Water Flow in Glaciers 1. Introduction 2. Water sources 3. Water flow (a) permeability (b) hydraulic potential (c) pressure and conduit size (d) direction of flow (e) unsteady state conditions 4. Storage 5. Subglacial drainage systems (a) Discrete systems (b) Distributed systems

References Bennett, M.R. and Glasser, N.F. (1996) Glacial geology: ice sheets and landforms. Wiley, Chichester. Chapter 4 Glacial meltwater

Introduction What is the impact of water in glaciers? In mass balance Sliding Subglacial sediment deformation Hydrological systems Sediment transport

Water sources Sources ice melt snow melt rainfall runoff from ice-free slopes release of stored water

Surface melting temperature radiation flux highly variable in time and space Rainfall rain on snow events greater runoff generation highly variable in time and space Englacial and subglacial melt friction from ice deformation (sliding) more constant in time?

Water flow Permeability primary permeability secondary permeability

Primary permeability intact ice and snow high for snow and firn - linked pore spaces very low for ice ice at pmp interconnected veins and lenses between ice crystals Secondary permeability tunnels and passage ways (mm - m's) most water draining through glaciers

Hydraulic potential Available energy at a particular time and place Surface streams - potential depends on elevation At base - depends on elevation and pressure In an englacial or subglacial stream: = 0 + e + P w where Ø = hydraulic potential Ø 0 = a constant (conduit size & shape) Ø e = elevation potential P w = water pressure

The elevation potential is the product of the weight of water and it elevation: e = w.g.z where w = water density g = gravitational acceleration z = elevation

In natural conditions water pressure can vary between: atmospheric cryostatic Cryostatic pressure is the product of the weight and thickness of the ice: P i = i.g.(H-z) where P i = ice pressure i = ice density H = altitude of the ice surface z = elevation at site

Vadose zone connected with the atmosphere at atmospheric pressure potential depends on elevation Phreatic zone saturated no air in conduits above atmospheric pressure

Effective pressure N = P i - P w When P w is zero the effective pressure is the cryostatic pressure Controls glacier motion bed deformation

If P w = P i (ie N=0) the water can support the whole weight of the glacier the water can lift the glacier off its bed Local scale where cryostatic pressures are lower than normal eg downstream side of protuberances Large scale subglacial lakes

Pressure and conduit size Pressure in water filled conduits controlled by: Frictional heat melt and passage enlargement Ice deformation pressure gradient between the ice and water tendency to decrease passage size

Equilibrium conditions P w = P i + P m where Pm = pressure change to melting or contraction

Positive N (N = P i – P w ) ice deformation rates increase large pressure differences between the water conduit and ice lead to rapid closure Negative Pm pressure drop due to efficient melting melt rates increase with increasing passage radius Larger channels carry more water dissipate more heat to the area of their walls

Two important implications: 1. Melting and deformation allow conduit expansion and contraction in response to P w increases and decreases If P w increases N falls, reducing conduit closure rates passages can only become larger through melting If P w falls, the increased pressure gradient between the ice and water accelerates closure until an equilibrium is reached Enlargement by by melting is rapid (hrs) Contraction change by ice deformation is slow days - weeks)

2. Because melt rates increase with conduit radius Inverse relationship between water pressure and conduit radius Largest passages have lowest pressures water will flow toward larger channels following the pressure gradient large passages grow at expense of smaller ones branching networks

Direction of flow Direction of flow determined by hydraulic potential Equipotential lines: the pressure of the overlying ice is equal to water pressure it generates Geometry determined by variation in ice thickness (major) slope of underlying topography (minor) Once it reaches the bed water will flow to the snout at right angles to equipotential contours defined by intersections of equipotential surfaces with the bed

Non steady state conditions Equation for water pressure (P w =P i +P m ) is based on a steady state condition internal plumbing in equilibrium considered reasonable under normal conditions ok for basal melting Rapid fluctuations high discharges rapidly fed from surface water backs up faster than conduits can enlarge opposite to inverse relationship between conduit radius and P w

However: conduits enlarge rapidly and close slowly therefore the most common condition is a low pressure system water pressure close to atmospheric during most of ablation season tendency for vertical englacial drainage tendency for subglacial drainage to follow the slope

Storage Water storage in lakes and ponds if a barrier exists subglacial englacial supraglacial proglacial

