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An ExcelTM spreadsheet program for reconstructing the surface profile of former mountain glaciers and ice caps

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Abstract

A new Excel™ spreadsheet program is introduced, which calculates the surface profiles of former glaciers using an exact solution of a ‘perfectly plastic’ glacier model. Two versions of the model are presented. The basic model requires only bed topography along a flowline and a yield stress for ice as inputs. The latter can be tuned using ‘target ice elevations’ derived from geomorphological mapping. A more sophisticated form of the model allows the yield stress to vary along the flowline, and incorporates the effect of valley-side drag on the glacier profile.

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... In this study we used a method developed by Schilling and Hollin (1981) that adapts Nye's (1952) equation of mechanical equilibrium to valley glaciers, introducing a shape factor that represents the proportion of the driving stress induced on the bed surface. This method, described in detail and automatized by Benn and Hulton (2010), calculates the surface profiles of former glaciers using an exact solution of a "perfectly plastic" glacier model. With these ice surface profiles, a DEM is created in order to obtain the ice thickness of the glacier. ...
... Where h is the ice surface elevation, H the glacier thickness (H = h-B), where B is the bed elevation, τY is the yield stress, Δx is a specified distance interval along the x-axis, ρ is the glacier ice density (~900 kg m −3 ) and g is the gravitational acceleration (9.81 m s −2 ). To find the surface profile for an irregular bed, is necessary to calculate it in a succession of discrete steps (i, i + 1, i + 2, etc) (Benn and Hulton, 2010). ...
... In the equation (1), τY and H are those at step i, and unrepresentative of the interval between step i and i + 1. According to Benn and Hulton (2010), because the values τY and H in equation (1) are those at step i, and may be unrepresentative of the interval between step i and i + 1, there may be a tendency for the calculated points to either overshoot or undershoot the desired value. This problem was solved by Van der Veen (1999) in equation (2), calculating the basal shear stress and ice thickness for the midpoint of the interval i to i + 1 and extracting h + 1, using a quadratic equation solved by factoring, setting the equation equal to zero and factor. ...
Article
The Aneto, located on the Maladeta Massif (Central Pyrenees), is the largest glacier of the Pyrenees. The glacier is 675 m long, occupies an area of 48.64 ha and has a maximum altitude of 3269 m. In this study, we present a detailed area, volume, ice thickness, and Equilibrium Line Altitude reconstruction of the glacier for different periods (LIA, 1957, 1983, 2000, 2006, 2015, and 2017) and analyze its retreat. To estimate the glacier extent during the LIA, the moraines were mapped by using photo interpretation techniques whereas for the recent stages digital satellite images and aerial photographs were used. Moreover, we estimated the topography of the glacier using a simple steady-state model that assumes a perfectly plastic ice rheology, which allowed reconstructing the theoretical ice profiles of the glacier. To reconstruct the ice surface, a digital elevation model was created and combined with the bedrock topography in order to obtain the ice thickness of each stage. The results of the study reveal a considerable retreat of the Aneto Glacier since the LIA. The length of the glacier has reduced from 1970 to 675 m from LIA to2017, and its tongue has retreated from 2385 to 3029 m a.s.l. Furthermore, the glaciated area has been reduced from 245 to 48.64 ha from LIA to 2017 and the ELA has risen from 2919 to 3139 m a.s.l. The data obtained indicates that in the LIA–2017 period the glacier volume has been reduced from 82.57 m × 106 m3 to 3.48 m × 106 m3 and the maximum ice thickness from 95 to 27m. We also reconstructed the climatic conditions, showing an increase in temperature of ~1.14°C from LIA to 2017. These data reveal a vast retreat of the glacier since the LIA, which has accelerated since the 1980’s and even more since the year 2000.
... After that, we carried out the glacier reconstruction by using the ArcGIS toolbox 'GlaRe' (Pellitero et al., 2015(Pellitero et al., , 2016 in the same work environment. This is a semi-automatic tool that implements the procedures proposed by Benn and Hulton (2010), relying on the Van der Veen (1999) equation for modeling the past ice thickness along a flowline. First, we digitized the main and tributary flowlines by hand from terminus to the headwall. ...
... To simplify the glacier reconstruction, we assumed that shear-stress remained constant along the flowline and throughout time. To achieve a realistic value, we modelled shear stress along the flowline by using the Profiler v2 Excel™ spreadsheet of Benn and Hulton (2010) so that the modelled ice thickness matches the current glacier topography. We obtained an average value of 95 kPa, within the normal shear-stress range (50-150 kPa) and very close to the average typical 100 kPa value observed in current glaciers (Benn and Hulton, 2010). ...
... To achieve a realistic value, we modelled shear stress along the flowline by using the Profiler v2 Excel™ spreadsheet of Benn and Hulton (2010) so that the modelled ice thickness matches the current glacier topography. We obtained an average value of 95 kPa, within the normal shear-stress range (50-150 kPa) and very close to the average typical 100 kPa value observed in current glaciers (Benn and Hulton, 2010). Thus, we used this value in the toolboxes contained in 'GlaRe' to reconstruct the past ice thicknesses along the flowlines. ...
Article
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The objective of this work is to chronologically establish the origin of the different glacial and rock glacier complex landforms deposited by Héðinsdalsjökull glacier (65°39′ N, 18°55′ W), in the Héðinsdalur valley (Skagafjörður fjord, Tröllaskagi peninsula, central northern Iceland). Multiple methods were applied: geomorphological analysis and mapping, glacier reconstruction and equilibrium-line altitude calculation, Cosmic-Ray Exposure dating (in situ cosmogenic ³⁶Cl), and lichenometric dating. The results reveal that a debris-free glacier receded around 6.6 ± 0.6 ka, during the Holocene Thermal Maximum. The retreat of the glacier exposed its headwall and accelerated paraglacial dynamics. As a result, the glacier terminus evolved into a debris-covered glacier and a rock glacier at a slightly higher elevation. The front of this rock glacier stabilized shortly after it formed, although nuclide inheritance is possible, but its sector close the valley head stabilized between 1.5 and 0.6 ka. The lowest part of the debris-covered glacier (between 600 and 820 m altitude) collapsed at ca. 2.4 ka. Since then, periods of glacial advance and retreat have alternated, particularly during the Little Ice Age. The maximum advance during this phase occurred in the 15th to 17th centuries with subsequent re-advances, namely at the beginning of the 19th and 20th centuries. After a significant retreat during the first decades of the 20th century, the glacier advanced in the 1960s to 1990s, and then retreated again, in accordance with the local climatic evolution. The internal ice of both the debris-covered and the rock glacier have survived until the present day, although enhanced subsidence provides evidence of their gradual degradation. A new rock glacier developed from an ice-cored moraine from around 1940–1950 CE. Thus, the Holocene coupling between paraglacial and climatic shifts has resulted in a complex evolution of Héðinsdalsjökull, which is conflicting with previously proposed models: a glacier, which had first evolved into a debris-covered and rock glacier, could later be transformed into a debris-free glacier, with a higher sensitivity to climatic variability.
... First, key landforms and deposits within the DB catchment ( Fig. 1 and Table S1) were grouped to define distinct stages of ice retreat or stillstand/re-advance, based on their radiometric age ( 10 Be surface-exposure and luminescence burial dating), spatial distribution and geomorphological significance. Second, for each defined ice-front position, 2D ice-surface profiles were generated using the Excel™ spreadsheet program Profiler v.2 (Benn and Hulton, 2010), which is based on a steady-state solution of a 'perfectly plastic' ice model. We propagated the 2D ice profiles into the DB valley and its major tributaries, using as ice-front and icesurface constraints the identified landforms/deposits grouped into the same paleoglacial stage (Fig. 6, Table S1). ...
... Present-day topography along the main hydrographic channels was used as input for glacier bed topography (Fig. 6A). Shape-factor (f) values were calculated along the DB valley and its tributaries as input in the Profiler v.2 model, in order to include the valley side-drag effects on ice thickness (Benn and Hulton, 2010). We calculated f according to Eq. (12) from Benn and Hulton (2010) for a total of 62 crosssections (13 in DB valley and 49 in tributaries; Fig. 6A). ...
... Inputs and fitting of Profiler v.2(Benn and Hulton, 2010) for paleoglacial reconstructions. A) Location of modern hydrographic channels (black lines) used as glacier bed input, and of the cross sections in the DB valley (blue segments) and tributaries (red segments) for which shape factors (f) were calculated. ...
Article
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Paleoglacial reconstructions in the European Alps have mainly focused on specific climatic periods such as the Last Glacial Maximum (LGM) or the Younger Dryas, with few studies investigating post-LGM Alpine glacier fluctuations encompassing broader temporal periods. In this study, we present a detailed reconstruction of the post-LGM glacial history of the Dora Baltea catchment, which hosted one of the main Quaternary glacial systems of the western European Alps. By combining existing and new chronological constraints from glacial and postglacial landforms/deposits into 2D and 3D ice surface reconstructions, we quantitatively reproduce the timing and ice-configuration of six LGM to early Holocene paleoglacial stages. Our deglaciation sequence along the Dora Baltea valley can be correlated with specific Lateglacial to Holocene paleoclimatic periods, in line with post-LGM glacier reconstructions from other Alpine areas. We estimated paleo equilibrium-line altitudes (ELAs) for each ice stage, using empirical ice-geometric methods. Our results indicate a low ELA sensitivity to ice decay during the early stages of deglaciation, despite significant glacier retreat from the piedmont into the massifs, suggesting a major role of catchment topography in controlling ELA estimates of large glacial systems. Finally, we provide chronological constraints for two major valley-slope collapse events, both postdating the Dora Baltea glacier withdrawal but implying different landscape response time to deglaciation as well as different triggering factors.
... Other computational methods exist to estimate the ELA of paleoglaciers. [6] presents an Excel TM spreadsheet to calculate the ice surface profiles of a former mountain glacier or ice cap, given bed topography and a yield stress. [7] provides a Python-based ArcGIS toolbox to automatically calculate glacier ELAs with a choice of methods (Accumulation-Area Ratio, Area-Altitude-Balance Ratio, Area-Altitude, or median elevation). ...
... Similar to [6,8], the presented ELA model also estimates the glacier surface based on centerline ice flow, given bed topography. It also aims to automate many of the steps in calculating an ELA to provide an easy-to-use and widely applicable method of ELA estimation. ...
... Each model run consists of 1,000 simulations in order to approximate a continuous distribution in plausible ELA values. The Monte Carlo simulations do 150 increase the computational load, especially compared to the automated methods of [6,7], taking ∼1 minute to process one glacier on a single core. The model code, however, utilizes parallel processing, enabling much greater scalability to larger data sets with the proper hardware. ...
Article
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Alpine glaciers, with their valuable combination of highly sensitive response to climate and near-global extent, are powerful tools for investigating previous and present climate changes. They also represent critical water resources for areas around the globe, with the potential for far-reaching effects in a warming world. Advancements to understand and model glacial changes and the variables influencing them are therefore paramount. Many glacier models fall into one of two endmembers: either highly complex transient models requiring careful tuning of multiple parameters to individual glaciers, or basic empirical correlations of glacier area and length with few considerations for local and regional variations in characteristics. Here we detail a physical steady-state model for alpine glaciers relating directly to glacier mass balance (via the equilibrium line altitude) while retaining the simplicity of other morphology methods, and simultaneously including error estimates. We provide custom MATLAB functions as a user-friendly and generally-applicable method to estimate glacier equilibrium line altitudes from only a limited number of glacier bed topography and glacier width measurements. As a test of the model’s efficacy, we compare the model results for present-day glaciers in the Swiss Alps with previously published estimates of equilibrium line altitudes and intermediate model outputs. •The method estimates glacier equilibrium line altitudes from a limited set of bed topography measurements and constraints on glacier width •The method is based on continuity equations, reducing the need for empirical coefficients tuned with measured data •The method uses Monte Carlo sampling and bootstrapping to generate uncertainty bounds on the equilibrium line altitude estimates
... This approach relies heavily on geomorphologic evidences and not explicitly on glacier physics, and the results depend on the practitioner's experience about glaciers. Numerical models formulated from physics are routinely used to reconstruct palaeoglacier [18][19][20][21][22], and respect geomorphologic evidences and glacier mechanism. But some models are more complex in theory and mechanism, and need input many parameters, which leads to the application of numerical models not widely. ...
... This model is called 'perfect plasticity' model, which have been available for several study [19,23]. Benn and Hulton (2010) developed a user-friendly excel spreadsheet program to calculate the surface profiles of former glaciers basing on the 'perfectly plastic' glacier model [21], which facilitate the reconstruction of palaeoglaciers. In this study, the palaeoglacier profiles were calculated by this spreadsheet developed by Benn and Hulton. ...
Article
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Reconstruction of palaeoglacier is important for understanding the mechanism of palaeo-climatic change and predicting water resource in Tibet. The climate and water resource are sensitive to global change in western Nyainqêntanglha Range. However, the data of how glacier changed in its area and equilibrium line, particularly its volume are still in paucity. In this study, we generated the palaeoglacier landform map by field investigation and 3S (RS, GPS and GIS) technology, reconstructed the palaeoglaciers surface by glacial landforms and glacier model, accordingly estimated the ice volume and equilibrium line altitude (ELA), and then discussed the palaeo-climate during the last glacial maximum (LGM) in the Qugaqie valley. During the LGM, the Qugaqie glacier was about 18.5 km long and 102.1 m thick in average. It covered an area of 59.1 km ² and had a volume of 6.05 km ³ , which were 8.34 times of the area and 18.33 times of the ice volume of the modern glacier. The 75.3% of Qugaqie valley was covered by glacier. The palaeo-ELA was 5405∼5496 m with a depression of 400 to 300 m, which confirms Shi Yafeng’s point that an even global ELA lowering value of about 1000 m didn’t virtually exist.
