Transcript Slide 1

EART163 Planetary Surfaces
Francis Nimmo
Last Week - Wind
• Sediment transport
– Initiation of motion – friction velocity v*, threshold
grain size dt, turbulence and viscosity
– Sinking - terminal velocity
– Motion of sand-grains – saltation, sand flux, dune
motion



dt  10

  f (  s   f ) g 
2
1/ 3
qs  C
 f v*3
g
4 (  s   f )dg
v
3
 f CD
• Aeolian landforms and what they tell us
This week – “Water”
• Only three bodies: Earth, Mars, Titan
• Subsurface water – percolation, sapping
• Surface flow
– Water discharge rates
– Sediment transport – initiation, mechanisms, rates
• Channels
• Fluvial landscapes
Caveats
1. “Most geologic work is done by large, infrequent events”
2. Almost all sediment transport laws are empirical
Subsurface Flow
• On Earth, there is a water table below which the
pores are occupied by fluid
• This fluid constitutes a reservoir which can recharge
rivers (and is drained by wells)
• Surface flow happens if infiltration into the
subsurface is exceeded by the precipitation rate
Flow in a permeable medium
vd
vd
k
H k dP
vd   f g 

L  dx
vd is the Darcy velocity (m/s)
k is the permeability (m2)
 is the viscosity (Pa s), typical
value for water is 10-3 Pa s
• Darcy velocity is the average flow velocity of fluid through
the medium (not the flow velocity through the pores)
• Permeability controls how fast fluid can flow through the
medium – intrinsic property of the rock.
• Permeable flows are almost always low Reynolds numbers –
so what?
Permeability and porosity
• Permeability can vary widely
• Porosity is the volume fraction of rock occupied by voids
• High porosity usually implies high permeability
Rock type
Permeability (m2)
Gravel
10-9 – 10-7
Loose sand
10-11 – 10-9
Permeable basalt
10-13 – 10-8
Fractured crystalline rock
10-14 – 10-11
Sandstone
10-16 – 10-12
Limestone
10-18 – 10-16
Intact granite
10-20 – 10-18
Porosity and permeability
Grain size 2b, pore diameter 2a
A unit cell includes 3 pore cylinders
Porosity ( ):
3 a 2

2
4 b
 b
k
18
2
Permeability (k):
a
2
• Permeability increases with grain size b and porosity 
• E.g. 1mm grain size, porosity 1% implies k~2x10-12 m2
Response timescale
• If the water table is disturbed, the response timescale
depends on the permeability
• The hydraulic diffusivity (m2s-1) of the water table is
k
 hyd 
P Does this make sense?

k is permeability,  is viscosity, P is the pressure perturbation
• Knowing  allows us to calculate the time t it takes a
disturbance to propagate a distance d: t=d2/
• Example: a well draws down the local water table by
10 m. If it takes 1 year for this disturbance to
propagate 1 km, what value of k/ is implied?
When does subsurface flow matter?
• Subsurface flow is generally very slow compared to
surface flow, so it does much less geological work
• But at least on present-day Mars, water is not stable at
the surface, while it is stable in the subsurface.
• So subsurface flow may matter on Mars.
• On Earth, it matters in regions with high permeability
where the rock is soluble (e.g. limestone or chalk)
• Titan may also have regions where “rock” dissolution
is important?
Groundwater sapping on Mars?
Do blunt amphitheatres necessarily indicate groundwater sapping?
Or might they be a sign of ancient surface runoff?
Lamb et al. 2008
Sediment transport
• At low velocities, bed-load dominates (saltation +
traction + rotation)
• At intermediate velocities/low grain sizes, suspended
load can be important
• At high velocities, entire bed moves (washload)
• Solution load is usually minor
Sediment Transport
• A column of water on a slope exerts a shear stress t
t   f ghsin a
• This stress will drive fluid motion
f
d
h
a
• If the fluid motion is
rapid enough, it can also
overcome gravity +
cohesion and cause
sediment transport
• The shear stress t is a
useful measure of
whether sediment
transport is likely
Transport Initiation
• Just like aeolian transport, we can define a friction
velocity u* which is related to the shear stress t
• The friction velocity u*=(t/f )1/2=(gh sin a)1/2
• The critical friction velocity required to initiate
sediment transport depends on the grain size d
u
*
crit
 s   f

 
f

1/ 2




gd 
1/ 2
 1/ 2
Does this equation
make sense?
• The dimensionless constant  is a function of u* and d
and is a measure of how hard it is to initiate movement.
• A typical value of  is 0.1 (see next page)
Shields Curve
Sediment
transport
harder