Subglacial Scale mm -2 to 1000's km -2 eg 8000 km -2 beneath the east Antarctic ice sheet Areas of low hydraulic potential surrounded by high hydraulic potential

Supraglacial and englacial Usually temporary Englacial - usually closed conduits or crevasses Seasonal supraglacial lakes on temperate glaciers

Ice dammed lakes Glacier ice forming a barrier to local or regional drainage Settings: ice-free valley sides blocked by a glacier in trunk valleys where a glacier has blocked drainage a junction between two valley glaciers Polar and subpolar glaciers eg Glacial Lake Agassiz Hudson Bay-draining rivers

Proglacial lakes Topographic barriers moraines over-deepened troughs

Subglacial drainage systems Importance ice velocity glacier stability bed deformation sediment erosion, transport and deposition Discrete and distributed systems efficiency

Discrete systems Rothlisberger channels (R-channels) Nye channels (N-channels) Tunnel Valleys Distributed systems Films Linked cavity networks Braided canal networks Porewater flow

R-channels Incised upwards into the ice floored by rock Steady state pressures lower than cryostatic pressure Path governed by hydraulic gradient at the bed surface slope (large impact) bed gradient (small impact) May flow uphill In valley glaciers tendency to flow away from the centre line driven by convex profiles

Evidence tunnel portals boreholes Eskers Dye tracing

N-channels Incised into the substrate Single channels and braided networks Imply erosion in a concentrated areas topographic focusing? Evidence Former channels in bedrock Modern observations Dye tracing

Tunnel Valleys Branching channel networks in soft sediment Bottom - N-channel Top -R-channel Develop to allow efficient drainage of subglacial aquifers (Boulton and Hindmarsh 1987) Evidence Glacial geologic record

Water films Thin films carrying most discharge (Weertman 1972) More than 1mm, tend to channel (theory - Walder 1982) Therefore limited ability to carry water Source local pressure melting? protuberances regelation Particle sizes used to reconstruct film thickness (eg Calcite beds - Hallet) Most cases thinner than a few

Linked cavity systems Cavities develop between the base of the ice and bedrock Lliboutry (1986, 1979) Linked by narrow orifices Low velocities and transit times Evidence Reconstructions from limestone terrains cavities identifiable from solution features Dye tracing diffuse, multi-peaked returns

Opposite behaviour to R-channels channels: negative relationship between discharge and pressure cavities form where P w >P i therefore increases in water pressure result in increases in capacity (Q) no tendency to capture melt from smaller cavities tend to be stable features Breaks down a high discharges where melting becomes important pressure in cavity maintenance mode switch for surging? (Kamb 1987)

Braided canal systems Branching, low pressure channels develop in till when Darcian flow cannot evacuate the water (Shoemaker 1986) Modeling: (Walder and Fowler 1994) n predicts dendritic drainage system unstable unless the n substrate is very stiff n speculation on wide, braided systems of canals n pressure relations similar to linked cavity system n a stable, distributed system Argument that should be recognisable in the geologic record n broad lenses of sorted sediments

Porewater Movement Rock beds - insignificant (ex. Limestone) Unconsolidated sediments Two mechanisms 1. Bulk movement n water carried with mineral grains 2. Darcian flow n flow relative to mineral grains n driven by a hydraulic gradient

Where k = hydraulic conductivity A = sample cross-sectional area transverse to flow n = fluid viscosity p/d = pore water pressure gradient

The hydraulic conductivity of most sediment is low u discharges will be low unless pressures are very high u not efficient, unlikely to evacuate the large amounts of water u probably occurs alongside other mechanisms Connections between porewater and channel flow established (Hubbard et al. 1995, Boulton & Hindmarsh, 1987) u High pressure - water forced into till u Low pressure - water returned to channel

1. Bed depressions steeper than equipotenial lines ponding occurs because hydraulic potential increases towards the edges of the depression

2. Surface depressions hydraulic potential beneath the depression is lower than surrounding areas a water cuploa with a domed surface hydraulic potential at the bed exceeds that at the surface of the reservoir may expand until regions of gradient shrink connections made to external subglacial pathways rapid enlargement of conduits catastrophic drainage eg Grimsvotn

R channels Steeply arched melting dominant channel flows down hill Wide and low where freezing occurs channel flows up hill decrease in energy available for melt pressure decreases Evidence tunnel portals boreholes Eskers Dye tracing