Drainage from waterfilled crevasses along the margins of ...d284f45nftegze.cloudfront.net/dlampkin/...2013_Saturated_Crevasse… · of saturated crevasses reached its maximum extent,

Drainage from water-filled crevasses along the marginsof Jakobshavn Isbræ: A potential catalyst for catchment expansion

D. J. Lampkin,1,2 N. Amador,1 B. R. Parizek,3 K. Farness,4 and K. Jezek4

Received 24 May 2012; revised 13 January 2013; accepted 29 January 2013.

[1] Saturated crevasses occur in local depressions within the shear margins of JakobshavnIsbræ at inflections in the ice stream’s flow direction. Spatio-temporal variability of sevendistinctive saturated crevasse groups was examined during the 2007 melt season. The areaof saturated crevasses reached its maximum extent, ~1.8 km2, in early July, and remainedlargely constant until early August. Filling rates are correlated with regional melt production,while drainage rates are highly correlated with areal extent. Estimates on potential drainagevolume from the largest crevasse system are ~9.23� 10�3 km3� 2.15� 10�8 km3

and ~ 4.92� 10�2 km3� 3.58� 10�8 km3, respectively, over a 16 day interval and aremore than required for a distributed basal hydrologic system across this area totemporarily flood bedrock obstacles believed to control basal sliding. Future drainageevents, likely extending farther inland with warming, could result in enhanced lateralmass discharge into the ice stream, with implications for the dynamic evolution of theentire basin.

Citation: Lampkin, D. J., N. Amador, B. R. Parizek, K. Farness and K. Jezek (2013), Drainage from water-filledcrevasses along the margins of Jakobshavn Isbræ: A potential catalyst for catchment expansion, J. Geophys. Res. EarthSurf., 118, doi:10.1002/jgrf.20039.

1. Introduction

1.1. Motivation and Prior Work

[2] The Greenland Ice Sheet (GIS) has recently experiencedthinning along its margins accompanied by increaseddischarge and a large acceleration in flow speed [Krabillet al., 2004; Joughin et al., 2004; Alley et al., 2005a,2005b; Hanna et al., 2008; Rignot et al., 2008]. Recentestimates indicate a doubling of mass contribution to sea levelfrom the GIS over the past decade, where mass discharge hasincreased from 0.23� 0.08 mm/yr between 1993 and 2003 to0.59� 0.10 mm/yr between 2000 and 2011 [Shepherd et al.,2012]. The majority of the GIS mass loss is due to changesin the dynamics of a few large ice streams [Rignot andKanagaratnam, 2006; Stearns andHamilton, 2007, Figure 7b;Zwally et al., 2011]. Jakobshavn Isbræ drains approximately6% of the GIS surface area, is the fastest ice stream inGreenland [Bindschadler, 1984; Echelmeyer et al., 1991],

and has perhaps undergone the most severe changes in thepast decade, with flow velocities roughly doubling fromapproximately 5.7 km a�1 to upwards of 12 km a�1 [Joughinet al., 2004]. Holland et al. [2008] suggest that these recentchanges on Jakobshavn were initiated by the incursion ofrelatively warm waters from the Irminger Sea into the deepfjord of this ice stream. As the authors point out, such anincursion would result in an increase in basal melting alongJakobshavn Isbræ’s floating ice tongue, likely contributingto the eventual breakup of the ice tongue and the concomitantloss of buttressing of outlet-glacier flow.[3] Coincident with observed changes in flow dynamics

on Jakobshavn, there has been an increase in surface meltalong the margins of the GIS, specifically over the last coupledecades, where GIS has exhibited a 30% increase in meltwater runoff from the ablation zone, extension of the meltseason by an average of 10 days and total runoff contributing15% to observed global sea level rise [Zwally et al., 2002;Box et al., 2004; Box et al., 2006]. Surface melt along theice-sheet margin collects in topographic depressions on theice sheet, forming supraglacial melt lakes [Lüthje et al.,2006; Box and Ski, 2007]. Several efforts have been madeto evaluate the spatial and temporal distribution of these lakesalong the GIS ablation zone [Bryzgis and Box, 2005; Lüthjeet al., 2006; Box and Ski, 2007;McMillan et al., 2007; Sneedand Hamilton, 2007; Sundal et al., 2009; Lampkin, 2011;Lampkin and VanderBerg, 2011], with some lakes observedto be as large as 10 km2 [Box and Ski, 2007]. Episodicdrainage of these lakes to the bed occurs through moulins,conduits that penetrate the entire ice thickness. This process,involving hydro-fracture and the Walder instability, has beenobserved and theoretically established [Walder, 1986; Das

1Institute of Arctic and Alpine Research, University of Colorado,Boulder, Colorado, USA.

2Department of Geoscience, College of Earth and Mineral Sciences,Pennsylvania State University, University Park, Pennsylvania, USA.

3Mathematics and Geosciences, Pennsylvania State University, DuBois,DuBois, Pennsylvania, USA.

4Byrd Polar Research Center, The Ohio State University, Columbus,Ohio, USA.

Corresponding author: D. J. Lampkin, Department of Geoscience,College of Earth and Mineral Sciences, Pennsylvania State University,University Park, PA 16802, USA. ([email protected])

©2013. American Geophysical Union. All Rights Reserved.2169-9003/13/10.1002/jgrf.20039

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JOURNAL OF GEOPHYSICAL RESEARCH: EARTH SURFACE, VOL. 118, 1–19, doi:10.1002/jgrf.20039, 2013

et al., 2008; Alley et al., 2005a, 2005b; van der Veen, 2007].Such drainage events cause local uplift, acceleration, andsubsidence [Boon and Sharp, 2003; Fountain et al., 2005;Das et al., 2008]. Several studies have addressed delivery ofsurface melt water to the bedrock through moulins and lakedrainage through propagation of water-filled cracks due tohydrofracture through modeling and observations and haveidentified three primary factors that drive the hydrofractureprocess: (1) the influence of tensile and compressive normalstresses that open or close crevasses, (2) crevasse closuredue to ice overburden pressure, and (3) crevasse opening dueto water pressure and heat transfer due to turbulent flow orlatent heat from freezing of melt water within the crack[Weertman, 1973; van der Veen, 1998; Scambos et al., 2000;Alley et al., 2005a, 2005b; van der Veen, 2007; Das et al.,2008; Krawczynski et al., 2009; Tsai and Rice, 2010]. Specif-ically, Das et al. [2008] observed all of these characteristicfeatures within a 24 h period in western Greenland duringrapid drainage (<2 h) of a large surface lake. Krawczynskiet al. [2009] determine that supraglacial lake sizes that rangebetween 0.25 and 0.8 km diameters contain sufficient waterto hydro-fracture through sub-freezing ice approximately1.5 km thick, thus signifying the importance of collectedsurface water to overall ice-sheet hydrology and mass loss.Furthermore, these drainage events are responsible for trans-ferring large volumes of water to the base of the ice sheetwhere it can alter ice-sheet dynamics [Zwally et al., 2002;Parizek and Alley, 2004; Bartholomew et al., 2010].[4] Little work has been done to explore the potential

impact that infiltrated melt water could have on JakobshavnIsbræ’s mass flux, though data suggest it is not responding toenhanced seasonal melt [Echelmeyer and Harrison, 1990].Recent efforts to characterize and monitor changes in theablation zone environment have been focused on supraglaciallakes, where many of the lakes appear to be wholly outside ofthe main region of fast flowing ice streams [Lampkin, 2011].However, a large proportion of the main trunk of Jakobshavnice stream is well within the ablation zone and is exposed tosignificant surface melt, accumulated runoff, and pondingduring the summer months.[5] Heavily crevassed zones within the shear margins of

Jakobshavn Isbræ, referred to as Jakobshavn, are intermittentlyinundated and drain. We refer to these water-filled features as“saturated crevasses.” As melt-water availability and waterdepth increase, saturated crevasses are subject to hydrofractureand drainage conditions. In crevassed zones such as these,conditions necessary for crack propagation are differentthan for an individual crack. Elastic stress near the tip of anindividual crevasse is influenced by the spacing betweencrevasses. Van der Veen [1998] determined that stressintensity is enhanced with increased spacing but is less thanthat for a single crevasse. Furthermore, closely spaced cracksact to buttress each other from larger external tensile stressesnear the edges of a crack system [Weertman, 1973].Therefore, an assemblage of crevasses require about 3 to 4 timesmore stress than a single crack and substantial hydrostaticpressure from melt-water to sustain crack propagation[van der Veen, 1998]. In what follows, we show that these con-ditions for drainage are met in the saturated crevasse systemsexamined in this analysis. They represent important reservoirsof surface melt water that could have a direct impact on icestream flow behavior [Parizek et al., 2010].

