Water Flow in Glaciers 1. Introduction 2. Water sources 3. Water flow (a) permeability (b) hydraulic potential (c) pressure and conduit size (d) direction.

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 + Pw

whereØ = hydraulic potentialØ0 = a constant (conduit size & shape)Øe = elevation potentialPw = water pressure

The elevation potential is the product of the weight of water and it elevation:

e = w.g.z

wherew = water densityg = gravitational accelerationz = elevation

In natural conditions water pressure can vary between:

• atmospheric• cryostatic

Cryostatic pressure is the product of the weight and thickness of the ice:

Pi = i.g.(H-z)

wherePi = ice pressurei = ice densityH = altitude of the ice surfacez = 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 = Pi - Pw

When Pw is zero the effective pressure is the cryostatic pressure

Controls• glacier motion• bed deformation

If Pw = Pi (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

Pw = Pi + Pm

wherePm = pressure change to melting or contraction

Positive N (N = Pi – Pw )• 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 Pw increases and decreases

If Pw increases N falls, reducing conduit closure rates

passages can only become larger through melting

If Pw 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 (Pw=Pi+Pm) 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 Pw

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 glacierseg 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 Pw>Pi

• 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) predicts dendritic drainage system unstable unless the substrate is very stiff speculation on wide, braided systems of canals pressure relations similar to linked cavity system a stable, distributed system

Argument that should be recognisable in the geologic record

broad lenses of sorted sediments

Porewater Movement

Rock beds - insignificant (ex. Limestone)

Unconsolidated sediments

Two mechanisms

1. Bulk movement water carried with mineral grains

2. Darcian flow flow relative to mineral grains 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

d

pkAQ

The hydraulic conductivity of most sediment is low discharges will be low unless pressures are very high not efficient, unlikely to evacuate the large amounts

of water probably occurs alongside other mechanisms

Connections between porewater and channel flow established (Hubbard et al. 1995, Boulton & Hindmarsh, 1987)

High pressure - water forced into till Low pressure - water returned to channel

Table 5.1 Hydraulic conductivities of selected sediments

K (ms-1)Clay < 10-9

Silts 10-9 to 10-7

Fine sand 10-7 to 10-5

Coarse sand 10-5 to 10-2

Gravel 10-2 to 10-0

Till 10-12 to 10-6

Source: Freeze & Cherry (1979)

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