Fractal characteristics of dense stream networks

Schüller, Daniel; Rao, A. Ramachandra; Jeong, Garrett D.

doi:10.1016/s0022-1694(00)00395-4

Cited by 48 publications

(46 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The constructal relationships between mainstream length L ω and the area A ω of a river basin with streams up to order ω are determined by using Table 4 together with Table 2 and are shown in Table 5. Gray (1961) found β∼0.568 while Muller (1973) reported that β∼0.6 for river basins b8000 mi 2 (1 mile = 1609.3 m), β∼0.5 for basins between 8000 and 100,000 mi 2 , and β∼0.47 for basins N 100,000 mi 2 (see also Schuller et al, 2001). The constructal rule for the exponent β is the following:…”

Section: River Network As Constructal Fluid Treesmentioning

confidence: 98%

“…In river basins, R L ranges between 1.5 and 3.5 and is typically 2; while R B ranges between 3 and 5, typically 4 (Rodríguez-Iturbe and Rinaldo, 1997). The mainstream length L ω and the area A ω of a river basin with streams up to order ω are related through Hack's law (Hack, 1957; see also Rodríguez-Iturbe and Rinaldo, 1997;Schuller et al, 2001):…”

Section: Scaling Laws Of River Basinsmentioning

confidence: 99%

See 1 more Smart Citation

Constructal view of scaling laws of river basins

Reis¹

2006

Geomorphology

View full text Add to dashboard Cite

35-56.] proposed scaling laws that are considered to describe rather accurately the actual river basins. What we show here is that these scaling laws can be anticipated based on Constructal Theory, which views the pathways by which drainage networks develop in a basin not as the result of chance but as flow architectures that originate naturally as the result of minimization of the overall resistance to flow (Constructal Law).

show abstract

Section: River Network As Constructal Fluid Treesmentioning

confidence: 98%

Section: Scaling Laws Of River Basinsmentioning

confidence: 99%

Constructal view of scaling laws of river basins

Reis¹

2006

Geomorphology

View full text Add to dashboard Cite

show abstract

“…The 120 lumped approach will be coined as the (T)opography, (H)ydrology, (RO)ck structure and 121 (W)eathering model, or simply THROW model. The module developed for assessing the spring 122 watershed morphologic parameters is based on the concepts of stream order (Strahler, 1957) and 123 statistical self-similarity of drainage networks (Horton, 1945;Schuller et al, 2001). In an attempt to 124 account for the particularities of fluid transport in fractured rocks as described above, the area of 125 fluid-mineral interaction will be approximated in the geochemical module by a formula hinging on 126 rock fracture spacings, openings and porosities (Snow, 1968;Pacheco and Alencoão, 2006).…”

Section: Influence Of the Exposed Surface Area 638mentioning

confidence: 99%

Integrating topography, hydrology and rock structure in weathering rate models of spring watersheds

Pacheco

Weijden

2012

Journal of Hydrology

View full text Add to dashboard Cite

We are very pleased with your decision regarding our manuscript. We addressed the very minor corrections pointed out by reviewer #2, as can be consulted in the DOC file Revision_Notes. The revised version of the manuscript is given in the DOC file Reviewer #1No corrections to be made. Reviewer #21)The abstract contains some formulas. I think it is better to delete them from the abstract.The formulas were deleted. 2)p.7, 155: Please check the calculation of percolation time of soil water to reach the bedrock. Based on the given K, it should be at least 3.75 days, i.e. >3.75 days.The sentence was corrected: where the text was "< 3,75 days" is now "at least 3,75 days". 3)p.8, 188-190: The sequence of sentences beginning with "Altogether." do not make sense. How does a model operating with a minimum amount of information affects the type of methods used in the model?The sentence was deleted (in fact, it was not an essential sentence). 4)Perhaps a better phrase can be used instead of the term "aquifer formation constant". It sounds like the hydraulic conductivity and porosity have something to do with the formation of the aquifer.Throughout the text (in 7 places), the term "formation constants", although used regularly in hydrologic texts to describe aquifer hydraulic parameters such as K and n e , was replaced by "hydraulic parameters". 5)p.19, 461-64: Here the authors mention that no spring flow discharge was information was available. However, it is not clear what was done to compensate for this. The authors should make it clear to the reader by rephrasing the sentence and using better wording, what was done exactly. Perhaps this issue can be clarified in the previous methods section of the manuscript.The way how we compensated for the lacking of spring flow discharges is explained in the section "Aquifer Formation Hydraulic Parameters and Travel Times of Spring Watersheds". However, in the section ("Aquifer Formation Hydraulic Parameters and Travel Times of Stream Watersheds") we now added the following sentence to make this more clear: "The hydraulic conductivities (K) and effective porosities (n e ) resulting from this characterization were then used as proxies of the K and n e values of the spring watersheds, as explained in the next section, which also describes how groundwater travel times were downscaled from the larger (stream) the smaller (spring) scales." The papers corresponding to the reference numbers are given in the legend of RESEARCH HIGHLIGHTS• develop a weathering model that incorporates rock structure in the rate equation• conceive a weathering model especially designed for fracture artesian springs•Create a model that integrates topography, hydrology, rock structure and weathering evaluation of morphologic parameters is subjective due to difficulties in conceiving the catchment 21 geometry. Besides, when springs emerge from crystalline massifs, rock structure must be accounted 22 in formulas describing the area of minerals exposed to the percolating fluids, for a realistic 23 evaluation of th...

show abstract

“…, Muller(1973), Mandelbrot(1983), Mesa and Gupta(1987), Peckham(1995), Birnir(2008), Schuller et al(2001) (1) (Lee, 2015 (Rigon et al, 1996;Yoo, 2009 …”

mentioning

confidence: 99%