1

Glacier hydrology

Thomas SchulerDepartment of Geosciencesthomas.schuler@geo.uio.no

GEO 4420, 19.10.2006Glacier hydrology

Relevance:• Water resource (climate change scenario)

• Ice dynamics (sliding, surge, icestreams)

• Geo-hazards (outburst floods)

• (Erosion, sediment transport)

2nd part: applied glaciology

Glacier hydrologywater sources(not treated)

water movementthrough a glacier

characteristics of glacial runoff

hydrologist

Water sources

Topography, geologyInflow from surroundings, groundwater

Climate, topographyRain

• surface energy balance• ice deformation• sliding velocity, geothermal heat flux

Melt-water:• surface ~0.1-10 m a-1

• internal• basal

ControlSource

} 0.01 m a-1

2

Glacier runoff and climate change

Q ?

Characteristics: Seasonal Variation

Jan Mar May Jul Sep Nov Jan0

1

2

3

4

Pard

é-co

effic

ient

Seine (Paris)'Oceanic'

Dnjepr (Kamenka)'Snow'

Rhone (Gletsch)'Glacier'

Characteristics: Summary

Annual runoff

Seasonal variation

Diurnal variation

Year-to-year variability

Runoff correlation

Aperiodic variations

Decrease for pos mass balIncrease for neg mass bal

Runoff concentration duringmelt season

Pronounced diurnal cyclicity

Reduced at moderate glacierization’Glacier compensation effect’

Outburst floods

Pos. correlation with tempNeg. correlation with precip

VARIABLE CHARACTERISTICVernagtferner 1992

3-Jan 3-Mar 2-May 1-Jul 30-Aug 29-Oct 28-De0

2

4

6

8

10

Dis

char

ge (m

3 /s)

0 20 40 60 80 1000.10

0.15

0.20

0.25

Characteristics: Diurnal Variation Vernagtferner 1992

16-Jul 21-Jul 26-Jul 31-Jul 5-Aug 10-Aug0

2

4

6

8

10

Dis

char

ge (m

3 /s)

Seasonal evolution: 1. Increase in meltwater production

(Lower albedo due to more ice at surface)Increase in amplitude

2. Increase in efficiency of water transportFaster arrival of peak discharge

3

Response to warming: Annual runoff

Q P E G S= − + −∆

Jansson et al. 2003

Glacier hydrologySLOW

• ~ 0.5 m/h• ~ Porous ground

water aquiferFAST

• ~ 0.5 m/s• ~ Karst aquifer

Response to warming

Hock et al. 2003

VERNAGTFERNER

19781998

19-Jul24-Jul

29-Jul3-Aug

8-Aug13-Aug

18-Aug23-Aug

28-Aug0

4

8

12

Dis

char

ge (

m3 s-1

)

Photos: Schuler

Response to warming: Diurnal Variations

4

Response to warming: Summary

Specific runoff

Seasonal variation

Diurnal fluctuation

Year-to-year variability

Runoff correlation

Increase Decrease

Reduced runoff concentrationProlongation of melt season

Increase Decrease

Increase or decrease Increasedepending onInitial glacierization

Increased pos corr Decreasedwith temp

VARIABLE CHANGE UNDER CLIMATE WARMING

Initial stage Later stage

Glacier hydrologywater sources(not treated)

water movementthrough a glacier

characteristics of glacial runoff

Hydrologist/ glaciologist

Subglacial drainageRöthlisberger channel (R-channel) Röthlisberger, 1972

• Enlargement due to frictional heating• Closure due to ice deformation

dynamic channel geometryseasonal evolution !

• Steady-state:Pw ~ Q-b

inverse pressure-discharge relationshiparborescent structure !!

Drenering gjennom isen

Friksjon skaper varme

Varme smelter is

Stream channels On Vibeke Gletscherin East Greenland, Photo: M. Hambrey

5

Drainage systems and water pressure

courtesy: U.H. Fischer

Channelized drainage systems

Röthlisberger Hooke Nye Walder & Fowler

• hydraulically efficient (variable pressure)• dynamic geometry (dependent on water flux)• arborescent structure (localized feature)

Linked cavity system Subglacial sediment

Water film

Distributed drainage systems

Kamb, 1987

Boulton, 1974

Weertman, 1972

• Hydraulically unefficient (high pressure)• Stable features (no evolution)• Non-arborescent structure (distributed)

Drainage systems and water pressure

courtesy: U.H. Fischer

6

Relevance to ice dynamicsdtotal = ddeformation + dbasaldtotal

ddeformation

dbasal

pw

sliding law:

vbasal ~ (pi -pw)-1}

effective pressure

glacier

lake

outlet

hi

seal (?)

hw

distance x

Special case: jøkulhlaup

• Water masses dammed by a glacier• Dam-stability controled by ice-thickness and filling level• Outbursts may occur periodically and cause destructive floods

( ) ( )n

w

i

w hhn

gABxz

xhtQ

LgC

dtdA

⎟⎠⎞

⎜⎝⎛ −−−+⎟

⎠⎞

⎜⎝⎛

∆∆

+∆∆

−= *2transfer)heat(1)( ργρρ

Time-dependent geometry of an ice-walled conduit:

Nye, 1976; Spring & Hutter, 1982; Clarke, 1982; Ng, 1998; Clarke, 2003

Modeling discharge through a R-channel

size melt-enlargement creep-closure

Model results: jøkulhlaup

glacier

lake

hihw

lake level evolution

flood hydrograph

channel evolution

7

Instability of channelized drainage

ice-dammed lake glacier

subglacial channel

glacier snout:outlet portal

Jøkulhlaup in Norway

Photos: Hjelmaas

Apr04 Jul04 Oct04 Jan05 Apr05 Jul05 Oct05

26/08/05 28/08/05 30/08/05 01/09/05 03/09/05 05/09/050

10

20

30

40

50

60

wat

er le

vel (

m) 10

20

30

40

50

water level(m

)

vannstand Øvre Messingmalmvatn

~ 1000 m3 s-1

geofonutslag

Blåmannsisen jøkulhlaup 2005

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Case study: Applied glacier hydrology at Høganesbreen

Can water intrusions in a mine beneathHøganesbreen be evacuated subglacially?

