Quantifying Wedge-Ice Volumes in Yedoma and Thermokarst Basin Deposits

PERMAFROST AND PERIGLACIAL PROCESSESPermafrost and Periglac. Process. (2014)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/ppp.1810

Quantifying Wedge-Ice Volumes in Yedoma and Thermokarst Basin Deposits

Mathias Ulrich,1* Guido Grosse,2,3 Jens Strauss3 and Lutz Schirrmeister3

1 Leipzig University, Institute for Geography, Leipzig, Germany2 Geophysical Institute, University of Alaska Fairbanks, Fairbanks, AK, USA3 Alfred Wegener Institute Helmholtz Center for Polar and Marine Research, Telegrafenberg, Potsdam, Germany

* CoGeogE-ma

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ABSTRACT

Wedge-ice volume (WIV) is a key factor in assessing the response of ice-rich permafrost landscapes to thaw and inquantifying deep permafrost soil carbon inventories. Here, we present a method for calculating WIV in late PleistoceneYedoma deposits and Holocene thermokarst basin deposits at four study areas in Siberia and Alaska. Ice-wedge polygonsand thermokarst mound (baydzherakh) patterns were mapped on different landscape units using very high-resolution (0.5m/pixel) satellite imagery (WorldView-1 and GeoEye-1). In a geographic information system (GIS) environment,Thiessen polygons were automatically created to reconstruct relict ice-wedge polygonal networks, and field andpublished data on ice-wedge dimensions were used to generate three-dimensional subsurface models that distinguishbetween epi- and syngenetic ice-wedge geometry. The results reveal significant variations inWIV between the study sitesand within certain terrain units. Calculated maximumWIV ranges from 31.4 to 63.2 vol% for Yedoma deposits and from6.6 to 13.2 vol% for thermokarst basin deposits. Copyright © 2014 John Wiley & Sons, Ltd.

KEY WORDS: permafrost; ground ice; polygonal networks; GIS; remote sensing; Arctic

INTRODUCTION

Ice-rich permafrost landscapes undergo major geomorpho-logical change and hydrological reorganisation upon thaw(French, 2007; Shur and Jorgenson, 2007; Rowland et al.,2010; Grosse et al., 2011). Thus, detailed knowledge ofground-ice content and distribution is necessary to predictsite-specific landscape changes and to plan infrastructurein such regions (Nelson et al., 2002). Ground-ice contentis also a major factor in estimating organic carbon (OC)pools in permafrost (Strauss et al., 2013) and landscapeand ecosystem modelling of permafrost thaw impacts(Couture and Pollard, 2007). Estimates for OC pools below theactive layer, however, have large uncertainties because of limiteddata on ice contents (Hugelius et al., 2013; Kuhry et al., 2013).The total ground-ice content of a deposit comprises pore

and segregated ice (cryostructures) and massive ice bodiessuch as ice wedges (French and Shur, 2010). Although thevolume of pore and segregated ice can be determined fromsediment samples of known volume and weight taken fromcores or exposures, the volume of large ice bodies that are

rrespondence to: M. Ulrich, Leipzig University, Institute forraphy, Johannisallee 19a, 04103 Leipzig, Germany.il: [email protected]

right © 2014 John Wiley & Sons, Ltd.

seldom fully exposed is more difficult to quantify (Mackay,1977; Kanevskiy et al., 2013). Ice wedges are the mostcommon massive ice bodies in permafrost (Lachenbruch,1962; Mackay, 1990), and their networks are often expressedat the terrain surface as polygonal patterns that can beidentified on high-resolution remote sensing imagery (Musteret al., 2012). Ice-wedge polygons have been used to recon-struct local environmental conditions during their formation,based on specific morphometries, micro-topographies andpolygon sizes (Plug and Werner, 2002; Ulrich et al., 2011;Haltigin et al., 2012; Morse and Burn, 2013).