... Similar models based on the assumption that ice deforms plastically have been extensively used on Earth to reconstruct paleo ice volumes (Ng et al., 2010) and more recently have applied to contemporary LDA deposits on Mars (Fastook et al., 2014;Karlsson et al., 2015;Parsons et al., 2011;Schmidt et al., 2019;Weitz et al., 2018). We adapt the numerical method described by Benn and Hulton (2010), driven by parameters from Karlsson et al. (2015). Perfect-plasticity models assume that ice deforms in response to glaciological driving stress (τ D , determined by gravity, ice thickness, and surface slope) when a threshold yield stress τ y is surpassed. ...
... Here, the three choices of taking H * to be H i , (H i + H i+1 )/2 and H i+1 amount to forward, central, and backward difference approximations, respectively. As discussed by Benn and Hulton (2010), the forward scheme breaks down at the start of the integration because H = 0 at the ice margin (i = 1); only the central and backward schemes are appropriate there. We adopt the backward approximation, that is, H * = h i+1 −B i+1 , so that substituting this into Equation 2, rearranging, leads to the quadratic equation ...
Article
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High obliquity excursions on Mars are hypothesised to have redistributed water from the poles to nourish mid-latitude glaciers. Evidence of this process is provided by different types of viscous flow features (ice-rich deposits buried beneath sediment mantle) located there today, including lobate debris aprons (LDAs). During high obliquity extremes, ice may have persisted even nearer the equator, as indicated by numerous enigmatic depressions bounded on one side by either isolated mesas or scarps, and on the other by a lava unit. These depressions demarcate the past interaction between flowing lava and ghost LDAs (GLDAs), which have long since disappeared. We term these features GLDA depressions, about which little is known besides their spatial extent. This collection of depressions implies tropical ice loss over an area ∼100,000 km2. To constrain their history in Kasei Valles we derive model ages for GLDA depressions, mesas and the lava flow from crater counts. We use a 2D model of glacial ice constrained by the topography of GLDA depressions to approximate the surface and volume of former glacial ice deposits. The model reconstructs former ice surfaces along multiple flowlines orientated normal to GLDA depression boundaries. This reconstruction indicates that 1,400–3,500 km3 of ice—similar to that present in Iceland on Earth—existed at ∼1.3 Ga when the lava was emplaced. Dating shows that GLDAs survived for up to ∼1 billion years following lava emplacement, before their final demise.
... We model a two-dimensional ice surface along a transect from the interpreted ice margin and 80 km up ice ( Figure 15). This steady-state modeling was done using the simplified assumption that the ice-sheet is perfectly plastic (Benn and Hulton, 2010). A topographic profile was used as an input together with shear stress values, based on estimation of inferred values from the land-terminating part of West ...
... Figure 15: The proposed environment of formation. Calculated ice surface using the method proposed by Benn and Hulton (2010) and hydropotential (Shreve, 1972). Geomorphology and from the national elevation model (Lantmäteriet, 2020). ...
Article
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Knowledge about processes beneath ice sheets, and in particular the processes connected to subglacial hydrology, is crucial for an understanding of ice sheets and how they react in a warming climate. Recently, v-shaped subglacial landforms (murtoos) have been found in those parts of the former Fennoscandian Ice Sheet where rapid ice-margin retreat occurred. Based on their geomorphology and distribution, murtoos have been suggested to form where the bed experienced high influxes of meltwater. Here, we investigate the sedimentology and internal structure of murtoos at four localities in southern Sweden to better understand murtoo genesis. The excavated murtoos consist of heterogenous diamict showing reasonably strong fabrics interbedded with sorted sediments. Sediments show signs of ductile deformation and lquefaction. We interpret these landforms as subglacial landforms created by till deposition and sedimentation from meltwater with subsequent deformation. Cross-cutting relationships and inter-bedding of sorted sediments suggest a stepwise formation including periodic deformation events. We propose a model that is based on a dynamic subglacial meltwater system. We suggest that the subglacial environment is within the distributed system where the bed receives meltwater from repeated influxes of supraglacially derived meltwater. The processes suggested in this model of formation are strikingly similar to the character of glaciological and hydrological dynamics observed on the Greenland ice sheet today.
... In practice, long profiles of the glaciers were calculated with the EXCEL-spreadsheet provided by Benn and Hulton (2010). This also allows the calculation of a shape factor for each cross section based on its hydraulic radius. ...
... Grey shaded values show input parameters and other values were calculated from these. Shape factor values in italics were calculated using the Excel spreadsheet byBenn & Hulton (2010), while other values were transferred from appropriate cross sections. ...
Article
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The Kellerjoch forms a small isolated massif at the northernmost rim of the central Eastern Alps of Tyrol and shows a number of geomorphological features of glacial and periglacial origin. Mapping yields evidence of two local glaciations postdating the Last Glacial Maximum. Using a simple glaciological approach the palaeoglaciers related to these events were reconstructed. The older glaciation yields an equilibrium line altitude (ELA) ranging from 1660 m for the maximum extent to 1800 m a.s.l. for the innermost moraine. For the younger glaciation, ELAs were reconstructed at 1905 m and 1980 m (depending on the reconstruction) for the Kellerjoch palaeoglacier 2, as well as 1870 m and 2060 m a.s.l. for the Proxen palaeoglacier and the Gart palaeoglacier, respectively. A comparison with published data from the Eastern Alps shows that the older glaciation in the Kellerjoch region likely corresponds to the Gschnitz stadial. Low basal shear stresses of the glacier tongues point towards a cold and dry climate, similar to the reconstruction for the Gschnitz type locality at Trins. The younger glaciation cannot unambiguously be assigned to a specific Late Glacial ice advance, but a Younger Dryas age is a distinct possibility.
... A three-dimensional palaeoglacier reconstruction was performed for the different glacial phases using the 'GLaRe' ArcGIS toolbox devised by Pellitero et al. (2016). Former ice thickness was estimated by applying a perfect-plasticity physical-based rheological model along flowlines from the termini to the headwall (Veen Van der, 1999;Benn and Hulton, 2010). Such a toolbox requires only a flowline, a tentative palaeoglacier geometryapproximated from lateral or frontal morainesand a digital elevation model. ...
... Such a toolbox requires only a flowline, a tentative palaeoglacier geometryapproximated from lateral or frontal morainesand a digital elevation model. Ice thickness was modelled by using a constant shear stress of 100 kPa (Paterson, 1994;Benn and Hulton;. The effect of lateral side drag was corrected by integrating shape factors (F-factor) obtained from cross-sections (Schilling and Hollin, 1981). ...
Article
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The Upper Garonne Basin included the largest glacial system in the Pyrenees during the last glacial cycle. Within the long‐term glacial retreat during Termination‐1 (T‐1), glacier fluctuations left geomorphic evidence in the area. However, the chronology of T‐1 glacial oscillations on the northern slopes of the Central Pyrenees is still poorly constrained. Here, we introduce new geomorphological observations and a 12‐sample dataset of 10Be cosmic‐ray exposure ages from the Ruda Valley. This U‐shaped valley, surrounded by peaks exceeding 2800 m a.s.l., includes a sequence of moraines and polished surfaces that enabled a reconstruction of the chronology of the last deglaciation. Following the maximum ice extent, warmer conditions prevailing at ~15–14 ka, during the Bølling–Allerød (B–A) Interstadial, favoured glacial retreat in the Ruda Valley. Within the B–A, glaciers experienced two phases of advance/stillstand with moraine formation at 13.5 and 13.0 ka. During the early Younger Dryas (YD), glacial retreat exposed the highest surfaces of the Saboredo Cirque (~2300–2350 m) at 12.7 ka. Small glaciers persisted only inside the highest cirques (~2470 m), such as in Sendrosa Cirque, with moraines stabilising at 12.6 ka. The results of this work present the most complete chronology for Pyrenean glacial oscillations from the B–A to the YD.
... This is a derivation from the perfect plasticity assumption formula (τ = ρgHsinα) for the calculation of basal shear stress (τ) at the glacier bed [27], with ρ and α being ice density (~900 kgm −3 ) and ice surface slope, respectively. Details and explanations on the derivation of Equation (2) can be found in Benn and Hulton (2010) [29] and Van Der Veen (2013) [30]. For the reconstruction of paleo-glacier surfaces, we manually drew the flowlines according to the convex and concave directions on topographic contours of the valley. ...
... Because the latero-frontal moraines of the three Holocene events can be clearly traced up to the contemporary glacier tongue, we tuned the τ av on cross sections (with a 50 m step length) along the flow line, until the modeled ice thicknesses matched the heights of the lateral and frontal moraines. For the middle and upper parts of the paleo-glacier during each glacial stage, we used the basal shear stress value obtained at the upper end of the lateral moraine [29]. The shear stress values that have been assigned along the flowlines of the three paleo-glaciers are shown in Figure 3. ...
Article
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The dating of well-preserved Holocene moraines in the Qiangyong Valley, southern Tibetan Plateau (TP), offers great potential for reconstructing Holocene glacier extents and examining climate changes in the region. Guided by Holocene moraine features, this study used Geographic Information System (GIS) model tools to reconstruct paleo-glacier surfaces and glacier equilibrium line altitude (ELA) depressions for three Holocene glacial stages in the valley. The GIS-based models showed that the Qiangyong Valley contained ice volumes of 8.1 × 108, 6.2 × 108, and 4.6 × 108 m3 during the early Holocene, Neoglacial, and Little Ice Age (LIA) glacial stages, and that the ELA was decreased by ~230 ± 25, ~210 ± 25, and ~165 ± 25 m, respectively, compared to modern conditions. Furthermore, the summer temperatures were estimated to be 1.56–1.79, 1.37–1.64, and 1.29–1.32 °C cooler than present to support the three Holocene glacier extents, based on the evidence that the respective precipitation increased by 20–98, 13–109, and 0.9–11 mm relative to the present, which were derived from the lacustrine pollen data for the southern TP. By comparison, this study found that the amplitudes of the ELA-based summer temperature depressions were much larger than the pollen-based counterparts for the three glacial stages, although the two proxies both showed increasing trends in the reconstructed summer temperatures.
... The Vialov equation is essentially the mass conservation equation in the shallow ice approximation for flat glacier bed. Analytic expressions describing longitudinal glacier profiles are needed in studying several aspects of glaciology (e.g., [1,2,[9][10][11]). It is customary to search for solutions in the finite interval x ∈ [0, L], where the glacier summit is located at x = 0 and the terminus is at x = L, and L is the length of the glacier or ice cap. ...
... This is formally a Friedmann equation for a universe with scale factor a(t) analogous to h(x), curvature index K = −E, filled with a perfect fluid with constant equation of state parameter w = n + 4 3n (11) and energy density ρ(a) = ρ 0 /a 3(w+1) = ρ 0 /a 4(n+1)/n , with ...
Preprint
Using a suitable rescaling of the independent variable, a Lagrangian is found for the nonlinear Vialov equation ruling the longitudinal profiles of glaciers and ice caps in the shallow ice approximation. This leads to a formal analogy between the (rescaled) Vialov equation and the Friedmann equation of relativistic cosmology, which is explored. This context provides a new symmetry of the (rescaled) Vialov equation and gives, at least formally, all its solutions using a generating function, which is the Nye profile for the degenerate case of perfectly plastic ice.
... 10 ArcGIS toolbox devised by Pellitero et al. (2016). It estimates past ice thickness along a flowline by applying the perfect-plasticity physicalbased numerical model of Van der Veen (1999) following the calculation routines later proposed by Benn and Hulton (2010). The toolbox only requires a flowline, a tentative paleoglacier geometry (approached as a basin whose boundaries are defined by the position of lateral and/or frontal moraines) and a digital elevation model. ...
... The toolbox only requires a flowline, a tentative paleoglacier geometry (approached as a basin whose boundaries are defined by the position of lateral and/or frontal moraines) and a digital elevation model. Ice thickness was modelled by using an average shear stress of 100 kPa (Paterson, 1994;Benn and Hulton, 2010). Ice thicknesses were corrected based on shape factors (F-factor) obtained from a number of representative cross-sections in order to reduce the error of modelled values to <10% . ...
Article
The Central Pyrenees hosted a large ice cap during the Late Pleistocene. The cirques under relatively low-altitude peaks (2200–2800 m) include the greatest variety of glacial landforms (moraines, fossil debris-covered glaciers and rock glaciers), but their age and formation process are poorly known. Here, we focus on the headwaters of the Garonne River, namely on the low-altitude Bacivèr Cirque (highest peaks at ~2600 m), with widespread erosive and depositional glacial and periglacial landforms. We reconstruct the pattern of deglaciation from geomorphological observations and a 17-sample dataset of ¹⁰Be Cosmic-Ray Exposure (CRE) ages. Ice thickness in the Bacivèr Cirque must have reached ~200 m during the maximum ice extent of the last glacial cycle, when it flowed down towards the Garonne paleoglacier. However, by ~15 ka, during the Bølling-Allerød (B-A) Interstadial, the mouth of the cirque was deglaciated as the tributary glacier shrank and disconnected from the Garonne paleoglacier. Glacial retreat was rapid, and the whole cirque was likely to have been deglaciated in only a few centuries, while paraglacial processes accelerated, leading to the transformation of debris-free glaciers into debris-covered and rock glaciers in their final stages. Climate conditions prevailing at the transition between the B-A and the Younger Dryas (YD) favored glacial growth and the likely development of small moraines within the slopes of the cirque walls by ~12.9 ka, but the dating uncertainties make it impossible to state whether these moraines formed during the B-A or the YD. The melting of these glaciers favored paraglacial dynamics, which promoted the development of rock glaciers as well as debris-covered glaciers. These remained active throughout the Early Holocene until at least ~7 ka. Since then, the landscape of the Bacivèr Cirque has seen a period of relative stability. A similar chronological sequence of deglaciation has been also detected in other cirques of the Pyrenees below 3000 m. As in other mid-latitude mountain regions, the B-A triggered the complete deglaciation of the Garonne paleoglacier and promoted the development of the wide variety of glacial and periglacial landforms existing in the Bacivèr cirque.
