Hydrogeological analysis of slug tests in glacier boreholes

Hydrogeological analysis of slug tests in glacier boreholes

Bernd KULESSA1 Bryn HUBBARD2 Mike WILLIAMSON3 Giles H BROWN2

1Department of Geography University of Wales Swansea Singleton Park Swansea SA2 8PP UKE-mail bkulessaswanseaacuk

2Centre for Glaciology Institute of Geography and Earth Sciences University of Wales Aberystwyth SY23 3DB UK3St Catherinersquos College University of Cambridge Cambridge CB2 1RL UK

ABSTRACT Slug testing allows estimation of subglacial hydraulic properties by evaluating the responseof a coupled boreholendashsubglacial flow system to an artificial displacement of its steady-state hydraulichead However existing models developed specifically for application to slug-test data collected inglacier boreholes are challenging to apply in practice Here we demonstrate that conventional linearmethods which are relatively readily applicable and widely used in groundwater studies can also beused to estimate subglacial hydraulic properties Overdamped underdamped and critically dampedslug-test data were recorded in fluctuating boreholes drilled to the bed of Haut Glacier drsquoArolla ValaisSwitzerland We find that non-linear effects in the data are negligible supporting the application ofconventional hydrogeological methods Results suggest that the hydraulic conductivity of theunconsolidated sediments within the area influenced by a major subglacial drainage channel isenhanced (several 10ndash2m sndash1 typical of gravelly sand) compared to areas outside the zone of influence(0110ndash2m sndash1 typical of silty sand) A distance to a flow boundary within the subglacial aquiferinferred on the basis of slug-test analysis was found to coincide with the actual location of thesubglacial channel Sensitivity analyses reveal that uncertainties in borehole and filter radii as well asthe storage coefficient of the subglacial aquifer are more likely to affect the accuracy of the hydraulicand distance estimates than uncertainties regarding the repeatability of the slug-test responses andcurve-fitting procedures involved in the conventional hydrogeological methods

LIST OF SYMBOLS

a Iterative parameter in Van der Kamp modelA Non-linear parameter reflecting turbulence in boreholeb Iterative parameter in Van der Kamp modelbSL Thickness of subglacial aquifer (m)D Distance to constant-head boundary in Guyonnet

method (m)F Parameter reflecting viscous loss in boreholeg Acceleration of gravity (981m sndash2)h Displacement of hydraulic head in subglacial

aquifer (m)H Displacement of hydraulic head in borehole in

low-transmissivity models (m)H0 Initial hydraulic head displacement in low-

transmissivity models (m)K Subglacial hydraulic conductivity (m sndash1)Le Effective length of borehole water column (m)n Index of iteration in Van der Kamp modelrA Radial distance from centre of borehole (m)rBH Borehole radius (m)rF Radius of borehole filter (m)S Subglacial storage coefficientt Elapsed time of slug test (s)tC Time of match in CooperndashBredehoeft method (s)

tD Dimensionless time in Kipp model

tdev Time of 1 deviation in Guyonnet method (s)

T Subglacial transmissivity (m2 sndash1)

w Displacement of hydraulic head in borehole in high-transmissivity models (m)

w0 Initial water-level displacement in high-transmissivitymodels (m)

Dimensionless storage parameter in CooperndashBredehoeftmodel

K Dimensionless storage parameter in Kipp model

Dimensionless time parameter in CooperndashBredehoeftmodel

K Dimensionless time parameter in Kipp model

Damping constant in Van der Kamp model (sndash1)

Skin factor in Kipp model

Damping factor in Kipp model

Angular frequency of oscillation in van der Kampmodel (Hz)

1 INTRODUCTIONSlug testing in glacier boreholes has the potential to yieldimportant information about hydraulic properties of sub-glacial drainage systems (Stone and Clarke 1993 Iken andothers 1996 Stone and others 1997 Kulessa and Murray2003) The method is identical to slug tests routinelyapplied to confined or unconfined groundwater aquifers Itinvolves artificial displacement of the steady-state boreholewater level (WL) typically by insertion (falling-head test(FHT)) or removal (rising-head test (RHT)) of a sealed pipeto displace a volume of water and monitoring the

Journal of Glaciology Vol 51 No 173 2005

Formerly at Centre for Glaciology Institute of Geography and EarthSciences University of Wales Aberystwyth SY23 3DB UKPresent address School of Geographical Sciences University of BristolBristol BS8 1SS UK

269

subsequent WL recovery (eg Kruseman and de Ridder1994) The characteristics of the recovery signal serve asindicators of subsurface hydraulic conditions and can beanalyzed for hydraulic properties of the boreholendashaquifersystem At Haut Glacier drsquoArolla Valais Switzerlandunconsolidated water-saturated sediments of varying thick-ness have temperate ice as an upper boundary and bedrockas a lower boundary (eg Hubbard and others 1995Harbor and others 1997) This situation compares well withthat of a conventional confined aquifer (eg Fetter 2001)The underlying assumptions of this analysis are that theborehole is hydraulically well connected to the aquiferimplying that a change in aquifer hydraulic head willinstantaneously result in an equivalent change in boreholeWL and that there is negligible lateral or vertical leakageinto the aquifer Such fluctuating boreholes (Smart 1996)are commonly characterized by a noticeable WL dropwhen the glacier bed is reached during drilling as well asby marked daily WL variations In contrast unconnectedboreholes are typically water-filled and non-fluctuating(Smart 1996)

Three distinct types of slug-test response may beexpected chiefly depending on borehole water-columnlength and aquifer transmissivity which together determinethe degree of water-column inertial effects The latter arenegligible in the overdamped case (exponential non-oscillating decay) and significant in the underdamped case(exponential oscillating decay) with critical dampingrepresenting the transitional response (Bredehoeft andothers 1966) A coupled boreholendashaquifer flow system oflow transmissivity and small water-column length is likely toproduce an overdamped response while an underdampedresponse may be expected if transmissivity is high and water-column length is large (Bredehoeft and others 1966) In theoverdamped case water-flow rates in the boreholendashaquifersystem are commonly small enough for turbulent effects tobe neglected supporting the use of linear slug-test modelsSuch models are analytically attractive involving manualmatching of observed responses with type curves in thesimplest case and have been widely used in groundwaterstudies for several decades (Butler 1997) In contrast in theunderdamped case water-flow rates could in some in-stances be so large that turbulence occurs requiring the useof non-linear models

Previously a unified model allowing for any degree ofdamping of slug-test responses was developed specificallyfor application in glaciology (Stone and Clarke 1993 Stoneand others 1997) Application to borehole response testsconducted at Trapridge Glacier Yukon Territory Canadatogether with extensive sensitivity analyses revealed thatnon-linear effects in the entire boreholendashsubglacial-aquiferflow system were not of concern during slug tests Motivated

by this conclusion the present study aims to investigate theuse of established linear slug-test models in estimatingsubglacial hydraulic properties This would allow rapidinterpretation of slug tests using either simple manualanalysis or widely available lsquolinearrsquo software packagesincreasing the appeal of this technique in hydro-glacialinvestigations

We initially ascertain that non-linear effects are notprevalent in our data The bulk of this study then aims (i) todemonstrate the application of a range of linear slug-testmodels that have been particularly popular in groundwaterstudies (Cooper and others 1967 Van der Kamp 1976Kipp 1985 Guyonnet and others 1993) to our data and(ii) to estimate the hydraulic properties of the subglacialsediments at the glacier along a transect traversing a majorsubglacial channel

2 SLUG-TEST METHODS21 Boreholendashsubglacial-aquifer flow systemMany different slug-test models have been developed ingroundwater studies each focusing on a particular physicalscenario defined by the properties of the well and the aquifer(eg Butler 1997) Choosing the right model for theparticular physical scenario to be investigated is importantto obtain reliable estimates of hydraulic properties Theconceptual geometry of the boreholendashsubglacial flow systemconsidered here is illustrated in Figure 1 A borehole ofradius rBH is connected to the subglacial aquifer of thicknessbSL via a fully penetrating filter of radius rF The water level isinitially displaced by an amount H0 due to slug insertionand subsequently gradually returns (H(t)) to the equilibriumWL (solid line in Fig 1) The filter accounts for subglacialexcavations due to sediment flushing and clogging in thevicinity of the borehole base as the hot-water drill reachesthe glacier bed (eg Stone and Clarke 1993) It thereforerepresents an annulus of larger hydraulic conductivity thanthe outlying subglacial aquifer The term borehole face isused to describe the cylindrical interface between the filterand the aquifer and ice and bedrock bounding the boreholewater column and the aquifer are assumed to be im-permeable (Fig 1) The rate of slug-induced water flow inthe subglacial aquifer is strongly dependent on its transmis-sivity (T given by hydraulic conductivity (K ) aquiferthickness (bSL)) which may therefore be estimated fromappropriate analysis of recovery curve characteristicsParticularly suitable and popular linear slug-test models forthe present physical scenario are the CooperndashBredehoeft(Cooper and others 1967) Van der Kamp (1976) and Kipp(1985) methods (eg Butler 1997) which are adapted hereto analyze overdamped underdamped and criticallydamped responses respectively

