Estimation of subglacial hydraulic properties from induced changes in basal water pressure: a theoretical framework for borehole-response tests

AbstractIn this paper we develop a theoretical model describing water motion in a coupled borehole-subglacial flow system. The theory applies to basal drainage systems having multiple and extensive interconnected flow paths. Within this domain it encompasses a broad range of flow regimes, from laminar Darcian flow in a thick permeable unit to turbulent sheet flow in a very thin layer. Important terms in the model are highlighted by recasting the problem in dimensionless form. The non-dimensional formulation indicates that there are four free parameters in the coupled system. These parameters characterize skin friction in the borehole, and diffusion, transmissivity and turbulent transport in the subglacial flow layer. Dimensionless results show that, under most circumstances, the effects of skin friction in the borehole are negligible. Diffusion, transmissivity and especially turbulent transport in the basal layer are found to influence subglacial water flow strongly. We use our model to predict fluctuations of borehole-water levels that result from different types of disturbances. We show how this framework can be used to estimate subglacial hydraulic properties by comparing model results with data collected during field experiments on Trapridge Glacier, Yukon Territory, Canada in 1989 and 1990.

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Interaction between water pressure in the basal drainage system and discharge from an Alpine glacier before and during a rainfall-induced subglacial hydrological event

Annals of Glaciology ◽

10.3189/s0260305500012325 ◽

1997 ◽

Vol 24 ◽

pp. 288-292 ◽

Cited By ~ 1

Author(s):

Andrew P. Barrett ◽

David N. Collins

Keyword(s):

Water Level ◽

Water Pressure ◽

Drainage System ◽

Water Levels ◽

Drainage Network ◽

Alpine Glacier ◽

Hydraulic Conditions ◽

Borehole Water ◽

Progressive Growth ◽

Resultant Increase

Combined measurements of meltwater discharge from the portal and of water level in a borehole drilled to the bed of Findelengletscher, Switzerland, were obtained during the later part of the 1993 ablation season. A severe storm, lasting from 22 through 24 September, produced at least 130 mm of precipitation over the glacier, largely as rain. The combined hydrological records indicate periods during which the basal drainage system became constricted and water storage in the glacier increased, as well as phases of channel growth. During the storm, water pressure generally increased as water backed up in the drainage network. Abrupt, temporary falls in borehole water level were accompanied by pulses in portal discharge. On 24 September, whilst borehole water level continued to rise, water started to escape under pressure with a resultant increase in discharge. As the drainage network expanded, a large amount of debris was flushed from a wide area of the bed. Progressive growth in channel capacity as discharge increased enabled stored water to drain and borehole water level to fall rapidly. Possible relationships between observed borehole water levels and water pressures in subglacial channels are influenced by hydraulic conditions at the base of the hole, distance between the hole and a channel, and the nature of the substrate.

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Estimation of hydraulic properties of subglacial till from ploughmeter measurements

Journal of Glaciology ◽

10.1017/s0022143000002033 ◽

1998 ◽

Vol 44 (148) ◽

pp. 517-522 ◽

Cited By ~ 18

Author(s):

Urs H. Fischer ◽

Neal R. Iverson ◽

Brian Hanson ◽

Roger LeB. Hooke ◽

Peter Jansson

Keyword(s):

Water Level ◽

Hydraulic Properties ◽

Water Pressure ◽

Inverse Correlation ◽

Borehole Water ◽

Potential Gradients ◽

Glacial Tills ◽

Basal Till ◽

Range Of Values ◽

Good Agreement

Abstract Force variations on a "ploughmeter" and fluctuations in subglacial water pressure have been measured in the same borehole at Storglaciaren, Sweden, to investigate hydraulic properties of the basal till layer. A strong inverse correlation of the pressure and force records, in conjunction with a significant lime lag between the two signals, suggests that pore-water pressures directly affect the strength of the till. Variations in sub-glacial water pressure result in potential gradients across the water till interlace at the bottom of the borehole that drive pressure waves downwards through the till layer when the borehole water level is high and back upwards when the water level is low. Analysis of the propagation velocity of this pressure wave indicates that the hydraulic diffusivity of Storglaciaren till is in the range 1.9−3.6 x 10−6m2s−1,in good agreement with estimates obtained in the laboratory. Hydraulic conductivity values associated with these difrusivities are between 10−9 and 10−8ms−1 and thus are well within the range of values for other glacial tills.

