Fluvial Processes III

1. Fluvial Processes III

2. Fluvial Processes I • Rainfall and runoff • Channelization and erosion • Drainage networks • Sediment transport – Shields curve • Velocity and discharge, Manning vs Darcy Weisback • Fluvial Processes II • Stream power and stable bedforms from ripples to antidunes • Floodplains, Levees, Meanders and braided streams • Alluvial fans and Deltas • Wave action and shoreline Processes • Fluvial Processes III • Groundwater tables • Subterranean flow rates • Springs and eruption of pressurized groundwater • Sapping as an erosional mechanism

3. Fluid mostly infiltrates surface • Infiltration rate fast at first until near-surface pores are filled, constant rate thereafter set by permeability • Fluid that doesn’t infiltrate the subsurface can runoff • Causes erosion • Surface with high infiltration rates are very resistant to erosion Melosh 2011

4. Nomenclature Unsaturated (Vadose) zone Capillary zone Groundwater table Phreatic Surface Saturated zone

5. Ponded liquids • (Precipitation – evaporation) vs. transport into the groundwater table

6. Groundwater flow – Darcy’s Law • Flow rate per unit area (not the same as flow velocity!) • η is the viscosity • dp/dx is the applied pressure gradient • k is the permeability • Permeability generally increases with porosity • Permeability has units of area 1 Darcy is 10-12 m-2 or (1 μm2) • Discharge = flow velocity x area • Where Φ is porosity • i.e. fraction of area covered by pores on a rock face is porosity

7. Models for permeability • Permeability is usually very directional • Not always directly related to pore space • Carman-Kozeny model relates flow through a packed bed to porosity • Where C’ is ~1/180 (for spherical particles) and depends on particle shape and tortuosity • Bigger particles or higher porosity means larger permeability Medium Sand

8. Within the saturated zone • Porosity decreases with depth • Salt precipitation increases with depth as water migration speeds slow • In a regolith, porosity scales exponentially with depth • Based on Apollo seismic data • On Earth permeability scales as a power law with depth • Not-applicable to surface permeabilities • Scaling to other planets then assume it’s the overburden pressure that matters • Replace z with z(g1/g2) • Where g1 is the gravity where the relationship was established… • …and g2 is the gravity on the planet that you’re interested in. Scaled to Mars Clifford & Parker 2001

9. Hydrologists usually work with hydraulic head instead of permeability • H: the height a column of water would rise to if unconfined • Height relative to what? Doesn’t matter, only relative heights drive flow. • Darcy’s law becomes: • Define a hydraulic conductivity:

10. Flow in a confined aquifer: Turcotte & Schubert, 2002

11. Flow in an unconfined aquifer • Discharge per meter of width (breaks down near h=0) • Applied to a dam w meters thick • Dupuit-Fuchheimer discharge

12. Changes with time • Liquid in u(x)h(x) • Liquid out u(x+dx)h(x+dx) • Examine small changes i.e. • Diffusion equation • If ε varies periodically then waves propagate out through the groundwater table • Wave amplitude decreases exponentially with x with e-folding distance • P = Period

13. Mix of permeable and impermeable layers can lead to perched aquifers and spring discharge • Especially true on the Colorado Plateau where permeable sandstone overlies impermeable slitstones • Seeps weaken rock by transporting cementing agents to the surface • Discharge transports sediment away

14. Sapping • Seeps weaken rock by transporting cementing agents to the surface • Discharge or runoff transports sediment away e.g. Najavo Sandstone e.g. Kayenta formation Backwasting here undermines rock above Collapse produces alcove that lengthens into channel Floor is set by the impermeable layer Brown Canyon, Utah Aharonson et al., 2002

15. Characteristics of sapping channels • Usually one main channel • Theatre-shaped alcove at head • Short stubby tributaries • Not a dendritic network – low stream order • Sapping channels vs. runoff • Sapping: Propagate backward via head-ward erosion • Runoff: down-cutting of pre-existing terrain Idaho and Utah Pelletier and Baker 2011 Mars, msss.com

16. Longitudinal profiles • Logarithmic for runoff • Piecewise linear for sapping channels • Knick points are common and migrate ‘upstream’ Aharonson et al., 2002 Ma’adim Vallis Brown’s Canyon Al-Qahira Vallis

17. Runoff dominates over sub-surface flow • Sub-surface flow dominates over runoff Pelletier and Baker 2011

18. More Mars Examples Pelletier and Baker 2011

19. Canyon de Chelly, Earth

20. Sapping vs runoff

21. Sapping on Titan? • Huygens descent probe • Dendritic channels leading into dark areas • River-like features – up to forth order channels • Sapping like features in other areas Sodeblom et al., 2007

22. Penetrometer data and methane detection indicate Titan’s surface is wet • Rounded cobbles indicate runoff has occured Zarnecki et al., 2005

23. Outflow Channels • Huge flood carved channels • Contains streamlined Islands • Likely that a large underground reservoir emptied catastrophically • Source region collapses to chaos terrain • Flood empties into northern lowlands • Up to 400km across and 2.5km deep • Discharge estimates up to 104-109 m3/sec

24. Terrestrial analogue • End of the last ice-age • Glacial lake Missoula- Ice-dam breaks Channeled scablands, Washington Outflow channel, Mars

25. Fluvial Processes I • Rainfall and runoff • Channelization and erosion • Drainage networks • Sediment transport – Shields curve • Velocity and discharge, Manning vs Darcy Weisback • Fluvial Processes II • Stream power and stable bedforms from ripples to antidunes • Floodplains, Levees, Meanders and braided streams • Alluvial fans and Deltas • Wave action and shoreline Processes • Fluvial Processes III • Groundwater tables • Subterranean flow rates • Springs and eruption of pressurized groundwater • Sapping as an erosional mechanism