... The geomorphology comprises a geomorphological map supplemented by the active landslide inventory, map of flood-prone areas, geometric 2D reconstruction of ancient palaeoglaciers and the karst cave inventory (Table 3). Also included is topographic restitution of the A Seara palaeoglacier based on field evidence and applying the numerical model described in Benn and Hulton (2010) and the ArcGIS GLARE toolbox (Pellitero et al. 2016). Karst caves were 3D modelled and integrated into GIS based on cave survey data following Ballesteros et al. (2019). ...
... Global changes occurred in the UGGp highlands since the maximum advance of glaciers before 21 cal ka BP (Muñoz Sobrino et al. 2001) to areas occupied by native forests and villages at present. a Maximum expansion of paleoglaciers reconstructed from previous works (Supplementary information 2). b 3D reconstruction of the A Seara palaeoglacier using the ArcGIS GLARE toolbox (Benn and Hulton 2010;Pellitero et al. 2016) and displayed in ArcScene. c Current distribution of villages and forests (derived from the MFE - Table 2) The GIS database was used for planning and technical designing of touristic resources, such as routes, activities, touristic information documents and interpretation centres. ...
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The management of a UNESCO Global Geopark (UGGp) requires a vast wealth of miscellaneous scientific knowledge that can be successfully organised using a Geographical Information System (GIS). This paper presents a pragmatic GIS database to assist in the suitable governance of the Courel Mountains UGGp (2017) in Northwest Spain. The database is structured in 66 coverages compiled from public sources and previous works or produced through traditional mapping (combining fieldwork and photointerpretation) and GIS tools. The acquired data was later homogenised and validated by a multidisciplinary team and archived in independent coverages. Forty thematic maps illustrate the broad range of cartographic information included in the GIS database. Among them, 25 basic maps provide an overview of the UGGp and 15 new maps focus on crosscutting and technical issues. All maps illustrate the huge potential of GIS to create new resources combining coverages and adapting the legend according to their purpose and audience. The database facilitates the suitable publishing of consistent outputs (e.g., brochures, books, panels, webpages, web serves), as well as the elaboration of technical data to assist the park management. The database furnishes information on the design of education actions, touristic routes, activities and Geopark facilities. The GIS database is also a supportive tool for scientific research and provides the necessary knowledge to conduct geoconservation actions based on land use, geological hazards and the occurrence of natural and cultural heritages. Altogether, the GIS database constitutes a powerful instrument for policy-making, facilitating the identification and evaluation of alternative strategy plans.
... Rekonstrukcija površine paleoledenikov temelji na računskem pristopu (Benn, Hulton, 2010), pri čemer pa so bile upoštevane tudi evidentirane geomorfološke oblike, ki nakazujejo izoblikovanost ter obseg ledenikov v preteklosti. Pri tem so bili pomembni bočni in čelni morenski nasipi ter sledovi ledeniške erozije na izpostavljeni kamninski podlagi (ang. ...
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The Krnica Valley represents one of the side glacial valleys of the Upper Sava Valley. The purpose of this research was to investigate the traces of glaciation in the valley. In the whole studied area between the Kriška wall and the mountain in the Klin area, five areas of the moraine ridges were identified, which, despite intense erosion and acummulation of geomorphic processes, are especially well preserved in the upper part of the Krnica Valley. For the younger three glacial stages in the area between the Kriška wall and the Krnica mountain hut, a reconstruction of the surface and the extent of paleo-glaciers with their associated equilibrium line altitudes was made. In the area between the youngest moraine ridge and the Kriška wall, two profiles were taken in 2015 with a georadar, the aim of which was to verify the possible existence of relict ice under the layer of firn and gravel. For the Krnica Valley area, equilibrium line altitudes (ELAs) were estimated at much lower altitudes compared to the other similar areas in the vicinity. For the first glacial stage, which most probably belongs to the period of the Little Ice Age, the ELA is estimated at 2010 m above sea level, which is 426 m lower than the ELA of the Triglav Glacier for the same period, 4.5 km away. The second and third glacial stages in the Krnica Valley probably belong to the Early Holocene and Younger Dryas periods, respectively, and their equilibrium line altitudes were estimated at 1954 m and 1727 m above sea level, respectively. The moraine ridges, lying to the north of the Krnica mountain hut, probably date to the later Pleistocene cooler periods, i.e. Last Glacial Maximum (LGM) with a peak of 21,000 years ago.
... The glacier geometry of the ice field and outlet glaciers was reconstructed by the GlaRe, a semi-automated GIS-based method (Pellitero et al., 2016), using the 9 m DEM of the study area (Milevski et al., 2013). The ice thickness from the current bed topography was generated by the GlaRe toolbox applying the parametrisation used by Profiler v.2 (Benn and Hulton, 2010). The glacier thickness was adjusted to geomorphic markers by varying the basal shear stress value (τ b ). ...
... The extent and ice-surface geometry of the LGM glacial advance were reconstructed in a GIS environment based on the distribution of moraines and glacial trimlines that mark the approximation of the ice-surface position (Benn et al., 2005). Ice thickness was assessed using a glacier profile model (Benn and Hulton, 2010) provided in the Pellitero et al. (2015) toolbox with the use of 50-100 kPa basal shear stress values (Cuffey and Paterson, 2010) and a calculated valley shape factor. We estimated the glacier's ELA by using the area altitude balance ratio (AABR) method, which is considered to be nonsensitive to glacial hypsometry (Furbish and Andrews, 1984;Osmaston, 2005;Rea, 2009;Pellitero et al., 2015). ...
Article
In the eastern Carpathians the legacy of glaciation is preserved in several isolated mountain massifs. This paper presents new mapping results of glaciated valley land systems in the Rodna Mountains, the highest part of the eastern Carpathians (2303 m above seal level). In most of the glacial valleys, the maximal Pleistocene extent is marked by freshly shaped moraines, which are referred in this study as the Pietroasa glacial stage and regarded as the last glacial maximum (LGM) advance. Only in three valleys do older Şesura glacial stage moraines (pre-LGM, likely Marine Oxygen Isotope Stage 6) occur. On the basis of the geomorphological record, we reconstruct the extent, surface geometry, and equilibrium line altitude (ELA) of Pietroasa-stage glaciers. The local ELA pattern of north-exposed glaciers in the Rodna Mountains shows a rising trend towards the southeast, which suggests dominant snow-bearing winds and orographically induced precipitation from the west. This finding fits well with the dominant palaeo-wind direction inferred from other Carpathian proxies and confirms the dominance of zonal circulation pattern during the global LGM in central eastern Europe.
... Glacier topography was interpolated from 25 theoretical ice surface profiles reconstructed comprising the routing pathways followed by glacier tongues along the valleys and inferred from geomorphological indicators of glacier flow direction. Theoretical ice surface profiles were adjusted following the methods explained in Benn and Hulton (2010), using the GlaRe toolbox for ArcGIS (Pellitero et al., 2016). Basal shear stress values up to 80e120 KPa were needed to adjust the theoretical ice surface profiles to existing geomorphological evidence, which are consistent with those observed in modern glaciers (50e150 KPa; Pellitero et al., 2016). ...
Article
In glaciated areas, the environmental evolution before MIS 2 is usually poorly constrained mainly due to the later glacial erosion during the global Last Glacial Maximum (LGM). However, in carbonate areas, karst caves can preserve records of pre-LGM paleoenvironment. We studied a cave (1350 m altitude) to establish the paleoenvironmental evolution of a glaciated karst area in Picos de Europa (SW Europe). For this objective, a glacial reconstruction, cave sedimentology analyses, and macro-and micromammal remains are com bined with ten UeTh, OSL and AMS 14 C ages. The paleo-glacial reconstruction indicates glaciers descended down to 810e1040 m of altitude covering an area of 36.18 km 2 in the surroundings of Covadonga Lakes during the glacial local maximum, with the equilibrium line altitude located at 1524 ± 36 m. The geomorphological study of the cave and the UeTh and OSL dates reveal the presence of three allochthonous alluvial sediment sequences at 132e135, 98e60 and ca. 36 ka. These last two sequences would come from the erosion of fluvioglacial sediments including teeth fragments of Pliomys coronensis (¼P. lenki), an unusual species in high areas of NW Spain during the Upper Pleistocene. In addition, remains of chamois (Rupicapra pyrenaica) dated in 37e33 cal ka BP constitutes the oldest evidence of chamois above 800 m asl in the region. All the presented data indicate the development of alpine glacier-free areas covered by fluvioglacial sediments at ca. 1450 m altitude at 98e60 and 37e33 ka, corresponding to glacial retreat stages.
... This is then solved iteratively, step by step, up-glacier from the frontal moraine (Eq. 2) (43,44) ...
Article
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The Younger Dryas (YD) was a period of rapid climate cooling that occurred at the end of the last glaciation. Here, we present the first palaeoglacier-derived reconstruction of YD precipitation across Europe, determined from 122 reconstructed glaciers and proxy atmospheric temperatures. Positive precipitation anomalies (YD versus modern) are found along much of the western seaboard of Europe and across the Mediterranean. Negative precipitation anomalies occur over the Fennoscandian ice sheet, the North European Plain, and as far south as the Alps. This is consistent with a more southerly and zonal storm track, which is linked to a concomitant southern location of the Polar Frontal Jet Stream, generating cold air outbreaks and enhanced cyclogenesis, especially over the eastern Mediterranean. This atmospheric configuration resembles the modern Scandinavian (SCAND) circulation over Europe (a blocking high pressure over Scandinavia pushing storm tracks south and east), and by analogy, a seasonally varying palaeoprecipitation pattern is interpreted.
... The second toolbox uses empirically determined mathematical relationships to calculate the paleo-ELA of the reconstructed glacier (Ohmura et al., 1992;Kerschner et al., 2000;Gonz alez Trueba and Serrano Cañadas, 2004;Benn and Hulton, 2010;Pellitero et al., 2015). For the Tandl paleo-ELA estimation the accumulation area to the total area ratio (AAR) method was used, implementing ratios of 0.6 and 0.65, common values suggested in literature (Gross et al., 1977;Bakke and Nesje, 2011). ...
Article
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Relict rockglaciers are distinctive indicators of past permafrost occurrence. Their lower limit is attributed to a former mean annual air temperature (MAAT) of below −2 °C. This study provides a comprehensive dataset of 34 ¹⁰Be exposure ages from boulders along two complex series of relict rockglaciers, called Tandl rockglaciers and Norbert rockglaciers (Carinthia, Austria). The lowest Tandl rockglacier complex stabilised around 14 ka at an elevation of 1350 m a.s.l., the lowest Norbert rockglaciers (1580 and 1730 m a.s.l.) stabilised around 15.7 ka. Additionally, in both study sites the low elevation relict rockglaciers interacted with glacial deposits of the local pre-Bølling glaciers (Gschnitz stadial glacier). Temperature lowering based on our data of the Gschnitz rockglaciers ranges between 6.3 and 4.5 °C compared to modern MAAT. The cross-cutting relationships of the rockglaciers and the glacial deposits together with the exposure ages of the rockglaciers, indicate that these rockglaciers, and therewith also permafrost, developed shortly after or even simultaneously with retreat of the Gschnitz stadial glaciers. This is the first permafrost formation in the Alpine areas after the retreat of the (warm-based) Last Glacial Maximum glaciers. The Tandl and Norbert rockglacier lobes located at higher elevations, up to about 2300 m a.s.l., finally stabilised in the early Holocene; ages of several dated lobes lie between 12-10 ka. At this time, which corresponds to the Egesen stadial (Younger Dryas) cold phase, rockglaciers and glaciers co-existed. From the lowest position of the Egesen rockglacier lobe at the Tandl site (1700 m a.s.l.), a temperature lowering for the Egesen stadial of −4.6 °C was calculated. This study highlights the potential of relict rockglacier deposits as an independent paleoclimate archive and their usefulness for reconstruction of past permafrost development and distribution in high mountain areas when they can be placed in a temporal framework.
... A geographic information system (GIS) approach was used for the reconstruction of palaeoglaciers on Mt Mavrovouni (Chapter 4). In particular, the surface and thickness of the former glaciers were reconstructed using the GlaRe toolbox, a semi-automated GIS tool based on the numerical technique of Benn and Hulton (2010) and developed by Pellitero et al. (2016). ...
