Hydraulic Geometry: Empirical Investigations and Theoretical Approaches

Eaton, Brett C.; Davidson, S. L.

doi:10.1016/b978-0-12-818234-5.00002-x

Cited by 16 publications

(29 citation statements)

References 101 publications

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“…The channel‐forming discharge is “a theoretical discharge that if maintained indefinitely would produce the same channel geometry as the natural long‐term hydrograph” (Copeland et al, ) and is the discharge that is approximately bankfull, controls channel cross‐sectional geometry, and transports more sediment than any other discharge. This discharge generally occurs with a recurrence interval of 1.5 to 2 years (Eaton, ; Leopold & Maddock, ). Terrestrial data sets are used to derive a relationship between discharge Q and channel width B

Q = a B^{c},

where a and c are coefficients that include all other boundary conditions, including bank strength and flow viscosity.…”

Section: Methods Used For Estimating Paleodischarge On Marsmentioning

confidence: 99%

“…Many martian studies use the relationship derived by Osterkamp and Hedman (), who related the active channel width to the 2‐year recurrence discharge, which is often assumed to approximate the channel forming discharge. Jacobsen and Burr () argued that this relation is only correlative and may yield inaccurate discharge estimate values, and argued for the use of hydraulic geometry relationships (e.g., Eaton, ) that instead relate bankfull channel width to bankfull discharge.…”

Section: Methods Used For Estimating Paleodischarge On Marsmentioning

confidence: 99%

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Assessing the Accuracy of Paleodischarge Estimates for Rivers on Mars

Morgan

Craddock

2019

Geophysical Research Letters

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Estimates of river paleodischarges have been used to constrain the former climate of Mars. Paleodischarge has been calculated using mechanistic approximations of the channel bed‐shear stress at the threshold of particle motion or correlative width‐discharge relations derived from empirical terrestrial hydraulic geometry data. We apply both these methods to a study set of gaged terrestrial rivers with field‐measured bankfull properties to assess the reliability of discharge estimates given similar uncertainties as ancient martian rivers. We find that the threshold method yields conservative values, provided a reasonable grain size is used. However, we find that digital elevation models of a similar resolution to those constructed from Context Camera (CTX) data may not be of sufficient resolution to be useful for estimating paleohydrologic conditions. Results from our analysis demonstrate the inherent uncertainties when approximating paleodischarges on Mars and stress the need to consider realistic boundary conditions when determining such values.

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Q = a B^{c},

where a and c are coefficients that include all other boundary conditions, including bank strength and flow viscosity.…”

Section: Methods Used For Estimating Paleodischarge On Marsmentioning

confidence: 99%

Section: Methods Used For Estimating Paleodischarge On Marsmentioning

confidence: 99%

Assessing the Accuracy of Paleodischarge Estimates for Rivers on Mars

Morgan

Craddock

2019

Geophysical Research Letters

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“…For example, Hayden et al (2019) demonstrated over 2 orders of magnitude of uncertainty in relating ridge width to paleo‐channel width due to lateral accretion and amalgamation of channel deposits during channel‐belt formation and scarp retreat during ridge exhumation. This uncertainty is amplified in calculations relying on channel width; for example, discharge is commonly calculated using a relation that depends approximately on channel width squared (e.g., Eaton, 2013; Williams, 1986, 1988).…”

Section: Introductionmentioning

confidence: 99%

Fluvial Sinuous Ridges of the Morrison Formation, USA: Meandering, Scarp Retreat, and Implications for Mars

