Structure, morphology and water flux of a subglacial drainage system, Midtdalsbreen, Norway - Willis et al, 2011

Structure, Morphology and Water Flux of a Subglacial Drainage System

• Study area: Midtdalsbreen, Norway, a temperate, northern outlet glacier of Hardangerjøkulen.
  • Extends from ~1380 to ~1862 m a.s.l.
  • ~4.8 km long.
  • Catchment area: 9.6 km2, with 6.7 km2 glacierised.
  • Maximum ice thickness: ~280 m.
  • Geology: granitic gneiss and phyllite bedrock.
  • Three meltwater streams: T1 (eastern, largest), T2 (central, moraine-dammed lake), and T3 (western, moraine-dammed lake).
  • Stream configurations have changed over the past 25 years.

Introduction

• Subglacial drainage pathways significantly influence glacier behavior.
  • Structure: location, alignment, interconnection.
  • Morphology: size, shape, roughness.
• Changes in drainage system structure are linked to:
  • Ice stream behavior over centuries to millennia (Vaughan et al., 2008).
  • Inter-annual changes in proglacial outlet streams (Rippin et al., 2003).
• Changes in drainage pathway morphology are linked to:
  • Glacier flow instabilities at various timescales:
    • Years/decades (surging) (Kamb et al., 1985; Björnsson, 1998).
    • Hours/days ('spring events') (Iken and Bindschadler, 1986; Bingham et al., 2003; Mair et al., 2003).
    • Comparable phenomena on the Greenland Ice Sheet (Bartholomew et al., 2010).
• Subglacial drainage systems control runoff response from glacierised catchments, modifying melt/rainfall inputs (Hock and Jansson, 2005).
• Understanding subglacial hydrology is crucial for:
  • Runoff regimes and water resource management (Kundzewicz et al., 2008).
  • Prediction of glacier floods (Huss et al., 2007).
• Subglacial drainage systems affect physical and chemical processes at the ice-bed interface, including sediment mobilization and solute acquisition (Tranter et al., 1996; Wadham et al., 2001).

Subglacial Drainage System Structure

• Studies use DEMs to calculate subglacial hydraulic potential (Shreve, 1972) and infer drainage system structure for different water pressure assumptions.
  • Examples: Holmlund, 1988; Sharp et al., 1993; Flowers and Clarke, 1999; Hagen et al., 2000; Copland and Sharp, 2001; Pälli et al., 2003; Rippin et al., 2003; Fischer et al., 2005; Vaughan et al., 2008; Le Brocq et al., 2009; Fricker et al., 2010.
• Some studies compare theoretical structures with independent observations to constrain steady-state water pressures.
• Sharp et al. (1993): Compared theoretical structures with dye tracing experiments, finding a better match with ice overburden pressure.
• Rippin et al. (2003): Proglacial stream positions at Midre Lovénbreen, Svalbard, indicated water pressures close to half ice overburden pressure, with some years closer to full overburden.
• Hagen et al. (2000): Proglacial stream location used to constrain water pressures beneath Finsterwalderbreen, Svalbard.
• Pälli et al. (2003): Outflow stream location, hydrochemistry, dye tracing, and moulin water pressures suggested water pressures close to ice overburden on Hansbreen and Werenskioldbreen, Svalbard.
• Willis et al. (2008): Dye tracing on Brewster Glacier, New Zealand, showed early melt season water pressures close to ice overburden, adjusting to lower pressures later in the season.
• Fricker et al. (2010): Calculated flow pathways beneath Whillans Ice Stream, Antarctica, showed lake drainage and filling events responding to water flow.

