José M Fernández-Fernández
email: josemariafernandez@ucm.es

The Tröllaskagi Peninsula in northern Iceland hosts more than a hundred small glaciers that have left a rich terrestrial record of Holocene climatic fluctuations in their forelands. Traditionally, it has been assumed that most of the Tröllaskagi glaciers reached their Late Holocene maximum extent during the Little Ice Age (LIA). However, there is evidence of slightly more advanced pre-LIA positions. LIA moraines from Iceland have been primary dated mostly through lichenometric dating, but the limitations of this technique do not allow dating of glacial advances prior to the 18 th or 19 th centuries. The application of 36 Cl Cosmic-Ray Exposure (CRE) dating to Tungnahryggsjökull moraine sequences in Vesturdalur and Austurdalur (central Tröllaskagi) has revealed a number of pre-LIA glacial advances at ~400 and ~700 CE, and a number of LIA advances in the 15 th and 17 th centuries, the earliest LIA advances dated so far in Tröllaskagi. This technique hence shows that the LIA chronology in Tröllaskagi agrees with that of other European areas such as the Alps or the Mediterranean mountains. The combined use of lichenometric dating, aerial photographs, satellite images and fieldwork shows that the regional colonization lag of the commonly used lichen species Rhizocarpon geographicum is longer than previously assumed. For exploratory purposes, an alternative lichen species (Porpidia soredizodes) has been tested for lichenometric dating, estimating a tentative growth rate of 0.737 mm yr -1 .

Introduction

The Tröllaskagi Peninsula (northern Iceland) hosts over 160 small alpine cirque glaciers (Björnsson, 1978; see synthesis in Andrés et al., 2016). Only a few of these small glaciers do not have supraglacial debris cover that allows them to react quickly to small climatic fluctuations (Caseldine, 1985b;Häberle, 1991;Kugelmann, 1991), compared to Revised manuscript with changes marked Click here to view linked References the reduced dynamism of the predominant rock glaciers and debris-covered glaciers (Martin et al., 1991;Andrés et al., 2016;Tanarro et al., 2019). As a result of their high sensitivity to climatic changes, the few debris-free glaciers in Tröllaskagi fluctuated repeatedly in the past, forming a large number of moraines in front of their termini (see Caseldine, 1983Caseldine, , 1985bCaseldine, , 1987;;Kugelmann, 1991 amongst others). However, the relation between glacier fluctuations and the climate is complicated due to: (i) the wellknown surging potential activity in Tröllaskagi (Brynjólfsson et al., 2012;Ingólfsson et al., 2016); (ii) the possibility of glaciers being debris-covered in the past, with the subsequent change of their climate sensitivity over time; (iii) the intense and dynamic slope geomorphological activity, paraglacial to a great extent (Jónsson, 1976;Whalley et al., 1983;Mercier et al., 2013;Cossart et al., 2014;Feuillet et al., 2014;Decaulne and Saemundsson, 2006;Saemundsson et al., 2018) that hides and erases the previous glacial features.

In Iceland, a great part of the research on glacial fluctuations during the late Holocene, LIA (Grove, 1988;1250-1850CE, see Solomina et al., 2016) and later stages has been approached through application of radiocarbon dating of organic material, analyzing lake sediment varves (Larsen et al., 2011;Striberger et al., 2012), dead vegetation remnants (Harning et al., 2018) and threshold lake sediment records (Harning et al., 2016b;Schomacker et al., 2016). These provide high-resolution records of glacier variability. In Tröllaskagi, very few reliable dates exist at present, obtained from radiocarbon and tephrochronology (Häberle, 1991(Häberle, , 1994;;Stötter, 1991;Stötter et al., 1999;Wastl and Stötter, 2005). They suggest that late Holocene glaciers were slightly more advanced than during the LIA maximum in Tröllaskagi. However, these techniques only provide minimum or maximum ages for Holocene glacier history in northern Iceland (Wastl and Stötter, 2005). In addition, at Tröllaskagi most of the moraines are at 600-1000 m a.s.l., where the applicability of tephrochronology is very limited (Caseldine, 1990) due to the great intensity of slope geomorphological processes.

In any case, most of the moraine datings of Tröllaskagi especially those of the last millenium comes from lichenometry (see synthesis in Decaulne, 2016). However, the ages derived from this technique tend to be younger if they are compared to those estimated from tephra layers (Kirkbride and Dugmore, 2001). Generally, there is disagreement about the validity of the results provided by lichenometry, due to the difficulty of the lichen species identification in the field, the complexity and reliability of the sampling and measurement strategies, the uncertainty estimates, the nature of the ages provided as relative, as well as the relative reliability at producing lichen growth curves of the different species, with an extreme dependence on local environmental factors (see [START_REF] Osborn | Lichenometric dating: Science or pseudo-science?[END_REF].

In fact, these problems had already been detected in northen Iceland, where in spite of the time elapsed since the first applications of this technique (Jaksch, 1970(Jaksch, , 1975(Jaksch, , 1984;;Gordon and Sharp, 1983;Maizels and Dugmore, 1985) and contrasting with its widespread use in the south and southeast of the island (Thompson and Jones, 1986;Evans et al., 1999;Russell et al., 2001;Kirkbride and Dugmore, 2001;Bradwell, 2001Bradwell, , 2004a;;Harris et al., 2004;Bradwell and Armstrong, 2006;[START_REF] Orwin | Identifying moraine surfaces with similar histories using lichen size distributions and the U2 statistic, Southeast Iceland[END_REF]Chenet et al., 2010 and others), there are still very few established growth rates for the lichen group Rhizocarpon geographicum (Roca-Valiente et al., 2016) from Tröllaskagi (Caseldine, 1983;Häberle, 1991;Kugelmann, 1991;Caseldine and Stötter, 1993; see synthesis in Decaulne, 2016). In general, the growth curves from Tröllaskagi suffer from a few control points (i.e. surfaces of known age) for calibration. This leads to considerable underestimation when lichen thalli sizes are beyond the calibration growth curve (Caseldine, 1990; see e.g. Caseldine, 1985b;Caseldine and Stötter, 1993;Kugelmann, 1991). That is to say, the extrapolation does not account for the decreasing growth rate with increasing age (i.e. non-linear growth). Kugelmann s (1991) growth curve has the highest number of control points to date (19 in total). In addition, the colonization lag in Tröllaskagi is poorly defined, although 10-15 years have been assumed for the Rhizocarpon geographicum (Caseldine, 1983;Kugelmann, 1991).

Other issues, such as the absence of large thalli (Maizels and Dugmore, 1985), lichen saturation (e.g. Wiles et al., 2010), and other environmental factors (Innes, 1985 and references included;Hamilton and Whalley, 1995) contribute to appreciable age underestimations when dating surfaces using this approach. Snow is also a major environmental factor for lichenometry in Iceland due to its long residence time on the ground (Dietz et al., 2012) and the avalanching frequency especially in Tröllaskagi , whose effect restricts the growth rate of lichens, and even destroys them (Sancho et al., 2017). These problems considerably limit the quality (reliability) of the lichenometric dating range of utility for applying lichenometric dating in Iceland, where the oldest ages estimated so far are between 160 and 220 years (Maizels and Dugmore, 1985;Thompson and Jones, 1986;Evans et al., 1999), thus preventing the dating of glacial advances prior to the 18 th century.

In spite of the high uncertainty of the lichenometric dating, many authors working in Tröllaskagi have treated their lichenometric results as absolute ages (see Caseldine, 1983Caseldine, , 1985bCaseldine, , 1987;;Kugelmann, 1991;Häberle, 1991;Caseldine and Stötter, 1993, amongst others). In fact, previously considered dates of LIA maximum glacier culmination are restricted to the very late 18 th and early 19 th centuries (Caseldine, 1983(Caseldine, , 1985b(Caseldine, , 1987;;Kugelmann, 1991;Caseldine and Stötter, 1993;Caseldine, 1991;Martin et al., 1991), very close to the applicability threshold of this method. Consequently, no evidence of previous advances during phases of the LIA that were more conducive to glacier expansion (probably colder; see e.g. [START_REF] Ogilvie | The past climate and sea-ice record from Iceland, Part 1: Data to A.D. 1780[END_REF]Ogilvie, , 1996;;[START_REF] Ogilvie | Sea ice, climate, and Icelandic fisheries in the eighteenth and nineteenth centuries[END_REF][START_REF] Ogilvie | Little Ice Age Research: a perspective from Iceland[END_REF] has been found (Kirkbride and Dugmore, 2001).

In the recent years, dating methods based on the Exposure to the Cosmic-Rays (CRE) have been introduced successfully to date moraines of the last millennium, and even formed during the LIA (Schimmelpfennig et al., 2012(Schimmelpfennig et al., , 2014;;Le Roy et al., 2017;Young et al., 2015;Jomelli et al., 2016;Li et al., 2016;Dong et al., 2017;Palacios et al., 2018). The cosmogenic nuclides 36 Cl and 3 He have been applied previously in northern Iceland to date the Pleistocene deglaciation. Principato et al. (2006) studied the deglaciation of Vestfirðir combining 36 Cl CRE dating of moraine boulders and bedrock surfaces with marine records and tephra marker beds. Andrés et al. (2018) reconstructed the deglaciation at the Late Pleistocene to Holocene transition at Skagafjörður through 36 Cl CRE dating applied to polished surfaces along a transect from the highlands to the mouth of the fjord. Brynjólfsson et al. (2015b) applied the same isotope to samples coming from the highlands and the fjords to reconstruct the glacial history of the Drangajökull region. The other cosmogenic isotope used is 3 He, applied to heliumretentive olivine phenocrysts by Licciardi et al. (2007) to determine eruption ages of Icelandic table mountains and to reconstruct the volcanic history and the thickness evolution of the Icelandic Ice Sheet during the last glacial cycle. However, CRE dating

has not yet been applied to the late Holocene glacial landforms both in Iceland as a whole and the Tröllaskagi Peninsula. CRE dating is an alternative to the use of highresolution continuous lacustrine records in northen Iceland, given the rarity of lakes in this peninsula, which limits the application of radiocarbon to date the deglaciation processes (Striberger et al., 2012;Harning et al., 2016b).

Nevertheless, CRE dating methods approach the nuclides detection limit when applied to very recent moraines (Marrero et al., 2016;Jomelli et al., 2016). This issue precludes the application of CRE dating to the abundant post-LIA moraines existing in some of the Tröllaskagi valleys whose headwalls are occupied by climate-sensitive debris-free glaciers (Caseldine and Cullingford, 1981;Caseldine, 1983Caseldine, ,1985b;;Kugelmann, 1991;Fernández-Fernández et al., 2017). Dating these post-LIA moraines allows to reconstruct recent climate evolution, and even to match and assess the climate reconstructions with the instrumental climate records (see Dahl and Nesje, 1992;Caseldine and Stötter, 1993;Fernández-Fernández et al., 2017). Futhermore, improving the knowledge of the recent evolution of alpine mountain glaciers, such as those of Tröllaskagi, is fundamental in the assessment of present global warming (Marzeion et al., 2014) The use of aerial photographs from different dates is a reliable approach to the glacier evolution during the last decades (Fernández-Fernández et al., 2017;Tanarro et al., 2019). The main advantage of this technique is the possibility of studying the evolution of glacier snouts in recent dates with high accuracy. In fact, there is no dependence on the glacial features (i.e. moraines), which circumvents moraine deterioration issues derived by the geomorphological activity of the slopes. However, the main shortcoming of the aerial photo imagery is the availability only on few dates, at least in Tröllaskagi.

This circumstance makes it impossible to obtain the glacier fluctuations with a high time resolution (i.e. only the periods between the available aerial photos; Fernández-Fernández et al., 2017;Tanarro et al., 2019), and hence to match them to short-term (decadal scale) climate fluctuations that are known to exert a major control especially on small mountain glaciers with short time responses (see Caseldine, 1985b;Sigurðsson, 1998;Sigurðsson et al., 2007;Fernández-Fernández et al., 2017). The only way to fill the gap between two dates with available aerial photos is through applying lichenometric dating (Sancho et al., 2011), as there is no tree species suitable to apply dendrochronology. In addition, the information provided by the aerial photo imagery (i.e. glacier snout position) constrains the period when the lichens appear and begin to grow, which circumvents many of the criticisms made on lichenometry (see [START_REF] Osborn | Lichenometric dating: Science or pseudo-science?[END_REF].

Moreover, a detailed geomorphological mapping allows for identification of stable moraines, not remobilized or destroyed by glacier advances or slope processes (avalanches, slope deformations, debris-flows, etc.) and also to reconstruct the glacier snout geometry throughout different phases (see Caseldine, 1981;Bradwel, 2004b;Principato et al., 2006 amongst others). The analysis of the moraine morphology and the glacial features on the forelands is a key tool to confirm whether the glaciers were debris-free or debris-covered in the past (Kirkbride, 2011;Janke et al., 2015;Knight, et al., 2018, amongst others) as this issue determines their climate sensitivity (see Fernández-Fernández et al., 2017;Tanarro et al., 2019).

The western and eastern Tungnahryggsjökull glaciers, in the Vesturdalur and Austurdalur Valleys (central Tröllaskagi), respectively (Fig. 1), are two of the few debris-free glaciers or almost debris-free in the case of the western glacier of the peninsula that are both small and highly sensitive to climatic fluctuations (Fernández-Fernández et al., 2017). This makes them ideal for studying glacial and climatic evolution during last last millennia.

The aim of our work was to apply the best methodology possible to analyze the glacial evolution of western and eastern Tungnahryggsjökull glaciers during the last millennia to the present. Applying for the first time a number of dating techniques to study the Late Holocene evolution of the two glaciers, the objectives of this paper are:

(i) To carry out a detailed geomorphological survey of the glacier forelands in order to map accurately well-preserved glacial features. This mapping is used both to devise the sampling strategy for dating, and also to reconstruct the palaeoglaciers in 3D in order to obtain glaciologic climate indicators such as the Equilibrium-Line Altitudes (ELAs).

These can be used as a proxy to infer palaeoclimatic information (see Dahl and Nesje, 1992;Caseldine and Stötter, 1993;Brugger, 2006;Hughes et al., 2010;Fernández-Fernández et al., 2017 amongst others).

(ii) To use aerial photographs / satellite imagery post-dating 1946 to map the glacier extent in each available date in order to improve the information of ELA evolution in the recent decades. Aerial photographs will be used to constrain the possible periods of lichen colonization and growth over stable boulders, and will be useful to identify phases of advance, stagnation or retreat of the glacier snouts. By this way we will complete the glacier evolution from pre-instrumental glacial stages (identified from geomorphological evidence, i.e. moraines) to their current situation.

(iii) To apply CRE dating when possible depending on the preservation degree of the glacial features, and when moraines were too old to be dated by lichenometry.

(iv) To apply lichenometric relative dating to recent moraines or those where CRE dating might not be suitable (i.e. limit of applicability) and provided that: 1) the geomorphological criteria evidence a good preservation of glacial features; and 2) aerial photographs constrain the earliest and oldest possible lichen ages. This approach will also allow to check the growth rates and colonization lags of the lichen species usually used in Iceland for lichenometric dating purposes.

The experimentation and validation of this methodological purpose will help to improve the knowledge of the recent climate evolution of northern Iceland. This is of maximum interest if we consider its location within the current atmospheric and oceanic setting, strongly linked to the evolution of the Meridional Overturning Circulation (Andrews and Giraudeau, 2003;Xiao et al., 2017), a key factor in the studies for the assessment of the global climate change effects (Barker et al., 2010;Chen et al., 2015 amongst others).

Moreover, if this proposal is valid, it could be applied to the research on the recent evolution of other mountain glaciers similar to those of Tröllaskagi. This aspect is a main research objective at present, as these glaciers represent the greatest contribution to the current sea-level rise (Jacob et al., 2012;Gardner et al., 2013 amongst others).

Regional setting

The Tröllaskagi Peninsula extends into the Atlantic Ocean at 66 12 N from the central highland plateau (65 23 N) of Iceland (Fig. 1). The fjords of Skagafj r ur (19 30 W) and E jafj r ur (18 10 W) separate it from the Skagi and Flate jarskagi peninsulas, respectively. Tröllaskagi is an accumulation of successive Miocene basalt flows, interspersed with reddish sedimentary strata (Saemundsson et al., 1980;Jóhannesson and Saemundsson, 1989). The plateau culminates at altitudes of 1000-1500 m a.s.l. (with the highest peak Kerling at 1536 m a.s.l.) and is dissected by deep valleys with steep slopes whose headwaters are currently glacial cirques. These cirques host more than 160 small glaciers, mostly north-facing, resulting from the leeward accumulation of snow from the plateau (Caseldine and Stötter, 1993) and reduced exposure to solar radiation.

In fact, deposits caused by rock-slope failure are common in Tröllaskagi valley slopes and have been considered a result of the final deglaciation during the early Holocene (Jónsson, 1976;Feuillet et al., 2014;Cossart et al., 2014;Coquin et al., 2015). Most of the glaciers are rock or debris-covered glaciers, due to the intense paraglacial activity affecting the walls that minimizes cosmogenic nuclide concentrations from earlier exposure periods on the cirque headwalls (Andrés et al, 2018).

The climate in Tröllaskagi is characterized by a mean annual air temperature (MAAT; 1901-1990 series) of 2 to 4 °C at sea level, dropping to between -2 and -4 °C at the summits (Etzelmüller et al., 2007). At the town of Akureyri, located in the east of the peninsula at the mouth of Eyjafjarðardalur (Fig. 1), the MAAT is 3.4 °C and the average temperature in the three summer months is about 9 to 10 °C (Einarsson, 1991). Annual precipitation ranges from 400 mm at lower altitudes to 2500 mm at the summits (Crochet et al., 2007).

The frontier location of Icelandic glaciers in relation to atmosphere and ocean systems (warm/moist Subtropical and cold/dry Arctic air masses; and the warm Irminger and cold East Greenland sea currents) makes them exceptionally sensitive to climate oscillations (Bergþórsson, 1969;Flowers et al., 2008;Geirsdóttir et al., 2009), and these debris-free glaciers are thus reliable indicators of climatic evolution and the impact of climate change on the cryosphere (see Jóhannesson and Sigurðsson, 1998;Bradwell, 2004b;Sigurðsson, 2005;Geirsdóttir et al., 2009;Fernández-Fernández et al., 2017).

The glaciers studied here are the western (6.5 km 2 ) and eastern (3.9 km 2 ) Tungnahryggsjökull, located in the Vesturdalur and Austurdalur valleys respectively, separated from each other by the crest of Tungnaryggur, and tributaries of the Kolbeinsdalur Valley (Fig. 1).

Methodology

Geomorphological mapping and glacier geometry mapping

Four summer field campaigns (2012, 2013, 2014 and 2015) were conducted in Vesturdalur and Austurdalur, with the objective of identifying moraines that clearly provided evidence of various glacial culminations of the western and eastern Tungnahryggsjökull glaciers. We identified the palaeo-positions of the glacier snouts, the glacier geometry and extent through photo interpretation of stereoscopic pairs and previous fieldwork. Mapping of glacial and non-glacial landforms was conducted on two enlarged 50-cm-resolution aerial orthophotos (National Land Survey of Iceland, 2015) plotted at scale 1:7000. These maps ere imported into an ArcGIS 1.4.1 database after geo-referencing. Finally, all the glacial linear landforms were digitized, and where the moraines were prominent, continuous, or well-preserved, they were assumed to represent major culminations, and hence, glacial stages. In addition to the geomorphological evidence, glacier variations in recent years were mapped, based on the photo interpretation of four historical aerial photographs from 1946, 1985, 1994and 2000(National Land Survey of Iceland, 2015), and also one SPOT satellite image (2005), previously geo-referenced in ArcGIS. For more details of the aerial photograph processing, see Fernández-Fernández and Andrés (2018). As the glacier headwalls are ice diffluences in both cases, it was assumed that: (i) the ice divides are the upper boundaries of the glaciers for the different stages, and (ii) the ice divide is invariant for the different stages/dates, following Koblet et al. (2010) as changes in the extent of the accumulation zone are smaller than the outlining differences derived from the operator mapping. Likewise, in the case of the upper glacier edge constrained by the cirque wall, the glacier geometry was also assumed to be invariant from stage to stage unless the aerial photographs showed otherwise.

