dorsal/arxiv
View SchemaGeometry of River Networks II: Distributions of Component Size and Number
| Authors | Peter Sheridan Dodds, Daniel H. Rothman |
|---|---|
| Categories | |
| ArXiv ID | physics/0005048 |
| URL | https://arxiv.org/abs/physics/0005048 |
| DOI | 10.1103/PhysRevE.63.016116 |
Abstract
The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method. Exponential relationships, known as Horton's laws, between stream order and ensemble-averaged quantities pertaining to network components are observed. We extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions. The relationships determined are drawn from a combination of theoretical analysis, analysis of real river networks including the Mississippi, Amazon and Nile, and numerical simulations on a model of directed, random networks. Underlying distributions of stream segment lengths are identified as exponential. Combinations of these distributions form single-humped distributions with exponential tails, the sums of which are in turn shown to give power law distributions of stream lengths. Distributions of basin area and stream segment frequency are also addressed. The calculations identify a single length-scale as a measure of size fluctuations in network components. This article is the second in a series of three addressing the geometry of river networks.
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"abstract": "The structure of a river network may be seen as a discrete set of nested\nsub-networks built out of individual stream segments. These network components\nare assigned an integral stream order via a hierarchical and discrete ordering\nmethod. Exponential relationships, known as Horton\u0027s laws, between stream order\nand ensemble-averaged quantities pertaining to network components are observed.\nWe extend these observations to incorporate fluctuations and all higher moments\nby developing functional relationships between distributions. The relationships\ndetermined are drawn from a combination of theoretical analysis, analysis of\nreal river networks including the Mississippi, Amazon and Nile, and numerical\nsimulations on a model of directed, random networks. Underlying distributions\nof stream segment lengths are identified as exponential. Combinations of these\ndistributions form single-humped distributions with exponential tails, the sums\nof which are in turn shown to give power law distributions of stream lengths.\nDistributions of basin area and stream segment frequency are also addressed.\nThe calculations identify a single length-scale as a measure of size\nfluctuations in network components. This article is the second in a series of\nthree addressing the geometry of river networks.",
"arxiv_id": "physics/0005048",
"authors": [
"Peter Sheridan Dodds",
"Daniel H. Rothman"
],
"categories": [
"physics.geo-ph"
],
"doi": "10.1103/PhysRevE.63.016116",
"title": "Geometry of River Networks II: Distributions of Component Size and Number",
"url": "https://arxiv.org/abs/physics/0005048"
},
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