Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 www.elsevier.com/locate/palaeo

Quantifying climate and mass balance in north during the ⁎ Brice R. Rea a, , David J.A. Evans b

a and Environment, School of Geosciences, University of Aberdeen, Aberdeen AB24 3UF, UK b Department of Geography, University of Durham, South Road, Durham DH1 3LE, UK Received 28 March 2006; received in revised form 6 October 2006; accepted 16 October 2006

Abstract

Øksfjordjøkelen is located at ∼70° N on the Troms– border in North Norway. During the Younger Dryas, it was decoupled from and sat just beyond the margin of the Scandinavian . At this time the major in Troms and Finnmark were ice-free with outlet from the icefield filling a number of smaller side valleys. Only one outlet from the icefield, Sörfjorddalen, is temporally well-constrained by 14C dating and association with the Main Shoreline (associated with a period of minimal crustal rebound dated to the Younger Dryas). Sörfjorddalen is reconstructed using a centre-line iterative model and assuming a no-slip basal boundary condition. This assumption of cold-based ice is supported by the geomorphological evidence of angular bouldery fronto-lateral formed during the Younger Dryas. The equilibrium line altitude for the Sörfjorddalen is calculated using both the Balance Ratio and Accumulation Area Ratio methods, and this is used to constrain the snout positions (generally to mapped moraines) of the other outlets. This approach assumes similarity of mass balance gradients and geometries of the outlet glaciers which is supported by present-day symmetry of the icefield. This method is extremely useful in such environments where dateable material is often difficult, if not impossible, to find. Some margins terminated in deep water where bathymetry was lacking, making calving quantification problematic with subsequent impacts on equilibrium line altitudes poorly constrained. These deep-water terminating snouts were discounted from subsequent palaeo-climate reconstructions. An empirical equilibrium line altitude temperature-precipitation relationship was used to define limits of required to sustain the reconstructed icefield. Palaeo-precipitation estimates were refined using a palaeo-temperature estimate for the Younger Dryas from Andøya. Calculations of ice flux through the equilibrium line altitude were used to further constrain the mass balance characteristics of the reconstructed icefield and these suggest similarities with ice masses found in the northern (Nordaustlandet) regions of Svalbard. © 2006 Elsevier B.V. All rights reserved.

Keywords: Scandinavian Ice Sheet; Equilibrium line altitude; ELA; Balance ratio; Accumulation area ratio; Palaeoclimate; Younger Dryas; Mass balance; Plateau icefield; Mass balance gradient

1. Introduction

Øksfjordjøkelen is a plateau icefield located on the Troms–Finnmark border in, North Norway (Fig. 1), a ⁎ Corresponding author. geographical position significant to understanding both E-mail address: [email protected] (B.R. Rea). and present and small-scale and large-scale climate

0031-0182/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.palaeo.2006.10.010 308 B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330

Fig. 1. Troms–Finnmark regions of North Norway, location of Øksfjordjøkelen, and the margin of the Scandinavian Ice Sheet (thick black line) during the Younger Dryas (from Sollid et al., 1973). Meterological stations at and Kvænangen are also shown.

dynamics. It is in a region currently affected by the sitions are defined by a combination of 14C dating, North Atlantic Oscillation, the Arctic Oscillation, the association with marine limits and an assumed com- Polar Front and the North Atlantic Drift. The aim of this monality of ELAs (Evans et al., 2002). Using a widely paper is to reconstruct the Younger Dryas (YD) con- applied temperature-precipitation relationship climate at figuration and ice dynamics of Øksfjordjøkelen which at the ELA is defined for a number of outlet glaciers. Ice this time had decoupled from the Scandinavian Ice flux through the ELA is calculated and in combination Sheet (SIS), the margin of which lay some 10 km further with reconstructed accumulation and gradients to the south (Sollid et al., 1973), with the main fjords allows quantitative estimates of mass balance to be being for the most part ice-free (Evans et al., 2002). Due made. Based on these estimates climatic conditions on to its size Øksfjordjøkelen is likely to have reacted the north-western margin of the Scandinavian Ice Sheet “rapidly” to the YD cooling and so the reconstructed YD are assessed. icefield may be assumed to be in equilibrium with its contemporary climate. The lack of organic material in 2. Background sedimentary deposits associated with the former limits of Øksfjordjøkelen, hampers the construction of chro- The fjords and plateaux of the Bergsfjord Peninsula nological control for all margins of the icefield. This were fully submerged beneath ice during the LGM (Rea paper presents an approach that utilises a single, well et al., 1996), and as proceeded, the ice sheet dated to approximate the ELA (equilibrium line margin retreated up the fjords producing regional mo- altitude) for the icefield during the YD. The ELA is raine systems during still stands or readvances (Ander- assumed to represent an integration of the local climate, sen, 1965; Sollid et al., 1973). The sea level history and mainly temperature and precipitation (Benn and Evans, ice retreat pattern in Finnmark and western Troms re- 1998), and not assumed to vary significantly over the gions have been investigated respectively by Sollid et al. icefield, though glacier hypsometry may significantly (1973) and Andersen (1965, 1968). Evans et al. (2002) alter the ELA (Benn and Lehmkuhl, 2000). The icefield have summarised and integrated these regional data sets, is reconstructed using a perfect-plasticity approximation placing them in context for the Bergsfjord Peninsula. for ten outlet glaciers that drain the plateau. Snout po- From oldest to youngest these are the L11 (15–14 ka 14C B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 309

BP), Outer Porsanger, Skarpnes (12.5 ka 14C BP), icefield landsystem (Rea et al., 1998; Rea and Evans, Tromso–Lyngen (12–10 ka 14C BP), Stordal (9–10 ka 2003) is summarised briefly here. Plateau summits of 14C BP) and Post-Stordal (Evans et al., 2002). Land- north Norway are characterized by a blockfield cover forms of relevance to this study are moraines, marine (Whalley et al., 1981; Gellatly et al., 1988; Rea et al., limits and associated deltas from the Tromsø–Lyngen 1996). Above outlet valley heads there may be marginal substage (T–LS) taken to be synonymous with the meltwater channels, bedrock erosional forms, such as Younger Dryas (Andersen, 1968; Sollid et al., 1973). The roches moutonnées and striae, and exposed bedrock T–LS is manifest in many localities in the region as a stripped of its former blockfield cover (Rea and Whalley, marine platform and shoreline notch (Main Shoreline). 1994; Rea et al., 1996). On the larger plateaux, low The shoreline is developed only outside and cross cuts amplitude and discontinuous moraines document the re- the distal faces of many T–LS moraines, indicating cession of Little maximum glaciers (Gellatly synchroneity of the features (Marthinussen, 1960, 1962). et al., 1989; Whalley et al., 1995). In valleys with The T–LS configuration of Øksfjordjøkelen was extensive rock faces the largest accumulations of glacial characterized by an expanded version of the present day occur as lateral and latero-frontal moraines plateau icefield from which outlet lobes descended into (Rea et al., 1998) formed from passively transported surrounding valleys and heads. The plateau supraglacial and englacial rock avalanche/rock fall

Fig. 2. (a) Glacial in outlet valleys from Øksfjordjøkelen related to the Tromsö–Lyngen Substage (Evans et al., 2002). (b) View along Isfjorden towards the southern margin of Øksfjordjøkelen, showing the plateau, the plateau icefield and the outlet of Isfjordjøkelen and its reconstituted glacier produced by ice avalanching down the precipitous fjord head. 310 B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330

