Journal of Glaciology , Vol. 49, No.166, 2003
Meltwatercirculation and permeability ofArctic summer sea ice derived fromh ydrological field experiments
Johannes FREITAG,1 Hajo EICKEN2 1AlfredWegener Institute for Polar and Marine Research, P.O.Box 120161,D-27515 Bremerhaven, Germany E-mail: [email protected] 2Geophysical Institute,University of Alaska Fairbanks,P.O.Box 757320,903 Koyukuk Drive,Fairbanks,Alaska 99775-7320,U.S.A.
ABSTRACT.Permeabilityand meltwater flowhave been studied insea ice inthe Siberianand central Arctic duringthe summers of1 995and 1 996.A bail-test technique hasbeenadapted to allow for measurements ofin situ permeability,foundto range between 10^11 and 10^8 m2.Permeabilityvaried by about a factorof 2between1 995 (above-normalmelt rates) and1996(below-normal melt rates).Release offluorescent tra- cers (fluorescein,rhodamine) furthermore allowedthe derivationof flowvelocities and assessment ofthe relevantdriving forces. Hydraulicgradients in rough ice andwind stress inpondedice werefound to be particularlyimportant, driving meltwater overdistances ofseveralmeters per day.Themid- tolate-summer ice wasfound to be permeableenough tocompletely divert meltwater fromthe surface intothe ice interior.Itis shown,however , that lowerpermeabilities ofthe upperice layersas wellas refreezing ofmeltwater,par- ticularlyduring the earlymelt season,foster the developmentof surface melt ponds.
INTRODUCTION others, 2002)).Thepermeability also affects the transport ofparticulateand dissolved matter throughthe ice,which Seaice inthe Arctic regionsis affectedby extensive melting influencesnutrient supplyto biological sea-ice communities duringsummer .Theice coveris reducedfrom about (Cotaand others, 1987;Hudier andIngram, 1994). 6 2 6 2 15610 km inMarch toabout 7 610 km atthe endof sum- While theimportance of permeabilityhas beenidentified mer (Parkinsonand others, 1987).Thereduction of ice cover- in studiesof oil pollution (Wolfeand Hoult, 1974; Martin, ageand total ice volumetakes place through a combination 1979)and saltfluxes in new ice(Cox and Weeks,1 975; Eide ofsurface, bottom and lateral melt. Maykutand Perovich and Martin, 1975; Ono and Kasai, 1985; Wettlauferand (1987)estimated that the fractionof surfacemelting accounts others,1997),actualmeasurements of intrinsicsea-ice perme- forup to 50% of the wholemelted volume,with the other ability areonly available fromKasai and Ono (1984)and twoprocesses contributing25% each. The extent ofsurface Saeki and others( 1986).Both studied artificialyoung ice melt exhibitsa strongmeridional gradient in the Arctic grown in asmall tank, thus not taking into accountthe time Ocean.R ussiandrift-station datashow an increase ofsurface evolution of secondarypore space, which iscrucialin deter- ablationfrom 50.2 m ice a^1 inthe centralArctic toup to mining thepermeability of thickerice. F urthermorethe 1.0 m a^1 overthe Siberianshelf seas (Romanov,1993). strongtemperature gradients in thethin icelead toa strong Theextent ofsurficialmelt dependson the totalsurface verticalheterogeneity of permeabilityand induce phase ablation,the permeabilityof the underlyingice layersand changeswith brine percolatingthrough theice (Kasai and the forces drivingvertical and horizontal advection of melt- Ono, 1984).Golden and others( 1998)found thatyoung sea water.Of these processes the former hasbeen studied in icedisplays thesame critical behavior characteristicof aper- detailduring numerous field campaigns (U ntersteiner,1961; colationtransition, as it is known, forcompressed powders of Hanson,1 965;Langleben, 1 969;Makshtas and Podgorny , largepolymer particles. However ,theanalogy in porestruc- 1996),butthe latter twohave received little ornoattention. tureis restrictedto the brine layersof columnar seaice, ignor- Theappearance and persistence ofsurfacemelt puddles,for ing thedevelopment of drainage structuresduring aging. example,depends strongly on the amountof meltwater While insitu measurements ofpermeabilityare a stan- percolatingdownwards (controlled by permeability) and dardtechnique in hydrogeology (F reeze andCherry ,1979), the horizontalexchange between the low-albedopuddle verylittle hasbeen done to apply this approachto sea ice. andthe surroundingwhite ice. Thepermeability and Theonly study of whichwe are aware is the workby Milne meltwater fluxescontrol the temporalevolution of ice andothers (1977)who recorded the floodingof blindholes albedoduring the course ofthe melt season(Maykut, 1986; drilledat three sites onmulti-yearice floes.They tested the Morassutti andLeDrew ,1995).Atypicalsequence consists applicabilityof the Darcyformula, but did not derive actual ofan initial retainment ofmeltwater ina shallowlayer of permeabilities. Our approachwas to apply a single-holebail vastexpanse at the ice surface andwithin the remaining test, determiningthe non-stationaryreadjustment ofthe snowlayer (lowering of albedo) ,followedby drainage and water/brinelevel in the boreholewith a highspatial and lateralshrinkage of these extendedmelt puddles(increase temporalresolution. Apart from assessing the permeability, inalbedo (F etterer andU ntersteiner,1998;Eicken and it willbe shownthat the transitionpoint between turbulent 349 Freitag and Eicken: Meltwater circulation and permeability of Arctic sea ice andlaminar inflow can be utilizedto derive a characteristic identifiedwith the aidof the dimensionless Reynoldsnum- porescale controlling the macroscopicpermeability . ber Re,expressingthe ratioof inertial to viscous forces: Tracer studies ofmeltwater fluxesare a standard U2r» Re 2 techniquein glacier hydraulics (Behrens andothers, 1983; ˆ ² … † Gaspar,1987;Ka « ss,1992).Insea-ice research, dyeshave been witha characteristic flowvelocity U (m s^1),the dynamic employedto visualize small-scale exchangeprocesses viscosity ² (kg m^1 s^1)anda characteristic poredimension (Bennington,1967;Eideand Martin, 1975).Experiments on r (m) such asthe meanpore or tube radius.In a tube,the ascaleof