Quantifying polygonal patterns with aerial and satelliteimagery to determine wedge-ice volume (WIV) has beenconducted mostly at local scales (Pollard and French, 1980;Couture and Pollard, 1998; Bode et al., 2008; Güntheret al., 2013; Kanevskiy et al., 2013; Morse and Burn, 2013).With the advent of very high-resolution satellite sensors,semi-automated image classification techniques and spatialanalysis tools in geographic information system (GIS), itshould now be possible to extend such studies to much largerareas (Skurikhin et al., 2013).

Our objective is to develop a simple GIS-based methodfor calculating WIV using remote sensing and limitedground data. Our approach maps polygonal networks from veryhigh-resolution satellite remote sensing imagery, supplemented

Received 29 November 2013Revised 25 April 2014

Accepted 30 April 2014

M. Ulrich et al.

with field observations of the wedge-ice type, depth andwidth. We compare WIV results from ice-rich permafrostlandscapes in Siberia and Alaska, and differentiate WIV inlandscape units containing late Pleistocene syngeneticallyfrozen ice-rich deposits (Yedoma) (Strauss et al., 2012;Schirrmeister et al., 2013) and Holocene epigeneticpermafrost deposits in drained thermokarst lake basins(van Everdingen, 2005; French, 2007).

METHODS

Study Sites

Study sites were chosen based on the availability of bothremote sensing data and field data (Figure 1). Mappingareas were selected to represent polygonal networks inHolocene thermokarst basin deposits and networks orthermokarst mounds (baydzherakhs) outlining former ice-wedge polygons in Yedoma deposits in the same region(Figure 2). First, information about the wedge-ice type,vertical extent (i.e. depth) and width for a specific site wasobtained in as much detail as possible (Table 1). Becausepolygon-mapping accuracy depends on the resolution ofthe remote sensing data used (Ulrich et al., 2011), we usedonly space-borne imagery with a very high spatial resolutionof 0.5 m/pixel, in our case WorldView-1 and GeoEye-1imagery (Supporting Information Table S1).We focused on four sites in the continuous permafrost

zone: three in northeast Siberia (Ebe-Basyn-Sise Island,Cape Mamontov Klyk and the Buor Khaya Peninsula) andone in northwest Alaska (northern Seward Peninsula)(Figure 1). All sites are characterised by Yedoma landscapes,which feature uplands of late Pleistocene ice- and organic-richsilty deposits containing segregated ice and large syngeneticice wedges that are part of a relict polygonal ice-wedgesystem (Schirrmeister et al., 2011, 2013). The uplands aredissected by numerous thermokarst lakes and drained lake

Figure 1 Location of study sites within the zone of continuous permafrost: (a)Ebe-Basyn-Sise Island. (b) Cape Mamontov Klyk. (c) Buor Khaya Peninsula.(d) Seward Peninsula. Map of permafrost distribution modified after Brownet al. (2002). This figure is available in colour online at wileyonlinelibrary.com/journal/ppp

Copyright © 2014 John Wiley & Sons, Ltd.

basins, as well as by thermo-erosional valleys formed duringthe Holocene. Polygonal networks with epigenetic ice wedgesdeveloped in thermokarst basins after lake drainage andpermafrost aggradation (Wetterich et al., 2009; Jones et al.,2012; Regmi et al., 2012).

Polygonal Pattern Mapping

Ice-wedge polygons were digitised manually withinArcGISTM (Figure 2). In order to assess the influence of areaand location of the mapping region on the resulting averagepolygon diameter, an initial mapping area of 500 × 500 m atthe Ebe-Basyn-Sise site was subdivided into four 250 m and25 100 m squares that were individually analysed for thepolygon diameter (Figure 3). Because the mean of themapped polygon diameter and the polygon morphometryshowed only small variations between each 250 m square(Figure 3), we decided that a mapping area of 250 × 250m (62 500 m2) adequately captured average polygon charac-teristics and we used this area size for all sites. Only clearlyrecognisable cracks and troughs enclosing an individualpolygon were mapped along their centrelines (Figure 4a).A polygon was considered in the data-set if the individualpolygon form could be identified precisely. Finally, thediameter of each polygon was calculated as the square rootof the ratio of the quadruple polygon area to circle constant(√(4 × area/π)) (Ulrich et al., 2011).

