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1 Glacier hydrology GEO 4420, Glacier hydrology Relevance: Water resource (climate change scenario) Ice dynamics (sliding, surge, icestreams) Geo-hazards (outburst floods) (Erosion, sediment transport) Thomas Schuler Department of Geosciences 2nd part: applied glaciology Glacier hydrology Water sources water sources (not treated) water movement through a glacier characteristics of glacial runoff Source Melt-water: surface ~ m a -1 internal basal } 0.01 m a -1 Rain Control surface energy balance ice deformation sliding velocity, geothermal heat flux Climate, topography hydrologist Inflow from surroundings, groundwater Topography, geology 1

2 Glacier runoff and climate change Pardé-coefficient Characteristics: Seasonal Variation Dnjepr (Kamenka) 'Snow' Rhone (Gletsch) 'Glacier' Seine (Paris) 'Oceanic' Q? 0 Jan Mar May Jul Sep Nov Jan Annual runoff Seasonal variation Characteristics: Summary VARIABLE CHARACTERISTIC Decrease for pos mass bal Increase for neg mass bal Runoff concentration during melt season Discharge (m3/s) Vernagtferner Jan 3-Mar 2-May 1-Jul 30-Aug 29-Oct 28-De Discharge (m 3 /s) Characteristics: Diurnal Variation Vernagtferner Jul 21-Jul 26-Jul 31-Jul 5-Aug 10-Aug Diurnal variation Year-to-year variability Runoff correlation Aperiodic variations Pronounced diurnal cyclicity Reduced at moderate glacierization Glacier compensation effect Pos. correlation with temp Neg. correlation with precip Outburst floods Seasonal evolution: 1. Increase in meltwater production (Lower albedo due to more ice at surface) Increase in amplitude 2. Increase in efficiency of water transport Faster arrival of peak discharge

3 Response to warming: Annual runoff Q= P E+ G S SLOW ~ 0.5 m/h ~ Porous ground water aquifer Glacier hydrology FAST ~ 0.5 m/s ~ Karst aquifer Jansson et al Response to warming Response to warming: Diurnal Variations VERNAGTFERNER Hock et al Discharge (m 3 s -1 ) Jul 24-Jul 29-Jul 3-Aug Photos: Schuler 8-Aug 13-Aug 18-Aug 23-Aug 28-Aug 3

4 Response to warming: Summary VARIABLE Glacier hydrology CHANGE UNDER CLIMATE WARMING Initial stage Specific runoff Increase Year-to-year variability Runoff correlation Later stage water movement through a glacier Decrease Reduced runoff concentration Prolongation of melt season Seasonal variation Diurnal fluctuation water sources (not treated) Increase Decrease Increase or decrease depending on Initial glacierization Increase Increased pos corr with temp Decreased Hydrologist/ glaciologist Subglacial drainage Röthlisberger channel (R-channel) Enlargement due to frictional heating Closure due to ice deformation Æ dynamic channel geometry Æ seasonal evolution! characteristics of glacial runoff Drenering gjennom isen Röthlisberger, 1972 Friksjon skaper varme Varme smelter is Steady-state: Pw ~ Q-b Æ inverse pressure-discharge relationship Æ arborescent structure!! Stream channels On Vibeke Gletscher in East Greenland, Photo: M. Hambrey 4

Fischer Röthlisberger Hooke Nye Walder & Fowler Distributed drainage systems Linked cavity system Subglacial sediment Drainage systems

5 Drainage systems and water pressure Channelized drainage systems hydraulically efficient (variable pressure) dynamic geometry (dependent on water flux) arborescent structure (localized feature) courtesy: U.H. Fischer Röthlisberger Hooke Nye Walder & Fowler Distributed drainage systems Linked cavity system Subglacial sediment Drainage systems and water pressure Boulton, 1974 Kamb, 1987 Water film Hydraulically unefficient (high pressure) Stable features (no evolution) Non-arborescent structure (distributed) Weertman, 1972 courtesy: U.H. Fischer 5

6 Relevance to ice dynamics Special case: jøkulhlaup dtotal = ddeformation + dbasal dtotal lake ddeformation hw hi glacier sliding law: outlet vbasal ~ (pi -pw)-1 } pw distance x seal (?) effective pressure dbasal Water masses dammed by a glacier Dam-stability controled by ice-thickness and filling level Outbursts may occur periodically and cause destructive floods Modeling discharge through a R-channel Model results: jøkulhlaup channel evolution lake level evolution Nye, 1976; Spring & Hutter, 1982; Clarke, 1982; Ng, 1998; Clarke, 2003 lake hw Time-dependent geometry of an ice-walled conduit: ρ g h z da ρ g * + = C w Q (t ) (1 γ ) + ( heat transfer) 2 AB w h h ρi L x x dt n ( size melt-enlargement ) hi glacier flood hydrograph n creep-closure 6

level (m) 60 50 40 30 20 geofonutslag vannstand Øvre Messingmalmvatn ~ 1000 m 3 s -1 40 30 20 10

7 Instability of channelized drainage Jøkulhlaup in Norway ice-dammed lake glacier subglacial channel glacier snout: outlet portal Photos: Hjelmaas Apr04 Jul04 Oct04 Jan05 Apr05 Jul05 Oct05 50 water level (m) geofonutslag vannstand Øvre Messingmalmvatn ~ 1000 m 3 s water level (m) /08/05 28/08/05 30/08/05 01/09/05 03/09/05 05/09/05 Blåmannsisen jøkulhlaup

Case study: Applied glacier hydrology at Høganesbreen

beneath Høganesbreen be evacuated subglacially?

water intrusions trouble mining activities beneath

Høganesbreen Pumping the water from the mine is

intrusions in the mine be evacuated subglacially?