=0.05-0.2
Minimum grain size
(as with aeolian transport)
Small grains
Low velocities
Large grains
High velocities
Transport initiation
Easiest on Titan – why?
Slope=0.001
Burr et al. 2006
Water and sediment discharge
Water discharge rate (m2s-1) is well-established and depends on
dimensionless friction factor fw:
1 3/ 2
qw 
h
g sin a
fw
Sediment discharge rate (m2s-1) is not well-established. The
formula below is most suitable for steep slopes. It also depends on
a dimensionless friction factor fs:
f
1 3/ 2
2 1/ 2
qs  h (sin a ) g
fs
s   f
The friction factors are empirical but are typically ~0.05
Worked example: cobbles on Titan
u
*
crit
 s   f

 
f

1/ 2




gd 
1/ 2
 1/ 2 d=10cm so u*=11 cm/s (for =0.1)
g=1.3 ms-2, f=500 kgm-3, s=1000 kgm-3
fw=0.05
30 km
u*=(gh sin a)1/2 so h=9 m (for sin a
= 0.001)
1 3/ 2
qw 
h
g sin a
fw
Fluid flux = 20 m2s-1
For a channel (say) 100m wide,
discharge rate = 2000 m3/s
Catchment area of say 400 km2,
rainfall rate 18 mm/h
Comments?
Braided vs. Meandering Channels
Image 2.3 km wide. Why are the
meanders high-standing?
• Braided channels are more common at high slopes and/or high
discharge rates (and therefore coarse sediment load – why?)
• Meanders seem to require cohesive sediment to form – due to
clays or plants on Earth, and clays or ice on Mars
Meanders on Venus (!)
• Presumably very low
viscosity lava
• Some channels
extend for >1000 km
• Channels do not
always flow “downstream” – why?
Image width 50 km
Fluvial landscapes
• Valley networks on Mars
• Only occur on ancient
terrain (~4 Gyr old)
• What does this imply about
ancient Martian
atmosphere?
100 km
30 km
• Valley network on Titan
• Presumably formed by
methane runoff
• What does this imply about
Titan climate and surface?
Fluvial Landscapes
• Martian networks resemble those of the Earth,
suggesting prolonged lifetime – clement climate?
Stepinksi and Stepinski 2006
Landscape Evolution Models
Martian Outflow channels
• Large-scale fluvial features,
indicating massive (liquid) flows,
comparable to ocean currents on
Earth
• Morphology similar to giant postglacial floods on Earth
• Spread throughout Martian history,
but concentrated in the first 1-2
Gyr of Martian history
• Source of water unknown –
possibly ice melted by volcanic
eruptions (jokulhaups)?
flow
direction
50km
150km
Baker (2001)
Martian Gullies
• A very unexpected discovery
(Malin & Edgett, Science 283, 23302335, 2000)
• Found predominantly at high
latitudes (>30o), on pole-facing
slopes, and shallow (~100m
below surface)
• Inferred to be young – cover
young features like dunes and
polygons
• How do we explain them?
Liquid water is not stable at the
surface!
• Maybe even active at present
day?
Alluvial Fans
• Consequence of a sudden change in slope – sediment
gets dumped out
• Fans can eventually merge along-strike to form a
continuous surface – a bajada
Schon et al. 2009
Martian sediments in outcrop
Opportunity (Meridiani)
Cross-bedding indicative of prolonged fluid flows
Lakes
Clearwater Lakes Canada
~30km diameters
Gusev, Mars
150km
Titan lakes are (presumably)
methane/ethane and occur mainly near
the poles – why?
How do we know they are liquid-filled?
Gusev crater shows little evidence for
water, based on Mars Rover data
Titan, 140km across (false colour)
Summary
• Subsurface water – percolation, sapping
k dP
vd 
 dx
 hyd 
k

P
• Surface flow
– Water discharge rates
– Sediment transport – initiation, mechanisms, rates
u  ghsin a
*
u
*
crit
 s   f

 
f

1/ 2




• Channels – braided vs. meandering
• Fluvial landscapes
gd 
1/ 2
 1/ 2
Erosion
• Erosion will remove small, near-surface craters
• But it may also expose (exhume) craters that were previously
buried
• Erosion has recently been recognized as a major process on
Mars, but the details are still extremely poorly understood
• The images below show examples of fluvial features which
have been exhumed: the channels are highstanding. Why?
channel
meander
Malin and Edgett, Science 2003