Modelling of surface to basal hydrology across the Russell Glacier Catchment Sam GAP Modelling Workshop, Toronto November 2010
Collaborators Alun Hubbard Centre for Glaciology Institute of Geography and Earth Sciences Aberystwyth University, UK Gwenn E. Flowers Department of Earth Sciences Simon Fraser University BC, Canada Christian Schoof Earth and Ocean Sciences University of British Columbia BC, Canada
Hydrology Ice dynamics Interactions Effective pressure at the ice-bed interface governs glacier sliding The non-linear relationship between surface meltwater and glacier speedup is not credibly captured by current models This is needed to reduce uncertainties in glacier and ice sheet contributions to sea level Effective pressure also acts at the groundwater exchange
Hydrology Ice dynamics Interactions Effective pressure at the ice-bed interface governs glacier sliding The non-linear relationship between surface meltwater and glacier speedup is not credibly captured by current models This is needed to reduce uncertainties in glacier and ice sheet contributions to sea level Effective pressure also acts at the groundwater exchange
Hydrology Ice dynamics Interactions Effective pressure at the ice-bed interface governs glacier sliding The non-linear relationship between surface meltwater and glacier speedup is not credibly captured by current models This is needed to reduce uncertainties in glacier and ice sheet contributions to sea level Effective pressure also acts at the groundwater exchange
Hydrology Ice dynamics Interactions Effective pressure at the ice-bed interface governs glacier sliding The non-linear relationship between surface meltwater and glacier speedup is not credibly captured by current models This is needed to reduce uncertainties in glacier and ice sheet contributions to sea level Effective pressure also acts at the groundwater exchange
Hydrology Ice dynamics Interactions Effective pressure at the ice-bed interface governs glacier sliding The non-linear relationship between surface meltwater and glacier speedup is not credibly captured by current models This is needed to reduce uncertainties in glacier and ice sheet contributions to sea level Effective pressure also acts at the groundwater exchange
Ice-flow Model ( et al., JGR, 2010) Higher-order stresses: 1st-order approximation of the Stokes equation (Blatter, 1995; Pattyn, 2002), includes longitudinal stress gradients Flow-band: 2-D flowline model with flow-unit width parameter Lateral Drag: lateral shear stress parameterization, includes sliding at the side walls and glacier basin shape Coulomb friction law: basal sliding rule (Schoof, 2005)
Ice-flow Model ( et al., JGR, 2010) Higher-order stresses: 1st-order approximation of the Stokes equation (Blatter, 1995; Pattyn, 2002), includes longitudinal stress gradients Flow-band: 2-D flowline model with flow-unit width parameter Lateral Drag: lateral shear stress parameterization, includes sliding at the side walls and glacier basin shape Coulomb friction law: basal sliding rule (Schoof, 2005)
Ice-flow Model ( et al., JGR, 2010) Higher-order stresses: 1st-order approximation of the Stokes equation (Blatter, 1995; Pattyn, 2002), includes longitudinal stress gradients Flow-band: 2-D flowline model with flow-unit width parameter Lateral Drag: lateral shear stress parameterization, includes sliding at the side walls and glacier basin shape Coulomb friction law: basal sliding rule (Schoof, 2005)
Ice-flow Model ( et al., JGR, 2010) Higher-order stresses: 1st-order approximation of the Stokes equation (Blatter, 1995; Pattyn, 2002), includes longitudinal stress gradients Flow-band: 2-D flowline model with flow-unit width parameter Lateral Drag: lateral shear stress parameterization, includes sliding at the side walls and glacier basin shape Coulomb friction law: basal sliding rule (Schoof, 2005)
