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

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?

Greenland Ice Sheet Current volume ~2.9x10 6 km 3 (~7m sea level equivalent) Net mass loss currently ~200 Gt/yr (~0.6 mm/yr sea level rise) Timescale ~10,000 years

Antarctic Ice Sheet Current volume ~27x10 6 km 3 (~58m sea level equivalent) Net mass loss currently ~100 Gt/yr (~0.3 mm/yr sea level rise) Timescale ~300,000 years

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

Greenland ice sheet mass balance 800 D 600 Discharge calving 400 SMB Surface balance (SMB) -1 ) 200 Mass flux (Gt yr accumulation - runoff 0 0 Eq. SLR (mm yr 0.5 MB -200 1.0 -400 -1 ) 1.5 -600 1960 1970 1980 1990 2000 2010 Year van den Broeke et al 2016 Greenland is losing mass - due to decreased SMB and increased discharge

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

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

Greenland ice sheet Jacobshavn Kangerlussuag aspect x50 Bed topography Elevation 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 including seasonal , diurnal , and episodic acceleration events (measured by GPS) heat for are rates, Water pressure stud- the distinguish small Ice speed (GPS) Zwally et al 2002 Runoff Time van de Wal et al 2015 obtained The positive feedback with increased surface melt?

Greenland ice sheet velocities Longer term measurements, over a period of increasing surface melt, appear to show a slight decreasing trend in average velocity . e.g. van de Wal et al 2015, Stevens et al 2016 km 4 Melt (w.e. m yr − 1 ) 50 a 0 10 20 Greenland 3 40 2 c 30 120 Area (km 2 ) 2,000 68.6° N 80 1 C N 20 1,000 120 40 b B A 0 0 10 110 400 600 800 1,000 1 1 , Change (%) , Elevation (m.a.s.l.) 0 2 0 0 –0.1 m yr − 2 , P = 0.80 0 0 100 0 8 6 0 Velocity (m yr − 1 ) 0 0 0 90 –10 80 1,200 a –20 Area (km 2 ) 800 67.9° N 70 400 0 –30 –30 0 30 Change (%) 60 10 b Change (%) 0 –40 –1.5 m yr − 2 , P < 0.01 R 2 = 0.79 –10 50 –20 –30 400 600 800 1,000 –50 40 Elevation (m.a.s.l.) 51° W 50° W 49° W 1985 1990 1995 2000 2005 2010 2015 Year Tedstone et al 2015 suggests a weak, possibly inverse, relationship between runoff and average velocity

Ice flow z = s u ⇡ u b h z x z = b f τ b � r Basal resistance must approximately balance the ‘ driving stress ’ τ d = � ρ i gh ∂ s (down-slope component of weight) ∂ x N = ρ i gh � p w τ b = C ( N ) u 1 /m Basal resistance related to ice speed by a friction law b effective pressure �r φ ⇡ � ρ i g r s � ( ρ w � ρ i ) g r b Basal water flow is driven by the hydraulic potential gradient i.e. both ice and water flow roughly in direction of surface slope.

2 m Mount Robson, Canada

1 m Vernagtferner, Austria

1 m Hochjochferner, Italy

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

A model of the evolving drainage system Water flow 0 10 20 30 40 50 60 20 t = 50d 8 15 10 h 5 4 a 8 S 0 20 t = 150d 4 15 y (km) 10 5 8 b 0 20 t = 500d 8 4 15 10 5 Channel segments connected on a planar c 0 0 10 20 30 40 50 60 graph, coupled to a continuum ‘sheet’. x (km) Werder et al 2013

Steady-state driven by surface runoff τ b = cNu 1 /m + friction law b Water flow Subglacial discharge Effective pressure Ice speed

Subglacial discharge Ice speed (areal m 2 /s) Time Hewitt 2013, EPSL

Summary I Increases in surface melt can both increase and decrease average ice speeds. 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 or decadal-scale models (e.g. CMIP6 models)

Ice-sheet mass balance = a m z = s e V � q c z x h m x m Z d V Z Global mass conservation d t = ( a � m ) d x � q c A ⇡ � r Surface mass balance (SMB) depends primarily on surface elevation a � m ⇡ � r � � e.g. s e equilibrium line altitude (ELA) a � m = λ ( s � s e ) Z λ ( s s e ✓ u � d x m ◆ q c = h m Calving flux is related to ice velocity and margin advance/retreat d t

Land terminating glaciers Accumulation Surface melting Subglacial discharge

Land terminating glaciers Accumulation Surface melting +/- Subglacial discharge

Marine terminating glaciers Accumulation Surface melting Calving Subglacial discharge

Marine terminating glaciers Accumulation Surface melting Calving +/- +/- Subglacial discharge

Marine terminating glaciers Accumulation Surface melting Calving Subglacial discharge

Marine terminating glaciers Accumulation Surface melting Calving + Subglacial discharge

Marine terminating glaciers Accumulation Surface melting Calving + Subglacial discharge

A reduced model = a m z = s e V � q c z x b m f τ b x m Z d V Z Global mass conservation d t = ( a � m ) d x � q c q c = F ( V ; N, s e , f ) A ✓ ◆ τ 0 = µN ⇡ � ρ i gh ∂ s Assumes a ‘plastic’ (rate-independent) friction law ∂ x ice volume / elevation determined purely by margin position and basal friction cf. Nye 1951, Weertman 1961 Uses a boundary-layer analysis to relate calving flux to local water depth b m ◆ n +2 q c = A (2 ρ i g ) n ✓ − ρ i ˆ f flotation factor cf. Schoof 2007, Tsai et al 2015 Q ( f ) b m µ ρ o

A reduced model = a m z = s e V � q c � ✓ ◆ � ρ i = f b m f τ b ρ o x m d V d t = F ( V ; N, s e , f ) V

A reduced model A decrease in bed strength results in a lowering of the surface and increased velocity increased rate of mass loss 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 )

A reduced model = a m z = s e V � q c � ✓ ◆ � ρ i = f b m f τ b ρ o x m d V d t = F ( V ; N, s e , f ) V

Summary I Increases in surface melt can both increase and decrease average ice speeds. 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 or decadal-scale models (e.g. CMIP6 models) 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.