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Abstract The objective of this thesis is to address temporal gaps in the glacial history of the Pindus Mountains in northwest Greece with new insights from the study of the glacial record of Mt Mavrovouni and its connection with the respective records in southern Greece and in the Balkans. The glacial geomorphology of Mt Mavrovouni was mapped and the timing of Late Pleistocene glaciations was constrained by cosmogenic 36Cl exposure ages from ophiolitic glacial boulders within a well-preserved glacial/periglacial sequence. These ages indicate that the most extensive Late Pleistocene glaciers reached their terminal positions at 26.6 ± 6.6 ka suggesting a Late Pleistocene local glacial maximum close in timing to the Last Glacial Maximum (27-23 ka). This timing was confirmed by 36Cl ages from limestone glacial boulders in a similar study in the nearby Mt Tymphi. The consistency of these ages validates the theoretical suitability of cosmogenic 36Cl exposure dating on ophiolites while it constitutes the only chronology of Late Pleistocene glaciations on the mountains of Greece that is independent from inherent issues in surface exposure dating of limestones such as weathering rates of rock surfaces. At the same time the geochronological framework of Late Pleistocene glaciations in the Pindus mountains in northwest Greece is now one of the best dated in western Balkans. New evidence and a detailed review of glacial studies in the mountains of Greece provided a new synthesis of our current understanding of the Quaternary glacial history of Greece. The ice cover during the largest Middle Pleistocene glaciations (MIS 12/ MIS 6) was more extensive than previously thought. Latest evidence from Mt Tymphi, Mt Smolikas and Mt Chelmos along with findings of other glacial studies in western Balkans suggests that valley glaciers radiated from central ice field/ice caps throughout this region during the most extensive Middle Pleistocene glaciations. Ice extent was considerably smaller during the Last Glacial Cycle (MIS 5d – MIS 2) whereas during the Holocene only very small glaciers formed in some deep-cirques thanks to strong local topographical and climatic controls. Finally, an analysis of regional palaeoclimatic records showed that moisture supply of the atmospheric systems seems to have been the most critical factor for the formation of glaciers in the mountains of Greece. Moreover, the Late Pleistocene Equilibrium Line Altitudes across Greece indicate a wetter climate in southern Greece that can be attributed to different palaeoatmospheric circulation mechanisms in central Mediterranean that forced moisture supply into a SW-NE track.
... GlaRe also includes a toolset for instances in which part of the paleoglacier bed is presently covered by ice, which is the case for all the glaciers we reconstructed in South Greenland. The additional tool was employed before the aforementioned procedures, to estimate the subglacial bed topography, based on an inversion of an ice surface profile model by Benn and Hulton (2010) (Pellitero et al., 2016). We used the ArcticDEM 2 m resolution mosaic (Porter et al., 2018) for the modern ice surfaces in our analyses. ...
Article
Local glaciers and ice caps (GICs) respond sensitively and quickly, on the scale of decades to centuries, to climate variations. Continuous records of past fluctuations in GIC size provide information on the timing and magnitude of Holocene climate shifts, and a longer-term perspective on 21st century glacier retreat. Although there is broad-scale agreement on millennial-scale trends in Holocene climate variability and fluctuations in local GICs in Greenland, regional variations are only loosely constrained. Here we present three Holocene proglacial lake sediment records from South Greenland, an area with abundant local glaciers but few Holocene-length paleoclimate records. In addition, we use geospatial analysis to model past equilibrium-line altitudes (ELAs) and thereby constrain the magnitude of ablation-season temperature change during the warmest and coolest periods of the Holocene. Physical and geochemical sedimentary characteristics show that two of the proglacial lakes continued to receive glacial meltwater input until ∼7.3 and ∼7.1 ka BP. The survival of local glaciers implies that South Greenland remained relatively cool, and that summer temperatures gradually warmed, but did not warm well beyond 1.2 °C above present in the early Holocene. In the mid-Holocene, from ∼7.1 to 5.5 ka BP, organic sedimentation at these two sites indicates that local glaciers became very small, or more likely melted away completely. The glaciers within the third lake’s catchment melted away prior to ∼5.2 ka BP, as sediments deposited earlier in the Holocene could not be dated at this site. We estimate that summer temperatures increased by at least 1.2–1.8 °C above present by ∼7.3–7.1 ka BP. Our results are consistent with other observations that suggest a north-to-south gradient in the timing of Holocene thermal maximum conditions, with southern Greenland experiencing a delayed warming relative to other regions in Greenland. As summer temperatures cooled in the Neoglacial, our records show that sustained glacier regrowth began ∼3.1 ka BP with glaciers in the southernmost catchment, which at present, receive the most precipitation. In the other two catchments, which host smaller glaciers in a drier environment, regrowth began at ∼1.3 and ∼1.2 ka BP, the timing of which is in agreement with other glacial records from the Arctic Atlantic region. Local glaciers reached their maximum late Holocene extents during a cooler, second phase of the Little Ice Age (LIA) ∼0.2-0.1 ka BP, that we estimate was at least 0.4–0.9 °C cooler than present. Overall, these findings improve understanding of the spatio-temporal dynamics of Holocene glacier and climate change in Greenland, potentially yielding valuable information about their future response.
... In this study, we perform a complete ELA reconstruction in Chirripó paleoglacier system through MGE, AA, AAR and AABR methods during the LGM. We will focus the discussion in the AAR and AABR because they are considered the most appropriate methods for ELA reconstructions (Osmaston, 2005;Rea, 2009;Benn and Hulton, 2010;Campos et al., 2019). Regarding the AAR method, we chose the paleo-ELA values derived of the ratio 0.65 because this value has been frequently used in tropical regions (Porter, 2001;Osmaston, 2005) whereas a balance ratio of 2.0 is typical for the AABR in the extratropical glaciers (Lachniet and Vázquez-Selem, 2005). ...
Article
Several high areas of Central America show evidence of past glacial activity, including glacial cirques, polished and striated bedrock surfaces and moraine deposits. As glacial remnants, these morphologies can guide the understanding of past climate conditions, such as during the Last Glacial Maximum (LGM). Based on aerial imagery (1:25,000), detailed Digital Elevation Model (DEM) and field geomorphic assessments, we establish paleo-equilibrium line altitudes using four methods: Median Glacier Elevation (MGE), Accumulation Area Ratio (AAR), Area x Altitude (AA), and Area-Altitude Balance Ratio (AABR) during the LGM for the Chirripó National Park in Costa Rica. In addition, we calculate the LGM paleo-temperature decrease multiplying several modern atmospheric lapse rates by the equilibrium line altitude depression. In addition, a Generalized Linear Model (GLM) was applied to describe linkages between obtained paleoglacier areas and multiple land surface parameters such as Basin location, Analytical Hillshading, Aspect, Area Surface Radiation, Diurnal Anisotropic Heating, Slope, Terrain Ruggedness Index, and Wind Exposition. Our results determined thirty-one paleo equilibrium line altitudes (paleo-ELAs) and a mean altitude of~3490 m a.s.l. Some of the moraines used in this study have been recently dated, confirming the extension of the glaciers during LGM used to calculate the ELAs. We also obtained an annual average temperature decrease of~10.5°C applying a lapse rate of 0.65°C/100. Moreover, Wind Exposition and Terrain Ruggedness Index were the land surface parameters with greater statistical correlation for paleo-glacier areas. Therefore, our results provide new knowledge into the reconstruction of the maximum expansion of the LGM on tropical landscapes.
... To estimate the ELA at each particular point in time, glacier reconstruction was performed in the GIS environment on the basis of the distribution of moraines (Benn et al., 2005). For larger valley glaciers (Pp stage), ice thickness was assessed using a glacier profile model (Benn and Hulton, 2010) provided in the Pellitero et al. (2015) toolbox with the use of 80-100 kPa basal shear stress values (Cuffey and Paterson, 2010) and a calculated valley shape factor. To place Lateglacial ELAs in the context of their depression in comparison to full LGM conditions, the ELA of three LGM glaciers in the study area was also estimated from published glacier geometries (Zasadni and Kłapyta, 2014). ...
Article
The timing of glacier disappearance and rock glacier stabilization in the highest massifs of the Carpathians is still poorly documented. In this paper, we establish the extent and chronology of the final stages of glaciation and timing of stabilization of the uppermost rock glaciers in the Tatra Mountains, which are the highest (2654 m a.s.l.), northernmost (N 49°12′), and coldest range in the Carpathians. On the base of morphostratigraphic principles, Schmidt Hammer tests and glacier equilibrium line altitude (ELA) estimation, we assigned moraines and rock glaciers in the Mt. Kriváň massif (SW part of High Tatras) to a threefold stratigraphic sequence with glacial stages/advances from older to younger: Popradské pleso (Pp), Suchá važecká I (Sv I) and Suchá važecká II (Sv II). Landforms attributed to two younger advances, Sv I and Sv II, were sampled for the purpose of cosmogenic ¹⁰Be surface exposure dating. Our data show that Pp and Sv I glacial advances occurred during the Oldest Dryas climatic downturn. The younger advance (Sv I) occurred just before the Bølling-Allerød (B/A) warming at 14.9 ± 0.4 ka, at this time small glaciers occupied lower glacial cirques in the study area. The youngest Sv II advance was characterized by rock glaciers and small debris-covered glaciers confined to the highest cirques. The mean exposure age of four relict rock glaciers of this stage is 11.1 ± 0.9 ka but individual rock glacier mean ages spanned between 11.8 and 10.4 ka. Our research results show that the youngest moraines and rock glaciers in the Tatra Mountains were formed during the Younger Dryas (YD), but the final permafrost melting and rock glacier stabilization period was delayed until the early Holocene, but no later than 10.4 ka. In high elevation cirque bottoms (up to 2120 m a.s.l.), the YD glaciers and rock glaciers readvanced across land which was ice-free as early as 14.8–14.2 ka. Thus, it is likely that during the B/A interphase, glaciers completely disappeared in the Tatra Mountains. The YD was the last period of glacial/periglacial activity in the massif. As we investigated one of the highest-situated rock glaciers in the Tatras (up to 2220 m a.s.l.), we conclude that all rock glaciers in this massif are relict landforms which developed in response to severe Lateglacial climate conditions. The Lateglacial climate of the Tatra Mountains is discussed herein on the basis of glacier equilibrium line altitude (ELA) estimation and the vertical distribution of rock glacier belts. We argue that paleoclimate significance of the presented geomorphological record may match paleobotanical proxy reconstructions and the results of climate simulations, but only if the impact of enhanced temperature seasonality on glacier mass balance and rock glacier activity is taken into account.
... Based on the geomorphological and chronological evidence, Dong et al. (2017) calculated the LGM ice surface elevations (h) of the main and tributary central flowlines of the valley, using a formula of h = (2sx/qg) 1/2 by Benn & Hulton (2010) with s, x, q and g being basal shear stress, upvalley distance from glacier end along flowline, ice density and gravitational acceleration, respectively. They extrapolated the flowline surface elevations onto the whole glacier extent grid and then obtained the LGM glacier thickness distribution by subtracting a digital elevation model (DEM) from the glacier surface elevation grid. ...
Article
A well‐preserved Last Glacial Maximum (LGM) moraine set in the Quemuqu Valley on the eastern slope of the Qiongmu Gangri Peak offers great potential for reconstructing LGM glacier extent and examining LGM climate in the region. This study employed a coupled and physics‐based mass balance and ice‐flow model to investigate glacier sensitivities to climate in the valley. Based on the sensitivity tests and the well‐preserved LGM moraines, the study also reconstructed the LGM glacier extent in the valley and assessed the magnitude of cooling for the LGM period. Model results suggest that the Quemuqu Valley sustained an ice volume of 6.80±0.16 km3 in the LGM period. Temperature depression of 3.1–4.3 °C, combined with 30–70% modern precipitation, is likely to have supported the LGM glacier extent in the valley. The temperature inference for the LGM period is comparable with other independent palaeoclimate evidence in the region. However, there is a large difference in the reconstructed glacier volume (ice thickness) between previous research and the current study. The glacier model used here directly calculates the ice thickness and needs relatively less field evidence to constrain the model simulations. It is therefore advocated to use such a model to reconstruct past glaciers and their corresponding climates for other valleys of the Tibetan Plateau.
... To estimate the reach of viscous flow-features possibly buried beneath the surface of unit NHt (see Section 9.2) we used a 2D model of perfect plasticity calculate ice thickness on Earth (e.g. Ng and al., 2010;Benn and Hulton, 2010) and Mars on (e. g. Parsons et al., 2011;Fastook et al., 2014;Karlsson et al., 2015;Schmidt et al., 2019;Hepburn et al., 2020a). ...
Article
The long-term cyclicity and temporal succession of glacial-periglacial (or deglacial) periods or epochs are keynotes of Quaternary geology on Earth. Relatively recent work has begun to explore the histories of the mid-to higher-latitudinal terrain of Mars, especially in the northern hemisphere, for evidence of similar cyclicity and succession in the Mid to Late Amazonian Epoch. Here, we carry on with this work by focusing on Protonilus Mensae [PM] (43-49 0 N, 37-59 0 E). More specifically , we discuss, describe and evaluate an area within PM that straddles a geological contact between two ancient units: [HNt], a Noachian-Hesperian Epoch transition unit; and [eHT] an early Hesperian Epoch transition unit. Dark-toned terrain within the eHt unit (HiRISE image ESP_028457_2255) shows continuous coverage by structures akin to clastically-sorted circles [CSCs]. The latter are observed in permafrost regions on Earth where the freeze-thaw cycling of surface and/or near-surface water is commonplace and cryoturbation is not exceptional. The crater-size frequency distribution of the dark-toned terrain suggests a minimum age of ~100 Ma and a maximum age of ~1 Ga. The age estimates of the candidate CSCs fall within this dispersion. Geochronologically, this places the candidate CSCs among the oldest periglacial landforms identified on Mars so far, by at least one and possibly two orders of magnitude. Unit HNt is adjacent to unit eHt and shows surface material that is relatively light in tone. The coverage is topographically irregular and, at some locations, discontinuous. Amidst the light-toned surface, structures are observed that are akin to clastically non-sorted polygons [NSPs] and polygonised thermokarst-depressions on Earth. Terrestrial polygon/thermokarst assemblages occur in permafrost regions where the freeze thaw cycling of surface and/or near-surface water is commonplace and the permafrost is ice-rich. The crater-size frequency distribution of the light-toned terrain suggests a minimum age of ~10 Ma and a maximum age of ~100 Ma. The age estimates of the candidate ice-rich assemblages fall within this dispersion. Geochronologically, this places them well beyond the million-year ages associated with most of the other candidate ice-rich assemblages reported in the literature. Stratigraphically intertwined with the two possible periglacial terrains are landforms and landscape features (observed or unobserved but modelled) that are indicative of relatively recent glaciation (~10 Ma-100 Ma) and glaciation long past (≥~ 1 Ga) to decametres of depth: glacier-(cirque) like features; viscous-flow features, lobate-debris aprons; moraine-like ridges at the fore, sides and midst of the aprons; and, patches of irregularly shaped (and possibly volatile-depleted) small-sized ridge/trough assemblages. Collectively, this deeply-seated intertwining of glacial and periglacial cycles suggests that the Mid to Late Amazonian Epochs might be more Earth-like in their cold-climate geology than has been thought hitherto.
