Glacier hydrology Ice -directed drainage Isdirigert drenering Supraglacial Lateral Englacial Subglacial

Supraglacial drainage - Kongsvegen, Svalbard

Superimposed ice forming

Mother earth is crying

Why do the glaciers accelerate ? Increased basal sliding: 1. More surface meltwater lubricate the bed 2. Less backpressure – calving and bottom melting under the floating ice 3. Sea water temperature and circulation Krabill et al. 2000

Future runoff from small glaciers and ice caps 2000 2100

Summer discharge curves - Bayelva

Water through-flow Response curves Water flow velocity: v ≥ 0,40 m/s

Deformable bed: Darcian flow, canals and R-channels Thin sediment layers can not transport large fluxes of water the drainage capacity will be exceeded by the water supply water will start flowing along the ice-till interface R-channel canal For small surface slopes (<0.1) water will drain in canals of high water pressure eroded into the sediments For large surface slopes (>0.1) water will drain in R-channels eroded into the ice Darcian flow: Follow the hydraulic gradient within the till Well sorted (grains of approximately all one size) materials have higher porosity than similarly sized poorly sorted materials (where smaller particles fill the gaps between larger particles). Consolidation takes place when a normal force is applied to the till. But since the till is water saturated, and water is incompressible, two outcomes are possible: First; if the water is free to drain, then fine. The soil will consolidate and the porosity decrease. Secondly, if the water is unable to drain or the conductivity is to small, the pore water pressure will increase. Increasing the pore water pressure means weakening the soil. I will explain more about this in a minute. A dilatant material is one in which viscosity increases with the rate of shear (also termed shear thickening). Finally, if now the ice on top of the till increases its speed, the saturated till can start shearing. Due to its inhomogeneity, the soil will increase its volume –> increasing its pore volume -> decreasing its pore pressure or increase its water volume. If the pore water pressure is reduced, the soil increases its yield strength, whereas if the water volume increases the soil becomes weaker than it was before shear deformation commenced Dilatancy - The mean of measured porosity for sediments underlying active Whillans and Bindschadler ice streams in West Antarctica lies in the range 0.40≤ n≤ 0.48 (Kamb 2001); such high values imply that these sediments are dilated. Because soils compress more readily than they decompress, there is a strong tendency for soils to reduce their pore volume when they are subjected to cycles of loading and unloading. Dilatancy is the only subglacial mechanical process that can greatly increase porosity and, in doing so, erase the memory of loading history that is encoded in the overconsolidation poc of the sediment. The different drainage systems influence the way glaciers move over their bed. We will now see how variable effective pressures changes the surface velocity of glaciers

Darcy’s flow law Fluid flow of fluid through a porous media where κ is permeability and μ viscosity

Subglacial drainage in quiescent stage tunnel system (R-channels) pw low and decrease with Q (Hock & Hooke 1993)

Non-deformable bed: High flux hydraulics R-channels: Melt enlargement and creep closure in competition Flowing water generates heat Channel enlargement into the ice Creep closure due to deformable ice Seasonal and diurnal geometry evolution Photo: Michael Hambrey courtesy: U.H. Fischer Steady-state: inverse pressure-discharge relation arborescent structure low surface-to-volume ratio

Subglacial drainage during surge– linked cavity - pw is high and increase with Q Links (Kamb 1987)

Engabreen

Engabreen – subglacial tunnel system

Bondhusbreen, Folgefonna

Bondhusbreen - Folgefonna

Deformation rate h = 160m Glens flow law: ė = A τⁿ Closure rate: dr/dt = A (P/n)ⁿ dr/dt ~ 100-150 mm/d If P = ρgh = 14 bar, n = 3: A = 0.36 y-1 bar-1 or 11.4 * 10-15 s-1kPa-3 - twice as high as Peterson

Ice deformation

Ice deformation

Engabreen – subglacial laboratory

Non-deformable bed: Low flux hydraulics Linked-cavity system Since the two systems discussed here Kamb, 1987

Nigardsbreen still advanced in 2004

Glaciers on deformable and non-deformable beds Hydraulics Darcian flow, canals and R-channels Hydraulics Linked cavities and R-channels So, now we have come to the core of this talk. I will focus on the processes that take place underneath glaciers that are underlain by deformable beds consisting of soft sediments, and contrast these with the processes that works underneath glaciers that are underlain by non-deformable beds as bedrock. A deformable bed consists of till. Till is a non-sorted material typical for glaciers. A non-deformable bed has no sediments between the basal ice and the bed. Both valley glaciers and ice sheets can rest on both kind of beds. Ice streams and surging glaciers have so far only been found on deformable beds. Bed displacement Sliding, deformation, free-slip Bed displacement Sliding Landforms streamlined forms (drumlins) Landforms Roches moutonnées, U-valleys

Non-deformable bed: Low flux hydraulics pi pw

Glacier dammed lakes - Vatnajökull – Iceland

Glacier dammed lake during a surge at Usherbreen, Svalbard

Glacier dammed lake – Blåmannsisen (fra R. Engeset, NVE)

Water level in lake Discharge from lake Water level in reservoir

Hubbard glacier surge – glacier dammed fjord

Hubbard glacier surge – glacier dammed fjord

Subglacial lake – Grimsvötn, Vatnajökull, Iceland

Subglacial lakes – stable -unstable

Moraine dammed lake – potential GLOF

Ice directed drainage Some equations: Ice overburden pressure Flotation level Effective pressure Fluid potential Potential gradient

Water pressure potential In one point: Φb= ρw g Zb+ Pw where Pw is the subglacial water pressure Pw= k ρi g hi where hi = Zs – Zb and k є [0, 1] Driving force – the potential difference:

Subglacial lakes in Antarctica

Location of observed lakes

Lake Vostok

(from Clarke, 2006)