As considered in section 1 the models for the analysis ofslug-test responses are applicable to either low-transmissiv-ity or high-transmissivity aquifers Linear models may beused in either case if turbulence in the boreholendashaquiferflow system is negligible If slug-induced turbulence is notnegligible as observed previously in some high-transmis-sivity aquifers (eg Butler 1997 McElwee and Zenner1998) non-linear models must be used Since theseapproaches are well established and covered in thepertinent groundwater literature (eg Butler 1997) wepresent only a brief summary here focusing on relevantmodel characteristics

Fig 1 Boreholendashsubglacial flow system geometry

Kulessa and others Hydrogeological analysis of slug tests in glacier boreholes270

22 Low-transmissivity aquifers221 CooperndashBredehoeft methodAssuming that transient flow in a low-transmissivity aquiferis confined and cylindrical occurring radially out of andback into the borehole face the hydraulic head in theaquifer (h) is appropriately described by (Cooper and others1965)

2hr2A

thorn 1rA

hrA

frac14 STht

eth1THORN

Here S is the storage coefficient (the pore volume changeper unit surface area of the glacier bed per unit head change)and rA is the horizontal distance from the axis of theborehole filter Equation (1) is based on the conservation offluid volume incorporating aquifer and fluid compressibilityin the storage term combined with Darcyrsquos law thusneglecting turbulence and assuming a homogeneous aqui-fer

The CooperndashBredehoeft model is a particularly popularmethod for the analysis of overdamped slug-test responses inlow-transmissivity confined aquifers (eg Butler 1997p 57) This method connects transient changes in hydraulichead in the aquifer (h (rAt)) with those in the borehole (H(t))induced by slug insertion or withdrawal consideringcontinuity of water flow at the borehole face (where rF frac14 rA)and neglecting water-column inertia

2rFTh rF teth THORN

rfrac14 r2BH

dH teth THORNdt

eth2THORN

The CooperndashBredehoeft model assumes that well losses arenegligible (h(rFt) frac14 H(t) for t gt 0) and that the slug isintroduced or withdrawn instantaneously (h(rA0) frac14 0 forrF lt rA lt 1 H(0) frac14 H0) It is also assumed that there are noflow boundaries within the portion of the aquifer influencedby the slug test (h(1t ) frac14 0 for t gt 0) and that elastic storagemechanisms as expressed by S in Equation (1) affect slug-test responses The CooperndashBredehoeft model considers thatthe analytical solution to this model can then be written as

H teth THORNH0

frac14 f eth THORN eth3aTHORNwhere

frac14 Ttr2BH

eth3bTHORN

frac14 r2F Sr2BH

eth3cTHORN

Here is the dimensionless time parameter and is thedimensionless storage parameter Cooper and others (1967)and Papadopulos and others (1973) plot H teth THORNH1

0 against thelogarithm of resulting in a series of type curvescharacterized by different values of Matching of appro-priately processed field data with the best-fit type curveallows estimation of aquifer transmissivity using a series ofwell-defined steps (eg Butler 1997 p 58)

222 Guyonnet methodSince the CooperndashBredehoeft model assumes that aquifersare unbounded systematic deviations between observedslug-test responses and best-fit type curves often occurwhere flow boundaries exist within the portion of the aquiferinfluenced by slug tests (eg Karasaki and others 1988Guyonnet and others 1993) Subglacial aquifers at Alpineglaciers are notoriously heterogeneous (eg Hubbard and

Nienow 1997) making the presence of flow boundarieswithin such portions likely Constant-head and no-flowboundaries would respectively result in faster and slowerWL recovery than predicted by the CooperndashBredehoeftmodel (eg Moench and Hsieh 1985) representing adiagnostic means of their identification in a joint plot ofobserved response and best-fit type curve Constant-headboundaries could be represented by water-filled subglacialchannels or cavities as discussed by Iken and others (1996)in a slug-test context or by transitions from connected tounconnected regions of the glacier bed (section 1) whichmay hydraulically force each other (eg Murray and Clarke1995) No-flow boundaries could potentially result wheresubglacial sediment layers pinch off Guyonnet and others(1993) evaluate the analytical solution to the CooperndashBredehoeft model (as summarized in Equations (3andashc)) todetermine the distance between the tested borehole andconstant-head or no-flow boundaries The Guyonnetmethod thus promises to be well suited to identifying thenature and location of such boundaries in subglacialhydrological systems at Alpine glaciers

Guyonnet and others (1993) consider that any particulardrawdown caused by a slug test will not travel beyond acertain distance (eg Sageev 1986) and focus on estimatingthis distance as a function of time specifically allowing forstorage in the test well which may critically decrease theimpact of a flow boundary on the response curve (egKarasaki and others 1988) Estimation of distance to theclosest flow boundary uses a series of well-defined stepsbased on a dimensionless formulation of the problem(Guyonnet and others 1993) Key to these steps are typecurves representing functions of deviation between meas-ured response curves and best-fit CooperndashBredehoeft typecurves and of storage in the borehole

23 High-transmissivity aquifersWhere the inertia of the borehole water column is signifi-cant its momentum causes more water to flow into or out ofthe borehole face than is predicted by the CooperndashBredehoeft model generating oscillatory responses (egBredehoeft and others 1966) In this case models based onthe conservation of momentum are most adequate for theanalysis of slug-test responses where the displacement ofborehole WL from static (w) can generally be expressed by(eg Butler 1997 p 153)

Le thornwg

d2wdt2

thorn Ag

dwdt

2

thorn Fgdwdt

thornw frac14 h eth4THORN

Here Le is the effective length of the borehole water columnplus some fraction of filter length (eg Butler 1997 p 153ndash154) A is a parameter reflecting the significance ofturbulence in the borehole (if A lt 1 turbulence is of littlesignificance eg Kabala and others 1985) F is a viscousloss parameter and g is the acceleration due to gravity It isassumed that there is no initial velocity of the water surfacein the well (dwdt frac14 0 for t frac14 0) and that slug insertion orwithdrawal is instantaneous (w(0) frac14 H0) For a completedescription of flow in a boreholendashaquifer system induced bya slug test Equation (4) must be coupled with a model suchas Equation (1) According to Butler (1997 p 154) there aretwo popular classes of linear high-transmissivity slug-testmodels These are Van der Kamp type linear models andgeneral linear methods (such as the Kipp method) both ofwhich are considered in the present study

Kulessa and others Hydrogeological analysis of slug tests in glacier boreholes 271

231 Van der Kamp methodThe Van der Kamp method connects a simplified version ofEquation (4) ignoring the non-linear term with Equation (1)to describe slug-induced flow in the boreholendashaquifersystem thus being subject to their combined initial andboundary conditions The damped-spring solution of clas-sical physics is applied to the resulting governing equationsThis solution is approximate in that it is valid neither for theinitial moments of the WL displacement (ie before the firstsinusoid peak) nor for responses that are not well within theunderdamped regime If n is an index of iteration (n 1)this solution suggests that aquifer transmissivity (Tn ) may beestimated from

Tn frac14 b thorn a ln Tn1 eth5aTHORNwhere

a frac14 r2BHg8Le

eth5bTHORN

b frac14 a ln 079r2F SffiffiffiffiffigLe

r eth5cTHORN

Le frac14 g2 thorn 2

eth5dTHORN

Equations (5andashd) use the notation of Wylie and Magnuson(1995) with and respectively representing the frequencyand the damping constant of the induced WL oscillationsWylie and Magnuson (1995) proposed a convenientspreadsheet approach for the implementation of the Vander Kamp method which we adopt in the present study