... The glacier thickness was estimated using a semi-automated GIS-based method (GlaRe, Pellitero et al., 2016), using the 9 m Digital Elevation Model (DEM) of the study area J o u r n a l P r e -p r o o f (Milevski et al., 2013). The GlaRe toolbox generates the ice thickness from the modern bed topography applying physical laws of ice flow along a user defined flowline (Benn and Hulton, 2010). ...
Article
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Several studies applied numerical age determination methods to examine glacial phases of the central Balkan Peninsula. However, the resulting datasets are contradictory, meaning that further discussion is needed. This study provides ¹⁰Be cosmic ray exposure (CRE) ages of a succession of glacial landforms in the Jablanica Mt. (North Macedonia), aiming at a better understanding of Late Pleistocene glacier development in the area. On the basis of the mapped glacial landforms, six glacial stages were identified and their mean equilibrium line altitudes (ELAs) were estimated. The CRE ages of five glacial stages - from the second oldest to the youngest - were determined between 16.8+0.8/−0.5 ka and 13.0+0.4/−0.9 ka. Accordingly, the most extensive glaciation in the Jablanica Mt. occurred before ~17 ka. The average ELA of the glaciers was 1792 ± 18 m a.s.l. during the largest ice extent, and 2096 ± 18 m during the last phase of the deglaciation. Independent reconstructions of key climatic drivers of glaciological mass balance suggest that glacial re-advances during the deglaciation were associated to cool summer temperatures before ~15 ka. The last glacial stillstand apparently resulted from a modest drop in summer temperature coupled with increased winter snow accumulation. In the study area no geomorphological evidence for glacier advance after ~13+0.4/−0.9 ka could be found. On the basis of independent climate proxies we propose that the last glacier advance occurred no later than ~13 ka, and glaciers were withdrawing during the Younger Dryas when low temperatures were combined with dry winters.
... The reconstructed glaciers were created using the GlaRe (Glacier Reconstruction) ArcGIS toolbox (Pellitero et al., 2015) which represent a semiautomated method of glacier reconstruction. Ice thickness was assessed along the flowline using a glacier profile model (Benn and Hulton, 2010) using basal shear stress values 50 to 100 kPa (Cuffey and Paterson, 2010) and a calculated valley shape factor. Ice thickness was adjusted to the mapped glacial landforms by fine-tuning their thickness using the basal shear stress values. ...
Article
The Polonyna Rivna (1480 m asl) and Borzhava (1682 m asl) ranges represent medium-high mountain massifs located in the north-western part of the Ukrainian Carpathians, where the legacy of the Pleistocene glaciation has long been unexplored. Based on the first detailed mapping of glacial landforms and sedimentological analysis, we document the presence of freshly-shaped outer moraines and glacial cirques and reconstruct the extent and ice-surface geometry of the six very small (0.09–0.78 km² area) palaeoglaciers. The specific feature of the area is the presence of extensive mountain-top plateaus that play an important role as additional areas for snowblow accumulation. The equilibrium line altitudes (ELAs) calculated from hypsometry of reconstructed local Last Glacial Maximum (LLGM) using the area x altitude balance ratio (AABR) 1.6 method is exceptionally low at 1138 m asl in the Polonyna Rivna and 1230 m asl in the Borzhava range. Excluding the topographic effect produced by additional snow accumulation the ELA shift upwards between 120 and 180 m which corresponds to 25–53% of the glacier elevation range. The resulted climatic ELA (1282–1352 m asl) together with the mean cirque floor altitude (1194 m asl) and mean elevation of the glacier fronts (994 m asl) represent the lowest values in the entire Carpathian arc. Our data indicate glacier-friendly conditions in the mountain massifs exceeding 1400 m asl in the windward NW part of the Ukrainian Carpathians where due to relatively cold air temperatures and orographic induced precipitation local topolimatic factors dictated the development of marginal glaciation.
... As the geomorphological evidence (terminal moraine and cirque walls) define sufficiently the limits of this palaeoglacier it was possible to use a geographical information systems approach (GIS) to calculate its palaeo-ELA at 2090 m above modern sea level. In particular, the surface, thickness and ELA of the former glaciers were reconstructed using the semi-automated GIS tools based on the numerical technique of Benn and Hulton (2010) and developed by Pellitero et al. (2015;2016). The ELA was calculated with the adaptation of the classic area-altitude balance ratio (AABR) method (Osmaston, 2005) using a balance ratio (BR) of 1.6, which is the average obtained on present-day glaciers in other Mediterranean mountains (Rea, 2009). ...
Article
A glacial geomorphological analysis of three valleys on Mt. Mavrovouni (North Pindus Mountains, Greece) is presented alongside a pilot study using cosmogenic ³⁶Cl to obtain surface exposure ages from iron-rich ophiolite glacial and periglacial boulders. At least three distinct morphostratigraphic units of glacial (moraines) and periglacial (relict pronival ramparts) origin have been identified. Four ³⁶Cl surface exposure ages were obtained from the stratigraphically youngest glacial and periglacial deposits. Although this limited dataset with relatively large uncertainties cannot support a robust geochronology, the ages are consistent with the ³⁶Cl-based chronologies of limestone-derived moraines on Mt. Tymphi (NW Greece) and Mt. Chelmos (S Greece), confirming that the last glaciers on this massif formed during the Last Glacial Maximum as also indicated by other studies in the Pindus mountains. At the same time it provides confidence in the suitability of ³⁶Cl dating for iron-rich samples, such as ophiolites, using an updated ³⁶Cl model that incorporates improved production rates for iron spallation. The presented preliminary chronology of moraines and pronival ramparts is based on those ages as well as on local and regional morphostratigraphic correlations. The stabilisation of the most extensive Late Pleistocene glaciers took place during the Last Glacial Maximum, at 27.0 ± 6.5 ka whereas the presence of pronival ramparts dated at 20.2 ± 4.8 ka suggests persisting cold and arid conditions. Older, still undated glacial deposits exist lower in the valleys which can be attributed to the Middle Pleistocene major glaciation phases (MIS 12/MIS 6), based on their relative morphostratigraphic position within the glacial sedimentary sequence.
... The GLARE GIS toolbox Glacier flowlines were defined from snout to source and the 'flowline ice thickness' tool was used to calculate ice thickness along the flowline, following Benn and Hulton (2010). A default shear stress of 100 kPa was used in the flowline thickness construction for Mount Tymphi and the cirques of Durmitor . ...
Thesis
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The Mediterranean mountains were glaciated during cold stages of the Pleistocene. This glacial record is often well preserved, providing an important archive of past temperature and moisture conditions that extends deep into the Middle Pleistocene. The most extensive glaciations occurred during the Middle Pleistocene, when large ice caps developed in the upland karsts of the Balkans. It is now clear that glaciers were present throughout the Late Pleistocene across the Mediterranean. Some small glaciers remain today, sustained by favourable topoclimatic factors, although many have declined in recent decades due to rising global temperatures. This thesis presents an up-to-date meta-analysis of the geochronological record for the Mediterranean, which highlights greater complexity in the timing of Pleistocene glaciation across the region than hitherto recognised. Key aspects of the glacial record lie outside the moraines in downstream river systems and in marine settings. Despite a wealth of dates for the Late Pleistocene, the timing of glacier maxima and deglaciation in the Balkans is poorly understood. New geomorphological mapping, 52 36Cl terrestrial cosmogenic nuclide exposure ages, and palaeoglacier modelling address a geographical gap in the Mediterranean record and a temporal gap in the previously undated Late Pleistocene and Holocene records at two sites in Greece and Montenegro. Late Pleistocene glaciers were restricted to the upper valleys and cirques at Mount Tymphi in the Pindus Mountains of northwest Greece and in the Durmitor Massif, in the Dinaric Alps of northern Montenegro. The timing of moraine formation and glacier retreat at Mount Tymphi is consistent with the Voidomatis River record downstream and the Ioannina basin pollen record. Glaciers were present in the high cirques of the Durmitor Massif during the Younger Dryas. In contrast, evidence of Younger Dryas glaciation is absent from Mount Tymphi. At Durmitor, Late Holocene moraines that pre-date the Little Ice Age have been identified for the first time in the Dinaric Alps and correspond with the Late Antique Little Ice Age at c. 600 CE. This research also examines the Late Pleistocene terrestrial cosmogenic nuclide (TCN) record for the wider Mediterranean region and demonstrates that mountain glaciers responded to repeated temperature and precipitation changes in the North Atlantic during the Late Pleistocene. While 36Cl dating has enhanced our understanding of the Late Pleistocene and Holocene record, challenges still remain that inhibit our geochronological and palaeoclimatic interpretations. A key conclusion from this research is that it is preferable to use multiple radiometric and relative dating methods in limestone glaciokarst settings.
... The glacier geometry of the ice field and outlet glaciers was reconstructed by the GlaRe, a semi-automated GIS-based method (Pellitero et al., 2016), using the 9 m DEM of the study area (Milevski et al., 2013). The ice thickness from the current bed topography was generated by the GlaRe toolbox applying the parametrisation used by Profiler v.2 (Benn and Hulton, 2010). The glacier thickness was adjusted to geomorphic markers by varying the basal shear stress value (τ b ). ...
Article
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In the Jakupica Mts a plateau glacier was reconstructed (max. area ∼45 km², max thickness: ∼260 m). The study area comprises six formerly glaciated valleys, five of which were fed by the plateau glacier and one had an independent cirque when local glaciation reached its maximum ice extent (MIE). The equilibrium line altitude (ELA) of the most extended glacial phase was at 2075⁺³⁷/-25 m asl. The ¹⁰Be cosmic ray exposure (CRE) age of this phase was estimated at 19.3+1.7/-1.3 ka, conformable with the Last Glacial Maximum (LGM). CRE ages from the next moraine generation placed the first phase of deglaciation to 18.2+1.0/-3.0 ka. The samples from the moraine of the penultimate deglaciation phase provided CRE ages with large scatter and biased towards old ages, which is probably the result of inherited cosmogenic nuclide concentrations within the rock. Glacio-climatological modelling was performed for the MIE, which has a well-established LGM age. The degree-day model was used to calculate the amount of accumulation required to sustain the glaciological equilibrium assuming a certain temperature drop at the ELA. The degree-day model constrained by the pollen-based July paleo-temperature reconstructions yielded an annual total melt at the LGM ELA comparable to or slightly higher than the current mean annual precipitation at the same elevation. These wetter LGM conditions inferred from the paleo-glaciological evidence in Jakupica Mts suggest an enhanced moisture advection in the region.
... The subglacial topography was determined based on the GPR data. A default shear stress value of 100 kPa (Benn and Hulton, 2010;Pellitero et al. 2016;Rea and Evans 2007) was used to run the GlaRe model. The moraine ridges' position was considered an indication of the downslope maximum ice extent during the LIA. ...
Article
Snezhnika and Banski Suhodol glacierets in the Pirin Mountains are the southernmost surface ice accumulations in Europe. Apart from direct snowfall, substantial inputs from avalanching feed both glacierets. Both glacierets appear to be more stable than any other small glacier in the Mediterranean region. Although accurate knowledge of ice thickness distribution and bedrock topography is essential to understand the long-term dynamics of these ice bodies, such data are lacking for the Balkan Peninsula glaciers. Detailed GPR measurements conducted in 2018 using a 100 MHz frequency antenna revealed a maximum thickness of 17 m at Banski Suhodol and 12 m at Snezhnika. Two distinct main layers revealed by density variations were inferred at Snezhnika and several clear internal reflections observed on the radargrams were associated with thin debris layers. Based on the morphological evidence of the former ice extents and high-resolution digital elevation models, 3D reconstructions of ice thickness distribution during the Little Ice Age (LIA) were generated. The results revealed that since LIA the volume of Snezhnika dropped by 123%, and that of Banski Suhodol by 83%. Both glacierets reached maximum thickness values 5 m greater than the present ones during LIA. For the first time, ERT measurements and miniature thermistors were used to investigate ground ice occurrence in the vicinity of the Pirin's glacierets. The ERT measurements revealed no glacial ice in the proglacial area of Banski Suhodol nor in the frontal moraine. Ice-rich frozen debris and frozen sediments without massive ice occur downslope the glacieret on a slope covered by loose rock deposits. Based on the ground surface thermal data, permafrost appears likely on this scree slope, where persistent or late lying snow cover occurs regularly. Our investigation revealed that permafrost is not necessarily related to rock glaciers occurrence in the Balkan Peninsula.
