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Glacier Hydrology Ian Hewitt, University of Oxford - PowerPoint PPT Presentation

Glacier Hydrology Ian Hewitt, University of Oxford hewitt@maths.ox.ac.uk Water sources - Basal melting - Surface melting, precipitation Subglacial hydrology - Sheet flow - Tunnels / channels - Cavities - Canals - Lakes Large-scale models Glacier


  1. Glacier Hydrology Ian Hewitt, University of Oxford hewitt@maths.ox.ac.uk

  2. Water sources - Basal melting - Surface melting, precipitation Subglacial hydrology - Sheet flow - Tunnels / channels - Cavities - Canals - Lakes Large-scale models

  3. Glacier hydrology Accumulation Surface melting (runoff) u s Internal creep u b Basal melting / freezing ‘Sliding’

  4. Thermal setting ⇠ ⇠ T T m T T m ⇠ T T m Basal freezing Basal melting Frozen bed (no sliding?) ) G ⇠ 0 . 06 W m � 2 Geothermal heating Basal melting ⇠ m ⇠ 10 mm y � 1 ⌧ b ⇠ 100 kPa = ⌧ b u b ⇠ 0 . 1 W m � 2 Frictional heating u b ⇠ 30 m y � 1

  5. Water sources in Antarctica Basal melting ~ 10 mm/y mm/y Pattyn 2010

  6. Water sources in Greenland Basal melting ~ 10 mm/y Surface runoff ~ 1 m/y mm yr -1 van den Broeke et al 2016 Aschwanden et al 2012

  7. Direction of subglacial water flow Z s H α Hydraulic potential Z b ⇤ φ = ρ w gZ b + p w in terms of effective pressure φ = ρ w gZ b + ρ i g ( Z s � Z b ) � N N = p i − p w � ∂ x ∂ x ∂ x = Ψ + ∂ N � ∂φ Potential gradient Ψ = ρ i g tan α + ( ρ w � ρ i ) g tan θ ∂ x − Potential gradient if water pressure were at overburden N = 0 Predominant control on water flow direction from surface slope

  8. Subglacial drainage systems Kamb & LaChapelle 1964, Lliboutry 1968, Walder & Hallet Röthlisberger 1972, 1979, Nye 1976 Alley et al 1986, Creyts & Schoof 2009 Walder & Fowler 1994 Increasing water flow

  9. Weertman film Weertman 1972, Walder 1982 Weertman suggested water could flow as a film ✓ ◆ h Q = h 3 ✓ ◆ Ψ + ∂ N Poiseuille flux 12 µ ∂ x Water flow dissipates energy through heating Leads to an instability � Larger h Larger flux Melting of ice roof Flow wants to concentrate in localized channels / tunnels However, a patchy film may still exist eg. Alley 1989, Creyts & Schoof 2009

  10. Röthlisberger channels Röthlisberger 1972, Nye 1976 Ice wall melting is counteracted by viscous creep Creep N = p i − p w = p i � p w Melting Röthlisberger/Nye theory (ignoring pressure dependence of melting temperature) ∂ t ∂ s ρ w ∂ S ∂ t + ∂ Q ∂ x = m water mass conservation + M Steady state ρ w ∂ S ∂ t = m � ˜ ASN n wall evolution ! 1 /n K 3 / 4 ρ i Ψ 11 / 8 n Q 1 / 4 n c N ⇡ ρ i L ˜ A ✓ ◆ ✓ ◆ Ψ + ∂ N local energy conservation mL = Q ∂ x Effective pressure INCREASES ◆ 1 / 2 momentum conservation ✓ Ψ + ∂ N with discharge Q = K c S 4 / 3 (turbulent flow parameterization) ∂ x Neighbouring channels compete with one another leads to an arterial network w w

  11. Röthlisberger channels + M in | Q = Q in p w = p out 500 N 0 m Hydraulic potential − 500 0 5 10 15 20 25 30 35 40 45 Distance km Discharge 10 Q m 3 s − 1 5 0 1500

  12. Jökulhlaups (GLOFs) Nye 1976, Spring & Hutter 1981, Clarke 2003 A success of the Röthlisberger channel theory is the application to ice dammed floods . ∂ t = S 4 / 3 Ψ 3 / 2 ∂ S Combine channel evolution equation � ˜ ASN n ρ i L � A L ∂ N with a lake filling equation at ∂ t = m L � Q x = 0 ρ w g Fowler 2009 � �� �������������� � � � � � � � � � � � � � ������������������������������������������������� ��

  13. Linked cavities Walder 1986, Kamb 1987 Cavities grow through sliding over bedrock Sliding Creep h r Model ∂ ˆ S ∂ t = U b h r � ˜ A ˆ SN n Smaller ‘orifices’ control the flow 10 m Approximate steady-state relationship Effective pressure DECREASES � N Flow is distributed N ( Q ) � Q < 0 with discharge Cavity size is controlled by parameter Λ = U b i.e. depends on effective pressure and sliding speed N n

  14. Drainage system stability Walder 1986, Kamb 1987, Schoof 2010, Hewitt 2011 Energy is still dissipated by water flow Sliding Melting Creep ∂ S ∂ t = m + U b h r � ˜ ASN n ρ i h r A linked cavity system can become unstable to produce channels eg. if discharge becomes sufficiently large, or sliding speed sufficiently low Conversely, a channel can become unstable to cavities eg. if discharge low, or sliding speed sufficiently high

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