232 Kipp methodAs outlined by Butler (1997 p 159ndash163 a brief summary ispresented here focusing on relevant aspects) general linearmodels have been developed to allow for any degree ofdamping overcoming the limitations of the Van der Kampmethod in this respect Out of these application of the type-curve approach included in the Kipp method has beenparticularly popular in field scenarios involving fully pene-trating borehole filters This approach conceptually con-siders the same analytical connection between flow inaquifer (ie using Equation (1)) and flow in the borehole (ieusing an equivalent simplification of Equation (4)) as the Vander Kamp method thus also being subject to their combinedinitial and boundary conditions Suffice it to say that the keydifference between the two methods is the mathematicalsolution to the simplified version of Equation (4) which inthe Kipp approach allows for any degree of damping Thisassumes that the magnitude of the dimensionless storageparameter (K Equation (6b)) is small and that the value ofthe inertial parameter (K Equations (6c and d)) is very largeThe latter is related to the times of match between the

measured response curve and the best-fit Kipp type curvethrough effective water-column length (Le) After Le K andK have respectively been determined from Equations (6a)(6b) and (6c) the transmissivity (T ) of the aquifer is estimatedfrom Equation (6d)

tD frac14 tffiffiffiffiffiffiffiffiffiffiffiffiLeg1

p eth6aTHORN

K frac14 r2BH2r2F S

eth6bTHORN

frac14 K thorn 025 ln Keth THORN2

ffiffiffiffiffiffiK

p eth6cTHORN

K frac14 Leg

Tr2F S

2

eth6dTHORN

Here tD is dimensionless time as used by the type curves t iselapsed time of slug test is the damping factor and is aparameter expressing the significance of the borehole skinSlug-test responses are respectively overdamped criticallydamped and underdamped for gt 1 frac14 1 and lt 1 andthe CooperndashBredehoeft solution applies for 5 whereinertial effects become negligible (Kipp 1985)

3 FIELD SITE AND SURVEY PROTOCOL31 Field siteHaut Glacier drsquoArolla is a small valley glacier located at thehead of Val drsquoHerens Valais Switzerland (Fig 2a) It has asurface area of 63 km2 and extends from 2560masl atits snout to 3500masl at its headwall (eg Richards andothers 1996) The survey site considered in the presentstudy is located in the eastern part of the ablation area(Fig 2b) and is predominantly underlain by unconsolidatedsediments (Copland and others 1997) A major melt-seasondrainage channel dominates subglacial water discharge inthe survey area during the late melt season in August (egHubbard and others 1995 Gordon and others 1998) Thischannel is located at the centre line of a variable pressureaxis (VPA) which defines the spatial limits of hydraulicinteraction between the channel and the surroundingdistributed subglacial drainage system (Fig 2c based ondata collected by Hubbard and others (1995) in the 1993melt season) Hubbard and others (1995) inferred thathydraulic interactions may extend to 140m transverse tochannel orientation causing systematic flushing of finesfrom the subglacial sediments The latter was confirmed byKulessa and others (2003) using electrical self-potentialmeasurements which indicated that clay minerals werelargely absent in the channel area during the late meltseason The concept of subglacial erosion also agrees withthe observation that sediment thickness (bSL) in this areaincreases from 005m near the subglacial channel togt02m away from it (Harbor and others 1997) which wemust consider when converting transmissivity (T ) to hy-draulic conductivity (K ) Flushing of fines was furthersuspected to lead to a gradual decrease in the hydraulicconductivity of the subglacial sediments away from thechannel (Hubbard and others 1995) We may evaluate thisinference further and estimate absolute values of hydraulicconductivity using slug-test data collected in boreholeslocated at different distances from the channel (Fig 2c)Some of our tested boreholes are located close to thechannel (located at the centre line of the VPA in Fig 2c)

Table 1 Summary of 1994 and 1995 slug tests reported in this studyBorehole locations are illustrated in Figure 2c

Borehole No Number of tests Julian day

9469 7 942319475 5 94231951 4 952229514 4 952309516 4 95224


and the typical duration of a slug test is short compared to adiurnal water discharge cycle in the channel The lattercould therefore potentially act as a constant-head boundaryduring a slug test (section 222)

32 Survey protocolBoreholes were drilled using hot pressurized water Sincedrilling rates commonly vary and glacier ice is hetero-geneous non-uniform borehole radii often result Filterradius may vary depending on the actual time the drill washalted at the base of the glacier and on the properties of thesubglacial material We initially assume that borehole andfilter radii have values of 005m and 025m respectively(Iken and others 1996) It is however important toinvestigate the impact of potential variations in theseparameters on our estimates of hydraulic conductivity andlocation of constant-head boundaries We therefore calcu-late standard errors for reasonable ranges of borehole(003ndash007m) and filter (005ndash025m) radii a practicalapproach to error analysis previously adopted by Kulessaand Murray (2003) The slug (a sealed pipe) was quicklyinserted into and subsequently quickly removed from aborehole while recovery of the WL was monitored with apressure transducer submerged in it The transducer wasconnected to a Campbell Scientific CR10 data loggertypically operated at 16Hz although in some cases thesampling rate was decreased to 02Hz after the initial 30 sof the test to save space on the logger Each test wascompleted within a few minutes allowing routine repetitivetests

Slug tests conducted at Haut Glacier drsquoArolla during the1994 and 1995 melt seasons are identified in Table 1 Allboreholes reported here were classified as fluctuating andlocated along a transect established transverse to ice flow(Fig 2c) Borehole labelling is such that the year of drilling isfollowed by the borehole number in that year Twelve slugtests were conducted in 1994 in two fluctuating boreholeslocated near the subglacial channel detected in 1993 (egSharp and others 1993 Hubbard and others 1995) In1995 12 slug tests were carried out in three boreholesspread over a comparatively large area (Table 1 Fig 2c) Allslug tests are labelled according to the type of displacementborehole number day of the year and time of test

4 RESULTSUnderdamped responses were recorded in BH 9469 andBH 9475 while overdamped responses dominated inBH 951 and BH 9514 Critical damping was observed inBH 9516

41 Underdamped responsesTypical slug-test responses recorded in BH 9469 andBH 9475 are presented in Figure 3 In the case ofBH 9469 initial displacement is just over 3m followedby an irregularly fluctuating WL After a few seconds theWL displacement begins to oscillate around the equilibriumWL and eventually assumes its natural frequency InBH 9475 maximum WL displacements of just under 2mare observed Subsequent high-frequency oscillations aredamped out after a few tens of seconds merging into WLcycles characterized by the natural frequency of the coupledboreholendashsubglacial-aquifer flow system The underdampedslug-test responses oscillate markedly longer than 1min

and pre-displacement WLs are commonly established atthe end of the tests The other slug tests conducted in BH9469 and BH 9475 (Table 1) yielded similar responsesignals

42 Overdamped responsesRHT 12221814 (Fig 4a) is representative of two falling-head and two rising-head tests conducted in BH 951 Thetest shown is characterized by high-frequency oscillationsover the first 3 s before establishing a pattern typical of anoverdamped slug-test response MaximumWL displacementis just over 1m recovering more rapidly (30 s) than theunderdamped slug-test responses which typically oscillatedfor gt1min (Fig 3) Two falling-head and two rising-headtests were performed in BH 9514 (Table 1) RHT 142301531 (Fig 4b) is characterized by exponential decayspersistent over 90 s Maximum WL displacements re-corded in BH 9514 are smaller (08m) than thoserecorded in BH 951 but are persistent over a longer timeperiod before the equilibrium WL is re-established (80 s)

Fig 2 Location of (a) Haut Glacier drsquoArolla in Switzerland (b) thesection of the ablation area surveyed in 1994 and 1995 and (c) theboreholes used in these years The location of the VPA in 1993 isalso shown in (c) The channel is located at the centre line of theVPA and direction of channelized water flow is from south tonorth


43 Critically damped responsesRHT 162241631 (Fig 5) is representative of the four slugtests conducted in BH 9516 (Table 1) After the first fewseconds of the test a relatively fast decay pattern is replacedby a slower WL rise lasting 30 s until the pre-displacementWL is re-established The decay pattern is characteristicallydifferent from the overdamped and underdamped responsesin that the initial WL recovery is relatively rapid and onlyvery slight irregular WL fluctuations are observed at latertimes This behaviour is typical of critical or at least near-critical damping conditions

