dorsal/arxiv
View SchemaGeometry of River Networks III: Characterization of Component Connectivity
| Authors | Peter Sheridan Dodds, Daniel H. Rothman |
|---|---|
| Categories | |
| ArXiv ID | physics/0005049 |
| URL | https://arxiv.org/abs/physics/0005049 |
| DOI | 10.1103/PhysRevE.63.016117 |
Abstract
River networks serve as a paradigmatic example of all branching networks. Essential to understanding the overall structure of river networks is a knowledge of their detailed architecture. Here we show that sub-branches are distributed exponentially in size and that they are randomly distributed in space, thereby completely characterizing the most basic level of river network description. Specifically, an averaged view of network architecture is first provided by a proposed self-similarity statement about the scaling of drainage density, a local measure of stream concentration. This scaling of drainage density is shown to imply Tokunaga's law, a description of the scaling of side branch abundance along a given stream, as well as a scaling law for stream lengths. This establishes the scaling of the length scale associated with drainage density as the basic signature of self-similarity in river networks. We then consider fluctuations in drainage density and consequently the numbers of side branches. Data is analyzed for the Mississippi River basin and a model of random directed networks. Numbers of side streams are found to follow exponential distributions as are stream lengths and inter-tributary distances along streams. Finally, we derive the joint variation of side stream abundance with stream length, affording a full description of fluctuations in network structure. Fluctuations in side stream numbers are shown to be a direct result of fluctuations in stream lengths. This is the last paper in a series of three on the geometry of river networks.
{
"annotation_id": "5b40df5f-0de0-42a2-bc0f-14499c1641e7",
"date_created": "2026-03-02T18:00:32.300000Z",
"date_modified": "2026-03-02T18:00:32.300000Z",
"file_hash": "a11138217317d4a193b66229b70cbe09774ac6301e86a76295da879788ac1e5c",
"private": false,
"record": {
"abstract": "River networks serve as a paradigmatic example of all branching networks.\nEssential to understanding the overall structure of river networks is a\nknowledge of their detailed architecture. Here we show that sub-branches are\ndistributed exponentially in size and that they are randomly distributed in\nspace, thereby completely characterizing the most basic level of river network\ndescription. Specifically, an averaged view of network architecture is first\nprovided by a proposed self-similarity statement about the scaling of drainage\ndensity, a local measure of stream concentration. This scaling of drainage\ndensity is shown to imply Tokunaga\u0027s law, a description of the scaling of side\nbranch abundance along a given stream, as well as a scaling law for stream\nlengths. This establishes the scaling of the length scale associated with\ndrainage density as the basic signature of self-similarity in river networks.\nWe then consider fluctuations in drainage density and consequently the numbers\nof side branches. Data is analyzed for the Mississippi River basin and a model\nof random directed networks. Numbers of side streams are found to follow\nexponential distributions as are stream lengths and inter-tributary distances\nalong streams. Finally, we derive the joint variation of side stream abundance\nwith stream length, affording a full description of fluctuations in network\nstructure. Fluctuations in side stream numbers are shown to be a direct result\nof fluctuations in stream lengths. This is the last paper in a series of three\non the geometry of river networks.",
"arxiv_id": "physics/0005049",
"authors": [
"Peter Sheridan Dodds",
"Daniel H. Rothman"
],
"categories": [
"physics.geo-ph"
],
"doi": "10.1103/PhysRevE.63.016117",
"title": "Geometry of River Networks III: Characterization of Component Connectivity",
"url": "https://arxiv.org/abs/physics/0005049"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "ba8d255a-07d9-4d31-a9f0-49eeed6854c6",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}