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Modelling the evolution of subglacial tunnels due to varying water input

Journal of Glaciology ◽

10.1017/s002214300000201x ◽

1998 ◽

Vol 44 (148) ◽

pp. 485-497 ◽

Cited By ~ 21

Author(s):

Paul M. Cutler

Keyword(s):

Water Pressure ◽

Drainage System ◽

Water Levels ◽

Initial Shape ◽

Initial Area ◽

Physically Based ◽

Dimensional Finite Element ◽

Borehole Water ◽

Low Tunnels ◽

Tunnel Cross Section

AbstractThe time evolution of a subglacial tunnel cross-section is examined usine a two-dimensional finite-element ice-flow model coupled to an idealized drainage system. Simulations are driven by physically based calculations of surface water-input variations at Slorgiaciaren, Sweden. Highlights of the model are its ability to handle unsteady conditions and irregular tunnel shapes. Agreement between modelled water pressure and borehole water levels is good. The following conclusions are reached: (i) Tunnels adapt to fluctuating inflow on time-scales of days. Storms, during which effective pressure ranges from 0 to 0.9 MPa, cause significant adjustments but daily fluctuations due solely to melt-water inflow are minor, (ii) Open-channel flow may become commonplace late in the ablation season, (iii) Initial tunnel shape influences subsequent tunnel evolution and seasonal water-pressure variation. Over the course of a summer, tunnels retain some of their initial shape, though in all experiments the width-to-height ratio increased with time, (iv) Tunnel contraction forms broad low tunnels. However, (v) given two tunnels of equal initial area, the higher narrower one expands more rapidly. Thus, more semi-circular tunnels may capture How from broader neighbours early in the summer.

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Interaction between water pressure in the basal drainage system and discharge from an Alpine glacier before and during a rainfall-induced subglacial hydrological event

Annals of Glaciology ◽

10.1017/s0260305500012325 ◽

1997 ◽

Vol 24 ◽

pp. 288-292 ◽

Cited By ~ 11

Author(s):

Andrew P. Barrett ◽

David N. Collins

Keyword(s):

Water Level ◽

Water Pressure ◽

Drainage System ◽

Water Levels ◽

Drainage Network ◽

Alpine Glacier ◽

Hydraulic Conditions ◽

Borehole Water ◽

Progressive Growth ◽

Resultant Increase

Combined measurements of meltwater discharge from the portal and of water level in a borehole drilled to the bed of Findelengletscher, Switzerland, were obtained during the later part of the 1993 ablation season. A severe storm, lasting from 22 through 24 September, produced at least 130 mm of precipitation over the glacier, largely as rain. The combined hydrological records indicate periods during which the basal drainage system became constricted and water storage in the glacier increased, as well as phases of channel growth. During the storm, water pressure generally increased as water backed up in the drainage network. Abrupt, temporary falls in borehole water level were accompanied by pulses in portal discharge. On 24 September, whilst borehole water level continued to rise, water started to escape under pressure with a resultant increase in discharge. As the drainage network expanded, a large amount of debris was flushed from a wide area of the bed. Progressive growth in channel capacity as discharge increased enabled stored water to drain and borehole water level to fall rapidly. Possible relationships between observed borehole water levels and water pressures in subglacial channels are influenced by hydraulic conditions at the base of the hole, distance between the hole and a channel, and the nature of the substrate.