5 INTERPRETATION

51 Evaluation of non-linear effectsWe found that application of linear slug-test models to ourdata produced statistically significant fits between measuredresponses and calculated responses (underdamped case) ortype curves (overdamped and critically damped cases) Thisprovides an initial diagnostic indicator that non-lineareffects are most probably negligible (eg Butler 1997McElwee 2001 Kulessa and Murray 2003) Since Stone andothers (1997) found that slug tests are generally unlikely tocause turbulence in subglacial aquifers we are confidentthat non-linear effects in the aquifer beneath Haut GlacierdrsquoArolla are not of concern Extensive sensitivity analysesconducted by Stone and Clarke (1993) strongly suggestedthat slug-test induced turbulence in glacier boreholes is alsonegligible However in the present case hydraulic headswere often larger (up to gt100m) than those reported byStone and Clarke (1993) (50m or less) increasing thelikelihood of turbulence occurring in the borehole during

slug tests In order to ascertain beyond doubt that the latter isnot of concern we have evaluated the magnitude of thenon-linear parameter A in Equation (4) (Williamson 2003)It was found to be of the order of 10ndash6 for both underdampedand overdamped responses and 10ndash4 for those that werecritically damped Since turbulence in the borehole isnegligible for A lt 1 (section 23) these findings indicatebeyond reasonable doubt that such non-linearity may alsobe neglected corroborating the findings of Stone and Clarke(1993) We are therefore confident that slug-test inducedturbulence in the entire boreholendashsubglacial flow system atHaut Glacier drsquoArolla may be neglected suggesting thatapplication of linear slug-test models is correct

52 Underdamped responses

521 Determination of subglacial transmissivityStone and others (1997) stressed the importance of removingnon-slug-test related trends in WL from the response dataWe use an approach similar to theirs which involves fittinga straight line through and subsequently subtracting it fromour data In addition the data prior to the first peak of WLdisplacement are removed from oscillating slug-test re-sponses to satisfy the assumptions involved in the Van derKamp model and the conditions of the approximate solution(Krauss 1974 Van der Kamp 1976)

Following data preparation curve matching is employedto derive natural frequency and damping constant by least-squares minimization of the misfit between measured andcalculated responses The match between prepared fielddata and calculated oscillations is excellent (see example inFig 6) for all 12 underdamped slug tests analyzed Enteringnatural frequency and damping constant into Equation (5)

Fig 3 Typical underdamped slug-test responses recorded in (a) BH9469 and (b) BH 9475 The grey lines indicate the pre-displace-ment WLs

Fig 4 Typical overdamped slug-test responses recorded in (a) BH951 and (b) BH 9514 The grey lines indicate the pre-displacementWLs Sampling interval was changed to 5 s where black circlesreplace solid lines at later times


typically results in convergence after three iterations basedon a tolerance of 01 Effective water-column lengths arecalculated to be 90m and 128m for BH 9569 and BH9575 which respectively are in good and fair agreementwith the observed pre-test WLs of 85m and 111mAssuming a storage coefficient (S ) of 110ndash4 which is atypical value for confined aquifers (Freeze and Cherry 1979p 60) a borehole radius (rBH) of 005m and a filter radius(rF) of 025m we obtain transmissivity (T ) estimates of132 10ndash3m2 sndash1 for BH 9469 and 57 10ndash3m2 sndash1 forBH 9475

522 Sensitivity analysisThe transmissivities calculated in the previous sectionrepresent lsquobest estimatesrsquo assuming that (i) slug-testresponses are perfectly repeatable (ii) the least-squares fitsbetween measured and calculated responses have a R2 of 1and (iii) previously reported values of the storage coefficient(S ) and borehole (rBH) and filter (rF) radius also apply at HautGlacier drsquoArolla In practice however some errors normallyarise when repeating slug tests and fitting calculatedresponses and both radii and the storage coefficient couldbe somewhat different at Haut Glacier drsquoArolla than at otherglaciers In order to investigate the effect of these

uncertainties on our transmissivity estimates we conductsensitivity analysis using the approach suggested by Kulessaand Murray (2003) Each of the six uncertain parameters(response repeatability oscillation frequency () dampingconstant () borehole radius (rBH) filter radius (rF) andstorage coefficient (S )) is assigned an error range within thelimits of reason Each parameter is then varied individuallywithin its given error range relative to the best estimates ofthe other parameters The resulting six transmissivity rangesare then used to calculate an overall standard deviation

The resulting variations in transmissivity are summarizedin Table 2 Response repeatability and curve-fitting errorshave minor impact on transmissivity compared to variations

Table 2 Results of sensitivity analysis for underdamped slug-test responses Note that transmissivity is inversely related to filter radius (rF) andstorage coefficient (S ) Error ranges for repeatability and curve fits were different for each borehole and are not explicitly shown to avoidovercrowding the table

Error range BH 9469 BH 9475Tmin Tmax Tmin Tmax

10ndash3m2 sndash1 10ndash3m2 sndash1 10ndash3m2 sndash1 10ndash3m2 sndash1

Rep Different for each borehole 117 148 55 59Fit I Different for each borehole 130 135 55 59Fit II Different for each borehole 121 146 49 68rBH (m) 005+ 002

ndash 00180 281 34 122

rF (m) 025+ 015ndash 02

184 117 82 50

S 00001+ 00099ndash 00000999

243 51 109 18

Repeatability of measured response curves Curve fit depending on frequency parameter Curve fit depending on damping parameter

Fig 6 Application of the Van der Kamp method matching ofprepared field data (grey lines) and calculated oscillations (smoothblack lines) for (a) BH 9469 and (b) BH 9475

Fig 5 Typical slug-test response recorded in BH 9516 suspectedto be critically damped The grey line indicates the pre-displacement WL


in the other three parameters (Table 2) Of the latterborehole radius (rBH) and the storage coefficient (S ) have aparticularly strong influence causing transmissivity vari-ations of almost one order of magnitude Note thattransmissivity is inversely related to filter radius (rF) and SThe standard deviation of the transmissivity range reported inTable 2 was calculated to be 52 10ndash3m2 sndash1 for BH 9469and 2410ndash3m2 sndash1 for BH 9475 We therefore concludethat the subglacial sediments at BH 9469 and BH 9475have respective transmissivities of (132 52 THORN10ndash3m2 sndash1

and (5724) 10ndash3m2 sndash1

53 Overdamped responses

531 Determination of subglacial transmissivityThe overdamped slug-test responses recorded in BH 951and BH 9514 were initially prepared in the same way as theunderdamped responses (previous section) and subse-quently fitted by exponential signal decays (eg Fig 7aand b) During the first few seconds of a slug test high-frequency fluctuations are often superimposed on theexponential decay (Kulessa and Hubbard 1997) We ignorethese fluctuations in accordance with Butler and others(1996) who argued that such lsquofluctuations are related to testinitiation and should be ignored when considering thequality of the match between the best-fit model and the testdatarsquo All slug tests conducted in BH 951 produced avirtually identical match with the CooperndashBredehoeft typecurve for frac14 10ndash10 This type curve presented the best-fitchoice yielding tC frac14 23 s for all four tests (Fig 7c) WithrBH frac14 005m a transmissivity (T ) of 10610ndash4m2 sndash1 isobtained An analogous procedure applied to the responsesrecorded in BH 9514 yields tC frac14 69 s (Fig 7d) andT frac14 3610ndash4m2 sndash1 if rBH frac14 005m These calculatedtransmissivities are consistently lower than those inferredfrom analysis of underdamped slug-test responses recordedin BH 9469 and BH 9475 (Table 2)

532 Determination of subglacial constant-headboundariesIn this study the later portions of all measured responses liebelow the best-fit CooperndashBredehoeft type curve implyingfaster recovery (Fig 7c and d) and thus the presence of asubglacial constant-head boundary (Guyonnet and others1993) The presence of such boundaries is consistent withthe inhomogeneous nature of the subglacial drainage systemin the study area (section 31) Based on our best estimates oftransmissivity (T frac14 10610ndash4m2 sndash1 for BH 951 and36 10ndash4 m2 sndash1 for BH 9514) storage coefficient(S frac14 10 10ndash4) and borehole radius (rBH frac14 005m) weobtain respective distances of 5m and 65m from thebases of BH 951 and BH 9514 to the closest constant-headboundaries (Fig 8) using figure 6 in Guyonnet and others(1993) Both values appear reasonable considering thelimited radius of influence of the slug-test method ingeneral and the heterogeneous character of the subglacialdrainage system in the survey area in particular Hubbardand others (1995) located the centre of a subglacial channelat an easting of 606785 and BH 951 is located at6067875 (ie 25m from the channel Fig 2c) We thereforebelieve that the inferred constant-head boundary near thisborehole is probably associated with this preferential water-flow pathway The origin of the constant-head boundarynear BH 9514 and indeed its subglacial hydraulicconnection as such is probably related to preferentialseepage induced by water entering the glacier bed near theeastern margin where crevasses and surface streams arecommon