Fig. 2 (continued). material. Some subglacially-derived material appears in moraines. At lower altitudes in the outlet valleys the moraines and in valley bottoms as a patchy cover. bouldery latero-frontal moraines, shorelines and deltas Where outlet glaciers terminated in the fjords, ice mar- document the former limits of extended outlet glaciers. ginal locations are marked by Gilbert-type deltas. 3.2. Tromsö–Lyngen substage (T–LS) 3. Field evidence for Younger Dryas plateau icefield coverage Fig. 2 presents a simplified map illustrating the moraines and raised marine landforms mapped around 3.1. Present-day Øksfjordjøkelen (Evans et al., 2002). Local moraines and associated raised marine features (Evans et al., Øksfjordjøkelen currently covers ca. 40 km2, with 2002) have been temporally well-constrained using six outlet glaciers draining into surrounding valleys regional isobase maps (Marthinussen, 1960). During the (Fig. 2a). The altitudinal range of the plateau is ∼800– Older and Younger Dryas ten major outlet glaciers 1175 m and the altitudinal range of the icefield is ∼500– drained Øksfjordjøkelen, descending close to, or below, 1200 m, although Isfjordjøkelen avalanches ice down sea level which was ∼40–55 m above present-day sea the precipitous head of Isfjorden and into the sea (the level (increasing inland). Brief, valley-by-valley, last mainland European glacier to debouch ice directly descriptions of relevant T–LS geomorphological evi- into the sea; Fig. 2b). The ELA lies within the range dence (moraines, marine deltas and limits) are presented 900–1000 m based on the line altitude. Since the below. (LIA), ice retreat has revealed either Sörfjorddalen contains abundant geomorphological blockfield with patterned ground or areas that have been evidence of glacier activity (Fig. 2), with the oldest stripped of blockfield characterized by extensive areas moraine at the valley mouth cross cut by a marine bench of striated bedrock and roches moutonnées separated by at 43 m, and is interpreted to represent the Tromsø– moraines (Rea et al., 2000). In the valley heads, LIA Lyngen substage and Main Shoreline event. Mya outlet glaciers formed bouldery lateral and fronto-lateral truncata shells recovered from marine muds beyond B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 311 the moraine, have yielded radiocarbon ages of 11,130± valleys only frontal moraines and marine deltas ‘best 120 and 9759±70 yr BP (Evans et al., 2002). suited’ to the T–LS due to their association with sea The marine limit in Fjorddalen is 40 m asl, lower than level elevation can be identified. In order to test the the Main shoreline, indicating glacier occupation during validity of these terminus locations, a valley centre-line the T–LS. The outermost moraine has been assigned to flow model has been used to reconstruct Sörfjorddalen. the Tromsø–Lyngen substage (Evans et al., 2002), but it Glacier centreline altitudes, from Eq. (1), are overlaid lies at only 20 m, indicating that the glacier snout onto the DEM and the glacier margins interpreted terminated as a calving front in shallow water (∼25 m). manually along the valley sides and onto the plateau Three outlet glaciers drained east into Øksfjorden, where the margins where defined by the ice divides. which was ice-free at the fjord head by the end of the From the centreline and ice marginal co-ordinates a T–LS (Evans et al., 2002). The absence of the Main gridded 100 m glacier surface was produced. shoreline indicates that all three outlet glaciers filled The reconstruction is extrapolated to 3D and the ELA their valleys during the T–LS (Fig. 2); the marine limits limits are constrained using the balance ratio (BR) in the three valleys are at 38 m asl (Tverrfjorddalen), method (Furbish and Andrews, 1984; Benn and Evans, 30.5 m asl (Storelvdalen) and 34 m asl (Baccavuon- 1998; Benn and Lehmkuhl, 2000). The assumption is vag'gi) (Evans et al., 2002). made, that the ELA is a function of winter accumulation Two outlets drain to the south, with the marine limit and summer ablation only. No account is taken of local in Skalsadalen marked by an erosional bench cut at 64 m snow re-distribution effects on the ELA (Dahl and indicating the valley was ice-free prior to the T–LS (the Nesje, 1992; Mitchell, 1996; Benn and Ballantyne, Main shoreline should be ∼53 m) (Fig. 2). There are no 2005) because there is a lack of significant asymmetry in moraines present within the valley so the T–LS margin the current icefield geometry associated with the is unconstrained. Similarly, in Isfjorden, moraines and prevailing winds and moisture source. The ‘best suited’ marine limits, except those relating to the recent LIA T–LS snout positions are identified, where necessary, advances, are absent (Fig. 2). by selecting moraines that result in ELAs approximating Three glaciers drained west into Langfjord. A delta in that of Sörfjorddalen. Isdalen at 40 m demarcates a first approximation for the T–LS ice margin (Fig. 2). The lowest moraine appears 4.1. The model in Skognesdalen at ∼300 m. In n-Tverrfjorddalen the T–LS margin is likely represented by a bouldery latero- A valley centre-line reconstruction is constructed frontal moraine trimmed by a shoreline at 50 m asl. from a step-by-step calculation of Eq. (1) (Schilling and T–LS glacier limits are characterised by bouldery Hollin, 1981): moraines composed typically of debris from a supragla- cial source (Evans et al., 2002). Given the presence of sav Dx hiþ1 ¼ hi þ ð1Þ intact blockfield with patterned ground on the current siqg ti plateau surface and the fact that the blockfield is pre- Weichselian or even pre-glacial in age (Rea et al., 1996), where, h is ice surface elevation, τav is basal shear it is assumed that the plateau-ice was cold based during stress, s is a shape factor, ρ is ice density, g is the the TL–S. The bouldery, angular nature of the proposed acceleration due to gravity, Δx is step length, t is ice T–LS moraines leads to the further assumption that the thickness, and i refers to the iteration number. Ideally, if outlet glaciers were also at least partly cold-based. the glacier long profile is constrained by trimlines or Evidence for cold-based glacier snouts during earlier lateral moraines (Murray and Locke, 1989) and the stages, such as the L11 stage, is manifest in the basal shear stress is varied until the reconstruction moraines at the marine termini of the plateau icefield matches the geomorphology. In the absence of geo- outlets (Evans et al., 2002). morphological control, an arbitrary basal shear stress is assigned. This model is well suited for use in a spread- 4. Reconstruction sheet, which allows rapid graphical output of the results (Locke, 1995). No account is taken of sliding in the Only the inset latero-frontal moraine at the mouth of model as the ice is assumed to be cold based (see Sörfjorddalen is well constrained, by both radiocarbon above). dates (11,130±120 yr BP) and by association with a In order to compute Eq. (1), bedrock elevations are marine bench at 43 m asl (Fig. 2), which is equivalent to required along valley centrelines and on to the plateau to the Main Shoreline (Sollid et al., 1973). In the other an position. In order to obtain this data the 312 ..Ra ...Eas/Plegorpy aaolmtlg,Pleeooy26(07 307 (2007) 246 Palaeoecology Palaeoclimatology, Palaeogeography, / Evans D.J.A. Rea, B.R.

Fig. 3. Valley centre-line bedrock (grey) elevations and reconstructed ice surfaces (dashed line) for the 10 outlet glaciers from Øksfjordjøkelen. – 330 B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 313 current ice surface had to be replaced in the 100×100 m provided a series of x (distance from present-day grid DEM () by an ice-free shoreline) and y (bedrock elevation) co-ordinates. A plateau. Only limited data are available for current ice series of valley cross-profiles were also derived to depths of Øksfjordjøkelen and these were used in con- calculate s in Eq. (1) (Fig. 4). A model for each valley junction with ice marginal and nunatak bedrock heights centreline was then computed using Eq. (1) over the to interpolate a 100×100 m grid of the subglacial relevant number of iterations. Further details on the plateau surface. This data replaced the ice-covered parameterisation of Eq. (1) are given below: plateau in the original DEM grid, and a new ‘ice-free’ DEM was produced. 4.1.1. Shape factor Starting from present day sea level (40–55 m below For the plateau parts of the reconstruction, an sea level during the T–LS), bed elevations were infinitely wide approximation is used where the shape extracted from the ‘ice-free’ DEM along the centrelines factor is taken as 1. For valley sections of the glaciers, of the 10 outlet valleys, and were extended back along representative cross-profiles were chosen at intervals the plateau to an ice divide (Fig. 3). The ice divides along the valley that best characterised changes in valley locations were based on the current locations. This form. Typical valley cross profiles are shown in Fig. 4.

Fig. 4. Contour map of Sörfjorddalen (100 m intervals) showing the location, form and polynomial fits of representative cross-valley profiles. 314 B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330

Table 1 ties), giving values for m and n. A is then calculated Summary of step lengths used for the reconstruction of each outlet from: glacier Z length (m) n A ¼ððn−mÞhÞ− ax2 þ bx þ c ð3Þ Minimum Maximum Average m Sörfjorddalen 0.4 128.6 51.13 Fjorddalen 0.8 117 60.1 The value for p is calculated from the length of arc: Tverrfjorddalen 3.99 129 58.1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Storelvdalen 0.65 134 62.2  Z 2 Bac'cavuonvag'gi 2.28 198.8 60.65 n dy p ¼ 1 þ dx ð4Þ Isfjorden 1 130.64 72.6 dx Skalsadalen 0.5 130 61.7 m Isdalen 2.2 120.4 65.23 Skognesdalen 0.93 121.7 62.53 s is calculated for each iteration using the same quadratic n-Tverrfjorddalen 0.5 122.2 57.41 equation with only h, and thus, m and n varying (i.e. as the glacier thickness changes). Periodically a step change from one cross-profile to the next occurs as the A quadratic function is fitted to the valley cross-profiles reconstruction iterates up-valley. These step changes (Augustinus, 1992) in order to allow automation of the were not found to produce any equivalent steps in the shape factor calculation. reconstructed glacier surface. The shape factor s is given by: 4.1.2. Basal shear stress A Varying the basal shear stress so that the recon- s ¼ ð2Þ tp structed glacier surface matches the ice marginal geomorphology is the standard method for tuning the where, A and p are respectively, the cross-sectional area model (Schilling and Hollin, 1981; Murray and Locke, of the glacier and cross-sectional perimeter of the bed. 1989). However, latero-frontal moraines are the domi- The fitted approximation smoothes benches and nant features in the valleys and at only a few locations shoulders from the cross-profiles, but is acceptable as are lateral moraines found. Trimlines are conspicuously these are assumed to represent second order features. absent, reflecting mass wasting processes operating For a given value of h the location of the glacier margins since deglaciation (Evans et al., 2002) and the thermal are calculated from the roots of the quadratic equation regime of the T–LS glaciers (cold based). Given this (taking no account of submergent or emergent veloci- lack of calibration evidence the standard value of

