PTYS 554
Evolution of Planetary Surfaces
Fluvial Processes III
PYTS 554 – Fluvial Processes III
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Fluvial Processes I
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Fluvial Processes II
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Rainfall and runoff
Channelization and erosion
Drainage networks
Sediment transport – Shields curve
Velocity and discharge, Manning vs Darcy Weisback
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
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Groundwater tables
Subterranean flow rates
Springs and eruption of pressurized groundwater
Sapping as an erosional mechanism
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PYTS 554 – Fluvial Processes III
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Fluid mostly infiltrates surface
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Infiltration rate fast at first until near-surface pores are filled, constant rate thereafter set by
permeability
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Fluid that doesn’t infiltrate the subsurface can runoff
 Causes erosion
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Surface with high infiltration rates are
very resistant to erosion
Melosh 2011
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PYTS 554 – Fluvial Processes III
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Nomenclature
Groundwater table
Capillary
zone
Unsaturated
(Vadose)
zone
Phreatic Surface
Saturated
zone
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PYTS 554 – Fluvial Processes III
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Ponded liquids
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(Precipitation – evaporation) vs. transport into the groundwater table
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PYTS 554 – Fluvial Processes III
Groundwater flow – Darcy’s Law
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Flow rate per unit area (not the same as flow velocity!)
Q
k dp
= uDarcy = A
h dx
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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
uDarcy = uFlow f
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Where Φ is porosity
i.e. fraction of area covered by pores on a rock face is
porosity
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PYTS 554 – Fluvial Processes III
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Models for permeability
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Permeability is usually very directional
Not always directly related to pore
space
Carman-Kozeny model relates flow
through a packed bed to porosity
Dp 180 udarcy h (1- f )
=
Dx
Fs d 2
f3
rearrange :
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k = C'
2
d 2f 3
(1- f )
Medium Sand
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Where C’ is ~1/180 (for spherical
particles) and depends on particle
shape and tortuosity
Bigger particles or higher porosity
means larger permeability
PYTS 554 – Fluvial Processes III
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Within the saturated zone
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Porosity decreases with depth
Salt precipitation increases with depth as water
migration speeds slow
In a regolith, porosity scales exponentially with
depth
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Based on Apollo seismic data
f = foe-z g
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On Earth permeability scales as a power law with
depth
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Not-applicable to surface permeabilities
Scaled to Mars
k =10-4.4 z-3.2
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Scaling to other planets then assume it’s the
overburden pressure that matters
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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
PYTS 554 – Fluvial Processes III
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Hydrologists usually work with hydraulic head instead of permeability
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H: the height a column of water would rise to if unconfined
Height relative to what? Doesn’t matter, only relative heights drive flow.
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Darcy’s law becomes:
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Define a hydraulic conductivity:
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u=-
k dp
krg dH
=h dx
h dx
u = -K
dH
dx
where K =
krg
h
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p
H=
rg
PYTS 554 – Fluvial Processes III
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Flow in a confined aquifer:
Qunit area = uDarcy
H1 - H 2 )
(
=K
Turcotte &
Schubert, 2002
Dx
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PYTS 554 – Fluvial Processes III
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Flow in an unconfined aquifer
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Discharge per meter of width
(breaks down near h=0)
Q = u ( x) h ( x)
dh
h
dx
2Q
h=
xo - x
K
Q = -K
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Applied to a dam w meters thick
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Dupuit-Fuchheimer discharge
2
2
h
h
K ( 0 1)
Q=
2
w
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PYTS 554 – Fluvial Processes III
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Changes with time
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Liquid in u(x)h(x)
Liquid out u(x+dx)h(x+dx)
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Examine small changes i.e.
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h = ho + e where e << ho
¶e Kho ¶ 2e
@
¶t
f ¶x 2
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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
æ Kho ö P
ç
÷
è f øp
PYTS 554 – Fluvial Processes III
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Mix of permeable and impermeable
layers can lead to perched aquifers
and spring discharge
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Especially true on the Colorado
Plateau where permeable sandstone
overlies impermeable slitstones
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Seeps weaken rock by transporting
cementing agents to the surface
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Discharge transports sediment away
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PYTS 554 – Fluvial Processes III
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Sapping
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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
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PYTS 554 – Fluvial Processes III
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Characteristics of sapping channels
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Usually one main channel
Theatre-shaped alcove at head
Short stubby tributaries
Not a dendritic network – low stream order
Sapping channels vs. runoff
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Sapping: Propagate backward via head-ward erosion
Runoff: down-cutting of pre-existing terrain
Idaho and Utah
Mars, msss.com
Pelletier and Baker 2011
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PYTS 554 – Fluvial Processes III
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Longitudinal profiles
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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
PYTS 554 – Fluvial Processes III
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Runoff dominates over
sub-surface flow
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Sub-surface flow
dominates over runoff
Pelletier and Baker 2011
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PYTS 554 – Fluvial Processes III
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More Mars
Examples
Pelletier and Baker 2011
PYTS 554 – Fluvial Processes III
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Canyon de Chelly, Earth
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PYTS 554 – Fluvial Processes III
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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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PYTS 554 – Fluvial Processes III
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Sapping on Titan?
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Huygens descent probe
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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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PYTS 554 – Fluvial Processes III
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Penetrometer data and methane detection
indicate Titan’s surface is wet
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Rounded cobbles indicate runoff has occured
Zarnecki et al., 2005
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PYTS 554 – Fluvial Processes III
Outflow Channels
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Huge flood carved channels
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Contains streamlined Islands
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Likely that a large underground reservoir emptied
catastrophically
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Source region collapses to chaos terrain
Flood empties into northern lowlands
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Up to 400km across and 2.5km deep
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Discharge estimates up to 104-109 m3/sec
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PYTS 554 – Fluvial Processes III
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Terrestrial analogue
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End of the last ice-age
Glacial lake Missoula- Ice-dam breaks
Channeled scablands, Washington
Outflow channel, Mars
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PYTS 554 – Fluvial Processes III
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Fluvial Processes I
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
Fluvial Processes II





Rainfall and runoff
Channelization and erosion
Drainage networks
Sediment transport – Shields curve
Velocity and discharge, Manning vs Darcy Weisback
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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