533 Sensitivity analysis I transmissivityUsing the same approach to sensitivity analysis as that usedin the underdamped case (section 522) we found thatneither repeatability of the response signals nor variations inthe initial amplitude of the exponential decays alteredtransmissivity noticeably The sole parameter introducingmajor uncertainty is borehole radius (rBH) which may cause

Fig 7 Application of the CooperndashBredehoeft method preparedfield data (grey lines) and exponential decays (black lines) for (a) BH951 and (b) BH 9514 and logarithmically transformedexponential decays characterizing (c) BH 951 and (d) BH 9514(black lines) matched with the CooperndashBredehoeft type curve forfrac14 10ndash10 (grey lines) tC is the time of match in the CooperndashBredehoeft method and tdev is the time of 1 deviation in theGuyonnet method Sampling interval was changed to 5 s wherecircles replace solid lines at later times in (a) and (b) Note that theabscissa label in (c) and (d) is equal to the dimensionless timeparameter (see Equation (3b)) W0 is initial WL displacement


order-of-magnitude variations in transmissivity (Table 3)Together the transmissivity values listed in Table 3 produce astandard deviation of 37 10ndash4m2 sndash1 for BH 951 and1210ndash4m2 sndash1 for BH 9514

534 Sensitivity analysis II distance to constant-headboundaryIn the case of the Guyonnet method uncertain parametersare (i) the time of 1 deviation between the exponentialdecay and the CooperndashBredehoeft type curve (tdev)(ii) transmissivity (T ) (iii) borehole radius (rBH) and (iv) thestorage coefficient (Table 4) Uncertainty (i) is small for BH951 and negligible for BH 9514 (Table 4) which suggeststhat graphical estimation procedures are relatively accurateVariations in transmissivity and borehole radius typicallyresult in metre-scale variations of distance to the closestconstant-head boundary (Table 4) which together with thesmall graphical uncertainties would place reasonable errorbounds on distance to the closest constant-head boundary(10m for BH 951 15m for BH 9514) However unfor-tunately the storage coefficient has an overwhelming impacton this distance (Table 4) A storage coefficient of the orderof 10ndash2ndash10ndash3 as previously reported for unfrozen marinesediments beneath Bakaninbreen Svalbard (Porter and

Murray 2001) produces an unrealistically small distance(1m) In contrast a storage coefficient of the order of 10ndash7as previously reported for Gornergletscher Valais Switzer-land based on slug tests (Iken and others 1996) causesdistance to reach 145m for both BH 951 and BH 9514(Table 4) which is not unrealistically large (eg Butler 1997p 183) Inclusion of the latter increases the standarddeviation of the distance to the boundary to 29m forBH 951 and 23m for BH 9514 Note that distance isinversely related to borehole radius (rBH) and the storagecoefficient (S)

535 SummaryAnalysis of overdamped slug-test responses reveals that BH951 is underlain by unconsolidated sediments that have atransmissivity of 106 3710ndash4m2 sndash1 The base of thisborehole is located 5 29m from the closest subglacialconstant-head boundary which probably corresponds to thesubglacial channel detected by previous authors (section31) The sediments beneath BH 9514 have a transmissivityof (36 12)10ndash4 m2 sndash1 and its base is located6523m from the closest constant-head boundary Thelatter is probably associated with water entering the glacierbed at the eastern margin It is unlikely that the subglacial

Fig 8 Determination of dimensionless distance from dimensionlesstime and the borehole storage coefficient (after Guyonnet andothers 1993 fig 6) The dashed and solid arrows respectivelyreflect application of the Guyonnet method in BH 951 andBH 9514

Table 3 Results of sensitivity analysis for overdamped and critically damped slug-test responses Note that transmissivity is inversely relatedto filter radius (rF) in the Kipp case Error ranges for curve fits were different for each borehole and are not explicitly shown to avoidovercrowding the table

Error range BH 951 BH 9514 BH 9516

CooperndashBredehoeft CooperndashBredehoeft Kipp

Tmin Tmax Tmin Tmax Tmin Tmax

10ndash3m2 sndash1 10ndash3m2 sndash1 10ndash3m2 sndash1 10ndash3m2 sndash1 10ndash3m2 sndash1 10ndash3m2 sndash1

Fit I Different for each borehole 10 11 03 04 ndash ndashFit II Different for each borehole 11 11 04 04 45 51rBH (m) 005+002 07 21 02 07 26 106

ndash 001rF (m) 025+015 ndash ndash ndash ndash 160 14

ndash 01S 00001+00099

ndash 00000999ndash ndash ndash ndash 117 ndash

Fit of exponential decay curve to measured response curve (damping parameter only) Match between fitted exponential decay curve (or data for BH 9516)and type curve The Kipp K-value and thus transmissivity could not be calculated for S gt 00001

Table 4 Results of sensitivity analysis for Guyonnet method Notethat distance to constant head boundary (D) is inversely related toborehole radius (rBH) and storage coefficient (S )

BH 951 BH 9514

Dmin Dmax Dmin Dmax

m m m m

tD 45 55 6 7T 425 7 5 8rBH

72 49 68 63Ssect 145 007 145 01

Estimated accuracy is 05 s for all boreholes Transmissivity ranges arethose listed in row lsquoFit IIrsquo for CooperndashBredehoeft in Table 3 sectRanges arelisted in Tables 2 and 3


storage coefficient (S) is larger than 10ndash4 at either boreholesince unrealistically small distances to constant-headboundaries would result

54 Critically damped responses541 Determination of subglacial transmissivityThe Kipp method promises to allow both identification ofcritically damped response signals and estimation ofsubglacial hydraulic properties Data are initially preparedin the same way as underdamped slug-test data (sec-tion 521) The match between all four repeat tests in BH9516 and the Kipp type curve for frac14 15 is very good(Fig 9) The test responses in this borehole are therefore justoverdamped although the CooperndashBredehoeft solution doesnot apply since inertia is still significant (section 232)Using a filter radius (rF) of 025m a storage coefficient (S) of1010ndash4 and an effective water column length (Le) of231m as measured at the time of testing Equation (6d)yields a transmissivity (T ) of 4710ndash3m2 sndash1

542 Sensitivity analysisSimilar to the overdamped case (section 533) repeat slugtests were found to produce negligible transmissivity vari-ations (Table 3) Both borehole (rBH) and filter (rF) radii havean impact of up to approximately one order of magnitude ontransmissivity estimates transmissivity being inversely re-lated to rF and the storage coefficient (S) Reducing the latterfrom 1010ndash4 to 10 10ndash7 approximately doubled thetransmissivity estimate while the Kipp inertial parameter(K) and thus transmissivity (Equation (6d)) could not becalculated for S lt 10ndash4 (Table 3) This agrees with previous

conclusions based on application of the Guyonnet methodto the overdamped slug-test responses (section 534) andtherefore confirms that the subglacial storage coefficient isunlikely to be larger than this value

We conclude that the sediments below the base of BH 9516 have a transmissivity of (47 40)10ndash3m2 sndash1 and thatthe subglacial storage coefficient (S) in our study area isprobably of the order of 10ndash4 or smaller

6 SYNTHESIS OF SUBGLACIAL HYDRAULICCONDITIONSThe estimates of transmissivity for the five boreholesconsidered in the present study are synthesized in Figure 10together with inferred ranges of uncertainty Transmissivitieswithin the area of the 1993 VPA (boreholes 9469 9475951 and 9516) are enhanced compared to BH 9514which was located outside the VPA This distribution ofsubglacial transmissivity supports the inferences of Hubbardand others (1995) who postulated that systematic flushing offines is likely to decrease the water-flow resistance of thesubglacial sediments located within the VPA compared tothose located outside it (section 31)