Glacier reconstruction and equilibrium-line altitude (ELA) calculation

Benn and Hulton s (2010) glacier reconstruction approach using a physical-based model describing ice rheology and glacier flow (Van der Veen, 1999) was preferred to arbitrary hand-drawn contouring (e.g. Sissons, 1974) in order to achieve more robust reconstructions (Fernández-Fernández and Andrés, 2018). This model operates on deglaciated areas with non-extant glaciers. As this is not the case in our study area, we approached the glacier bedrock b tentati el estimating the ice thickness spatial distribution on the two glaciers studied. The VOLTA ( Volume and Topograph Automation ) ArcGIS toolbo (James and Carrivick, 2016) was applied with the default parameters. It only requires the glacier outline and its digital elevation model (DEM). In the first step, the tool olta_1_2_centreline creates the glacier centrelines, and then the tool olta_1_2_thickness estimates ice thickness at points along them, assuming perfect-plasticity rheology, and interpolates the values using a glaciologically correct routine. The final result is an ice-free DEM in which we reconstructed the glacier. The former glacier surface topographies at the different stages/dates were reconstructed applying the semi-automatic GLaRe ArcGIS toolbo designed b [START_REF] Pellitero | GlaRe, a GIS tool to reconstruct the 3D surface of palaeoglaciers[END_REF], which implements the Benn and Hulton (2010) numerical model and estimates ice-thickness along glacier flowlines. To simplify the glacier surface modelling, shearstress was assumed to be constant along the glacier flowline and over time. Using the value 110 kPa for the shear-stress resembles best the current longitudinal profile of the glaciers in the Benn and Hulton (2010) spreadsheet. This value can be considered appropriate as it falls within the normal shear-stress range of 50-150 kPa observed in current glaciers and is very close to the standard value of 100 kPa [START_REF] Paterson | The Physics of Glaciers, 3 rd Edition[END_REF]. The glacier contours were manually adjusted to the ice surface elevation values of the icethickness points estimated b GLaRe instead of using an interpolation routine, to obtain a more realistic surface (concave and convex contours above and below the ELA).

Finall , e calculated the ELAs automaticall b using the ELA calculation ArcGIS toolbox [START_REF] Pellitero | A GIS tool for automatic calculation of glacier equilibrium-line altitudes[END_REF]. The methods comprised: (i) AABR (Area Altitude Balance Ratio; [START_REF] Osmaston | Estimates of glacier equilibrium line altitudes by the Area × Altitude, the Area × Altitude Balance Ratio and the Area × Altitude Balance Index methods and their validation[END_REF] with the ratio 1.5±0.4 proposed for Norwegian glaciers by Rea (2009) and successfully tested on Tröllaskagi debris-free glaciers in Fernández-Fernández et al. (2017); and (ii) the AAR (Accumulation Area Ratio) with the ratio 0.67 previously used by Stötter (1990) and Caseldine and Stötter (1993) for Tröllaskagi glaciers. Alternative approaches for ELA calculation in northern Iceland have been carried out by considering morphometric parameters of glacial cirques (altitude ratio, cirque floor, minimum point; Ipsen et al., 2018). However, we preferred the methods considering the glacier hypsometry as they reflect more evident changes from stage to stage (Fernández-Fernández et al., 2017;Fernández-Fernández and Andrés, 2018), if compared to morphometric parameters of the cirques. In this sense, the cirque floor elevation is derived from the last erosion period, and it is impossible to know the values corresponding to previous glacial stages.

Lichenometric dating procedures

Lichenometry was used as a relative dating tool, assuming that the lichens increase in diameter with respect to age. The results aim to complete the age control (of recent landforms non suitable for CRE dating) on the periods between aerial photos of known date as it has been applied successfully to control lichen (Sancho et al., 2011) and bryophyte (Arróniz-Crespo et al., 2014) growth during primary succession in recently deglaciated surfaces. First, we surveyed the moraines thoroughly, starting from the current glacier snouts downwards, looking for large stable boulders (i.e. well embedded in the moraine, not likely of having been overturned or remobilized by slope processes which could have affected lichen growth, e.g. snow avalanches, debris-flows, rockfall, landslides or debris-flows) with surfaces valid for dating (not weathered or resulting from block break). Lichenometry was applied to date moraine ridge boulders with the following criteria and assumptions: (i) boulders must clearly belong to the moraine ridge; (ii) lichen species should be abundant enough to allow measurements of a number of thalli at each location and hence enable surfaces to be dated under favourable environmental conditions such as basaltic rocks in subpolar mountains; (iii) only the largest lichen (circular or ellipsoidal thalli) of species Rhizocarpon geographicum, located on smooth horizontal boulder surfaces, was measured; (iv) the lichenometric procedures should not be applied when the lichen thalli coalesce on the boulder surface and individual thalli cannot be identified. We preferred the geomorphological criterion (stability vs. slope processes) to the establishment of lichenometry plots of a fixed area (e.g. Bickerton and Matthews, 1992) to ensure that lichens were measured on reliable boulders. This measurement strategy tries to circumvent or at least to minimize the specific problems of Tröllaskagi when dating glacial features so that: (i) snow accumulation should be lower in the moraine crest; (ii) lichen ages will be estimated only for the boulders located on the crests used to map and reconstruct the glaciers; and

(iii) and lichens subjected to thalli saturation (coalescence) or high competition are not measured.

First, Rhizocarpon geographicum lichens were measured with a Bernier calibrator.

Then, digital photographs for high-precision measurements were taken of the most representative of the largest thallus located in each selected boulder (Suppl. figure SF1), using an Icelandic króna coin (21 mm diameter) parallel to the surface of the lichen as a graphic scale. We preferred the single largest lichen approach as previously has been done in Tröllaskagi for lichenometric dating of moraines (Caseldine, 1983(Caseldine, , 1985b(Caseldine, , 1987;;Kugelmann, 1991). The photos were scaled in ArcGIS to real size and lichen thalli were outlined manually through visual inspection of the photos and measured automatically with high accuracy according to the diameter of the smallest circle which can circumscribe the lichen outline (Suppl. figure SF1). We preferred the simple geometrical shape of the circle and its diameter to identify the largest axis to circumvent the problem of complex-shaped lichens. Similar procedures for lichen thalli measurement from photographs are outlined in Hooker and Brown (1977).

Then, we initially applied a 0.44 mm yr -1 constant growth rate and a 10-year colonization lag (Kugelmann, 1991) to the measurement of the largest Rhizocarpon geographicum lichen (longest axis). This growth rate is derived from the lichen growth curve with the highest number of control points so far in Tröllaskagi (Kugelmann, 1991), and it is very similar to that reported from the near Hörgárdalur valley (Häberle, 1991). However, the authors are aware that using a constant growth rate implies not taking account the growth rate decline with increasing age. Other longer colonization lags of 15, 20, 25 and 30 years were added to the age estimate from the growth rate in order to test the colonization lag originally assumed by Kugelmann (1991), on the suspicion of longer colonization lags reported elsewhere (Caseldine, 1983;Evans et al., 1999, Table 1). The resulting ages were compared to the dates of historical aerial photographs where the glacier snout positions constrain the maximum and minimum ages of the lichen stations.

In the case of Porpidia cf. soredizodes, since no growth rate value has been described so far, a value will be tentatively estimated in this study. For this reason, we took measurements of the two species in the same sampling locations wherever possible. It should be noted that visual distinction between Porpidia cf. soredizodes and Porpidia tuberculosa is not always conclusive based on morphological characteristics, but we feel confident using the measurements of the Porpidia cf. soredizodes we identified in the field.

36 Cl Cosmic-Ray Exposure (CRE) dating

Where the thalli either coalesced and prevented identification of the largest thallus or dating results indicated that a moraine was too old to be dated by this method, rock samples were collected for CRE dating. The criteria for boulder and surface selection where the same as for lichenometric purposes: stable boulders with no signs of being affected by slope processes (landslides, debris-flows) or postglacial overturning, well embeded in themoraine, and with no sign of surface weathering or previous boulder break. The cosmogenic nuclide 36 Cl was chosen because of the basalt lithology ubiquitous in Iceland, which lacks quartz, which is needed for standard 10 Be CRE methods. Using a hammer and chisel, samples were collected from flat-topped surfaces of moraine boulders. In order to obtain a maximum time constraint for the deglaciation of both surveyed valleys, two samples were taken from Elliði (Fig. 1), a glacially polished ridge downstream from the Tungnahryggsjökull forelands separating Kolbeinsdalur to the north and Víðinesdalur to the south. The laboratory procedures applied for 36 Cl extraction from silicate whole rock samples were those described in Schimmelpfennig et al. (2011). Note that the samples had not enough minerals to perform the 36 Cl extraction on mineral separates, which is generally the preferred approach to minimize the uncertainties in age exposure estimates, as in mineral separates 36 Cl is often produced by less and better known production pathways than in whole rock samples (Schimmelpfennig et al., 2009). The samples were crushed and sieved to 0.25-1 mm in the Physical Geography Laboratory in the Complutense University, Madrid. Chemical processing leading to 36 Cl extraction from the whole rock was carried out at the Laboratoire National des Nucléides Cosmogéniques (LN 2 C) at the Centre Europe n de Recherche et d Enseignement des G osciences de l En ironnement (CEREGE), Aix-en-Provence (France). Initial weights of about 120 g per sample were used. A chemically untreated split of each sample was set aside for analyses of the chemical composition of the bulk rocks at CRPG-SARM. First, the samples were rinsed to remove dust and fines. Then, 25-30% of the mass was dissolved to remove atmospheric 36 Cl and potentially Cl-rich groundmass by leaching with a mixture of ultra-pure dilute nitric (10% HNO 3 ) and concentrated hydrofluoric (HF) acids. In the next step, 2 g aliquots were taken to determine the major element concentrations; these were analysed by ICP-OES at CRPG-SARM. Then, before total dissolution, ~260 µL of a 35 Cl carrier solution (spike) manufactured in-house (concentration: 6.92 mg g -1 ;

35 Cl/ 37 Cl ratio: 917) were added to the sample for isotope dilution (Ivy-Ochs et al., 2004). Total dissolution was achieved with access quantities of the above mentioned acid mixture. Following total dissolution, the samples were centrifuged to remove the undissolved residues and gel (fluoride complexes such as CaF 2 ). Next, chlorine was precipitated to silver chloride (AgCl) by adding 2 ml of silver nitrate (AgNO 3 ) solution at 10%. After storing the samples for two days in a dark place to allow the AgCl to settle on the bottom, the supernatant acid solution was extracted by a peristaltic pump.

To reduce the isobaric interferences of 36 S during the 36 Cl AMS measurements, the first precipitate was re-dissolved in 2 ml of ammonia (NH 3 +H Cl (g Ti) -1 yr -1 for Ti spallation (Fink et al., 2000), 1.9±0.2 atoms 36 Cl (g Fe) -1 yr -1 for Fe spallation (Stone et al., 2005) and 696±185 neutrons (g air) -1 yr -1 for the production rate of epithermal neutrons for fast neutrons in the atmosphere at the land/atmosphere interface (Marrero et al., 2016). Elevation-latitude scaling factors were based on the time in ariant St scheme (Stone et al., 2000). The high-energy neutron attenuation length value applied was 160 g cm -2 .

All production rates from spallation of Ca mentioned above are based on calibration samples with a predominant Ca composition. Iceland is permanently affected by a lowpressure cell, the Icelandic Low (Einarsson, 1984). As the atmospheric pressure modifies the cosmic-ray particle flux, and thus has an impact on the local cosmogenic nuclide production rate, the atmospheric pressure anomaly has to be taken into account when scaling the SLHL production rates to the study site. Only Licciardi et al. s (2008) production rate already accounts for this anomaly, as the calibration sites of study are located in south western Iceland (see also Licciardi et al., 2006). On the other hand, Stone et al. s (1996) and Schimmelpfennig et al. s (2011) production rates were calibrated in Tabernacle Hill (Utah, western U.S.A.) and Etna volcano (Italy), respectively, hence they need to be corrected for the atmospheric pressure anomaly when applied in Iceland. Dunai (2010) advises including any long-term atmospheric pressure anomaly at least for Holocene exposure periods. Therefore, the local atmospheric pressure at the sample locations was applied in the scaling factor calculations when using the Stone et al. (1996) (Reimer et al., 2013).

Results

Geomorphological mapping, aerial photos and identified glacial stages

Based on photo-interpretation of aerial photographs and fieldwork, two geomorphological maps were generated at ~1:7000 scale, in which well preserved moraine segments, current glacier margins and stream network were also mapped (Figs.

2 and 3). In Vesturdalur, over 1000 moraine ridge fragments (including terminal and lateral moraine segments) were identified and mapped, with increased presence from Following these criteria, we retained 12 glacial stages based on the geomorphological mapping of the Vesturdalur foreland (Fig. 2). We were able to verify in the field that the selected sections had not been affected by postglacial slope processes as none of these moraines was cut by debris-flows or deformated/covered by landslides. The palaeoposition of the glacier terminus was clearly defined by pairs of latero-frontal moraines in stages 1, 4 and 6. In stages 2, 3, 5, 9, 10, 11 and 12, it was poorly defined by short latero-frontal moraines on one side of the valley, very close to the river, with their prolongation and intersection with the river assumed to be the former apex, and so a tentative terminus geometry was drawn. The lateral geometry of the tongue was accurately reconstructed in stages 6, 8 and 9 based on long and aligned, ridge fragments, and in the other stages an approximate geometry was drawn from the terminus to the headwall. The greatest retreat between consecutive stages (1 km) occurred in the transition from the stage 1 to the stage 2. No intermediate frontal moraines were observed in the transect between the stages 1 and 2.

In Austurdalur, over 1600 moraine ridge fragments were identified and mapped.

Following the same criteria as in Vesturdalur, 13 stages were identified based on the geomorphological evidence (Fig. 3). The furthest moraines marking the maximum extent of the eastern Tungnahryggsjökull appear at ST1). The stages identified on the basis of the geomorphological mapping and those obtained from glacier outlining over historical aerial photos sum up to a total of 17 stages for each glacier.

Glacier length, extent and volume

The reconstructed glacier surfaces corresponding to the different glacial stages is shown in Suppl. figure SF3. The length of the glaciers during their reconstructed maximum ice extent was unequal, with the western Tungnahryggsjökull being 6.5 km long, and the eastern glacier being 3.8 km long (Suppl. table ST2). The same occurred with the area, 9.4 and 5.3 km 2 , respectively (Suppl. table ST3). Over the different stages, the western glacier lost 31% of its area and retreated 51% of its total length (Suppl. tables ST2 and ST3) while there was less shrinkage of the eastern glacier both in area loss (26%) and length (34%). Figs. 2B and 3B and Suppl. table ST2 show only one reversal during the general retreating trend, in the stage 15 of the western and the stage 16 of the eastern Tungnahryggsjökull. The greatest area losses occurred in the transition to the stages 2, 4, 7, 9 and 14 (>3%) on the western glacier while losses between stages in the eastern glacier were lower except for the transition between the stages 14 and 17, where a noticeable reduction of the accumulation area was observed in the aerial photos of 1946 and 1985, and the satellite image of 2005 (Fig. 3B). The volumes calculated from the reconstructed glacier DEM and the corrected bed DEM show that the glaciers reached ~1.10 km 3 (western) and ~0.47 km 3 (eastern) at their recorded maximum extent corresponding to their outmost moraines. From the oldest to the most recent stage they lost 30% and 23% of their ice volume, respectively. The losses between consecutive stages of the glaciers were in general lower than 3% with the exception of the stages 2, 4, 7, 9 (western) and stage 14 (eastern), where the values ranged from 3% to 10% (Suppl. table ST3). Only one slight inversion of the volume trend is seen in the stages 15 of the western glacier and in 16 of the eastern glacier.

Equilibrium-Line Altitudes (ELAs)

The application of the AAR (0.67) method showed ELAs ranging from 1021 to 1099 m a.s.l. (western glacier) and from 1032 to 1065 m a.s.l. (eastern glacier) for the different reconstructed stages. This means an overall rise of 78 and 33 m respectively (Table 1)

from the maximum to the minimum extent recorded. The results from applying the AABR (1.5) show the same trend and similar ELAs, with differences of up to ±15 m compared with those obtained from the AAR. The AABR-ELAs tend to be higher than the AAR-ELAs, especially in the second half of the reconstructed stages with the most remarkable differences occurring in the eastern Tungnahryggsjökull (Table 1).

However, the error derived from the uncertainties associated to the applied balance ratio (BR, ±0.4) tends to decrease as the glaciers get smaller. The greatest change in the ELA between consecutive stages is found between the stages 1 and 2 in the western glacier (+26 m), fully coincident with the largest retreat measured, about 1 km. An interesting result is that the ELA rise is attenuated in both glaciers from stage 10 onwards, with stage-to-stage variations close to zero predominating, and with only one inversion (-3 m) occurring in the western glacier between the stages 14 and 15 (Table 1).

Lichenometric dating

Altogether 2). In general, the further away the lichenometry stations are, the older are the ages (Figs. 2 and3), with the inversions mentioned above. Apparently the lichenometrydated moraines are younger than the CRE-dated distal moraines.

The absence of Rhizocarpon geographicum lichens in 2015 at lichenometry station TUW-1 (uncovered by the glacier at some time between 1994 and 2000; Suppl. figure SF2) suggests a colonization lag of at least 15-21 years. In addition, it is only when the colonization lag is assumed to be longer than 10 years and shorter than 30 years that the ages obtained at stations TUW-3 and TUE-2 are in good agreement with the ages deduced from the aerial photos (Table 2).

During the 2015 field campaign, the species Porpidia cf. soredizodes was absent in station TUE-0, located on a glacially polished threshold uncovered by the glacier after 2005 (post-stage 17). However, it was found in stations TUW-1 and TUE -1, dated to 1994-2000 and 1946-1985 respectively, based on the position of the snouts in the aerial photos (Suppl. figure SF2). These observations suggest a colonization lag from 10 to 15-21 years, thus shorter than for Rhizocarpon geographicum.

36 Cl CRE dating

The detailed geomorphological analysis carried out on the numerous moraine ridges of both valleys has greatly limited the number of boulders reliable for successfully applying 36 Cl CRE and lichenometry dating methods. Due to the great intensity of the slope processes (especially snow avalanches and debris-flows), only a few boulders are well-preserved, sometimes only one in each moraine ridge that retains its original glacier location. Thus, it should be highlighted that this issue prevented performing a statistically valid sampling for both methods (see e.g. Schaefer et al., 2009;Heymann et al., 2011).

During the fieldwork campaigns in the forelands of the western and eastern Tungnahryggsjökull glaciers, 12 samples from stable and very protrusive moraine boulders (Suppl. figure SF4) were collected in areas where lichenometric dating was not suitable because of lichen thalli coalescence, and also 2 samples from a polished ridge downwards the confluence of Vesturdalur and Austurdalur (Suppl. figure SF5). The input data for exposure age calculations, namely sample thickness, topographic shielding factor, major element concentrations of bulk/target fractions, are summarized in the Suppl. tables ST5, ST6, ST7 and ST8 includes the 36 Cl CRE ages calculated according to different Ca spallation production rates and the distance to the most recent glacier terminus position mapped. In Vesturdalur, 8 samples were collected from 5 moraines corresponding to 5 of the stages identified on the geomorphological map (Fig. 2). Samples TUW-9 and TUW-10 (2011) production rate yielded dates older by 15% on average (Suppl. table ST8). These small differences do not represent statistical difference given the calculated age uncertainties.

were

Discussion

36 Cl CRE dating

The dates obtained in both valleys range from 380±200 CE to 1640±90 CE and are significantly younger than the ages from Elliði polished ridge (Suppl. table ST8). TUW-14 (670±210 CE) could be the only outlier as it is significantly older than the other sample obtained from the same moraine of the stage 3 (TUW-13; 1470±130 CE) and also older than the samples TUW-15 (1460±110 CE) and TUW-16 (1220±190 CE), from the moraine of the previous stage 2 (Fig. 2). This would imply assuming nuclide inheritance for sample TUW-14 due to either remobilization of an earlier exposed moraine boulder (see Matthews et al., 2017) or to previous exposure periods, but the high geomorphological dynamism of the slopes limits this possibility (Andres et al., 2019). Another possible interpretation is that the samples TUW-15 and TUW-16 (stage 2) would be the outliers since they may have experienced incomplete exposure due to post-depositional shielding (Heymann, 2011). The possibility of both samples being affected by proglacial processes can be ruled out given the distance to the meltwaters channel or the absence of glacial burst features (see Caseldine, 1985a) in the surroundings of the sampled boulders. Thus, the ages of samples TUW-14 and TUW-13 would indicate that the moraine of stage 3 was built during two overlapped glacial advances at 670±210 CE and 1470±130 CE. In Austurdalur, the interpretation of the ages is also complex. Samples TUE-9 (740±170 CE) and TUE-10 (1460±100 CE) from the same moraine are significantly different, but it is difficult to decide whether or not one of these two samples is an outlier. It is also possible that the younger age indicates the timing of a further readvance with the snout reaching the same moraine. It would be necessary to take more samples, but it will be difficult to find other sectors of these moraines that are not affected by slope processes, especially debris-flows. The hypothesis of supraglacial debris duming can be rejected due to the lack of supraglacial debris or other features indicative of a palaeo debris-covered glacier. Other possibility to be consider is that older boulders may be incorporated in the formation of push moraines as has been shown in maritime Scandinavia, and identified to give overestimated ages for LIA-moraines (Matthews et al., 2017). The asynchronocity of glacial advances and retreat in both valleys should not be surprising as glaciers can retreat or advance differently in adjacent valleys due to a number of factors such as hypsometry, aspect, gradient, etc. Caseldine (1985b) suggested a high climate sensiti it of the glacier in Vesturdalur due to its steeper all floor and thinness , which could explain a different behaviour of the glacier compared to the eastern glacier. (Häberle, 1991(Häberle, , 1994)), and given the uncertainties of our dates (200 yr), also with Drangajökull (NW Iceland) advancing at the sime time (~300 CE; Harning et al., 2018). On the other hand, Meyer and Venzke (1985) had already suggested the presence of pre-LIA moraines at Klaengshóll (eastern cirque, tributary of Skíðadalur). Caseldine (1987Caseldine ( , 1991) ) proposed a date of 5310±345 cal. BCE as the youngest for a moraine in that cirque, based on tephrochronology (tephra layer Hekla 5 dated in a similar ground in Gljúfurárdalur) and rock weathering measurements using the Schmidt hammer technique. Based on the big size of some moraines in Skíðadalur and Holárdalur, Caseldine (1987Caseldine ( , 1991) ) also supports the hypothesis of pre-LIA moraines formed during several advances. All this information is not in agreement with the hypothesis that all the glaciers in Tröllaskagi reached their maximum ice extent since the Early Holocene during the LIA (Hjort et al., 1985;Caseldine, 1987Caseldine, , 1991;;Caseldine and Hatton, 1994).