... The choice of the basal shear stress is thus considered the major source of uncertainty in our glacier reconstructions. Since it is unrealistic that the driving stress of topographically constrained glaciers is entirely supported by the basal shear stress (Benn and Hulton, 2010), the ice thickness at points along glacier flowlines in topographically constrained areas was recalculated by incorporating a dimensionless shape factor (f). It was derived from automatically created cross-sections using the 'automatic ice thickness recalculation with f factor' tool in GlaRe. ...
Article
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During the Late Pleistocene, an ice cap temporarily rested on the highest summit of the Black Forest, Feldberg, and on the surrounding region. Moraines inside the last glaciation maximum ice extent document subsequent glacial standstills and/or re-advances, but the chronology of the deglaciation remains largely unknown. In Sankt Wilhelmer Tal, moraines were mapped, and suitable moraine boulders were sampled for ¹⁰Be cosmic ray exposure (CRE) dating. Equilibrium line altitudes (ELAs) during moraine formation were reconstructed to evaluate whether these can be used for local stratigraphical correlations. Geomorphological mapping revealed numerous ice-marginal positions in the main valley and in two tributary valleys. CRE ages and ELAs indicate two discrete phases of glacial standstills and/or re-advances by 17–16 ka at the latest and no later than 14 ka, respectively. Differing ELAs across the study area preclude the use of ELAs for local stratigraphical correlations. Recalculated ¹⁰Be CRE ages from other localities in Central Europe indicate similar periods of moraine formation, thus raising the question of a common climatic forcing. Additional sets of CRE ages are needed to answer this question. In addition, future studies should concentrate on determining the age of the last glaciation maximum in the Black Forest.
... The 3D ice surface position was reconstructed in a GIS environment based on mapped distribution of the landforms of glacial accumulation (moraines, scattered erratic boulders) and erosional features (U-shaped valleys, trimlines) (Benn et al., 2005). Ice thickness was assessed along the flowline using a glacier profile model (Benn and Hulton, 2010) provided in the Pellitero et al. (2015) toolbox with the use of 50-100 kPa basal shear stress values (Cuffey and Paterson, 2010) and a calculated valley shape factor. Ice thickness was adjusted to the mapped glacial landforms by fine-tuning their thickness using the basal shear stress values. ...
Article
The Chornohora and Svydovets massifs represent the highest part of the Ukrainian Carpathians (2061 m a.s.l.) and the north-eastmostmountain area in Europe, which was subject to mountain glaciation during the Quaternary. This region represents one of the least explored areas in terms of glacial geomorphology in Europe, which is crucial for validating the inferred zonal/meridional mode of atmospheric circulation on the continent during glacial stages. Based on new mapping of glacial landforms and sediments, we reconstruct the extent and ice-surface geometry as well as establish equilibrium line altitudes (ELAs) using the Area-Altitude-Balance-Ratio method for 40 palaeo-glaciers in the study area during the local Last Glacial Maximum (LLGM). Additionally, we list the inventory and morphometric characteristics of glacial cirques in the studied massifs (n = 77), which together with the local ELA pattern are discussed in the context of palaeo-wind directions and dominant precipitation patterns during the LGM. ELA values for the Svydovets (1401 m a.s.l.) and Chornohora (1516 m a.s.l.) massifs were much lower than those for the Rodna Mountains (1697 m) in the Northern Romanian Carpathians located 80 km to the southeast, and for the Tatra Mountains (1580 m) located 350 km to the northwest. In the Ukrainian Carpathians both glacier ELA and cirque elevations show a rising trend towards the southeast of 4 m km−1 controlled by preferential moisture transport from the northwest. This suggests that the dominant W-NW precipitation regime in effect during the LGM was similar to present-day conditions. This supports a previous glacial-geomorphologic reconstruction from the Rodna Mountains in Northern Romania and is in line with both model simulations and regional palaeo-wind proxies that show an enhanced mid-latitude North Atlantic zonal circulation pattern over central Europe during the LGM.
... Generally, the low-lying valley mouths required a lower shear stress (50 kPa) to yield realistic ice-thicknesses, which is compatible with the glacier overriding thicker sediment fills with low yield strength at these locations (Thorp, 1991;Iverson et al., 2003). For the steep glacial troughs of the Basson and Bassa valleys, an additional F-factor adjustment, which is a function of the glacier width and thickness, was applied to account for lateral drag exerted by the valley walls (Nye, 1952;Benn & Hulton, 2010;Pellitero et al., 2016). ...
Article
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Small, peripheral mountain glaciers that remained independent from the large ice-streams throughout the Pleisto-cene glaciations represent an important source of paleoclimatic information in the European Alps. Here, we present new evidence on the evolution of the Silisia Valley and paleoglaciers on the northern side of Mount Raut (Carnic Prealps, NE Italy). The area is characterized by the presence of a variety of sediments and landforms, among them two generations of conglomerates and several deposits of glacigenic origin. The conglomerates are related to the infill and subsequent incision of the Silisia Valley during Plio (?)-Pleistocene times, whereas most of the glacigenic deposits can be ascribed to glacier advances during the Last Glacial Maximum (LGM) and following Late Glacial stadials. During the LGM, the glacial system extended from the headwalls of Mount Raut (2026 m a.s.l.) down to an elevation of 440 m, and had an equilibrium line altitude (ELA) of 1260 m (Accumulation-Area-Balance Ratio method-AABR). Assuming present-day amounts of precipitation, this corresponds to a mean summer air temperature (MSAT) depression of 8.5 or 9.4°C (V =±2.2°C), when compared to two recent (1960-1990) climatic records in the area. Two phases of glacier stabilization during the Late Glacial were inferred from frontal moraine systems at higher elevations. During the first one, the glaciers had an ELA of 1590 m (corresponding to an MSAT lowering of 6.2 or 7.1°C), whereas at the second one the ELA was at 1740 m (MSAT lowering of 5.3 or 6.1°C). Our results allow to better understand the long-term Pleistocene evolution of this sector of the southeastern Alps, probably driven by the interplay between climatic fluctuations and phases of tectonic uplift. We further provide new insights on paleoglaciers of the last glacial cycle that may help in the validation of regional climatic models.
... Glacier reconstruction was performed in the GIS environment based on the mapped distribution of moraines and scattered erratic boulders . Ice thickness was assessed along the flowline using a glacier profile model (Benn and Hulton, 2010) provided in the Pellitero et al. (2015) toolbox with the use of basal shear stress values 50 to 100 kPa (Cuffey and Paterson, 2010) and a calculated valley shape factor. Ice thickness was adjusted to the mapped glacial landforms by fine-tuning their thickness using the basal shear stress values. ...
Article
In the Northern Romanian Carpathians (NRC) small Pleistocene cirque glaciers have formed in several isolated mountain massifs exceeding 1800 m asl. This paper brings forward new geomorphological evidence of marginal glaciation in the Călimani, Suhard, and Gurghiu Mountains which are the southernmost glaciated areas of the NRC. We reconstructed the extent and ice-surface geometry for 12 palaeo-glaciers in the study area during the Maximal Ice Extent (MIE) which is attributed to LGM. The equilibrium line altitudes (ELAs) calculated using the area-altitude-balance-ratio (AABR) 1.6. were between 1740 m and 1870 m which is the highest value in the Eastern Carpathians and one of the highest in the entire Carpathians. The specific features of the Călimani and Gurghiu Mountains are the extensive, gentle outer slopes of volcanic calderas that play an important role as additional areas for snowblow accumulation. Inclusion of the potential snow contribution area (snowblow and avalanche accumulation) in the ELA calculation resulted in an additional upward ELA shift up to 66 m (up to 40% of the glacier elevation range). Our data indicate that small cirque glaciation in the NRC could develop when mountain ranges are at least 100 m above the extrapolated regional ELA. The general ELA pattern in the NRC shows a positive trend (∼3 m/km) which could reflect both the general rise in temperature and the starvation of precipitation toward the southeast. However, the observed eastward ELA rise on W-E transects in the Eastern Carpathians shows a pure precipitation effect and indicates the influence of zonal atmospheric circulation in the far interior of Europe during the LGM.
... A three-dimensional palaeoglacier reconstruction was carried out for the different glacial phases using the 'GLaRe' ArcGIS toolbox developed by Pellitero et al. (2016) and a 10-m resolution DEM, which implements a perfect-plasticity physical-based numerical model (Van der Veen 1999; Benn and Hulton 2010) that reconstructs past ice thickness assuming an average shear stress of 100 kPa along a set of flowlines (Paterson 1994;Benn and Hulton 2010). And finally, equilibrium-line altitudes (ELAs) were calculated using the automatic toolbox developed by Pellitero et al. (2015) through the methods Accumulation Area Ratio (Porter 1975; AARs: 0.6 ± 0.05) and the Area Altitude Balance Ratio (AABR; Osmaston 2005). ...
Article
Full-text available
The Upper Garonne Basin included the longest glacier in the Pyrenees during the Late Pleistocene. During major glacial advances, the Garonne palaeoglacier flowed northwards along ~ 80 km from peaks of the axial Pyrenees exceeding 2800–3000 m until the foreland of this mountain range at the Loures–Barousse–Barbazan basin (LBBb), at 420–440 m. Here, the palaeoglacier formed a terminal moraine complex that is examined in this work. Based on geomorphological observations and a 12-sample data set of ¹⁰Be Cosmic-Ray Exposure (CRE) ages, the timing of the maximum glacial extent was constrained as well as the onset of the deglaciation from the end of the Last Glacial Cycle (LGC). Chronological data shows evidence that the external moraines in this basin were abandoned by the ice at the end of the Penultimate Glacial Cycle (PGC) and the onset of the Eemian Interglacial, at ~ 129 ka. No evidence of subsequent glacial advances or standstills occurred during the LGC in this basin were found, as the few existing datable boulders provided in the internal moraine showed inconsistent ages, thus probably being affected by post-glacial processes. The terminal basin was already deglaciated during the global Last Glacial Maximum at 24–21 ka, as revealed by exposure ages of polished surfaces at the confluence of the Garonne-La Pique valleys, 13 km south of the entrance of the LBBb. This study introduces the first CRE ages in the Pyrenees for the glacial advance occurred during the PGC and provides also new evidence that glaciers had already significantly shrunk during the LGM.
... The reconstructed glaciers were created using the GlaRe (Glacier Reconstruction) ArcGIS toolbox (Pellitero et al., 2015) which represent a semiautomated method of glacier reconstruction. Ice thickness was assessed along the flowline using a glacier profile model (Benn and Hulton, 2010) using basal shear stress values 50 to 100 kPa (Cuffey and Paterson, 2010) and a calculated valley shape factor. Ice thickness was adjusted to the mapped glacial landforms by fine-tuning their thickness using the basal shear stress values. ...
... The estimated ice thicknesses, together with the elevation of contemporary glacier-adjacent terrain (LINZ, 2011) were combined using the MATLAB RegulariseData3D function to generate an ice-free topography in the (currently) glacierised catchment at 100 m resolution. The ArcGIS Glacier Reconstruction (GlaRe) toolset (Pellitero et al., 2016) was then used to generate an approximated bare-ice glacier surface from a central flowline using a 2D perfect-plasticity central difference model (Benn and Hulton, 2010). The model initialisation point at the glacier terminus was defined from historical imagery from 1904, when the terminus was~100 m from the LIA moraine (Fig. 3). ...
Article
Flood reconstruction is essential for establishing magnitude-frequency relationships and assessments of contemporary geohazards and risks. Traditionally, flood reconstructions rely upon the analysis of evidence acquired from a single discipline. This lack of integration limits the insights into a flood's source, pathway, and receptors (i.e. impacts). Here, our aim is to test the integration of qualitative historical documentary material with quantitative geomorphological and sedimentological evidence to reconstruct glacial lake outburst floods (GLOFs) in 1913 at Kea Point, Mount Cook National Park, Aotearoa New Zealand. Written documentary records show that, following heavy rainfall, GLOF events occurred in January and March, after the temporary impoundment of water between the glacier surface and lateral moraine. Peak flood discharge was estimated from slope-area and exposed boulder measurements as 316–1077 m³s⁻¹ and 496–1622 m³s⁻¹ respectively. Sedimentological information, combined with geomorphic mapping, a DEM derived from Structure from Motion (SfM) photogrammetry, and satellite imagery was used to describe the overall physical impact of the GLOF. Information from written documentary records, however, enabled a more detailed reconstruction of the timeline of the two floods and their impacts proximate to the original ‘Hermitage Hotel’, which was subsequently relocated. Our integrated approach exemplifies the informative level of multi-faceted detail that can be retrieved for historical flood events. We propose a framework for future studies that seek to reconstruct flood events and their source, pathway and receptors through combining evidence from historical documents/artefacts, sedimentological/geomorphological data, and integration with environmental monitoring/modelling outputs.
... A three-dimensional palaeoglacier reconstruction was carried out for the different glacial phases using the 'GLaRe' ArcGIS toolbox developed by Pellitero et al. (2016) and a 10-m resolution DEM, which implements a perfect-plasticity physical-based numerical model (Van der Veen 1999; Benn and Hulton 2010) that reconstructs past ice thickness assuming an average shear stress of 100 kPa along a set of flowlines (Paterson 1994;Benn and Hulton 2010). And finally, equilibrium-line altitudes (ELAs) were calculated using the automatic toolbox developed by Pellitero et al. (2015) through the methods Accumulation Area Ratio (Porter 1975; AARs: 0.6 ± 0.05) and the Area Altitude Balance Ratio (AABR; Osmaston 2005). ...
