EART163 Planetary Surfaces

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

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 • 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? vd 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 vd

Permeability and porosity • Permeability can vary widely • Porosity is the volume fraction of rock occupied by voids • High porosity usually implies high permeability

a Porosity and permeability Grain size 2b, pore diameter 2a A unit cell includes 3 pore cylinders 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

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/fis 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 • 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

Transport Initiation • Just like aeolian transport, we can define a friction velocityu* which is related to the shear stress t • The friction velocity u*=(t/rf)1/2=(ghsina)1/2 • The critical friction velocity required to initiate sediment transport depends on the grain size d Does this equation make sense? • 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)

Shields Curve Sediment transport harder q q=0.05-0.2 Minimum grain size (as with aeolian transport) Large grains High velocities Small grains Low 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: 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 q=0.1) u*=(ghsina)1/2so 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

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 “down-stream” – 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 • Valley network on Titan • Presumably formed by methane runoff • What does this imply about Titan climate and surface? 30 km

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

Landscape Evolution Models

flow direction 150km 50km 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)? 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 • 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 • Surface flow • Water discharge rates • Sediment transport – initiation, mechanisms, rates • Channels – braided vs. meandering • Fluvial landscapes

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

EART163 Planetary Surfaces