Previous field studies reported the ability of subglacialsediments to transmit water in terms of hydraulic conduct-ivity (K ) more often than transmissivity (T ) (Table 5)Transmissivities obtained for boreholes 951 9516 and9514 were therefore converted to hydraulic conductivitiesusing Harbor and othersrsquo (1997) sediment thickness datacollected in the 1995 melt season (we do not have sedimentthickness estimates for boreholes 9469 and 9475) These

Fig 9 Application of the Kipp method matching of prepared fielddata (black circles) with the Kipp type curve for frac14 15 W0 isinitial WL displacement

Fig 10 Subglacial drainage conditions transverse to ice-flowdirection as inferred from slug tests The location of the VPA in1993 (see text) is also shown

Table 5 Approximate hydraulic conductivities (K ) of glacial till and unconsolidated subglacial sediments Freeze and Cherry (1979) did notspecify methods of investigation

Glaciermaterial Hydraulic conductivity Source Method

m sndash1

Gornergletscher Switzerland 210ndash2 Iken and others (1996) Slug testsBakaninbreen Svalbard (8279) 10ndash3 Kulessa and Murray (2003) Slug testsmidre Lovenbreen Svalbard (1905) 10ndash5 Kulessa and Murray (2003) Slug testsStorglaciaren Sweden 10ndash8ndash10ndash9 Fischer and others (1998) Ploughmeter measurementsTrapridge Glacier Canada 510ndash4 Stone and others (1997) Connection-drainage testsSouth Cascade Glacier WA USA 10ndash4ndash10ndash7 Fountain (1994) WL variationsGlacial till 10ndash6ndash10ndash12 Freeze and Cherry (1979) ndash


authors found that sediment thickness near the location ofBH 951 is close to the lower end of the inferred range(01m) and increases to values of 026m near BH 9514Table 6 summarizes the hydraulic conductivities (K ) forthese three boreholes using an uncertainty range of( 005m for the estimates of sediment thickness Hydraulicconductivity decreases by more than an order of magnitudefrom gt110ndash2m sndash1 within the VPA (BH 951 BH 9516) to0110ndash2m sndash1 outside the VPA (BH 9514) These valuesfall within the range for clean sand according to Freeze andCherry (1979 p 29) although overlap with other materialranges suggests the presence of gravelly sand within theVPA and silty sand outside it Nonetheless it must becautioned that slug tests are only successful in hydraulicallywell-connected boreholes and by their very nature thereforesample only particularly transmissive areas of the glacierbed (eg Stone and others 1997 Kulessa and Murray 2003)It is therefore not possible to estimate the hydraulicconductivities of unconnected less transmissive regions ofthe glacier bed using slug tests

7 CONCLUSIONSUsing slug-test data collected in boreholes drilled throughHaut Glacier drsquoArolla we have demonstrated that hydraulicproperties of unconsolidated subglacial sediments can beestimated using conventional linear models that have beenpopular in groundwater studies for some time Such modelsare more readily applied to such data than the interpretationtechniques previously developed for hydro-glacial investiga-tions We initially demonstrated that slug tests are unlikely toinduce turbulent flow in the coupled boreholendashaquifer flowsystem which confirms earlier findings by Stone and Clarke(1993) and Stone and others (1997) We subsequently usedthe Van der Kamp (1985) Kipp (1985) and CooperndashBredehoeft (Cooper and others 1967) methods to determinesubglacial hydraulic properties from underdamped criticallydamped and overdamped slug-test responses Sensitivityanalyses reveal that the repeatability of slug tests and thecurve-fitting procedures involved in the three methods areless likely to generate significant errors in hydraulic esti-mates than geometrical and hydrological parameter uncer-tainties in the coupled boreholendashsubglacial flow system Thisis particularly true for borehole radius and aquifer storagecoefficient in the Van der Kamp case borehole radius in theCooperndashBredehoeft case and most notably filter radius inthe Kipp case We have further demonstrated that additionalapplication of the Guyonnet method (Guyonnet and others1993) which exploits systematic deviations between meas-ured responses and CooperndashBredehoeft type curves is wellsuited to estimating the distance from tested boreholes tosubglacial flow boundaries The accuracy of the distanceestimates was found to be 3m being strongly sensitive touncertainties in the aquifer storage coefficient It is note-worthy that Freeze and Cherry (1979 p 60) argue that thestorage coefficient for confined aquifers generally rangesbetween 5 10ndash3 and 5 10ndash5 which is a much smallerrange than that used here for error estimation (10ndash2ndash10ndash7)We prefer to use the latter since these values were inferredfrom in situ borehole measurements at warm-based glaciers(Iken and others 1996 Porter and Murray 2001) althoughthe error estimates for the Van der Kamp and Guyonnetcases decrease noticeably if the smaller Freeze and Cherry(1979) range is considered

The key findings of this study regarding the subglacialhydraulic system at Haut Glacier drsquoArolla are that thehydraulic conductivity of the unconsolidated subglacialsediments decreases from 1ndash3 10ndash2m sndash1 (gravelly sand)near a subglacial channel to 01 10ndash2m sndash1 (silty sand)70m from it and that inferred subglacial flow boundariescoincide with the subglacial channel The storage coefficientof the subglacial sediments is probably of the order of 10ndash4

or smaller

ACKNOWLEDGEMENTSThis work was funded by a University of Wales Post-graduate Studentship which is gratefully acknowledgedThanks to the numerous assistants who helped drill theboreholes and conduct the slug tests in the field We alsothank J Walder G Flowers and an anonymous refereefor their detailed comments on earlier versions of themanuscript

REFERENCESBredehoeft JD HH Cooper Jr and IS Papadopulos 1966

Inertial and storage effects in wellndashaquifer systems an analoginvestigation Water Resour Res 2(4) 697ndash707

Butler JJ Jr 1997 The design performance and analysis of slugtests Boca Raton FL Lewis Publishers

Butler JJ Jr CD McElwee and W Liu 1996 Improving thequality of parameter estimates obtained from slug tests GroundWater 34(3) 480ndash490

Cooper HH Jr JD Bredehoeft IS Papadopulos andRR Bennett 1965 The response of wellndashaquifer systems toseismic waves J Geophys Res 70(16) 3915ndash3926

Cooper HH Jr JD Bredehoeft and IS Papadopulos 1967Response of a finite-diameter well to an instantaneous charge ofwater Water Resour Res 3(1) 263ndash269

Copland L J Harbor and M Sharp 1997 Borehole videoobservation of englacial and basal ice conditions in a temperatevalley glacier Ann Glaciol 24 277ndash282

Fetter C 2001 Applied hydrogeology Englewood Cliffs NJPrentice Hall

Fischer UH NR Iverson B Hanson RLeB Hooke andP Jansson 1998 Estimation of hydraulic properties of sub-glacial till from ploughmeter measurements J Glaciol 44(148)517ndash522

Fountain AG 1994 Borehole water-level variations and impli-cations for the subglacial hydraulics of South Cascade GlacierWashington State USA J Glaciol 40 293ndash304

Freeze RA and JA Cherry 1979 Groundwater Englewood CliffsNJ Prentice Hall

Table 6 Approximate range of hydraulic conductivity (K ) in theeastern section of the survey area depending on best estimates ofsediment thickness (bSL) beneath BH 951 BH 9516 and BH 9514

BoreholeNo

EastingSwiss grid

Sedimentthickness

Hydraulicconductivity

m msndash1

951 6067874 01 (1105) 10ndash2

9516 6068126 015 (3127) 10ndash2

9514 6068572 gt025 0110ndash2

Error range is less than one decimal place


Gordon S M Sharp B Hubbard C Smart B Ketterling andI Willis 1998 Seasonal reorganization of subglacial drainageinferred from measurements in boreholes Hydrol Process12(1) 105ndash133

Guyonnet D S Mishra and J McCord 1993 Evaluating thevolume of porous medium investigated during slug tests GroundWater 31(4) 627ndash633

Harbor J M Sharp L Copland B Hubbard P Nienow andD Mair 1997 The influence of subglacial drainage conditionson the velocity distribution within a glacier cross sectionGeology (Boulder) 25(8) 739ndash742

Hubbard B and P Nienow 1997 Alpine subglacial hydrologyQuat Sci Rev 16(9) 939ndash955

Hubbard BP MJ Sharp IC Willis MK Nielsen and CC Smart1995 Borehole water-level variations and the structure of thesubglacial hydrological system of Haut Glacier drsquoArolla ValaisSwitzerland J Glaciol 41(139) 572ndash583

