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 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 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 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)

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?

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 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)

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

Transport initiation Easiest on Titan – why? d2 - terminal velocity? Slope=0.001 d1/2 – grain size 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*=(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

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

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)

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

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

d Aquifer Water table T L

h 1.25 km