Preprint
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The Upper Garonne Basin included the longest glacier in the Pyrenees during the Late Pleistocene. During major glacial advances, the Garonne palaeoglacier flowed northwards along ~ 90 km from peaks of the axial Pyrenees exceeding 2,800-3,000 m until the foreland of this mountain range at the Loures-Barouse-Barbazan basin, at only 420–440 m. Here, the palaeoglacier formed a terminal moraine complex that is examined in this work. Based on geomorphological observations and a 12-sample dataset of 10Be Cosmic-Ray Exposure (CRE) ages, we have constrained the timing of the maximum glacial extent as well as the onset of the deglaciation from the end of the Last Glacial Cycle (LGC). Chronological data shows evidence that the external moraines in this basin were abandoned by the ice at the end of the Penultimate Glacial Cycle (PGC) and the onset of the Eemian Interglacial, at ~ 129 ka. No evidence of subsequent glacial advances or standstills occurred during the LGC in this basin were found, as the few existing datable boulders provided in the internal moraine showed inconsistent ages, thus probably being affected by post-glacial processes. The terminal basin was already deglaciated during the global Last Glacial Maximum at 24 − 21 ka, as revealed by exposure ages of polished surfaces at the confluence of the Garonne-La Pique valleys, 13 km south of the entrance of the Loures-Barousse-Barbazan basin. This study introduces the first CRE ages in the Pyrenees for the glacial advance occurred during the PGC and provides also new evidence that glaciers had already significantly shrunk during the LGM.
... In the case of the Sofía Peak, the sample SO-3 (41.6 ± 2.8 ka) was obtained at a gentle local divide separating divergent ice flow directions (Lavoie et al., 2015). Here, the ice velocity and flow would have been very limited as basal shear stress tends to diminish towards zero as the divide is approached (Benn and Hulton, 2010). Therefore, inefficient erosion would not have removed the inherited nuclides and consequently, the apparent exposure age of 41.6 ± 2.8 ka (SO-3) would not indicate the timing of the last deglaciation but the accumulation of different exposure periods. ...
Article
Full-text available
The small ice caps distributed across the Antarctic Peninsula region have undergone large ice volume changes since the Last Glacial Cycle, in line with most of the Antarctic continent. While the surface extent of glacial shrinking is relatively well known, the timing of glacial oscillations and the magnitude of ice thinning remain little investigated. Cosmic-Ray Exposure (CRE) dating applied on ice-free vertical sequences can provide insights about the temporal framework of glacial oscillations. However, the potential occurrence of nuclide inheritance may overestimate the real timing of the last glacial retreat. This problem has been observed in many areas in Continental Antarctica, but similar studies have not yet been conducted in environments of the Maritime Antarctica, such as the South Shetland Islands (SSI). This research focuses on the Hurd Peninsula ice cap (HPIC, ca. 60°22′ W, 62°40’ S), located in the SW of Livingston Island, SSI. Past climate oscillations since the Last Glacial Cycle have determined the amount of ice stored in the ice cap. Today, this polythermal ice cap is surrounded by several nunataks standing out above the ice. Three of them have been selected to explore their deglaciation history and to test the potential occurrence of nuclide inheritance in deglaciated bedrocks associated with polythermal glaciers. We present a new dataset with 10 10Be exposure dates. Some of them were found to be anomalously old, evidencing that nuclide inheritance is present in bedrocks associated with polythermal ice caps and suggesting complex glacial exposure histories. We attribute this to limited erosion, given the gentle slope of the nunatak margins and the cold-based character of the surrounding ice. The remaining samples allowed to approach local surface-elevation changes of the HPIC. Our results suggest that ice thinning started during the Last Glacial Maximum (LGM) at ∼22 ka but intense glacial shrinking occurred from ∼18 to ∼13 ka, when the nunataks became exposed, being particularly intense at the end of this period (∼14–13 ka) coinciding with the time of the meltwater pulse 1a (MWP-1a) and the end of the Antarctic Cold Reversal (ACR).
Article
La altitud de la línea de equilibrio de los glaciares nos indica en qué punto el glaciar está en equilibrio con el clima, en ese punto la cantidad de masa ganada es equivalente a la que se pierde. Es muy común la utilización de la altitud de la línea de equilibrio glaciar como indicador climático, por ello se hace necesario disponer del estado actual de los glaciares, o de su estado durante la época de cuando se quiere reconstruir el clima. Para obtener estos datos es necesario disponer de la superficie, e idealmente, del volumen de los glaciares. Para obtener estas delimitaciones se propone una metodología de trabajo que empieza por realización de esquemas geomorfológicos con el objetivo de poder deducir los límites alcanzados por el hielo en otras épocas y posteriormente proceder a su reconstrucción y al cálculo de las líneas de equilibrio glaciar. Este estudio presenta el estado del arte de las metodologías y los procedimientos utilizados en las últimas décadas para realizar reconstrucciones glaciares y calcular la altitud de las líneas de equilibrio glaciar.
Article
Using a suitable rescaling of the independent variable, a Lagrangian is found for the nonlinear Vialov equation ruling the longitudinal profiles of glaciers and ice caps in the shallow ice approximation. This leads to a formal analogy between the (rescaled) Vialov equation and the Friedmann equation of relativistic cosmology, which is explored. This context provides a new symmetry of the (rescaled) Vialov equation and gives, at least formally, all its solutions using a generating function, which is the Nye profile for the degenerate case of perfectly plastic ice.
Article
Although numerous global Last Glacial Maximum (gLGM) dating-based paleoclimatic and paleoglacial reconstructions exist for the Tibetan Plateau, no such study is available for the mountains to the Tibetan Plateau's east. Mount Taibai lies east of the Tibetan Plateau, and is known to have experienced glaciation during the Quaternary. In this study, optically stimulated luminescence (OSL) dating was employed to determine the ages of two lateral moraines in the Eryehai Valley on Mount Taibai. The ages obtained were 22.1 ± 1.7–18.7 ± 1.1 ka and 25.8 ± 1.8–24.3 ± 1.5 ka, constrain the timing of the gLGM glaciation in the study area. Using GlaRe and equilibrium-line altitude (ELA) calculations, these two toolboxes, based on a Geographic Information System (GIS), were used to reconstructed the extent of the study area's paleoglacial surface and the ∆ELA. The glacial coverage and ELA for the gLGM in the Eryehai Valley on Mount Taibai were 0.17 km³ and 3351.5 ± 5 m above sea level (asl), respectively. This gLGM ELA is lower than the modern theoretical ELA (4816.5 m asl) by 1465 ± 5 m. From the sporopollen records of the Zoigê Basin in the northwestern Mount Taibai, the precipitation during the gLGM period was equivalent to 60–80% of the present, combined with this record, ∆ELA-based models of the precipitation–temperature relationship (P-T) and the temperature lapse rate (LR) model at the ELA indicate that this area was 7.0–9.4 °C colder during the gLGM. Combined with other paleoclimatic proxies, a decrease in temperature emerges as the primary driver of glaciation during the gLGM on Mount Taibai. Paleoclimatic reconstructions of paleoglaciers on the Tibetan Plateau and its adjacent mountains also indicate that a drop in temperatures was the principal driver of glacial advances in these regions during the gLGM. Regions affected by the East Asian Monsoon, the Indian Monsoon and the Westerlies would have experienced a greater cooling during the gLGM, while regions blocked by high mountains, and therefore less affected by monsoons and westerly winds, would have seen less cooling.
Article
Reconstructions of former ice sheets and glaciers provide important palaeoglaciological information about their behaviour in response to climate changes. Glacial trimlines record both the margin positions and palaeo ice thickness, enabling the production of empirically constrained 3-Dimensional reconstructions. However, the literature review into the characteristics, interpretation, and use of glacial trimlines here presented shows that these features have been under-utilised and are poorly described in the existing literature, with a confusing terminology currently in use. A new classification scheme and terminology for trimline identification and interpretation is developed to better facilitate further research into these common features of glacierised and formerly glaciated landscapes.
Article
The long-term cyclicity and temporal succession of glacial-periglacial (or deglacial) periods or epochs are keynotes of Quaternary geology on Earth. Relatively recent work has begun to explore the histories of the mid- to higher-latitudinal terrain of Mars, especially in the northern hemisphere, for evidence of similar cyclicity and succession in the Mid to Late Amazonian Epoch. Here, we carry on with this work by focusing on Protonilus Mensae [PM] (43–49⁰ N, 37–59⁰ E). More specifically, we discuss, describe and evaluate an area within PM that straddles a geological contact between two ancient units: [HNt], a Noachian-Hesperian Epoch transition unit; and [eHT] an early Hesperian Epoch transition unit. Dark-toned terrain within the eHt unit (HiRISE image ESP_028457_2255) shows continuous coverage by structures akin to clastically-sorted circles [CSCs]. The latter are observed in permafrost regions on Earth where the freeze-thaw cycling of surface and/or near-surface water is commonplace and cryoturbation is not exceptional. The crater-size frequency distribution of the dark-toned terrain suggests a minimum age of ~100 Ma and a maximum age of ~1 Ga. The age estimates of the candidate CSCs fall within this dispersion. Geochronologically, this places the candidate CSCs among the oldest periglacial landforms identified on Mars so far, by at least one and possibly two orders of magnitude. Unit HNt is adjacent to unit eHt and shows surface material that is relatively light in tone. The coverage is topographically irregular and, at some locations, discontinuous. Amidst the light-toned surface, structures are observed that are akin to clastically non-sorted polygons [NSPs] and polygonised thermokarst-depressions on Earth. Terrestrial polygon/thermokarst assemblages occur in permafrost regions where the freeze thaw cycling of surface and/or near-surface water is commonplace and the permafrost is ice-rich. The crater-size frequency distribution of the light-toned terrain suggests a minimum age of ~10 Ma and a maximum age of ~100 Ma. The age estimates of the candidate ice-rich assemblages fall within this dispersion. Geochronologically, this places them well beyond the million-year ages associated with most of the other candidate ice-rich assemblages reported in the literature. Stratigraphically intertwined with the two possible periglacial terrains are landforms and landscape features (observed or unobserved but modelled) that are indicative of relatively recent glaciation (~10 Ma - 100 Ma) and glaciation long past (≥ ~ 1 Ga) to decametres of depth: glacier-(cirque) like features; viscous-flow features, lobate-debris aprons; moraine-like ridges at the fore, sides and midst of the aprons; and, patches of irregularly shaped (and possibly volatile-depleted) small-sized ridge/trough assemblages. Collectively, this deeply-seated intertwining of glacial and periglacial cycles suggests that the Mid to Late Amazonian Epochs might be more Earth-like in their cold-climate geology than has been thought hitherto.
Article
The quantitative reconstructions of past climate changes on the Tibetan Plateau derived from glacial record based on glacier-climate models have been reported in existing researches. However, compared with low altitude areas and the vast majority parts of the Tibetan Plateau, modeled paleoclimate conditions from glacial record are still lack. This hampers the advancing understanding of regional climate–glacier interactions. The glacial history of Burhan Budai Shan provides an opportunity to reconstruct paleoclimate conditions since the penultimate glacial cycle. We applied a coupled mass balance and ice flow model to estimate paleoclimate during the early Holocene, MIS3 and penultimate glacial cycle. On the southern model domain, the model results suggested that the temperature drops ranged from −0.5~0.1 °C and 2.4~3.9 °C with precipitation being 140~200% and 30~100% of present during the MIS3 and penultimate glacial cycle, respectively. On the northern model domain, the early Holocene temperature was lower than present levels by 0.5~1.5 °C which presented separate evidence for the early Holocene precipitation being 80~150% of modern values. The model results in the model domain are generally consistent with other climate records on the Tibetan Plateau.
Article
Glaciers provide an impressive application of fluid mechanics and materials, and thermal physics. The basic microphysical properties of ice determine the shape of a glacier or ice cap. The order of magnitude of the maximum ice thickness is predicted using Weisskopf’s heuristic argument for the maximum height of a mountain, which involves only the specific latent heat of fusion and the acceleration of gravity. The local thickness of a glacier depends on the assumed ice rheology. The equations describing the steady state longitudinal glacier profile differ greatly for perfectly plastic ice and for ice following Glen’s law. Analytical solutions of these equations are derived: they fit well the data for ice caps but less so for alpine glaciers. Volume-area scaling, a major tool of glaciology, is discussed in relation with glacier profiles.
Article
Owing to the remoteness of the Longriba area and the lack of dating records, it is extremely challenging to reconstruct the chronology and extent of the paleoglaciers in this area. In this paper, we combined limited observational data with automated modelling for paleoglacial reconstructions. We first identified a broadly distributed paleoglacier from satellite imagery and field investigation based on the sediment-landform assemblage principle and dated it to 23.1±1.4∼19.5±1.2 ka by 10Be exposure dating, corresponding to the global Last Glacial Maximum (gLGM). Then, we reconstructed the extent and ice surface of 171 paleoglaciers formed during the similar period based on geomorphological evidence and ‘ice surface profile’ modelling. The results showed that the paleoglacial coverage was 426.5 km2, with an ice volume of 38.1 km3, in the Longriba area. The reconstructed equilibrium line altitudes (ELAs) based on modelled ice surfaces yielded an average of 4245±66 m above sea level (asl), ∼725±73 m lower than the present ELA (4970±29 m asl). The temperature was ∼5.51–6.68 °C lower, and the precipitation was ∼30–34% less in Longriba, during the gLGM compared to the present day. This glacial advance was mainly driven by colder climate that was synchronous with Northern Hemisphere cooling events.
