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| Titel |
Horton laws for Hydraulic-Geometric variables and their scaling exponents in self-similar river networks |
| VerfasserIn |
V. K. Gupta, O. J. Mesa |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
2198-5634
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics Discussions ; 1, no. 1 ; Nr. 1, no. 1 (2014-04-16), S.705-753 |
| Datensatznummer |
250115090
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| Publikation (Nr.) |
 copernicus.org/npgd-1-705-2014.pdf |
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| Zusammenfassung |
| An analytical theory is presented to predict Horton laws for five
Hydraulic-Geometric (H-G) variables (stream discharge Q, width W, depth
D, velocity U, slope S, and friction n'). The theory builds on
the concept of dimensional analysis, and identifies six independent
dimensionless River-Basin numbers. We consider self-similar Tokunaga
networks and derive a mass conservation equation in the limit of large
network order in terms of Horton bifurcation and discharge ratios. It is
applied to obtain self-similar solutions of type-1 (SS-1), and predict Horton
laws for width, depth and velocity as asymptotic relationships. Exponents of
width and the Reynold's number are predicted. Assuming that SS-1 is valid for
slope, depth and velocity, corresponding Horton laws and the H-G exponents
are derived. The exponent values agree with that for the Optimal Channel
Network (OCN) model, but do not agree with values from three field
experiments. The deviations are substantial, suggesting that H-G in network
does not obey optimality or SS-1. It fails because slope, a dimensionless
River-Basin number, goes to 0 as network order increases, but, it cannot be
eliminated from the asymptotic limit. Therefore, a generalization of SS-1,
based in self-similar solutions of Type-2 (SS-2) is considered. It introduces
two anomalous scaling exponents as free parameters, which enables us to show
the existence of Horton laws for channel depth, velocity, slope and Manning's
friction. The Manning's friction exponent, y, is predicted and tested
against observed exponents from three field studies. We briefly sketch how
the two anomalous scaling exponents could be estimated from the transport of
suspended sediment load and the bed load. Statistical variability in the
Horton laws for the H-G variables is also discussed. Both are important open
problems for future research. |
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