squaremeters directed towardsquantification of critical Reynoldsnumber forthe transitionbetween meltwater andbrine fluxes have not been carried out to a laminarand turbulent flowhas been measured to Re largeextent, however.Theexchange of nutrients, inparticu- c ˆ 2300(Schlichting, 1 982).Forporous media with a complex larin the bottomice layers,has been quantified in several porestructure, the transitionis gradualand occurs forcrit- ice biologicalstudies (Cotaand others, 1987;Arrigoand icalReynolds numbers of1^1 0(Bear,1972).Inthe case of others, 1993;Hudier andIngram, 1 994).Ina pilotstudy , turbulence andeven for more dominantinertial forces, the Weissenberger (1994)employeda photometrictechnique to specific dischargeis nolonger a linearfunction of the determine lateralbrine and meltwater migrationin Arctic imposedpressure gradient,but decreases relativeto laminar seaice. Thestudy demonstrated the needfor refined flow.Conceptsfor the descriptionof turbulent flowthrough samplingtechniques andincreased sensitivity .Inthis study, porousmedia are reviewed in Marsily ( 1986). experiments devotedto the quantificationof lateral melt- Thepore space of seaice consists ofprimaryand second- waterfluxes on summer Arctic seaice havebeen carried arypores. Primary pores areformed as brinepockets at the oututilizing fluorescent tracers andnewly developed ice^waterinterface duringfreezing .Itisafinenetwork of samplingtechniques. mainlylayered structure withcharacteristic poresizes of Theoverall aim of this contributionis toprovide permea- 0.1mm orless. Duringice aging,and due to brine drainage, bilitydata of naturalsummer Arctic seaice, obtainedduring afractionof the primarypore space is transformed toa set twoship expeditions in 1 995and 1 996,toestimate the con- ofverticallyoriented tubular drainage structures attended straints onvertical brine and meltwater percolationthrough bysmaller ,radiallyorientated tributary tubes (Weeks and the ice matrix.F urthermore afirst tracer-based datasetof lat- Ackley,1986).Thesesecondary pores, being 0. 1toa fewmm eralsurface meltwater fluxesis presented toassess the larger- insize, aretherefore much largerand could determine the scalepermeability and driving forces .Thismay also allow for permeabilityof the wholepore space. In the limit ofonly acritical reappraisalof the assumptionunderlying previous onevertically oriented tube-like pore within an ice cylinder studies ofArctic ice growthand ablation, namely that the flux of radius R,the poreradius r andthe permeability k of ofmeltwater andenergy through sea ice canbe consideredas max the ice cylinderare related by aone-dimensionalproblem ,ignoringlateral advection and exchange,and is notcontrolled by the hydraulicpermeability r p4 8R2k : 3 max ˆ … † ofthe ice cover.Thelatter problemhas been addressed in Assuminglaminar flow ,the meanvelocity can be expressed more detailin a follow-upstudy as part of the SurfaceHeat byHagen^Poiseuille’ slaw.Themeanvelocity is set toequal Budgetof the Arctic Ocean(SHEBA) study (Eicken and the specific dischargederived from Darcy’ slawmultiplied others, 2002). bythe ratioof cross-sectional areasbetween the ice cylinder andthe poretube. Equation ( 3)is determined byseparating HYDROLOGICAL BACKGROUND the poreradius. In bail tests (discussed below) rmax is used asaroughestimate ofanupperlimit ofporesize. Forthese Themigration of fluidsthrough a porousmedium depends calculations, R isthe radiusof the ice cylinderbeneath the onits permeability.Thepermeability of aporousmedium is blindholes. definedin the empiricallaw of Darcy,that describes the lin- Duringsummer ,brineand meltwater motionin the sea- earrelationship between discharge and driving force, when ice system canbe driven by external imposed pressure afluidis forcedthrough the pores ofaporousmedium: gradientsor by internal density variations. At free melt- k watersurfaces, airflowinduces a lateralpressure gradient. u p 1 Atthe bottomand the side facesof ice floes,the internal ˆ ² r … † poresystem is incontact with the openwater and therefore ^1 withspecific discharge u (m s ),imposedeffective pressure sensitive toocean currents. Gravitationalforces acton melt- ^3 2 gradient p (N m ),permeability k (m )anddynamic waterthat is formedon ice surfaces abovesea level. Any rise r ^1 ^1 viscosity ² (kg m s ).Thepermeability is apropertyof the ordepressionof anice floe,assuming a newisostatic equilib- porousmedium whichallows advection of fluid through the rium, canalso induce an imposed hydraulic head. connectedpathways along their geometry.Forthe simple geometryof a tube the permeabilityis proportionalto the cross-section areaof the tube.The specific dischargeis the AREAOFINVESTIGA TION volumetricflux through a verticallyoriented cross-section areaincluding solid and void faces. In the case ofexclusively Thehydrological field experiments werecarried out during gravitationalforces, the imposedpressure gradientcan be twoexpeditions in successive summer seasons inthe north- expressed bythe hydraulicgradient »g¢H=¢L in the ern LaptevSea and central Arctic (Fig.1).Duringthe joint directionof the mainfluid flow ,withdensity » (kg m^3), Russian^GermanAR CTIC95expedition of R V Polarstern gravitationalacceleration g (m s^2),andwater-level differ- inJ uly^September1 995,almost the entire studyperiod was ence ¢H (m) betweentwo selected observationpoints and characterizedby typical summer conditionsof meltingfirst- their lateraldistance ¢L (m).Theapplicability of Darcy’ s yearice withmelt-puddle coverageof 30^50%. During the lawis limited tothe case oflaminarflow .Thelimit is usually expeditionAR CTIC96with the Swedishicebreaker Oden 350 Freitag and Eicken: Meltwatercirculation and permeability of Arctic sea ice
Fig.2.(a)Experimental set-up of an insitu bail test. (b)A time series of the hydraulic head recorded within the borehole. The measurements are represented by open circles;the dashed line is an exponential fit to the data inthe laminar branch of the curve.