8 Case study: Applied glacier hydrology at Høganesbreen Coal mining in Svea Can water intrusions in a mine beneath Høganesbreen be evacuated subglacially? SNSK requested recommendations from UiO Problem: water intrusions trouble mining activities beneath the glacier Idea: drainage tunnel to the bed of Høganesbreen Pumping the water from the mine is expensive Høganesbreen Gruvefonna Can water intrusions in the mine be evacuated subglacially? Høganesbreen Gruvefonna?? mine During summer Q max ~ m 3 d -1???? drainage tunnel mine 8

Strategy Can we expect a channelized drainage system in the region where the

(hydraulic potential mapping surface & bedrock topography) Bedrock topography by

so, will the water drain gravitationally away from the mine?

Interpolation of ice-thickness measurements and construction of a bedrock map

9 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) Bedrock topography by radar upper part of Høganesbreen in the area of the planned drainage tunnel If so, will the water drain gravitationally away from the mine? (R-channel model glacier geometry, ice temperature & water discharge) Interpolation of ice-thickness measurements and construction of a bedrock map Direction of water flow From experience: Water flow follows the topographic gradient pump (high pressure) and Water flows from high pressure to lower pressure 9

10 Hydraulic potential Hydraulic potential mapping h Definition: Φ = ρw g z + pw Assume: pw= f pi = f ρigh, Alternative: express Φ in terms of water column H = z+h, f є [0,1] pw=ρwgh) principles: water flows from higher to lower potential flow is perpendicular to isopotential lines f = 0.5 f = 1.0 Modeling discharge through a R-channel f = 0.0 Model input: water discharge in the mine (estimated from pump rates) short artic melt saison Nye, 1976; Spring & Hutter, 1982; Clarke, 1982; Ng, 1998; Clarke, Time-dependent geometry of an ice-walled conduit: ρ g h z da ρ g * + = C w Q (t ) (1 γ ) + ( heat transfer) 2 AB w h h ρi L x x dt n ( size melt-enlargement creep-closure ) time (d) n Two scenarios were calculated using different flow law parameters for the ice 10

11 Model results: pressure evolution in the artificial drainage tunnel Even in an extreme case, open-channel conditions will last for less than two months We recommend NOT to proceed with the construction of an artificial drainage tunnel Under pressurized conditions, water would drain into rather than away from the mine future mining area will be significantly enlarged Water transfer from the glacier to the mine Will the amount of water input increase with the enlargement of the mine? And, if so, can we estimate how much? bedrock underneath the glacier disturbed by collapsing mine 11

Approach Melt model validation Melt-water production,

mine M = (MF + a ice/snow *DIR) * T+ (Hock, 1999) Transfer

evolution of melt-water intrusions (total volume, peak

1) Perfect and direct vertical water transfer 2) Lateral

12 Approach Melt model validation Melt-water production, spatially distributed Monitoring of water discharge in the mine M = (MF + a ice/snow *DIR) * T+ (Hock, 1999) Transfer model glacier surface mine Records of pump rate Future evolution of melt-water intrusions (total volume, peak discharge) Model results Contributing glacier surface? 1) Perfect and direct vertical water transfer 2) Lateral water influx along the glacier bed (hydraulic potential surface) Svea Nord Svea Nord 12

Results Subglacial catchment Distribution of subglacial hydraulic potential based

melt production (1.7*10 6 m 3 ) accounts only for 60% of measured discharge (2.

steps of future enlargement Calculated melt water volume (2.

83*10 6 m 3 ) Transfer glacier mine Prediction surface melt water + rain linear

discharge (k=14d) With the enlargement of the mine, the volume of water intrusions

13 Results Subglacial catchment Distribution of subglacial hydraulic potential based on maps of bedrock topography and glacier surface: H = z + ρ i / ρ w h i Modeled melt production (1.7*10 6 m 3 ) accounts only for 60% of measured discharge (2.8*10 6 m 3 ) Mapping the subglacial catchment area for the actual mine and several steps of future enlargement Calculated melt water volume (2.85*10 6 m 3 ) agrees with measured discharge (2.83*10 6 m 3 ) Transfer glacier mine Prediction surface melt water + rain linear reservoir mine discharge melt water production measured discharge simulated discharge (k=14d) With the enlargement of the mine, the volume of water intrusions will progressively increase up to 3.5 times of the actual value. Diurnal peak discharge will increase similarly (54*10 3 m 3 s *10 3 m 3 s -1 ). 13

14 Summary of results Calibrated melt model (80% accuracy) Delineation of the subglacial catchment area using subglacial 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 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

15 2003 Can increase in permeability enlarge the catchment area? 2005 Model explains ~50% of observed water volume? Svea Nord Model structure Model structure Meltwater production & routing at surface Meltwater production & routing at surface Distributed melt model Exchange controled by gradient in hydraulic potential Exchange controled by hydraulic potential gradient Englacial storage Englacial storage Continuity & Darcy physics (nonlinear conductivity) Subglacial watersheet Subglacial watersheet Continuity & Darcy physics (nonlinear conductivity) Groundwater Sveagruva Groundwater Continuity & Darcy physics 15

16 permeable impermeable 16

Physics of Glaciers: Glacier Hydraulics

Introduction Theory Examples References Physics of Glaciers: Glacier Hydraulics Mauro A. Werder VAW / ETHZ 27.11.2017 Introduction Theory Examples References Problems Front matters Me: postdoc at VAW specialising