Transcript PYTS 554 – Fluvial Processes III
PTYS 554 Evolution of Planetary Surfaces
Fluvial Processes III
PYTS 554 – Fluvial Processes III
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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PYTS 554 – Fluvial Processes III
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
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Surface with high infiltration rates are very resistant to erosion Melosh 2011
Nomenclature PYTS 554 – Fluvial Processes III Groundwater table Phreatic Surface Capillary zone Unsaturated (Vadose) zone Saturated zone
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PYTS 554 – Fluvial Processes III
Ponded liquids
(Precipitation – evaporation) vs. transport into the groundwater table
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PYTS 554 – Fluvial Processes III Groundwater flow – Darcy
’
s Law
Flow rate per unit area (not the same as flow velocity!)
Q A
=
u
Darcy
= -
k
h
η is the viscosity
dp dx
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 μm 2 )
Discharge = flow velocity x area
u Darcy
=
u Flow
f
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
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
D
p
D
x
= 180
u
darcy
F
s
d
2 h
rearrange
: ( 1 f 3 f ) 2
k
=
C
' (
d
2 f 3 1 f ) 2
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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PYTS 554 – Fluvial Processes III
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
f = f
o
e
-
z
g
On Earth permeability scales as a power law with depth
k
= 10 4.4
z
3.2
Scaling to other planets then assume it ’s the overburden pressure that matters
1 /g 2 ) Where g 1 is the gravity where the relationship was established… …and g 2 is the gravity on the planet that you interested in.
’
re
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Scaled to Mars Clifford & Parker 2001
PYTS 554 – Fluvial Processes III
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.
H
=
p
r
g
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Darcy
’
s law becomes:
u
= -
k
h
dp dx
= -
k
r
g
h
dH dx
Define a hydraulic conductivity:
u
= -
K dH dx where K
=
k
r
g
h
PYTS 554 – Fluvial Processes III
Flow in a confined aquifer:
Q unit area
=
u Darcy
=
K
(
H
1 -
H
2 D
x
) 10
Turcotte & Schubert, 2002
Flow in an unconfined aquifer
Discharge per meter of width (breaks down near h=0)
Q
= ( ) ( )
Q
= -
K dh h dx h
= 2
Q K x o
-
x
PYTS 554 – Fluvial Processes III
Applied to a dam w meters thick
Dupuit-Fuchheimer discharge
Q
=
K
2 (
h
0 2 -
h
1 2 )
w
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Changes with time
Liquid in u(x)h(x) Liquid out u(x+dx)h(x+dx) PYTS 554 – Fluvial Processes III
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Examine small changes i.e.
h
=
h
o
+ e
where
e <<
h
o
¶e ¶
t
@
Kh o
f ¶ 2 e ¶
x
2
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
Kh o
f ö ø
P
p
PYTS 554 – Fluvial Processes III
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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PYTS 554 – Fluvial Processes III
Sapping
Seeps weaken rock by transporting cementing agents to the surface Discharge or runoff transports sediment away e.g. Najavo Sandstone Backwasting here undermines rock above Collapse produces alcove that lengthens into channel Floor is set by the impermeable layer e.g. Kayenta formation Brown Canyon, Utah Aharonson et al., 2002
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PYTS 554 – Fluvial Processes III
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
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Mars, msss.com
Idaho and Utah Pelletier and Baker 2011
PYTS 554 – Fluvial Processes III
Longitudinal profiles
Logarithmic for runoff Piecewise linear for sapping channels
Knick points are common and migrate
‘
upstream
’
Aharonson et al., 2002
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Ma
’
adim Vallis Al-Qahira Vallis Brown
’
s Canyon
Runoff dominates over sub-surface flow PYTS 554 – Fluvial Processes III
Sub-surface flow dominates over runoff
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Pelletier and Baker 2011
PYTS 554 – Fluvial Processes III
More Mars Examples
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Pelletier and Baker 2011
Canyon de Chelly, Earth PYTS 554 – Fluvial Processes III
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PYTS 554 – Fluvial Processes III
Sapping vs runoff
Runoff
Downcutting through terrain Dendritic network – high order Channels narrow to points Logarithmic longitudinal profile
Sapping
Headward erosion of alcove Few tributaries – low order Channel head is theatre-shaped Flat piecewise segments for floors 20
PYTS 554 – Fluvial Processes III
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
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Sodeblom et al., 2007
PYTS 554 – Fluvial Processes III
Penetrometer data and methane detection indicate Titan
’
s surface is wet
Rounded cobbles indicate runoff has occured
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Zarnecki et al., 2005
PYTS 554 – Fluvial Processes III
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 10 4 -10 9 m 3 /sec
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PYTS 554 – Fluvial Processes III
Terrestrial analogue
End of the last ice-age Glacial lake Missoula- Ice-dam breaks Channeled scablands, Washington
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Outflow channel, Mars
PYTS 554 – Fluvial Processes III
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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