Subglacial Drainage System Morphology

• Techniques for estimating size, shape, and roughness of subglacial drainage pathways (Hubbard and Nienow, 1997).
  • Dye tracing is a common method (Burkimsher, 1983; Hock and Hooke, 1993; Nienow et al., 1998; Schuler et al., 2004).
• Dye breakthrough curves and derived measures (mean transit velocity, dispersivity, tracer recovery) are used to infer drainage pathway morphology.
• Surface melt-fed subglacial pathways:
  • Classified as channelised or distributed.
  • Morphology inferred from dye breakthrough curve parameters and glacio-hydrological theory (Fountain and Walder, 1998).
• Glaciers may be drained by:
  • Hydraulically efficient semi-circular R-channels.
  • Less hydraulically efficient broad-low Hooke-channels.
  • Hydraulically inefficient linked cavities.
  • Combinations of these (Willis et al., 1990; Bingham et al., 2005).
• Dye tracer experiments:
  • Haut Glacier d’Arolla, Switzerland: Lower ~80% drained by channelised system, upper ~20% by distributed system (Nienow, 1993).
    • Channelized system: water flow velocities of ~0.3–0.8 m/s, dispersivities <10 m.
    • Distributed system: flow velocities
  • Repeat injections on Haut Glacier d’Arolla: Main subglacial drainage pathways become more hydraulically efficient over the summer (Nienow et al., 1998).
  • John Evans Glacier, Nunavut, Canada: Similar findings (Bingham et al., 2005; 2006).

Objective and Rationale

• Limited consensus on spatially averaged steady-state water pressure (at, close to, or well below ice overburden).
• Inconsistent understanding of subglacial drainage system morphology variations in space and time.
• Need for longer-term studies to observe decadal changes in subglacial drainage elements.
• This study utilizes a comprehensive data set from Midtdalsbreen, Norway.
  • Detailed surface topography and ice radar survey.
  • Meteorological measurements.
  • High temporal resolution snow accumulation and melt records.
  • Discharge measurements in proglacial streams since the late 1980s.
  • Dye tracing experiments since the late 1980s.

Aims and Approach

• Investigate subglacial drainage system structure and morphology of Midtdalsbreen using glacier hydraulic potential theory, degree-day melt modeling, and dye tracing.
• Aims:
  • Compute theoretical subglacial drainage system structures based on 11 different assumptions of subglacial water pressure (0 to 100% ice overburden pressure).
  • Calculate spatial distribution of surface melt and quantify meltwater volume flowing along subglacial drainage pathways for different theoretical drainage system structures.
  • Compare theoretical drainage system structures and volumes with proglacial outflow streams, discharge measurements, and dye tracing results to constrain the subglacial water pressure regime.
  • Determine the likely morphology of subglacial flow pathways using detailed analysis of dye return curves.

Field Site: Midtdalsbreen, Norway

• Temperate, northern outlet glacier of Hardangerjøkulen.
• Extends from ~1380 to ~1862 m a.s.l.
• ~4.8 km long.
• Total catchment area: 9.6 km2, with 6.7 km2 glacierised (Ragner, 1997).
• Maximum measured ice thickness: ~280 m.
• Geology beneath: predominantly granitic gneiss and phyllite bedrock (Hagen, 1978).
• Runoff concentrates in three meltwater streams (T1, T2, T3).
  • T1 (eastern): largest, braided stream, disappears beneath snow-covered dead ice, emerges from rock step.
  • T2 (central): exits into moraine-dammed lake, outlet stream passes over rock step and beneath dead ice.
  • T3 (western): drains through moraine-dammed lake before flowing over the rock step.
• Proglacial stream configuration has changed over the last 25 years.
  • In 1987/8 and 1993/4, T3 and T2 flowed east and merged with T1.
  • In 2008, T3 drained west, and T2 drained north, merging further down valley.

