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

g

vCq

f

s

3*

3/12

)(10

gd

fsf

t

tf dv

5.3*

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

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

dx

dPk

L

Hg

kv 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

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

Porosity and permeability

Grain size 2b, pore diameter 2a

A unit cell includes 3 pore cylinders

2

2

4

3

b

a 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

• Porosity-permeability relationship is also important for

compaction timescale (Week 4)

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

Pk

hyd

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

*

gdu

f

fs

crit

• 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? Balance

turbulent stress

against gravity.

Shields Curve

=0.05-0.2

Sediment

transport

harder

Small grains

Low velocities

Large grains

High velocities

Minimum grain size

(as with aeolian transport)

Transport initiation

Burr et al. 2006

Slope=0.001

Easiest on Titan – why?

d1/2 –

grain size

d2 - terminal velocity?

Water and sediment discharge

asin1 2/3 ghf

qw

w

fs

f

s

s ghf

q

a

2/122/3 )(sin

1

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

*

gdu

f

fs

crit

30 km

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

fw=0.05

asin1 2/3 ghf

qw

w

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

flow

direction

150km

Baker (2001)

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

Malin and Edgett, Science 2003

meander

channel

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, Mars

150km

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

dx

dPkvd

P

khyd

2/12/1

2/1

*

gdu

f

fs

crit

asin* ghu

T

d

L

Water

table

Aquifer

1.25 km

h