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The studied dataset from the Southern Carpathians permitted the quantification of a considerable amount of inherited ¹⁰Be in the glacial boulders and bedrock samples the cirque area. The samples from the glacial phases of largest extension display no signs of significant inheritance, and enabled the establishment of a deglaciation chronology in the southern valleys of the Retezat Mts. The timing of the maximum glacier extent (20.6+0.8/−1.3 ka) coincided with the Last Glacial Maximum, which was followed by five deglaciation phases during the Lateglacial having partly overlapping ages due to fast glacier retreat (at 18.4+0.7/−1.1 ka; 16.9 ± 0.9 ka, 15.8+0.9/−0.6 ka, 15.6 +0.8/−0.8 ka and 14.4 ± 0.5 ka) but could be distinguished by the position of their terminal moraines. This is the first study providing evidence on the maximum ice extent coinciding with the Last Glacial Maximum and subsequent fast deglaciation during the Lateglacial in several valleys of the Retezat Mts. The currently available geochronological data do not support the assumption of any major glacial re-advance after Greenland Stadial 2.1a in the Retezat Mts. Given the lack of independent geochronological data, the amount of inherited cosmogenic nuclides is tentatively estimated by accepting the youngest cosmic ray exposure age(s) as the time of moraine deposition and abandonment by the glacier. The calculated amount of inherited ¹⁰Be enables the estimation of a glacial erosion depth of 1.1–1.6 m for the bedrock samples and 1.4–1.8 m for the glacial boulders. The duration of the ice-covered and ice-free periods was adjusted in relation to independent paleoenvironmental and paleoclimatological data. The glacial denudation rate in the cirques was estimated at 19–28 mm/kyr and 24–33 mm/kyr for bedrock and boulders, respectively. The limited glacial erosion in the cirques during the last glaciation is attributed to frozen-bed conditions with no considerable glacial deepening during the more extended glacial phases. Only when warming led to the retreat of the glaciers to their cirques, they become steeper and shift to being warm-based and thus more erosive. However, the limited time spent under these conditions appears to be too short to remove material from the cirque floors in sufficient depth (>3 m) to reset the cosmogenic clock. This suggests that the development of the cirques must have taken place during several subsequent glacial phases, providing an indirect confirmation of repeated Quaternary glaciations in the Retezat Mts.
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The flow of valley glaciers is examined in the light of recent laboratory experiments on the behaviour of ice under load. Simple expressions are given for the velocity distributions in some cases of laminar flow, and the modification of a pure laminar flow theory necessary to explain the formation of transverse crevasses and thrust planes is considered. The paper ends with some remarks about the formation of crevasse patterns on the surfaces of glaciers. The statical equilibrium of a circular ice cap is discussed in an appendix.
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At Hardangerjøkulen, central southern Norway, detailed knowledge of the number, age and magnitude of Holocene glacier fluctuations is used to reconstruct variations in equilibrium-line altitude (ELA) for the last 10 000 years. Present and past ELAs are based on an accumulation-area ratio (AAR) of 0.7 and are adjusted for land uplift. A synchronous relationship between advanced glacier positions and the highest pine-tree limits (Pinus sylvestris L.) is demonstrated for the early to mid-Holocene in southern Scandinavia, which indicates that warm summers were compensated for by high winter precipitation. Based on pine-tree limit fluctuations as a measure of mean ablation-season temperature, Holocene variations in winter precipitation at Hardangerjøkulen have been calculated by substitution in the close exponential relationship between mean ablation-season temperature and winter precipitation at the ELA of Norwegian glaciers. Setting the winter precipitation during the period AD 1961-1990 at 100%, mean values varied from about 65 to c. 175%. The wettest phase, at c. 8500-8300 cal. BP, experienced a mean summer temperature of c. 1.35°C warmer than at present, and may be regarded as a climatic analogue for the increase in precipitation which may accompany greenhouse warming of the atmosphere during the next century. These early-Holocene 'greenhouse centuries' ended abruptly within 30-50 years, and changed into a climatic regime dominated by dry winters and by summers only a little warmer than at present. The transition is synchronous with the most notable δ 18O minimum recorded in Greenland ice cores at 8210 ± 30 years ago (before AD 1990), and is tentatively suggested as a Holocene analogue for the climatic instability (which may have been) recorded in the GRIP ice core during the last interglacial period (the Eemian).
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The flow of valley glaciers is examined in the light of recent laboratory experiments on the behaviour of ice under load. Simple expressions are given for the velocity distributions in some cases of laminar flow, and the modification of a pure laminar flow theory necessary to explain the formation of transverse crevasses and thrust planes is considered. The paper ends with some remarks about the formation of crevasse patterns on the surfaces of glaciers. The statical equilibrium of a circular ice cap is discussed in an appendix.
Article
This new edition of a successful textbook will supply advanced undergraduate and graduate students with the tools they need to understand modern glaciology. Practicing glacial geologists and glaciologists will also find the volume useful as a reference book. Relatively simple concepts are followed by more mathematically advanced chapters. Student exercises are included.
Article
Fundaments of Glacier Dynamics presents an introduction to modelling the flow and dynamics of glaciers. The emphasis is more on developing and outlining procedures than on providing a complete overview of all aspects of glacier dynamics. Derivations leading to frequently-used equations are presented step-by-step to allow the reader to grasp the mathematical details and approximations involved and gain the understanding needed to apply similar concepts to different applications. The first four chapters discuss the background and theory needed for glacier modelling. The central part of the book discusses simple analytical solutions and time-evolving numerical models that are used to study general aspects of glacier dynamics and important feedback mechanisms. The final three chapters discuss applications specific to smaller mountain glaciers, the Greenland Ice Sheet, and the Antarctic Ice Sheet, respectively. This book will be suitable for graduate courses in geophysics and will also serve as a reference volume for scientists active in all aspects of glaciology and related research. Standard undergraduate mathematics and physics are sufficient background for studying the text.
Article
This new edition of a successful textbook will supply advanced undergraduate and graduate students with the tools they need to understand modern glaciology. Practicing glacial geologists and glaciologists will also find the volume useful as a reference book. Relatively simple concepts are followed by more mathematically advanced chapters. Student exercises are included.
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Geomorphological mapping in the West Drumochter Hills provides evidence of a readvance of locally nourished glaciers during the Loch Lomond (Younger Dryas) Stade, in the form of an icefield 67.7 km2 in area drained by outlet glaciers. The icefield limits accord broadly with those proposed by Sissons (1980) but all geomorphic, stratigraphic and sedimentological evidence conflicts with a recent proposal that the landforms in the area reflect southwestwards retreat of the last ice sheet. Up-valley continuity of recessional moraines indicates that the ice remained active and close to climatic equilibrium during the earlier stages of glacier retreat, consistent with slow warming following the coldest part of the stade. The pattern of equilibrium line altitudes (ELAs) across the icefield is consistent with transfer of snow by westerly and southerly winds. The ELA of the reconstructed icefield as a whole is 622–629 m, although this figure is likely to be lower than the regional (climatic) ELA because the icefield probably received additional snow blown from adjacent plateau surfaces and slopes. Inclusion of potential snow-blow areas in the ELA calculation yields a value of 648–656 m; the climatic ELA is therefore likely to have lain between 622 and 656 m. Mean June to August temperature at the ELA, based on chironomid assemblages at two sites, falls within the range 4.0 ± 0.7°C. Empirical relationships between temperature and precipitation at modern glacier ELAs indicate that mean annual precipitation (MAP) at the ELA was 1977 ± 464 mm, statistically indistinguishable from modern values. Comparison with precipitation values calculated for the Isle of Mull on the west coast suggest that the precipitation gradient across the Central Highlands of Scotland was steeper during the Loch Lomond Stade than at present, probably as the result of efficient scavenging of precipitation from westerly airflows by the West Highland Icefield. Copyright © 2005 John Wiley & Sons, Ltd.
Article
Unlike other methods of estimating the Equilibrium Line Altitude of present or former glaciers from morphometric data (as distinct from direct observations of the glacier mass balance), the Area×Altitude, the Area×Altitude Balance Ratio and the Area×Altitude Balance Index methods take explicit account of hypsometric differences between glaciers and thus yield more reliable results. In addition they offer the means of applying various mass balance/altitude relationships of increasing complexity and examining which of these is most correct; the last of these methods is newly developed to permit the application of any desired relationship. Their general adoption has been restricted hitherto by computational problems, but this objection is removed by the easy-to-use spread sheets presented in this paper. By whatever method estimates are derived, it is essential to validate the optional variables used in the computations and methods for doing this are set out.
Article
Past fluctuations of tropical and sub-tropical glaciers provide important palaeoclimate proxies for regions where other forms of evidence are rare. However, published equilibrium-line altitude (ELA) estimates for tropical and sub-tropical glaciers at the LGM vary widely, reflecting the diversity of methods and approaches employed by different research groups. This complicates regional and global comparisons of ELA estimates, and emphasises the need for standardised methods. The distinctive character of tropical and sub-tropical glaciers, however, means that standard methods for reconstructing former glacier limits, ELAs, and palaeoclimate need to be adapted for local conditions. Many methods of ELA reconstruction explicitly or implicitly make assumptions about glacier mass balance gradients, and care needs to be taken that the choice of accumulation area ratios (AARs), balance ratios (BRs) and terminus-to-head ratios (THARs) is appropriate, as such indices are influenced by climatic regime, debris cover and other factors. ELA reconstructions should employ multiple methods, and should be cross-checked and fully reported, to allow assessment of the accuracy of ELA estimates. Reliable glacier chronologies are equally important. Dating should be based on multiple radiometric techniques wherever possible, and method of dating, the type of material dated, and the context of the date must all be reported.
Article
With the increasing use of digital elevation models in palaeo-glacier reconstructions and the availability of freeware spreadsheets the Area-Altitude Balance Ratio (AABR) and Balance Ratio (BR) methods are becoming increasingly used in palaeo-glacier reconstruction for estimating Equilibrium Line Altitudes (ELA) and subsequently deriving quantitative estimates of palaeo-climate. While there are many data detailing contemporary Accumulation Area Ratios, there are still only a few studies that have established, from contemporary environments, AABR/BR ratios. Publicly available glacier mass balance (World Glacier Monitoring Service, US Geological Survey, and Norwegian Water Directorate) and spatial extent datasets provided the basis for this research. From a time series of mass balance, regressing specific net balance against ELA allows the zero net balance ELA to be identified. Once the zero balance ELA is established, the glacier hypsometry above and below the ELA is defined. The AABR/BR is calculated by using (the right hand side) the following: where, bnab and bnac are the net mass balance gradients in the ablation and accumulation zones respectively, and are the area-weighted mean altitudes of the accumulation and ablation areas respectively and Aac and Aab are the areas of the accumulation and ablation areas respectively. AABRs are calculated for a suite of glaciers located across a range of climatic zones and glacier types, with Antarctica being excluded. The following “representative” AABRs are found: a global AABR = 1.75 ± 0.71; Mid-latitude maritime = 1.9 ± 0.81; High-latitude = 2.24 ± 0.85; North America – West Coast = 2.09 ± 0.93; North America – Eastern Rockies = 1.11 ± 0.1; Canadian Arctic = 2.91 ± 0.35; Svalbard = 2.13 ± 0.52; Western Norway = 1.5 ± 0.4; European Alps = 1.59 ± 0.6; Central Asia = 1.75 ± 0.56; Kamchatka = 3.18 ± 0.16. This study provides an empirically derived dataset characterising AABR ratios which may be used for ELA estimation in palaeo-glacier reconstructions and for palaeo-climate quantification.
Article
Øksfjordjøkelen is located at ∼ 70° N on the Troms–Finnmark border in North Norway. During the Younger Dryas, it was decoupled from and sat just beyond the margin of the Scandinavian Ice Sheet. At this time the major fjords in Troms and Finnmark were ice-free with outlet glaciers from the icefield filling a number of smaller side valleys. Only one outlet from the icefield, Sörfjorddalen, is temporally well-constrained by 14C dating and association with the Main Shoreline (associated with a period of minimal crustal rebound dated to the Younger Dryas). Sörfjorddalen is reconstructed using a valley centre-line iterative model and assuming a no-slip basal boundary condition. This assumption of cold-based ice is supported by the geomorphological evidence of angular bouldery fronto-lateral moraines formed during the Younger Dryas. The equilibrium line altitude for the Sörfjorddalen is calculated using both the Balance Ratio and Accumulation Area Ratio methods, and this is used to constrain the snout positions (generally to mapped moraines) of the other outlets. This approach assumes similarity of mass balance gradients and geometries of the outlet glaciers which is supported by present-day symmetry of the icefield. This method is extremely useful in such environments where dateable material is often difficult, if not impossible, to find. Some margins terminated in deep water where bathymetry was lacking, making calving quantification problematic with subsequent impacts on equilibrium line altitudes poorly constrained. These deep-water terminating snouts were discounted from subsequent palaeo-climate reconstructions. An empirical equilibrium line altitude temperature-precipitation relationship was used to define limits of climate change required to sustain the reconstructed icefield. Palaeo-precipitation estimates were refined using a palaeo-temperature estimate for the Younger Dryas from Andøya. Calculations of ice flux through the equilibrium line altitude were used to further constrain the mass balance characteristics of the reconstructed icefield and these suggest similarities with ice masses found in the northern (Nordaustlandet) regions of Svalbard.
Plateau icecap landsystems
  • Rea
Rea, B.R., Evans, D.J.A., 2005. Plateau icecap landsystems. In: Evans, D.J.A. (Ed.), Glacial Landsystems..
Fundamentals of Glacier Dynamics. Balkema, Rotterdam 462 pp. D.I. Benn
  • Van
  • C J Veen
Van der Veen, C.J., 1999. Fundamentals of Glacier Dynamics. Balkema, Rotterdam 462 pp. D.I. Benn, N.R.J. Hulton / Computers & Geosciences 36 (2010) 605–610