Ice streams, shear margins, and glacier stick-slip motion v (m/yr) - PowerPoint PPT Presentation

Ice streams, shear margins, and glacier stick-slip motion v (m/yr) 4000 1000 300 75 20 5 a Rignot et al., 2011 1.5

Part 1. Background on ice streams 2

Ice Stream Ice Ridge Ice Ridge Ice Stream Ice Shelf Ice Ridge

How certain is future Antarctic mass balance? Mass in 15 Ice Streams 1 km thickness 50 km width 1 km/yr flow velocity (other smaller mass fluxes, see Shepherd et al., 2012) Mass out Mass imbalance Imbalance is equal to the discharge of just two ice streams. How sure are we that this calculation will remain the same?

Current state-of-the-art ice sheet models Model Observed Tuned “Basal Sliding Parameter” v (m/yr) α (Pa yr/m) 1/2 4000 4000 150 1000 1000 300 300 100 75 75 50 20 20 5 5 a b 0 1.5 1.5 Morlighem et al. 2013 • The simulations shown are 3D, thermo-viscous creeping flow simulations with real bathymetric data. • Variation in flow speeds results largely from the tuned basal sliding parameter rather than from actual physical processes. • For this reason, such a description may have some utility if interpreted as a linearization about current conditions, but • it is unlikely that models such as this can forecast complex future changes. 9

Rapid ice velocities are primarily controlled by subglacial conditions. Direction of ice flow Basal Shear Stress 800 m ice thickness z Ice y x 120 km ice stream width Bed z x

Direct observation of the ice-bed interface: the WISSARD experiment 1. Fast sliding is facilitated by glacial till. ˚ ˚ ˚ ˚ ˚ ˚ JPL Photo ˚ ˚ ˚ ˚ ˚ ˚ W ˚ W 7 0 ˚ 1 Floating Ice Grounded Ice GPS stations 11

Direct observation of the ice-bed interface: the WISSARD experiment 2. Subglacial water pressures can be very high. ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ Image Width ~ 0.15 m JPL Photo ˚ ˚ W ˚ W 7 0 ˚ 1 Floating Ice Grounded Ice GPS stations 12

Direct observation of the ice-bed interface: the WISSARD experiment Image Width ~ 0.15 m JPL Photo Fast flowing ice streams exist because of the lubricating effect of a water-saturated subglacial till. 13

Ice Stream Ice Ridge Ice Ridge Shear Margin Ice Stream Ice Shelf Ice Ridge

Ice stream shear margins Shear margins are the lateral boundaries of the ice streams. This causes a large velocity gradient. Suckale et al 2014 15

Ice stream shear margins The shear margin velocity gradient causes shear heating. Suckale et al 2014 16

Subglacial hydrology 17

Part 2. Ice stream variability 18

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˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ GPS observations ˚ ˚ ˚ ˚ ˚ ˚ ˚ B. Map of the Whillans Ice Plain (WIP) ˚ 160 ˚ W 170 ˚ W ˚ ˚ W 1 5 180 ˚ 0 ˚ W 160 ˚ W W 0 ˚ 1 7 8 8 ˚ S 5 ˚ 5 S Floating Ice Floating Ice Grounded Ice Grounded Ice GPS stations GPS stations 8 8 ˚ S 4 ˚ 4 S 8 8 ˚ S 3 ˚ 3 S 1 5 180 ˚ 0 ˚ W 160 ˚ W W 0 ˚ 7 1 21

The Whillans Ice Stream is decelerating. Beem et al. 2014 2018

˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ ˚ W ˚ 0 ˚ 1 7 1 5 180˚ 0 ˚ W 160˚W 170˚W 1 8 8 ˚S 5 e I c ˚ d 5 S e d n u o r G 0.8 Sliding Floating Ice Velocity 8 8 ˚S 0.6 4 ˚ 4 S (mm/s) Direction of ice flow 0.4 8 8 ˚S 3 ˚ 3 S 0.2 1 5 180˚ 0 ˚ W 160˚W 170˚W 0 Total duration of sliding is 30 min.

Episodic ice motion Winberry et al., 2014 24

Slip event dynamics (a) M7 slip event (GPS data) 60 initial acceleration (~200 s) 50 GPS velocity (m/d) μ 40 Vmax 30 ~50 m/d 20 10 0 gradual deceleration (~1500 s) -1000 0 1000 2000 3000 4000 Time (s) μ

Seismic tremor occurs during sliding. Particle 500 Velocity (nm/s) -500 Sliding Velocity (m/day) GPS Jan 12 Jan 13 Jan 14 Velocity (m/day) Time (s) 26 Data from IRIS

Long term goal: to quantify the processes that determine the strength of the ice-bed interface. I validate an improved glacier sliding law against two observations: 1. Ice stream stick slip motion (a) M7 slip event (GPS data) 60 initial acceleration (~200 s) 50 GPS velocity (m/d) μ 40 Vmax 30 ~50 m/d 20 10 0 gradual deceleration (~1500 s) -1000 0 1000 2000 3000 4000 Time (s) Grounding Zone 2. Tremor during ice stream slip events μ Seismic Particle Velocity (nm/s) 500 -500 1000 s 3000 s 0 s 2000 s

