1. EART163 Planetary Surfaces
Francis Nimmo

2. 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
Aeolian landforms and what they tell us

3. 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

4. Caveats 1. “Most geologic work is done by large, infrequent events”
2. Almost all sediment transport laws are empirical

5. 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

6. Flow in a permeable mediumvd
vd is the Darcy velocity (m/s)
k is the permeability (m2)
h 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?

7. 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
* Permeability can be highly scale-dependent! (e.g. fractures)

8. Porosity and permeability
Grain size 2b, pore diameter 2a
A unit cell includes 3 pore cylinders a
Porosity (f ):
Permeability (k):
Permeability increases with grain size b and porosity f
E.g. 1mm grain size, porosity 1% implies k~2x10-12 m2
Porosity-permeability relationship is also important for compaction timescale (Week 4)

9. 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
Does this make sense?
k is permeability, h is viscosity, DP is the pressure perturbation
Knowing k allows us to calculate the time t it takes a disturbance to propagate a distance d: t=d2/k
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/f is implied?

10. 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?

11. 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

12. 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

13. Sediment Transport
A column of water on a slope exerts a shear stress t
This stress will drive fluid motion
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 rf d h a

14. 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/rf )1/2=(gh sin a)1/2
The critical friction velocity required to initiate sediment transport depends on the grain size d
Does this equation make sense? Balance turbulent stress against gravity.
The dimensionless constant q is a function of u* and d and is a measure of how hard it is to initiate movement.
A typical value of q is 0.1 (see next page)

15. Shields Curve q q=0.05-0.2 Sediment transport harder
Minimum grain size
(as with aeolian transport)
Small grains
Low velocities
Large grains
High velocities

16. Transport initiation Easiest on Titan – why? d2 - terminal velocity?
Slope=0.001
d1/2 –
grain size
Burr et al. 2006

17. Water and sediment discharge
Water discharge rate (m2s-1) is well-established and depends on dimensionless friction factor 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:
The friction factors are empirical but are typically ~0.05

18. Worked example: cobbles on Titan
d=10cm so u*=11 cm/s (for q=0.1)
u*=(gh sin a)1/2 so h=9 m (for sin a = 0.001)
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?
g=1.3 ms-2, rf=500 kgm-3, rs=1000 kgm-3
fw=0.05
30 km

19. 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

20. Meanders on Venus (!) Presumably very low viscosity lava
Some channels extend for >1000 km
Channels do not always flow “down-stream” – why?
Image width 50 km

21. Fluvial landscapes Valley networks on Mars
Only occur on ancient terrain (~4 Gyr old)
What does this imply about ancient Martian atmosphere?
100 km
Valley network on Titan
Presumably formed by methane runoff
What does this imply about Titan climate and surface?
30 km

22. Fluvial Landscapes
Martian networks resemble those of the Earth, suggesting prolonged lifetime – clement climate?
Stepinksi and Stepinski 2006

23. Landscape Evolution Models

24. Martian Outflow channels
Large-scale fluvial features, indicating massive (liquid) flows, comparable to ocean currents on Earth
Morphology similar to giant post-glacial 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)?
50km
flow
direction
150km
Baker (2001)

25. Erosion & Exhumation
Erosion (aeolian?) is 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 apparently been exhumed: the channels are highstanding. Why?
These exhumed meanders are attractive targets for future Mars sample return missions
channel
meander
Malin and Edgett, Science 2003

26. Martian Gullies
A very unexpected discovery (Malin & Edgett, Science 283, , 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?

27. 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

28. Martian sediments in outcrop
Opportunity (Meridiani)
Cross-bedding indicative of prolonged fluid flows

29. 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)

30. Summary Subsurface water – percolation, sapping Surface flow
Water discharge rates
Sediment transport – initiation, mechanisms, rates
Channels – braided vs. meandering
Fluvial landscapes

31. d
Aquifer
Water
table T L

32. h
1.25 km