Table 2 ELAs calculated for the reconstructed Tromsø–Lyngen Substage outlet glaciers from Øksfjordjøkelen Outlet glacier Snout- Accumulation area ratio ELA (masl) Balance ratio ELA (masl) averaged (Benn and Gemmell/Osmaston) grounding 0.5 0.6 0.8 1.636 2.2 line water depth (m) Sörfjorddalen – 690 515a 340 605/589a 569/549 Fjorddalen 24 635 515a 328 575/565a 543/527 Tverrfjorddalen – 620 550a 395 570/578a 541/547 Storelvdalen 35 856 791 369 665/669 626/621 Bac’cavuonvag’gi 14 653 482a 346 596/564a 560/525 Isfjorden 160b 1002 917 580 – /747 – /686 Skalsadalen – 815 750 279 588/639a 550/592 Isdalen 92b 870 800 315 – /634 – /587 Skognesdalen – 617 568a 411 552/536a 530/511 n-Tverrfjorddalen – 615 556a 402 593/582a 563/553 Where applicable the ELA has been adjusted to account for lowering due to a calving glacier margin. The Balance Ratio ELAs are calculated using the spreadsheets of Benn and Gemmell (1997) and Osmaston (2005). a used in calculating the mean T–LS ELA. b the maximum centreline water depth and not a snout averaged value, as detailed bathymetry is not available. ..Ra ...Eas/Plegorpy aaolmtlg,Pleeooy26(07 307 (2007) 246 Palaeoecology Palaeoclimatology, Palaeogeography, / Evans D.J.A. Rea, B.R. – 330

Fig. 5. Mass balance curves of Langfjordjøkelen for the periods (a) 1988–1998 and (b) 1998–2004 (data from Norwegian Water Resources and Energy Directorate). 315 316 B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330

0.1 MPa was used (Nye, 1952; Schilling and Hollin, proportion of its area above the ELA. Typically this is 1981; Locke, 1995) for all the reconstructions. 0.5–0.8 with an AAR of ∼0.6 assumed to characterise valley/ glaciers (Porter, 1975; Nesje and Dahl, 4.1.3. Step length 2000). A potential problem with the AAR method of This is the distance along the valley from successive ELA estimation is that it takes no account of glacier points where Eq. (1) is calculated. As described above hypsometry (i.e. the distribution of area with altitude). the valley centreline topography was extracted directly The BR method takes account of the glacier hypsometry from the DEM, and step lengths were determined by the (Furbish and Andrews, 1984) and is becoming more slicing algorithm in Surfer©, and are variable, depen- widely adopted as a standard method for the calculation dent upon where the valley centreline crossed a gridline of ELAs (Benn and Lehmkuhl, 2000; Kaser and in the DEM. A summary of the statistics of step length Osmaston, 2002; Kovanen and Slaymaker, 2005), data is provided in Table 1. The auto-extracted steps especially with the provision of freeware spreadsheets worked well and no oscillations or jumps in the glacier that allow automated calculation from area–altitude data profiles were created for any of the reconstructions. (Benn and Gemmell, 1997; Osmaston, 2005). The hypsometry of plateau icefield outlet glaciers is such 4.1.4. First step and the snout that larger areas are found towards higher altitudes when For the first iteration of Eq. (1), ti =0, therefore ti+1, compared to alpine style glaciers. Thus only balance cannot be calculated, so an arbitrary value (absolute ratios are discussed further here, but ELAs derived using magnitude depended upon the initial step length) was the AAR method (AAR–ELA) are shown in Table 2 for chosen. Though a potential source of error, the iterative comparison and further details can also found in Evans calculations quickly conform to a profile controlled by et al. (2002). Balance ratios in the range 1.8–2.2 have the local bedrock gradient (Schilling and Hollin, 1981). been reported (Meier and Tangborn, 1965; Furbish and Further modifications were subsequently made to Andrews, 1984) with values of around 2 thought to be account for calving glacier snouts (see below). representative of maritime mid-latitude glaciers (Benn and Gemmell, 1997). One general assumption when 4.1.5. Lakes and Valley Fills applying this technique is that the BR for any particular The valley centreline bed elevation data derived from glacier remains constant as the ELA changes (i.e. the DEM presents both lake surfaces and valley bottom climate changes). There are no mass balance data with fills as the valley floor. As no data was which to calculate the current ELA for Øksfjordjøkelen available on lake depths or on the sediment depths no and therefore the current BR for the icefield outlet correction was made for this as it is thought to represent glaciers. However, mass balance data are available for a minor error. Firstly for the lakes as they are all small in the neighbouring Langfjordjøkelen, for the majority of comparison to the length-scale of the glaciers and the period 1989–2004, from the Norwegian Water secondly, the cross-valley fitted quadratic functions Resources and Energy Directorate (NVE). These data suggest shallow lakes. Thirdly, it is not possible to show a highly variable mass balance gradient (Fig. 5a), quantify pre-existing sediment depths in lake or valley with the ELA ranging from ∼675 m towards a more bottoms. recent trend of negative mass balance across the whole glacier (Fig. 5b). Regressing specific net balance against 5. ELA estimation ELA altitude, allows the zero net balance ELA to be identified from a time series of mass balance data There are a number of different methods that may be (Hagen et al., 1991; Benn and Evans, 1998; Benn and utilised for ELA estimation, including the toe to Lehmkuhl, 2000). Fig. 6 shows that the zero net balance headwall altitude ratio, and the median elevation of for Langfjordjøkelen, from 1989–2004, is 736.5 m. glaciers (Benn and Evans, 1998; Nesje and Dahl, 2000), Taking 736.5 m as the ‘equilibrium’ ELA for the but only the accumulation area ratio (AAR) (Porter, present-day climate, the BR is given by the following: 1977; Kuhn, 1989; Benn and Evans, 1998; Benn and P Lehmkuhl, 2000; Nesje and Dahl, 2000) and the balance ¼ bnab ¼ zac Aac ð Þ BR P 5 ratio (BR) methods are discussed here (Furbish and bnac zab Aab Andrews, 1984; Benn and Gemmell, 1997; Benn and Lehmkuhl, 2000). where, bnab and bnac are the net mass balance gradients in The AAR method is based on the assumption that the ablation and accumulation zones ¯zac and ¯zac are the under equilibrium conditions a glacier has a fixed area-weighted mean altitudes of the accumulation and B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 317

Fig. 6. Zero net balance for Langfjordjøkelen (data from Norwegian Water Resources and Energy Directorate). ablation areas (measured positively from the ELA) and valley (Evans et al., 2002) can only be matched by the Aac and Aab are the areas of the accumulation and ablation ice surface if a basal shear stress of 0.15 MPa is used, areas (Furbish and Andrews, 1984). Given the highly which led Evans et al. (2002) to the conclusion that the variable nature of the mass balance record (Fig. 5)theBR highest lateral moraine was from the Skarpnes substage. is calculated using the right hand side of Eq. (5). Taking For simplicity, and to avoid varying the basal shear the zero net balance ELA of 736.5 m gives the BR for stress up-glacier, a uniform basal shear stress of Langfjordjøkelen as 1.636. Values of 1.636 and 2.2 will 0.1 MPa was used. The slight mismatch to the latero- be used to calculate BR-ELAs for the reconstructed T–LS frontal moraine is assumed to have insignificant outlet glaciers. effects on subsequent ice surface area and ice flux calculations. 6. Results The BR-ELAs are 605/584 and 569/546 (first value is calculated using the Benn and Gemmell (1997) 6.1. Sörfjorddalen spreadsheet and the second value is calculated using the Osmaston (2005) spreadsheet) for ratios of 1.636, and The T–LS latero-frontal moraine ridge located at the 2.2 respectively (Table 2). It should be noted that both valley mouth (Fig. 2) is the best temporally constrained the spreadsheets of Benn and Gemmell (1997) and outlet from the icefield. A basal shear stress of 0.1 MPa Osmaston (2005) were used to calculate the BR as they produces a glacier snout that is slightly thick, compared may produce different values for the ELA for the same to the geometry of the latero-frontal moraine ridge, dataset. Osmaston (2005) has suggested that the method even accounting for the emergent velocity. Lowering of Benn and Gemmell (1997) overestimates the true the basal shear stress to 0.06 MPa produced a fit to the ELA. However, using the Osmaston (2005) spreadsheet moraine geometry. The highest lateral moraine in the and a BR of 1.636 the ELA for Langfjordjøkelen was 318 B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 calculated as 731 m, while the Benn and Gemmell 410/434 m for BR of 1.636 and 2.2 respectively), (1997) spreadsheet gave an ELA of 742 m. Larger indicating that the T–LS moraine lies further up-valley. differences, between the two methods, result when Based on the modelling, a snout position located just hypsometry extremes are found beyond the altitudes of up-valley from Tverrfjordvatnet places the ELA at ¯zac and ¯zab and (measured positive from the ELA) as the approximately the correct elevation. However, the sea Benn and Gemmell (1997) spreadsheet takes no account was excluded from the valley during the T-LS as the of these. The ELA for Sörfjorddalen, the only dated ice marine limit is 38 m. The lack of either moraines and margin, was then used as a calibration for the other associated deltas or the Main shoreline could be reconstructions. The other glacier reconstructions were explained by low debris inputs and/or a lack of marine started from the ‘likely’ T–LS snout positions and the activity, due to the shelter provided by the embayment ELAs were calculated. If necessary the snout was then (Evans et al., 2002). Alternatively, the T–LS moraine moved and the reconstruction re-run until the ELA lay may be in the lake, concurrent with the lateral moraine close to that of Sörfjorddalen. The details for each outlet located directly south of Tverrfjordvatnet, which was are given below. later notched by a shoreline at 38 m. This slightly advanced snout position (compared to the ELA 6.2. Fjorddalen requirements) could result from coalescence with ice draining from the three-basin accumulation area A moraine ridge located at the valley mouth at 20 m directly to the northwest above Tverrfjordvatnet (Fig. was interpreted as the T–LS ice margin. However, 2a). In order to approximate the correct ELA the T–LS terminating at this altitude the glacier must have had a ice margin is located at 50 m altitude, approximately calving snout. A number of simple calving relationships 1 km up-valley from the present-day shoreline (Fig. have been established for tidewater and lake calving 2a), which would have been just above the T–LS sea glaciers of the form: level. c ¼ khw ð6Þ 6.4. Storelvdalen where, c is the calving rate, k is an empirical constant and The outermost bouldery latero-frontal moraine was hw is water depth. Calving rates may be calculated along the taken by Evans et al. (2002) as the most likely position of glacier centreline or averaged across the snout and values the T–LS snout. Accounting for calving associated with −1 −1 for k between 2.0 a (lacustrine) and 28 a (tidewater) the T–LS sea level (50 m) reduces the ELA accordingly have been reported (Brown et al., 1982; Warren et al., (Table 2). Given the rapid water depth increase and lack −1 1995). Avalue of 17 a is adopted here as it represents the of bounding valley sides as the glacier exited the valley best value for a centreline ice depth only calculation and entered Øksfjord, it is unlikely that the snout (Brown et al., 1982) which is used subsequently for two extended any significant distance further out into the outlets, and is close to the mid-point between upper and fjord. Given the problems of accurately accounting for lower limits for k for the snout averaged water depth used calving losses it is difficult to further refine the snout subsequently for three outlets. For Fjorddalen, hw is taken position. as 24 m (moraine altitude 20 m, T–LS marine limit ∼44 m from Evans et al. (2002)). While currently there is 6.5. Bac'cavuonvag'gi significant debate regarding the applicability of such a calving law (Van der Veen, 2002), simplicity of calculation The marine limit in the valley is a bench notched into makes the use of Eq. (6) desirable in this situation. A a frontal moraine at 34 m asl (Evans et al., 2002; Fig. 2), calving snout reduces the ELA (the ELA is recalculated in indicating exclusion of the sea during the T–LS. The both spreadsheets by simply adding the area removed by T–LS sea level would have been 51.5 m asl giving hw calving onto the lowest contour interval and recalculating) as 14 m (slightly modified from Evans et al., 2002), and and the calving corrected ELA for a BR of 1.636 is 575/ accounting for calving gives BR-ELAs that reasonably 570 m (Table 2). approximate those in Sörfjorddalen (Table 2). This indicates that the outermost bouldery moraine is the 6.3. Tverrfjorddalen location of the T–LS snout, where the glacier likely remained until some time post Stordal but pre Tapes, The reconstruction originating from the present-day when the 34 m marine bench was notched in the shoreline yielded very low ELAs (e.g. 439/468 m and moraine. B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 319

