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

• Aeolian landforms and what they tell us

gv

Cq fs

3*

3/12

)(10

gd

fsft

Df

fs

Cdg

v )(

34

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

dxdPk

LHgkv fd

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 permeabilityGrain size 2b, pore diameter 2aA unit cell includes 3 pore cylinders

2

2

43

ba Porosity ( ):

18

22bk Permeability (k):

a

• 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

Pkhyd

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?

Does this make sense?

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?

Lamb et al. 2008

Do blunt amphitheatres necessarily indicate groundwater sapping?Or might they be a sign of ancient surface runoff?

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

• This stress will drive fluid motion

h

d

a

at singhf

f

• 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

2/12/1

2/1

*

gduf

fscrit

• The critical friction velocity required to initiate sediment transport depends on the grain size d

• 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)

Does this equation make sense?

Shields Curve

=0.05-0.2

Sediment transport harder

Small grainsLow velocities

Large grainsHigh velocities

Minimum grain size(as with aeolian transport)

Transport initiation

Burr et al. 2006

Slope=0.001

Easiest on Titan – why?

Water and sediment discharge

asin1 2/3 ghf

qw

w

fs

f

ss gh

fq

a

2/122/3 )(sin1

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

Worked example: cobbles on Titan

d=10cm so u*=11 cm/s (for =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?

2/12/1

2/1

*

gduf

fscrit

30 km

g=1.3 ms-2, f=500 kgm-3, s=1000 kgm-3

fw=0.05asin1 2/3 gh

fq

ww

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 (!)

Image width 50 km

• Presumably very low viscosity lava

• Some channels extend for >1000 km

• Channels do not always flow “down-stream” – why?

Fluvial landscapes• Valley networks on Mars• Only occur on ancient

terrain (~4 Gyr old)• What does this imply about

ancient Martian atmosphere?

30 km

• Valley network on Titan• Presumably formed by

methane runoff• What does this imply about

Titan climate and surface?

100 km

Fluvial Landscapes

Stepinksi and Stepinski 2006

• Martian networks resemble those of the Earth, suggesting prolonged lifetime – clement climate?

Landscape Evolution Models

• 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)?

Martian Outflow channels

50km

flowdirection

150km

Baker (2001)

Martian Gullies• A very unexpected discovery

(Malin & Edgett, Science 283, 2330-2335, 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

Schon et al. 2009

• Consequence of a sudden change in slope – sediment gets dumped out

• Fans can eventually merge along-strike to form a continuous surface – a bajada

Martian sediments in outcrop

Opportunity (Meridiani)

Cross-bedding indicative of prolonged fluid flows

Lakes

Titan, 140km across (false colour)

Gusev, Mars150km

Clearwater Lakes Canada~30km diameters

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

Summary• Subsurface water – percolation, sapping

• Surface flow– Water discharge rates– Sediment transport – initiation, mechanisms, rates

• Channels – braided vs. meandering• Fluvial landscapes

dxdPkvd

Pkhyd

2/12/1

2/1

*

gduf

fscrit

asin* ghu

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?

Malin and Edgett, Science 2003meander

channel