1.2. Objectives

[6] Here we perform, to our knowledge, the first investiga-tion into the potential for activation of enhanced lateral iceflow from the catchment into Jakobshavn’s main channeldue to quantifiable melt water infiltration into shear margins.Inasmuch, this analysis includes novel efforts to evaluate themagnitude of melt water drainage from saturated crevassesalong the flanks of Jakobshavn during the 2007 melt season(Figure 1). With an estimate of the minimal water storagecapacity of select saturated crevasses, comparison to obser-vations elsewhere on the GIS, and theoretical understanding,we illustrate how drainage events from these features canimpact mass flux across the shear margins. Strain rates arecalculated and used to understand changes in tensionalforces during drainage periods and to estimate theoreticaldepths of crevasses. We then estimate saturated crevasseinundation depth and determine the volume of drainage fromrepeat visible satellite imagery.

2. Data

[7] Several sources of data are used to evaluate the charac-teristics of the saturated crevasse systems examined in thiswork. Areal extent of saturated crevasses, surface velocity,and strain rates are derived from Landsat-7 ETM+opticalimagery. Ice sheet surface elevation data are from a digitalterrain model (DTM) derived from SPOT-5 stereoscopicpairs. Meteorological data used to assess surface melt ratesis from select stations in the study region that are part ofthe Greenland Climate Network (GC-NET).

2.1. Satellite Data

[8] Optical imagery derived from Landsat-7 ETM+SLC-offpanchromatic data at 12.4 m2 spatial resolution were used tomanually delineate the boundaries of observable saturatedcrevasse features and were retrieved from the USGS LPDAAC(http://edcsns17.cr.usgs.gov/EarthExplorer/). Landsat scenesacquired on 6 June, 22 June, 8 July, 24 July, and 9 Augustduring the 2007 melt season over path (9), and row (11) wereused, as they were cloud free and completely cover the studyregion. Each Landsat scene is approximately 170 km (north-south) by 183 km (east-west). ETM+SLC-off images sufferfrom periodic missing data due to a malfunction in theonboard scan-line corrector. Missing scan-line values werecorrected using a spatial linear filling routine, where missingpixel values were filled through linear interpolation. Themissing scan lines are uniform throughout each image (1 or2 pixels in width through the center of the scenes) with anincrease in the width of missing lines near the image margins(roughly 15 pixels on average). Each scenewas atmosphericallycorrected using the atmospheric radiative transfer model 6S[Vermote et al., 1997] and converted from digital counts tosurface reflectance. A summary of scene characteristics usedin this analysis are detailed in Table 1.

2.2. Elevation Data

[9] Surface elevation (zs) used in this analysis is derivedfrom a digital terrainmodel (DTM) (see appendix for notation).The DTM surface elevation data were acquired from theSPOT SPIRIT data archive (http://polardali.spotimage.fr:8092/IPY/dalisearch.aspx). Surface elevation is estimatedfrom stereoscopic panchromatic (0.48–0.71mm) SPOT-5

LAMPKIN ET AL.: DRAINAGE FROM WATER-FILLED CREVASSES

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http://edcsns17.cr.usgs.gov/EarthExplorer/

http://polardali.spotimage.fr:8092/IPY/dalisearch.aspx

http://polardali.spotimage.fr:8092/IPY/dalisearch.aspx

HRS images acquired over the study region during theInternational Polar Year (IPY) 2007 campaign [Korona etal., 2008]. The DTM has 10 m vertical accuracy with 90%confidence on surface slopes less than 20% and 40 mhorizontal resolution [Bouillon et al., 2006]. Performanceof surface height retrievals was better over the study regionas indicated by a comparison of SPOT elevations to ICESat

heights, resulting in a mean elevation difference of 0.3 m(for ICESat 3H period) and 4.8 m (for ICESat 3I) [Koronaet al., 2008].

2.3. Meteorological Data

[10] Estimates of surface ablation were derived from theapplication of a temperature-based method (equation (1))

Figure 1. The Greenland Ice Sheet highlighting the Jakobshavn Isbrae drainage basin in west-centralGreenland (inset A) along with the location of GCNET meteorological stations JAR1 and 2 as well theboundary of the study area (red box). The locations of inundated crevasse systems, called “saturatedcrevasses” and designated as CV1–CV7 (white circles) within the shear margins of the ice stream, aredepicted in inset (B). Background image is a Landsat-7 ETM+panchromatic image acquired on 8 July 2007.


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[Braithwaite and Olesen, 1989] that uses measured hourlyair temperatures from the Program for Regional ClimateAssessment (PARCA) GC-NET meteorological data archive[Steffen et al., 1996]. Air temperatures at the JAR1 andJAR2 GC-NET stations over the 2007 melt season were usedin this analysis. Station locations are marked in Figure 1.Hourly measured air temperatures acquired from GC-NETare aggregated to daily mean temperature (�T (�C)) and usedto calculate melt amount (at) in equivalent water height(mm day�1) given by

at ¼ a1�Htð Þ þ b1��T �Htð Þ �T ≤ 0;Ht ¼ 0�T > 0;Ht ¼ 0

�(1)

where a1 = 1 +/- 4 mm d�1 and b1 = 7.7 +/- 0.5 mm d�1 �C�1

are regression constants and Ht a binary positive degree-dayindex [Braithwaite and Olesen, 1989].

3. Methods

3.1. Delineation of Saturated Crevasses

[11] Boundaries of inundated or saturated regions withincrevasse fields along the flanks of Jakobshavn ice streamwere manually digitized using visual interpretation criteriafrom high-resolution cloud free, Landsat-7 ETM+SLC-offpanchromatic images. These saturated crevasse systems weredelineated based on the significant difference in reflectancebetween water and ice. Water demonstrates very lowreflectance relative to ice (or even saturated ice/firn) due toincreased absorption of radiation in the solar reflective partof the electromagnetic spectrum (EM). Only inundatedregions large enough to be visually discerned were mapped,as they represent features greater than the nominal spatialresolution of ETM+panchromatic data. Saturated crevasseregions that were either completely or significantly eclipsedby missing scan lines were not mapped. Each system ofinundated crevasses was grouped based on their relativespatial proximity. Therefore, we identified seven regions ofwater-filled crevasse systems that were clustered anddesignated as Crevasse System (CV) 1 to 7 (Figure 1). In thisanalysis, spanning the 2007 melt season, the delineatedboundaries of saturated crevasse systems for each cloud-free image date were used to estimate the total area for eachcrevasse group.

3.2. Derivation of Local Velocity and Strain Rate

[12] Surface strain rates were derived from estimate velocitybased on identification of distinctive crevasse features, whichmaintained their local configuration through the ETM+ imagetime series described in section 3.1. Several authors haveemployed a similar approach for estimating ice sheet surfacevelocities and strain rates from visible imagery [e.g.,Bindschadler and Scambos, 1991; Whillans and Tseng, 1995;

Price and Whillans, 2001]. Local surface velocities werederived from the displacement of crevasse features (Δx) overa time interval Δt between successive satellite images. Strainrates are estimated from the extensional component ofrelative change in measured velocity perpendicular to crevasseedges. Crevasse features that were consistently identifiablewere tracked over a time interval spanning from 6 June to 9August 2007 in close proximity to each saturated crevassegroup.