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Measuring glacier-motion fluctuations using a computer-controlled survey system

Canadian Journal of Earth Sciences ◽

10.1139/e86-071 ◽

1986 ◽

Vol 23 (5) ◽

pp. 727-733 ◽

Cited By ~ 1

Author(s):

Garry K. C. Clarke ◽

Robert D. Meldrum ◽

Sam G. Collins

Keyword(s):

Field Experiments ◽

Water Pressure ◽

Yukon Territory ◽

Measuring System ◽

Time Intervals ◽

Stationary Target ◽

Survey System ◽

Computer Controlled ◽

Glacier Flow ◽

Glacier Motion

We describe a computer-controlled, distance-measuring system designed for glacier-motion surveys. A Sharp PC-1500 pocket computer is used to control an AGA Geodimeter 122 infrared laser ranger. Slope distance and vertical angle are automatically measured and plotted at preselected time intervals and recorded on magnetic tape. As a demonstration, three field experiments were performed on Trapridge Glacier, Yukon Territory. In the first experiment the position of a glacier flow marker was measured at 1 min intervals for 39 h. The average velocity (toward the instrument) was found to be 2.99 mm h−1. Subglacial water pressure was simultaneously measured at the flow marker site. For the duration of the survey, water pressure was low, and there is no clear relationship between pressure variations and glacier motion. In the second experiment the distance to a stationary target was measured at 1 min intervals for 9 h. The calculated motion of this target was −0.149 mm h−1, giving an indication of the magnitude of uncorrected distance errors. The third experiment lasted 35 h and again involved measurements of glacier flow. The calculated target motion was 1.80 mm h−1 toward the instrument.

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Lumped-element model for subglacial transport of solute and suspended sediment

Annals of Glaciology ◽

10.1017/s0260305500015354 ◽

1996 ◽

Vol 22 ◽

pp. 152-159 ◽

Cited By ~ 8

Author(s):

Garry K. C. Clarke

Keyword(s):

Electrical Conductivity ◽

Differential Equations ◽

Water Pressure ◽

Water System ◽

Coupled System ◽

Yukon Territory ◽

Water Volume ◽

Charge Voltage ◽

Lumped Element ◽

Lumped Element Model

Present understanding of the subglacial water system and its role in transporting solute and sediment is largely based on subglacial observations of water pressure, turbidity and electrical conductivity and on portal measurements. Such data reveal a wealth of intriguing phenomena, but convincing interpretations can be elusive. Although a proper mathematical description of the subglacial water system would unquestionably lead to a coupled system of non-linear partial differential equations, it is not fruitful to introduce this level of complexity until the important physical processes have been identified and quantified. Lumped-element models offer an efficient approach to examining the complex but dimly perceived physics of the subglacial water system. Water volume, hydraulic head, discharge and flow resistance have the respective electrical analogues of charge, voltage, current and ohmic resistance. Thus, subglacial hydraulic circuits can be approximated by electrical circuits. Mathematically, this circuit description commonly leads to a coupled system of algebraic and differential equations which can be solved numerically. It is straightforward to enrich this representation by adding sources and sinks of solute and sediment. To demonstrate the method, model results are compared to records of subglacial pressure, electrical conductivity and turbidity measured beneath Trapridge Glacier, Yukon Territory, Canada.

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Lumped-element model for subglacial transport of solute and suspended sediment

Annals of Glaciology ◽

10.3189/1996aog22-1-152-159 ◽

1996 ◽

Vol 22 ◽

pp. 152-159

Author(s):

Garry K. C. Clarke

Keyword(s):