In south and central and northwest Iceland, the ice caps reached their Late Holocene maximum advance during the LIA (Brynjólfsson, et al. 2015a;Larsen et al. 2015;Harning et al., 2016a;Anderson et al., 2018;Geirsdóttir et al., 2018). But also pre-LIA advances have been identified and dated through radiocarbon and tephrochronology in a moraine sequence of Kvíárjökull (south-east Vatnajökull), the first of which occurred at Subatlantic times (before 110±240 cal. BCE) and the second at 720±395 CE (Black, 1990;cited in Guðmundsson, 1997). Considering the uncertainty of our ~400 and ~700 CE dates, these advances likely were coetaneous with other advances reported from southern Iceland in Kötlujökull (after 450±100 cal. CE, radiocarbon dated and supported by tephochronology; Schomaker et al., 2003) and Sólheimajökull (southern M rkdalsj kull, Ystagil stage ; Dugmore, 1989). In fact, the 669±211 CE advance of western Tungnahryggsjökull (stage 3) also overlaps with the Drangajökull and Langjökull advances at ~560 CE and 550 CE, respectively (Larsen et al., 2011;Harning et al., 2016a) during DACP, in response to the summer cooling between ~250 CE and ~750 CE (Harning et al., 2016a). These advances would correspond to the general atmospheric cooling in the North Atlantic reflected by widespread glacier advances (Solomina et al., 2016).

The timing of the stage 2 in Vesturdalur is difficult to define because the sample TUW-16 (1220±190 CE) has almost 200-year uncertainty, and thus overlaps with both the LIA and the higher temperatures of the Medieval Warm Period (MWP, Lamb, 1965; 950-1250 CE, see Solomina et al., 2016) not conducive to glacier development as it has been observed in northwest and central Iceland (Larsen et al., 2011;Harning et al., 2016a).

On the other hand, moraines in Greenland Arctic environments date within the MWP, based on cosmogenic nuclide dating (Young et al., 2015;Jomelli et al., 2016), suggesting a cooling in the western North Atlantic while the eastern sector remained arm. Iceland is located in the middle of this dipole see-sa pattern (Rogers and van Loon, 1979). Thus, the correlations with the glacier fluctuations Greenland or Norway, are complicated as the climate anomalies in both regions show opposing signs in the different see-saw modes. To increase the difficulty of interpretation, glaciers of Tröllaskagi are known to surge occasionally (Brynjólfsson et al., 2012;Ingólfsson et al., 2016), which could explain additional complexity in the glacial advances pattern, as it would not be driven by climatic variability. Brynjólfsson et al. (2012) pointed out that only four surges from three glaciers (Teigarjökull, Búrfellsjökull, Baegisárjökull) have been reported in the Tröllaskagi peninsula, where over 160 cirque glaciers exist.

LIA glacial advances (15 th -17 th centuries)

The remaining 36 Cl ages obtained from Vesturdalur and Austurdalur are within the 1450-1640 CE range (Suppl. table ST8; Table 3) and so correspond to different glacial advances or standstills during the second third of the LIA during the 15 th , 16 th and 17 th centuries. According to our results, one of the largest glacier extents of the LIA culminated in both valleys at the latest around the mid-15 th century (samples: TUW-12:

1450±100 CE / stage 6; TUE-10: 1460±100 CE / stage 4). This is a very early date compared to the LIA advances previously dated in Tröllaskagi. Earlier lichenometric research carried out in nearby valleys report more recent dates for the LIA maximum:

mid-18 th century in Barkárdalur (Häberle, 1991); early 19 th century in Baegisárjökull and Skríðudalur (Häberle, 1991), and in Búrfellsdalur and Vatnsdalur (Kugelmann, 1991, Fig. 7); mid-19 th century (1845-1875 CE) in Myrkárjökull, Vindheimajökull (Häberle, 1991), Þverárdalur, Teigardalur, Grýtudalur, Vesturárdalur (Kugelmann, 1991, Fig. 7),

Heiðinnamannadalur and Kvarnárdalur (Caseldine, 1991); and late 19 th century (1880s-1890s CE) in Gljúfurárdalur (Caseldine, 1985b(Caseldine, , 1991)). Caseldine (1991) proposed 1810-1820 CE as the date of the outer moraine of Vesturdalur based on a minimum lichenometric age. According to our 36 Cl moraine ages, the LIA maximum of Tungnahryggsjökull glaciers occurred ~400 years earlier than these dates. This should not be surprising as Kirkbride and Dugmore (2001) reported lichenometric ages >100 years younger than those derived from tephrochronology in the same landforms. Our results also give the earliest LIA dates based on moraine dating obtained so far in Iceland, compared to the previously published dates all obtained through lichenometric dating: 1740-1760 CE in south-east Iceland (Chenet et al., 2010). In northwestern Iceland, glaciolacustrine sediments recorded a contemporary expansion of Drangajökull at ~1400 CE (Harning et al., 2016a). Likewise a first major advance of Langjökull (western central Iceland; Fig. 1A) between 1450 and 1550 CE has been reported (Larsen et al., 2011), as well as advances in central Iceland between 1690 and 1740 CE (Kirkbride and Dugmore, 2006), based on varve thickness variance together with annual layer counting and C:N mass ratio, and tephrochronology (geochemical analysis), respectively.

The dates of samples TUW-13, TUW-12 and TUW-11 in Vesturdalur (average date 1470±120 CE; stages 3, 5 and 6) cannot be distinguished statistically if their internal uncertainty is considered (Fig. 4; Suppl. table ST8). The spatial scatter of these sampling sites (Fig. 2) may indicate frequent and intense terminus fluctuations in a short time interval. Different ages obtained from the moraines of the stages 3 and 4 in Vesturdalur and Austurdalur, respectively, may indicate that in the 15 th century the glacier termini reached the moraines deposited at ~700 CE (Figs. 2 and3) and rebuilt them, which may explain the large size of these moraines. Caseldine (1987) argued that other moraines in Skíðadalur were formed during more than one advance. Based on the size of the largest moraines, he also pointed out that many glaciers must have advanced to positions similar to those of the late 19 th century earlier in the Neoglacial.

The glacier advances in the 15 th century in Vesturdalur and Austurdalur may have been the result of different climate forcings during that century: negative radiative forcing and summer cooling were linked to intense volcanic activity (Miller et al., 2012), the low solar activity of the Spörer Minimum (1460-1550 CE; Eddy, 1976), the seaice/ocean feedback with increased sea ice (Miller et al., 2012) and the weakening of the Atlantic Meridional Overturning Circulation (AMOC) (Zhong et al., 2011). Solar activity may have played a major role in these glacial advances if we consider that the climate in the North Atlantic is higly influenced by solar activity variability (Jiang et al., 2015). On the contrary, historical records, although not determinant, suggest a mild climate for 1430-1550 CE (Ogilvie and Jonsdóttir, 2000), and especially for 1412-1470 CE [START_REF] Ogilvie | The past climate and sea-ice record from Iceland, Part 1: Data to A.D. 1780[END_REF]. This would also be compatible with increased precipitation and hence more winter snow in warm periods (Caseldine and Stötter, 1993;Stötter et al., 1999;Fernández-Fernández et al., 2017), and also with potential surge activity with glacial advances not directly linked to specific climate periods (e.g. Brynjólfsson et al., 2012;Ingólfsson et al., 2016).

In Vesturdalur, the dates of samples TUW-9 (1590±100 CE) and TUW-10 (1640±90 CE) are compatible with a cold period from the late 1500s to 1630 CE [START_REF] Ogilvie | Little Ice Age Research: a perspective from Iceland[END_REF]. Nevertheless, considering the uncertainties of these samples, their dates also overlap with the Maunder Minimum (1645-1715 CE) (Eddy, 1976), when the LIA maximum glacial advance occurred in the Alps (Holzhauser et al., 2005).

Lichenometric dating.

5. 2.1. 36 Cl CRE dating vs. lichenometric dating. Multiple lichen species dating approach.

The contrast between our CRE dating results and earlier lichenometry-based results published elsewhere evidences the clear underestimation of the latter. This could be explained either by lichen growth inhibition due to saturation of the rock surface and competition of other thalli (Wiles et al., 2010;Le Roy et al., 2017) or a colonization lag longer than assumed up to now, from 10 to 15 years in Tröllaskagi (Kugelmann, 1991;Caseldine, 1985b, respectively). However, other factors affect the reliability of the lichen-derived ages, and may explain the differences with CRE dates. One of them is the reliability of the growth rates and lichenometric calibration curves that are commonly assumed to be linear (constant) growth in northern Iceland (e.g. Caseldine, 1983Caseldine, , 1985b;;Häberle, 1991;Kugelmann, 1991), although it has been demonstrated that the lichen diameter growth declines with age (see e.g. Winkler, 2003, Fig. 4). This might lead to significant age underestimations for the oldest dates, putting potentially earlier dates in the 19 th century. Most of the fixed control points from which lichen growth rates have been derived in northern Iceland comprise abandoned gravestones, memorial stones, old bridges and mostly abandoned farmsteads (Caseldine, 1983;Kugelmann, 1991). Time of death is commonly assumed for gravestones, and abandonment date for farmsteads. Athough the latter is well known on the basis of historical documentation, the coloni ation lag sometimes relies on the the likel duration of the deterioration of the buildings after abandonment that depends on the quality and stability of the constructions (see Kugelmann, 1991), and hence affect the results. However, it should be highlighted that our approach circumvents this last issue by combining field observations with historical aerial photographs. In addition, given that lichen growth of Rhizocarpon subgenus depends mostly on available humidity, the location of the measured lichens has also a potential effect on the results, i.e. to microclimatic changes (see Innes, 1985;Hamilton and Whalley, 1995) between the location of the fixed points and the location on the moraine (crest: dryer and more exposed;

green zone on the proximal slope, etc.). In the literature cited above about lichenometrydated LIA advances no detailed information is provided about the location of the lichen measured for dating purposes, so potential error derived from this issue can not be assessed. Nevertheless, given that we measured lichens on horizontal flat surfaces where there is no restriction to the moisture recepit of the lichens, we can consider our results presented throughout the next sections valid. In any case, such a great difference of our CRE dates and the previous lichen-derived is more likely to be explained by the technical limitations of the technique rather than environmental factors.

Our field observations and historical aerial photos of known age restricted the dates of the moraines colonized by Rhizocarpon geographicum lichens. This approach would support the dates obtained from the 0.44 mm yr -1 growth rate of Kugelmann (1991) and the 20-year colonization lag. This rate is slightly higher than those reported from the Antarctic Peninsula (0.31 mm yr -1 ; Sancho et al., 2017), but lower than in Tierra del Fuego (0.63 mm yr -1 ; Sancho et al., 2011). The correlation between the sizes of largest ST4), which exceed the size of the biggest control point from hich Kugelmann s gro th rate as estimated (Kugelmann, 1991, Fig. 3). This problem reinforces the need of taking lichen-derived ages as relative. The interpretation of the chronology in Austurdalur is more complicated: the lichen sizes measured at the stations TUE-6 (1890s CE, stage 9) and TUE-7 (1880s CE; stage 7) yield more recent dates than at station TUE-5 (1860s CE; stage 10) despite being representative of earlier stages (Fig. 3). Given that this anomaly occurs in both lichen species, it is reasonable to conclude that an environmental factor could have affected the lichen populations at both stations. It could even indicate a date when the boulders may have been remobilized by postglacial processes.

Our chronology of the 19 th century glacial advances in both valleys (Table 2) does not coincide exactly with the phases identified by Kugelmann (1991) in Svarfaðardalur-Skíðadalur (1810, 1850, 1870-1880, 1890-1900 CE). It also differs appreciably from the chronology proposed by Caseldine (1985b) in Vesturdalur (moraines of 1868, 1878, 1887, 1898 CE). Nevertheless, it should be borne in mind that we are considering only two glaciers with their own glaciological properties. Moreover, we have estimated the ages from the growth rate (instead of a specific calibration growth curve), longer colonization lag based on field observations, and applied to the longest axis measurements (Kugelmann, 1991). On the other hand, micro-climatic differences between the location of fixed points and our lichen measured may occur. However, we recognise that the comparisons with Caseldine s (1985b) results are quite difficult since:

(i) the moraines dated by Caseldine are poorly located in his mapping (and hard to identify over aerial photos and our moraine mapping); (ii) we are not able to apply the same parameters to his measurements, as he used the mean longest axis of the five largest lichen is not provided (only the average value); and (iii) he recognised the lichen growth slowdown when dating the outermost moraine, which probably is one of those dated with 36 Cl in this work.

Our results, despite the limitations of the applied method, largely due to the low number of moraine boulders suitable for its application can be considered compatible and in good agreement with glacial advances and cold periods during the first third of the 19 th century as we show below. Martin et al. (1991) pointed out the existence of a moraine dated to ca. 1810-1820 CE in Western Tr llaskagi Tungnahr ggsj kull (ambiguousl , without providing any detail of its location), as well as others of this period in Svarfaðardalur, Búrfellsdalur and Vatnsdalur. Other dates obtained from more sophisticated statistical techniques applied to lichenometry dating procedures also evidenced a glacial advance phase 1810-1820 CE (Chenet et al., 2010). These advance phases were coetaneous with significant sea ice persistence in the early 1800s [START_REF] Ogilvie | Little Ice Age Research: a perspective from Iceland[END_REF], decreased solar activity, and strong volcanic eruptions (Dalton Minimum, 1790-1830 CE; Wagner et al., 2005). The moraines dated in Vesturdalur to around 1830 CE (TUW-7: 1830s CE, stage 10) and the early 1890s CE (TUW-5: 1890s CE, stage 12) are in good agreement with the glacial advances in Svarfaðardalur-Skíðadalur during the 1830s and early 1890s CE (Kugelmann, 1991, Fig. 8), as well as with the low temperatures and presence of sea ice at these dates (Koch, 1945;Ogilvie, 1996;Ogilvie and Jonsdóttir, 2000;[START_REF] Ogilvie | Little Ice Age Research: a perspective from Iceland[END_REF]Kirkbride, 2002). century; it would be the result of the accumulated effect of the temperature rise since the latter half of the 19 th century (Caseldine, 1987;Wanner et al., 2008). Thus, the subsequent advances would be the response to specific relative thermal minima within a warmer climate (Stötter et al., 1999). The date of TUW-3 (stage 13) representing the moraine abandonment in ~1940 CE is in agreement with the overall context of general glacier retreat as a result of the warmest decades of the 1930s and 1940s CE, which triggered an intense retreat of the glaciers (Einarsson, 1991;Martin et al., 1991;Kirkbride, 2002). The advances/standstills dated to the early 1950s CE in both Tungnahryggsjökull glaciers are likely to be synchronous given the similarity of the dates obtained (Table 2). They could represent glacial advances in consonance with the late 1940s early/mid-1950s CE cooling (Einarsson, 1991;Fernández-Fernández et al., 2017), recorded both in Akureyri and many other weather stations throughout Iceland. Caseldine (1983) found a similar chronology in Gljúfurárdalur (Skíðadalur headwater, 10 km to the east), with moraine deposition between mid-1910s and 1930mid-1910s and , around mid-1930s and late 1940s-1950 CE. CE. The subsequent trend of the Tungnahryggsjökull glaciers, inferred from aerial photographs, a satellite image, geomorphological mapping, and glacier reconstruction, was characterized by continuous retreat and volume loss, in line with the increasing temperature trend since the end of the LIA. This trend was only reversed between the mid-1960s and mid-1980s CE by a major cooling event (Einarsson, 1991;Sigurðsson, 2005;Fernández-Fernández et al., 2017) (Sigurðsson, 2005). In spite of these glacial fluctuations in response to the intense climatic fluctuations of the last century, the ELAs estimated in this paper only show a general rise of 5-10 m (Table 1). This small ELA increase may be derived from some artifacts of the glacier reconstruction or the attenuating effect of the increase in winter precipitation suggested by glacier-climate models (Caseldine and Stötter, 1993;Fernández-Fernández et al., 2017).

5

Final remarks:

Can the occurrence of pre-LIA glacial advances be confirmed? Was the LIA in northern Iceland the Holocene glacial maximum? Was it a single maximum advance?

Our results demostrate that Tungnahryggsjökull advanced during Late Holocene glacial stages prior to the LIA and reached considerably more advanced positions, even though the Iceland large ice caps reached generally their Late Holocene maximum advance during the LIA (Larsen et al. 2015, Harning et al., 2016a;Anderson et al., 2018, Geirsdóttir et al., 2018). The chronological data presented in the previous sections suggests that during the LIA the glaciers overlaped moraines deposited in pre-LIA glacial stages. Our results also show LIA advances since the 15 th century and are thus contrary to the traditional proposal of a single maximum LIA advance occurring during either mid-18 th or late-19 th centuries in Tröllaskagi peninsula, followed by subsequent minor readvances in an overall retreating trend (see Caseldine, 1983Caseldine, , 1985bCaseldine, , 1987;;Kugelmann, 1991;Martin et al., 1991). The use of the 36 Cl production rates from Ca spallation reported by Stone et al. (1996) does not lead to major changes in the interpretation and conclusions as the changes in the nominal dates (up to 90 yr earlier;

Table 3) are within the external uncertainty and also overlap with the results presented above based on the Licciardi et al. (2008) production rate. Similarly, if we consider the results derived by the Schimmelpfennig et al. (2011) production rate, we obtain even earlier ages, which still overlap with the results derived by the other production rates due to a higher external uncertainty (see Table 3). Although the snow cover duration is known to be high in northern Iceland (see Dietz et al., 2012), quantifying the effect of snow cover on sub-surface 36 Cl production is a complex issue: on the one side, snow lowers the isotopic production rates related to spallation reactions due to the shielding effect on high-energy neutrons (Benson et al., 2004;Schildgen et al., 2005), and on the other side it increases the 36 Cl production rate from thermal neutrons below the rock surface, due to the enhancing effect of hydrogen on these low-energy neutrons (Dunai et al., 2014). Both effects might cancel out depending on the composition of the samples, and their quantification is still debated and affected by high uncertainties (Zweck et al., 2013;Dunai et al., 2014;Delunel et al., 2014). Given this complexity, snow shielding was not applied. In any case its effect is unlikely to be higher than the uncertainty derived from extracting 36 Cl from whole rock instead of minerals.

Our results are in concordance with several valleys in northen Iceland, but also with the results that are being obtained in other sectors of Arctic and North Atlantic region in the last years, such as: in Baffin Island (northern Canada), where glaciers reached Late Holocene maximum positions prior to the LIA (Young et al., 2015; 10 Be dating), or

West Greenland, with several advances or stabilizations at 1450±90 CE and 1720±60 CE (Jomelli et al., 2016; 36 Cl dating). However, it is striking that the early LIA advances of northern Iceland reported in the present paper do not agree with maritime Norway with later maximum culminations (see Nesje et al., 2008) despite being the glaciated region most comparable with Iceland in terms of climate and glaciology. Our results also agree with farther and southern areas such as the Alps, with maximum advances at around 1430 CE (Schimmelpfennig et al., 2012(Schimmelpfennig et al., , 2014a); 10 Be dates; and

Sierra Nevada (Iberian Peninsula), where LIA advances have been reported between the 14 th and 17 th centuries (Palacios et al., 2019; 10 Be dates). Our detailed moraine mapping, combined with CRE dating in the surveyed valleys, clearly shows a number of advances throughout the LIA, in response to the great climatic variability of the region with alternating cold and mild/warm periods [START_REF] Ogilvie | The past climate and sea-ice record from Iceland, Part 1: Data to A.D. 1780[END_REF](Ogilvie, , 1996;;[START_REF] Ogilvie | Sea ice, climate, and Icelandic fisheries in the eighteenth and nineteenth centuries[END_REF][START_REF] Ogilvie | Little Ice Age Research: a perspective from Iceland[END_REF]Geirsdóttir et al., 2009) as occurred in the Alps (e.g. Schimmelpfennig et al., 2014a) or the Iberian mountains (e.g. [START_REF] Oliva | The Little Ice Age in Iberian mountains[END_REF]. The ELA calculations show that the major long-lasting rise of the glacier ELA (24-50 m depending on the calculation method) took place prior to 1900s/1910s.

According to the results, the evolution pattern described by Fernández-Fernández et al.