Previous Work on Midtdalsbreen

• Frontal position records from geomorphological and lichenometrical studies (Andersen and Sollid, 1971).
  • Neoglacial maximum extent at ~1750 AD, retreated by ~2.4 km since then.
  • Retreated steadily until 1930, stopped, then rapid retreat until 1960.
  • Stationary between 1960 and 1982.
  • Retreated ~10 m between 1982 and 1987/88, advanced ~30 m between 1987/88 and 1993/94, then retreated ~100 m between 1993/94 and 2008 (Konnestad, 1996; Andreassen et al., 2005; NVE, 2009; Kjøllmoen et al., 2010).
• Mass balance measurements:
  • ~ +1.3 m w.e. in 2000 and ~ -0.64 m w.e. in 2001 (Kjøllmoen, 2001; Krantz, 2002).
  • Upglacier shift in equilibrium-line altitude from ~1500 m to ~1785 m.
• Giesen et al. (2008): Net solar radiation dominates summer surface energy balance, contributing 75% of melt energy (2000–2006).
  • Turbulent fluxes supply 35% of energy.
  • Net longwave radiation and subsurface heat flux are energy sinks of 8% and 2%, respectively.
  • ~60% of melting occurs under cloudy skies.
• Water balance study (summer 1987): ~14 x $10^6 m^3$ of melt and rainwater entered, ~12.5 x $10^6 m^3$ left via proglacial stream, net storage of water (Willis et al., 1993a; 1993b).
• Glacier movement:
  • Faster in summer than winter.
  • Short-term motion events in spring, accelerating to 900% of background summer speeds (Willis, 1995).
  • Summer 2000 surface speeds: 4–40 m a-1 over the lower ablation area (Vaksdal, 2001).
  • Motion events associated with sediment flushing (Willis et al., 1996).
  • Sediment sources: debris flushed from glacier and slumping of proglacial debris (Drageset, 1997).
• Dye tracing studies:
  • Willis et al. (1990): 15 tracer investigations in 1987 and 1988.
  • Andersen (now Andreassen) (1996): 46 tests in 1993 and 1994.