3.3. Estimation of Saturated Crevasse Depth andInundation Volume

[13] The estimation of saturated crevasse inundation volumeor water-filled volume is complicated by the lack of ground-based methods for determining the amount of water containedin the saturated crevasse systems mapped in this analysis.Therefore, we have relied on satellite-based and theoreticalapproaches for estimating water volume in saturatedcrevasses.We assume that crevasse shape (acrossmany pixels)can be approximated by the sum of rectangular cylinderswithin each pixel. Therefore, in order to estimate volume, thearea and depth of water-filled crevasses are prerequisites.Saturated crevasse area is estimated through the approachdescribed in section 3.1. Independent estimates on theinundation depth within the saturated crevasse fields werederived using two methods, an optical retrieval approachbased on the magnitude of radiation attenuation in waterand a theoretical estimation of depth for an assemblage ofcrevasses in a given region based on the local strain rate.3.3.1. Optical Attenuation Model for Depth ofWater-Filled Crevasses[14] Crevasse inundation depth was estimated using a

method by Sneed and Hamilton [2007] to retrieve supraglaciallake depths over western Greenland. This approach is basedon the Bouguer-Lambert-Beer law (equation (3)), describingattenuation of optical radiation through a water column:

L zw; lð Þ ¼ L 0; lð Þe�Klzw (2)

where zw is depth of water column, L(zw, l) is spectral radianceleaving the water body at some depth and wavelength, L(0, l)is spectral radiance at zero depth, andKl is spectral attenuation.This approach assumes that the substrate of the lake is homo-geneous, the impact of dissolved organic or inorganic matteris negligible on absorption, there is no Raman scattering orfluorescence, and the lake surface is not substantially roughdue to wind. Following Sneed and Hamilton [2007], anestimate of zw over every pixel within the extent of eachsaturated crevasse system is given by

zw ¼ ln Ad � R1ð Þ � ln Rw � R1ð Þ�gd

(3)

where Ad is lake-bottom reflectance, R1 is reflectance ofoptically deep water, Rw is measured reflectance, and gd isthe effective attenuation coefficient, which represents diffuseattenuation of downwelling radiation. Attenuation of diffusedownwelling radiation is decomposed into absorption andscattering components, which are wavelength dependent.Mean absorption and scattering coefficients were calculatedacross the ETM+panchromatic wavelength interval using datacompiled in Smith and Baker [1981].R1 values were estimatedfrom a sample of deep-water pixels (within Disco Bay) for

Table 1. Summary of Landsat ETM+Scenes Characteristics

Acquisition DateSolar ZenithAngle (deg)

Solar Azimuthangle (deg)

CloudCover (%)

6 June 2007 42.90 171.72 0.0822 June 2007 46.37 170.59 0.038 July 2007 47.40 169.70 0.4824 July 2007 50.03 169.48 5.329 August 2007 54.03 170.10 0.03


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each scene. Great care was exercised to select pixels thatwere far from shore lines to insure that R1 estimates werenot biased by turbid water or pixels containing floating ice.3.3.2. Modified Nye Model for Depth of Water-FilledCrevasses[15] Given that zw retrievals provide only a minimum for

water-filled crevasse depth, an additional independentestimate is calculated for means of comparison. A modifiedversion of the Nye model (Nh) [Nye, 1955; Nye, 1957] forestimation of crevasse depths from measured ice sheet sur-face strain rates was employed. The basic Nye crevasse modelestimates the depth where longitudinal tensile stress rate isbalanced by creep closure due to ice overburden pressure.The Nye model does not explicitly account for stress concen-trations near the base of fractures but is well suited for a fieldof closely spaced crevasses where adjacent cracks suppressstress concentrations near crack tips [van der Veen, 1998;van der Veen, 1999; Benn et al., 2007]. The modified versionexpands on the original Nye approach by the addition of acritical yield strain rate term (_ecrit ), which determines mini-mum strain rates necessary to initiate crevasse propagation[Benn et al., 2007] as well as compensating for hydrostaticpressure assuming crevasses are inundated with water. Otherapproaches such as those proposed by Weertman [1973] dotake into account crack bottom stress concentration but areformulated for isolated fractures only and are not applicableto closely spaced fractures [Mottram, 2007]. The applicationof linear elastic fracture mechanics theory (LEFM) to cre-vasse formation and propagation for estimating fracturedepth based on simple-opening, mode I fractures was first de-rived by Smith [1976] and expanded by van der Veen [1998,1999], Rist et al. [1996], and Rist et al. [1999]. LEFM is notappropriate for the systems under evaluation in this study,primarily because the assumption of linear rheology is notsuitable for power-law glacier ice, is sensitive to fracture spac-ing which is not well constrained, and does not perform betterthan the modified Nye for predicting observed crevasse depths[Mottram and Benn, 2009; Otero et al., 2010].[16] We implement the modified Nye model for the depth

of a water-filled crack (Nh), as a theoretical comparison tothe above optical attenuation approach:

Nh ¼ 1

rig2

_E�A

� �1n

þ rwgdwð Þ" #

(4)

where _e� ¼ _e� _ecrit, A and n are flow-law parameters, ri andrw are density of ice and water, and g is acceleration due togravity. Because _ecrit is poorly constrained and widelyvariable, we assume existing crevasse penetrate to the depthwhere the tensile deviatoric stress is balanced by thecompressive overburden such that _e� ¼ _e. Given dw is notknown a priori, we calculate an initial estimate of crevassedepth using equation (4) for dw= 0 (crevasses free of water)(Nh,water-free). Assuming the crevasse systems examined in thisstudy are completely inundated, the water level is equivalentto the entire depth of the crevasse. Using equation (4), withdw=Nh,water-free, a final depth for a water-filled fracture isestimated. Though the Nye model is simple, it is appropriatefor this application, because crevasses along the margins ofthe ice stream are closely spaced and contain melt water dur-ing the summer months. Adjacent fractures act to distributestress over a broader area, reducing the concentration of forces

near the tip of any given crack. The modified Nye model ac-counts for the impact of water within the fractures, whichmaintains sufficient pressure due to the relatively higher den-sity of water over ice, such that the stress intensity near thecrack tip is greater than the elastic resistance of the crack wallsto deformation, facilitating crack propagation and deepercracks [Alley et al., 2005a, 2005b]. Strain rate estimates,extracted from visual feature tracking methods described insection 3.2, are used in equation (4) to calculate crevassedepths for each saturated crevasse system delineated. Table 2summarizes values used in the modified Nye method.[17] The modified Nye model accounts for the influence of

fracture toughness, which can exhibit vertical heterogeneity asa function of temperature, debris content, strain history, and cre-vasse spacing. The stress required to initiate a fracture can rangefrom 30 to 80 kPa [van der Veen, 1998] andmay be substantiallylower for temperate ice [Mottram and Benn, 2009].

4. Results

4.1. Surface Topography and Saturated Crevasses

[18] The relationships among surface elevation, slope(Δzs/Δx), and the location of saturated crevasse featuresidentified from satellite imagery are examined across severaltransects (Figure 2). Each transect is labeled (A-F) andbisects assemblages of saturated crevasse groups (CV1–CV7;Figure 1). The transects intercept the main trunk of Jakobshavn;therefore, the location of each saturated crevasse group isidentified relative to the boundaries of the ice stream(Figures 3–5). Figures 3–5 indicate that each saturatedcrevasse package (e.g., CV1–CV4, CV6–CV7; cf. CV5) isassociated with local depressions in zs, which tend to bepresent along the edges of the ice stream. Saturated crevasseregions along the surface are also associated with relativelymore variable terrain, with greater undulations over the scaleof tens of kilometers corresponding to basins flanked by highsurface slopes.