(2017) for the Tungnahryggsjökull glaciers should be revised as the 36 Cl CRE dates from the 15 th and 17 th centuries indicate that LIA maximum was reached earlier than previously thought. Thus, if we consider the ELA of the earliest LIA dates obtained with 36 Cl CRE (i.e. stages 5 and 4 of western and eastern Tungnahryggsjökull), these imply ELA depressions (with reference to the 2005 date) of 24-50 m (depending on the ELA calculation method), occurring for at least 560 years (Table 1) and not 150 years as had been previously assumed (Caseldine and Stötter, 1993;Fernández-Fernández et al., 2017).

Conclusions

(i) This paper highlights the detailed geomorphological analysis of the glacial landforms as an essential pre-requisite prior to the application of dating methods on them.

Nevertheless, this has greatly limited the number of valid moraine boulders to be dated, since the vast majority of those were affected by post-glacial processes. This isue which has prevented a statistically acceptable sampling and the validation or invalidation of the inconsistent ages ielded b se eral boulders, so a conclusive explanation cannot be given. (vi) From the measurements carried out in different lichenometry stations, growth of Porpidia cf. sporedizodes lichen appeared to be higher than in the case of Rhizocarpon geographicum, and also proportional to that. Its growth rate has been tentatively estimated for the first time, at around 0.737 mm yr -1 . However, further research on the growth rates of this species is required for its potential use in lichenometric dating as a complementary species, since it also shows a shorter colonisation lag than Rhizocarpon geographicum. photographs, satellite images and fieldwork shows that the regional colonization lag of the commonly used lichen species Rhizocarpon geographicum is longer than previously assumed. For exploratory purposes, an alternative lichen species (Porpidia soredizodes)

has been tested for lichenometric dating, estimating a tentative growth rate of 0.737 mm yr -1 .

Introduction

The Tröllaskagi Peninsula (northern Iceland) hosts over 160 small alpine cirque glaciers (Björnsson, 1978; see synthesis in Andrés et al., 2016). Only a few of these small glaciers do not have supraglacial debris cover that allows them to react quickly to small climatic fluctuations (Caseldine, 1985b;Häberle, 1991;Kugelmann, 1991), compared to

Manuscript for final publication

Click here to view linked References the reduced dynamism of the predominant rock glaciers and debris-covered glaciers (Martin et al., 1991;Andrés et al., 2016;Tanarro et al., 2019). As a result of their high sensitivity to climatic changes, the few debris-free glaciers in Tröllaskagi fluctuated repeatedly in the past, forming a large number of moraines in front of their termini (see Caseldine, 1983Caseldine, , 1985bCaseldine, , 1987;;Kugelmann, 1991 amongst others). However, the relation between glacier fluctuations and the climate is complicated due to: (i) the wellknown surging potential activity in Tröllaskagi (Brynjólfsson et al., 2012;Ingólfsson et al., 2016); (ii) the possibility of glaciers being debris-covered in the past, with the subsequent change of their climate sensitivity over time; (iii) the intense and dynamic slope geomorphological activity, paraglacial to a great extent (Jónsson, 1976;Whalley et al., 1983;Mercier et al., 2013;Cossart et al., 2014;Feuillet et al., 2014;Decaulne and Saemundsson, 2006;Saemundsson et al., 2018) that hides and erases the previous glacial features.

In Iceland, a great part of the research on glacial fluctuations during the late Holocene, LIA (Grove, 1988; 1250-1850 CE, see Solomina et al., 2016) and later stages has been approached through application of radiocarbon dating of organic material, analyzing lake sediment varves (Larsen et al., 2011;Striberger et al., 2012), dead vegetation remnants (Harning et al., 2018) and threshold lake sediment records (Harning et al., 2016b;Schomacker et al., 2016). These provide high-resolution records of glacier variability. In Tröllaskagi, very few reliable dates exist at present, obtained from radiocarbon and tephrochronology (Häberle, 1991(Häberle, , 1994;;Stötter, 1991;Stötter et al., 1999;Wastl and Stötter, 2005). They suggest that late Holocene glaciers were slightly more advanced than during the LIA maximum in Tröllaskagi. However, these techniques only provide minimum or maximum ages for Holocene glacier history in northern Iceland (Wastl and Stötter, 2005). In addition, at Tröllaskagi most of the moraines are at 600-1000 m a.s.l., where the applicability of tephrochronology is very limited (Caseldine, 1990) due to the great intensity of slope geomorphological processes.

In any case, most of the moraine datings of Tröllaskagi especially those of the last millenium comes from lichenometry (see synthesis in Decaulne, 2016). However, the ages derived from this technique tend to be younger if they are compared to those estimated from tephra layers (Kirkbride and Dugmore, 2001). Generally, there is disagreement about the validity of the results provided by lichenometry, due to the difficulty of the lichen species identification in the field, the complexity and reliability of the sampling and measurement strategies, the uncertainty estimates, the nature of the ages provided as relative, as well as the relative reliability at producing lichen growth curves of the different species, with an extreme dependence on local environmental factors (see [START_REF] Osborn | Lichenometric dating: Science or pseudo-science?[END_REF].

In fact, these problems had already been detected in northen Iceland, where in spite of the time elapsed since the first applications of this technique (Jaksch, 1970(Jaksch, , 1975(Jaksch, , 1984;;Gordon and Sharp, 1983;Maizels and Dugmore, 1985) and contrasting with its widespread use in the south and southeast of the island (Thompson and Jones, 1986;Evans et al., 1999;Russell et al., 2001;Kirkbride and Dugmore, 2001;Bradwell, 2001Bradwell, , 2004a;;Harris et al., 2004;Bradwell and Armstrong, 2006;[START_REF] Orwin | Identifying moraine surfaces with similar histories using lichen size distributions and the U2 statistic, Southeast Iceland[END_REF]Chenet et al., 2010 and others), there are still very few established growth rates for the lichen group Rhizocarpon geographicum (Roca-Valiente et al., 2016) from Tröllaskagi (Caseldine, 1983;Häberle, 1991;Kugelmann, 1991;Caseldine and Stötter, 1993; see synthesis in Decaulne, 2016). In general, the growth curves from Tröllaskagi suffer from a few control points (i.e. surfaces of known age) for calibration. This leads to considerable underestimation when lichen thalli sizes are beyond the calibration growth curve (Caseldine, 1990; see e.g. Caseldine, 1985b;Caseldine and Stötter, 1993;Kugelmann, 1991). That is to say, the extrapolation does not account for the decreasing growth rate with increasing age (i.e. non-linear growth). Kugelmann s (1991) growth curve has the highest number of control points to date (19 in total). In addition, the colonization lag in Tröllaskagi is poorly defined, although 10-15 years have been assumed for the Rhizocarpon geographicum (Caseldine, 1983;Kugelmann, 1991).

Other issues, such as the absence of large thalli (Maizels and Dugmore, 1985), lichen saturation (e.g. Wiles et al., 2010), and other environmental factors (Innes, 1985 and references included;Hamilton and Whalley, 1995) contribute to appreciable age underestimations when dating surfaces using this approach. Snow is also a major environmental factor for lichenometry in Iceland due to its long residence time on the ground (Dietz et al., 2012) and the avalanching frequency especially in Tröllaskagi , whose effect restricts the growth rate of lichens, and even destroys them (Sancho et al., 2017). These problems considerably limit the quality (reliability) of the lichenometric dating range of utility for applying lichenometric dating in Iceland, where the oldest ages estimated so far are between 160 and 220 years (Maizels and Dugmore, 1985;Thompson and Jones, 1986;Evans et al., 1999), thus preventing the dating of glacial advances prior to the 18 th century.

In spite of the high uncertainty of the lichenometric dating, many authors working in

Tröllaskagi have treated their lichenometric results as absolute ages (see Caseldine, 1983Caseldine, , 1985bCaseldine, , 1987;;Kugelmann, 1991;Häberle, 1991;Caseldine and Stötter, 1993, amongst others). In fact, previously considered dates of LIA maximum glacier culmination are restricted to the very late 18 th and early 19 th centuries (Caseldine, 1983(Caseldine, , 1985b(Caseldine, , 1987;;Kugelmann, 1991;Caseldine and Stötter, 1993;Caseldine, 1991;Martin et al., 1991), very close to the applicability threshold of this method. Consequently, no evidence of previous advances during phases of the LIA that were more conducive to glacier expansion (probably colder; see e.g. [START_REF] Ogilvie | The past climate and sea-ice record from Iceland, Part 1: Data to A.D. 1780[END_REF]Ogilvie, , 1996;;[START_REF] Ogilvie | Sea ice, climate, and Icelandic fisheries in the eighteenth and nineteenth centuries[END_REF][START_REF] Ogilvie | Little Ice Age Research: a perspective from Iceland[END_REF] has been found (Kirkbride and Dugmore, 2001).

In the recent years, dating methods based on the Exposure to the Cosmic-Rays (CRE)

have been introduced successfully to date moraines of the last millennium, and even formed during the LIA (Schimmelpfennig et al., 2012(Schimmelpfennig et al., , 2014 Cl CRE dating applied to polished surfaces along a transect from the highlands to the mouth of the fjord. Brynjólfsson et al. (2015b) applied the same isotope to samples coming from the highlands and the fjords to reconstruct the glacial history of the Drangajökull region. The other cosmogenic isotope used is 3 He, applied to heliumretentive olivine phenocrysts by Licciardi et al. (2007) to determine eruption ages of Icelandic table mountains and to reconstruct the volcanic history and the thickness evolution of the Icelandic Ice Sheet during the last glacial cycle. However, CRE dating

has not yet been applied to the late Holocene glacial landforms both in Iceland as a whole and the Tröllaskagi Peninsula. CRE dating is an alternative to the use of highresolution continuous lacustrine records in northen Iceland, given the rarity of lakes in this peninsula, which limits the application of radiocarbon to date the deglaciation processes (Striberger et al., 2012;Harning et al., 2016b).

Nevertheless, CRE dating methods approach the nuclides detection limit when applied to very recent moraines (Marrero et al., 2016;Jomelli et al., 2016). This issue precludes the application of CRE dating to the abundant post-LIA moraines existing in some of the Tröllaskagi valleys whose headwalls are occupied by climate-sensitive debris-free glaciers (Caseldine and Cullingford, 1981;Caseldine, 1983Caseldine, ,1985b;;Kugelmann, 1991;Fernández-Fernández et al., 2017). Dating these post-LIA moraines allows to reconstruct recent climate evolution, and even to match and assess the climate reconstructions with the instrumental climate records (see Dahl and Nesje, 1992;Caseldine and Stötter, 1993;Fernández-Fernández et al., 2017). Futhermore, improving the knowledge of the recent evolution of alpine mountain glaciers, such as those of Tröllaskagi, is fundamental in the assessment of present global warming (Marzeion et al., 2014) The use of aerial photographs from different dates is a reliable approach to the glacier evolution during the last decades (Fernández-Fernández et al., 2017;Tanarro et al., 2019). The main advantage of this technique is the possibility of studying the evolution of glacier snouts in recent dates with high accuracy. In fact, there is no dependence on the glacial features (i.e. moraines), which circumvents moraine deterioration issues derived by the geomorphological activity of the slopes. However, the main shortcoming of the aerial photo imagery is the availability only on few dates, at least in Tröllaskagi.

This circumstance makes it impossible to obtain the glacier fluctuations with a high time resolution (i.e. only the periods between the available aerial photos; Fernández-Fernández et al., 2017;Tanarro et al., 2019), and hence to match them to short-term (decadal scale) climate fluctuations that are known to exert a major control especially on small mountain glaciers with short time responses (see Caseldine, 1985b;Sigurðsson, 1998;Sigurðsson et al., 2007;Fernández-Fernández et al., 2017). The only way to fill the gap between two dates with available aerial photos is through applying lichenometric dating (Sancho et al., 2011), as there is no tree species suitable to apply dendrochronology. In addition, the information provided by the aerial photo imagery (i.e. glacier snout position) constrains the period when the lichens appear and begin to grow, which circumvents many of the criticisms made on lichenometry (see [START_REF] Osborn | Lichenometric dating: Science or pseudo-science?[END_REF].

Moreover, a detailed geomorphological mapping allows for identification of stable moraines, not remobilized or destroyed by glacier advances or slope processes (avalanches, slope deformations, debris-flows, etc.) and also to reconstruct the glacier snout geometry throughout different phases (see Caseldine, 1981;Bradwel, 2004b;Principato et al., 2006 amongst others). The analysis of the moraine morphology and the glacial features on the forelands is a key tool to confirm whether the glaciers were debris-free or debris-covered in the past (Kirkbride, 2011;Janke et al., 2015;Knight, et al., 2018, amongst others) as this issue determines their climate sensitivity (see Fernández-Fernández et al., 2017;Tanarro et al., 2019).

The western and eastern Tungnahryggsjökull glaciers, in the Vesturdalur and Austurdalur Valleys (central Tröllaskagi), respectively (Fig. 1), are two of the few debris-free glaciers or almost debris-free in the case of the western glacier of the peninsula that are both small and highly sensitive to climatic fluctuations (Fernández-Fernández et al., 2017). This makes them ideal for studying glacial and climatic evolution during last last millennia.

The aim of our work was to apply the best methodology possible to analyze the glacial evolution of western and eastern Tungnahryggsjökull glaciers during the last millennia to the present. Applying for the first time a number of dating techniques to study the Late Holocene evolution of the two glaciers, the objectives of this paper are:

(i) To carry out a detailed geomorphological survey of the glacier forelands in order to map accurately well-preserved glacial features. This mapping is used both to devise the sampling strategy for dating, and also to reconstruct the palaeoglaciers in 3D in order to obtain glaciologic climate indicators such as the Equilibrium-Line Altitudes (ELAs).

These can be used as a proxy to infer palaeoclimatic information (see Dahl and Nesje, 1992;Caseldine and Stötter, 1993;Brugger, 2006;Hughes et al., 2010;Fernández-Fernández et al., 2017 amongst others).

(ii) To use aerial photographs / satellite imagery post-dating 1946 to map the glacier extent in each available date in order to improve the information of ELA evolution in the recent decades. Aerial photographs will be used to constrain the possible periods of lichen colonization and growth over stable boulders, and will be useful to identify phases of advance, stagnation or retreat of the glacier snouts. By this way we will complete the glacier evolution from pre-instrumental glacial stages (identified from geomorphological evidence, i.e. moraines) to their current situation.

(iii) To apply CRE dating when possible depending on the preservation degree of the glacial features, and when moraines were too old to be dated by lichenometry.

(iv) To apply lichenometric relative dating to recent moraines or those where CRE dating might not be suitable (i.e. limit of applicability) and provided that: 1) the geomorphological criteria evidence a good preservation of glacial features; and 2) aerial photographs constrain the earliest and oldest possible lichen ages. This approach will also allow to check the growth rates and colonization lags of the lichen species usually used in Iceland for lichenometric dating purposes.

The experimentation and validation of this methodological purpose will help to improve the knowledge of the recent climate evolution of northern Iceland. This is of maximum interest if we consider its location within the current atmospheric and oceanic setting, strongly linked to the evolution of the Meridional Overturning Circulation (Andrews and Giraudeau, 2003;Xiao et al., 2017), a key factor in the studies for the assessment of the global climate change effects (Barker et al., 2010;Chen et al., 2015 amongst others).

Moreover, if this proposal is valid, it could be applied to the research on the recent evolution of other mountain glaciers similar to those of Tröllaskagi. This aspect is a main research objective at present, as these glaciers represent the greatest contribution to the current sea-level rise (Jacob et al., 2012;Gardner et al., 2013 amongst others).

Regional setting

The Tröllaskagi Peninsula extends into the Atlantic Ocean at 66 12 N from the central highland plateau (65 23 N) of Iceland (Fig. 1). The fjords of Skagafj r ur (19 30 W)

and E jafj r ur (18 10 W) separate it from the Skagi and Flate jarskagi peninsulas, respectively. Tröllaskagi is an accumulation of successive Miocene basalt flows, interspersed with reddish sedimentary strata (Saemundsson et al., 1980;Jóhannesson and Saemundsson, 1989). The plateau culminates at altitudes of 1000-1500 m a.s.l. (with the highest peak Kerling at 1536 m a.s.l.) and is dissected by deep valleys with steep slopes whose headwaters are currently glacial cirques. These cirques host more than 160 small glaciers, mostly north-facing, resulting from the leeward accumulation of snow from the plateau (Caseldine and Stötter, 1993) and reduced exposure to solar radiation.

In fact, deposits caused by rock-slope failure are common in Tröllaskagi valley slopes and have been considered a result of the final deglaciation during the early Holocene (Jónsson, 1976;Feuillet et al., 2014;Cossart et al., 2014;Coquin et al., 2015). Most of the glaciers are rock or debris-covered glaciers, due to the intense paraglacial activity affecting the walls that minimizes cosmogenic nuclide concentrations from earlier exposure periods on the cirque headwalls (Andrés et al, 2018).

The climate in Tröllaskagi is characterized by a mean annual air temperature (MAAT;

1901-1990 series) of 2 to 4 °C at sea level, dropping to between -2 and -4 °C at the summits (Etzelmüller et al., 2007). At the town of Akureyri, located in the east of the peninsula at the mouth of Eyjafjarðardalur (Fig. 1), the MAAT is 3.4 °C and the average temperature in the three summer months is about 9 to 10 °C (Einarsson, 1991). Annual precipitation ranges from 400 mm at lower altitudes to 2500 mm at the summits (Crochet et al., 2007).

The frontier location of Icelandic glaciers in relation to atmosphere and ocean systems (warm/moist Subtropical and cold/dry Arctic air masses; and the warm Irminger and cold East Greenland sea currents) makes them exceptionally sensitive to climate oscillations (Bergþórsson, 1969;Flowers et al., 2008;Geirsdóttir et al., 2009), and these debris-free glaciers are thus reliable indicators of climatic evolution and the impact of climate change on the cryosphere (see Jóhannesson and Sigurðsson, 1998;Bradwell, 2004b;Sigurðsson, 2005;Geirsdóttir et al., 2009;Fernández-Fernández et al., 2017).

The glaciers studied here are the western (6.5 km 2 ) and eastern (3.9 km 2 )

Tungnahryggsjökull, located in the Vesturdalur and Austurdalur valleys respectively, separated from each other by the crest of Tungnaryggur, and tributaries of the Kolbeinsdalur Valley (Fig. 1).

Methodology

Geomorphological mapping and glacier geometry mapping

Four summer field campaigns (2012, 2013, 2014 and 2015) were conducted in Vesturdalur and Austurdalur, with the objective of identifying moraines that clearly provided evidence of various glacial culminations of the western and eastern Tungnahryggsjökull glaciers. We identified the palaeo-positions of the glacier snouts, the glacier geometry and extent through photo interpretation of stereoscopic pairs and previous fieldwork. Mapping of glacial and non-glacial landforms was conducted on two enlarged 50-cm-resolution aerial orthophotos (National Land Survey of Iceland, 2015) plotted at scale 1:7000. These maps ere imported into an ArcGIS 1.4.1

database after geo-referencing. Finally, all the glacial linear landforms were digitized, and where the moraines were prominent, continuous, or well-preserved, they were assumed to represent major culminations, and hence, glacial stages. In addition to the geomorphological evidence, glacier variations in recent years were mapped, based on the photo interpretation of four historical aerial photographs from 1946, 1985, 1994and 2000(National Land Survey of Iceland, 2015), and also one SPOT satellite image ( 2005), previously geo-referenced in ArcGIS. For more details of the aerial photograph processing, see Fernández-Fernández and Andrés (2018). As the glacier headwalls are ice diffluences in both cases, it was assumed that: (i) the ice divides are the upper boundaries of the glaciers for the different stages, and (ii) the ice divide is invariant for the different stages/dates, following Koblet et al. (2010) as changes in the extent of the accumulation zone are smaller than the outlining differences derived from the operator mapping. Likewise, in the case of the upper glacier edge constrained by the cirque wall, the glacier geometry was also assumed to be invariant from stage to stage unless the aerial photographs showed otherwise.

Glacier reconstruction and equilibrium-line altitude (ELA) calculation

Benn and Hulton s (2010) glacier reconstruction approach using a physical-based model describing ice rheology and glacier flow (Van der Veen, 1999) was preferred to arbitrary hand-drawn contouring (e.g. Sissons, 1974) in order to achieve more robust reconstructions (Fernández-Fernández and Andrés, 2018). This model operates on deglaciated areas with non-extant glaciers. As this is not the case in our study area, we 2010) spreadsheet. This value can be considered appropriate as it falls within the normal shear-stress range of 50-150 kPa observed in current glaciers and is very close to the standard value of 100 kPa [START_REF] Paterson | The Physics of Glaciers, 3 rd Edition[END_REF]. The glacier contours were manually adjusted to the ice surface elevation values of the icethickness points estimated b GLaRe instead of using an interpolation routine, to obtain a more realistic surface (concave and convex contours above and below the ELA).