SNSK requested recommendations from UiO

Coal mining in Svea

??mine

Gruvefonna

Problem: water intrusions troublemining activities beneath the glacier

Høga

nesb

reen

During summer Q max ~50 000 m3 d-1

Pumping the waterfrom the mine isexpensive

??mine

Gruvefonna

Høga

nesb

reen

Can water intrusions in the mine be evacuatedsubglacially?

drainage tunnel??

Idea: drainage tunnel to the bed of Høganesbreen

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Strategy

• Can we expect a channelized drainage system in the region where the tunnel should connect to the glacier bed?(hydraulic potential mapping surface & bedrock topography)

• If so, will the water drain gravitationally away from the mine?(R-channel model

glacier geometry, ice temperature & water discharge)

Bedrock topography by radar

upper part of Høganesbreen in the area of theplanned drainagetunnel

Interpolation of ice-thickness

measurements

and constructionof a bedrock map Direction of water flow

From experience:• Water flow follows the

topographic gradient

and• Water flows from high

pressure to lowerpressurepump

(high pressure)

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Hydraulic potentialDefinition: Φ = ρw g z + pw

Alternative: express Φ in terms of water column H = z+h, pw=ρwgh)

principles: water flows from higher to lower potential

flow is perpendicular to isopotential lines

Hydraulic potential mapping

Assume: pw= f pi = f ρigh, f є [0,1]h

f = 1.0 f = 0.5 f = 0.0

( ) ( )n

w

i

w hhn

gABxz

xhtQ

LgC

dtdA

⎟⎠⎞

⎜⎝⎛ −−−+⎟

⎠⎞

⎜⎝⎛

∆∆

+∆∆

−= *2transfer)heat(1)( ργρρ

Time-dependent geometry of an ice-walled conduit:

Nye, 1976; Spring & Hutter, 1982; Clarke, 1982; Ng, 1998; Clarke, 2003

Modeling discharge through a R-channel

size melt-enlargement creep-closure

Model input: water discharge in the mine(estimated from pump rates)

0 50 100 150 200time (d)

short artic melt saison

Two scenarios were calculated using different flow law parameters for the ice

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Model results: pressure evolution in theartificial drainage tunnel

• Even in an extreme case,open-channel conditionswill last for less than twomonths

• Under pressurized conditions,water would drain into ratherthan away from the mine

We recommendNOT to proceed withthe construction of an artificial drainagetunnel

Will the amount of water input increasewith the enlargementof the mine?

And, if so, can weestimate how much?

future mining areawill be significantly

enlarged

Water transfer from the glacier to the mine

bedrock underneath the glacierdisturbed by collapsing mine

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Approach

Melt-water production, spatially distributed

Monitoring of water discharge in the mine

Transfer modelglacier surface – mine

Future evolution of melt-water intrusions (total volume, peak discharge)

M = (MF + aice/snow*DIR) * T+

(Hock, 1999)

Records of pump rate

Melt model validation

Model results

Svea Nord

Contributing glacier surface?1) Perfect and directvertical water transfer

2) Lateral water influx along theglacier bed (hydraulic potential surface)

Svea Nord

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Results

Modeled melt production (1.7*106

m3) accounts only for 60% of measured discharge(2.8*106 m3)

Subglacial catchmentDistribution of subglacial hydraulic potential based on maps of bedrock topographyand glacier surface:

H = z + ρi / ρw hi

Mapping the subglacial catchment area for the actualmine and several steps of future enlargement

Calculated melt water volume(2.85*106 m3) agrees withmeasured discharge(2.83*106 m3)

Transfer glacier mine

melt water production

measured discharge

simulated discharge (k=14d)

surface melt water + rain linear reservoir mine discharge

Prediction

With the enlargement of the mine, the volume of water intrusionswill progressively increase up to 3.5 times of the actual value.Diurnal peak discharge will increase similarly(54*103 m3 s-1 190*103 m3 s-1).

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Summary of results• Calibrated melt model (80% accuracy)

• Delineation of the subglacial catchment area usingsubglacial hydraulic potential.

• Transfer glacier mine can be described using a linear reservoir approach (k = 14 d).

• The model predicts a progressive increase of the water intrusions up to a factor of 3.5 with enlargement of the mine.

• The scenarios are based on meteo data from 2003 and assume parameter values being constant. Thus, the actual form of the hydrograph will vary from year to year (according to weather pattern).

Where does all this Where does all this water come from??water come from??

Comparison meteo data

Mass balance from stake readings:

2003: ~-1200 mm w.e.

2004: ~-1400 mm w.e.

Probably slightly more melt in 2004

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2003

2005

Model explains ~50% ofobserved water volume

Svea Nord

Can increase in permeability enlarge the catchment area?

?

Model structure

Meltwater production & routing at surface

Englacial storage

Subglacial watersheet

Groundwater

Exchange controled by gradient in hydraulic potential

Model structure

Sveagruva

Meltwater production & routing at surface

Englacial storage

Subglacial watersheet

Groundwater

Distributed melt model

Continuity & Darcy physics(nonlinear conductivity)

Exchange controled by hydraulic potential gradient

Continuity & Darcy physics

Continuity & Darcy physics(nonlinear conductivity)

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impermeable

permeable