Hayden

Lamb

2020

JGR Planets

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Sinuous ridges have been interpreted as evidence for ancient rivers on Mars, but relating ridge geometry to paleo-hydraulics remains uncertain. Three analog ridge systems from the Morrison Formation, Utah, are composed of sandstone caprocks, up to 50 m wide and 8 m thick, atop mudstone flanks. Ridge caprocks have narrowed significantly compared to sandstone bodies preserved in outcrop, consistent with a new ridge-erosion model that can be used to estimate original sandstone-body extent. Ridge networks represent caprocks intersecting at distinct stratigraphic levels, rather than a preserved channel network. Caprocks are interpreted as amalgamated channel belts, rather than inverted channels, with dune and bar cross stratification that was used to reconstruct paleo-channel dimensions. Curvilinear features on ridge tops are outcropping lateral accretion sets (LAS) from point bars and indicate meandering. We found that caprock thickness scales with paleo-channel depth and LAS curvature scales with paleo-channel width. Application of these relations to a ridge in Aeolis Dorsa, Mars, yielded consistent water discharge estimates (310-1,800 m 3 /s). In contrast, using ridge width or ridge radius of curvature as paleo-channel proxies overestimated discharge by a factor of 30-500. In addition, the ridge-erosion model suggests that scarp retreat may be less efficient on Mars, resulting in taller and wider ridges, with more intact caprocks. Altogether, our results support the hypothesis that ridges are exhumed channel belts and floodplain deposits implying long-lived fluvial activity recorded within a depositional basin. Plain Language Summary Ridges across Mars have sinuous shapes that resemble rivers, but they are topographic highs (hills) rather than troughs. These landforms potentially hold valuable clues about ancient rivers that once flowed on Mars, but to decipher these clues, we must understand how the ridges formed. We studied ridges in Utah that resemble the Martian ridges and may have formed in a similar way. We found that the Utah ridges are composed of sandstone caprocks that overlie mudstone and are from a thick sequence of sedimentary rocks from the Jurassic period. The sandstones were deposited by rivers as a channel belt, and the mudstones represent the neighboring river floodplains. These rocks were subsequently uplifted, and ridges formed as the weaker mudstones eroded faster than the sandstones. We found that both the thickness of the sandstones and curvature of bar-accretion surfaces within can be used to approximate ancient river water discharge. We also found that the sandstones have been narrowed by erosion, and we developed a scarp-erosion model describing this process. We applied the methods tested in Utah to ridges on Mars and found consistent agreement. Our results suggest that the ridges on Mars are exhumed and eroded deposits from ancient river-channel belts.

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“…Power laws and logarithmic or exponential functions have this property. A well‐known fluvial example is that channel width and mean depth appear to follow simple power‐law relations with bankfull discharge over the full range from laboratory channels and irrigation canals to the largest continent‐draining rivers (Lacey, 1930; Leopold and Maddock, 1953; Eaton, 2013).…”

Section: Introductionmentioning

confidence: 99%

Limits to scale invariance in alluvial rivers

Ferguson

2020

Earth Surf Processes Landf

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Assumptions about fluvial processes and process–form relations are made in general models and in many site‐specific applications. Many standard assumptions about reach‐scale flow resistance, bed‐material entrainment thresholds and transport rates, and downstream hydraulic geometry involve one or other of two types of scale invariance: a parameter (e.g. critical Shields number) has the same value in all rivers, or doubling one variable causes a fixed proportional change in another variable in all circumstances (e.g. power‐law hydraulic geometry). However, rivers vary greatly in size, gradient, and bed material, and many geomorphologists regard particular types of river as distinctive. This review examines the tension between universal scaling assumptions and perceived distinctions between different types of river. It identifies limits to scale invariance and departures from simple scaling, and illustrates them using large data sets spanning a wide range of conditions. Scaling considerations and data analysis support the commonly made distinction between coarse‐bed and fine‐bed reaches, whose different transport regimes can be traced to the different settling‐velocity scalings for coarse and fine grains. They also help identify two end‐member sub‐types: steep shallow coarse‐bed ‘torrents’ with distinctive flow‐resistance scaling and increased entrainment threshold, and very large, low‐gradient ‘mega rivers’ with predominantly suspended load, subdued secondary circulation, and extensive backwater conditions. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd

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Hydraulic Geometry: Empirical Investigations and Theoretical Approaches

Cited by 16 publications

References 101 publications

Assessing the Accuracy of Paleodischarge Estimates for Rivers on Mars

Assessing the Accuracy of Paleodischarge Estimates for Rivers on Mars

Fluvial Sinuous Ridges of the Morrison Formation, USA: Meandering, Scarp Retreat, and Implications for Mars

Limits to scale invariance in alluvial rivers

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