◽  
Channel Length ◽  
River Networks ◽  
Scaling Exponent ◽  
Flow Paths ◽  
Drainage Networks ◽  
Length Scaling ◽  
Basin Area

Abstract. Percolation theory can be used to find water flow paths of least resistance. Application of percolation theory to drainage networks allows identification of the range of exponent values that describe the tortuosity of rivers in real river networks, which is then used to generate the observed scaling between drainage basin area and channel length, a relationship known as Hack's law. Such a theoretical basis for Hack's law may allow interpretation of the range of exponent values based on an assessment of the heterogeneity of the substrate.

Comparison of natural and urban drainage network characteristics based on Gibbs’ Model

2020 ◽  
Author(s):  
Kyungjae Kim ◽  
Yongwon Seo
Keyword(s):  
River Networks ◽  
Urban Drainage ◽  
Drainage Network ◽  
Stream Network ◽  
Network Characteristics ◽  
Drainage Networks ◽  
Long Time ◽  
Alternative Measures ◽  
Urban Catchments ◽  
The Difference

<p>Natural catchments have formed efficient river networks for a long time. similarly, urban drainage networks have been developed with the purpose of efficiently draining rainfall from catchments to flood mitigation. In this study, we analyzes and compares the characteristics between the naturally formed river networks for a long time and the artificially formed drainage networks using Gibbs’ Model. Gibbs’ Model is a stochastic stream network model, which can generate multiple realizations of stochastic networks based on a single parameter value of . Gibbs‘ Model was applied to a total number of 239 urban catchments in Seoul, South Korea and 70 natural catchments in the Midwestern areas of US. Topographic characteristics of catchments are analyzed along with the efficiency of drainage networks, which are presented by for both natural and urban catchments. The result of this study demonstrates the difference between natural and artificial drainage network characteristics and suggests a new alternative measures to mitigate flood risks in urban catchments facing extreme hydrologic events with climate change.</p>

scholarly journals Explanation of the values of Hack's drainage basin, river length scaling exponent

2015 ◽  
Vol 2 (4) ◽  
pp. 1355-1361 ◽  
Author(s):  
A. G. Hunt
Keyword(s):  
Percolation Theory ◽  
Theoretical Basis ◽  
Drainage Basin ◽  
Channel Length ◽  
River Networks ◽  
Scaling Exponent ◽  
Flow Paths ◽  
Drainage Networks ◽  
Length Scaling ◽  
Basin Area

Abstract. Percolation theory can be used to find water flow paths of least resistance. The application of percolation theory to drainage networks allows identification of the range of exponent values that describe the tortuosity of rivers in real river networks, which is then used to generate the observed scaling between drainage basin area and channel length, a relationship known as Hack's law. Such a theoretical basis for Hack's law allows interpretation of the range of exponent values based on an assessment of the heterogeneity of the substrate.

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