Transport Laws and Geomorphic Form

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 Similarity of Form

Conservation Equations Mass conservation U: uplift, E: Erosion, q s : sediment tranport (Dietrich eq 4) A full understanding of geomorphic form requires transport laws and specification of sediment production rates.

Also see discussion of Kirkby p. 25

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 NOTATION S = Actual sediment transport (per unit flow width L 2 T -1 ) C = Sediment Transporting Capacity (per unit flow width L 2 T-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 h  0; 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 (q s ) 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 ). 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})

Transport Limited Weathering Limited

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?)