Finall , e calculated the ELAs automaticall b using the ELA calculation ArcGIS toolbox [START_REF] Pellitero | A GIS tool for automatic calculation of glacier equilibrium-line altitudes[END_REF]. The methods comprised: (i) AABR (Area Altitude Balance Ratio; [START_REF] Osmaston | Estimates of glacier equilibrium line altitudes by the Area × Altitude, the Area × Altitude Balance Ratio and the Area × Altitude Balance Index methods and their validation[END_REF] with the ratio 1.5±0.4 proposed for Norwegian glaciers by Rea (2009) and successfully tested on Tröllaskagi debris-free glaciers in Fernández-Fernández et al. (2017); and (ii) the AAR (Accumulation Area Ratio) with the ratio 0.67 previously used by Stötter (1990) and Caseldine and Stötter (1993) for Tröllaskagi glaciers. Alternative approaches for ELA calculation in northern Iceland have been carried out by considering morphometric parameters of glacial cirques (altitude ratio, cirque floor, minimum point; Ipsen et al., 2018). However, we preferred the methods considering the glacier hypsometry as they reflect more evident changes from stage to stage (Fernández-Fernández et al., 2017;Fernández-Fernández and Andrés, 2018), if compared to morphometric parameters of the cirques. In this sense, the cirque floor elevation is derived from the last erosion period, and it is impossible to know the values corresponding to previous glacial stages.

Lichenometric dating procedures

Lichenometry was used as a relative dating tool, assuming that the lichens increase in diameter with respect to age. The results aim to complete the age control (of recent landforms non suitable for CRE dating) on the periods between aerial photos of known date as it has been applied successfully to control lichen (Sancho et al., 2011) and bryophyte (Arróniz-Crespo et al., 2014) growth during primary succession in recently deglaciated surfaces. First, we surveyed the moraines thoroughly, starting from the current glacier snouts downwards, looking for large stable boulders (i.e. well embedded in the moraine, not likely of having been overturned or remobilized by slope processes which could have affected lichen growth, e.g. snow avalanches, debris-flows, rockfall, landslides or debris-flows) with surfaces valid for dating (not weathered or resulting from block break). Lichenometry was applied to date moraine ridge boulders with the following criteria and assumptions: (i) boulders must clearly belong to the moraine ridge; (ii) lichen species should be abundant enough to allow measurements of a number of thalli at each location and hence enable surfaces to be dated under favourable environmental conditions such as basaltic rocks in subpolar mountains; (iii) only the largest lichen (circular or ellipsoidal thalli) of species Rhizocarpon geographicum, located on smooth horizontal boulder surfaces, was measured; (iv) the lichenometric procedures should not be applied when the lichen thalli coalesce on the boulder surface and individual thalli cannot be identified. We preferred the geomorphological criterion (stability vs. slope processes) to the establishment of lichenometry plots of a fixed area (e.g. Bickerton and Matthews, 1992) to ensure that lichens were measured on reliable boulders. This measurement strategy tries to circumvent or at least to minimize the specific problems of Tröllaskagi when dating glacial features so that: (i) snow accumulation should be lower in the moraine crest; (ii) lichen ages will be estimated only for the boulders located on the crests used to map and reconstruct the glaciers; and

(iii) and lichens subjected to thalli saturation (coalescence) or high competition are not measured.

First, Rhizocarpon geographicum lichens were measured with a Bernier calibrator.

Then, digital photographs for high-precision measurements were taken of the most representative of the largest thallus located in each selected boulder (Suppl. figure SF1), using an Icelandic króna coin (21 mm diameter) parallel to the surface of the lichen as a graphic scale. We preferred the single largest lichen approach as previously has been done in Tröllaskagi for lichenometric dating of moraines (Caseldine, 1983(Caseldine, , 1985b(Caseldine, , 1987;;Kugelmann, 1991). The photos were scaled in ArcGIS to real size and lichen thalli were outlined manually through visual inspection of the photos and measured automatically with high accuracy according to the diameter of the smallest circle which can circumscribe the lichen outline (Suppl. figure SF1). We preferred the simple geometrical shape of the circle and its diameter to identify the largest axis to circumvent the problem of complex-shaped lichens. Similar procedures for lichen thalli measurement from photographs are outlined in Hooker and Brown (1977).

Then, we initially applied a 0.44 mm yr -1 constant growth rate and a 10-year colonization lag (Kugelmann, 1991) to the measurement of the largest Rhizocarpon geographicum lichen (longest axis). This growth rate is derived from the lichen growth curve with the highest number of control points so far in Tröllaskagi (Kugelmann, 1991), and it is very similar to that reported from the near Hörgárdalur valley (Häberle, 1991). However, the authors are aware that using a constant growth rate implies not taking account the growth rate decline with increasing age. Other longer colonization lags of 15, 20, 25 and 30 years were added to the age estimate from the growth rate in order to test the colonization lag originally assumed by Kugelmann (1991), on the suspicion of longer colonization lags reported elsewhere (Caseldine, 1983;Evans et al., 1999, Table 1). The resulting ages were compared to the dates of historical aerial photographs where the glacier snout positions constrain the maximum and minimum ages of the lichen stations.

In the case of Porpidia cf. soredizodes, since no growth rate value has been described so far, a value will be tentatively estimated in this study. For this reason, we took measurements of the two species in the same sampling locations wherever possible. It should be noted that visual distinction between Porpidia cf. soredizodes and Porpidia tuberculosa is not always conclusive based on morphological characteristics, but we feel confident using the measurements of the Porpidia cf. soredizodes we identified in the field.

36 Cl Cosmic-Ray Exposure (CRE) dating

Where the thalli either coalesced and prevented identification of the largest thallus or dating results indicated that a moraine was too old to be dated by this method, rock samples were collected for CRE dating. The criteria for boulder and surface selection where the same as for lichenometric purposes: stable boulders with no signs of being affected by slope processes (landslides, debris-flows) or postglacial overturning, well embeded in themoraine, and with no sign of surface weathering or previous boulder break. The cosmogenic nuclide 36 Cl was chosen because of the basalt lithology ubiquitous in Iceland, which lacks quartz, which is needed for standard 10 Be CRE methods. Using a hammer and chisel, samples were collected from flat-topped surfaces of moraine boulders. In order to obtain a maximum time constraint for the deglaciation of both surveyed valleys, two samples were taken from Elliði (Fig. 1), a glacially polished ridge downstream from the Tungnahryggsjökull forelands separating Kolbeinsdalur to the north and Víðinesdalur to the south. The laboratory procedures applied for 36 Cl extraction from silicate whole rock samples were those described in Schimmelpfennig et al. (2011). Note that the samples had not enough minerals to perform the 36 Cl extraction on mineral separates, which is generally the preferred approach to minimize the uncertainties in age exposure estimates, as in mineral separates 36 Cl is often produced by less and better known production pathways than in whole rock samples (Schimmelpfennig et al., 2009) (CEREGE), Aix-en-Provence (France). Initial weights of about 120 g per sample were used. A chemically untreated split of each sample was set aside for analyses of the chemical composition of the bulk rocks at CRPG-SARM. First, the samples were rinsed to remove dust and fines. Then, 25-30% of the mass was dissolved to remove atmospheric 36 Cl and potentially Cl-rich groundmass by leaching with a mixture of ultra-pure dilute nitric (10% HNO 3 ) and concentrated hydrofluoric (HF) acids. In the next step, 2 g aliquots were taken to determine the major element concentrations; these were analysed by ICP-OES at CRPG-SARM. Then, before total dissolution, ~260 µL of a 35 Cl carrier solution (spike) manufactured in-house (concentration: 6.92 mg g -1 ;

35 Cl/ 37 Cl ratio: 917) were added to the sample for isotope dilution (Ivy-Ochs et al., 2004). Total dissolution was achieved with access quantities of the above mentioned acid mixture. Following total dissolution, the samples were centrifuged to remove the undissolved residues and gel (fluoride complexes such as CaF 2 ). Next, chlorine was precipitated to silver chloride (AgCl) by adding 2 ml of silver nitrate (AgNO 3 ) solution at 10%. After storing the samples for two days in a dark place to allow the AgCl to settle on the bottom, the supernatant acid solution was extracted by a peristaltic pump.

To reduce the isobaric interferences of 36 S during the 36 Cl AMS measurements, the first precipitate was re-dissolved in 2 ml of ammonia (NH 3 +H 2 O 1:1 vol NH 4 OH), and 1 ml of a saturated solution of barium nitrate (Ba(NO 3 ) 2 ) was added to the samples to precipitate barium sulphate (BaSO 4 ). It was removed by centrifuging and filtering the supernatant with a syringe through acrodisc filters. AgCl was precipitated again with 3-4 ml of diluted HNO 3 (1:1 vol). The precipitate was collected by centrifuging, rinsed, and dried in an oven at 80 ºC for 2 days.

The final AgCl targets were analysed by accelerator mass spectrometry (AMS) to measure the 35 Cl/ 37 Cl and 36 Cl/ 35 Cl ratios, from which the Cl and 36 Cl concentration were inferred. The measurements were carried out at the Accélérateur pour les Sciences de la Terre, Environnement et Risques (ASTER) at CEREGE in March 2017 using when scaling the SLHL production rates to the study site. Only Licciardi et al. s (2008) production rate already accounts for this anomaly, as the calibration sites of study are located in south western Iceland (see also Licciardi et al., 2006). On the other hand, Stone et al. s (1996) and Schimmelpfennig et al. s (2011) production rates were calibrated in Tabernacle Hill (Utah, western U.S.A.) and Etna volcano (Italy), respectively, hence they need to be corrected for the atmospheric pressure anomaly when applied in Iceland. Dunai (2010) advises including any long-term atmospheric pressure anomaly at least for Holocene exposure periods. Therefore, the local atmospheric pressure at the sample locations was applied in the scaling factor calculations when using the Stone et al. (1996) and Schimmelpfennig et al. (2011) production rates. Instead of the standard value of 1013.25 hPa at sea level, a sea level value of 1006.9 hPa (Akureyri meteorological station; Icelandic Meteorological Office, 2018) was used. The atmospheric pressure correction assumed a linear variation of temperature with altitude. The results presented and discussed below are based on the 36 Cl production rate for Ca spallation of Licciardi et al. (2008) as it is calibrated for Iceland and considers the atmospheric pressure anomaly. The exposure ages presented throughout the text and figures include analytical and production rate errors unless stated otherwise. Our <2000 yr CRE ages have also been rounded to the nearest decade, and then converted to CE dates through their substraction from the year 2015 (i.e.

fieldwork and sampling campaign). In order to achieve robust comparisons of our results with those obtained by radiocarbon or tephrochronology, we have calibrated the 14 C ages previously published in the literature through the OxCal 4.3 online calculator (https://c14.arch.ox.ac.uk/oxcal/OxCal.html) implementing the IntCal13 calibration curve (Reimer et al., 2013).

Results

Geomorphological mapping, aerial photos and identified glacial stages

Based on photo-interpretation of aerial photographs and fieldwork, two geomorphological maps were generated at ~1:7000 scale, in which well preserved moraine segments, current glacier margins and stream network were also mapped (Figs.

2 and 3). In Vesturdalur, over 1000 moraine ridge fragments (including terminal and lateral moraine segments) were identified and mapped, with increased presence from 1.7 km upwards to the current glacier terminus. In the analysis, we retained only ridge fragments if they are at least 50 m long, protruding 2 m above the valley bottom and the alignment of glacial boulders embedded in the moraine crest is preserved, as indicators of major glacial culminations and well preservation state. Otherwise we considered either they represented insignificant glacial stages or were most probably affected by post-glacial slope reworking.

Following these criteria, we retained 12 glacial stages based on the geomorphological mapping of the Vesturdalur foreland (Fig. 2). We were able to verify in the field that the selected sections had not been affected by postglacial slope processes as none of these moraines was cut by debris-flows or deformated/covered by landslides. The palaeoposition of the glacier terminus was clearly defined by pairs of latero-frontal moraines in stages 1, 4 and 6. In stages 2, 3, 5, 9, 10, 11 and 12, it was poorly defined by short latero-frontal moraines on one side of the valley, very close to the river, with their prolongation and intersection with the river assumed to be the former apex, and so a tentative terminus geometry was drawn. The lateral geometry of the tongue was accurately reconstructed in stages 6, 8 and 9 based on long and aligned, ridge fragments, and in the other stages an approximate geometry was drawn from the terminus to the headwall. The greatest retreat between consecutive stages (1 km) occurred in the transition from the stage 1 to the stage 2. No intermediate frontal moraines were observed in the transect between the stages 1 and 2.

In Austurdalur, over 1600 moraine ridge fragments were identified and mapped.

Following the same criteria as in Vesturdalur, 13 stages were identified based on the geomorphological evidence (Fig. 3). The furthest moraines marking the maximum extent of the eastern Tungnahryggsjökull appear at 1.3 km from the current terminus. In ST1). The stages identified on the basis of the geomorphological mapping and those obtained from glacier outlining over historical aerial photos sum up to a total of 17 stages for each glacier.

Glacier length, extent and volume

The reconstructed glacier surfaces corresponding to the different glacial stages is shown in Suppl. figure SF3. The length of the glaciers during their reconstructed maximum ice extent was unequal, with the western Tungnahryggsjökull being 6.5 km long, and the eastern glacier being 3.8 km long (Suppl. table ST2). The same occurred with the area, 9.4 and 5.3 km 2 , respectively (Suppl. table ST3). Over the different stages, the western glacier lost 31% of its area and retreated 51% of its total length (Suppl. tables ST2 and ST3) while there was less shrinkage of the eastern glacier both in area loss (26%) and length (34%). Figs. 2B and 3B and Suppl. table ST2 show only one reversal during the general retreating trend, in the stage 15 of the western and the stage 16 of the eastern Tungnahryggsjökull. The greatest area losses occurred in the transition to the stages 2, 4, 7, 9 and 14 (>3%) on the western glacier while losses between stages in the eastern glacier were lower except for the transition between the stages 14 and 17, where a noticeable reduction of the accumulation area was observed in the aerial photos of 1946 and 1985, and the satellite image of 2005 (Fig. 3B). The volumes calculated from the reconstructed glacier DEM and the corrected bed DEM show that the glaciers reached ~1.10 km 3 (western) and ~0.47 km 3 (eastern) at their recorded maximum extent corresponding to their outmost moraines. From the oldest to the most recent stage they lost 30% and 23% of their ice volume, respectively. The losses between consecutive stages of the glaciers were in general lower than 3% with the exception of the stages 2, 4, 7, 9 (western) and stage 14 (eastern), where the values ranged from 3% to 10% (Suppl. table ST3). Only one slight inversion of the volume trend is seen in the stages 15 of the western glacier and in 16 of the eastern glacier.

Equilibrium-Line Altitudes (ELAs)

The application of the AAR (0.67) method showed ELAs ranging from 1021 to 1099 m a.s.l. (western glacier) and from 1032 to 1065 m a.s.l. (eastern glacier) for the different reconstructed stages. This means an overall rise of 78 and 33 m respectively (Table 1)

from the maximum to the minimum extent recorded. The results from applying the AABR (1.5) show the same trend and similar ELAs, with differences of up to ±15 m compared with those obtained from the AAR. The AABR-ELAs tend to be higher than the AAR-ELAs, especially in the second half of the reconstructed stages with the most remarkable differences occurring in the eastern Tungnahryggsjökull (Table 1).

However, the error derived from the uncertainties associated to the applied balance ratio (BR, ±0.4) tends to decrease as the glaciers get smaller. The greatest change in the ELA between consecutive stages is found between the stages 1 and 2 in the western glacier (+26 m), fully coincident with the largest retreat measured, about 1 km. An interesting result is that the ELA rise is attenuated in both glaciers from stage 10 onwards, with stage-to-stage variations close to zero predominating, and with only one inversion (-3 m) occurring in the western glacier between the stages 14 and 15 (Table 1).

Lichenometric dating

Altogether 17 lichenometry stations (8 in Vesturdalur and 9 in Austurdalur) were set up during fieldwork in the two glacier forelands. Their spatial distribution and correspondence with the different glacial stages are given in Figs. 2 and 3 and Suppl.

table ST4. The table also shows the measurements of the largest Rhizocarpon geographicum thalli found during fieldwork in the moraines (stages) to which the stations correspond. TUE-0 was the only station where no lichen of either species was found in 2015. Unlike Porpidia cf. soredizodes thalli, which are present in all the remaining lichenometry stations, Rhizocarpon geographicum thalli suitable for measuring (ellipsoidal, not coalescent) were only found in stations TUW-2 to TUW-7 in Vesturdalur, and in TUE-2 to TUE-7 in Austurdalur.

The measurements considered the diameter of the smallest circle bounding the thallus outline as representative of the longest axis (Suppl. figure SF1). The obtained values ranged from 19.3 to 71.5 mm in Vesturdalur, and from 19.0 to 47.7 mm in Austurdalur 1994-2000 and 1946-1985 respectively, based on the position of the snouts in the aerial photos (Suppl. figure SF2). These observations suggest a colonization lag from 10 to 15-21 years, thus shorter than for Rhizocarpon geographicum.

36 Cl CRE dating

The detailed geomorphological analysis carried out on the numerous moraine ridges of both valleys has greatly limited the number of boulders reliable for successfully applying 36 Cl CRE and lichenometry dating methods. Due to the great intensity of the slope processes (especially snow avalanches and debris-flows), only a few boulders are well-preserved, sometimes only one in each moraine ridge that retains its original glacier location. Thus, it should be highlighted that this issue prevented performing a statistically valid sampling for both methods (see e.g. Schaefer et al., 2009;Heymann et al., 2011).

During the fieldwork campaigns in the forelands of the western and eastern Tungnahryggsjökull glaciers, 12 samples from stable and very protrusive moraine boulders (Suppl. figure SF4) were collected in areas where lichenometric dating was not suitable because of lichen thalli coalescence, and also 2 samples from a polished ridge downwards the confluence of Vesturdalur and Austurdalur (Suppl. figure SF5). The input data for exposure age calculations, namely sample thickness, topographic shielding factor, major element concentrations of bulk/target fractions, are summarized in the Suppl. tables ST5, ST6, ST7 and ST8 includes the 36 Cl CRE ages calculated according to different Ca spallation production rates and the distance to the most recent glacier terminus position mapped. In Vesturdalur, 8 samples were collected from 5 moraines corresponding to 5 of the stages identified on the geomorphological map (Fig. 2). Samples TUW-9 and TUW-10 (2011) production rate yielded dates older by 15% on average (Suppl. table ST8). These small differences do not represent statistical difference given the calculated age uncertainties.

were

Discussion

36 Cl CRE dating

The dates obtained in both valleys range from 380±200 CE to 1640±90 CE and are significantly younger than the ages from Elliði polished ridge (Suppl. table ST8). TUW-14 (670±210 CE) could be the only outlier as it is significantly older than the other sample obtained from the same moraine of the stage 3 (TUW-13; 1470±130 CE) and also older than the samples TUW-15 (1460±110 CE) and TUW-16 (1220±190 CE), from the moraine of the previous stage 2 (Fig. 2). This would imply assuming nuclide inheritance for sample TUW-14 due to either remobilization of an earlier exposed moraine boulder (see Matthews et al., 2017) or to previous exposure periods, but the high geomorphological dynamism of the slopes limits this possibility (Andres et al., 2019). Another possible interpretation is that the samples TUW-15 and TUW-16 (stage 2) would be the outliers since they may have experienced incomplete exposure due to post-depositional shielding (Heymann, 2011). The possibility of both samples being affected by proglacial processes can be ruled out given the distance to the meltwaters channel or the absence of glacial burst features (see Caseldine, 1985a) in the surroundings of the sampled boulders. Thus, the ages of samples TUW-14 and TUW-13 would indicate that the moraine of stage 3 was built during two overlapped glacial advances at 670±210 CE and 1470±130 CE. In Austurdalur, the interpretation of the ages is also complex. Samples TUE-9 (740±170 CE) and TUE-10 (1460±100 CE) from the same moraine are significantly different, but it is difficult to decide whether or not one of these two samples is an outlier. It is also possible that the younger age indicates the timing of a further readvance with the snout reaching the same moraine. It would be necessary to take more samples, but it will be difficult to find other sectors of these moraines that are not affected by slope processes, especially debris-flows. The hypothesis of supraglacial debris duming can be rejected due to the lack of supraglacial debris or other features indicative of a palaeo debris-covered glacier. Other possibility to be consider is that older boulders may be incorporated in the formation of push moraines as has been shown in maritime Scandinavia, and identified to give overestimated ages for LIA-moraines (Matthews et al., 2017). The asynchronocity of glacial advances and retreat in both valleys should not be surprising as glaciers can retreat or advance differently in adjacent valleys due to a number of factors such as hypsometry, aspect, gradient, etc. Caseldine (1985b) (Häberle, 1991(Häberle, , 1994)), and given the uncertainties of our dates (200 yr), also with Drangajökull (NW Iceland) advancing at the sime time (~300 CE; Harning et al., 2018). On the other hand, Meyer and Venzke (1985) had already suggested the presence of pre-LIA moraines at Klaengshóll (eastern cirque, tributary of Skíðadalur). Caseldine (1987Caseldine ( , 1991) ) proposed a date of 5310±345 cal. BCE as the youngest for a moraine in that cirque, based on tephrochronology (tephra layer Hekla 5 dated in a similar ground in Gljúfurárdalur) and rock weathering measurements using the Schmidt hammer technique. Based on the big size of some moraines in Skíðadalur and Holárdalur, Caseldine (1987Caseldine ( , 1991) ) also supports the hypothesis of pre-LIA moraines formed during several advances. All this information is not in agreement with the hypothesis that all the glaciers in Tröllaskagi reached their maximum ice extent since the Early Holocene during the LIA (Hjort et al., 1985;Caseldine, 1987Caseldine, , 1991;;Caseldine and Hatton, 1994).