Fig. 7. Øksfjordjøkelen reconstructed for the Tromsö–Lyngen Substage. The hypsometry for each outlet is also shown. 320 B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330

6.6. Isfjorden eastwards, towards the valley mouth. Alternatively, the benches may represent lake shorelines cut during T–LS During the LIA the glacier snout terminated just deglaciation. below present day sea level at the fjord-head. Beyond, the fjord deepens rapidly, indicating the T–LS glacier 6.8. Isdalen terminated in deep water (e.g. 500 m beyond the LIA moraine the present-day water depth is 107 m, which Evans et al. (2002) suggested a grounding line equates to a T–LS water depth of 160 m). With such located in approximately 100 m of water. Here this is water depths the calving losses will dominate the revised slightly to 92 m using a single water depth value altitude of the ELA. All that can be said for sure is of 44 m (from the 1:50000 ) plus that the T–LS snout was located at, or beyond the LIA isostatic rebound. The ELA altitudes defined by the BR moraine within Isfjorden. The outer limit is constrained method, accounting for calving losses, are shown in by the pre-T–LS marine limit in Skalsadalen (see Table 2. The Benn and Gemmell spreadsheet could not below), which requires that Isfjordjøkelen had retreated calculate an ELA taking account of calving in the back at least as far as the junction between Skalsadalen manner indicated above. It should be noted that the and Isfjorden (Fig. 2). A re-advance beyond this point absolute position of the ice margin again could not be during the T–LS would seem unlikely. It should be accurately established due to problems in quantifying noted that the Benn and Gemmell spreadsheet could not calving losses. calculate an ELA taking account of calving in the manner indicated above so the BR in Table 2 only has a 6.9. Skognesdalen BR calculated using Osmaston (2005). The moraines located at the mouth of the hanging 6.7. Skalsadalen valley post-date the T–LS, based on the ELA recon- structions. Reasonable ELAs are obtained for a glacier As mentioned above, the high marine limit of 64 m terminating beyond the mouth of the hanging valley, on asl in Skalsadalen indicates that the valley was ice-free the steep valley side of Langfjord, at or around the Main prior to the T–LS. The present lake surface is at an shoreline (45 m asl). The steepness of the valley side at altitude of 50 m and so the valley mouth would have this point makes it unlikely that the snout extended any been at sea level during construction of the Main significant distance beyond the marine limit and also shoreline. The possibility of a calving margin grounded accounts for the lack of a moraine or delta, marking the in the lake was investigated and approximations of the ice margin (Fig. 2). cross-valley profile (derived from curves fitted to the cross sections cut perpendicular to the valley/lake long 6.10. n-Tverrfjorddalen axes) suggest that water depths are unlikely to have been significantly greater than 30 m, and would not produce The fjord-head latero-frontal moraine is trimmed by a sufficient calving to lower the ELA to fit with 50 m shoreline that has been related to the earlier Sörfjorddalen. Based on the geomorphology and Skarpnes substage (Evans et al., 2002) but the BR- reconstruction the best interpretation is that at some derived ELAs indicate that the T–LS ice margin was point prior to the T–LS the valley rapidly deglaciated as also located at this moraine, indicating that the T–LS the main trunk glacier retreated into Isfjorden. As glacier attained dimensions similar to those of the relative sea level dropped the basin would have become Skarpnes substage glacier (Evans et al., 2002). tidal or isolated forming a lake and with the onset of the T–LS the glacier filled the basin and advanced to the 6.11. Summary valley mouth, terminating in a very shallow tidewater setting. Such an interpretation requires that the benches By using the temporally well-constrained limits of at 64 m, 58 m and 55 m at the head of Skalsavatnet, were the glacier that filled Sörfjorddalen it was possible to preserved during the T–LS advance. This is entirely define the likely ELAs for Øksfjordjøkelen outlet feasible given the assumption made here that the ice is glaciers during the T–LS. By iteration of snout cold-based. Additionally, ice flow to the west along positions, where necessary accounting for calving Skalsadalen would have been limited in extent, and losses, it has been possible in some instances to indeed the topography of the bottom of Skalsavatnet identify the T–LS moraines and in others to may be such that ice flow was directed entirely approximate the location of the snout where no B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 321 moraines exist or the glacier terminated below present- Nesje and Dahl, 2000). Provided the glacier is in day sea level. For snouts terminating in deep water the equilibrium with climate, the glacier's ELA provides a lack of moraines and detailed bathymetry make it proxy of the climate (temperature and precipitation) at difficult to account for the calving losses making that point in time. As climate changes so the glacier accurately constraining snout positions impossible. ELA will rise and fall in response. Table 2 shows the However, it is unlikely that the actual ice margins ELAs obtained from the reconstructed outlet glaciers of were markedly different from those shown in Fig. 7. Øksfjordjøkelen during the T–LS. It is clear that the glaciers experiencing significant calving losses differ 7. The T–LS (Younger Dryas) climate somewhat from the control site in Sörfjorddalen and the remainder of the outlets. Due to the problems with As the T–LS moraines lie significantly beyond those calculating mass losses due to calving and the lack of of the LIA it can be assumed that the climate was either detailed palaeobaythmetry for snouts extending below colder and/or had more snowfall during the T–LS. The present-day sea level, Storelvdalen, Isfjorden and ELA is of particular importance as it represents the Isdalen will be discounted from the following discus- position of zero net balance, and its altitude is con- sions. Taking the remaining seven outlet glaciers the trolled, in most instances, by the interplay between mean ELA for Øksfjordjøkelen during the T–LS is 531± winter precipitation and summer temperature (e.g. 33 m for an AAR of 0.6, 583±7 m and 579±12 m for a Loewe, 1971; Sutherland, 1984; Ohmura et al., 1992; BR of 1.636 using the spreadsheet calculations of Benn

