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

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). Possibility of positive feedback? Increased surface melting increased ice speeds larger ablation area / increased discharge. Zwally et al 2002 Melt (w.e. m yr − 1 ) 4 km a 50 0 10 20 Greenland 3 40 2 Longer term observations suggest No. Increased c 120 Area (km 2 ) 2,000 30 1 80 N 68.6° N C 1,000 120 melting decreased average ice speeds (due 20 40 b B A 0 0 110 10 400 600 800 1,000 Elevation (m.a.s.l.) to more efficient subglacial drainage). 1,000 1,200 –0.1 m yr − 2 , P = 0.80 Change (%) 100 0 Velocity (m yr − 1 ) 800 600 90 –10 80 1,200 a Area (km 2 ) –20 800 67.9° N 70 400 0 –30 –30 0 30 60 Change (%) 10 b Change (%) 0 –40 –1.5 m yr − 2 , P < 0.01 R 2 = 0.79 50 –10 –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 But… decreased ice speeds may be more significant for ice loss. c d

Tidewater glaciers � q c Ice discharge (calving + frontal melting) controls dynamic mass loss. Primary control on discharge is ice depth at margin.

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

Ice margin evolution margin ice flux calving + frontal melting = q m � q c z x h m x m � d t d x m = q m � q c h m d t

Ice margin evolution margin ice flux calving + frontal melting = q m � q c z x h m x m � d t d x m = q m � q c h m q c ⇡ q m d t

Ice margin evolution margin ice flux calving + frontal melting = q m � q c z x h m x m � d t d x m = q m � q c h m q c ⇡ q m d t Q q m = Q ( h m ) Discharge primarily determined by ice + calving criterion dynamics (near-margin force balance) h m = h f cf. Schoof 2007, Hindmarsh 2012 h m

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

Global mass conservation + a calving + frontal melting � q c z x x m Z b Z x m Z x m d V Ice volume V = h d x d t = a d x � q c 0 0

Global mass conservation + a calving + frontal melting � q c z x x m Z b Z x m Z x m d V Ice volume V = h d x d t = a d x � q c Z 0 0 d x m ∂ V d t ∂ x m

Conventional ice-sheet model + a u ( x, z, t ) ( b Ice h ( x, t ) = z x τ b Substrate x m Z b Z s Force balance (Stokes flow + sliding law) ice velocity / flux q = u d z b ∂ h ∂ t + ∂ q Mass conservation ice thickness ∂ x = a Z

Plastic bed ice-sheet model + a u ( x, z, t ) ( b Ice h ( x, t ) = z x ✓ ◆ Substrate x m τ b = τ 0 u ≥ 0 ( r 2 τ 0 ρ i g ( x m − x ) 1 / 2 h = e.g. flat bed Force balance ice thickness √ Z x ✓ ◆ a − ∂ h q = d x Mass conservation ice velocity / flux ∂ t 0 cf. plastic ice models (Nye 1951, Weertman 1961, 1976, Ultee & Bassis 2016) Ice velocity is not unconstrained - it does what is needed to maintain the

Example One dimensional glacier with an over-deepened bed 1500 Elevation [m] 1000 500 0 -500 0 20 40 60 80 100 Distance [km] Ice volume and ice flux at margin depend on margin position: 100 1 Discharge [10 6 m 2 /y] Ice volume [10 6 m 2 ] � Q ( h f ( x m )) V ( x m ) 80 0.8 60 0.6 40 0.4 20 0.2 0 0 0 50 100 0 50 100 x m x m Z Margin position [km] Margin position [km] 0 Z x m d V d t = a d x � Q ( h f ( x m )) 0 Z

Strengthening bed Impose a gradual increase of basal stress (hydrology-induced) induces retreat Z Z x m d x m d τ 0 ∂ V a d x � Q ( h f ( x m )) � ∂ V = d t d t ∂ x m ∂τ 0 0 0 y 120 100 50 y 80 Basal stress [kPa] 60 100 100 y 50 Margin position [km] 0 1 Discharge [10 6 m 2 /y] 150 y 0.5 0 -100 0 100 200 200 y Time [y]

Weakening bed In contrast, a weakening bed results in initial advance, then retreat - much lower Z cumulative discharge Z x m d x m d τ 0 ∂ V a d x � Q ( h f ( x m )) � ∂ V = d t d t ∂ x m ∂τ 0 0 0 y 120 100 50 y 80 Basal stress [kPa] 60 100 100 y 50 Margin position [km] 0 1 Discharge [10 6 m 2 /y] 150 y 0.5 0 -100 0 100 200 Time [y] 200 y

Ocean forcing Q Impose an increase in the floatation fraction required for calving h m = fh f Z Z x m d x m ∂ V = a d x � Q ( h f ( x m ) , f ) ( d t ∂ x m 0 r Compare with strengthening bed: 1.1 1 120 Floatation fraction 100 0.9 80 Basal stress [kPa] 100 60 50 100 Margin position [km] 50 0 Margin position [km] 0 1 Discharge [10 6 m 2 /y] 1 0.5 Discharge [10 6 m 2 /y] 0.5 0 -100 0 100 200 0 Time [y] -100 0 100 200 Time [y] very similar response

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.