Ice-flow Model ( et al., JGR, 2010) Higher-order stresses: 1st-order approximation of the Stokes equation (Blatter, 1995; Pattyn, 2002), includes longitudinal stress gradients Flow-band: 2-D flowline model with flow-unit width parameter Lateral Drag: lateral shear stress parameterization, includes sliding at the side walls and glacier basin shape Coulomb friction law: basal sliding rule (Schoof, 2005)
Subglacial Model ( & Flowers, Proc. R. Soc. A, 2010) A mixed subglacial drainage network which includes dynamic switching between drainage components (Flowers, 2008) Distributed - macroporous water sheet - low capacity and efficiency - characteristic of winter Channelized - ice-walled conduits - high capacity and efficiency - characteristic of summer Uplift - When large amounts of water impinge on the glacier bed high water pressures are generated and cause flexure of the overlying ice - This uplift effect is modelled by treating the glacier as a uniform static beam
Subglacial Model ( & Flowers, Proc. R. Soc. A, 2010) A mixed subglacial drainage network which includes dynamic switching between drainage components (Flowers, 2008) Distributed - macroporous water sheet - low capacity and efficiency - characteristic of winter Channelized - ice-walled conduits - high capacity and efficiency - characteristic of summer Uplift - When large amounts of water impinge on the glacier bed high water pressures are generated and cause flexure of the overlying ice - This uplift effect is modelled by treating the glacier as a uniform static beam
Subglacial Model ( & Flowers, Proc. R. Soc. A, 2010) A mixed subglacial drainage network which includes dynamic switching between drainage components (Flowers, 2008) Distributed - macroporous water sheet - low capacity and efficiency - characteristic of winter Channelized - ice-walled conduits - high capacity and efficiency - characteristic of summer Uplift - When large amounts of water impinge on the glacier bed high water pressures are generated and cause flexure of the overlying ice - This uplift effect is modelled by treating the glacier as a uniform static beam
Subglacial Model ( & Flowers, Proc. R. Soc. A, 2010) A mixed subglacial drainage network which includes dynamic switching between drainage components (Flowers, 2008) Distributed - macroporous water sheet - low capacity and efficiency - characteristic of winter Channelized - ice-walled conduits - high capacity and efficiency - characteristic of summer Uplift - When large amounts of water impinge on the glacier bed high water pressures are generated and cause flexure of the overlying ice - This uplift effect is modelled by treating the glacier as a uniform static beam
Subglacial Hydrology Model Image taken from Creyts & Clarke, J. Geophys. Res., 2010
Image taken from Flowers, Hydrol. Process., 2008
Q N u b Q > Q Q N u b Graph taken from Hewitt & Fowler, Hydrol. Process., 2008
A Test Case An idealized mountain glacier
Sheet discharge, m 3 s 1 240 220 0.8 Conduit discharge, m 3 s 1 240 220 3 2.5 Time, days 200 180 160 140 0.6 0.4 0.2 Time, days 200 180 160 140 2 1.5 1 0.5 120 0 0 2 4 Distance downglacier, km 120 0 2 4 Distance downglacier, km 0
Time, days Conduit cross-sectional area, m 2 240 2 220 200 180 160 140 120 0 2 4 Distance downglacier, km 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 Subglacial water pressure, flotation fraction 240 Time, days 220 200 180 160 140 120 0 2 4 Distance downglacier, km 1 0.8 0.6 0.4 0.2
240 Basal speed, m a 1 50 Basal shear stress, k Pa 240 220 40 220 50 Time, days 200 180 160 30 20 Time, days 200 180 160 40 30 20 140 10 140 10 120 0 2 4 Distance downglacier, km 120 0 0 2 4 Distance downglacier, km
Time, days Basal longitudinal stress, k Pa 240 80 220 200 180 160 140 60 40 20 20 40 60 80 120 0 2 4 Distance downglacier, km 0 Time, days 240 220 200 180 160 140 Vertical uplift, cm 120 0 2 4 Distance downglacier, km 1.2 1 0.8 0.6 0.4 0.2
Comments Model captures seasonal and diurnal cycles as well as the spring-transition Such features have been well observed in Alpine glacier system (e.g. Haut Glacier d Arolla) Increasing evidence of similar behaviour on Arctic glaciers, including Russell (e.g. Bartholomew, 2010) Suggesting a unified treatment of basal processes across a range of scales