Fig.1.Mapof the site locations during the expeditions in1995 twodifferent flowregimes duringone measurement. At and 1996. The position of abuoy deployed in 1995 and highhydraulic heads when the inflowinto the blindhole resampled in 1996 is also indicated. starts andthe localflow velocities are at their maximum, the fluidmigration through the porespace is dominatedby inAugust and September 1996,the experimentalsites were inertialforces orcouldeven be turbulent. Duringthe ensu- locatedmore tothe north.Different ice conditionsin 1 996 inginflow ,the hydraulichead and the specific dischargeare ledto greatly reduced surface ablation,with melt-puddle continuouslydecreasing .Thepronounced discontinuities in the curves suggesttransitions betweenturbulent and coverage 51%and a substantialsnow cover remaining throughoutthe summer (Haasand Eicken, 200 1).Most of laminarflow .Inthe laminarflow regime, the hydraulic headshows an exponential decay ,graduallysubsiding to the ice sampledwas second- ormulti-year;with the aidof a buoydeployed in 1 995,afirst-year ice fieldstudied during zero.Assuming Darcy’ slaw(Equation ( 1))forthe laminar branchrequires that the specific discharge( dh=dt) is ARCTIC95was resampled in1 996. ˆ proportionalto the drivingforce, here expressed bythe hydraulichead h t .Assumingfurthermore exclusivelyver- … † INSITU PERMEABILITY MEASUREMENTS ticallyoriented pores such that inflowonly affects the ice volumedirectly underneath the boreholecross-section, the Method recoverycurve is givenas k g»t h t h t e¡ exp ²L 4 Thepermeability has been derived from bail tests onblind … † ˆ … 0† … † holes,drilled at different spots withinthe sea-ice cover.Ina withhydraulic head h t (m),permeability k (m2) and … † exp bailtest, the adjustment ofthe water-levelhorizon to equi- ice thickness L (m) underneaththe borehole.The data are libriumis analyzed.Such bail tests arewidely used inhydro- welldescribed byan exponentialfunction. The exponent of geology(Dullien, 1979;F reeze andCherry ,1979)andhave the fitted functionwould thus providea valuefor a vertical beenadapted for sea-ice conditions.Figure 2a shows a permeabilityunder the assumptionthat seaice is laterally sketch ofthe experimentalset-up. Theblind holes with a impermeable.Laboratory experiments indicate,however , fixeddiameter of9 1mm andvariable length were sealed that the ice hasa non-zerolateral permeability (F reitag, lengthwiseby an aluminum tu be,which effectively sealed the 1999).On average,permeability is oneorder of magnitude perimeter ofthe corehole. Thewater level was measured with lowerin the horizontalthan in the verticaldirection. Totake anultrasonicsensor mountedon topof the tube witha reso- the lateralpermeability into account, we derived a correc- lution of 0.5mm andamaximumsampling rate of20Hz. tionfunction from numerical simulations. The three- § Priorto every measurement, waterwas removed with a dimensionalsimulations were carried out using the soft- valvebail to induce flow into the sealedhole. At the endof ware Modflow,whichis basedon a finite-differences ap- eachmeasurement, the totalice thickness andthe fractionof proachof fluidmotion in porousmedia (Kinzelbach, 1995). ice underthe blindhole were measured bydrilling . Figure3a^c illustrate the modeledshift ofthe equipotential Figure2b displaysa typicaltime series ofthe hydraulic pressure lines byvarying the ratio kl=kv oflateral to vertical head h t .Thehydraulic head describes the difference in permeability.Theregime ofinflow under the blindhole … † heightbetween the actualwater-level horizon and the becomes widerwith increasing kl=kv.Forall ratios the equilibriumsea-water level. In general, the hydraulichead exponentialform of the simulated recoverycurves is pre- decreases ina step-like fashionfollowed by an exponential served.The simulation runs weredone with k =k 0 l v ! decay.Figures2b and6 show h t curves witha singletrans- (onlyvertically permeable) , k =k 0.01,0.1and1(isotropic … † l v ˆ itionpoint in the range0.05^0 .10m. Thisbehavior identifies medium).Thepermeability k exp derivedfrom the recovery 351 Freitag and Eicken: Meltwater circulation and permeability of Arctic sea ice
Fig.3.Model calculations of the pressure field during abail test for three different ratios between lateral permeability kl and vertical permeability kv.In avertical cross-section the initialisobars are plotted for constant intervals.(a)The Fig.5.Relationship between the derived correction factor ® and simulation with laterally impermeable ice;(b)the case for a icethickness Lunderneath theborehole. ® dependslinearly on L ratio of kl/kv=0.1;and(c)the isotropic case with kl = kv. with rising slopes for increasing kl/kv ratio which reflects the enhanced inflow due to lateral permeability. curveof ameasurement basedon Equation ( 4)corresponds tothe case of kl=kv =0andhas to be convertedinto the more chargeremains constantand tends toincrease towardsboth realistic case of k =k 0.1(Freitag,1999).Tothis end,a cor- boundaries.Different totalice thicknesses donot change the l v ˆ rection factor ® isintroduced. ® is definedas the ratioof the dischargelevel, but separatethe boundaryeffects. However, dischargethrough a laterallypermeable medium andthe it is evidentthat for increasing ratio kl=kv the discharge dischargethrough a laterallyimpermeable medium, increases aswell.F rom the modelresults it isestablished that assumingequal values for vertical permeability ,imposed ® dependslinearly on the ice thickness underthe blindhole hydraulicheads and geometrical dimensions: withrising slopes forincreasing ratios kl=kv (Fig.5).Thelin- uexp earityis limited toblind holes in the interior ofthe ice col- ® : 5 umn,at least 20cm awayfrom either boundary,whichis ˆ uv … † fulfilledfor 95% of the drilledholes. U nderthese restrictions ® is independentof the absolutevalue of vertical permeabil- ® L canexpressed by … † ityand imposed hydraulic head, but depends on geometric 1 ® L 0:3 3:5 m¡ L with k =k 0:01; parameters. FollowingDarcy’ slaw(Equation ( 1))inthe case 0:01… † ˆ ‡ l v ˆ 1 ofexclusivevertical permeability ,the dischargeis inversely ® L 0:17 10:7 m¡ L with k =k 0:1; 0:1… † ˆ ‡ l v ˆ proportionalto the ice thickness L underneaththe blind 1 ®1 L 0:15 32:4 m¡ L with kl=kv 1 hole.As shownin Figure 4, this negativecorrelation breaks … † ˆ ‡ ˆ downin the case ofadditional lateral permeability ,whichis andthe ice thickness L (m).Overall,the verticalpermeabil- expectedbecause increasing L leadsto increasing lateral ity kv ofsea ice is derivedfrom measurements usingEquation (4)forthe laminarbranch of h t to estimate k followedby fluxes.Except near the ice surfaceand bottom, the totaldis- … † exp acorrectionwith ® L that yields 0:1… † k k exp : 6 v ˆ 0:17 10:7 m 1L … † ‡ ¡ Theexpanded measurements ofinflow not only in the laminarflow regime butalso for the inertialand turbulent flowregimes providefurther informationabout the pore structure ofsea ice. F ora homogeneousporous medium witha highlytortuous and connected pore structure, the transitionbetween different flowregimes isveryweak and notdetectable ina h t curve.In contrast, the h t curves of … † … † seaice showsharp transitions. Most probablythe transitions takeplace in the largetubes ofthe secondarypores. This implies that the flowthrough the fewsuch largepores dominatesthe wholedischarge, since otherwisethe trans- itionsignal would not be apparent in the h t curves. It … † seems that the verticalpermeability of seaice iscontrolled bysecondary pores, with the consequencethat fluidmigra- tionis mainlyrestricted tosuch pores atleast duringthe Fig.4.Relationship between discharge and ice thickness L summer period.T oconfirmthe explanationof the discon- underneath the borehole in asimulated bail-test geometry. tinuities inthe h t curves, weestimate the radiusof a verti- … † The model runs are performed in ice with kl/kv =1(isotropic), callyoriented tube assumingthat the hydraulichead hcrit at 0.1,0.01and 0(laterally impermeable).The hydraulic head is the discontinuitycorresponds to the critical valuefor the kept constant.The total ice thickness is 1,2and 4m. transitionto turbulent flow.Theflow field is described by 352 Freitag and Eicken: Meltwatercirculation and permeability of Arctic sea ice
Fig.6.Time series of the hydraulic head measured repeatedly at the same blind hole.
Hagen^Poiseuille’slaw.Themean velocity at the transition Fig.7.(a)F requency distributions of in situ permeabilities canbe expressed bythe critical Reynoldsnumber .Thenthe measured during the expedition in summer 1995 (solidline) , tube radius r is given as 1996 (dotted line)and for artificial sea ice measured by Saeki and others (1986)in the laboratory (dashed line).(b)The fate 2 3 4² L Recrit of meltwater illustrated in across-section through an ice floe. r 2 : 7 ˆ s»ghcrit … † Depending on permeability,the meltwater either percolates downwards and disappearsfrom the ice surface (k 4kcrit) or Theposition of the discontinuityin the measured h t curve … † is partially retained at the ice surface (k 5kcrit). determines the hydraulichead hcrit.If multiple discontinu- ities occur,then that correspondingto the lowesthydraulic headis chosenfor hcrit.Thephenomenon of multiple trans- meabilities mostlyoriginate from the specificationof the itionsis the result ofatemporaryincrease ofthe Reynolds ratiobetween lateral and vertical permeability .Thegeo- number after atransitionfrom turbulent tolaminar flow metric meanof permeabilitydecreases byapproximately a dueto large velocities in the case oflaminar flow .Inthe factorof 0.3whenthe ratio k =k 0.1is replacedby 1 (case l v ˆ vicinity of Recrit andlarge hydraulic heads, Re can shift ofisotropy).Incomparison, uncertainties dueto the meas- severaltimes fromvalues above and below Recrit. Here, a urement process andthe exponentialfit (6%) arenegligible. critical Reynoldsnumber of2300 is assumed basedon meas- Inprinciple, the bail-test methodis limited tothe ice below urements inundisturbed pipe flow (Schlichting, 1982). freeboardand yields integrated values of vertical permea- Thepermeability is verysensitive tochanges in pore bilities. space.A changeof oneorder of magnitude in the radiiof a verticalbundle of tubes wouldchange the permeabilityby 4 Results orders ofmagnitude (Equation ( 3)).However,the pore spaceof seaice dependson temperature andbrine salinity . At24 stations 122measurements werecarried out in 46 dif- Forexample, drainage networks formed during the melt ferent boreholes.The hole depths rangedbetween 0. 6and periodsignificantly change the characterof the porespace. 1.70m inice oftotal thickness 0.8^5.25m. Thelower Bailtests takethe characteristic sea-ice features intoaccount branchesof the recoverycurves arevery well described by andavoid pore-space changes in sofar as fluidwith slightly exponentialfits, witha weaksystematic deviationdue to different temperature andsalinity is onlyflowing through transitions tolaminar flow .Thetotal error ofthe exponent pores duringthe measurement itself. Repeated measure- isestimated as6%becauseof the uncertaintyin identifying ments atthe same boreholeshow the permeabilitychanges the upperlimit ofthe fit interval,which represents the limit causedby the measurement itself (Fig.6).Therate ofin- ofthe fullydeveloped laminar flow regime. At29 boreholes crease inwater level grew with every measurement. The (63%)the recoverycurves indicatea cleartransition derivedpermeability increases byroughly 7% per measure- betweenturbulent andlaminarinflow . ment cycle.This increase iscausedby the inflowof warm, Thevertical permeabilities ofsummer Arctic seaice more salinewater .Sucheffects aremonitored for each derivedfrom the recoverycurves arein the range1 0 ^11^ location,and consequently the extrapolatedpermeabilities 10^7 m2,withgeometrical means of8 610^10 m2 (1995) and forthe limitingcase ofunchanged pores havebeen reduced 4610^10 m2 (1996)(Fig.7).Thevertical permeabilities repre- by2^1 0%dependingon the measured wideningeffect. sent integralvalues of the lowerentire section ofthe ice cover. Thebail tests samplean ice volumeon a scaleof cubic Meanand modal permeabilities differby one order of mag- meters andare thus more affectedby heterogeneities than nitudebetween measurements in1 995and 1996.These dif- arelaboratory measurements. Nevertheless, the effective ferences areexplained by the differences inice ageand, in pore-channelvalues derived from the transitionpoints refer particular,the highlycontrasting thermal regimes witha onlyto the ice volumeclose to the blindhole, where the inflow climatologicaldecrease inablation to the north(Romanov , velocityhas its maximum.U ncertainties inthe derivedper- 1993)and an unusually cold melt seasonin 1 996(Haas and 353 Freitag and Eicken: Meltwater circulation and permeability of Arctic sea ice
Fig.8.Pore-channel radii derived from flow-regime transi- tions inthe measured time series vs permeability.Data of the 1995 expedition are shown as open circles,data for 1996 as open squares.For comparison,the maximum accessible tube radius is plotted asadotted line based on Equation (2).