Data and Methods

• Proglacial stream discharge:
  • Gauging Station (GS) established on the main proglacial stream, ~500 m from the glacier snout (1987, 1988, 1993, 1994, 2008).
  • Water stage logged using pressure transducer/logger.
  • Stage-discharge curves established using velocity-area technique (except 1994, salt dilution method).
  • Continuous discharge measurements throughout each field season.
  • During the 1980s and 1990s, all water from streams T1, T2, and T3 coalesced upstream of GS, representing the water flux from the whole glacier.
  • In 2008, streams T2 and T3 merged downstream of GS, so measurements represented flow from T1 only.
  • In 1987, 26 discharge measurements made at a subsidiary GS (SGS) on the T3 stream.
  • In 1994, ten point measurements of discharge were also made here using the salt-dilution method.
• Dye tracing:
  • Experiments undertaken in 1987, 1988, 1993, 1994, and 2008 (8, 7, 10, 26, and 22 tests, respectively).
  • Mostly in July and August, with some in June and September.
  • Mean injection time: 13:30 (standard deviation 1 h, 55 min).
  • Injections into surface moulins/crevasses with flowing water.
    • Exceptions: ice marginal streams and holes in the snow.
  • Injection site positions determined by ground survey (1980s/1990s) and GPS (2008).
  • Rhodamine B powder or Rhodamine WT liquid (20% solution) used as dye.
  • Dye emergence detected using Turner Designs fluorometer (1980s/1990s) and Seapoint fluorometer (2008).
  • In the 1980s, water sampled at GS in the main proglacial stream.
  • In the 1990s and 2008, continuous flow fluorometry was used with data logged every minute (1993–94) and 5 min (2008).
• Parameters calculated for each dye return curve:
  • Transit distance (x, m).
  • Residence time (tm, s).
  • Transit speed (um, ms-1): $um = x/tm$
  • Dispersion coefficient (D, m2s-1): A measure of the width of the dye return curve
    $D = \frac{x^2}{t<em>m} * \frac{t</em>j}{4t<em>m^2} [ ln^2(t</em>m/t_j)]^{-1/2}$
  • Dispersivity (d, m): $d = D/um$
  • Dye recovery (P, %): $P = 100 * W/W_0$
• Digital elevation models (DEMs):
  • Surface elevation data collected by differential GPS (dGPS) measurements in May 1995.
  • 3500 points collected on the glacier, differentially corrected using base station data.
  • Data for inaccessible areas obtained by digitizing NVE 1:10,000 topographical map.
  • 25-m resolution DEM derived using the topogrid interpolation tool in ArcGIS.
  • Bedrock topography measured using a dense network of RES profiles (1995, 2001–2004).
  • Radar wave velocity of 169 m/ms used to convert return time to ice depth.
  • Digital maps of ice thickness and bedrock topography produced using Inverse Distance Weighting and Triangulated Irregular Network interpolation.
  • 25-m resolution bed DEM obtained by subtracting the ice thickness grid from the surface DEM of 1995.
• Theoretical subglacial drainage system structure: Total subglacial hydraulic potential (Φ) is the sum of elevation and pressure potentials and can be expressed as: $\Phi = \rho<em>i g h + k(\rho</em>i - \rho_w)gz$
  • Eleven steady-state subglacial water pressure conditions were modelled ranging from k = 0 to k = 1 at 0.1 k increments.
• Grids of subglacial hydraulic potential were used to map the subglacial drainage system structure using the hydrological toolkit within the Spatial Analyst extension of ArcGIS v.9.2 software with steps:
  • Flow direction was calculated
  • Sinks were identified
  • Fill tool to fill all sinks
  • Flow directions were recalculated
  • Flow accumulation tool was used to calculate the number of upstream cells flowing to each cell and to map subglacial drainage system structure.
  • Watersheds for the three proglacial streams were determined by including every cell that contributed flow to a given ‘pour point’ using the watershed tool.
• Surface melt and subglacial discharge
  • A distributed positive degree-day model is used to estimate the total melt across the glacier during the 2003–2004 hydrological year.
  • Derive surface melt rates, use data from the automatic weather station (AWS) maintained by the Institute for Marine and Atmospheric Research, Utrecht University
    $M = DDF * \sum T_+ * \Delta t$
    The AWS surface height and albedo data showed that the transition from snow to ice occurred on 5 July (Day 186). The corresponding degree- day factors derived for snow and ice were 4.7 and 6.9 mm d-1 °C-1, respectively. The other model parameters used were a temperature lapse rate of 6.7 °C km-1, a summer precipitation gradient of 8% 100 m-1; and a temperature threshold for rain or snow of 1 °C.

Results and Discussion

• Subglacial drainage structure and catchments from dye tracing:

  • Moulins on the east of the glacier feed T1 and those on the west feed T3.
  • Moulins J and DW on the central part of the lower glacier within 650 m of the glacier snout feed T2.

• Theoretical subglacial drainage structure and catchments

  • Ice thickness increases progressively upglacier to ~300 m near the ice divide with Rembesdalsskåka.
    When k=1, contour patterns are very similar to those of surface elevation
  • The k = 0 structure is the simplest, with one main drainage axis running along the centreline of the glacier down the deepest part of the valley, fed by tributaries from either side. The main drainage path extends from the ice divide and emerges close to where the real T2 stream exits the glacier
  • For k = 0.4, a major switch occurs producing drainage structures and catchments that are very different to those for lower k values. Now, the drainage network beneath the upper glacier is routed towards the east of the glacier, and the largest catchment is up stream of T1. Another distinct network draining the lower west part of the glacier extends ~1.5 km up glacier from the stream T3. A small catchment exists in the lower central glacier with a small stream draining to T2.
  • At k = 0.9, another switch occurs. Now, the drainage network beneath the upper glacier is routed towards the west, and the largest catchment is upstream from T3. The T1 catchment is still quite large, draining the eastern half of the glacier, and the T2 catchment is small, as it was for the k = 0.4 to k = 0.8 reconstructions. The k = 1 reconstruction is essentially the same as that for k = 0.9.