Iken A K Fabri and M Funk 1996 Water storage and subglacialdrainage conditions inferred from borehole measurements onGornergletscher Valais Switzerland J Glaciol 42(141)233ndash248

Kabala ZJ GF Pinder and PCD Milly 1985 Analysis ofwellndashaquifer response to a slug test Water Resour Res 21(9)1433ndash1436

Karasaki K JCS Long and PA Witherspoon 1988 Analyticalmodels of slug tests Water Resour Res 24(1) 115ndash126

Kipp KL Jr 1985 Type curve analysis of inertial effects in theresponse of a well to a slug test Water Resour Res 21(9)1397ndash1408

Krauss I 1974 Die Bestimmung der Transmissivitat von Grund-wasserleitern aus dem Einschwingverhalten des Brunnen-Grundwasserleitersystems J Geophys 40 381ndash400

Kruseman GP and NA de Ridder 1991 Analysis and evaluationof pumping test data Wageningen International Institute forLand Reclamation and Improvement

Kulessa B and B Hubbard 1997 Interpretation of boreholeimpulse tests at Haut Glacier drsquoArolla Switzerland AnnGlaciol 24 397ndash402

Kulessa B and T Murray 2003 Slug-test derived differences in bedhydraulic properties between a surge-type and non-surge-typeSvalbard glacier Ann Glaciol 36 103ndash109

Kulessa B B Hubbard and GH Brown 2003 Cross-coupled flow modeling of coincident streaming and electro-chemical potentials J Geophys Res 108(B 23818) (1010292001JB001167)

McElwee CD 2001 Application of a nonlinear slug test modelGround Water 39(5) 737ndash744

McElwee CD and MA Zenner 1998 A nonlinear model foranalysis of slug-test data Water Resour Res 34(1) 55ndash66

Moench AF and PA Hsieh 1985 Analysis of slug test data in awell with finite-thickness skin In Memoirs of the 17th Inter-national Congress on the Hydrogeology of Rocks of LowPermeability Tucson AZ International Association of Hydrol-ogy 17ndash29

Murray T and GKC Clarke 1995 Black-box modeling of the sub-glacial water system J Geophys Res 100(B7) 10231ndash10245

Papadopulos IS JD Bredehoeft and HH Cooper Jr 1973On the analysis of slug test data Water Resour Res 9(4)1087ndash1089

Porter PR and T Murray 2001 Mechanical and hydraulicproperties of till beneath Bakaninbreen Svalbard J Glaciol47(157) 167ndash175

Richards KS and 9 others 1996 An integrated approach tomodelling hydrology and water quality in glacierized catch-ments Hydrol Process 10 479ndash508

Sageev A 1986 Slug test analysis Water Resour Res 22(8)1323ndash1333

Sharp M and 6 others 1993 Geometry bed topography anddrainage system structure of the Haut Glacier drsquoArolla Switzer-land Earth Surf Process Landforms 18(6) 557ndash571

Smart CC 1996 Statistical evaluation of glacier boreholes asindicators of basal drainage systems Hydrol Process 10599ndash613

Stone DB and GKC Clarke 1993 Estimation of subglacialhydraulic properties from induced changes in basal waterpressure a theoretical framework for borehole-response testsJ Glaciol 39(132) 327ndash340

Stone DB GKC Clarke and RG Ellis 1997 Inversion ofborehole-response test data for estimation of subglacial hy-draulic properties J Glaciol 43(143) 103ndash113

Van der Kamp G 1976 Determining aquifer transmissivity bymeans of well response tests the underdamped case WaterResour Res 12(1) 71ndash77

Williamson M 2003 The investigation and application of fullynon-linear as compared to linear slug test models as a techniquefor estimating subglacial hydraulic properties (MPhil thesisUniversity of Cambridge)

Wylie A and S Magnuson 1995 Spreadsheet modeling of slugtests using the Van der Kamp method Ground Water 33(2)326ndash329

MS received 26 September 2004 and accepted in revised form 1 May 2005


subsequent WL recovery (eg Kruseman and de Ridder1994) The characteristics of the recovery signal serve asindicators of subsurface hydraulic conditions and can beanalyzed for hydraulic properties of the boreholendashaquifersystem At Haut Glacier drsquoArolla Valais Switzerlandunconsolidated water-saturated sediments of varying thick-ness have temperate ice as an upper boundary and bedrockas a lower boundary (eg Hubbard and others 1995Harbor and others 1997) This situation compares well withthat of a conventional confined aquifer (eg Fetter 2001)The underlying assumptions of this analysis are that theborehole is hydraulically well connected to the aquiferimplying that a change in aquifer hydraulic head willinstantaneously result in an equivalent change in boreholeWL and that there is negligible lateral or vertical leakageinto the aquifer Such fluctuating boreholes (Smart 1996)are commonly characterized by a noticeable WL dropwhen the glacier bed is reached during drilling as well asby marked daily WL variations In contrast unconnectedboreholes are typically water-filled and non-fluctuating(Smart 1996)

Three distinct types of slug-test response may beexpected chiefly depending on borehole water-columnlength and aquifer transmissivity which together determinethe degree of water-column inertial effects The latter arenegligible in the overdamped case (exponential non-oscillating decay) and significant in the underdamped case(exponential oscillating decay) with critical dampingrepresenting the transitional response (Bredehoeft andothers 1966) A coupled boreholendashaquifer flow system oflow transmissivity and small water-column length is likely toproduce an overdamped response while an underdampedresponse may be expected if transmissivity is high and water-column length is large (Bredehoeft and others 1966) In theoverdamped case water-flow rates in the boreholendashaquifersystem are commonly small enough for turbulent effects tobe neglected supporting the use of linear slug-test modelsSuch models are analytically attractive involving manualmatching of observed responses with type curves in thesimplest case and have been widely used in groundwaterstudies for several decades (Butler 1997) In contrast in theunderdamped case water-flow rates could in some in-stances be so large that turbulence occurs requiring the useof non-linear models

Previously a unified model allowing for any degree ofdamping of slug-test responses was developed specificallyfor application in glaciology (Stone and Clarke 1993 Stoneand others 1997) Application to borehole response testsconducted at Trapridge Glacier Yukon Territory Canadatogether with extensive sensitivity analyses revealed thatnon-linear effects in the entire boreholendashsubglacial-aquiferflow system were not of concern during slug tests Motivated

by this conclusion the present study aims to investigate theuse of established linear slug-test models in estimatingsubglacial hydraulic properties This would allow rapidinterpretation of slug tests using either simple manualanalysis or widely available lsquolinearrsquo software packagesincreasing the appeal of this technique in hydro-glacialinvestigations

We initially ascertain that non-linear effects are notprevalent in our data The bulk of this study then aims (i) todemonstrate the application of a range of linear slug-testmodels that have been particularly popular in groundwaterstudies (Cooper and others 1967 Van der Kamp 1976Kipp 1985 Guyonnet and others 1993) to our data and(ii) to estimate the hydraulic properties of the subglacialsediments at the glacier along a transect traversing a majorsubglacial channel

2 SLUG-TEST METHODS21 Boreholendashsubglacial-aquifer flow systemMany different slug-test models have been developed ingroundwater studies each focusing on a particular physicalscenario defined by the properties of the well and the aquifer(eg Butler 1997) Choosing the right model for theparticular physical scenario to be investigated is importantto obtain reliable estimates of hydraulic properties Theconceptual geometry of the boreholendashsubglacial flow systemconsidered here is illustrated in Figure 1 A borehole ofradius rBH is connected to the subglacial aquifer of thicknessbSL via a fully penetrating filter of radius rF The water level isinitially displaced by an amount H0 due to slug insertionand subsequently gradually returns (H(t)) to the equilibriumWL (solid line in Fig 1) The filter accounts for subglacialexcavations due to sediment flushing and clogging in thevicinity of the borehole base as the hot-water drill reachesthe glacier bed (eg Stone and Clarke 1993) It thereforerepresents an annulus of larger hydraulic conductivity thanthe outlying subglacial aquifer The term borehole face isused to describe the cylindrical interface between the filterand the aquifer and ice and bedrock bounding the boreholewater column and the aquifer are assumed to be im-permeable (Fig 1) The rate of slug-induced water flow inthe subglacial aquifer is strongly dependent on its transmis-sivity (T given by hydraulic conductivity (K ) aquiferthickness (bSL)) which may therefore be estimated fromappropriate analysis of recovery curve characteristicsParticularly suitable and popular linear slug-test models forthe present physical scenario are the CooperndashBredehoeft(Cooper and others 1967) Van der Kamp (1976) and Kipp(1985) methods (eg Butler 1997) which are adapted hereto analyze overdamped underdamped and criticallydamped responses respectively