In south and central and northwest Iceland, the ice caps reached their Late Holocene maximum advance during the LIA (Brynjólfsson, et al. 2015a;Larsen et al. 2015;Harning et al., 2016a;Anderson et al., 2018;Geirsdóttir et al., 2018). But also pre-LIA advances have been identified and dated through radiocarbon and tephrochronology in a moraine sequence of Kvíárjökull (south-east Vatnajökull), the first of which occurred at Subatlantic times (before 110±240 cal. BCE) and the second at 720±395 CE (Black, 1990;cited in Guðmundsson, 1997). Considering the uncertainty of our ~400 and ~700 CE dates, these advances likely were coetaneous with other advances reported from southern Iceland in Kötlujökull (after 450±100 cal. CE, radiocarbon dated and supported by tephochronology; Schomaker et al., 2003) and Sólheimajökull (southern M rkdalsj kull, Ystagil stage ; Dugmore, 1989). In fact, the 669±211 CE advance of western Tungnahryggsjökull (stage 3) also overlaps with the Drangajökull and Langjökull advances at ~560 CE and 550 CE, respectively (Larsen et al., 2011;Harning et al., 2016a) during DACP, in response to the summer cooling between ~250 CE and ~750 CE (Harning et al., 2016a). These advances would correspond to the general atmospheric cooling in the North Atlantic reflected by widespread glacier advances (Solomina et al., 2016).

The timing of the stage 2 in Vesturdalur is difficult to define because the sample TUW-16 (1220±190 CE) has almost 200-year uncertainty, and thus overlaps with both the LIA and the higher temperatures of the Medieval Warm Period (MWP, Lamb, 1965; 950-1250 CE, see Solomina et al., 2016) not conducive to glacier development as it has been observed in northwest and central Iceland (Larsen et al., 2011;Harning et al., 2016a).

On the other hand, moraines in Greenland Arctic environments date within the MWP, based on cosmogenic nuclide dating (Young et al., 2015;Jomelli et al., 2016), suggesting a cooling in the western North Atlantic while the eastern sector remained arm. Iceland is located in the middle of this dipole see-sa pattern (Rogers and van Loon, 1979). Thus, the correlations with the glacier fluctuations Greenland or Norway, are complicated as the climate anomalies in both regions show opposing signs in the different see-saw modes. To increase the difficulty of interpretation, glaciers of Tröllaskagi are known to surge occasionally (Brynjólfsson et al., 2012;Ingólfsson et al., 2016), which could explain additional complexity in the glacial advances pattern, as it would not be driven by climatic variability. Brynjólfsson et al. (2012) mid-18 th century in Barkárdalur (Häberle, 1991); early 19 th century in Baegisárjökull and Skríðudalur (Häberle, 1991), and in Búrfellsdalur and Vatnsdalur (Kugelmann, 1991, Fig. 7); mid-19 th century (1845-1875 CE) in Myrkárjökull, Vindheimajökull (Häberle, 1991), Þverárdalur, Teigardalur, Grýtudalur, Vesturárdalur (Kugelmann, 1991, Fig. 7),

Heiðinnamannadalur and Kvarnárdalur (Caseldine, 1991); and late 19 th century (1880s-1890s CE) in Gljúfurárdalur (Caseldine, 1985b(Caseldine, , 1991)). Caseldine (1991) proposed 1810-1820 CE as the date of the outer moraine of Vesturdalur based on a minimum lichenometric age. According to our 36 Cl moraine ages, the LIA maximum of Tungnahryggsjökull glaciers occurred ~400 years earlier than these dates. This should not be surprising as Kirkbride and Dugmore (2001) reported lichenometric ages >100 years younger than those derived from tephrochronology in the same landforms. Our results also give the earliest LIA dates based on moraine dating obtained so far in Iceland, compared to the previously published dates all obtained through lichenometric dating: 1740-1760 CE in south-east Iceland (Chenet et al., 2010). In northwestern Iceland, glaciolacustrine sediments recorded a contemporary expansion of Drangajökull at ~1400 CE (Harning et al., 2016a). Likewise a first major advance of Langjökull (western central Iceland; Fig. 1A) between 1450 and 1550 CE has been reported (Larsen et al., 2011), as well as advances in central Iceland between 1690 and 1740 CE (Kirkbride and Dugmore, 2006), based on varve thickness variance together with annual layer counting and C:N mass ratio, and tephrochronology (geochemical analysis), respectively.

The dates of samples TUW-13, TUW-12 and TUW-11 in Vesturdalur (average date 1470±120 CE; stages 3, 5 and 6) cannot be distinguished statistically if their internal uncertainty is considered (Fig. 4; Suppl. table ST8). The spatial scatter of these sampling sites (Fig. 2) may indicate frequent and intense terminus fluctuations in a short time interval. Different ages obtained from the moraines of the stages 3 and 4 in Vesturdalur and Austurdalur, respectively, may indicate that in the 15 th century the glacier termini reached the moraines deposited at ~700 CE (Figs. 2 and3) and rebuilt them, which may explain the large size of these moraines. Caseldine (1987) argued that other moraines in Skíðadalur were formed during more than one advance. Based on the size of the largest moraines, he also pointed out that many glaciers must have advanced to positions similar to those of the late 19 th century earlier in the Neoglacial.

The glacier advances in the 15 th century in Vesturdalur and Austurdalur may have been the result of different climate forcings during that century: negative radiative forcing and summer cooling were linked to intense volcanic activity (Miller et al., 2012), the low solar activity of the Spörer Minimum (1460-1550 CE; Eddy, 1976), the seaice/ocean feedback with increased sea ice (Miller et al., 2012) and the weakening of the Atlantic Meridional Overturning Circulation (AMOC) (Zhong et al., 2011). Solar activity may have played a major role in these glacial advances if we consider that the climate in the North Atlantic is higly influenced by solar activity variability (Jiang et al., 2015). On the contrary, historical records, although not determinant, suggest a mild climate for 1430-1550 CE (Ogilvie and Jonsdóttir, 2000), and especially for 1412-1470 CE [START_REF] Ogilvie | The past climate and sea-ice record from Iceland, Part 1: Data to A.D. 1780[END_REF]. This would also be compatible with increased precipitation and hence more winter snow in warm periods (Caseldine and Stötter, 1993;Stötter et al., 1999;Fernández-Fernández et al., 2017), and also with potential surge activity with glacial advances not directly linked to specific climate periods (e.g. Brynjólfsson et al., 2012;Ingólfsson et al., 2016).

In Vesturdalur, the dates of samples TUW-9 (1590±100 CE) and TUW-10 (1640±90 CE) are compatible with a cold period from the late 1500s to 1630 CE [START_REF] Ogilvie | Little Ice Age Research: a perspective from Iceland[END_REF]. Nevertheless, considering the uncertainties of these samples, their dates also overlap with the Maunder Minimum (1645-1715 CE) (Eddy, 1976), when the LIA maximum glacial advance occurred in the Alps (Holzhauser et al., 2005).

Lichenometric dating.

5. 2.1. 36 Cl CRE dating vs. lichenometric dating. Multiple lichen species dating approach.

The contrast between our CRE dating results and earlier lichenometry-based results published elsewhere evidences the clear underestimation of the latter. This could be explained either by lichen growth inhibition due to saturation of the rock surface and competition of other thalli (Wiles et al., 2010;Le Roy et al., 2017) or a colonization lag longer than assumed up to now, from 10 to 15 years in Tröllaskagi (Kugelmann, 1991;Caseldine, 1985b, respectively). However, other factors affect the reliability of the lichen-derived ages, and may explain the differences with CRE dates. One of them is the reliability of the growth rates and lichenometric calibration curves that are commonly assumed to be linear (constant) growth in northern Iceland (e.g. Caseldine, 1983Caseldine, , 1985b;;Häberle, 1991;Kugelmann, 1991), although it has been demonstrated that the lichen diameter growth declines with age (see e.g. Winkler, 2003, Fig. 4). This might lead to significant age underestimations for the oldest dates, putting potentially earlier dates in the 19 th century. Most of the fixed control points from which lichen growth rates have been derived in northern Iceland comprise abandoned gravestones, memorial stones, old bridges and mostly abandoned farmsteads (Caseldine, 1983;Kugelmann, 1991). Time of death is commonly assumed for gravestones, and abandonment date for farmsteads. Athough the latter is well known on the basis of historical documentation, the coloni ation lag sometimes relies on the the likel duration of the deterioration of the buildings after abandonment that depends on the quality and stability of the constructions (see Kugelmann, 1991), and hence affect the results. However, it should be highlighted that our approach circumvents this last issue by combining field observations with historical aerial photographs. In addition, given that lichen growth of Rhizocarpon subgenus depends mostly on available humidity, the location of the measured lichens has also a potential effect on the results, i.e. to microclimatic changes (see Innes, 1985;Hamilton and Whalley, 1995) between the location of the fixed points and the location on the moraine (crest: dryer and more exposed;

green zone on the proximal slope, etc.). In the literature cited above about lichenometrydated LIA advances no detailed information is provided about the location of the lichen measured for dating purposes, so potential error derived from this issue can not be assessed. Nevertheless, given that we measured lichens on horizontal flat surfaces where there is no restriction to the moisture recepit of the lichens, we can consider our results presented throughout the next sections valid. In any case, such a great difference of our CRE dates and the previous lichen-derived is more likely to be explained by the technical limitations of the technique rather than environmental factors.

Our field observations and historical aerial photos of known age restricted the dates of the moraines colonized by Rhizocarpon geographicum lichens. This approach would support the dates obtained from the 0.44 mm yr -1 growth rate of Kugelmann (1991) and the 20-year colonization lag. This rate is slightly higher than those reported from the Antarctic Peninsula (0.31 mm yr -1 ; Sancho et al., 2017), but lower than in Tierra del Fuego (0.63 mm yr -1 ; Sancho et al., 2011). The correlation between the sizes of largest ST4), which exceed the size of the biggest control point from which Kugelmann s gro th rate as estimated (Kugelmann, 1991, Fig. 3). This problem reinforces the need of taking lichen-derived ages as relative. The interpretation of the chronology in Austurdalur is more complicated: the lichen sizes measured at the stations TUE-6 (1890s CE, stage 9) and TUE-7 (1880s CE; stage 7) yield more recent dates than at station TUE-5 (1860s CE; stage 10) despite being representative of earlier stages (Fig. 3). Given that this anomaly occurs in both lichen species, it is reasonable to conclude that an environmental factor could have affected the lichen populations at both stations. It could even indicate a date when the boulders may have been remobilized by postglacial processes.

Our chronology of the 19 th century glacial advances in both valleys (Table 2) does not coincide exactly with the phases identified by Kugelmann (1991) in Svarfaðardalur-Skíðadalur (1810, 1850, 1870-1880, 1890-1900 CE). It also differs appreciably from the chronology proposed by Caseldine (1985b) in Vesturdalur (moraines of 1868, 1878, 1887, 1898 CE). Nevertheless, it should be borne in mind that we are considering only two glaciers with their own glaciological properties. Moreover, we have estimated the ages from the growth rate (instead of a specific calibration growth curve), longer colonization lag based on field observations, and applied to the longest axis measurements (Kugelmann, 1991). On the other hand, micro-climatic differences between the location of fixed points and our lichen measured may occur. However, we recognise that the comparisons with Caseldine s (1985b) results are quite difficult since:

(i) the moraines dated by Caseldine are poorly located in his mapping (and hard to identify over aerial photos and our moraine mapping); (ii) we are not able to apply the same parameters to his measurements, as he used the mean longest axis of the five largest lichen is not provided (only the average value); and (iii) he recognised the lichen growth slowdown when dating the outermost moraine, which probably is one of those dated with 36 Cl in this work.

Our results, despite the limitations of the applied method, largely due to the low number of moraine boulders suitable for its application can be considered compatible and in good agreement with glacial advances and cold periods during the first third of the 19 th century as we show below. Martin et al. (1991) pointed out the existence of a moraine dated to ca. 1810-1820 CE in Western Tr llaskagi Tungnahr ggsj kull (ambiguousl , without providing any detail of its location), as well as others of this period in Svarfaðardalur, Búrfellsdalur and Vatnsdalur. Other dates obtained from more sophisticated statistical techniques applied to lichenometry dating procedures also evidenced a glacial advance phase 1810-1820 CE (Chenet et al., 2010). These advance phases were coetaneous with significant sea ice persistence in the early 1800s [START_REF] Ogilvie | Little Ice Age Research: a perspective from Iceland[END_REF], decreased solar activity, and strong volcanic eruptions (Dalton Minimum, 1790-1830 CE;Wagner et al., 2005). The moraines dated in Vesturdalur to around 1830 CE (TUW-7: 1830s CE, stage 10) and the early 1890s CE (TUW-5: 1890s CE, stage 12) are in good agreement with the glacial advances in Svarfaðardalur-Skíðadalur during the 1830s and early 1890s CE (Kugelmann, 1991, Fig. 8), as well as with the low temperatures and presence of sea ice at these dates (Koch, 1945;Ogilvie, 1996;Ogilvie and Jonsdóttir, 2000;[START_REF] Ogilvie | Little Ice Age Research: a perspective from Iceland[END_REF]Kirkbride, 2002). century; it would be the result of the accumulated effect of the temperature rise since the latter half of the 19 th century (Caseldine, 1987;Wanner et al., 2008). Thus, the subsequent advances would be the response to specific relative thermal minima within a warmer climate (Stötter et al., 1999). The date of TUW-3 (stage 13) representing the moraine abandonment in ~1940 CE is in agreement with the overall context of general glacier retreat as a result of the warmest decades of the 1930s and 1940s CE, which triggered an intense retreat of the glaciers (Einarsson, 1991;Martin et al., 1991;Kirkbride, 2002). The advances/standstills dated to the early 1950s CE in both Tungnahryggsjökull glaciers are likely to be synchronous given the similarity of the dates obtained (Table 2). They could represent glacial advances in consonance with the late 1940s early/mid-1950s CE cooling (Einarsson, 1991;Fernández-Fernández et al., 2017), recorded both in Akureyri and many other weather stations throughout Iceland. Caseldine (1983) found a similar chronology in Gljúfurárdalur (Skíðadalur headwater, 10 km to the east), with moraine deposition between mid-1910s and 1930mid-1910s and , around mid-1930s and late 1940s-1950 CE. CE. The subsequent trend of the Tungnahryggsjökull glaciers, inferred from aerial photographs, a satellite image, geomorphological mapping, and glacier reconstruction, was characterized by continuous retreat and volume loss, in line with the increasing temperature trend since the end of the LIA. This trend was only reversed between the mid-1960s and mid-1980s CE by a major cooling event (Einarsson, 1991;Sigurðsson, 2005;Fernández-Fernández et al., 2017) (Sigurðsson, 2005). In spite of these glacial fluctuations in response to the intense climatic fluctuations of the last century, the ELAs estimated in this paper only show a general rise of 5-10 m (Table 1). This small ELA increase may be derived from some artifacts of the glacier reconstruction or the attenuating effect of the increase in winter precipitation suggested by glacier-climate models (Caseldine and Stötter, 1993;Fernández-Fernández et al., 2017).

Post

Final remarks:

Can the occurrence of pre-LIA glacial advances be confirmed? Was the LIA in northern Iceland the Holocene glacial maximum? Was it a single maximum advance?

Our results demostrate that Tungnahryggsjökull advanced during Late Holocene glacial stages prior to the LIA and reached considerably more advanced positions, even though the Iceland large ice caps reached generally their Late Holocene maximum advance during the LIA (Larsen et al. 2015, Harning et al., 2016a;Anderson et al., 2018, Geirsdóttir et al., 2018). The chronological data presented in the previous sections suggests that during the LIA the glaciers overlaped moraines deposited in pre-LIA glacial stages. Our results also show LIA advances since the 15 th century and are thus contrary to the traditional proposal of a single maximum LIA advance occurring during either mid-18 th or late-19 th centuries in Tröllaskagi peninsula, followed by subsequent minor readvances in an overall retreating trend (see Caseldine, 1983Caseldine, , 1985bCaseldine, , 1987;;Kugelmann, 1991;Martin et al., 1991). The use of the 36 Cl production rates from Ca spallation reported by Stone et al. (1996) does not lead to major changes in the interpretation and conclusions as the changes in the nominal dates (up to 90 yr earlier;

Table 3) are within the external uncertainty and also overlap with the results presented above based on the Licciardi et al. (2008) production rate. Similarly, if we consider the results derived by the Schimmelpfennig et al. (2011) production rate, we obtain even earlier ages, which still overlap with the results derived by the other production rates due to a higher external uncertainty (see Table 3). Although the snow cover duration is known to be high in northern Iceland (see Dietz et al., 2012), quantifying the effect of snow cover on sub-surface 36 Cl production is a complex issue: on the one side, snow lowers the isotopic production rates related to spallation reactions due to the shielding effect on high-energy neutrons (Benson et al., 2004;Schildgen et al., 2005), and on the other side it increases the 36 Cl production rate from thermal neutrons below the rock surface, due to the enhancing effect of hydrogen on these low-energy neutrons (Dunai et al., 2014). Both effects might cancel out depending on the composition of the samples, and their quantification is still debated and affected by high uncertainties (Zweck et al., 2013;Dunai et al., 2014;Delunel et al., 2014). Given this complexity, snow shielding was not applied. In any case its effect is unlikely to be higher than the uncertainty derived from extracting 36 Cl from whole rock instead of minerals.

Our results are in concordance with several valleys in northen Iceland, but also with the results that are being obtained in other sectors of Arctic and North Atlantic region in the last years, such as: in Baffin Island (northern Canada), where glaciers reached Late Holocene maximum positions prior to the LIA (Young et al., 2015; 10 Be dating), or West Greenland, with several advances or stabilizations at 1450±90 CE and 1720±60 CE (Jomelli et al., 2016; 36 Cl dating). However, it is striking that the early LIA advances of northern Iceland reported in the present paper do not agree with maritime Norway with later maximum culminations (see Nesje et al., 2008) despite being the glaciated region most comparable with Iceland in terms of climate and glaciology. Our results also agree with farther and southern areas such as the Alps, with maximum advances at around 1430 CE (Schimmelpfennig et al., 2012(Schimmelpfennig et al., , 2014a); 10 Be dates; and

Sierra Nevada (Iberian Peninsula), where LIA advances have been reported between the 14 th and 17 th centuries (Palacios et al., 2019; 10 Be dates). Our detailed moraine mapping, combined with CRE dating in the surveyed valleys, clearly shows a number of advances throughout the LIA, in response to the great climatic variability of the region with alternating cold and mild/warm periods [START_REF] Ogilvie | The past climate and sea-ice record from Iceland, Part 1: Data to A.D. 1780[END_REF](Ogilvie, , 1996;;[START_REF] Ogilvie | Sea ice, climate, and Icelandic fisheries in the eighteenth and nineteenth centuries[END_REF][START_REF] Ogilvie | Little Ice Age Research: a perspective from Iceland[END_REF]Geirsdóttir et al., 2009) as occurred in the Alps (e.g. Schimmelpfennig et al., 2014a) or the Iberian mountains (e.g. [START_REF] Oliva | The Little Ice Age in Iberian mountains[END_REF]. The ELA calculations show that the major long-lasting rise of the glacier ELA (24-50 m depending on the calculation method) took place prior to 1900s/1910s.

According to the results, the evolution pattern described by Fernández-Fernández et al. (2017) for the Tungnahryggsjökull glaciers should be revised as the 36 Cl CRE dates from the 15 th and 17 th centuries indicate that LIA maximum was reached earlier than previously thought. Thus, if we consider the ELA of the earliest LIA dates obtained with 36 Cl CRE (i.e. stages 5 and 4 of western and eastern Tungnahryggsjökull), these imply ELA depressions (with reference to the 2005 date) of 24-50 m (depending on the ELA calculation method), occurring for at least 560 years (Table 1) and not 150 years as had been previously assumed (Caseldine and Stötter, 1993;Fernández-Fernández et al., 2017).

Conclusions

(i) This paper highlights the detailed geomorphological analysis of the glacial landforms as an essential pre-requisite prior to the application of dating methods on them.

Nevertheless, this has greatly limited the number of valid moraine boulders to be dated, since the vast majority of those were affected by post-glacial processes. This isue which has prevented a statistically acceptable sampling and the validation or invalidation of the inconsistent ages ielded b several boulders, so a conclusive explanation cannot be given. (vi) From the measurements carried out in different lichenometry stations, growth of Porpidia cf. sporedizodes lichen appeared to be higher than in the case of Rhizocarpon geographicum, and also proportional to that. Its growth rate has been tentatively estimated for the first time, at around 0.737 mm yr -1 . However, further research on the growth rates of this species is required for its potential use in lichenometric dating as a complementary species, since it also shows a shorter colonisation lag than Rhizocarpon geographicum.