Eicken,200 1).Theice permeabilities arecomparable to those ofsand and karst systems (Freeze andCherry ,1979). Inthese systems, subsurfacedrainage systems similar to those inseaice arecreated dueto the karstificationprocess. Thereusually exists acontinuouspath made up of larger pores towhich most ofthe flowis confined(David, 1993). Fig.9.Tracer site R11219/220 in deformed ice withconcentra- Thehydraulic similarity of seaice tokarst systems sug- tion profilesalong four transects (T1,T2,T3,T4).Thegraphs gests that the ``critical path’’ofthese pores determines the show the profiles 3hours (solid circles) and16 hours (open permeabilityof Arctic seaice insummer . circles) after dye injection. Gray areas are melt ponds. Comparedto measurements onartificial sea ice attem - peratures of^5to^20³ C bySaeki and others (1986),permea- bilities ofsummer Arctic seaice areat least twoto three samplepositions, a lateralpermeability can be calculated orders ofmagnitude larger .Suchcomparatively high per- basedon Darcy’ slaw(Equation ( 1)). meabilityis explainedby the evolutionand widening of the Thetracer hasto be non-reactive in the seaice, such that secondarypore-channel system inArctic seaice, mostlyas a the adsorptiononto the ice matrixand the photochemically result ofbrinedrainage and internal melting processes. The induceddecay is negligibleduring the measurement interval. cleartransition from turbulent tolaminar flow in the bore- Forour tracer studies, the fluorescent dyesfluorescein (F) holeexperiments suggests that the permeabilityof ice is andsulforhodamine B (S)werechosen as tracers (Gaspar, controlledby individual large tubes orchannels.F orthose 1987; Ka« ss, 1992).Fluoresceinwith a lowtendency to adsorb sets ofmeasurements exhibitinga distinct transitionpoint ontoice surfaces anda lowdetection limit onthe orderof inthe recoverycurve, a tube radiushas been calculated 10^6 mg L^1 is suitablefor short-term measurements with basedon Equation ( 7)(Fig .8).Thetube radiiare in the time-scales 5 1day.Forlong-term experiments sulforhoda- range r 0.5^2.5mm andcorrespond to the upperlimit mine Bisused, becauseof its insensitivityto light decay in e ˆ ofpore-channel sizes reported byother authors (Martin, comparisonwith fluorescein. However ,the detection and 1979;W akatsuchiand Saito, 1985).However,the correlation the adsorptionlimit ofsulforhodamine B are2 orders of betweenpermeability and tube radiusis notdefinite. Higher magnitudehigher than those offluorescein. Ka « ss (1992) permeabilities donot always imply higher tube radii. givesan overviewof further physicalcharacteristics. Thedye concentration was determined byfluorometric analysisat excitation wavelengths of 491nm(F),565nm (S), TRACERSTUDIES correspondingto the emission maximumat 5 12nm (F), Method 590nm (S).Theintensity ofthe fluorescencesignal depends linearlyon the dyeconcentration over 6 (F)and4 (S)orders With the aidof non-reactive dye tracers, fluidflow through ofmagnitude. The different excitationand emission wave- the ice canbe directlyrecorded. In the tracer experiments, lengthsof fluorescein and sulforhodamine B allowedsimul- the dyehas been injected intothe waterof boreholes or melt taneoususe ofboth tracers. Thefluorometric analysis is pondson the ice floe,measuring the dispersionof fluid at specific fora substance andinsensitive topollution. Because different samplepositions around the injectionpoint. The ofthe temperature dependence,all fluorescence measure- progressionof the peakin dye concentration allows an ments werecarried out at the same temperature of1 0³C in estimate ofthe averagespecific discharge.If the driving the laboratoryon board the research vessel. forces areknown, such asthe hydraulichead between two Anexperimentalsite consisted ofanarrayof blindholes 354 Freitag and Eicken: Meltwatercirculation and permeability of Arctic sea ice
conditions,the decayof fluoresceinis uncertainand its term inthe mass-balanceequation has an error of30%. The accuracycan be increased when both tracers, fluorescein andsulforhodamine B, are used simultaneously.Inthe pres- ent configuration,the tracer test methodis limited tolateral flow,since the concentrationvalues are integrated over the entire depthof the borehole.
