Hydrologically-induced slow-down as a mechanism for tidewater - - PowerPoint PPT Presentation

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Hydrologically-induced slow-down as a mechanism for tidewater - - PowerPoint PPT Presentation

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Hydrologically-induced slow-down as a mechanism for tidewater glacier retreat Ian Hewitt, University of Oxford Subglacial hydrology and ice flow Drainage of surface meltwater to the bed affects ice speed (due to influence on water pressure).

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Hydrologically-induced slow-down as a mechanism for tidewater glacier retreat

Ian Hewitt, University of Oxford

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Subglacial hydrology and ice flow

Drainage of surface meltwater to the bed affects ice speed (due to influence on water pressure). But… decreased ice speeds may be more significant for ice loss. Longer term observations suggest No. Increased melting decreased average ice speeds (due to more efficient subglacial drainage). Possibility of positive feedback? Increased surface melting increased ice speeds larger ablation area / increased discharge.

Tedstone et al 2015

1 2 3 4

Melt (w.e. m yr−1)

a

1985 1990 1995 2000

Year

2005 2010 2015 40 50 60 70 80 90 100 110 120

Velocity (m yr−1)

–0.1 m yr−2, P = 0.80 –1.5 m yr−2, P < 0.01 R2 = 0.79

b

400 600 800 1,000

Elevation (m.a.s.l.)

1,000 2,000

N

c

40 80 120

Area (km2)

c d

Zwally et al 2002

67.9° N 68.6° N 51° W 50° W 49° W 600 800 1,000 1,200 C B A 10 20 km –50 –40 –30 –20 –10 10 20 30 40 50 Change (%) –30 30 400 800 1,200 a 400 600 800 1,000 Elevation (m.a.s.l.) –30 –20 –10 10 Change (%) Change (%) Area (km2)

b

Greenland

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Tidewater glaciers

Ice discharge (calving + frontal melting) controls dynamic mass loss. Primary control on discharge is ice depth at margin. qc

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Most rapid mass loss caused by retreat into over-deepening. Such retreat is induced by a decrease in supply from upstream.

Tidewater glaciers

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xm x z

Ice margin evolution

calving + frontal melting margin ice flux = qm qc dt

  • hm

dxm dt = qm qc hm

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xm x z

Ice margin evolution

calving + frontal melting margin ice flux = qm qc dt

  • hm

dxm dt = qm qc hm qc ⇡ qm

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xm x z

Ice margin evolution

calving + frontal melting margin ice flux = qm qc dt

  • hm

dxm dt = qm qc hm qc ⇡ qm

  • cf. Schoof 2007, Hindmarsh 2012

hm qm = Q(hm) Discharge primarily determined by ice dynamics (near-margin force balance) + calving criterion Q hm = hf

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Extreme Ice Survey - Time-lapse camera Columbia Glacier, Alaska

Time-lapse movie

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xm x z calving + frontal melting qc

Global mass conservation

V = Z xm h dx Ice volume Z

b

dV dt = Z xm a dx qc + a

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xm x z calving + frontal melting qc

Global mass conservation

V = Z xm h dx Ice volume Z

b

dV dt = Z xm a dx qc + a Z ∂V ∂xm dxm dt

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Conventional ice-sheet model

Mass conservation Force balance (Stokes flow + sliding law) ice thickness

x z

h(x, t) = + a

Ice Substrate

b u(x, z, t) ( ice velocity / flux τb ∂h ∂t + ∂q ∂x = a Z Z

b

q = Z s

b

u dz xm

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Plastic bed ice-sheet model

Mass conservation Force balance ice velocity / flux ice thickness

  • cf. plastic ice models (Nye 1951, Weertman 1961, 1976, Ultee & Bassis 2016)

e.g. flat bed τb = τ0 u ≥ 0 ( ✓ ◆ h = r2τ0 ρig(xm − x)1/2 √ q = Z x ✓ a − ∂h ∂t ◆ dx Ice velocity is not unconstrained - it does what is needed to maintain the

x z

h(x, t) = + a

Ice Substrate

b u(x, z, t) ( xm

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Example

Margin position [km]

50 100

Ice volume [106 m2]

20 40 60 80 100

xm V (xm) One dimensional glacier with an over-deepened bed Ice volume and ice flux at margin depend on margin position:

Margin position [km]

50 100

Discharge [106 m2/y]

0.2 0.4 0.6 0.8 1

Q(hf(xm)) xm

Distance [km]

20 40 60 80 100

Elevation [m]

  • 500

500 1000 1500

Z dV dt = Z xm a dx Q(hf(xm)) Z

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0 y 50 y 100 y 150 y 200 y

Strengthening bed

60 80 100 120 Basal stress [kPa] 50 100 Margin position [km]

Time [y]

  • 100

100 200 0.5 1 Discharge [106 m2/y]

Z ∂V ∂xm dxm dt = Z xm a dx Q(hf(xm)) ∂V ∂τ0 dτ0 dt Impose a gradual increase of basal stress (hydrology-induced) induces retreat

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0 y 50 y 100 y 150 y 200 y

60 80 100 120 Basal stress [kPa] 50 100 Margin position [km]

Time [y]

  • 100

100 200 0.5 1 Discharge [106 m2/y]

In contrast, a weakening bed results in initial advance, then retreat - much lower cumulative discharge

Weakening bed

Z ∂V ∂xm dxm dt = Z xm a dx Q(hf(xm)) ∂V ∂τ0 dτ0 dt

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Ocean forcing

Impose an increase in the floatation fraction required for calving

0.9 1 1.1 Floatation fraction 50 100 Margin position [km]

Time [y]

  • 100

100 200 0.5 1 Discharge [106 m2/y] 60 80 100 120 Basal stress [kPa] 50 100 Margin position [km]

Time [y]

  • 100

100 200 0.5 1 Discharge [106 m2/y]

Compare with strengthening bed: very similar response Q hm = fhf Z ∂V ∂xm dxm dt = Z xm a dx Q(hf(xm), f) ( r

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Summary

Subglacial meltwater can both increase and decrease ice speeds. The decrease may be the more significant for ice loss. Conventional ice-sheet models are not yet equipped to investigate this. Plastic-bed ice-sheet models provide a useful means to examine margin retreat - limited by re-distribution of ice mass rather than by ice rheology / sliding law. Both an ocean-induced increase in calving rate and a hydrologically-induced decrease in upstream supply can precipitate rapid retreat.