Transport Laws and Geomorphic Form. Atacama Desert Columbia Hills Some of these slides are from...
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Transcript of Transport Laws and Geomorphic Form. Atacama Desert Columbia Hills Some of these slides are from...
Atacama Desert
Columbia Hills
Some of these slides are from Dietrich’s AGU talk
(full video linked on the class notes page or available at http://www.agu.org/webcast/fm08/presentations/langbein/)
Similarity of Form
Conservation Equations
• Mass conservation
U: uplift, E: Erosion, qs: sediment tranport
(Dietrich eq 4)
A full understanding of geomorphic form requires transport laws and specification of sediment production rates.
Transport Law of Gophers on Hillslopes
Initial diffusive approximation is improved by adding in the effects of ‘friction’ a nonlinear transport law. (Dietrich p. 13)
TRANSPORT LIMITED• Ample debris supply• S ~ C = D h• -z/ t = C/ x
NOTATIONS = Actual sediment transport (per unit flow width L2T-1)C = Sediment Transporting Capacity (per unit flow width L2T-1)D = Detachment rate from channel bed (LT-1)z = elevation; x = horizontal distance (1-D); t= time elapsed
EROSION LIMITED • Above are two limiting cases of a continuum• -z/ t = S/ x• dS/dx = D – S/h• Tends to Transport-Limited as h0; to Supply Limited as h (In Kirkby 1971 notation, k=1/h).
SUPPLY LIMITED• Debris limited by detachment/
weathering• S << C• - z/ t = D
‘Special’ Cases (described by Kirkby {after GK Gilbert}): Here notation is simplified to 1 spatial dimension
Slide from Kirkby and Wilgoose, 2005 IAG presentation
• Transport limited: Transport capacity (qs) is insufficient to overcome soil production rate (weathering, P)– E.g.,‘rounded hillslopes’; soil-mantled surfaces. As is the
general rule, different processes (forms of the transport law) predict different surface expressions:
‘Special’ Cases (described by Kirkby {after GK Gilbert})
• Weathering limited: Soil production P is the limiting factor in dz/dt. Bedrock typically is exposed.
On Earth, weathering and hence soil/sediment production rates couple strongly to sediment thickness (h) (Dietrich p 14-16).
• On weathering limited slopes, the form of the slope can be a strong function of lithology and structure.
• Often, this weathering limited case is most important at the highest part of the stream network.
‘Special’ Cases (described by Kirkby {after GK Gilbert})
Discussion questions:
• How do we understand the shape of landscapes? What controls whether a slope is mantled by soil or debris and shallow-sloping versus steeply-sloping and characterized by exposed bedrock?
Can we apply this approach to Mars?
Possible areas to think about: Gullied Landscapes? Valles Marineris wall retreat? Modification of craters and lava flows (perhaps different in Amazonian/Hesperian/Noachian?)