Results
Experiments in deformed ice with ahigh hydraulic gradient asmain driving force Ina rubblefield at station R 11219/220(Fig .9),amelt pond (as acenter location)was colored by fluorescein. The water levelof the pondwas 0.50 m a.s.l.The mean depth at the start ofthe experiment was0. 15m, decreasingto 0. 10m 16hourslater .Thesample positions are located in a segment of120³in the slopingsector ofthe pondvicinity .Themean depthof the holeswas 0.82 0.05m, withthe waterlevel at § 0.45 0.06 m. § Inthe directions ofall transects, the markedmeltwater migratedinto the surroundingice (Fig.9).Thedye concentrationin the ponddecreased andlocal concentra- tionmaxima built up within the ice.After 16hours,a con- centrationpeak had moved into the ice byabout 1 m. Assuminga two-dimensional,divergent radial flow with a pondradius of 1 .0m, the frontvelocity at r 2.0mbecomes ^5 ^1 ^1 ˆ u 1.3610 m s ( 0.05 m h ).With the measured hy- Fig.10.Tracer site R11220/221 in deformed ice with concentra- f ˆ ˆ draulicgradient of 0.5, the derivedlateral permeability is tion profilesalong threetransects (T1,T2,T3).Thegraphsshow k 1.3610^12 m2 usingDarcy’ slawin polar coordinates. the profiles 9.5 hours (solidcircles) ,16 hours (open circles) and l ˆ Toestimate the effectiveice-layer thickness through 22 hours(crosses) afterdye injection. Grayareas are melt ponds. whichthe meltwater is flowing,the mass balanceof the dye,spreading into the ice fromthe pond,must besolved. Themass budgethas at least twoterms, the term ofretained (¿ 0.05m, drilledto 40.5mbelowsea level) for water ˆ dye,diluted by water inflow into the pond,and the outflow samplingduring the measurements (Figs9 and1 0).Drilling portionof dyewithin the porespace of ice. Due tothe light orice coringimmediately prior to sampling or after dye sensitivity offluorescein, a third decayterm is added.F or injectionis problematicfor small-scale studies, since the simplificationand due to the lackof information about the removalof asubstantialice volumeinduces non-negligible rate changesunder different lightconditions, the same decay fluidflow that maythwart the actualmeasurement. constantis assumed forthe dyein the pondand within the ice Thereforethe injectionof dyesinto the center holeor melt matrix.Thus, the mass balanceis expressed by: pondwas delayed for 30 min untilthe waterlevels in the holeshad reached equilibrium. About 200 mg of dye dis- V C V t C t n ~x C x; t dV po po ˆ p… † p… † ‡ i… † i… † solvedin 50 mL meltwater wasmixed with the waterof the … ice… … 8a center hole.After injection,5^1 0mL ofwater was drawn … † V C C e¶t every6 hoursfrom the samplinglocations. Dye concentra- ‡ po… po ¡ po † tions weredetermined onboardthe research vessel witha withdye concentration C (mg L^1),watervolume V (m3), HITACHIF2000 fluorometer directly after sampling. ice porosity n anddecay constant ¶ (s^1).Theindices iand Unlikebail tests, tracer studies takethe drivingforces pindicateice andpond water values, and the indexo refers intoaccount, allowing quantitative estimates oflateral spe- tothe initialvalues. Assuming a cylindricalpond geometry cificdischarge and permeability .Tracer spreadingdue to andan equaldivision of the surroundingice intoan inflow moleculardiffusion is inthe rangeof centimeters per day andan outflow area in accordance with the localtopog- andis therefore negligible.The observed dispersion is thus raphy,the mass-balanceequation ( 8a)canbe written as: causedentirely by the motionof the fluid.Heterogeneities A d C e¶t A d t C t po po po ˆ p p… † p… † ofthe permeabilitydue to large channels, cracks or other º r discontinuities enlargethe dispersion.In such cases, amean 1 8b nd C r; ’; t r dr d’ … † frontvelocity cannot be estimated (Fig.10,transects 1and2 ). ‡ i i… † … … Themass balancefor the migrationaround melt pondscan 0 rp 2 besolvedif allheterogeneities areincluded. Because of the withpond surface area Ap (m ), depth dp (m), radius rp (m) simple deploymentof samplelocations, their densitycan be andeffective ice-layer thickness di (m).Thedecay constant increased,however ,totake those effects intoaccount. The hasbeen determined as ¶ 3.2610^5 s^1 byF reitag( 1999) ˆ largestuncertainty consists inthe quantitativespecification forfluorescein under comparable light conditions using a la- ofthe relevantdriving forces (e.g.the momentum transfer boratorysunshine simulator.Theporosity of the upperice bysurface winds).Furthermore, dueto the variablelight layeris estimated as n 0.2based on a densitymeasure- ˆ 355 Freitag and Eicken: Meltwater circulation and permeability of Arctic sea ice
Fig.11.Concentration profiles along wind direction at tracer Fig.12.Concentration profiles at tracer site R11247 inlevel site R11216 in level ice.The graph shows the initialconcentra- ice.The graph shows profiles along two transects intersecting tion (solid circles) and the profile 9hours (open circles) after at right angles for the initialconcentration (dotted line),and dye injection. the profiles 4hours (solid circles) and14 hours (open circles) after dye injection. ment (» 752 kg m^3).Usingthe concentrationvalues ˆ measured after 16hours(Fig. 9 )andthe pondparameters Thesample boreholes were drilled to 1 mdepth.During the (r 1.0 m, d 0.15 m, d (16 h) 0.10m) the mass- p ˆ po ˆ p ˆ 9hourexperiment the windspeed wasmeasured atinter- balanceequation ( 8b)gives the effectiveice-layer thickness valsof 1 0min ata heightof 1 0m. Themean velocity was ^1 di 0.17m.Theice-layerthickness hasthe same magnitude u 11.5 1.6 m s ,andthe directionvaried by 54³. ˆ ˆ § asthe pond,indicating that the meltwater flowis confined Themarked pond water migrated into the surrounding tothe surface layers. ice, forminga plumeoriented parallel to transect 1.Thisdir- The time td neededto discharge the