Stick-Slip Cycles: the Sequence of Events Flow Upstream station direction Downstream station

Stick-Slip Cycles: the Sequence of Events Ice compresses in the upstream direction Steady upstream motion Minimal downstream motion

Stick-Slip Cycles: the Sequence of Events During a slip event, ruptures propagate across the ice stream. Direction of rupture propagation Direction of slip

Stick-Slip Cycles: the Sequence of Events During a slip event, ruptures propagate across the ice stream. Not yet sliding Rupture front Sliding Direction of slip

Stick-Slip Cycles: the Sequence of Events The slip events ends when accumulated strain has been relieved.

The balance of forces Push from upstream ice Direction Basal shear of acts everywhere (Elastic) ice flow Shearing y x Ocean Tides 33

The balance of forces B. Map of the Whillans Ice Plain (WIP) 150 ˚ W 180 ˚ 1 6 W 0 ˚ 0 ˚ W 1 7 85 ˚ S S ˚ 5 8 84 ˚ S S ˚ 4 8 83 ˚ S S ˚ 3 8 150 ˚ W 180 ˚ 1 6 W 0 ˚ 0 ˚ W 7 1 Floating Ice Grounded Ice GPS stations 34

The balance of forces Vertical elastic shear Longitudinal Inertia Basal shear driving stresses Our simplified ice sheet model represents a depth integrated , cross- stream profile of an ice stream. Inertia plays only a limited role in our simulations, but including it serves as a check on our predictions. Most of the interesting dynamics come from the basal shear stress term.

Designing a stick-slip sliding law During sliding with Coulomb Sliding V 1 Friction , the frictional coefficient Velocity instantaneously jumps from a static 0 to a dynamic value. Dynamic coefficient of friction 𝜐 = 𝑔 𝜏 Friction Coefficient Static coefficient of friction Coulomb Friction cannot explain the re-strengthening that causes Time repeatable slip events and leads to numerical ill-posedness due to the infinitely sharp transition in strength. 36

Designing a stick-slip sliding law We use a Rate- and State- Sliding V 1 Dependent Frictional sliding law. Velocity Important properties: V 0 1. An instantaneous strength increase during acceleration (a stabilizing feature), Friction ~ a ~ b Coefficient 2. Evolution to a steady state value over a slip scale L. Sliding is said to be rate weakening if -3 -2 -1 0 1 2 3 4 b>a. Normalized Slip, u/L 3. Supports both steady and unstable sliding 4. The weakening length scale L is thought to scale with the grain size of the sheared material. 37

Designing a stick-slip sliding law Traditional glacier sliding laws (i.e., Weertman, 1957) are inconsistent with stick slip cycles. Shear Log ( ) Stick-slip in the presence of steady loading requires a basal sliding law Stress that results in cyclic acceleration and deceleration. Importantly, traditional glacier sliding Sliding Log ( ) laws exhibit unrealistic unbounded Velocity strength and may therefore overestimate the resistance to forces that favore ice acceleration.

One sliding law, two behaviors The transition between steady sliding and stick-slip occurs because of a balance between frictional weakening and elastic restoring force : Slip Friction ~ a ~ b Coefficient Stress -3 -2 -1 0 1 2 3 4 Normalized Slip, u/L 39

Fast slip and Slow Slip Whillans Ice Plain: Quasi-steady tidal modulation Inertial rupture Smooth tidal modulation Whillans-style slip event Inertially-limited slip event “Slow-Slip” 60 1000 A. W/W c = 0.8 B. W/W c = 1.1 C. W/W c = 2.0 200 Time (hr) 40 Time (s) 500 100 20 0 0 0 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 Distance (km) Distance (km) Distance (km) 100 km 0.03 3 15 Velocity (mm/s) D. E. F. 125 km 0.02 2 10 150 km 0.01 1 5 0 0 0 0 20 40 60 0 500 1000 0 50 100 150 200 250 Time (hr) Time (s) Time (s) High pore pressure Low pore pressure Slow slip events happen in a unique range of parameter space: • Pore pressures are low enough to cause stick—slip cycles, yet • Pore pressures are high enough to avoid inertial ruptures. 40

Stick-slip cycles are consistent stagnation Sliding Velocity (m/d) 50 40 ? ~ 30 20 10 0 355 356 357 358 359 360 Time (d) 1. Low water pressure causes stick-slip cycles: frictional weakening > elastic resistance to slip due to sliding depends on water pressure 2. Lower water pressure increases the absolute level of resistive shear stress Basal Resistive Stress > Driving Stresses Also depends on water pressure Absolute strength and weakening rate both depend on effective pressure. Details: The critical pore pressure p ∗ results from a linear stability analysis of perturbations to steady frictional sliding with rate and state friction (see, for example Rice et al., 2001; Lipovsky and Dunham, 2016).