Comments Model captures seasonal and diurnal cycles as well as the spring-transition Such features have been well observed in Alpine glacier system (e.g. Haut Glacier d Arolla) Increasing evidence of similar behaviour on Arctic glaciers, including Russell (e.g. Bartholomew, 2010) Suggesting a unified treatment of basal processes across a range of scales
Comments Model captures seasonal and diurnal cycles as well as the spring-transition Such features have been well observed in Alpine glacier system (e.g. Haut Glacier d Arolla) Increasing evidence of similar behaviour on Arctic glaciers, including Russell (e.g. Bartholomew, 2010) Suggesting a unified treatment of basal processes across a range of scales
Comments Model captures seasonal and diurnal cycles as well as the spring-transition Such features have been well observed in Alpine glacier system (e.g. Haut Glacier d Arolla) Increasing evidence of similar behaviour on Arctic glaciers, including Russell (e.g. Bartholomew, 2010) Suggesting a unified treatment of basal processes across a range of scales
Comments Model captures seasonal and diurnal cycles as well as the spring-transition Such features have been well observed in Alpine glacier system (e.g. Haut Glacier d Arolla) Increasing evidence of similar behaviour on Arctic glaciers, including Russell (e.g. Bartholomew, 2010) Suggesting a unified treatment of basal processes across a range of scales
Subglacial Floods Supraglacial Lake Drainage Event Das et al. Science, 2008 Supraglacial lake of volume 0.044 km3 Drains through 980 m of ice in 1.4 h 1.2 m of vertical uplift and 0.8 m of horizontal displacement Rapid response followed by subsidence and deceleration over 24 hrs Supraglacial lake on Belcher Glacier, Devon Island Ice Cap. Photo by A. Garner.
( a) 24 Time, hr 18 12 6 Q s m 3 s 1 60 40 20 (b ) Time, hr 24 18 12 6 Q c m 3 s 1 >500 400 300 200 (c) Time, hr P w s 24 18 12 6 P w/pi s >1 0.95 0.9 Time, hr 0 0 10 20 Distance downglacier, km (d ) 24 (g) Time, hr 18 12 6 0 0 10 20 Distance downglacier, km 24 18 12 6 S τ b m 2 k Pa 0 0 0 10 20 Distance downglacier, km 0 300 200 100 200 150 100 50 Time, hr 0 100 0 10 20 D istance downglacier, km ( e) ω 24 (h ) Time, hr 18 12 6 0 0 0 10 20 Distance d ownglacier, km 24 18 12 σ xx m k Pa 0.4 0.3 0.2 0.1 40 20 0 6 20 0 0 10 20 D istance downglacier, km ( f ) Time, hr ( i) Time, hr 0 0 10 20 Distance d ownglacier, km 24 18 12 6 300 200 100 0 0 0 10 20 D istance downglacier, km 24 18 12 6 u b σ x y m a 1 k Pa 50 0 0 0 10 20 Distance d ownglacier, km 100
Comments Pre-existing channel network needed to dissipate flood response as quickly as observed Regular seasonal melt as well as lake tapping events condition subglacial system Model limitations - multi-directional flow of flood water Other processes - horizontal turbulent hydraulic fracture for basal crack propagation (Tsai & Rice, JGR, 2010) Supraglacial lake drainage events a regular occurrence within the Russell Glacier Catchment
Comments Pre-existing channel network needed to dissipate flood response as quickly as observed Regular seasonal melt as well as lake tapping events condition subglacial system Model limitations - multi-directional flow of flood water Other processes - horizontal turbulent hydraulic fracture for basal crack propagation (Tsai & Rice, JGR, 2010) Supraglacial lake drainage events a regular occurrence within the Russell Glacier Catchment
Comments Pre-existing channel network needed to dissipate flood response as quickly as observed Regular seasonal melt as well as lake tapping events condition subglacial system Model limitations - multi-directional flow of flood water Other processes - horizontal turbulent hydraulic fracture for basal crack propagation (Tsai & Rice, JGR, 2010) Supraglacial lake drainage events a regular occurrence within the Russell Glacier Catchment