Electrical Conductivity ◽

Differential Equations ◽

Water Pressure ◽

Water System ◽

Coupled System ◽

Yukon Territory ◽

Water Volume ◽

Charge Voltage ◽

Lumped Element ◽

Lumped Element Model

Present understanding of the subglacial water system and its role in transporting solute and sediment is largely based on subglacial observations of water pressure, turbidity and electrical conductivity and on portal measurements. Such data reveal a wealth of intriguing phenomena, but convincing interpretations can be elusive. Although a proper mathematical description of the subglacial water system would unquestionably lead to a coupled system of non-linear partial differential equations, it is not fruitful to introduce this level of complexity until the important physical processes have been identified and quantified. Lumped-element models offer an efficient approach to examining the complex but dimly perceived physics of the subglacial water system. Water volume, hydraulic head, discharge and flow resistance have the respective electrical analogues of charge, voltage, current and ohmic resistance. Thus, subglacial hydraulic circuits can be approximated by electrical circuits. Mathematically, this circuit description commonly leads to a coupled system of algebraic and differential equations which can be solved numerically. It is straightforward to enrich this representation by adding sources and sinks of solute and sediment. To demonstrate the method, model results are compared to records of subglacial pressure, electrical conductivity and turbidity measured beneath Trapridge Glacier, Yukon Territory, Canada.

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Estimation of hydraulic properties of subglacial till from ploughmeter measurements

Journal of Glaciology ◽

10.3189/s0022143000002033 ◽

1998 ◽

Vol 44 (148) ◽

pp. 517-522 ◽

Cited By ~ 1

Author(s):

Urs H. Fischer ◽

Neal R. Iverson ◽

Brian Hanson ◽

Roger LeB. Hooke ◽

Peter Jansson

Keyword(s):

Water Level ◽

Hydraulic Properties ◽

Water Pressure ◽

Inverse Correlation ◽

Borehole Water ◽

Potential Gradients ◽

Glacial Tills ◽

Basal Till ◽

Range Of Values ◽

Good Agreement

AbstractForce variations on a "ploughmeter" and fluctuations in subglacial water pressure have been measured in the same borehole at Storglaciaren, Sweden, to investigate hydraulic properties of the basal till layer. A strong inverse correlation of the pressure and force records, in conjunction with a significant lime lag between the two signals, suggests that pore-water pressures directly affect the strength of the till. Variations in sub-glacial water pressure result in potential gradients across the water till interlace at the bottom of the borehole that drive pressure waves downwards through the till layer when the borehole water level is high and back upwards when the water level is low. Analysis of the propagation velocity of this pressure wave indicates that the hydraulic diffusivity of Storglaciaren till is in the range 1.9−3.6 x 10−6m2s−1,in good agreement with estimates obtained in the laboratory. Hydraulic conductivity values associated with these difrusivities are between 10−9 and 10−8ms−1 and thus are well within the range of values for other glacial tills.

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Impact of subglacial hydrology on the release of water from temporary storage in an Alpine glacier

Annals of Glaciology ◽

10.3189/172756405781813735 ◽

2005 ◽

Vol 40 ◽

pp. 67-75 ◽

Cited By ~ 1

Author(s):

Nick J. Rutter

Keyword(s):

Surface Runoff ◽

Water Pressure ◽

Water Storage ◽

Water Transfer ◽

Water Levels ◽

Alpine Glacier ◽

Diurnal Cycles ◽

Borehole Water ◽

Hydraulic Gradients ◽

Phase Relationships

AbstractPeriods of storage and release of surface runoff that is routed englacially and subglacially are identified from a time series of cumulative water balance between 31 July and 11 September 1999 at Findelengletscher, Switzerland. The influence of subglacial hydrology on water routing within the glacier, and therefore on trends of water storage and release, is determined through comparisons of phase relationships between daily maxima, daily minima and diurnal ranges of borehole water levels, supraglacial runoff and proglacial discharge. Variations of water levels in 21 boreholes in the ablation zone suggest that although subglacial drainage is spatially dynamic, hydrologically efficient tunnel–conduit-style drainage dominates diurnal cycles of water transfer through the glacier. Over longer periods, however, storage and release of subglacially routed water is greatly influenced by the coexistence of, and temporary interconnections between, hydrologically inefficient distributed drainage and the tunnel–conduit network. Water levels in three boreholes indicate that after water storage increases in distributed drainage, hydraulic gradients between the different drainage systems may increase sufficiently to cause connections that initiate release of water when: (1) low maximum daily surface runoff causes low water pressures in the tunnel–conduit system; or (2) reorganization within distributed drainage causes spatially localized increases in water pressure.

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