Calculating the WIV of Yedoma deposits is challengingbecause thin Holocene cover deposits frequently obscurerelict ice-wedge systems. However, polygons are oftenexposed along thermokarst or thermo-erosion features,where baydzherakhs reveal the remnant polygonal networkwith Yedoma deposits, in particular the location of formerpolygon centres that existed before ice-wedge melting.Therefore, the polygonal geometry can be mapped bymeasuring the distance between adjacent baydzherakhcentres using a line feature class in ArcGISTM. Specifically,we measured the distances from the centre of one individualbaydzherakh to that of each neighbouring and clearly iden-tifiable baydzherakh (Figs. 2 and 4a).

To reconstruct the polygonal network based on polygon-centre points, we created Thiessen (Voronoi) polygons inArcGISTM, a procedure that is implemented in moststandard GIS software to display the spatial distribution ofselected point data. First, all mapped polygon-centre pointswere automatically placed and connected in a triangulatedirregular network (TIN) in ArcGISTM. Perpendicular bisec-tors were then generated for each triangle edge, formingthe edges of the Thiessen polygons, which should representthe network around the baydzherakhs (Figs. 4a and 5). Totest the validity of this approach, we compared the resultsfrom manual mapping of well-developed ice-wedge poly-gons and baydzherakh distances with the results fromThiessen polygons generated using the polygon-centrepoints for the same study site. Visually, the results are sim-ilar, suggesting that Thiessen polygons probably representthe former ice-wedge network (Figure 5). Based on this

Permafrost and Periglac. Process., (2014)

Figure 2 Satellite image subsets of mapped polygonal patterns on thermokarst basin deposits (left) and Yedoma deposits (right). Mapping was performed within apredefined area of 62 500 m2 (box size). On Yedoma deposits, baydzherakh centres were mapped with point distances except for site (a) Ebe-Basyn-Sise Island(72°54’N, 123°23’E), which could be recognised on the surface as a polygonal ice-wedge system. (b) Cape Mamontov Klyk (73°32’N, 118°05’E). (c) BuorKhaya Peninsula (71°39’N, 132°19’E). (d) Seward Peninsula (66°33’N, 164°27’W). North is at the top. For details on the satellite data, see SupportingInformation Table S1.

Wedge-Ice Volume Calculation in Yedoma and Thermokarst Basin Deposits

Copyright © 2014 John Wiley & Sons, Ltd. Permafrost and Periglac. Process., (2014)

Table

1Resultsof

polygonmapping,therangeof

ice-wedge

sizesused

asinputforthree-dimension

alsubsurface

model

(3D

SSM)creatio

nandresulting

wedge-ice

volumes

(WIV

)forthermokarstbasinandYedom

adepositsat

each

site.

Site

Meanof

themapped

polygondiam

eter,m

(Min/M

ax)

Ice-wedge

size

inthermokarstdeposits,m

Top

width/bottom

width/depth

Ice-wedge

size

inYedom

adeposits,m

Top

width/bottom

width/depth

WIV

inthermokarst

deposits(%

)WIV

inYedom

adeposits(%

)

Therm

okarst

Yedom

aMin

Max

Min

Max

Min

Max

Min

Max

Ebe-Basyn-Sise1

12.7

(6.5

/22.0)

17.6

(8.4

/27.8)