Comments Pre-existing channel network needed to dissipate flood response as quickly as observed Regular seasonal melt as well as lake tapping events condition subglacial system Model limitations - multi-directional flow of flood water Other processes - horizontal turbulent hydraulic fracture for basal crack propagation (Tsai & Rice, JGR, 2010) Supraglacial lake drainage events a regular occurrence within the Russell Glacier Catchment
Comments Pre-existing channel network needed to dissipate flood response as quickly as observed Regular seasonal melt as well as lake tapping events condition subglacial system Model limitations - multi-directional flow of flood water Other processes - horizontal turbulent hydraulic fracture for basal crack propagation (Tsai & Rice, JGR, 2010) Supraglacial lake drainage events a regular occurrence within the Russell Glacier Catchment
Comments Pre-existing channel network needed to dissipate flood response as quickly as observed Regular seasonal melt as well as lake tapping events condition subglacial system Model limitations - multi-directional flow of flood water Other processes - horizontal turbulent hydraulic fracture for basal crack propagation (Tsai & Rice, JGR, 2010) Supraglacial lake drainage events a regular occurrence within the Russell Glacier Catchment
Russell Glacier Catchment Modelling Numerical Model - Ice Dynamics - Basal Sliding - Subglacial Hydrology - Other Hydrology Components
Ice Dynamics Model (Pattyn, 2008) A 3-D transient higher-order/full-stokes ice-flow model Image taken from Frank Pattyn s homepage
Basal Sliding ( ) u 1/n b τ b = C u b + N n N, Λ = λ maxa Λ m max The hydrology will be coupled to the ice mechanics by use of a Coulomb friction law (Schoof, 2005) This is a pressure dependent sliding rule utilizing the spatial and temporal variations in basal water pressure from the hydrology model Overcomes problem of standard sliding laws that allow arbitrarily large basal shear stresses regardless of effective pressure Implemented as a non-linear Robin-type boundary condition which cannot be solved independently but forms part of the solution to the ice-flow problem
Basal Sliding ( ) u 1/n b τ b = C u b + N n N, Λ = λ maxa Λ m max The hydrology will be coupled to the ice mechanics by use of a Coulomb friction law (Schoof, 2005) This is a pressure dependent sliding rule utilizing the spatial and temporal variations in basal water pressure from the hydrology model Overcomes problem of standard sliding laws that allow arbitrarily large basal shear stresses regardless of effective pressure Implemented as a non-linear Robin-type boundary condition which cannot be solved independently but forms part of the solution to the ice-flow problem
Basal Sliding ( ) u 1/n b τ b = C u b + N n N, Λ = λ maxa Λ m max The hydrology will be coupled to the ice mechanics by use of a Coulomb friction law (Schoof, 2005) This is a pressure dependent sliding rule utilizing the spatial and temporal variations in basal water pressure from the hydrology model Overcomes problem of standard sliding laws that allow arbitrarily large basal shear stresses regardless of effective pressure Implemented as a non-linear Robin-type boundary condition which cannot be solved independently but forms part of the solution to the ice-flow problem
Basal Sliding ( ) u 1/n b τ b = C u b + N n N, Λ = λ maxa Λ m max The hydrology will be coupled to the ice mechanics by use of a Coulomb friction law (Schoof, 2005) This is a pressure dependent sliding rule utilizing the spatial and temporal variations in basal water pressure from the hydrology model Overcomes problem of standard sliding laws that allow arbitrarily large basal shear stresses regardless of effective pressure Implemented as a non-linear Robin-type boundary condition which cannot be solved independently but forms part of the solution to the ice-flow problem