• Subglacial discharge modelling

  • As melt rates are elevation dependent, melt rates increase from ~2.0 m w.e. a−1 in the accumulation area to >5.0 m w.e. a−1 at the snout

• Subglacial drainage system structure

  • steady-state water pressure beneath Midtdalsbreen during the summer lies between 40% and 80% of ice overburden pressure

• Subglacial drainage system structure – steady-state water pressure
  Water pressure operating at 70% ice overburden. In the short term, of course, elements will continuously enlarge and contract in response to the water flowing through them and the effects this has on wall melting, effective pressures and wall creep.

• Subglacial drainage system structure – stability
  relatively stable geometry of the glacier has remained largely unaltered over last 20 years
  A drainage system where pa< pw< pi during the summer was suggested by similar work on Brewster Glacier, New Zealand (Willis et al., 2008).

• Subglacial drainage morphology from dye tracing
  derived from our tests on Midtdalsbreen are comparable, reflect predominantly the morphology of the drainage pathway through which the dye has passed and are not influenced significantly by time of injection
  experiments conducted on the eastern part of the glacier tended to produce simple curves with a single asymmetrical peak emerging in T1 and all dye was flushed through the glacier in a few hours
  shapes of the return curves for the other tests from the lower central glacier are not known since they either produced null returns (moulins H, L and M) or returns in T2 but where the full curve was not measured (moulin J).
  transit speeds for the tests that emerged in T1 varied between 0.03 and 0.96 m s-1, with an average of 0.43 m s-1
  Transit speeds for the T3 tests ranged between 0.007 and 0.086 m s-1, with an average of 0.039 m s-1.

• Subglacial water flux and transit speeds

  • For the k = 0.7 reconstruction, water fluxes beneath the central and western part of the glacier are much less than those beneath the eastern half
  • there is a functional relationship between transit speeds for water and average water flux with low fluxes in the drainage pathways feeding T2, T3 and some of those feeding T1 associated with low transit speeds, and increasing fluxes in the pathways feeding T1 associated with correspondingly increasing speeds

• Shape and roughness of subglacial drainage pathways

  • Flow path speed can also be determined theoretically using the Gauckler–Manning–Strickler equation: $ufp = Rfp2/3Sfp1/2nfp-1$

• We make two assumptions about the shape of the drainage pathway:

  • Semi-circular conduit: $XSAH = \frac{pr^2}{2}$
  • Broad low conduit: $XSAH = L$ where L is the circle of radius a segment of a circle, i.e. the space between the chord of a circle and the arc subtended by that chord.

• At high discharges > 0.45 m3 s-1 , where ufp > 0.4 m s-1

• The Same conclusion was reached about the channels beneath Gornergletscher using a slightly different methodology to the one used here (Werder and Funk, 2009).

Summary and Conclusions

• This study is the first to combine glacier hydraulic potential theory, degree-day melt modeling, and dye tracing to investigate the drainage system structure and morphology of a glacier (Midtdalsbreen, Norway).
• The subglacial drainage system in the summer is adjusted to a steady-state water pressure less than ice overburden and more than atmospheric.
• The results align with late melt season tests performed somewhere else.
• Water flowing down moulins located on or close to preferential drainage axes carrying large subglacial water fluxes from up glacier flows faster suggesting more channelized drainage.
• Surface and bed DEMs, melt modeling support the earlier hypothesis.
• This suggests that on average across the glacier and through the summer melt season, the rate of enlargement of the drainage system elements (conduits, linked cavities) by thermal/mechanical processes is balanced by their rate of closure by creep deformation and that the net result is a water pressure operating at 70% ice overburden.
• The main eastern drainage network feeding T1 consists of a hydraulically efficient system dominated by channels that are broad and low.
• The smaller western drainage network feeding T3 consists of a hydraulically inefficient distributed system, dominated by channels that are exceptionally broad and very low.
  The even smaller central drainage network draining to T2 also consists of a hydraulically inefficient distributed system, dominated by channels that are very broad and exceptionally low.