4.2. Crevasse Depth Estimation

[19] Twomethods were used to derive estimates of saturatedcrevasse depths. Figure 6 (graphic inset) illustrates thedifference between zw (optical-based model) and Nh

(modified Nye model) depths for an idealized crevassesystem. Equation (4) was applied to each Landsat scene fromwhich saturated crevasse boundaries were delineated toproduce an estimate of zw. Figure 6 shows the distribution

Table 2. List of Input Parameters for Estimating Crevasse DepthsUsing the Modified Nye Model

Input Variable Symbol Parameter Value

Longitudinal strainrate (s�1)a

_e __

Gravitationalacceleration (m s�2)

g 9.81

Ice density (kg m�3)b ri 917, 600Water density (kg m-3) rw 1000Flow-law rate factor(Pa-3s-1)

A 3.48� 10�25

[Cuffey and Paterson, 2010, p. 74]Flow-law exponent n 3

aStrain rates converted from d-1 to s-1 as input to modified Nye depthmodel.

bTwo ice density values were used to represent ice (917) and bulk firn(600) in crack depth calculations.


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of zw for every pixel within the saturated region on eachimage date for crevasses CV1–CV3. Retrieved depths as wellas mean, maximum, and minimum values are illustrated.Additionally, estimated Nh depths are depicted for twospecifications of ice density. Comparison of zw and Nh forCV4–CV7 are shown in Figure 7. Estimated mean zw depthsfor each image date tend to range between 2 and 10 m, whilethe Nh depths vary from 100 to 125 m at rice = 917 (kg m�3)to values upwards of 250 m for water-filled cracks across allcrevasse groups. zw depths tend to be skewed towardshallower depths with small variations in mean depths asthe melt season advances over most crevasse groups. Nh

depths tend to be quiet large compared to zw (~170% greater)with water-filled cracks at 600 (kg m�3) occupyingdepths reaching close to half the ice thickness over mostcrevasse groups.

4.3. Temporal Variability of Saturated Crevasse Area

[20] An evaluation of the temporal change in delineatedsaturated crevasse area indicates an increase in area for most

saturated crevasse systems, with peak extent reached in earlyJuly (with maximum near ~1.8 km2) followed by sharpdecreases systematically across most features (Figure 8).The onset of inundation and drainage vary for each saturatedcrevasse system. CV1, CV2, and CV3 appear early in themelt season (6 June) with a total area of ~0.15 km2. CV6demonstrate a dramatic increase in area between 6 Juneand 22 June, reaching its peak area on 22 June. By 22 June,CV6 is superseded by CV2 on 8 July, where CV2 comprisesthe largest proportion (0.73 km2) of the total area (~1.8 km2)with a maximum extent of ~0.75km2 (Figure 8a). Later inthe melt season (24 July–9 August), CV7 becomes filled,while CV5 demonstrates a large proportion of total area.Additionally, there is sharp decline in the proportion of totalarea shared by CV2 and CV6 near the end of the melt season(Figure 8a). Most saturated features (except CV1) remain in-undated throughout the analysis period up until the lastimage date (9 August).[21] During the analysis period, there is evidence of periods

of filling and drainage as indicated by sustained increases and

Figure 2. (a) Schematic defining coordinate system and variables related to tributary ice flow acrossJakobshavn shear margins into the main trunk of the ice stream. Relative positions of saturated crevassesand drainage of melt water to bedrock/ice interface are also illustrated. (b) Location of transects acrosssaturated crevasse systems (A–F) from which surface elevation and slope profiles are derived.


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decreases in areal extent (Figure 8b). All groups except CV7filling early in the analysis period (6 June; Figure 8b). Eachgroup demonstrates different rates in filling, where CV2,CV4, CV5, and CV6 show relatively dramatic increase in areabetween 6 and 22 June, in contrast to CV1 which is modest.Among the groups that demonstrate relatively rapid filling,CV4 and CV5 areal increase are less dramatic than those ofCV2 and CV6 (Figure 8b). After reaching their peaks, CV6and CV2 demonstrate dramatic decreases in area, such thatby 24 July, their areas are less than all but CV1. Effectively,these trends indicate that as the peak melt period approaches,there is a systematic increase in the area of inundation formost saturated crevasses, but the relative proportion or rateof increase is different for each saturated crevasse system.Similarly, there are differential changes in area due todrainage for most saturated crevasse systems after 8 July.

[22] The temporal changes in saturated crevasse area formost groups correspond to changes in regional melt amount(Figure 8a). The period of maximum areal extent correspondsto the peak in melt amount near 8 July. The relationshipbetween areal extent and melt is most prevalent between8 and 24 July, which corresponds to a dramatic decrease inmelt amount at the lower elevation station (JAR2).[23] Additionally, changes in areal extent as a result filling

and drainage throughout the analysis period are highlycorrelated to elevation, where low elevation crevasse groupstend to be larger, fill earlier in the season and experiencehigher magnitudes of melting than at higher elevations.

4.4. Saturated Crevasse Filling Rates

[24] It is assumed that the rate of filling or inundation isrelated to the magnitude of melt produced, which is

Figure 3. Profiles of surface elevation (zs) (top panels) and surface slope (Δzs/Δx) (lower panels) overCV1 (A-A0) and CV4 (B-B0), illustrating the relative location of saturated crevasse systems and theboundaries of the ice stream main trunk.

Figure 4. Profiles of surface elevation (zs) (top panels) and surface slope (Δzs/Δx) (lower panels) overCV2 (C-C0) and CV5 (D-D0), illustrating the relative location of saturated crevasse systems and theboundaries of the ice stream main trunk.


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functionally dependent on elevation. In order to explore thishypothesis, the rate of crevasse filling ( _o) was calculated bythe change in area between the first image date (6 June) andthe maximum or peak area achieved during the analysisperiod. _o is plotted as a function of the mean elevation for eachsaturated crevasse group (<zs>) (Figure 9). Interestingly, therelationship between _o and< zs> varies across all saturatedcrevasse groups. CV3 and CV7 have decreasing< zs> forincreasing _o , whereas _o for CV1, CV2, CV4, CV5, andCV6 groups appear to increase with< zs>. Results indicatea more complicated set of processes that drive the filling rateof saturated crevasses, beyond the impact of melt-waterproduction, transport, and infiltration into crevasses scaledby elevation. The source of melt water that fills crevassescan come directly from melt generated within the crevasseor melt from outside of the crevasse that has been transportedinto the crevasse via channels.

4.5. Saturated Crevasse and Local Strain Rate

[25] Local strain rates ( _e), estimated using the techniquesdescribed in section 3.2, demonstrate spatial variabilityalong the ice stream margin in the vicinity of the saturatedcrevasse systems of interest in this analysis (Figure 10).Strain rates between 0.0002 d�1 and 0.012 d�1 correspondto locations along the ice stream margin where there arechanges in horizontal ice flow direction over relatively shortdistances on the order of several kilometers. Additionally,there is some variation in the local strain rates across thesaturated crevasse systems, where CV4 and CV7 exhibitstrain rates that vary from ~0.00022 to 0.026 d�1, whileCV2, CV6, and CV5 range from ~0.004 to 0.019 d�1 overthe analysis period.