Figure captions.

  taken from two boulders in the moraine that correspond to the left latero-frontal edge of the glacier during the stage 7, ~1 km from the 2005 CE (stage 17) glacier terminus (measured along the flowline from the reconstructed terminus apex); they yielded consistent dates of 1590±100 CE and 1640±90 CE. Samples TUW-11 and TUW-12 were extracted from the moraines corresponding to the glacial stages 6 and 5, at 185 m and 465 m downstream respectively (~1.2 km and ~1.5 km respectively from the 2005 CE snout), and gave consistent dates 1480±120 CE and 1450±100 CE. The next 36 Cl samples (TUW-13 and TUW-14) were taken from two adjacent moraine boulders on the left latero-frontal moraine ridge corresponding to the stage 3, at 264 m downstream (1.8 km from the 2005 CE snout); they yielded dates of 1470±130 CE and 670±210 CE, which are significantly different from each other. The most distant samples (TUW-15 and TUW-16) were extracted from the stage 2 moraine, ~400 m downstream from the moraine ridge corresponding to stage 3 (2.2 km from the 2005 CE terminus). They yielded dates of 1460±110 CE and 1220±190 CE, respectively, that are consistent which each other and in chronological order with sample TUW-13 from the stage 3. However, these ages are not in agreement with the oldest date of TUW-14 (670±210 CE) from the stage 3.Four 36 Cl samples were taken from two prominent moraines in the Austurdalur valley (Fig.3). Samples TUE-9 and TUE-10 were collected on the frontal moraine corresponding to stage 4 (1 km from the 2005 CE glacier terminus) and yield significantly different dates of 740±170 CE and 1460±100 CE. Samples TUE-11 and TUE-12 were taken from two moraine boulders located on the ridge of the left lateral moraine that records the maximum ice extent (Fig.3). Their calculated 36 Cl dates, 380±200 CE and 400±200 CE, are consistent with each other and in stratigraphic order with the ages from stage 4.The dates derived fromStone et al. (1996) Ca spallation production rate are similar to those presented above, only 4% older. Those derived from the Schimmelpfennig et al.

  figure SF2), as the positions of their termini are more advanced than in 1985 (stages 14

(

  ii) Applying36 Cl CRE dating for the first time in the Tröllaskagi peninsula enabled us to identify pre-LIA glacial advances in Vesturdalur and Austurdalur. Thus, the western and eastern Tungnahryggsjökull glaciers did not reach their Late Holocene maximum extent during the LIA. The maximum extent for the eastern glacier was dated to ~400 CE. For the western glacier a latest date of ~700 CE and an earliest of 16300 years ago (when the Elliði crest was deglaciated) have been obtained. (iii) The LIA maximum in Vesturdalur and Austurdalur was reached by the 15 th century at the latest. A combination of detailed moraine mapping and 36 Cl CRE dating confirm a number of glacial advances between the 15 th and 17 th centuries, the earliest LIA advances dated in Tröllaskagi at present. (iv) For the recent dates, the complementary use of aerial photographs, a satellite image and fieldwork has aided to obtain lichenometry-derived ages tentatively in good agreement with the morpho-stratigraphic order of the glacial landforms. It has also compensated some of the limitations and error sources of lichenometric dating. Thus, it has proved to be a useful tool to assess the colonization lags and the validity of the lichenometry-derived ages. (v) Fieldwork on recently deglaciated surfaces and historical aerial photographs have shown clearly that the colonization lag of Rhizocarpon geographicum lichen species is from 15-21 to 30 years, considerably longer than previously assumed in Tröllaskagi. Colonization of the Porpidia cf. soredizodes species is shorter, between 10 and 21 years.

Figure 1 .

 1 Figure 1. Location of the Tungnahryggsjökull glaciers and their forelands (C)

Figure 2 .

 2 Figure 2. Geomorphological map of the Vesturdalur foreland. (A) General view of the

Figure 3 .

 3 Figure 3. Geomorphological map of the Austurdalur foreland. (A) General view of the

Figure 4 .

 4 Figure 4. 36 Cl CRE ages and internal (anal tical) uncertaint at 1 le el of the samples from Vesturdalur and Austurdalur. Note that the samples clustering around 500 yr (15 th

Figure 5 .

 5 Figure 5. Correlation between largest thalli (longest axis) of species Rhizocarpon

  approached the glacier bedrock b tentativel estimating the ice thickness spatial distribution on the two glaciers studied. The VOLTA ( Volume and Topograph Automation ) ArcGIS toolbo(James and Carrivick, 2016) was applied with the default parameters. It only requires the glacier outline and its digital elevation model (DEM). In the first step, the tool volta_1_2_centreline creates the glacier centrelines, and then the tool volta_1_2_thickness estimates ice thickness at points along them, assuming perfect-plasticity rheology, and interpolates the values using a glaciologically correct routine. The final result is an ice-free DEM in which we reconstructed the glacier. The former glacier surface topographies at the different stages/dates were reconstructed applying the semi-automatic GLaRe ArcGIS toolbo designed b Pellitero et al. (2016), which implements the Benn and Hulton (2010) numerical model and estimates ice-thickness along glacier flowlines. To simplify the glacier surface modelling, shearstress was assumed to be constant along the glacier flowline and over time. Using the value 110 kPa for the shear-stress resembles best the current longitudinal profile of the glaciers in the Benn and Hulton (

  . The samples were crushed and sieved to 0.25-1 mm in the Physical Geography Laboratory in the Complutense University, Madrid. Chemical processing leading to 36 Cl extraction from the whole rock was carried out at the Laboratoire National des Nucléides Cosmogéniques (LN 2 C) at the Centre Europe n de Recherche et d Enseignement des G osciences de l Environnement

  contrast to the other valley, moraines populate the glacier foreland more densely and regularly on both sides of the valley. Most of them are <50 m long with a few exceeding 100-200 m. The frontal moraine ridge fragments in Austurdalur clearly represent the geometry of the terminus in all the stages, as they are well-preserved and are only bisected by the glacier meltwater, with the counterparts easily identifiable. The most prominent (over 2 m protruding over the bottom of the valley) and well preserved moraines are those marking the terminus position at stages 1 to 8, with lengths ranging from 170 to 380 m.Both glaciers were also outlined on aerial photosof 1946, 1985, 1994 (only for western Tungnahryggsjökull), and 2000, and on a SPOT satellite image(2005), and hence new recent stages from the past century were studied for the Tungnahryggsjökull, five for the western glacier(stages 13, 14, 15, 16 and 17) and four for the eastern glacier (stages 11, 15, 16 and 17) (Suppl. figure SF2; Suppl. table

  taken from two boulders in the moraine that correspond to the left latero-frontal edge of the glacier during the stage 7, ~1 km from the 2005 CE (stage 17) glacier terminus (measured along the flowline from the reconstructed terminus apex); they yielded consistent dates of 1590±100 CE and 1640±90 CE. Samples TUW-11 and TUW-12 were extracted from the moraines corresponding to the glacial stages 6 and 5, at 185 m and 465 m downstream respectively (~1.2 km and ~1.5 km respectively from the 2005 CE snout), and gave consistent dates 1480±120 CE and 1450±100 CE. The next 36 Cl samples (TUW-13 and TUW-14) were taken from two adjacent moraine boulders on the left latero-frontal moraine ridge corresponding to the stage 3, at 264 m downstream (1.8 km from the 2005 CE snout); they yielded dates of 1470±130 CE and 670±210 CE, which are significantly different from each other. The most distant samples (TUW-15 and TUW-16) were extracted from the stage 2 moraine, ~400 m downstream from the moraine ridge corresponding to stage 3 (2.2 km from the 2005 CE terminus). They yielded dates of 1460±110 CE and 1220±190 CE, respectively, that are consistent which each other and in chronological order with sample TUW-13 from the stage 3. However, these ages are not in agreement with the oldest date of TUW-14 (670±210 CE) from the stage 3.Four 36 Cl samples were taken from two prominent moraines in the Austurdalur valley (Fig.3). Samples TUE-9 and TUE-10 were collected on the frontal moraine corresponding to stage 4 (1 km from the 2005 CE glacier terminus) and yield significantly different dates of 740±170 CE and 1460±100 CE. Samples TUE-11 and TUE-12 were taken from two moraine boulders located on the ridge of the left lateral moraine that records the maximum ice extent (Fig.3). Their calculated 36 Cl dates, 380±200 CE and 400±200 CE, are consistent with each other and in stratigraphic order with the ages from stage 4.The dates derived fromStone et al. (1996) Ca spallation production rate are similar to those presented above, only 4% older. Those derived from the Schimmelpfennig et al.

(

  ii) Applying36 Cl CRE dating for the first time in the Tröllaskagi peninsula enabled us to identify pre-LIA glacial advances in Vesturdalur and Austurdalur. Thus, the western and eastern Tungnahryggsjökull glaciers did not reach their Late Holocene maximum extent during the LIA. The maximum extent for the eastern glacier was dated to ~400 CE. For the western glacier a latest date of ~700 CE and an earliest of 16300 years ago (when the Elliði crest was deglaciated) have been obtained. (iii) The LIA maximum in Vesturdalur and Austurdalur was reached by the 15 th century at the latest. A combination of detailed moraine mapping and 36 Cl CRE dating confirm a number of glacial advances between the 15 th and 17 th centuries, the earliest LIA advances dated in Tröllaskagi at present. (iv) For the recent dates, the complementary use of aerial photographs, a satellite image and fieldwork has aided to obtain lichenometry-derived ages tentatively in good agreement with the morpho-stratigraphic order of the glacial landforms. It has also compensated some of the limitations and error sources of lichenometric dating. Thus, it has proved to be a useful tool to assess the colonization lags and the validity of the lichenometry-derived ages. (v) Fieldwork on recently deglaciated surfaces and historical aerial photographs have shown clearly that the colonization lag of Rhizocarpon geographicum lichen species is from 15-21 to 30 years, considerably longer than previously assumed in Tröllaskagi. Colonization of the Porpidia cf. soredizodes species is shorter, between 10 and 21 years.

Figure 1 .

 1 Figure 1. Location of the Tungnahryggsjökull glaciers and their forelands (C)

Figure 2 .

 2 Figure 2. Geomorphological map of the Vesturdalur foreland. (A) General view of the

Figure 3 .

 3 Figure 3. Geomorphological map of the Austurdalur foreland. (A) General view of the

Figure 4 .

 4 Figure 4. 36 Cl CRE ages and internal (anal tical) uncertaint at 1 level of the samples from Vesturdalur and Austurdalur. Note that the samples clustering around 500 yr (15 th

Figure 5 .

 5 Figure 5. Correlation between largest thalli (longest axis) of species Rhizocarpon

  Figure 1 Click here to download high resolution image

  Table 3 includes the 36 Cl CRE ages converted to CE

dates format presented throughout the text. The dates presented below are based on the

Licciardi et al. (2008)

Ca spallation production rate.

Aiming to obtain a maximum (oldest) age for the onset of the deglaciation in the valleys studied, two samples (ELLID-1 and ELLID-2) were extracted from the western sector of Elliði, a 660-m-high glacially polished crest separating Viðinesdalur and Kolbeinsdalur valleys (Suppl. figure

SF5

), and located at 11 km downstream from the confluence of Vesturdalur and Austurdalur valleys. Both samples yielded dates of 14300±1700 BCE and 14200±1700 BCE.

  , this should be considered as a minimum age since this probably indicates when the retreating and thinning glacier uncovered the ridge, and thus the start of the final deglaciation of the main valley. From this point to the outmost frontal moraines surveyed in this paper, no glacially polished outcrops or erratic boulders suitable for

	However

5.

Cl CRE dating results from glacially polished surfaces on the Elliði crest show an age of 14250±1700 yr (mean) for the Kolbeinsdalur deglaciation (Suppl. figure

SF5

).

36

Cl sampling were found, impeding us to provide further chronological constraints for the deglaciation pattern of these valleys.

Our 36 Cl CRE dating results suggest late Holocene glacial advances prior to the LIA, at around ~400 and ~700 CE, in Vesturdalur and Austurdalur, respectively, coinciding with the Dark Ages Cold Period (DACP) (between 400 and 765 CE) in central Europe, according to

Helama et al. (2017)

. In fact, recent synthesis about Icelandic lake records indicate a strong decline in temperature at 500 CE

(Geirsdóttir et al., 2018)

.

The presence of Late Holocene moraines outside the outermost LIA moraines in other valleys of Tröllaskagi has been suggested through radiocarbon dating and tephrochronology in the Vatnsdalur (first, between 4880±325 cal. BCE (tephra Hekla 5) and 3430±510 cal. BCE, and another after 1850±425 cal. BCE;

Stötter, 1991)

, Lambárdalur (before 3915±135 cal. BCE;

Wastl and Stötter, 2005)

, Þverárdalur (before 3500±130 cal. BCE;

Wastl and Stötter, 2005)

, Kóngsstaðadalur (after 1945±170 cal. BCE;

Wastl and Stötter, 2005), Barkárdalur (between 375±375 cal. BCE and 190±340 cal. CE and before 460±200 cal. CE; Häberle, 1991) and Baegisárdalur (2280±205 cal. BCE and 1050±160 cal. CE; Häberle, 1991)

valleys. Specifically, our oldest 36 Cl dates (~400 and ~700 CE) coincide with glacial advances that are radiocarbon dated from intra-morainic peat bogs in other valleys in Tröllaskagi and southern Iceland, e.g. the

Barkárdalur II stage (ca. 460 CE)

in Subatlantic times

  Rhizocarpon geographicum and Porpidia cf. soredizodes thalli at the same stations showed a proportionality between the largest thalli of both species: thalli of Porpidia cf.soredizodes species grow faster than those of Rhizocarpon geographicum. The sizes of the largest Rhizocarpon geographicum thalli were plotted against the sizes of the largest Despite the low number of lichenometry stations surveyed and the limitations of this dating approach discussed in the previous sections, our results are in accordance with the geomorphological logic and with the chronological frame obtained from historical aerial photos. The ages derived from Rhizocarpon geographicum thalli measurements at lichenometry stations pre-dating 1946 suggest that the western and eastern

	Tungnahryggsjökull culminated successive advances/standstills around the 1830s,
	1840s, 1860s and 1890s CE (Figs. 2 and 3, Table 2). Ages tentatively estimated from
	Porpidia cf. soredizodes thalli considering its apparently higher growth rate suggest
	glacial advances/standstills around the 1800s (Figs. 2 and 3, Table 2). No inconsistence
	(age inversions) is detected in the lichenometry-dated moraine sequence, but we
	Rhizocarpon several glacial advances or standstills are tentatively placed in the 19 th and 20 th
	centuries, in the context of a general retreat from the most advanced LIA positions, as
	discussed in the next section.
	5.2.2. LIA glacial advances/standstills: 19 th century

geographicum lichens (Fig.

5

). The slope of the best-fit linear curve obtained was around 1.675 (r 2 =0.82) that suggests that Porpidia cf. soredizodes lichens grow 1.675 times faster than those of Rhizocarpon geographicum. So if we assume 0.44 mm yr -1 growth rate for Rhizocarpon geographicum lichens, a tentative growh rate of Porpidia cf. soredizodes would be 0.737 mm yr -1 . However, this approach should be taken with caution due to the limited number of lichens (n=7) used of each species.

Aiming to obtain a tentative date (Table

2

), this growth rate was applied to the largest Porpidia cf. soredizodes lichens found in those stations where no Rhizocarpon geographicum lichens could be measured (TUW-1, TUW-8, TUE-1 and TUE-8).

Assuming colonization lags of 20 and 15 years for Rhizocarpon geographicum and Porpidia cf. soredizodes lichens, respectively, and the above-mentioned growth rates, recognise that some age underestimation may occur since: (i) we assume linear growth when applying a growth rate; and (ii) our 19 th dates were derived from >40-45 mmdiameter lichens (Table

2

and Suppl. table

  .2.3. Post-LIA glacial advances/standstills. Lichen-derived ages from Rhizocarpon geographicum thalli suggest the ocurrence of glacial advances or standstills at the first half of the 20 th century, culminating in 1910s,

1930s, 1940s and 1950s CE, although the 1930s CE date (TUE-3; stage 12)

disagrees with the date inferred from the aerial photos, at some point between 1946 and 1985 CE (Suppl. figure SF2; Table

2

). However, the 1910s CE date in both valleys is in good agreement with the moraine abandonment during the first two decades of the 20 th

  Ogilvie, A.E.J., 1984. The past climate and sea-ice record from Iceland, Part 1: Data to A.D. 1780. Clim. Change 6, 131 152. doi:10.1007/BF00144609 Ogilvie, A.E.J., Jónsdóttir, I., 2000. Sea ice, climate, and Icelandic fisheries in the eighteenth and nineteenth centuries. Arctic 53, 383 394. doi:10.14430/arctic869 Ogil ie, A.E.J., J nsson, T., 2001. Little Ice Age Research: a perspecti e from Costas, O., López-Moreno, J.I., López-Sáez, J.A., Martínez-Cortizas, A., Moreno, A., Prohom, M., Saz, M.A., Serrano, E., Tejedor, E., Trigo, R., Valero-Garcés, B., Vicente-Serrano, S.M., 2018. The Little Ice Age in Iberian mountains. Earth-Science Rev. 177, 175 208. doi:10.1016/j.earscirev.2017.11.010 Orwin, J.F., Mckinzey, K.M., Stephens, M.A., Dugmore, A.J., 2008. Identifying moraine surfaces with similar histories using lichen size distributions and the U2 statistic, Southeast Iceland. Geogr. Ann. Ser. A Phys. Geogr. 90 A, 151 164. Paterson, W.S.B., 1994. The Physics of Glaciers, 3 rd Edition. Pergamon/Elsevier,

	Iceland. Clim. Change 48, 9 52.
	Oliva, M., Ruiz-Fernández, J., Barriendos, M., Benito, G., Cuadrat, J.M., Domínguez-
	Castro, F., García-Ruiz, J.M., Giralt, S., Gómez-Ortiz, A., Hernández, A., López-
	or	pseudo-science?	Quat.	Res.	(United	States)	83,	1 12.
	methods	and	their	validation.	Quat.	Int.	138 139,	22 31.
	London.
	Pellitero, R., Rea, B.R., Spagnolo, M., Bakke, J., Hughes, P., Ivy-Ochs, S., Lukas, S.,
	Ribolini, A., 2015. A GIS tool for automatic calculation of glacier equilibrium-line
	altitudes. Comput. Geosci. 82, 55 62. doi:10.1016/j.cageo.2015.05.005
	Pellitero, R., Rea, B.R., Spagnolo, M., Bakke, J., Ivy-Ochs, S., Frew, C.R., Hughes, P.,
	Ribolini, A., Lukas, S., Renssen, H., 2016. GlaRe, a GIS tool to reconstruct the 3D
	surface	of	palaeoglaciers.	Comput.	Geosci.	94,	77 85.

doi:10.1111/j.1468-0459.2008.00168.x Osborn, G., McCarthy, D., LaBrie, A., Burke, R., 2015. Lichenometric dating: Science doi:10.1016/j.yqres.2014.09.006 Osmaston, H., 2005. Estimates of glacier equilibrium line altitudes by the Area × Altitude, the Area × Altitude Balance Ratio and the Area × Altitude Balance Index doi:10.1016/j.quaint.2005.02.004 Palacios, D., Gómez-Ortiz, A., Alcalá-Reygosa, J., Andrés, N., Oliva, M., Tanarro, L.M., Salvador-Franch, F., Schimmelpfennig, I., Fernández-Fernández, J.M., Léanni, L., 2019. The challenging application of cosmogenic dating methods in residual glacial landforms: The case of Sierra Nevada (Spain). Geomorphology 325, 103 118. doi:10.1016/j.geomorph.2018.10.006 doi:10.1016/j.cageo.2016.06.008 Figure captions.

Table captions Table 1 .

 captions1 Glacial Equilibrium-Line Altitudes (ELAs) calculated over Tungnahryggsjökull glaciers through the application of the AAR and AABR methods over the 3D glacier reconstructions.