N/A

1.0/0.0/3.0

3.0/0.5/8.0

5.0/0.7/12.0

N/A

8.2

20.2

31.4

CapeMam

ontovKlyk2

23.0

(13.8/32.8)11.7*(5.2

/19.3)0.2/0.0/1.0

1.4/0.0/3.0

1.0/0.8/8.0

4.0/3.0/20.0

1.0

6.6

16.7

56.1

BuorKhaya

Peninsula3

23.8

(14.4/34.8)14.9*(7.2

/28.7)0.9/0.0/2.0

3.0/0.0/6.0

2.0/1.5/5.0

6.0/5.0/18.0

4.0

13.2

23.9

63.2

Sew

ardPeninsula4

20.6

(11.8/31.5)16.7*(6.8

/36.4)0.8/0.0/1.5

1.5/0.0/3.0

2.5/1.0/5.0

4.0/2.0/8.0

4.2

7.7

21.0

34.5

Note:

WIV

calculations

arebasedon

thetotalvolumeof

each

individual3D

SSM

(see

SupportingInform

ationTableS2).*

Determined

bymeasuring

thedistance

be-

tweenadjacent

baydzherakhcentres.

1Dataon

ice-wedge

sizesby

Schirrm

eister

etal.(2003).2Dataon

ice-wedge

sizesby

Meyer

andDereviagin(2004)

and

Schirrm

eister

etal.(2008,

2011).

3Dataon

ice-wedge

sizesby

Strauss

andSchirrm

eister

(2011).4Dataon

ice-wedge

sizesby

Parsekian

etal.(2011)

andG.Grosse

(unpublisheddata).

M. Ulrich et al.


similarity and the goodness of fit between the diameter ofthe manually mapped polygons and the automatically de-rived Thiessen polygons (Figure 6), this approach appearsto be quicker for mapping polygons across large areas.Non-conformities during Thiessen polygon generationoccur at the edges of mapped polygonal patterns, becausethe lack of neighbouring points prevents the correct gener-ation of a Thiessen polygon. Such polygons were excludedfrom further analysis.

WIV Calculation

WIV calculations were completed in ArcGISTM 3D Analystby creating a set of three-dimensional subsurface models(3D SSMs) of wedge ice and sediment columns based onthe TIN polygons. A TIN contains a triangular network ofmass points and is a vector-based representation of thesurface terrain that can be derived from elevation data inalmost any GIS software. In addition, the ice-wedge type,vertical extent (i.e. depth) and width at our specific siteswere extracted from the literature or from our field data(Table 1). The 3D SSMs used contour-based elevation dataassigned to the mapped ice-wedge polygons in thermokarstbasins and to the Thiessen polygonal networks on Yedoma(Figure 7).

WIV calculations included several stages (Figure 4).First, a buffer representing widths at the top of the icewedges was created around the polygon edges (i.e. mappedfrost cracks and trough centrelines) (Figure 4b). Second, anelevation equal to the vertical extent of the ice wedge wasassigned to the new buffer polygons, while an elevation ofzero was assigned to the mapped frost cracks and troughcentrelines to represent the base of the wedge. For Yedomaice wedges, a second buffered network was generated andassigned with an elevation of zero representing the wedgewidth at the bottom, with the simplified assumption thatthe shape of syngenetic ice wedges resembles an invertedisosceles trapezoid in which the width decreases onlyslightly downward. In contrast, epigenetic ice wedges inthermokarst basins are usually wedge- (or V) shaped(Mackay, 1990).

Based on the top and bottom contour lines, a 3D SSMwas calculated for each site that represents the volume ofthe sediment-rich column in the centre of the polygons(Figure 4c). Because the WIV is represented by the gapsbetween the polygon-centre columns (Figure 7), it can becalculated as the difference between the total volume (icewedges plus sediment column) and the 3D SSM of thepolygon centres. The total volume of a polygonal pattern(Supporting Information Table S2) was calculated inArcGISTM 3D Analyst as the volume below an imaginarysurface plane completely covering the mapped polygonalfield and assigned with an elevation equal to the verticalextent of the ice wedge. The output is a vector layer thatseparates the areas representing the ice-wedge network fromthe areas representing the polygon-centre sediments andassigns volumes to both (Figure 4d).