4.6. Saturated Crevasse Drainage Rates

[26] Conditions related to observed declines in saturatedcrevasse area were examined. CV3 and CV7 were omittedfrom this part of the analysis because they reach peak arearelatively late in the times series, providing few samples fordetermining the relationship between maximum saturated

extent (Apeak), strain rate and observed drainage rates ( _Ψ ).Drainage rate ( _Ψ) was calculated as the difference in area atpeak extent (Apeak) and area measured on the last image datefor each crevasse group. We examined relationships betweenApeak and _Ψ over each saturated crevasse group (Figure 11a).A strong linear relationship (r = 0.91) exists between _Ψ andApeak, where saturated crevasse experiencing large extentsin saturation are associated with high drainage rates. Wealso examine relationships between mean strain rates (<_e>)calculated from estimated strain rates at point locations inclose proximity to each saturated crevasse group (Figure 11b)and _Ψ . Figure 11b demonstrates that a relatively weakrelationship (r = 0.14) between the magnitude of strain anddrainage rate. CV1, CV4, and CV2 appear to follow a linearrelationship, but CV5 and CV6 are not consistent with thisrelationship. CV5 demonstrates relatively low drainage ratesunder high strain rates, while CV6 maintains relativelyhigher drainage rates under the lowest mean strain rate ofall groups.

4.7. Potential Drainage Volume From LargestSaturated Crevasse System

[27] A single saturated crevasse system was selected toillustrate the impact of melt water drainage on local massflux along the shear margins of the ice stream. The CV2system was selected (Figure 12) because it demonstratesthe largest inundation extent during its peak period of allsaturated crevasse groups examined in this analysis. Thelargest magnitude of drainage from CV2 occurs between8 and 24 July. We estimate total potential volume of drainedmelt water during the 16 day interval between 8 and 24 Julythrough delineated inundation area on these two image datesand depth of crevasses. Two independent drainage volumesare derived based on estimates of depth using the opticalattenuation and modified Nye methods. The opticalattenuation approach provides a minimum depth and drainagevolume. The modified Nye model provides a theoreticalbenchmark to compare to potential drainage volume derivedfrom the optical attenuation model. The optical attenuation

Figure 5. Profiles of surface elevation (zs) (top panels) and surface slope (Δzs/Δx) (lower panels) overCV3 and CV6 (E-E0) and CV7 (F-F0), illustrating the relative location of saturated crevasse systems andthe boundaries of the ice stream main trunk.


8

model provides a spatially distributed retrieval of crevassedepths derived directly from Landsat imagery over each pixelwithin the delineated boundaries of saturated regions. This isnot case for depths from the modified Nye model. Measuredstrain rates at 7 points within close proximity to the CV2 groupwere gridded (using ri=917 kg/m

3) to the same resolution asthe Landsat ETM+panchromatic imagery using the InverseDistance Weighting (IDW) scheme [Shepard, 1968]. IDW

provides an interpolated value u(x) at a given point x basedon samples ui for i=0, 1, 2, . . ., N given by

u xð Þ ¼XNi¼0

wi xð ÞuiXN

j¼0wj xð Þ

(5)

and the weights wj(x) given by

Figure 6. Comparison of inundation depth for saturated crevasse systems (a) CV1, (b) CV2, and (c)CV3, based on Bouguer-Lambert-Beer Law of radiation attenuation using the methods of Sneed andHamilton [2007] for crevasse water depth (zw) and the Nye model for (Nh) [Nye, 1955; Nye 1957]. Themodified Nye used here provides a theoretical upper limit on mean crevasse depths calculated from strainrates measured at locations in close proximity to each crevasse group for ice density values (ri) of 917 and600 (kg/m3). Estimates of zw are derived for each pixel within the delineated boundaries of saturatedcrevasse groups for each cloud-free Landsat ETM+panchromatic image (DOY 173, 189, 205, and221). The mean, maximum and minimum values of zw are depicted. Estimates of Nh are depicted for airfilled, high and low density, and water filled, high and low density. The lower-right panel illustrates agraphic representation of Nh and zw.


9

wi xð Þ ¼ 1

d x; xið Þni (6)

where x is the interpolated location, xi is a sample of aknown strain rate, d is the distance between x and xi, N arethe total number of measured strain points (6), and ni is thepower parameter set to 2. For ni ≤ 2, values farther awayfrom the interpolated location dominate the estimate. Themajority of samples are less than 10 km away from everyother point in the vicinity of the CV2 group. Gridded strainrates were input to the modified Nye model to providespatially distributed estimates of fracture depths within the

boundary of drained area over the CV2 group. The griddeddepths were then used to estimate potential drainage volume.[28] Based on depths using the optical attenuation model,

the decrease in volume from CV2 between 8 and 24 Julyfrom ~38.6� 10�3 km3 to 29.87� 10�3 km3, represents apotential drainage volume (VOE) of 9.23� 10�3 km3. Potentialdrainage volume based on the modified Nye model (VNE)represents a decrease in volume from 6.33� 10�2 to1.41� 10�2 km3 over the 16 day interval resulting in4.92� 10�2 km3 of drained water.[29] In order to determine if our assumption of not

accounting for _ecrit in volume estimates using the modified

Figure 7. Comparison of inundation depth for saturated crevasse systems (a) CV4, (b) CV5, (c) CV6,and (d) CV7, using the same methods described in Figure 6.


10

Nye model was reasonable, we evaluate the total estimatedvolume in CV2 on 8 July. Using a value of 7.53� 10�2 a�1

(equivalent to a stress of 60 kPa) for _ecrit we estimate a differ-ence in total volume of 3.43� 10�4 km3. In this sensitivityanalysis, the value used for _ecrit is near the upper end of theestimated range for fracture toughness and only results in asmall difference in estimated volume.

4.8. Assessment of Uncertainty

[30] Uncertainty in potential drainage volume based oncrevasse depths using the optical attenuation model (OE)and the modified Nye model (NE) are a function of errorin the determination of crevasse inundation area (ga) andestimated depth (gd) from the two methods over the CV2group during peak drainage (see section A for full detailson error derivations briefly described below).

4.8.1. Uncertainty Due to Delineated Area[31] Errors in ga are primarily dependent on the spatial

resolution of the Landsat ETM+ sensor (ga_pixel). Undercertain circumstances, the ability to fully resolve an openfracture given ETM+pan-sharpened panchromatic bandspatial resolution (12.4 m2) is compromised when fracturewidths are comparable to the spatial resolution. Thereforeabsolute uncertainty in estimated drained area (ΓArea) is 17.5m

2.4.8.2. Uncertainty in Potential Volume DrainageEstimates from Optical Attenuation Model[32] Uncertainty in crevasse depths from the optical atten-

uation model is a function of several factors. The applicationsof the optical attenuation model to retrieval of supraglaciallake depths over the Greenland Ice Sheet were assessed bySneed and Hamilton [2011] assuming that inelastic scatteringthrough the water column, surface waves, and dissolved orparticulate matter have negligible impacts on estimateddepth. Given this, we conclude that much of the uncertaintyin the optically depth retrieval is driven by a combinationof sensor radiometric noise and atmospheric correction(gd_rad/atmos). The uncertainty in total potential drainagevolume estimates using the optical attenuation approach is21.5 m3 or 2.15� 10�8 km3.4.8.3. Uncertainty in Potential Volume DrainageEstimates from Modified Nye Model[33] Components of gd based on depth estimations using the

modified Nye approach are primarily a function of uncertaintyin the estimated velocity used to derive strain rates. Therefore,gd for the Nye model can be decomposed into contributionsdue to sensor spatial resolution, scene-to-scene geometricregistration (gd_geo), and interpolation error (ME). The totalerror from the Nye model is ΓNye = gd _ geo + gd _ grid + gd _ pixelwhich is 34.3 m. Therefore, uncertainty in total potentialdrainage volume for estimates using the Nye method is38.5 m3 or 3.58� 10�8 km3.4.8.4. Other Sources of Uncertainty[34] Total error in zw is dominated by limitations in the

spatial resolving capacity of the Landsat ETM+ system.

Figure 8. Evaluation of the temporal variability of saturatecrevasse systems in this study. Temporal variability of (a)inundated area for each saturate crevasse group (cumulative)delineated from each cloud-free Landsat ETM+panchromaticimage date compared to time series of surface melt amount (at)at GC-NET stations JAR 1 (962m elevation) and JAR 2 (568melevation), and of (b) delineated area for each saturated crevassesystem depicting periods of growth and decay indicative ofpartial drainage events.