	Table 2. Surface ages estimated from Kugelmann s (1991) 0.44 mm yr -1 growth rate for different colonization lags. The ages obtained from Rhizocarpon geographicum lichens discussed throughout the text are those derived from a 20-yr colonization lag. The figures in italics correspond to ages tentatively inferred from the largest Porpidia soredizodes lichen, assuming a 0.737 mm yr -1 growth rate and a 15-year colonization lag (see section 5.2.1). The Tröllaskagi Peninsula in northern Iceland hosts more than a hundred small glaciers that have left a rich terrestrial record of Holocene climatic fluctuations in their forelands. Traditionally, it has been assumed that most of the Tröllaskagi glaciers reached their Late Holocene maximum extent during the Little Ice Age (LIA). However, there is evidence of slightly more advanced pre-LIA positions. LIA moraines from Iceland have been primary dated mostly through lichenometric dating, but the limitations Table 3. Abstract of this technique do not allow dating of glacial advances prior to the 18 th or 19 th

36

Cl CRE ages converted to CE/BCE dates according to the different 36 Cl production rates from Ca spallation. Uncertainties include the analytical and production rate error. centuries. The application of 36 Cl Cosmic-Ray Exposure (CRE) dating to Tungnahryggsjökull moraine sequences in Vesturdalur and Austurdalur (central Tröllaskagi) has revealed a number of pre-LIA glacial advances at ~400 and ~700 CE, and a number of LIA advances in the 15 th and 17 th centuries, the earliest LIA advances dated so far in Tröllaskagi. This technique hence shows that the LIA chronology in Tröllaskagi agrees with that of other European areas such as the Alps or the Mediterranean mountains. The combined use of lichenometric dating, aerial

  ; LeRoy et al., 2017; Young et al., 2015; Jomelli et al., 2016; Li et al., 2016; Dong et al., 2017; Palacios et al., 2018). The cosmogenic nuclides 36 Cl and 3 He have been applied previously in

northern Iceland to date the Pleistocene deglaciation.

Principato et al. (2006)

studied the deglaciation of Vestfirðir combining 36 Cl CRE dating of moraine boulders and bedrock surfaces with marine records and tephra marker beds.

Andrés et al. (2018)

reconstructed the deglaciation at the Late Pleistocene to Holocene transition at Skagafjörður through 36

  Table 3 includes the 36 Cl CRE ages converted to CE dates format presented throughout the text. The dates presented below are based on the Licciardi et al. (2008) Ca spallation production rate.Aiming to obtain a maximum (oldest) age for the onset of the deglaciation in the valleys studied, two samples (ELLID-1 and ELLID-2) were extracted from the western sector of Elliði, a 660-m-high glacially polished crest separating Viðinesdalur and

	Kolbeinsdalur valleys (Suppl. figure SF5), and located at 11 km downstream from the
	confluence of Vesturdalur and Austurdalur valleys. Both samples yielded dates of
	14300±1700 BCE and 14200±1700 BCE.

  suggested a high climate sensitivit of the glacier in Vesturdalur due to its steeper all floor and thinness , which could explain a different behaviour of the glacier compared to the eastern glacier.Cl CRE dating results from glacially polished surfaces on the Elliði crest show an age of 14250±1700 yr (mean) for the Kolbeinsdalur deglaciation (Suppl. figureSF5).

	intra-morainic peat bogs in other valleys in Tröllaskagi and southern Iceland, e.g. the
	Barkárdalur II stage (ca. 460 CE) in Subatlantic times
	However, this should be considered as a minimum age since this probably indicates
	when the retreating and thinning glacier uncovered the ridge, and thus the start of the
	final deglaciation of the main valley. From this point to the outmost frontal moraines
	surveyed in this paper, no glacially polished outcrops or erratic boulders suitable for
	36 Cl sampling were found, impeding us to provide further chronological constraints for
	the deglaciation pattern of these valleys.
	Our 36 Cl CRE dating results suggest late Holocene glacial advances prior to the LIA, at
	around ~400 and ~700 CE, in Vesturdalur and Austurdalur, respectively, coinciding
	with the Dark Ages Cold Period (DACP) (between 400 and 765 CE) in central Europe,
	according to Helama et al. (2017). In fact, recent synthesis about Icelandic lake records
	indicate a strong decline in temperature at 500 CE (Geirsdóttir et al., 2018).
	The presence of Late Holocene moraines outside the outermost LIA moraines in other
	valleys of Tröllaskagi has been suggested through radiocarbon dating and
	tephrochronology in the Vatnsdalur (first, between 4880±325 cal. BCE (tephra Hekla 5)
	and 3430±510 cal. BCE, and another after 1850±425 cal. BCE; Stötter, 1991),
	Lambárdalur (before 3915±135 cal. BCE; Wastl and Stötter, 2005), Þverárdalur (before
	3500±130 cal. BCE; Wastl and Stötter, 2005), Kóngsstaðadalur (after 1945±170 cal.
	BCE; Wastl and Stötter, 2005), Barkárdalur (between 375±375 cal. BCE and 190±340
	cal. CE and before 460±200 cal. CE; Häberle, 1991) and Baegisárdalur (2280±205 cal.
	BCE and 1050±160 cal. CE; Häberle, 1991) valleys. Specifically, our oldest 36 Cl dates
	(~400 and ~700 CE) coincide with glacial advances that are radiocarbon dated from

  The remaining36 Cl ages obtained from Vesturdalur and Austurdalur are within the 1450-1640 CE range (Suppl. table ST8; Table3) and so correspond to different glacial advances or standstills during the second third of the LIA during the 15 th , 16 th and 17 th centuries. According to our results, one of the largest glacier extents of the LIA culminated in both valleys at the latest around the mid-15 th century (samples: TUW-12: 1450±100 CE / stage 6; TUE-10: 1460±100 CE / stage 4). This is a very early date compared to the LIA advances previously dated in Tröllaskagi. Earlier lichenometric research carried out in nearby valleys report more recent dates for the LIA maximum:

	pointed out that
	only four surges from three glaciers (Teigarjökull, Búrfellsjökull, Baegisárjökull) have
	been reported in the Tröllaskagi peninsula, where over 160 cirque glaciers exist.
	5.1.2. LIA glacial advances (15 th -17 th centuries)

  Rhizocarpon geographicum and Porpidia cf. soredizodes thalli at the same stations showed a proportionality between the largest thalli of both species: thalli of Porpidia cf.soredizodes species grow faster than those of Rhizocarpon geographicum. The sizes of the largest Rhizocarpon geographicum thalli were plotted against the sizes of the largest Rhizocarpon geographicum lichens (Fig.5). The slope of the best-fit linear curve obtained was around 1.675 (r 2 =0.82) that suggests that Porpidia cf. soredizodes lichens grow 1.675 times faster than those of Rhizocarpon geographicum. So if we assume 0.44 mm yr -1 growth rate for Rhizocarpon geographicum lichens, a tentative growh rate of Porpidia cf. soredizodes would be 0.737 mm yr -1 . However, this approach should be taken with caution due to the limited number of lichens (n=7) used of each species.Despite the low number of lichenometry stations surveyed and the limitations of this dating approach discussed in the previous sections, our results are in accordance with the geomorphological logic and with the chronological frame obtained from historical aerial photos. The ages derived from Rhizocarpon geographicum thalli measurements at lichenometry stations pre-dating 1946 suggest that the western and eastern Tungnahryggsjökull culminated successive advances/standstills around the 1830s, 1840s, 1860s and 1890s CE (Figs.2 and 3, Table 2). Ages tentatively estimated from Porpidia cf. soredizodes thalli considering its apparently higher growth rate suggest glacial advances/standstills around the 1800s (Figs.2 and 3, Table2). No inconsistence (age inversions) is detected in the lichenometry-dated moraine sequence, but we recognise that some age underestimation may occur since: (i) we assume linear growth when applying a growth rate; and (ii) our 19 th dates were derived from >40-45 mmdiameter lichens (Table2and Suppl. table

	Assuming colonization lags of 20 and 15 years for Rhizocarpon geographicum and
	Porpidia cf. soredizodes lichens, respectively, and the above-mentioned growth rates,
	several glacial advances or standstills are tentatively placed in the 19 th and 20 th
	centuries, in the context of a general retreat from the most advanced LIA positions, as
	discussed in the next section.
	5.2.2. LIA glacial advances/standstills: 19 th century

Aiming to obtain a tentative date (Table

2

), this growth rate was applied to the largest Porpidia cf. soredizodes lichens found in those stations where no Rhizocarpon geographicum lichens could be measured (TUW-1, TUW-8, TUE-1 and TUE-8).

  -LIA glacial advances/standstills. Lichen-derived ages from Rhizocarpon geographicum thalli suggest the ocurrence of glacial advances or standstills at the first half of the 20 th century, culminating in 1910s, 1930s, 1940s and 1950s CE, although the 1930s CE date (TUE-3; stage 12) disagrees with the date inferred from the aerial photos, at some point between 1946 and 1985 CE (Suppl. figure SF2; Table2). However, the 1910s CE date in both valleys is in good agreement with the moraine abandonment during the first two decades of the 20 th

  . Two moraines have been dated after the 1950s CE. The date obtained in station TUE-1 (1970s CE; stage 14) agrees with the date deduced from the 1946 and 1985 aerial photographs (Suppl. figureSF2). However, the

	surging glaciers after 2000
	The aerial photographs from 1994 (stage 15 western Tungnahryggsjökull) and 2000
	(stage 16) show a reversal in the trend of both Tungnahryggsjökull glaciers (Suppl.
	figure SF2), as the positions of their termini are more advanced than in 1985 (stages 14
	and 15; see Fernández-Fernández et al., 2017). These advances in Vesturdalur and
	Austurdalur, culminating after 1985 in a period non-conducive to glacier expansion,
	may have been linked to above average precipitation for 1988-1995, which prevented a
	negative mass balance of the glaciers (Sigurðsson, 2005). The 2000 aerial photo (stage
	16) and 2005 SPOT satellite image (stage 17) display the retreat of both glaciers. This
	trend was reinforced by the sudden warming initiated in 1995, which triggered
	decreased snowfall, negative mass balances for 1996-2000, and retreat of the non-

date estimated in station

TUW-1 (1970s CE; between stages 15 and 16

) is prior to that obtained from the 1994 and 2000 aerial photographs. The reason for this mismatch may be a non-linear growth phase of the Porpidia cf. soredizodes thalli measured (i.e. its real growth rate may have been lower than the estimated). Nevertheless, more research on this species is required to use it successfully in lichenometric dating.

Table captions Table 1 .

 captions1 Glacial Equilibrium-Line Altitudes (ELAs) calculated over Tungnahryggsjökull glaciers through the application of the AAR and AABR methods over the 3D glacier reconstructions.

Table 2 .

 2 Surface ages estimated from Kugelmann s (1991) 0.44 mm yr -1 growth rate for different colonization lags. The ages obtained from Rhizocarpon geographicum lichens discussed throughout the text are those derived from a 20-yr colonization lag. The figures in italics correspond to ages tentatively inferred from the largest Porpidia soredizodes lichen, assuming a 0.737 mm yr -1 growth rate and a 15-year colonization lag (see section 5.2.1).Table 3. 36 Cl CRE ages converted to CE/BCE dates according to the different 36 Cl production rates from Ca spallation. Uncertainties include the analytical and production rate error.

	Stage	W Tungnahryggsjökull			E Tungnahryggsjökull
		AAR (0.67)	Δ	AABR (1.5±0.4)	Δ	AAR (0.67)	Δ	AABR (1.5±0.4)	Δ
	1	1021	-	1006 +25/-20	-	1032	-	±20	-
	2	1047	+26	1032 ±20	+26	1032	0	±15	+5
	3	1052	+5	1037 +20/-15	+5	1034	+2	±15	+2
	4	1054	+2	1049 +20/-15	+12	1037	+3	±15	+3
	5	1059	+5	1059 ±15	+10	1041	+4	±15	+4
	6	1067	+8	1062 +20/-10	+3	1042	+1	±15	+1
	7	1072	+5	1072 +15/-10	+10	1046	+5	±15	+5
	8	1076	+4	1081 ±15	+9	1047	+1	±15	+6
	9	1082	+6	1087 +15/-10	+6	1054	+7	+15/-10	+2
	10	1086	+4	1091 +15/-10	+4	1055	+1	+15/-10	+6
	11	1094	+8	1099 +15/-10	+8	1061	+6	±10	+11
	12	1094	0	1099 +15/-5	0	1060	-1	±10	-1
	13	1094	0	1099 +15/-5	0	1061	+1	+15/-10	+1
	14	1100	+6	1110 ±10	+11	1060	-1	±10	+4
	15	1102	+2	1107 +15/-5	-3	1061	+1	+15/-10	+1
	16	1098	-4	1108 +10/-5	+1	1061	0	±10	0
	17	1099	+1	1109 +15/-5	+1	1065	+4	±10	+4

Table 1 . Glacial Equilibrium-Line Altitudes (ELAs) calculated over Tungnahryggsjökull glaciers through the application of the AAR and AABR methods over the 3D glacier reconstructions. Delta (Δ) is referred to the change with respect to the previous stage.

 1

Table 1 Click here to download Table: Table_1.docxTable 2 . Surface exposure ages estimated from Kugelmann's (1991) 0.44 mm yr -1 growth rate for different colonization lags. The stars indicate that either the date does not agree with the date deduced from aerial photos (*) or the date is incoherent with the moraine chronostratigraphy (**). The figures in italics correspond to dates tentatively inferred from the largest Porpidia soredizodes lichen, assuming a 0.737 mm yr -1 growth rate and a 10-year colonization lag.

 12

	Comment [JM1]: Asumiendo que el
	sector del frente en el que se
	encuentra el bloque, ha permanecido
	estático, estable desde 1946

Table 2 Click here to download Table: Table_2.docx

 2

Table 3 . 36 Cl CRE ages converted to CE/BCE dates according to the different 36 Cl production rates from Ca spallation. Uncertainties include the analytical and production rate error.

 3

	Sample name	Dates (CE/BCE)
		Licciardi et al. (2008)	Stone et al. (1996) Ca	Schimmelpfennig et
		Ca spallation prod. rate	spallation prod. rate	al. (2011) Ca
				spallation prod. rate
	Moraine boulders at Vesturdalur (W Tungnahryggsjökull foreland)
	TUW-9	1590 ± 100	1570±100	1520±120
	TUW-10	1640±90	1620±90	1580±110
	TUW-11	1480±120	1470±120	1420±140
	TUW-12	1450±100	1430±110	1370±120
	TUW-13	1470±130	1450±130	1400±150
	TUW-14	670±210	620±210	500±250
	TUW-15	1460±110	1430±110	1370±120
	TUW-16	1220±190	1200±190	1130±210
	Moraine boulders at Austurdalur (E Tungnahryggsjökull foreland)
	TUE-9	740±170	660±170	510±210
	TUE-10	1460±100	1430±100	1360±120
	TUE-11	380±200	290±200	110±250
	TUE-12	400±200	320±190	150±240
	Glacially polished ridge Elliði
	ELLID-1	14300±1700	14900±1600	16600±2100
	ELLID-2	14200±1700	14800±1700	16500±2100

Table 3 Click here to download Table: Table_3.docx

 3

Acknowledgements

This paper was supported by the project CGL2015-65813-R (Spanish Ministry of Economy and Competitiveness) and Nils Mobility Program (EEA GRANTS), and with the help of the High Mountain Physical Geography Research Group (Complutense University Madrid). We thank the Icelandic Association for Search and Rescue, the Icelandic Institute of Natural History, the Hólar University College, and David Palacios Jr. and María Palacios for their support in the field. José M. Fernández-Fernández received a PhD fellowship from the FPU programme (Spanish Ministry of Education, Culture and Sport; reference FPU14/06150). The 36 Cl measurements were performed at the ASTER AMS national facility (CEREGE, Aix en Provence), which is supported by the INSU/CNRS and the ANR through the "Projets th matiques d e cellence" program for the "Equipements d e cellence" ASTER-CEREGE action and IRD. Acknowledgements This paper was supported by the project CGL2015-65813-R (Spanish Ministry of Economy and Competitiveness) and Nils Mobility Program (EEA GRANTS), and with the help of the High Mountain Physical Geography Research Group (Complutense University Madrid). We thank the Icelandic Association for Search and Rescue, the Icelandic Institute of Natural History, the Hólar University College, and David Palacios Jr. and María Palacios for their support in the field. José M. Fernández-Fernández received a PhD fellowship from the FPU programme (Spanish Ministry of Education, Culture and Sport; reference FPU14/06150). The 36 Cl measurements were performed at the ASTER AMS national facility (CEREGE, Aix en Provence), which is supported by the INSU/CNRS and the ANR through the "Projets th matiques d e cellence" program for the "Equipements d e cellence" ASTER-CEREGE action and IRD.

Supplementary figures captions

SF1. Examples of Rhizocarpon geographicum group and Porpidia soredizodes thalli measured over scaled field photos from the lichenometric station TUW-3. The lines refer to the minimum circle (white) bounding the thalli outlines (yellow) and the diameter of the circle (black). Note the contrasted size of the largest thalli in the different species. ST7. Concentrations of the 36 Cl target elements Ca, K, Ti and Fe, determined in splits taken after the chemical pre-treatment (acid etching).

ST8. 36 Cl analytical data and CRE dating results according to different 36 Cl production rates from Ca spallation. 36 Cl/ 35 Cl and 35 Cl/ 37 Cl ratios were inferred from measurements at the ASTER AMS facility. The numbers in italic correspond to the internal (anal tical) uncertaint at 1 le el.

Graphical Abstract

Highlights

A multi-disciplinary approach reconstructs Late Holocene glacial evolution.

High-detail moraine mapping was done for two glacier forelands.

Late Holocene glacial maximum occurred prior to the Little Ice Age.

Maximum Little Ice Age glacial culminations were prior to the 19 th century.

Porpidia soredizodes species is tested for lichenometric dating.

Highlights

inhouse standard SM-CL-12 with an assigned value of 1.428 (±0.021) x 10 -12 for the 36 Cl/ 35 Cl ratio (Merchel et al., 2011) and assuming a natural ratio of 3.127 for the stable ratio 35 Cl/ 37 Cl.

When calculating exposure ages, the Excel TM spreadsheet for in situ 36 Cl exposure age calculations proposed by Schimmelpfennig et al. (2009) was preferred to other online calculators (e.g. CRONUS Earth; Marrero et al., 2016) as it allows input of different 36 Cl production rates from spallation, referenced to sea level and high latitude (SLHL).

Thus, three SLHL 36 Cl production rates from Ca spallation, i.e. the most dominant 36 Cl production reaction in our samples, were applied to allow comparisons both with other Icelandic areas (57.3±5.2 atoms 36 Cl (g Ca) -1 yr -1 ; Licciardi et al., 2008) and other areas of the world (48.8±3.4 atoms 36 Cl (g Ca) -1 yr -1 , Stone et al., 1996; 42.2±4.8 atoms 36 Cl (g Ca) -1 yr -1 , Schimmelpfennig et al., 2011). For 36 Cl production reactions other than Ca spallation, the following SLHL 36 Cl production parameters were applied: 148.1±7.8 atoms 36 Cl (g K) -1 yr -1 for K spallation (Schimmelpfennig et al., 2014b), 13±3 atoms 36 Cl (g Ti) -1 yr -1 for Ti spallation (Fink et al., 2000), 1.9±0.2 atoms 36 Cl (g Fe) -1 yr -1 for Fe spallation (Stone et al., 2005) and 696±185 neutrons (g air) -1 yr -1 for the production rate of epithermal neutrons for fast neutrons in the atmosphere at the land/atmosphere interface (Marrero et al., 2016). Elevation-latitude scaling factors were based on the time invariant St scheme (Stone et al., 2000). The high-energy neutron attenuation length value applied was 160 g cm -2 .

All production rates from spallation of Ca mentioned above are based on calibration samples with a predominant Ca composition. Iceland is permanently affected by a lowpressure cell, the Icelandic Low (Einarsson, 1984). As the atmospheric pressure modifies the cosmic-ray particle flux, and thus has an impact on the local cosmogenic nuclide production rate, the atmospheric pressure anomaly has to be taken into account (Suppl. table ST4). Only one size inversion (decreasing size with increasing distance to the current terminus) was detected in Austurdalur in the station TUE-6 (Fig. 3).

Rhizocarpon geographicum thalli were absent in the nearest stations (TUW-1 and TUE-1) and were coalescent in the most distant stations (TUW-8 and TUE-8) in both glacier forelands. On the other hand, Porpidia cf. soredizodes thalli measurements ranged from 18.3 to 148.4 mm in Vesturdalur, and from 16.8 to 141.8 mm in Austurdalur (Suppl.

table ST4

). A size inversion of Porpidia cf. soredizodes thalli is also observed in TUE-6 and in TUE-7.

When the ages of Rhizocarpon geographicum lichens are calculated applying a 0.44 mm yr -1 growth rate and a 10-year colonization lag following Kugelmann (1991) 2). In general, the further away the lichenometry stations are, the older are the ages (Figs. 2 and3), with the inversions mentioned above. Apparently the lichenometrydated moraines are younger than the CRE-dated distal moraines.

The absence of Rhizocarpon geographicum lichens in 2015 at lichenometry station TUW-1 (uncovered by the glacier at some time between 1994 and 2000; Suppl. figure SF2) suggests a colonization lag of at least 15-21 years. In addition, it is only when the colonization lag is assumed to be longer than 10 years and shorter than 30 years that the ages obtained at stations TUW-3 and TUE-2 are in good agreement with the ages deduced from the aerial photos (Table 2).

During the 2015 field campaign, the species Porpidia cf. soredizodes was absent in station TUE-0, located on a glacially polished threshold uncovered by the glacier after 2005 (post-stage 17). However, it was found in stations TUW-1 and TUE-1, dated to

Supplementary table ST1

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Supplementary table ST2

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Supplementary table ST3

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Supplementary table ST4

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Supplementary table ST5

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Supplementary table ST6

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Supplementary table ST7

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Supplementary table ST8

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