Figure 3 Maps showing the effect of different mapping area sizes on polygon size statistics for thermokarst basin deposits (left) and Yedoma deposits(right) at the Ebe-Basyn-Sise study site. Mapping box area and mean of the mapped polygon diameter (given in metres) are illustrated in yellow for 500 ×500 m, blue for 250 × 250 m and red for 100 × 100 m squares. Each square is considered individually. Generally, the differences in the mean value ofpolygon diameters increase with decreasing mapping area. Thus, variations in polygon geomorphometry at a specific site should be compensated by alarger mapping area. This figure is available in colour online at wileyonlinelibrary.com/journal/ppp


To determine the potential range of WIV at our studysites, we created separate 3D SSMs for the maximum andminimum ice-wedge widths and depths (Table 1). TheWIV was calculated for a generalised horizontal layer thatcontains ice wedges. The active layer thickness and micro-topography of the polygons were not considered.Finally, we calculated the equivalent ground-ice thick-

ness (EGIT) of the WIV to elucidate the potential im-pacts of ice-wedge melt on the landscape. The EGITrepresents an equivalent (theoretical) ice layer that corre-sponds solely to the volume of wedge ice in a givendeposit thickness.

RESULTS AND DISCUSSION

WIV and the Potential for Surface Subsidence

The highest WIV was calculated for Yedoma deposits,reflecting the prevalence of very large syngenetic icewedges in these thick sediments. The calculated WIV max-ima represent the maximum amount of wedge ice at eachsite, with the highest values obtained for Yedoma of theBuor Khaya Peninsula (63.2 vol%) and Cape MamontovKlyk (56.1 vol%) sites. Smaller WIV maxima were calcu-lated for Yedoma sites on the Seward Peninsula (34.5 vol%) and Ebe-Basyn-Sise (31.4 vol%), where ice wedgesare considerably smaller (Table 1). The WIV minima forYedoma deposits range from 23.9 vol% for the BuorKhaya Peninsula to 16.7 vol% for Cape Mamontov Klyk.The WIV maxima in Holocene thermokarst basin

deposits range from 13.2 vol% for the Buor Khaya


Peninsula to 6.6 vol% for Cape Mamontov Klyk. Valuesfor minimum WIV in thermokarst basin deposits varybetween 4.2 vol% for the Seward Peninsula and 1.0 vol%for Cape Mamontov Klyk.

Generally, the WIV values are consistent with the ice-wedge type and age of the host material. Yedoma andthermokarst basin deposits differ considerably in theirwedge-ice contents (Table 1; Figure 7). The largest WIVhighlights the potential impact that permafrost disturbanceand thaw could have on these sites (Rowland et al., 2010;Grosse et al., 2011). Assuming an EGIT from the WIV, weare able to estimate the potential surface subsidence causedby complete melting of ice wedges alone. For estimatingthe EGIT, the total deposit thickness is an importantparameter, which in most cases is not represented by themaximum ice-wedge depths used in our calculations.Thus, adopting an average Yedoma deposit thickness of19.4 m derived from 20 Siberian and Alaskan sites byStrauss et al. (2013, cf. Table S2), the EGIT related toour calculated WIV maxima (Table 1) would range onaverage from 12.3 m to 6.1 m in Yedoma deposits.Accordingly, for an average thermokarst basin depositthickness of 5.5 m derived from ten Siberian and Alaskansites by Strauss et al. (2013, cf. Table S3), the EGIT corre-sponding to the maximum WIV range in Holocenethermokarst basin deposits (Table 1) would range between0.7 m and 0.4 m.

