Changes in glacier sliding and their influence on ice-sheet mass - - PowerPoint PPT Presentation

Changes in glacier sliding and their influence on ice-sheet mass loss

Ian Hewitt, Mathematical Institute, University of Oxford

(i) How does meltwater penetrating to the bed of a glacier or ice sheet affect its motion? (ii) What implications does this have for ice loss / sea level?

Changes in glacier sliding and their influence on ice-sheet mass loss

Ian Hewitt, Mathematical Institute, University of Oxford

Net mass loss currently ~200 Gt/yr (~0.6 mm/yr sea level rise) Greenland Ice Sheet Current volume ~2.9x106 km3 (~7m sea level equivalent) Timescale ~10,000 years

Antarctic Ice Sheet Net mass loss currently ~100 Gt/yr (~0.3 mm/yr sea level rise) Current volume ~27x106 km3 (~58m sea level equivalent) Timescale ~300,000 years

Accumulation Runoff Calving / Ocean melting ~700 Gt/y ~400 Gt/y ~500 Gt/y Ice sheet mass balance [~2000 Gt/y] [~2100 Gt/y] Geothermal heating

• 600
• 400
• 200

200 400 600 800 1960 1970 1980 1990 2000 2010 Mass flux (Gt yr

• 1)

Year D SMB MB 0.5 1.0 1.5

• Eq. SLR (mm yr
• 1)

van den Broeke et al 2016

Surface balance (SMB) Discharge

accumulation - runoff

Greenland ice sheet mass balance

calving

Greenland is losing mass - due to decreased SMB and increased discharge

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

Greenland ice sheet Ice speed (Jan/Feb 2018 from Sentinel 1) Elevation

Bed topography Elevation Greenland ice sheet

Jacobshavn Kangerlussuag aspect x50

Ice speed (Jan/Feb 2018 from Sentinel 1)

Laura Stevens

Greenland ice sheet velocities Summer drainage of surface meltwater causes significant fluctuations in ice speed

heat for are rates, stud- the distinguish small

• btained

The

van de Wal et al 2015

Ice speed (GPS) Runoff

Time

including seasonal, diurnal, and episodic acceleration events (measured by GPS) Water pressure

Zwally et al 2002

positive feedback with increased surface melt?

67.9° N 68.6° N 51° W 50° W 49° W 6 8 1 , 1 , 2 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

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)

Tedstone et al 2015

Greenland ice sheet velocities Longer term measurements, over a period of increasing surface melt, appear to show a slight decreasing trend in average velocity. suggests a weak, possibly inverse, relationship between runoff and average velocity

e.g. van de Wal et al 2015, Stevens et al 2016

Ice flow

x z

h u ⇡ ub

Basal resistance must approximately balance the ‘driving stress’ (down-slope component of weight) Basal resistance related to ice speed by a friction law f τb

• r

τd = ρigh ∂s ∂x τb = C(N) u1/m

b

N = ρigh pw

effective pressure

z = s z = b

Basal water flow is driven by the hydraulic potential gradient

rφ ⇡ ρigrs (ρw ρi)grb

i.e. both ice and water flow roughly in direction of surface slope.

2 m Mount Robson, Canada

Vernagtferner, Austria 1 m

1 m Hochjochferner, Italy

Evolution of the subglacial drainage system Increased efficiency Isolated water cavities Water pressure increases (so basal resistance decreases) with increasing meltwater flux Melt-enlarged channels Water pressure decreases (so basal resistance increases) with increasing meltwater flux

5 10 15 20

t = 50d

a

4 8 8

10 20 30 40 50 5 10 15 20

t = 500d

c

4 8 x (km)

5 10 15 20

t = 150d

b

4 8 y (km)

60 10 20 30 40 50 60

Water flow S

h

A model of the evolving drainage system Channel segments connected on a planar graph, coupled to a continuum ‘sheet’.

Werder et al 2013

Subglacial discharge Effective pressure Ice speed Steady-state driven by surface runoff + friction law

Water flow

τb = cNu1/m

b

Time Ice speed Subglacial discharge (areal m2/s)

Hewitt 2013, EPSL

Summary I Numerical models are increasingly able to reproduce observed patterns of seasonal velocity change (with some tuning) e.g. Bougamont et al 2014, Hoffman et al 2016. But computations are expensive - these processes are not yet in any continental

• r decadal-scale models (e.g. CMIP6 models)

Increases in surface melt can both increase and decrease average ice speeds.

Ice-sheet mass balance

x z

qc = a

z = se m

se equilibrium line altitude (ELA) e.g.

λ(s

se

V ⇡ r

• a m = λ(s se)

xm Surface mass balance (SMB) depends primarily on surface elevation

⇡ r a m

Calving flux is related to ice velocity and margin advance/retreat Global mass conservation

Z dV dt = Z

A

(a m) dx qc hm Z qc = hm ✓ u dxm dt ◆

Accumulation Surface melting Subglacial discharge

Land terminating glaciers

Accumulation Surface melting Subglacial discharge

+/- Land terminating glaciers

Accumulation Surface melting Subglacial discharge Calving

Marine terminating glaciers

Accumulation Surface melting Subglacial discharge Calving

Marine terminating glaciers +/- +/-

Accumulation Surface melting Subglacial discharge Calving

Marine terminating glaciers

Accumulation Surface melting Subglacial discharge Calving

Marine terminating glaciers +

Accumulation Surface melting Subglacial discharge Calving

Marine terminating glaciers +

A reduced model Assumes a ‘plastic’ (rate-independent) friction law ice volume / elevation determined purely by margin position and basal friction

• cf. Nye 1951, Weertman 1961

✓ ◆ τ0 = µN ⇡ ρigh ∂s ∂x

Global mass conservation

Z dV dt = Z

A

(a m) dx qc

Uses a boundary-layer analysis to relate calving flux to local water depth

qc = A(2ρig)n µ ˆ Q(f) ✓ − ρi ρo bm ◆n+2 f

flotation factor cf. Schoof 2007, Tsai et al 2015

qc = F( V ; N, se, f) bm

x z

bm

qc = a

z = se m V

xm f τb

V dV dt = F( V ; N, se, f)

A reduced model qc = a

z = se m V

xm

• = f

✓ ρi ρo bm ◆

f τb

A decrease in bed strength results in a lowering of the surface and increased velocity A reduced model An increase in bed strength results in initially decreased velocities… but this induces margin retreat, which may lead to even larger mass loss (tidewater-glacier retreat) increased rate of mass loss

V dV dt = F( V ; N, se, f)

A reduced model qc = a

z = se m V

xm

• = f

✓ ρi ρo bm ◆

f τb

Summary I Numerical models are increasingly able to reproduce observed patterns of seasonal velocity change (with some tuning) e.g. Bougamont et al 2014, Hoffman et al 2016. But computations are expensive - these processes are not yet in any continental

• r decadal-scale models (e.g. CMIP6 models)

Increases in surface melt can both increase and decrease average ice speeds. Summary II Changes in ice speed do not necessarily translate to changes in mass, with potential to influence ice loss in either direction. Inland slow-down of the ice-sheet may help induce tidewater-glacier retreat, with potential to precipitate more rapid ice loss.