Fig. 8. Three commonly used relationships for temperature and precipitation at the ELA. 322 B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 and Gemmell (1997) and Osmaston (2005) respectively. Table 3b It is worth noting that this value is altered little if the Present-day precipitation and temperatures for Øksfjordjøkelen and temperatures required to lower the ELA on Øksfjordjøkelen to the calving snouts of Fjorddalen and Bac'cavuonvag'gi are altitudes reconstructed for the T–LS, assuming no sea level change in not included (581±7 m and 584±14 m). The advantage precipitation relative to the present of using the BR method over the AAR method can Oks present-day T–LS ELA clearly be seen by the exaggerated hypsometry of ELA 950 m 580 m Skalsadalen (Fig. 7). The BR method takes account of ELA annual precipitation (mm) 3400 2624 the large area of the lying at the lowest Derived (from Eq. (9)) sea level 13.21±0.76 9.06±0.47 altitude, while the AAR cannot account for this. The summer temperature (°C) resulting AAR-derived ELA is 750 m, while the BR- The present-day precipitation was derived from the Loppa precipita- derived ELAs are 588 m and 639 m respectively for the tion record (corrected to sea level at Langfjordjøkelen by correlation Benn and Gemmell (1997) and Osmaston (2005) with the NVE winter balance record) and a precipitation gradient of spreadsheets (Table 2). Indeed for a number of the 15%/100 m, derived from the Langfjordjøkelen winter balance other outlets, which have a significant percentage of their gradient. accumulation area lying towards the top of their altitudinal range, the AAR-derived ELA underestimates the BR-derived ELA, accounting for the lower AAR- 1994). The duration of the T–LS (Younger Dryas) is derived mean ELA. For this reason only the BR-ELA ∼1000 yr (Birks et al., 1994) so the assumption is made calculations will be used in subsequent climate that the reconstructed Øksfjordjøkelen was in equilibri- interpretations. um with the Younger Dryas climate. Although the present-day zero net balance ELA on Langfjordjøkelen is taken as 736.5 m (Fig. 6), based on 7.1. Temperature-Precipitation estimates field observations, the firn-line (here taken as a proxy for the ELA) on Øksfjordjøkelen lies somewhere in the Once reconstructed, empirical relationships derived region of 900–1000 m. The mid-point of this at 950 m from present-day glaciers, may be applied to glacier suggests an ELA depression (ΔELA) during the T–LS palaeo-ELAs to derive palaeo-climate information (e.g. of 370±∼13 m (the ELA range derived from Benn and Porter, 1975; Sutherland, 1984; Ballantyne, 1990;Nesje, Gemmell (1997) lies almost inside the range derived 1992; Dahl and Nesje, 1996; Lie et al., 2003, Kovanen from Osmaston (2005) so these limits are used to and Slaymaker, 2005; Benn and Ballantyne, 2005). Three characterise the BR results). commonly used relationships relating temperature and Given the limited size of the reconstructed ice mass precipitation at the ELA are given below: (area ∼87 km2; maximum ice thickness ∼350 m; maxi- mum outlet length ∼8.9 km) and assuming ablation at (1) from Norwegian glaciers, Ballantyne (1990); the snout of 1–3ma− 1 the response time should be in the order of 100–350 yr, (Johannesson et al., 1989; Paterson, A ¼ 915e0:339t ð7Þ

where, at the ELA, A is the winter (October– Table 3a April) accumulation in millimetres water equiva- Present-day precipitation and temperatures for Øksfjordjøkelen and – precipitation levels (corrected to sea level using a precipitation lent and t is the mean summer (June August) gradient of 15%/100 m) required to lower the present day ELA on temperature in °C. Øksfjordjøkelen to the altitudes reconstructed for the T–LS, assuming (2) a “tabulated global formula” from Kotlyakov and no sea level temperature change relative to present Krenke (1982): Present-day T–LS ELA 2:85 ELA 950 m 580 m A ¼ 1:33ðt þ 9:66Þ ð8Þ ELA mean summer temperature 4.53 3.01 6.38 5.45 Derived (from Eq. (9)) sea level 896 668 1549 1349 where, at the ELA, A and t are as for Eq. (7). precipitation (mm) (3) and from a global data set Ohmura et al. (1992); Two values are presented for each ELA altitude relating to lapse rates A ¼ 9t2 þ 296t þ 645 ð9Þ of 0.5 and 0.66 °C/100 m respectively. The present-day sea level T precipitation is 1400 mm, derived from the Loppa precipitation record (corrected to sea level at Langfjordjøkelen by correlation with the NVE where, at the ELA, AT is the winter accumulation winter balance record) and a precipitation gradient of 15 %/100 m, plus the summer precipitation in millimetres water derived from the Langfjordjøkelen winter balance gradient. equivalent. B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 323

All three relationships are plotted together on Fig. 8, following discussions. In order to assess changes in though it should be noted that in Eq. (9) the climate associated with the reconstructed ELA depres- accumulation is total annual precipitation at the ELA. sions, present-day temperature precipitation data is Knowing either parameter (A or t) at the ELA allows the required. Temperature data are available from two unknown to be readily derived (e.g. Ballantyne, 1990; Norwegian Meteorological Institute weather stations in Rea et al., 1999; Kovanen and Slaymaker, 2005; Benn the vicinity, Loppa (∼30 km NW) and Kvænangen and Ballantyne, 2005), but having such independent (∼35 km south) (Fig. 1). Both sites are close to sea level, estimates for either parameter is a fundamental problem, (Loppa 10 m and Kvænangen 6 m), with Loppa being especially when the reconstructed ice mass is so close to more exposed to maritime influences than Kvænangen. an ice sheet margin. Taking the present-day ELA of Øksfjordjøkelen to be Benn and Ballantyne (2005) suggest that Eq. (9) is 950 m (see above) and applying lapse rates of 0.5 °C/ most appropriate for palaeoclimate reconstructions as it 100 m (Laaksonen, 1976) and 0.66 °C/100 m (Green and is derived from a global dataset which removes regional Harding, 1980), the equivalent summer sea level complexities. Intuitively, if a regionally derived rela- temperature (taken as the average of the Loppa and tionship is available (7) this may represent the best Kvænangen data) of 9.3 °C gives the mean summer approximation, though the question of applicability to temperature at the ELA as 4.53 °C and 3.01 °C former climates remains. Brevity precludes discussion respectively. ELA lowering can be driven by increasing of the results but all three relationships were used to winter/total precipitation or reducing mean summer reconstruct the former climates and indicated that the temperature. Table 3a presents the sea level precipitation Ballantyne relationship was the least applicable to required to sustain the T–LS glaciers shown in Fig. 7, conditions experienced by Øksfjordjøkelen during the assuming no sea level temperature change compared with T–LS. Given uncertainties associated with permanent/ present. Considering the alternative situation, there is no seasonal sea-ice cover it was decided best to concur with precipitation change (present-day precipitation was the view expressed by Benn and Ballantyne (2005) so derived from the Loppa precipitation record, corrected only the Ohmura et al. (1992) relationship is used in the by correlation with the winter balance record from

Fig. 9. Reconstructed mean summer temperatures for Andøya from Alm (1993). Øvre Æråsvatn lake is situated at 44 m. 324 B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330

Table 4 ature data are more readily available, derived from – T LS annual precipitation (corrected to sea level using a precipitation biological information such as tree-line altitudes, pollen gradient of 15%/100 m) derived using the mean summer temperature record from Andøya (Fig. 9) assemblages, and chironomids. The closest record for the northern part of Norway covering the T–LS comes from ELA 580 m the island of Andøya (Alm, 1993; Birks et al., 1994). ELA mean summer temperature 2.2 1.3 Fig. 9 shows the reconstructed mean summer temperature (mean sea level temperature 5.1 °C) at sea level. The original data presented by Alm (1993) are Derived sea level precipitation (mm) 708 558 (assuming a precipitation gradient of 15%/100 m) given as mean July temperatures (tJ) and have been corrected to mean summer temperature (t)followingBenn Two values are presented representing lapse rates of 0.5 and 0.66 °C/ 100 m. and Ballantyne (2005): ¼ ⁎ : ð Þ Langfjordjøkelen, and a precipitation gradient of 15%/ t tJ 0 97 10 100 m, derived from the Langfjordjøkelen winter balance This gives a minimum mean summer temperature gradient), so ELA lowering is driven entirely by reduction (corrected to present-day sea level) for the early (coldest) in temperature. Table 3b presents the sea level tempera- part of the T–LS of 5.1 °C. Calculating Eq. (9) using – tures required to support the T LS, assuming no this temperature provides precipitation estimates for the precipitation change. T–LS, and these are presented in Table 4. The data presented in Tables 3a,b provides two end- member scenarios of climate change as only one of the input parameters to Eq. (9) varies (i.e. temperature or 7.2. Mass balance gradients precipitation). In reality this is unlikely to happen and precipitation changes are likely to be accompanied by The assumption that Øksfjordjøkelen was in equilib- temperature changes. In all likelihood the lowered ELAs rium with the climate during the T–LS requires that required to sustain the T–LS glaciers (Fig. 7) are the the net mass balance is zero (accumulation equals result of reduced temperature and precipitation. The ablation) and so ice flux through the ELA must equal present-day sea level precipitation values presented in the net accumulation and thus net ablation. To calculate Table 3a can be assumed to represent the upper limit for the ice flux (discharge — Qice) through the ELA, the – – T LS and the reconstructed T LS temperatures pre- area-averaged ice velocity (vaa) and cross-sectional – sented in Table 3b represent the highest possible T LS area of the glacier at the ELA (ELAcsa) are required. sea level temperatures (i.e. the true values are likely to The cross-sectional area is extracted from the glacier be lower due to reduced precipitation). reconstructions. The centreline ice surface velocity Ideally, Eq. (9) is computed using independently (vs) is calculated from the valley centreline ice depth derived temperature or precipitation data. Palaeo-temper- at the ELA (hc) and the ascribed basal shear stress