Besides using average deposit thicknesses as describedbefore, Table 2 shows EGIT calculations from the wholeWIV range of our four study sites for various thicknessesof Yedoma and thermokarst basin deposits as reported inthe literature (e.g. Kanevskiy et al., 2011; Schirrmeister


Figure 4 Procedure for wedge-ice volume (WIV) calculation using high-resolution remote sensing and field data. (a) Mapping of ice-wedge polygons (thermokarstbasins) or baydzherakhs and derived Thiessen polygons (Yedoma uplands). (b) Buffer creation around the polygon edges based on uppermost ice-wedge widths. Inthe case of Yedoma ice wedges, the second buffered network representing the wedge width at the bottom is not illustrated. (c) Creation of triangulated irregularnetwork (TIN)-based three-dimensional (3D) subsurface models. For details on 3D visualisation, see Figure 7. (d) The resulting vector layer divides the volumesfor the wedge ice (blue) and the polygon-centre sediments (dark grey). This figure is available in colour online at wileyonlinelibrary.com/journal/ppp

M. Ulrich et al.

et al., 2011; Strauss et al., 2013). Assuming a range in thethickness of Yedoma deposits from 5 m to 50 m in northernpermafrost regions, we infer that the EGIT based on ourcalculated WIV maxima would range from 3.2 m to 31.6 m,respectively. For a range of thermokarst basin deposit thick-nesses of 1 to 15 m, the maximum WIV calculated for Holo-cene thermokarst basin deposits corresponds to an EGIT of0.1 to 2.0 m, respectively.Although the WIV in Holocene thermokarst basin

deposits is comparatively small due to young and smallice wedges, the total volumetric ground-ice content in suchsettings can be similar to that of Yedoma deposits due toabundant pore and segregated ice (Kanevskiy et al., 2013;Strauss et al., 2013). To determine fully the thaw subsi-dence potential of any deposit, both the volume of excess


pore and segregated ice and the WIV must be consideredwhen estimating an ice layer equivalent to the totalground-ice content (Günther et al., 2013).

Polygon Diameter

Size differences between mapped polygons in the late Pleisto-cene andHolocene deposits (Table 1) are largely in agreementwith the inferred age of these landscape units (Figure 5).Smaller polygon diameters were expected for Yedomadeposits because climate conditions during their formationwere much colder. Moreover, when thermal contractioncracking occurs over a long period of time, polygon subdi-vision is increased on older surfaces (Lachenbruch, 1962;Plug and Werner, 2002). The mean polygon diameter at


Figure 5 Comparison of polygon geomorphometry between manuallymapped polygonal patterns (white lines) and automatically derived Thiessenpolygons (blue lines). For each site, polygonal networks on thermokarst basindeposits are shown on the left and polygonal networks on Yedoma deposits onthe right. White values correspond to the average of the mapped polygon sizesand the average of the measured distances between adjacent baydzherakhcentres. Blue values indicate the average of Thiessen polygon sizes. (a)Ebe-Basyn-Sise Island. (b) Cape Mamontov Klyk. (c) Buor KhayaPeninsula. (d) Seward Peninsula. At sites (b–d), the Thiessen polygonalnetworks were derived from the centre points of mapped baydzherakhs. Thisfigure is available in colour online at wileyonlinelibrary.com/journal/ppp



the drained thermokarst lake basin site on Ebe-Basyn-Sise,however, is exceptionally small compared to the polygondiameter on the local Yedoma deposits (Figure 5a). Onereason could be high thermal contraction cracking activityin the drained lake basin (Figure 2a). In this case, it appearsthat gradual lake drainage resulted in a dense orthogonallyoriented ice-wedge network parallel to the retreating lakeshore. The local nature and activity of ice-wedge polygondevelopment are also influenced by other climate and subsur-face factors, such as air and ground temperature variations,ground-ice content, grain size, or ground insulation (Mackay,1990; Christiansen, 2005; Ulrich et al., 2011; Morse andBurn, 2013).

Uncertainties in WIV Calculations

WIV is a critical parameter for quantifying soil OC budgets,assessing the general vulnerability of an area to disturbanceand thaw, and designing engineering solutions forinfrastructure. Data on ice-wedge size are often based onobservations from coastal, riverine, or lake bluff expo-sures, where ice wedges can be exposed by erosion alongvarious angles and so the actual ice-wedge width may beoverestimated (Mackay, 1977). Our calculation of poten-tial minimum and maximum WIV shows that ice-wedgesize is an important parameter for quantifying total WIVat an individual study site and therefore requires field datacollection on ice-wedge width and depth to reduce uncer-tainties in the WIV calculation.

