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