Table 5 Ice discharge through the ELA calculated for 1 BR=1.636 (using Benn and Gemmell (1997) spreadsheet) and 2 BR=1.636 (using Osmaston (2005) spreadsheet) Sörfjorddalen Fjorddalen Tverrfjorddalen Bac'cavuonvag'gi Skalsadalen Skognesdalen n-Tverrfjorddalen WE W E Cross-sectional area at 1 135,852a 146,498 76,880 35,523 13,051 156,057 82,807 119,150 233,465 the ELA 2 144,119a 73,263 30,892 14,485 228,784 78,216 106,777 246,571 Centre-line ice surface 1 11.96/4.22 13.35/4.71 17.59/6.21 8.56/1.91 6.01/2.20 20.63/7.28 9.54/3.37 17.26/ 31.42/ − 1 velocity vs (m a ) 6.09 11.09 2 12.14/4.28 17.69/6.24 8.95/3.16 7.72/2.73 20.58/7.26 8.90/3.14 16.08/ 33.56/ 5.68 11.85 Ice discharge (m3 a−1) 1 154,2472/ 123,2047/ 851,701/ 221,733/ 203,4064/ 497,832/ 365,4076/ 544,402 434,840 300,600 78,259 717,905 175,706 1,289,674 2 1,038,818/ 816,569/ 263,837/ 2,965,605/ 438,528/ 629,5208/ 366,642 288,201 93,119 1,046,684 154,775 2,221,838 The cross sectional area has been calculated from a fitted 2nd order polynomial, except where otherwise indicated. Two values are provided for the centre-line ice surface velocity (vs) because two values of A were used in Eq. (11), relating to temperatures between the pressure melting point (0 °C) and −2°C(Paterson, 1994). a cross-section approximated as a trapezium. B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 325

(0.1 MPa) assuming laminar flow and no valley side equal to the net accumulation and ablation at the area- influence: weighted mean altitudes ¯zac and ¯zab of the accumulation and ablation zones respectively (Furbish and Andrews, n 2As hc 1984; Benn and Gemmell, 1997). The net accumulation vs ¼ ð11Þ n þ 1 and ablation gradients (bnab and bnac) can be derived from the ice flux through the ELA and the glacier where, A is a temperature dependent constant and n is a hypsometry (Murray and Locke, 1989). The Benn and constant, both from the flow law for ice (Paterson, 1994). Gemmell (1997) spreadsheet calculates the altitudes of Surface ice velocities for the valley centre flowline at the ¯zac and ¯zab , and the Osmaston (2005) spreadsheet has ELA are calculated using Eq. (11) for selected outlets been modified to obtain equivalent altitudes (area- and are shown in Table 5. It is important to note the altitude weighted mean altitudes). Table 6 shows the significant difference in centreline ice surface velocity derived mass balance gradients for outlet glaciers not resulting from the two choices of A in Eq. (11). For a severely affected by calving. cold-based glacier (i.e. no slip at the ice-bed interface), n-Tverrfjorddalen appears to be erroneous in com- vaa is given by 0.63vs (Nye, 1965; Raymond, 1980) and parison with the other glaciers and suggests that the Qice is calculated as 0.63*vs*ELAcsa and the results for geometry has been incorrectly defined. The accumula- the selected outlet glaciers are presented in Table 5. tion gradient would be reduced somewhat if the plateau For a glacier in equilibrium the ice flux through the to the north (Fig. 7) had been included in the ELA (Qice) must equal the total accumulation above the reconstruction as it would, most certainly, have been – ELA (d¯acAac) and the total ablation below the ELA glaciated and contributing mass during the T LS. A (d¯abAab): further contributing factor may be the configuration of the valley. The valley centre-line long profiles in Fig. 3 ¼ P ¼ P ð Þ Qice dac Aac dab Aab 12 show that n-Tverrfjorddalen has the longest and lowest profile. The combined effects of narrowness of the where, d¯ac is the mean accumulation in the accumulation valley and height of the valley sides produce significant zone and d¯ab is the mean ablation in the ablation zone. shading which could have reduced summer ablation and Assuming that the accumulation and ablation gradients thereby enhanced the accumulation gradient. Additional are linear, the altitudes of the values of d¯ac and d¯ab are accumulation from the plateau to the north would not

Table 6 Mass balance gradients for the reconstructed outlet glaciers Glacier ELA determinant ELA Ice temperature 0 °C Ice temperature −2°C (m) Accumulation gradient Ablation gradient Accumulation gradient Ablation gradient (mm/m) (mm/m) (mm/m) (mm/m) Sörfjorddalen BR 1.636 (B and G) 605.00 0.81 2.90 0.29 1.03 BR 1.636 (Os) 589.00 0.80 1.31 0.28 0.46 Fjorddalen BR 1.636 (B and G) 575.00 0.65 0.98 0.23 0.35 BR 1.636 (Os) 565.00 0.48 – 0.17 – Tverrfjorddalen BR 1.636 (B and G) 570.00 0.59 – 0.21 – BR 1.636 (Os) 578.00 0.59 – 0.21 – Bac'cavonvag'gi BR 1.636 (B and G) 596.00 2.86 5.67 1.01 2.00 BR 1.636 (Os) 564.00 1.91 3.12 0.67 1.10 Skalsadalen BR 1.636 (B and G) 588.00 1.02 1.89 0.36 0.67 BR 1.636 (Os) 639.00 0.36 – 0.13 – Skognesdalen BR 1.636 (B and G) 552.00 0.35 – 0.12 – BR 1.636 (Os) 536.00 0.32 – 0.11 – n-Tverrfjorddalen BR 1.636 (B and G) 593.00 –––– BR 1.636 (Os) 582.00 1.00 1.64 0.35 0.58 averages BR 1.636 (B and G) 1.09±0.3 2.31±0.63 0.39±0.11 0.81±0.22 BR 1.636 (Os) 0.81±0.17 1.59±0.39 0.29±0.11 0.56±0.14 B and G and Os indicate, Benn and Gemmell (1997) spreadsheet and Osmaston (2005) spreadsheet respectively. The ice temperature represents the values used for A in Eq. (11), with 0 °C providing an upper limit for ice flux assuming a no-slip boundary. No ablation gradients are calculated for the calving margins. n-Tverrfjorddalen has been excluded from the average calculation. (±one standard error). 326 B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330

Table 7 ablation gradients for the T–LS, at a location just – Change in sea level precipitation from the present day to the T LS beyond the margin of the Scandinavian Ice Sheet (Fig. 1, T–LS ELA=580 m Table 6). The assumption is made (above) that the T–LS sea level mean summer temperature 5.1 °C icefield and outlet glaciers are cold-based. Calculations (present-day 9.3 °C) using an ice temperature of 0 °C represent the upper % change in sea level precipitation −49.4 −60.1 limit for ice flux and consequently for accumulation and compared with present-day (1400 mm) ablation gradients. While it is possible that basal tem- T–LS summer temperature is derived from the Andøya temperature peratures are lower than −2 °C, it is thought that this record (Fig. 9) and present-day precipitation totals are derived from the represents a reasonable lower limit for ice flow through Loppa precipitation record (corrected to sea level at Langfjordjøkelen by correlation with the NVE winter balance record) and a precipitation the ELA. Reducing the basal temperatures further gradient of 15%/100 m, derived from the Langfjordjøkelen winter simply reduces the ice flux through the ELA, lowering balance gradient. the mass balance gradients. necessarily have significantly altered the position of the 8. Discussion snout, as this could have been maintained by calving. Discounting n-Tverrfjorddalen, results from the re- A lack of in situ organic material in the moraines maining outlets provide generalised accumulation and and associated sediments produced by outlets from

Fig. 10. Mass balance gradients from selected glaciers across the world representing different climatic regimes. The reconstructed mass balance gradients and ELA for Øksfjordjøkelen are indicative of a high-latitude sub-polar setting. (Data from Kuhn, 1984). B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 327

Fig. 11. Mass balance regions of the Svalbard archipelago (Hagen et al., 2003). Associated mass balance gradients are shown in Table 8.

Øksfjordjøkelen during the T–LS makes dating prob- iteration until the ELA is close to that of Sörfjorddda- lematic. The development of cosmogenic dating, while len, though this was complicated for a number of offering an alternative dating technique, is reliant upon outlets as they ended in deep water where there was no active subglacial transport of material in order to zero available bathymetry. Calculation of the ELA is thus the signal. The evidence presented above suggests that critical for defining the geometry of individual glaciers and active subglacial transport was limited and also to subsequent climatic inferences. Table 2 (Evans et al., 2002). The age of the T–LS ice margin in presents the ELAs calculated using typical AARs and Sörfjorddalen is well constrained by direct dating with BRs. The mean AAR-ELA is 531±33 m (AAR — 0.6) 14C analysis of in situ Mya truncata shells and by which is significantly lower than the mean BR-ELAs of indirect dating through association of moraines and the 582±7 m and 578±12 m calculated for a BR of 1.636 T–LS marine limit (Evans et al., 2002). None of the using, respectively, the Benn and Gemmell (1997) and other ice margins were temporally so well constrained. Osmaston (2005) spreadsheets. The hypsometry of pla- Unless there are very significant localised climatic teau icefield outlets illustrate clearly the advantage of effects, outlet glaciers from an icefield the size of the BR method over the AAR method. Compared with Øksfjordjøkelen should have ELAs that lie within a the present-day ELA (∼950 m) the BR-ELA equates to relatively small altitudinal range, assuming that the a lowering of some 370±∼13 m during the T–LS. ELA is a function of the winter precipitation and sum- These are comparable and in reasonable agreement mer ablation. Using this approach the most appropriate with results from southern Norway (Nesje, 1992; Dahl moraines and likely snout locations are constrained by and Nesje, 1992), and from Lenangsbreen, located