As considered in section 1 the models for the analysis ofslug-test responses are applicable to either low-transmissiv-ity or high-transmissivity aquifers Linear models may beused in either case if turbulence in the boreholendashaquiferflow system is negligible If slug-induced turbulence is notnegligible as observed previously in some high-transmis-sivity aquifers (eg Butler 1997 McElwee and Zenner1998) non-linear models must be used Since theseapproaches are well established and covered in thepertinent groundwater literature (eg Butler 1997) wepresent only a brief summary here focusing on relevantmodel characteristics

Fig 1 Boreholendashsubglacial flow system geometry



2hr2A

thorn 1rA

hrA

frac14 STht

eth1THORN



2rFTh rF teth THORN

rfrac14 r2BH

dH teth THORNdt

eth2THORN


H teth THORNH0


frac14 Ttr2BH

eth3bTHORN

frac14 r2F Sr2BH

eth3cTHORN







Le thornwg

d2wdt2

thorn Ag

dwdt

2

thorn Fgdwdt






a frac14 r2BHg8Le

eth5bTHORN


r eth5cTHORN


eth5dTHORN





p eth6aTHORN

K frac14 r2BH2r2F S

eth6bTHORN


ffiffiffiffiffiffiK

p eth6cTHORN

K frac14 Leg

Tr2F S

2

eth6dTHORN





9469 7 942319475 5 94231951 4 952229514 4 952309516 4 95224












5 INTERPRETATION

















ndash 00180 281 34 122

rF (m) 025+ 015ndash 02

184 117 82 50

S 00001+ 00099ndash 00000999

243 51 109 18

























ndash 01S 00001+00099




BH 951 BH 9514

Dmin Dmax Dmin Dmax

m m m m

tD 45 55 6 7T 425 7 5 8rBH

72 49 68 63Ssect 145 007 145 01














m sndash1






or smaller














BoreholeNo

EastingSwiss grid

Sedimentthickness


m msndash1

951 6067874 01 (1105) 10ndash2

9516 6068126 015 (3127) 10ndash2

9514 6068572 gt025 0110ndash2



































2hr2A

thorn 1rA

hrA

frac14 STht

eth1THORN



2rFTh rF teth THORN

rfrac14 r2BH

dH teth THORNdt

eth2THORN


H teth THORNH0


frac14 Ttr2BH

eth3bTHORN

frac14 r2F Sr2BH

eth3cTHORN







Le thornwg

d2wdt2

thorn Ag

dwdt

2

thorn Fgdwdt






a frac14 r2BHg8Le

eth5bTHORN


r eth5cTHORN


eth5dTHORN





p eth6aTHORN

K frac14 r2BH2r2F S

eth6bTHORN


ffiffiffiffiffiffiK

p eth6cTHORN

K frac14 Leg

Tr2F S

2

eth6dTHORN





9469 7 942319475 5 94231951 4 952229514 4 952309516 4 95224












5 INTERPRETATION

















ndash 00180 281 34 122

rF (m) 025+ 015ndash 02

184 117 82 50

S 00001+ 00099ndash 00000999

243 51 109 18

























ndash 01S 00001+00099




BH 951 BH 9514

Dmin Dmax Dmin Dmax

m m m m

tD 45 55 6 7T 425 7 5 8rBH

72 49 68 63Ssect 145 007 145 01














m sndash1






or smaller














BoreholeNo

EastingSwiss grid

Sedimentthickness


m msndash1

951 6067874 01 (1105) 10ndash2

9516 6068126 015 (3127) 10ndash2

9514 6068572 gt025 0110ndash2




































a frac14 r2BHg8Le

eth5bTHORN


r eth5cTHORN


eth5dTHORN





p eth6aTHORN

K frac14 r2BH2r2F S

eth6bTHORN


ffiffiffiffiffiffiK

p eth6cTHORN

K frac14 Leg

Tr2F S

2

eth6dTHORN





9469 7 942319475 5 94231951 4 952229514 4 952309516 4 95224












5 INTERPRETATION

















ndash 00180 281 34 122

rF (m) 025+ 015ndash 02

184 117 82 50

S 00001+ 00099ndash 00000999

243 51 109 18

























ndash 01S 00001+00099




BH 951 BH 9514

Dmin Dmax Dmin Dmax

m m m m

tD 45 55 6 7T 425 7 5 8rBH

72 49 68 63Ssect 145 007 145 01














m sndash1






or smaller














BoreholeNo

EastingSwiss grid

Sedimentthickness


m msndash1

951 6067874 01 (1105) 10ndash2

9516 6068126 015 (3127) 10ndash2

9514 6068572 gt025 0110ndash2












































5 INTERPRETATION

















ndash 00180 281 34 122

rF (m) 025+ 015ndash 02

184 117 82 50

S 00001+ 00099ndash 00000999

243 51 109 18

























ndash 01S 00001+00099




BH 951 BH 9514

Dmin Dmax Dmin Dmax

m m m m

tD 45 55 6 7T 425 7 5 8rBH

72 49 68 63Ssect 145 007 145 01














m sndash1






or smaller














BoreholeNo

EastingSwiss grid

Sedimentthickness


m msndash1

951 6067874 01 (1105) 10ndash2

9516 6068126 015 (3127) 10ndash2

9514 6068572 gt025 0110ndash2



































5 INTERPRETATION

















ndash 00180 281 34 122

rF (m) 025+ 015ndash 02

184 117 82 50

S 00001+ 00099ndash 00000999

243 51 109 18

























ndash 01S 00001+00099




BH 951 BH 9514

Dmin Dmax Dmin Dmax

m m m m

tD 45 55 6 7T 425 7 5 8rBH

72 49 68 63Ssect 145 007 145 01














m sndash1






or smaller














BoreholeNo

EastingSwiss grid

Sedimentthickness


m msndash1

951 6067874 01 (1105) 10ndash2

9516 6068126 015 (3127) 10ndash2

9514 6068572 gt025 0110ndash2










































ndash 00180 281 34 122

rF (m) 025+ 015ndash 02

184 117 82 50

S 00001+ 00099ndash 00000999

243 51 109 18

























ndash 01S 00001+00099




BH 951 BH 9514

Dmin Dmax Dmin Dmax

m m m m

tD 45 55 6 7T 425 7 5 8rBH

72 49 68 63Ssect 145 007 145 01














m sndash1






or smaller














BoreholeNo

EastingSwiss grid

Sedimentthickness


m msndash1

951 6067874 01 (1105) 10ndash2

9516 6068126 015 (3127) 10ndash2

9514 6068572 gt025 0110ndash2






















































ndash 01S 00001+00099




BH 951 BH 9514

Dmin Dmax Dmin Dmax

m m m m

tD 45 55 6 7T 425 7 5 8rBH

72 49 68 63Ssect 145 007 145 01














m sndash1






or smaller














BoreholeNo

EastingSwiss grid

Sedimentthickness


m msndash1

951 6067874 01 (1105) 10ndash2

9516 6068126 015 (3127) 10ndash2

9514 6068572 gt025 0110ndash2














































ndash 01S 00001+00099




BH 951 BH 9514

Dmin Dmax Dmin Dmax

m m m m

tD 45 55 6 7T 425 7 5 8rBH

72 49 68 63Ssect 145 007 145 01














m sndash1






or smaller














BoreholeNo

EastingSwiss grid

Sedimentthickness


m msndash1

951 6067874 01 (1105) 10ndash2

9516 6068126 015 (3127) 10ndash2

9514 6068572 gt025 0110ndash2













































m sndash1






or smaller














BoreholeNo

EastingSwiss grid

Sedimentthickness


m msndash1

951 6067874 01 (1105) 10ndash2

9516 6068126 015 (3127) 10ndash2

9514 6068572 gt025 0110ndash2





































or smaller














BoreholeNo

EastingSwiss grid

Sedimentthickness


m msndash1

951 6067874 01 (1105) 10ndash2

9516 6068126 015 (3127) 10ndash2

9514 6068572 gt025 0110ndash2

































































Documents

Hydrogeological analysis of slug tests in glacier boreholes