Data for Ashley River to test channel network and river basin heterogeneity concepts

McKerchar, AI; Ibbitt, Richard P.; Brown, Scott; Duncan, Maurice J.

doi:10.1029/97wr02573

Cited by 20 publications

(22 citation statements)

References 11 publications

(7 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Real channel networks exhibit statistical variability in their topology, geometry (Veitzer and Gupta, 2000) and hydraulic geometry (Ibbitt, 1997;McKerchar et al, 1998). There is a long history of published literature in geomorphology that has been devoted to understanding this variability (Jarvis and Woldenberg, 1984).…”

Section: Geomorphologic Analysismentioning

confidence: 99%

Role of coupled flow dynamics and real network structures on Hortonian scaling of peak flows

Mantilla

Gupta

Sánchez

2006

Journal of Hydrology

View full text Add to dashboard Cite

We investigate how channel flow dynamics on real river networks produces scaling in peak flows. Scaling relations have been defined by log-log linearity between peak flow statistics and drainage areas for idealized mean self-similar networks like Peano and Mandelbrot Viscek. Unlike idealized basins, drainage areas and link lengths in real basins vary statistically. We use Horton-Strahler order as scale parameter instead of drainage area, and use the Hortonian framework to analyze these network structures. A river-network oriented GIS is used to extract the drainage network for the Walnut Gulch basin, Arizona in the United States. It provides the link connectivity structure and the geometric variables for numerically solving coupled link-based mass and momentum conservation equations. The equations are solved for spatially uniform and instantaneous injection of runoff under three different scenarios of flow in the channels: 1) Constant Velocity, 2) Constant Friction, and 3) Spatially Variable Friction. We find that Hortonian scaling in peak flows does not hold for the constant friction scenario. The scaling exponents of peak flows for the other two cases are larger than the scaling exponent of the peaks of the width functions. This property of scaling exponents for a real network is opposite to previous findings for idealized mean self-similar networks. An empirical scaling analysis of peak flows on the Walnut Gulch basin is briefly explained to provide preliminary empirical support to our theoretical findings.

show abstract

Section: Geomorphologic Analysismentioning

confidence: 99%

Role of coupled flow dynamics and real network structures on Hortonian scaling of peak flows

Mantilla

Gupta

Sánchez

2006

Journal of Hydrology

View full text Add to dashboard Cite

show abstract

“…OCNs have been analytically shown to produce three universality classes in terms of scaling exponents, but none of these predictions agrees with the data (Maritan et al, 1996). Two comprehensive field programs were carried out in New Zealand (NZ) to test the OCN predictions McKerchar et al, 1998). However, the observed values of the H-G exponents substantially deviated from the OCN predictions that is explained in greater detail in Sects.…”

Section: Background and Methodsmentioning

confidence: 84%

“…In making this plot, the theoretical condition − ω → ∞ is incorporated by omitting order 6 and 5 streams from the analysis. Mantilla (2014) found that the basin has a large number of the 1st order streams that are mostly missed in the map that McKerchar et al (1998) presented. Therefore, the Horton plot is made for streams of order ω = 2, 3, 4, shown in Fig.…”

Section: Test Of Horton Laws and The R Q = R A Relationship For The Amentioning

confidence: 99%

“…An important issue in estimating field values of the H-G exponents is the measurement errors that are inherent to measuring the H-G variables, which affect their scaling exponents. For example, Ibbitt et al (1998) and McKerchar et al (1998) have given standard errors for each of the H-G exponents that are listed in Table 1. We use these fieldestimated values in testing theoretical predictions against their observed values from three basins in Sects.…”

Section: Data Setsmentioning

confidence: 99%

See 1 more Smart Citation

Horton laws for hydraulic–geometric variables and their scaling exponents in self-similar Tokunaga river networks

Gupta

Sánchez

2014

Nonlin. Processes Geophys.