Table 8 Present-day (based on observations from ~1960–1999) regional mass balance gradients for Svalbard and reconstructed Tromsö–Lyngen Substage (Younger Dryas) Øksfjordjøkelen (temperature refers to the choice of A in Eq. (11)) Region 1 2 3 4 5 6 7 8 9 10 11 13 Øks 0 °C Øks −2°C Accumulation gradient (mm/m) 2.4 2.0 1.4 1.7 2.3 1.5 1.5 2.0 1.5 1.0 1.6 3.0 1.0 0.4 Ablation gradient (mm/m) 6.4 5.8 3.7 4.2 4.4 3.3 2.7 2.2 2.2 2.4 3.0 6.4 2.0 0.7 For regions see Fig. 11. Data are from Hagen et al. (2003). 328 B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 some 90 km to the southwest, where Bakke et al. associated with latitude (Table 8). The reconstructed (2005) report a double T–LS moraine system related to mass balance gradients for Øksfjordjøkelen are more ELAs of 542 m and 569 m (adjusted for T–LS sea comparable (especially for the warmer ice scenario) level). with the shallower gradients found in the northern Quantifying the climatic changes required to lower (Nordaustlandet) regions (8–10) (Fig. 11). glacier ELAs is an important component of glacier Though the T–LS climate was undoubtedly signif- reconstructions. Palaeoceanographic research can pro- icantly drier than present-day there was still substantial vide high resolution proxies for marine temperatures and precipitation, which requires access to a moisture source conditions, and terrestrial palaeotemperatures can be (i.e. open water). This supports the notion of a derived from various sources (e.g. tree lines, , seasonally ice-free corridor extending northwards from chironomid assemblages), but glaciers are almost the Færøe and Shetland Islands along the Norwegian uniquely placed to provide data on palaeo-precipitation. coast (Koc et al., 1993) reaching at least as far north as Eqs. (7), (8) and (9) can provide upper limits to the Øksfjordjøkelen. The presence of a seasonally ice-free precipitation and temperature required to lower ELAs corridor has significant implications for the timing of (Tables 3a,b) but provide better estimates when one precipitation during the T–LS. If the winter sea ice parameter is derived independently (Table 4). The proxy extended far to the south, the likelihood would be that temperature record from Andøya (Fig. 9) and the palaeo- winter precipitation would be reduced with accumula- precipitation estimates (Table 4) suggest that mean tion being more significant during the spring, summer summer sea level temperature was 5.1 °C, some 4.2 °C and autumn. Given such unknowns/complexities using lower than the present-day (9.3 °C). The data presented in the Ohmura global temperature-precipitation relation- Table 7 suggest a reduction between 50% (lapse rate of ship (Eq. (9)) for reconstructions across glacials– 0.5 °C/100 m) to 60% (lapse rate of 0.66 °C/100 m) is the most appropriate and supports the mean sea level precipitation compared with present-day. view expressed by Benn and Ballantyne (2005). Accumulation and ablation gradients are representa- tive of the climate regime in which a glacier is located, 9. Conclusions provided there are no significant effects from other factors, for example, shading, snow-blow or avalanch- Ten outlet glaciers from Øksfjordjøkelen have been ing. High gradients are indicative of high flux through reconstructed for the T–LS, based on a single dated the ELA (high activity (Meier et al., 1971; Andrews, moraine. Field evidence and the commonality of the 1972)), and are generally found in mid-latitude maritime ELA, calculated using the BR method, (Furbish and regions, where the marine environment represents a Andrews, 1984) has been used to constrain the major heat and moisture source. Conversely low remaining ice margins. Due to a lack of fjord bathymetry gradients (low activity) are found in high latitude and reconstructions of the glaciers terminating in the main continental areas, away from moisture sources. Al- trunk fjords are rendered to first order approximations though ice masses in high latitudes may be proximal to and were discounted from subsequent climatic inter- the marine environment, permanent and seasonal sea-ice pretations. The remaining reconstructed ELAs are in cover limits moisture availability. From the geomor- good agreement with a reconstruction of Lenangsbreen, phological evidence the assumption was made (above) in Lyngen, about 90 km to the SW (Bakke et al., 2005). that during the T–LS Øksfjordjøkelen was cold-based. A commonly applied empirical temperature–precipi- This assumption exerts a significant control on the tation relationship was used to estimate palaeo-climatic reconstructed mass balance gradients shown in Table 6. conditions at the ELA, which was subsequently corrected The average mass balance gradients calculated for to sea level for ease of comparison. The T–LS mean Øksfjordjøkelen are plotted on Fig. 10 alongside mass summer sea level temperature was obtained from a pollen balance gradients for a sample of glaciers from around record on Andøya (Alm, 1993) and was 5.1 °C. Preci- the world (data from Kuhn, 1984). What is clearly pitation estimates suggest that the T–LS was between apparent is that the reconstructed mass balance gradients 50% to 60% drier than present-day, although there was are indicative of present-day high-latitude maritime still significant precipitation (∼≥558 mm a−1 at sea icefields/glaciers. level). This supports the presence of an, at least seasonal, Present-day Svalbard provides the best analogues. ice-free corridor extending north along the coast of Hagen et al. (2003) sub-divided the archipelago into 13 Norway. Accumulation and ablation gradients have been regions defined by major drainage basins (Fig. 11), and estimated from the calculated ice flux through the ELA show a lowering of mass balance gradient broadly and also indicate a sub-polar type environment, similar to B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330 329 the drier-colder parts of Svalbard (regions 8–10 Fig. 11) Birks, H.H., Paus, A., Svendsen, J.I., Alm, T., Mangerud, J., Landvik, or parts of the Canadian Arctic (Fig. 10) at the present-day J.Y., 1994. Late Weichselian environmental change in Norway, including Svalbard. Journal of Science 9, 133–145. (though the cold-based ice assumption is the first-order Brown, C.S., Meier, M.F., Post, A., 1982. Calving speed of Alaskan control). By extending this type of reconstruction to other tidewater glaciers with applications to the Columbia Glacier, locations along the western margin of the Scandinavian . U.S.Geological Survey Professional Paper 1258-C. Ice Sheet it should be possible to reconstruct palaeo- Dahl, S.O., Nesje, A., 1992. Palaeoclimatic implications based on precipitation along the whole margin, thus making quan- equilibrium-line altitude depressions of reconstructed Younger Dryas and Holocene cirque glaciers in Inner Nordfjord, western tification of palaeo-climate on a larger-scale possible. Norway. Palaeogeography, Palaeoclimatology, Palaeoecology 94, 87–97. Acknowledgements Dahl, S.O., Nesje, A., 1996. A new approach to calculating equilibrium-line altitudes and pine-tree limits: a case study from, Thanks to Helge Andersen for use of his barn, boat- Hardangerjøkelen, central southern Norway. The Holocene 6, 381–398. house and slipway and to Gerrard Kerr for a friendly Evans, D.J.A., Rea, B.R., Hansom, J.D., Whalley, W.B., 2002. The voice and excellent craic. Fieldwork elements were geomorphology and style of plateau icefield glaciation in a fjord undertaken in 1992 on the Queen's University Arctic terrain, Troms–Finnmark, north Norway. Journal of Quaternary Norway Earthwatch Expedition. DJAE would like to Science 17, 221–239. thank the Robertson Bequest of the University of Furbish, D.J., Andrews, J.T., 1984. The use of hypsometry to indicate long-term stability and response of valley glaciers to changes in Glasgow. Thanks also to two anonymous reviewers mass transfer. Journal of 30, 199–211. and the Finn Surlyk for useful comments and sugges- Gellatly, A.F., Whalley, W.B., Gordon, J.E., Hansom, J.D., 1988. tions that helped improve this paper. Thermal regime and geomorphology of plateau ice caps of : observations and implications. 16, 983–986. References Gellatly, A.F., Whalley, W.B., Gordon, J.E., Hansom, J.D., Twigg, D.R., 1989. Recent glacial history and climate change, Bergsfjord, Troms– Alm, T., 1993. Øvre Æråsvatnet - palynostratigraphy of a 22000 to Finnmark, Norway. Norsk Geografisk Tidsskrift 43, 19–30. 10000 BP lacustrine record on Andøya, northern Norway. Boreas Green, F.H.W., Harding, R.J., 1980. The altitudinal gradients of air 22, 177–188. temperature in southern Norway. Geografiska Annaler 62 (A), Andersen, B.G., 1965. Glacial chronology of western Troms, north 29–36. Norway. In: Wright, H.E., Frey, D.G. (Eds.), International Studies Hagen, J.O., Lefauconnier, B., Liestøl, O., 1991. on the Quaternary, VII INQUA Congress, Boulder, Colorado. in Svalbard since 1912. In: Kotlyakov, V.M., Ushakov, A., Geological Society of AmericaSpecial Paper, vol. 84, pp. 35–54. Glazovsky, A. (Eds.), Glaciers–Ocean–Atmospheric Interactions. Andersen, B.G., 1968. Glacial geology of western Troms, North IAHS Publication, vol. 208. Great Yarmouth, United Kingdom, Norway. Norges Geologisk Underskole 256, 1–160. pp. 313–328. Andrews, J.T., 1972. Glacier power, mass balances, velocities and Hagen, J.O., Melvold, K., Pinglot, F., Dowdeswell, J.A., 2003. On the net potential. Zeitschrift fur Geomorphologie, NF 13, 1–17. mass balance of the glaciers and ice caps in Svalbard, Norwegian Augustinus, P.C., 1992. The influence of rock mass strength on glacial Arctic. Arctic, Antarctic, and Alpine Research 35, 264–270. valley cross-profile morphometry: a case study from the Southern Johannesson, T., Raymond, C., Waddington, E., 1989. Timescale for , New Zealand. Surface Processes and Landforms 17, adjustment of glaciers to changes in mass balance. Journal of 39–51. Glaciology 35, 355–369. Bakke, J., Dahl, S.O., Paasche, Ø., Løvlie, R., Nesje, A., 2005. Glacier Kaser, G., Osmaston, H., 2002. Tropical Glaciers. Cambridge fluctuations, equilibrium-line altitudes and palaeoclimate in University Press, Cambridge. Lyngen, northern Norway, during the late glacial and Holocene. Koc, N., Jansen, E., Haflidason, H., 1993. Paleoceanographic recons- The Holocene 15, 518–540. tructions of surface ocean conditions in the , Iceland and Ballantyne, C.K., 1990. The Holocene glacial history of Lyngshal- Norwegian Seas, through the last 14-ka based on diatoms. Qua- vöya, northern Norway: chronology and climatic implications. ternary Science Reviews 12, 115–140. Boreas 19, 93–117. Kotlyakov, V.M., Krenke, A.N., 1982. Investigation of the hydrolog- Benn, D.I., Gemmell, A.M.D., 1997. Calculating equilibrium line alti- ical conditions of alpine regions by glaciological methods. In: tudes of former glaciers by the balance ratio method: a new computer Glen, J.W. (Ed.), Hydrological Aspects of Alpine and High- spreadsheet. Glacial Geology and Geomorphology (http://ggg.qub. Mountain Areas. IAHS Publication, vol. 138, pp. 31–42. ac.uk/papers/full/1997/tn011997/tn01.html). Kovanen, D.J., Slaymaker, O., 2005. Fluctuations of the Deming Benn, D.I., Evans, D.J.A., 1998. Glaciers and Glaciation. Arnold, Glacier and theoretical equilibrium line altitudes during the Later London. and Early Holocene on Mount Baker, , Benn, D.I., Lehmkuhl, F., 2000. Mass balance and equilibrium-line USA. Boreas 34, 157–175. altitudes of glaciers in high-mountain environments. Quaternary Kuhn, M., 1984. Mass budget imbalances as a criterion for a climatic International 65/66, 15–29. classification of glaciers. Geografiska Annaler 66A, 229–238. Benn, D.I., Ballantyne, C.K., 2005. Palaeoclimatic reconstruction Kuhn, M., 1989. The response of the equilibrium line to climate fluc- from Loch Lomond Readvance glaciers in the Westy Drumochter tuations: theory and observations. In: Oerlemans, J. (Ed.), Glacier , Scotland. Journal of 20, 577–592. Fluctuations and Climate Change. Kluwer, Dordrecht, pp. 407–417. 330 B.R. Rea, D.J.A. Evans / Palaeogeography, Palaeoclimatology, Palaeoecology 246 (2007) 307–330