initialpond volume ectioncoincides with the mainwind direction (Fig .11). isthe quotientof that pondvolume to the meanvolume flux. Duringthe 9hours,the maximumdye concentration Thevolume flux is givenas the productof lateraldischarge movedlaterally into the ice by1 .4m, yieldinga specific dis- u nu multipliedby the outflowarea A ºr d : ^5 ^1 ˆ f ˆ p p charge of u 4.3610 m s .Thewind stress affects the 2 ˆ ºrpdp rp watercirculation in the pondand induces a mainflux down- td : 9 wind.However ,ashort legof the plumealso extended into ˆ nufºrpdp ˆ nuf … † the ice againstthe mainwind direction (Fig .11). td isestimated tobe 53hours. Thus, after 16hoursapproxi- matelyone-third of the pondwater would have been ex- Experiments in level ice without wind stress andlarge-scale hydraulic changed.In the same time period,a loweringof the water gradients levelin the pondby one-third was observed. The missing AtstationR 11247,experiments wereconducted in level ice volumecorresponds to the expectedoutflowing volume. 4100mawayfrom the ice-floeedge. Instead of a melt pond, Thereforeit canbe assumed that there wasno inflow during dyewas mixed into the waterin a holeat the center ofthe the observationperiod, which is alsosupported by the change samplingarray .Theboreholes were 0. 61and0 .69m deep. ofthe fluorescencesignal. I twasapproximately reduced by Thesampling positions were arranged crosswise aroundthe anamount expected for the decaydue to radiation. Com- center hole.During the measurements, the meanwind speed paredto the enhanceddecay in the pondarea due to direct was 5.2 0.5 m s^1 andnever exceeded 6 ms ^1.Ice freeboard § exposure,the fluorescencesignal of pore water within the was0. 33m, such that windstress most likelydid not affect ice matrixremains ata higherlevel. Consequently ,the max- meltwater flow.Becauseof the veryflat topography ,it is imum ofthe fluorescencesignal is foundwithin the ice and assumed that nolarge-scale hydraulic head was imposed. notwithin the ponditself (Fig.9). Inall boreholes separated 50.65m fromthe center hole, Ina further experiment ata melt pondin deformed ice, lowconcentrations of dye were detected (Fig.12).Themeas- the dispersioncurves showa strongheterogeneity of the lat- uredconcentrations were 4 orders ofmagnitudelower than eralpermeabilities ofthe surroundingice (Fig.10). the initialconcentrations. N odirectionaltrend isapparent Transect 3is locatedin ice oflow permeability with an fromthe data.The maximum concentration remained at the upperlimit for k of 2.3610^13 m2 anda frontvelocity below ^1 center points.Thedecrease is exponentialrather thanlinear . uf 0.020 m h .Thehighly permeable zone of transect 2 ˆ ^12 2 ^1 Ingeneral, the concentrationdecreased withdistance to a hasa lowerlimit for k of 9.0610 m and u 0.15 m h . f ˆ center hole.However ,three samplepositions show higher Themelt fluxthrough the ice oftransect1amountsto a front ^1 values14hoursafter t 0sthanpositions closer tothe center. velocity uf1 0.071m h at1 .50m distanceand uf2 ˆ ^1 ˆ ˆ Thisindicates that lateralfluid motion on the orderof 0.069 m h at2 .0m derivedfrom different time-steps. The ^1 ^12 2 0.2 m h is possible,but the motionis restricted tolocal dis- meanlateral permeability is determined as4.3 610 m . continuities(e.g .throughsecondary large pores or cracks). Experiments inlevel ice under wind stress Atstation R 11216the waterof amelt pondin level ice was DISCUSSION coloredwith fluorescein. The small pondcovered an area ofapproximately1 m 2 andhad an average depth of 0.08m. Basedon the measurements anddata presented above,we can 356 Freitag and Eicken: Meltwatercirculation and permeability of Arctic sea ice estimate the rates ofvertical meltwater percolationthrough Anotherimportant aspect that affects the mass and the ice cover.Thus,a critical permeability kcrit canbe deter- energybalance is the lateralmobility of the liquidphase in minedwhich separates the regime ofmeltwater retention and the upperice layers.This is supportedby the results ofthe poolingat the ice surfacefrom that allowing for complete tracer studies inthe vicinityof melt ponds.Qualitatively , downwarddrainage of melt (see Fig.7bfor illustration of fluidmotion covering 450 m d^1 wasobserved at some kcrit).Basedon climatological data (R omanov,1993),wehave locations.In deformed ice andridged areas the probability assumed amelt-season durationof 7 7dayswith a totalsurface ofencounteringconduits is considerablyhigher than in level melt of0. 53m (waterequivalent, snow and ice) ,yieldinga ice, resulting inlinkage and meltwater exchangebetween meanablation rate of6. 9mm d ^1.ForDarcian flow ,this ponds.The direction of lateral movement is controlledby results ina critical permeabilityof k 1.5610^13 m2. If the formationof highly permeable zones, resulting ina crit ˆ weallow for periods of enhancedsurface melt withablation hydrologicalheterogeneity .Anexampleof such heterogen- rates higherby a factorof 10, k 1.5610^12 m2. All meas- eityis givenin Figure1 0,with Figure 9 showinga contrast- crit ˆ urements presented here exceedthese valuesof kcrit, sug- ing,homogeneous permeable floe portion. Due tothe lower gestingthat inmid- tolate summer the sea-ice coveris albedo,the waterin the melt pondabsorbs more radiation permeableenough to completely drain the meltwater pro- thanthe surroundingice andwarms up to temperatures ducedat the surface.Thisraises the questionas towhat allows abovethe freezingpoint. The heat transported bythe lateral the formationof melt ponds(in particular those withwater flowcan be roughly calculated for the experiment atstation levelabove the equilibriumsurface) inthe first place.While R11219/220.Basedon measurements duringthe cruise, the lateralinflow of meltwater isofimportance,it wouldrequire temperature