Our calculated WIV minima are conservative valuesbecause minimum ice-wedge depths are likely unrepresenta-tive of the whole deposit thickness, and minimum ice-wedgesizes may relate to younger landscape componentsthat are unrepresentative of the larger area. Wesuggest that the actual WIV in a larger area of Yedomaand thermokarst basin deposits will be closer to our calculatedWIV maxima.

Our WIV calculations have limitations. First, ourassumption that the wedges are composed of 100 per centice may not always be the case because thermal contractioncracks can infill with ice, sediment, or mixtures of the two(French, 2007). For both Yedoma and thermokarst basindeposits, however, the wedges usually have very low sedi-ment contents, which therefore should result in only slightoverestimations in our WIV. Second, the shape and sizesof ice wedges vary considerably, and two or three genera-tions of syngenetic ice wedges can exist within the samepolygonal system. Hence, ice-wedge shape may changeover the time of deposit accumulation and thus vary withdepth (Mackay, 1990; Kanevskiy et al., 2011). Ourapproach generalises ice-wedge shape, and more detailed fieldknowledge of ice-wedge sizes and depths at specific siteswould improve WIV calculations. Geophysical methods suchas ground penetrating radar (GPR) are becoming more sophis-ticated in detecting the dimensions of subsurface ice bodiesand could provide valuable data for such assessments (Munroeet al., 2007; Bode et al., 2008; Watanabe et al., 2013). Third,


Figure 6 Relationship between manually mapped polygon sizes and automatically derived Thiessen polygon sizes. Scatter plots are shown for both thermokarstbasin and Yedoma deposits of (a) Ebe-Basyn-Sise Island, but only for thermokarst basin deposits of (b) CapeMamontov Klyk, (c) the Buor Khaya Peninsula and(d) the Seward Peninsula. (e) Linear regression values of all mapped polygon sizes against all Thiessen polygon sizes.

M. Ulrich et al.

our image-based polygon-mapping approach probably under-estimates ice-wedge density because some polygon cracks orice-wedge troughs have little or no visible surface expres-sion (Haltigin et al., 2010).Overall, our procedure for 3D WIV calculations includes

a realistic polygon geomorphometry, as well as the shapeand size of ice wedges at multiple specific sites (Figure 7).


Our technique therefore allows spatially explicit assessmentof WIV and provides more detail about ground-ice distribu-tion than WIV estimations from bluff exposures alone(Kanevskiy et al., 2011). It also enhances existing approachesthat rely on average polygon and/or ice-wedge geometries(Pollard and French, 1980; Günther et al., 2013; Kanevskiyet al., 2013; Strauss et al., 2013).


Figure 7 Examples of three-dimensional subsurface models (3D SSMs) for an ice-wedge polygonal field in a drained thermokarst lake basin on the BuorKhaya Peninsula (upper) and for a Thiessen polygonal network on Yedoma deposits on Ebe-Basyn-Sise Island (lower). Gaps between the polygon-centrecolumns represent an epigenetic ice-wedge network (upper) and a syngenetic ice-wedge network (lower). For further information on calculations based on3D SSMs, see WIV Calculation in the Methods section. This figure is available in colour online at wileyonlinelibrary.com/journal/ppp

Table 2 Equivalent ground-ice thickness (EGIT) for Yedoma and thermokarst basin deposits of various thicknesses.