Figure 9. Relationship between mean surface elevation(<zs>) and filling rate ( _o) defined as daily amount of meltwater input to each saturated crevasse group from the startof the analysis period (6 June 2007) up until the date of peakor maximum area.


11

Figure 10. Map showing distribution of estimated strain rates in proximity to each saturated crevassegroup (CV1–CV7) superimposed on a gray-scale Landsat ETM+panchromatic image showing themargins of Jakobshavn Isbræ. Strain rate magnitudes are depicted by the relative size of the circles at eachlocation. Mean strain rates were calculated for saturated crevasse groups for all points within the respectivered boxes bounding each group.

Figure 11. (a) Relationship between peak areal extent of each saturated crevasse group (Apeak) and drainagerate ( _Ψ). (b) Relationship between mean strain rates <_e> derived from averaging all strain estimates withinclose proximity to each saturated crevasse system and _Ψ demonstrating a strong correlation (r=0.91). _Ψrepresents the rate of change in the extent of area for each saturated crevasse system (the rate of drainage fromthe saturated crevasses) between each Landsat ETM+ image date. A weak relationship exists between <_e>and _Ψ (r = 0.14). Values in parenthesis above each point are the total number of locations in close proximity toeach saturated crevasse group from which <_e> is calculated.


12

Errors in Nh are derived from both the spatial resolution andthe interpolation routine. Other sources of uncertainty thatwere not evaluated in this analysis include the impact ofvariability in the flow-law rate factor (A) used to convertmeasured strain rates into stresses, which can result insignificant estimates of crevasse depths using the Nye model[Mottram and Benn, 2009]. Additionally, the Nye modelassumes crevasse depths are in equilibrium with local strainrates, and this may not be appropriate under circumstanceswhere there are large changes in longitudinal strain ratesindicative of rapid transitions from zones dominated byextension to compression as indicated by [Mottram andBenn, 2009]. We were not able to assess this condition duringthis analysis, and this, therefore, warrants further study.[35] Depth estimates using the Nh for the low-density case

may not be so unreasonable. Generally, the presence ofcrevasse reduces the bulk density of ice, due to the largenumber of voids in addition to the impact of melt alongcrevasse walls, which can reduce the rate of hydrostaticclosure near the surface, resulting in fractures that areunlikely to close once opened [Pfeffer and Bretherton, 1987;Sassolas et al., 1996; Mottram and Benn, 2009]. Sources ofmelting can be due to solar insolation. As fractures areadvected downstream, the reduced bulk density couldbe additive, resulting in deeper cracks and increased waterholding capacity over time.

5. Discussion

5.1. Potential for Drainage Impact on CatchmentExpansion

5.1.1. Drainage Impact on Shear Margin Mass Flux[36] Rapid drainage of saturated crevasses has the potential

to introduce surface-melt water to the subglacial systemalong the flanks of Jakobshavn, thereby altering ice dischargeinto the main trunk of the ice stream. Das et al. [2008]reported a tripling of ice velocity following rapid transmis-sion of 4.4� 10�2� 0.01 km3 of surface melt water to thebed of the ice sheet. Pressurization of the subglacial drainage

system can lead to a period of subglacial cavity growththat effectively decouples a portion of the ice from basalasperities, leading to enhanced ice flow [Walder, 1986].While meltwater impact on ice flow is highly dependent onthe temporal and spatial evolution between distributed andchannelized drainage within the subglacial hydrologic system[Schoof, 2010], if we assume that speed-up associated withdrainage scales linearly with our relative lower estimate ofinfiltrated potential drainage volume using the opticalattenuation approach from the CV2 crevasse system(9.23� 10�3 km3) can result in a ~42% speedup (seesection B for additional details). If vertical shear stresses,longitudinal stresses, and lateral drag are considered, thenlocal reduction of basal resistance (commensurate with ourlinear scaling of water volume to speed-up over a viscousbed) would be compensated regionally resulting in valuesless than 42%. This is consistent with observations of netincreases in annual ice motion in Greenland [Zwally et al.,2002; Joughin et al., 2008; Bartholomew et al., 2010]. Ourestimated impact of drainage on ice flow is strictly a roughestimate and is likely not valid as the magnitude of melt-water drained amount increases resulting in enhance basalchannelization.5.1.2. Drainage Impact on Catchment-Scale Mass Flux[37] Drainage from saturated crevasse systems may have a

broader impact on regional mass flux at the basin scale. Wepresent a conceptual model of the potential dynamic responseto injection of melt water from saturated crevasses intoJakobshavn Isbræ shear margins (Figure 13). This model isonly intended to demonstrate the likely consequences ofcrevasse drainage on the regional “pulling” power ofJakobshavn Isbræ. Mass flux through the shear marginsof Jakobshavn Isbræ is significant [Truffer and Echelmeyer,2003] and our analysis of saturated crevasse drainage indicatesthat basal lubrication has the potential to amplify this flux.More specifically, analogous settings and available melt watervolumes indicate enhanced basal sliding initiated by saturatedcrevasse drainage can lead to local thinning and enhancedmassdischarge into the main trunk (Figure 13, Steps 1 and 2).

Figure 12. A three dimensional representation of the distribution of estimated water depth (zw) using themethods of Sneed and Hamilton [2007] for the largest saturated crevasse system (CV2). Estimates of zwwere combined with those of extent for CV2 to derive an estimate of total water volume. Total watervolume contained within CV2 of 9.23� 10�3 km3 is assumed to drain and reach the bedrock/ice interfacebetween 8 and 24 July.


13

Increased mass discharge near Jakobshavn margins couldincrease longitudinal stress gradients upstream due to the“pulling force” of downstream sliding (Figure 13, Step 3),amplify available upstream basal melt water, sliding, andultimately increase inland flow speeds (Figure 13, Step 4)[Price et al., 2008]. This process could result in either anegative or positive feedback. As upstream regions experienceincreased thinning, upstream surface slopes decrease, whichreduces longitudinal gradients and stabilizes the system bypreventing further inland migration of basal sliding [Priceet al., 2008]. However, the increased thinning could alsolead to more surface melting and available water for basallubrication in regions with enhanced tensile stresses, whichmay activate sliding in upstream regions where the basalice was previously below the pressure melting point [Parizekand Alley, 2004]. The regional implications for saturatedcrevasse drainage are heavily dependent on how melt waterdrainage from saturated crevasses is distributed by the basalhydrologic network. Assuming inland propagation of fastflow is possible due to downstream drainage of saturatedcrevasses, additional drainage from supraglacial lakes thatoccupy regions upstream of the shear margins may amplifyinland fast flow. The integrated impact is an expansion of

the effective catchment area bounding Jakobshavn, resultingin potential increase of mass transfer from farther inland.[38] Though calculations in this analysis were for a single

saturated crevasse system, the implications are potentiallyfar reaching if this process is considered for all observedcrevasse systems along the margins of Jakobshavn. Van derVeen et al. [2011] delineated Jakobshavn channel boundariesin 1995, 2000, and 2005 by evaluating the transverse locationof minimum and maximum lateral shear stress to indicatewhere lateral drag changes from resisting driving stresswithin the main trunk to assisting driving stress in draggingslow moving ice outside of the main trunk. The shearmargins of Jakobshavn were relatively stable during thisperiod of rapid speed up and thinning due to the influenceof the basal topography in the main trunk [Truffer andEchelmeyer, 2003].

