Re-evaluation of the Relationship of Master Streams and Drainage Basins

Mueller, Jerry E.

doi:10.1130/0016-7606(1972)83[3471:rotrom]2.0.co;2

Cited by 46 publications

(26 citation statements)

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“…Hallet and Molnar, 2001). Mueller, 1972;Mesa and Gupta, 1987). An exponent, h = 0.5, means that basins are self-similar, while h > 0.5 is mostly interpreted as representing basin elongation with increasing size (Rigon et al, 1996), or as resulting from channel properties such as sinuosity (Willemin, 2000).…”

Section: Block Upliftmentioning

confidence: 99%

Coupled numerical–analytical approach to landscape evolution modeling

Goren

Willett

Herman

et al. 2014

Earth Surf Processes Landf

155

193

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The Earth's topography is shaped by surface processes that operate on various scales. In particular, river processes control landscape dynamics over large length scales, whereas hillslope processes control the dynamics over smaller length scales. This scale separation challenges numerical treatments of landscape evolution that use space discretization. Large grid spacing cannot account for the dynamics of water divides that control drainage area competition, and erosion rate and slope distribution. Small grid spacing that properly accounts for divide dynamics is computationally inefficient when studying large domains. Here we propose a new approach for landscape evolution modeling that couples irregular grid‐based numerical solutions for the large‐scale fluvial dynamics and continuum‐based analytical solutions for the small‐scale fluvial and hillslope dynamics. The new approach is implemented in the landscape evolution model DAC (divide and capture). The geometrical and topological characteristics of DAC's landscapes show compatibility with those of natural landscapes. A comparative study shows that, even with large grid spacing, DAC predictions fit well an analytical solution for divide migration in the presence of horizontal advection of topography. In addition, DAC is used to study some outstanding problems in landscape evolution. (i) The time to steady‐state is investigated and simulations show that steady‐state requires much more time to achieve than predicted by fixed area calculations, due to divides migration and persistent reorganization of low‐order streams. (ii) Large‐scale stream captures in a strike‐slip environment are studied and show a distinct pattern of erosion rates that can be used to identify recent capture events. (iii) Three tectono‐climatic mechanisms that can lead to asymmetric mountains are studied. Each of the mechanisms produces a distinct morphology and erosion rate distribution. Application to the Southern Alps of New Zealand suggests that tectonic advection, precipitation gradients and non‐uniform tectonic uplift act together to shape the first‐order topography of this mountain range. Copyright © 2014 John Wiley & Sons, Ltd.

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Section: Block Upliftmentioning

confidence: 99%

Coupled numerical–analytical approach to landscape evolution modeling

Goren

Willett

Herman

et al. 2014

Earth Surf Processes Landf

155

193

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“…Since similar datasets do not exist for comparison, we performed indirect validation of the proposed dataset via the Hack’s law.The Hack’s law is an empirical power law between drainage area, A and different measures of length, L , main flow or basin length, as written in equation (1), which was originally proposed by fixing C and n to 1.4 and 0.6 respectively 20 , the modified by 23,24 to improve the estimation of n , and finally generalized as cumulative density function for both basin area and length, as given by equations (2) and (3), most recently 25–27 .

\begin{matrix} (1) & L = C A^{bold-italicn} \end{matrix}

\begin{matrix} (2) & P true(A > a true) \propto a^{- β} \end{matrix}

\begin{matrix} (3) & P true(L_{B} > l true) \propto l^{- β / n} \equiv l^{- γ} \end{matrix}

where

\begin{matrix} (4) & β = 1 - n \end{matrix}

Using the proposed dataset, we first tested the accuracy of equation (1) by regressing C and n for all grids in each continent, then that of equations (2) and (3) in the long river in each continent.…”

Section: Technical Validationmentioning

confidence: 99%

A global distributed basin morphometric dataset

et al. 2017

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Basin morphometry is vital information for relating storms to hydrologic hazards, such as landslides and floods. In this paper we present the first comprehensive global dataset of distributed basin morphometry at 30 arc seconds resolution. The dataset includes nine prime morphometric variables; in addition we present formulas for generating twenty-one additional morphometric variables based on combination of the prime variables. The dataset can aid different applications including studies of land-atmosphere interaction, and modelling of floods and droughts for sustainable water management. The validity of the dataset has been consolidated by successfully repeating the Hack’s law.

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“…In as much as humid tropical climate has been visualized during Pliocene times based on evergreen type of plants (Awasthi and Prasad 1988), if this is true, the drainage area for the Pliocene river system could be therefore approximately 42925 km 2 . Leopold et al (1964) and Muller (1972) derived a simple regression equation between stream length and drainage area in the following manner.…”

Section: Estimation Of Drainage Basin Areamentioning

confidence: 99%

Paleochannel and paleohydrology of a Middle Siwalik (Pliocene) fluvial system, northern India

Khan¹,

Tewari²

2011

J Earth Syst Sci

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Late Cenozoic fresh water molasses sediments (+6000 m thick) deposited all along the length of the Himalayan fore deep, form the Siwalik Supergroup. This paper reports the results of the paleodrainage and paleohydrology of the Middle Siwalik subgroup of rocks, deposited in non-marine basins adjacent to a rising mountain chain during Pliocene. Well-exposed sections of these rocks have provided adequate paleodrainage data for the reconstruction of paleochannel morphology and paleohydrological attributes of the Pliocene fluvial system.Cross-bedding data has been used as inputs to estimate bankfull channel depth and channel sinuosity of Pliocene rivers. Various empirical relationships of modern rivers were used to estimate other paleohydrological attributes such as channel width, sediment load parameter, annual discharge, and channel slope and flow velocity. Computed channel depth, channel slope and flow velocity are supported independently by recorded data of scour depth, cross-bedding variability and Chezy's equation.The estimates indicate that the Middle Siwalik sequence corresponds to a system of rivers, whose individual channels were about 400 m wide and 5.2-7.3 m deep; the river on an average had a low sinuous channel and flowed over a depositional surface sloping at the rate of 53 cm/km. The 700-km long Middle Siwalik (Pliocene) river drained an area of 42925 km 2 to the north-northeast, with a flow velocity of 164-284 cm/s, as it flowed generally south-southwest of the Himalayan Orogen. Bed-load was about 15% of the total load of this river, whose annual discharge was about 346-1170 m 3 /s normally and rose to approximately 1854 m 3 /s during periodic floods. The Froude number of 0.22 suggests that the water flows in the Pliocene river channels were tranquil, which in turn account for the profuse development of cross-bedded units in the sandstone. The estimated paleochannel parameters, bedding characteristics and the abundance of coarse clastics in the lithic fill are rather similar to the modern braided rivers of Canada and India such as South Saskatchewan and Gomti, respectively.

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Re-evaluation of the Relationship of Master Streams and Drainage Basins

Cited by 46 publications

References 0 publications

Coupled numerical–analytical approach to landscape evolution modeling

Coupled numerical–analytical approach to landscape evolution modeling

A global distributed basin morphometric dataset

Paleochannel and paleohydrology of a Middle Siwalik (Pliocene) fluvial system, northern India

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