PTYS 554

Evolution of Planetary Surfaces

Fluvial Processes IIIFluvial Processes III

PYTS 554 – 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

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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

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Nomenclature

Unsaturated (Vadose) zone

Saturated zone

Capillary zoneGroundwater table

Phreatic Surface

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

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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

Groundwater flow – Darcy’s Law

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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

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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.

Clifford & Parker 2001

Scaled to Mars

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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:

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Flow in a confined aquifer:

Turcotte & Schubert, 2002

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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

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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

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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

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Sapping Seeps weaken rock by transporting cementing agents to the surface Discharge or runoff transports sediment away

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

e.g. Najavo Sandstone

e.g. Kayenta formation

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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 2011Mars, msss.com

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Longitudinal profiles Logarithmic for runoff Piecewise linear for sapping channels

Knick points are common and migrate ‘upstream’

Aharonson et al., 2002

Ma’adim Vallis

Al-Qahira Vallis Brown’s Canyon

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Runoff dominates over sub-surface flow

Sub-surface flow dominates over runoff

Pelletier and Baker 2011

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More Mars Examples

Pelletier and Baker 2011

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Canyon de Chelly, Earth

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Sapping vs runoff

Runoff Sapping

Downcutting through terrain Headward erosion of alcove

Dendritic network – high order Few tributaries – low order

Channels narrow to points Channel head is theatre-shaped

Logarithmic longitudinal profile Flat piecewise segments for floors

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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

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Penetrometer data and methane detection indicate Titan’s surface is wet

Rounded cobbles indicate runoff has occured

Zarnecki et al., 2005

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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

Outflow Channels

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Terrestrial analogue End of the last ice-age Glacial lake Missoula- Ice-dam breaks

Channeled scablands, Washington

Outflow channel, Mars

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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