5.2. Water-Filled Fracture Propagation and SaturatedCrevasse Drainage

[39] Water-filled crevasse systems examined in this analysisdemonstrate values in Nh that approach depths close to halfthe full ice thickness for this region [Gogineni et al., 2001].Once water occupies a significant proportion of a crack, the

Figure 13. Conceptual model of processes involved in enhanced tributary ice flow across Jakobshavnshear margins into the main trunk of the ice stream due to melt water injection into the shear margins fromsaturated crevasse drainage. (1) Drainage of surface melt water from saturated enhances basal lubricationresults in (2) increased mass flux across shear margins, which (3) promotes transmission of massimbalance upstream through longitudinal stresses and (4) draws ice farther away, with the potential toexpand the ice stream catchment boundary.


14

maximum depth possible can be as high as the full ice thick-ness (R. Alley, personal communication, 2012) [Alley et al.,2005a, 2005b]. For fully filled fractures, there should be suf-ficient hydrostatic pressure to prevent crack closure [van derVeen, 1998], which may be the case for most fractures exam-ined in this analysis given water levels likely exceed the topsof fractures. Furthermore, the large local deformation ratesassociated with shear stresses in excess of 300 kPa should fur-ther enhance crevasse depth [Truffer and Echelmeyer, 2003].Boon and Sharp [2003] found that ponded water ~ 7 m deepwas sufficient to drive crack propagation through 150 m of rel-atively cold ice. Saturated crevasses along Jakobshavn’s shearmargins are likely dominated by relatively warm ice due to la-tent heat transfer, insolation from infiltrated melt water [Lüthiet al., 2002; Alley et al., 2005a, 2005b], and strain heating[Truffer and Echelmeyer, 2003].[40] The rate of crack propagation has implications for

drainage timing. Van der Veen [2007] established that therate of melt influx, or filling, is primarily responsible forthe crack propagation rates, particularly through cold icewhere high flow rates are necessary to sustain sufficienthydrostatic pressures required to offset losses from refreezing[Alley et al., 2005a, 2005b]. Given the strong relationshipbetween peak or maximum inundation extent and drainagerate, (Figure 11a) and weak relationship between meanstrain rate and drainage rate (Figure 11b), it is likely thatfluctuations in extent, followed by variations in water depth,influence hydrostatic pressures responsible for driving crackpropagation. Given that estimated strain rate calculationsare limited both spatially and temporally, it is possible thatcrack depths are more dependent on water levels than tensilestress, because the tensile stresses likely exhibit littlevariability throughout a given melt season aside from periodsof drainage.

5.3. Saturated Crevasse Filling Rates and LocalHydrologic Conditions

[41] Perhaps counter-intuitively, filling rates increase withelevation across most saturated crevasse systems examined(Figure 9). While lower elevation systems experience highermelt rates and greater runoff, they are likely connected towell-developed englacial plumbing through moulins andcrevasse fields [e.g., Parizek et al., 2010], which are mostlydistributed throughout lower elevation regions of the ablationzone. Colgan et al. [2011] have demonstrated that crevassearea extent (crevasses> 2 m) has increased by ~13% overthe 24 year period from 1985 to 2009 within the SermeqAvannarleq area of our study region. Moulin density (averageof ~12 moulins/km2) within this region has increased by afactor of 10 over this same period, coincident with largernumbers at higher elevations following the migration of theequilibrium line altitude [Phillips et al., 2011]. Moulins thatare well connected to the bed can easily accommodate thesupply of melt water, limiting the magnitude and rate ofponding at the surface. Given fewer moulins in the area,saturated crevasse groups at higher elevations are more likelyto pond at greater rates. The relationship between surfacerunoff propensity, englacial infiltration, and saturated crevassefilling rates are supported by a transition in supraglacialchannel network configurations as a function of elevation.Commensurately, there is a transition from channels thatterminate into crevasse fields and moulins to more complicated

higher-order channel networks involving channel-to-channeland lake-to-channel topologies at an elevation of ~800m(D. L. Lampkin and J. VanderBerg, Investigating supraglacialmelt channel networks over the Jakobshavn drainage basinduring the 2007 melt season, submitted to Hydrological Pro-cesses, 2013). Elevations near or above the 800m level aredominated by more complicated surface water pathways,which may contribute to greater variability in the filling ratesbeyond the linear trend identified. This is observed in Figure 9,where CV3 and CV7 demonstrate relatively lower mean fillingrates at higher elevations over the analysis period. Understand-ing the long-term evolution of saturated crevasses will requireunraveling changes in surface melt-water production as wellas the complex interaction between surface melt-water routingand englacial infiltration.

5.4. Saturated Crevasse Drainage and JakobshavnIsbræ Flow Behavior

[42] Jakobshavn has undergone dramatic changes in thepast decade, including loss of its ice tongue, rapid speed upbetween 1995 and 2005 [Joughin et al., 2004, 2008; Farnessand Jezek, 2008], and significant thinning [Thomas, 2004].While the mechanisms driving these changes and theirlong-term implications are still not fully understood, severalexplanations have been proposed, including instability dueto the loss of resistive forces at the glacier terminus as a resultof reduced buttressing or calving-induced mass instability[Weertman, 1974; Thomas, 1979; Hughes, 1987; Thomas,2004; Howat et al., 2005, 2008]. Van der Veen et al. [2011]have recently suggested that increase in velocity overJakobshavn from 1995 to 2005 is best explained by weaken-ing of ice in the lateral shear margins, resulting in reducedresistance due to lateral drag and larger driving stresses.Weakening of lateral ice can occur through warming thecolder, stiffer upper few hundred meters of the ice column[van der Veen et al., 2011]. Cryo-hydrologic warming is alikely mechanism for rapid warming of subsurface ice, whereinfiltrated melt water can transfer heat throughout the ice col-umn through discharge within crevasses and moulins [Jarvisand Clarke, 1974; Phillips et al., 2010]. We posit that the pri-mary source of melt water injection into the shear marginscomes from saturated crevasses and that both mechanismscould have played roles in the recent speedup. We demon-strate that saturated crevasses form in preferential locationswithin the shear margins where sharp inflections in flow direc-tion correspond to small depressions in the basal topography.Assuming sufficient seasonal supply of melt water, saturatedcrevasse systems should be consistently inundated each year,resulting in softening of subsurface ice at critical points alongthe ice stream. These critical locations, where there are rela-tively steep edges and fronts associated with basins in the bed-rock, tend to increase shearing [Budd, 1971] and consequentlydrag. Therefore, preferential infiltration of melt water frominundated crevasse systems may not uniformly relieve dragalong the entire ice stream margin, but act to reduce resistanceat specific locations. There is some correlation between thelocations along the ice stream where there is an increase inwidth-averaged driving stress from 1995 to 2005 (estimatedby van der Veen et al. [2011]) and delineated saturatedcrevasses. The relationship between the spatio-temporalvariability of drainage from saturated crevasses and localresistive stresses will need to be explored.


15

6. Conclusion

[43] This analysis presents a novel evaluation of inundatedregions along the shear margins of Jakobshavn Isbræ. Thesesaturated crevasses are associated with topographic lows andinflections in the ice flow direction, indicating locations ofpreferential melt water storage. Rates of crevasse filling arecorrelated with regional melt rates, while drainage rates arecorrelated with short-term changes in maximum inundationextent. Saturated crevasses are likely sources of substantialvolumes of melt water injection that could be responsiblefor reduced lateral and basal drag. Estimates of potentialdrainage volume using the optical attenuation model clearlyrepresent an underestimation in stored and drained watervolume as compared to those from the Nye model, Generally,our range of estimated drainage volume is of a magnitudethat can theoretically affect basal sliding and mass flux intothe shear margins and includes volumes comparable tothose found in supraglacial lakes outside of the main trough.Therefore, these structures can serve as fast pathways fordelivering copious amounts of surface melt water to thesubglacial system. Inasmuch, these crevasse systems arecapable of contributing to the documented rapid speed up andthinning of Jakobshavn Isbræ over the last decade and mightplay a critical role in the future evolution of its catchment.