Subglacial Model (Schoof, Nature, 2010) - A unified treatment of linked cavities and channels - 2-D planform network of conduits - Switching between drainage components within a spatially extended drainage catchment S ij t S Q = c 3 S α Ψ 1/2 Ψ N = P i P w Ψ = ρ w g b = c 1 Q ij Ψ ij + u b h c 2 N n ij S ij s Pw s u b h c 1, c 2, c 3, α conduit cross-sectional area water discharge effective pressure hydraulic gradient basal sliding speed bedrock bump constants
Images taken from Schoof, Nature, 2010
Other Hydrology Components Supraglacial hydrology Englacial storage and transport Groundwater flow Image taken from Flowers, Hydrol. Process., 2008
Data - Surface and Bed Topography (DEM) - Automatic Weather Station (AWS) data used to obtain spatial and temporal melt variability - Surface Velocities - from kgps and remotely-sensed observations - Basal reflectance - indicators of stick-slip zones - Seismics - to ascertain bed properties - Observations of englacial storage and surface-to-bed transition times - Supraglacial lake/moulin locations, volumes and drainage times
Research Objectives Glacier catchment response to variable inputs of melt (seasonal, diurnal and lake tapping events) Influence of englacial storage and surface-to-bed transition times How does ice-flow and subglacial processes interact to produce temporal and spatial patterns in basal decoupling Dynamic response to basal boundary layer stress distribution Compare 2009 and 2010 melt seasons Russell glacier catchment under future climate projections
Research Objectives Glacier catchment response to variable inputs of melt (seasonal, diurnal and lake tapping events) Influence of englacial storage and surface-to-bed transition times How does ice-flow and subglacial processes interact to produce temporal and spatial patterns in basal decoupling Dynamic response to basal boundary layer stress distribution Compare 2009 and 2010 melt seasons Russell glacier catchment under future climate projections
Research Objectives Glacier catchment response to variable inputs of melt (seasonal, diurnal and lake tapping events) Influence of englacial storage and surface-to-bed transition times How does ice-flow and subglacial processes interact to produce temporal and spatial patterns in basal decoupling Dynamic response to basal boundary layer stress distribution Compare 2009 and 2010 melt seasons Russell glacier catchment under future climate projections
Research Objectives Glacier catchment response to variable inputs of melt (seasonal, diurnal and lake tapping events) Influence of englacial storage and surface-to-bed transition times How does ice-flow and subglacial processes interact to produce temporal and spatial patterns in basal decoupling Dynamic response to basal boundary layer stress distribution Compare 2009 and 2010 melt seasons Russell glacier catchment under future climate projections
Research Objectives Glacier catchment response to variable inputs of melt (seasonal, diurnal and lake tapping events) Influence of englacial storage and surface-to-bed transition times How does ice-flow and subglacial processes interact to produce temporal and spatial patterns in basal decoupling Dynamic response to basal boundary layer stress distribution Compare 2009 and 2010 melt seasons Russell glacier catchment under future climate projections
Research Objectives Glacier catchment response to variable inputs of melt (seasonal, diurnal and lake tapping events) Influence of englacial storage and surface-to-bed transition times How does ice-flow and subglacial processes interact to produce temporal and spatial patterns in basal decoupling Dynamic response to basal boundary layer stress distribution Compare 2009 and 2010 melt seasons Russell glacier catchment under future climate projections
Research Objectives Glacier catchment response to variable inputs of melt (seasonal, diurnal and lake tapping events) Influence of englacial storage and surface-to-bed transition times How does ice-flow and subglacial processes interact to produce temporal and spatial patterns in basal decoupling Dynamic response to basal boundary layer stress distribution Compare 2009 and 2010 melt seasons Russell glacier catchment under future climate projections
Questions?