Laaksonen, K., 1976. The dependence of mean air temperatures upon Porter, S.C., 1977. Present and past glaciation threshold in the Cascade latitude and altitude in Fennoscandia (1921–1950). Annales Aca- Range, Washington State, USE: constraints provided by palaeo- demiae scientiarum Fennicae. Series A 3, Geologica - Geographica environmental reconstructions. The Holocene 11, 607–611. 119. Raymond, C.F., 1980. Temperate valley glaciers. In: Colbeck, S.C. Lie, Ø., Dahl, S.O., Nesje, A., 2003. A theoretical approach to glacier (Ed.), Dynamics of Snow and Ice Masses. Academic Press, New equilibrium-line altitudes using meterological data and glacier York, pp. 79–139. mass-balance records from southern Norway. The Holocene 13, Rea, B.R., Whalley, W.B., 1994. Subglacial observations from 365–372. Oksfjordjokelen, North Norway. Earth Surface Processes and Locke, W.W., 1995. Modelling of icecap glaciation of the northern Landforms 19, 659–673. Rocky Mountains of Montana. Geomorphology 14, 123–130. Rea, B.R., Evans, D.J.A., 2003. Plateau icefield landsystems. In: Loewe, F., 1971. Considerations on the origin of the Quaternary ice Evans, D.J.A. (Ed.), Glacial Landsystems. Arnold, pp. 407–431. sheet of . Arctic and Alpine Research 3, 331–344. Rea, B.R., Whalley, W.B., Rainey, M.M., Gordon, J.E., 1996. Marthinussen, M., 1960. Coast and fjord area of Finnmark. In: Blockfields, old or new? Evidence and implications from some Holtedahl, O. (Ed.), Geology of Norway. Norges Geologiske plateaus in northern Norway. Geomorphology 15, 109–121. Undersøkelse, vol. 208, pp. 416–429. Rea, B.R., Whalley, W.B., Evans, D.J.A., Gordon, J.E., McDougall, Marthinussen, M., 1962. 14C datings referring to shorelines, trans- D.A., 1998. Plateau icefields: Geomorphology and dynamics. gressions, and glacial substages in northern Norway. Norges Geo- Journal of Quaternary Science 13, 35–54. logiske Undersøkelse 215, 37–67. Rea, B.R., Whalley, W.B., Dixon, T., Gordon, J.E., 1999. Plateau Meier, M.F., Tangborn, W.V., 1965. Net budget and flow of South icefields as contributing areas to valley glaciers and the potential Cascade Glacier, Washington. Journal of Glaciology 5, 547–566. impact on reconstructed ELAs: a case study from the Lyngen Alps, Meier, M.F., Tangborn, W.V., Mayo, L.R., Post, A., 1971. Combined North Norway. Annals of Glaciology 28, 97–102. ice and water balances lf Gulkana and Wolverine glaciers, Alaska, Rea, B.R., Evans, D.J.A., Dixon, T.S., Whalley, W.B., 2000. and South Cascade Glacier, Washington, 1965 and 1966 Contemporaneous, localized, basal ice-flow variations: implica- Hydrologic Years. USGS Prof. Paper 715-A. tions for bedrock erosion and the origin of p-forms. Journal of Mitchell, W.A., 1996. Significance of snowblow in the generation of Loch Glaciology 46, 470–476. Lomond (Younger Dryas) glaciers in the western Pennines, Schilling, D.H., Hollin, J.T., 1981. Numerical reconstructions of valley northern England. Journal of Quaternary Science 11, 233–248. glaciers and small ice caps. In: Denton, G.H., Hughes, T.J. (Eds.), Murray, D.R., Locke, W.W., 1989. Dynamics of the Late Pleistocene The Last Great Ice Sheets. Wiley & Sons, New York, pp. 207–220. Big Timber Glacier, Crazy Mountains, Montana, USA. Journal of Sollid, J.L., Andersen, S., Hamre, N., Kjeldsen, O., Salvigsen, O., Sturod, Glaciology 35, 183–190. S., Tveita, T., Wilhelmsen, A., 1973. Deglaciation of Finnmark, Nesje, A., 1992. Younger Dryas and Holocene glacier fluctuations and North Norway. Norsk Geografisk Tidsskrift 27, 233–325. equilibrium-line altitude variations in the Jostedalsbre region, Sutherland, D.G., 1984. Modern glacier characteristics as a basis for western Norway. Climate Dynamics 6, 221–227. inferring former climates with particular reference to the Loch Nesje, A., Dahl, S.O., 2000. Glaciers and Environmental Change. Lomond Stadial. Quaternary Science Reviews 3, 291–309. Arnold, London. Van der Veen, C.J., 2002. Calving glaciers. Progress in Physical Nye, J.F., 1952. The mechanics of glacier flow. Journal of Glaciology Geography 26, 96–122. 2, 82–93. Warren, C.R., Greene, D.R., Glasser, N.F., 1995. Glaciar Upsala, Pata- Nye, J.F., 1965. The flow of a glacier in a channel of rectangular elliptic gonia: rapid calving retreat in fresh water. Annals of Glaciology 21, or parabolic cross-section. Journal of Glaciology 5, 661–690. 311–316. Ohmura, A., Kasser, P., Funk, M., 1992. Climate at the equilibrium Whalley, W.B., Gordon, J.E., Thompson, D.L., 1981. Periglacial fea- line of glaciers. Journal of Glaciology 38, 397–411. tures on the margins of a receding plateau , Lyngen, North Osmaston, H., 2005. Estimates, of glacier equilibrium line altitudes by Norway. Journal of Glaciology 27, 492–496. the area×altitude, the area×altitude balance ratio and the area×- Whalley, W.B., Gordon, J.E., Gellatly, A.F., Hansom, J.D., 1995. altitude balance index methods and their validation. Quaternary Plateau and valley glaciers in north Norway: responses to climate International 138–139, 22–31. change over the last 100 years. Zeitschrift für Gletscherkunde und Paterson, W.S.B., 1994. The Physics of Glaciers, 3rd edition. Pergam- Glazialgeologie 31, 115–124. mon, Oxford. Porter, S.C., 1975. Equilibrium line altitudes of Quaternary glaciers in the Southern Alps, New Zealand. Quaternary Research 5, 27–47.