Depositthickness,m

EGIT Yedoma, m EGIT thermokarst, m

Min (WIV = 16.7%)1 Max (WIV = 63.2%)2 Min (WIV = 1.0%)3 Max (WIV = 13.2%)4

1 — - < 0.1 0.15 0.8 3.2 < 0.1 0.710 1.7 6.3 0.1 1.315 2.5 9.5 0.2 2.020 3.3 12.6 - -25 4.2 15.8 - -30 5.0 19.0 - -35 5.8 22.1 - -40 6.7 25.3 - -45 7.7 28.4 - -50 8.4 31.6 - -

Note: EGIT specifications for thicknesses > 15 m in thermokarst basin deposits and < 5 m in Yedoma deposits areexcluded from the calculations as these are seldom found in nature. Possible deposit thicknesses were used according toKanevskiy et al. (2011), Schirrmeister et al. (2011) and Strauss et al. (2013, cf. Supporting Information). 1 MinimumYedomaWIV among our four study sites. Identified at Cape Mamontov Klyk. 2 Maximum YedomaWIV among our fourstudy sites. Identified at Buor Khaya Peninsula. 3 Minimum Thermokarst WIV among our four study sites. Identified atCape Mamontov Klyk. 4 Maximum Thermokarst WIV among our four study sites. Identified at Buor Khaya Peninsula.


Copyright © 2014 John Wiley & Sons, Ltd. Permafrost and Periglac. Process., (2014)

M. Ulrich et al.

CONCLUSIONS

The average WIV for Yedoma deposits for the four studysites is 46.3%, which is slightly less than the ice-wedgecontent used in recent estimations of the circum-arcticpermafrost OC pool (~50 vol%). The WIV can vary consid-erably between different permafrost regions and within astudy site. Calculated WIV maxima range from 63.2 vol%to 31.4 vol% in late Pleistocene Yedoma deposits and from13.2 vol% to 6.6 vol% in Holocene thermokarst basindeposits in Siberia and Alaska. Maximum WIV can be morethan double the calculated minimum WIV at a site. Suchlocal aspects in WIV calculation should be considered whenthe vulnerability of permafrost landscapes to climate changeis assessed.Our technique for calculating WIV can be applied to any

permafrost region with polygonal patterned ground. Theapplication of 3D SSMs based on TINs enables the use oflarge data-sets, and the automatic creation of Thiessen poly-gons allows reconstruction of relict polygonal ice-wedgenetworks. Thiessen polygon creation based on polygon-centrepoints may facilitate mapping of polygonal patterned groundover large regions. Thus, more detailed and realistic valuesof ground-ice volumes in permafrost deposits could beimplemented in future assessments of the permafrost OC pooland the vulnerability of permafrost to thaw.


ACKNOWLEDGEMENTS

We thank V. E. Romanovsky, M. Kanevskiy, A. L. Kholodovand all colleagues of the Permafrost Laboratory (University ofAlaska Fairbanks (UAF), Fairbanks, Alaska, USA) as well asS. Wetterich (Alfred Wegener Institute (AWI) Potsdam, Ger-many) for fruitful discussion during an earlier stage of thiswork. This research has been supported financially by theGerman Federal Ministry of Science and Education (project01DM12011), and is part of the joint Russian-German projectPolygons in Tundra Wetlands: State and Dynamics underClimate Variability in Polar Regions (German Research Foun-dation (DFG), grant number HE3622-16-1). M. U. wassupported by the DFG (grant number UL426/1-1). G. G. wassupported by the NSF OPP (National Science Foundation -Office for Polar Programs, 0732735), NASA (NNX08AJ37G)and an European Research Council (ERC) Starting Grant(338335). J. S. was supported by the German National AcademicFoundation. We also thank F. Günther and P. P. Overduin (AWIPotsdam) for providing GeoEye-1 imagery. WorldView-1 datawere provided (to G. G.) through the Polar Geospatial Center atthe University of Minnesota. M. U. thanks A. and D. Kilbourn(Fairbanks, Alaska) for their great support and hospitality. The pa-per benefited fromEnglish proofreading byCandace S.O’Connor(UAF). Finally, wewould like to thankM.Kanevskiy, T.Haltiginand the Editor, J.Murton, for their reviews and helpful comments.

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