differencebetween meltwater andice is inflowareas larger by a factorof 100^1000than the pondarea assumed tobe dT 0.5K(Zachekand Darovskikh, 1 997). ^9 2 ˆ ^1 toexplain these numbers forpermeabilities of1 0 m . With With aspecific dischargeof u 0.06 m h the lateralheat ˆ ^2 pondscovering 41%ofthe surfacearea, this isanunrealis- fluxis calculatedto be F c»A dTu 10.6 W m which lat ˆ ˆ tic assumption.Rather ,it appearsthat the permeabilityin is approximatelyone-third of the net absorbedradiation in the upperice layers(for which we have few or no data) , Augustover 1 m 2 (c:specific heatcapacity; A:outflowarea) andin particular during the earlier melt season,is critical (Maykut,1 986).Sucha small-scale, positiveice-albedo feed- inallowing surface retention ofmelt. Thishas been inde- backmechanism maythus further acceleratethe melting pendentlyverified in a studyby Eicken and others (2002) process, asstudied inmore detailby Eicken and others (2002). carriedout over the entire durationof amelt seasonin first- andmulti-year ice inthe NorthAmerican Arctic. CONCLUSIONS Here, wecan still assess towhat extent the desalination andconcurrent reductions in ice porosity,akeyparameter Duringmid- tolate summer ,the hydrologicalproperties of incontrolling permeability ,contributeto a potentiallower- Arctic seaice arecomparable to a geologicalkarst system ingof permeabilityin the upperand interior ice layers.This (Fig.7).Thepore space with associated permeabilities ashigh includesrefreezing of surface waterdraining into the lower as 10^7 m2 acts asapotentialpathway for meltwater andcon- ice layers,which is dependenton the temperature difference trols the drainageand the amountof meltwater retainedat betweenmeltwater andthe surroundingice andthe resi- the ice surface.T racer studies demonstrated that the waterin dencetime ata givendepth level. F orrapid dissipation of melt pondsis inexchange with the porewater of the surround- meltwater inhighly permeable ice, onewould not expect to ingice. As driving forces, the hydraulicgradients in ridged see muchrefreezing due to reduced heat exchange between areasand wind stress havebeen identified. The mobility of meltwater andice matrix.Assuming an ice thickness of1 .0m meltwater hasimportant consequences, outlined below . witha meanporosity of 0.1anda hydraulichead of 0.1m, we obtainmean residence times withinthe ice ofbetween 2 s I.Theextent ofsurface meltingand hence the albedo,the emissivity andthe backscattercoefficient at microwave and5 hforthe rangeof permeabilities measured. Thetime- frequencies areaffected by meltwater migration.The scalefor heat transfer canbe roughly estimated byconsider- ingthe simplified case oflaminar flow in verticaltubes .For influenceon albedocan act in both directions. Vertical millimeter-sized tube radiithe freezingof the liquidphase meltwater percolationleads to an increase ofalbedo, takesplace in seconds wheninitial temperature differences becausethe liquidvolume above freeboard is reduced. Thelateral migration of meltwater inthe vicinityof of2^4³ C andzero-salinity meltwater areassumed. This melt pondsreduces the albedo,with the additionallat- implies that atleast inthe earlystage of melting ,whensur- facesnow is meltingabove a coldice layer,the meltwater eralheat flux increasing pond cross-sectional areas.In tends tofreeze atthe snow^iceinterface, resulting inthe for- general,such fluidmotion may be part of a positive mationof ice orice plugswithin pores of the upperice layers, feedbackmechanism. Highpermeabilities enhance effectivelysealing the ice surface.Such layers of superim- meltwater fluxesand transport ofsensible heat,thus leadingto increased internal melting, which in turn posedice havebeen observed in earlier studies (Cherepanov, 1973)aswell as inrecent tracer andpermeability experiments increases permeability.Presently it is notfully under- (Eickenand others, 2002).Subsequently,onlycomplete melt- stood,however ,towhat extent meltwater advection ingof such impermeablelayers would allow vertical trans- results inreduced permeabilities orthe sealingof parts of portof meltwater .Consideringthe highpermeabilities of the ice coverthrough ice formationinduced by double- diffusionprocesses (e.g.inthe case ofunder-ice meltponds the underlyingice, the boundaryconditions in the upper (Eicken,1994)). partof the ice areparticularly important in limiting vertical percolationduring summer melt.Theformation of superim- II.Meltwater migrationthrough sea ice is dominatedby posedice andother impermeable layersis controlledby the the dischargethrough individual large pore channels, temperature evolutionand the salinityof the meltwater, asisindicatedby the inflowmeasurements duringthe dependingin particular on the snowdepth. bailtests. Thisimplies that potentialfreezing or 357 Freitag and Eicken: Meltwater circulation and permeability of Arctic sea ice
thawingacts ina heterogeneousmanner ,resulting ina Eicken,H., H.R. Krouse, D .Kadkoand D .K.Perovich. 2002. Tracerstudies changeof pore-spacesize distributions insea ice. Con- ofpathways and rates of meltwater transport through Arctic summer sea ice. J.Geophys. Res. , 107(C10),8046.( 10.1029/2000JC000583.) tinuousmeltwater flowforms highlypermeable zones Eide, L. I.and S. Martin.1975.The formationof brine drainagefeatures in throughpositive feedback processes andthus enhances youngsea ice. J. Glaciol., 14(70),137^154. heterogeneity.Sealingof pores throughrefreezing melt- Fetterer,F.andN. U ntersteiner.1998.Observations of meltponds on Arctic waterand widening of larger pores alsoenhances the sea ice. J.Geophys.Res. , 103(C11),24,821^24,835. Freeze,R. A. andJ. A. Cherry, eds.1979. Groundwater. EnglewoodCliffs, NJ, heterogeneityin pore sizes. 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