6.1. Notation

Γoptical total uncertainty due to sensor radiometricnoise and atmospheric correction

ΓNye total uncertainty due to image registration,interpolation, and sensor spatial resolution

ΓArea absolute uncertainty in estimated drained areaga uncertainty in crevasse inundation areagd uncertainty in crevasse depth

ga_pixel uncertainty due to spatial resolution of theLandsat ETM+ sensor

gd_rad/atmos uncertainty due to sensor radiometric noise andatmospheric correction

gd_grid uncertainty due to interpolation of strain ratesgd_geo uncertainty due to image geometric registration

Δf difference in maximum and minimumenhancement factors equal to 2

Δx spatial displacement of crevasse featuresΔt time interval between successive satellite images_e measured strain rates from satellite imagery

e� strain rate adjusted for critical yield strain_ecrit critical yield strain rate

<_e> mean strain ratesri ice densityrw water density_Ψ saturated crevasse drainage rate_o saturated crevasse filling rateA flow-law rate factorAd bottom reflectance

Apeak maximum extent in saturated crevasse areaat surface melt amount in equivalent water heighta1 regression coefficient used to calculate melt

amountb1 regression coefficient used to calculate melt

amountdw water level in crevasse

fs enhancement factor used to scale drainagemagnitude from CV2 relative to that fromDas et al. [2008]

g gravitational accelerationgd effective attenuation coefficientHt binary positive degree-day indexKl spectral attenuation coefficient

L(zw, l) spectral radiance leaving the water body atsome depth and wavelength

L(0,l) spectral radiance at zero depthNh crevasse depth using modified Nye model

Nwater-free crevasse depth using modified Nye model forwater-free fractures

n flow-law exponentni inverse distance weighting (IDW) power law

parameterns number of points used to interpolate surface

strain rates measured from Landsat imagerynear the CV2 crevasse group

Qdas drainage from supraglacial lake observed byDas et al. [2008].

Qsatc Estimated potential drainage from CV2 usingoptical attenuation approach testimate depth

R1 reflectance of optically deep waterRw reflectance at some depth in the water column�T daily mean air temperature

u(x) interpolated value at a given point x using IDWui value of samples at points used in IDW

VOE estimate of potential drainage volume using theoptical attenuation model

VNE potential drainage volume using the modifiedNye model

vi initial background ice surface velocity measuredby Das et al. [2008]

vf final ice surface velocity measured after lakedrainage observed by Das et al. [2008]

wj(x) distance weights used in IDWyi estimated value used in calculating mean erroryi predicted value used in calculating mean errorzw crevasse depth based on optical attenuation

modelzs surface elevation

<zs> mean elevation for each saturated crevasse group

Appendix A: Derivation of Uncertainty Assessmentin Potential Volume Drainage Estimates[44] Given that most fractures are visually distinct, we

assume that errors related to spatial resolution are limitedto those segments of inundated fractures where the crackwalls are convergent in the horizontal plane near the crackedges and do not comprise a large proportion of the regionsmapped. For depths derived using the optical attenuationmodel, the relative relationships between solar geometryand crevasse orientations may impact both ga and gd byinfluencing the magnitude of shadowing within crevasses.Most crevasses maintain azimuths (generally north-south) thatare transverse to the main flow direction (towards the west).Solar azimuth angles during scene acquisitions indicate solarirradiance is primarily from the south/southwest (Table I)and are generally parallel to the prevailing fracture


16

orientations, with solar zenith angles (< 60�) indicatingreduced opportunity for shadowing. Therefore absoluteuncertainty in estimated drained area (ΓArea) is given by

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiga pixel

Adrain

� �2

þ ga pixel

Adrain

� �2s

(A1)

where Adrain is the estimated drained area between 8 and24 July over the CV2 crevasse group.[45] We assess uncertainty from gd_rad/atmos by examining

deep water pixel reflectance over the 8 July and two images.Deep water regions in the Landsat imagery demonstratereflectance values on the order of 0.07%. Ideally, reflectanceover deep water should be zero assuming the panchromaticband were completely free of noise (1.95 and 1.98Wm�2srmmexpressed in NEΔL for high and low gain pan band,respectively) [Scaramuzza et al., 2004] and that theatmospheric correction could completely remove the influenceof gaseous absorption on the shortwave components of thepanchromatic bandpass. A 1% difference in reflectance asinput to the optical attenuation model results in about a 10 cmdifference in estimated depth. Assuming the error in depthsderived from the optical attenuation model are an additivecombination of the impact of spatial resolution and sensor/data processing influences, the total error is Γoptical ¼ gapixel þgdrad=atmo which is 12.5 m. Therefore, the uncertainty intotal potential drainage volume estimates using the opticalattenuation approach is given by

OE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiΓoptical

VOE

� �2

þ Γarea

VOE

� �2s

(A2)

[46] We assess image registration by examining displace-ments in pixel over the rocky coast adjacent to the fjord thatJakobshavn drains. Rocky features should not exhibit anydiscernible displacement during the 16 day interval betweenthe July 8 and 24 scenes. We observed very small displace-ments no more than half a pixel (6.2 m). Lastly, we have toconsider errors associated with gridding strain rates (gd_grid).This was assessed through a cross-correlation analysis.Gridded strain rates were derived using IDW by removing asingle point. Afterwards, an assessment of interpolationerror was derived by comparing the estimated strain rate(yi) to measured strain rate (yi) for all seven point locationswhere strain rates were measured in the vicinity of the CV2group. An estimation of interpolation error is given by themean error (ME):

ME ¼ 1

ns

Xns

j¼1yi � yið Þ (A3)

with a value of -0.00203 d-1, where ns is the number ofmeasured strain rate points. This error results in a 15.7 mchange in depth based on the Nye model (for air-filled crackand ri = 917 kg m-3). Uncertainty in total potential drainagevolume for estimates using the Nye method is given by

NE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiΓNYE

VNE

� �2

þ Γarea

VNE

� �2s

(A4)

Appendix B: Derivation of Drainage Impact onShear Margin Mass Flux[47] We assess the potential impact of surface melt water

drainage from CV2 between 8 and 24 July 2007 on ice massflux relative to an observed tripling of ice velocity in responseto 4.4� 10�2� 0.01 km3 (Qdas) of water evacuated from asupraglacial lake documented by Das et al. [2008]. An initialbackground ice velocity (vi) of 0.25 m/day and final velocity(vf) of 0.75 m/day representing an enhancement of 0.5 m/daywas observed Das et al. [2008]. Using this data, we scale therelative impact of drainage from our largest saturated crevasse(CV2) of 9.23� 10�3 km3 through an “enhancement” factor(fs) which ranges between a value of (1) when Qdas = 0 km3

and (3) when Qdas = 4.4� 10�2 km3. Assuming fs scaleslinearly with available surface melt water input, then fs canbe estimated by

fs ¼ 1þ Δf =Qdas � Qsatc (B1)

where Δf is the difference in maximum (3) and minimum (1)enhancement factors, and Qsatc the measured drainage fromCV2. Given this, we provide a rough estimate of anenhanced ice velocity for melt water input at the magnitudeestimated using the relatively more conservative value werederived from the use of the optical attenuation method forcrevasse depth. Therefore, a vf for our value of melt waterinput from CV2 of Qsatc is given by

vf ¼ fs � vi (B2)

which represents ~42% speedup.

[48] Acknowledgments. This work was partially supported by NASA(grant number 09-CRYO09-15). B.R. Parizek was supported by the U.S.National Science Foundation under grants 0531211, 0758274, 0909335,and the Center for Remote Sensing of Ice Sheets (CReSIS) 0424589 andby NASA under grants NRA-04-OES-02, NNX-09-AV94G, and NNX-10-AI04G. We would like to thank R. Alley and S. Anandakrishnan, as wellas members of the Pennsylvania State University Ice and Climate Exploration(PSICE) Center for their input.

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