View full text Add to dashboard Cite

Abstract. An analytical theory is developed that obtains Horton laws for six hydraulic-geometric (H-G) variables (stream discharge Q, width W , depth D, velocity U , slope S, and friction n ) in self-similar Tokunaga networks in the limit of a large network order. The theory uses several disjoint theoretical concepts like Horton laws of stream numbers and areas as asymptotic relations in Tokunaga networks, dimensional analysis, the Buckingham Pi theorem, asymptotic self-similarity of the first kind, or SS-1, and asymptotic self-similarity of the second kind, or SS-2. A self-contained review of these concepts, with examples, is given as "methods". The H-G data sets in channel networks from three published studies and one unpublished study are summarized to test theoretical predictions. The theory builds on six independent dimensionless river-basin numbers. A mass conservation equation in terms of Horton bifurcation and discharge ratios in Tokunaga networks is derived. Assuming that the H-G variables are homogeneous and self-similar functions of stream discharge, it is shown that the functions are of a power law form. SS-1 is applied to predict the Horton laws for width, depth and velocity as asymptotic relationships. Exponents of width and the Reynolds number are predicted and tested against three field data sets. One basin shows deviations from theoretical predictions. Tentatively assuming that SS-1 is valid for slope, depth and velocity, corresponding Horton laws and the H-G exponents are derived. Our predictions of the exponents are the same as those previously predicted for the optimal channel network (OCN) model. In direct contrast to our work, the OCN model does not consider Horton laws for the H-G variables, and uses optimality assumptions. The predicted exponents deviate substantially from the values obtained from three field studies, which suggests that H-G in networks does not obey 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 on 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 friction. These two exponents are not predicted here. Instead, we used the observed exponents of depth and slope to predict the Manning friction exponent and to test it against field exponents from three studies. The same basin mentioned above shows some deviation from the theoretical prediction. A physical reason for this deviation is given, which identifies an important topic for research. Finally, 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.

show abstract

“…Flood statistics [1][2][3][4][5], water storage [6], drainage basin organization [7], relationships between channel dimensions and flow [8], extreme precipitation events [9], wind and weather fluctuations [10,11], stock and commodity markets fluctuations [12,13] , have all been noted to obey various power laws. Many physicists have searched for unifying concepts to explain such ubiquity.…”

mentioning

confidence: 99%

Relevance of percolation theory to power‐law behavior of dynamic processes including transport in disordered media

Hunt

2009

Complexity

View full text Add to dashboard Cite

P ower-law behavior seems ubiquitous in nature as well as in human endeavors. Flood statistics [1][2][3][4][5], water storage [6], drainage basin organization [7], relationships between channel dimensions and flow [8], extreme precipitation events [9], wind and weather fluctuations [10,11], stock and commodity markets fluctuations [12,13] , have all been noted to obey various power laws. Many physicists have searched for unifying concepts to explain such ubiquity. Perhaps, however, powerlaw behavior is not quite as universal as thought. Multifractal distributions originating from cascade processes as a related, but somewhat more complex, organizing principle have often been proposed to be the appropriate universal description [33, 34]. Some [35][36][37] have questioned whether a ''class'' of stretched exponential functions might better represent a larger or smaller fraction of the data. In the ac conductivity of disordered insulators, for example, several other frequencydependences [38-40], universal or not, have been suggested. This small sample of alternate ideas need not imply that alternative scenarios are always correct either. But simply because it is often asserted that nature follows power laws does not require such; in most cases the range and quality of data are probably not sufficient to distinguish the subtle differences between the various proposed distributions. But the recognition of the simplicity of the explanation that self-similar geometrical structures [41] could be the basis of so many geophysical manifestations of apparent power laws has certainly provided impetus to the interpretation that a large number of natural phenomena do follow power-law behavior.In the case that one believes that the observed behavior conforms to true power laws, what kind of underlying mechanism should one seek? At least six such unifying concepts, nonlinear dynamics (chaos) [42], self-organized criticality [43], hierarchical dynamics [44], highly optimized tolerance [45], minimum effort

show abstract

Data for Ashley River to test channel network and river basin heterogeneity concepts

Cited by 20 publications

References 11 publications

Role of coupled flow dynamics and real network structures on Hortonian scaling of peak flows

Role of coupled flow dynamics and real network structures on Hortonian scaling of peak flows

Horton laws for hydraulic–geometric variables and their scaling exponents in self-similar Tokunaga river networks

Relevance of percolation theory to power‐law behavior of dynamic processes including transport in disordered media

Contact Info

Product

Resources

About