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Modelling the thermal dynamics of perched permafrost talus slopes: insights from a recently destabilised site (Gislá landslide, October 6th 2020, Iceland)

Modéliser les dynamiques thermiques du permafrost dans les pentes d’éboulis : étude de cas d’un site récemment déstabilisé (glissement de Gislá, 6 octobre 2020, Islande)
Meven Philippe, Florence Magnin, Jean-Yves Josnin, Costanza Morino, Nicolas Monzie et Skafti Brynjólfsson

Résumés

Dans cet article, nous étudions la pente d’éboulis d'Eyjafirði (péninsule de Tröllaskagi, Islande du nord), où un glissement de terrain (une avalanche de débris) s'est produit en octobre 2020. Cet éboulis est situé en dehors des limites climatiques du permafrost, mais des indices géomorphologiques (i.e., des molards présents dans les dépôts de glissement) indiquent que la dégradation de permafrost azonal pourrait faire partie des facteurs déclenchants du glissement de terrain. La dynamique thermique des éboulis est actuellement mal comprise, car la convection de l'air (effet de cheminée) joue un rôle dans la persistance du pergélisol à leur base.

Nous utilisons donc le logiciel FEFLOW pour effectuer des simulations physiques en deux dimensions du transfert de chaleur dans l’éboulis d'Eyjafirði, de -20 000 ans à l’actuel. Nous testons la sensibilité de notre modèle à la porosité initiale/la teneur en glace de l’éboulis (0,3, 0,5 et 0,8), et la conductivité thermique (TC) de la phase rocheuse (0,75, 1,1 et 1,75 W.m-1.K-1).

L’analyse des températures de l’air montre un réchauffement général depuis les dernières ~ 40 années, soutenant l’hypothèse que la dégradation de permafrost pourrait faire partie des facteurs déclenchant du glissement de terrain. Bien que nous ne modélisions pas la convection de l'air, le pergélisol persiste à la base de l'éboulis dans tous les scénarios. L'augmentation de la porosité initiale/de la teneur en glace et la diminution de la TC de la phase rocheuse intensifient cette persistance du pergélisol dans l'éboulis. Notre approche n'est pas conventionnelle, car nous savons que de la glace était présente dans l’éboulis au moment du glissement de terrain. Nous en déduisons donc que la dynamique du pergélisol dans l’éboulis d’Eyjafirði est donc mieux représentée par le scénario avec une TC de 0,75 W.m-1.K-1.

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Notes de la rédaction

Reçu le 10 octobre 2024, définitivement accepté le 22 décembre 2024

Texte intégral

Authors acknowledge funding from the French Agence Nationale de la Recherche in the framework of the projects ANR-19-CE01-0010 PERMOLARDS and ANR-19-CE01-0018 WISPER, from the RETURN Extended Partnership, and from the European Union Next-GenerationEU (National Recovery and Resilience Plan – NRRP, Mission 4, Component 2, Investment 1.3 – D.D. 1243 2/8/2022, PE0000005). The authors are grateful towards Emmanuel Malet who helped with the retrieving of thermal sensors, and towards the two reviewers whose comments greatly improved the overall quality of the manuscript.

1. Introduction

1It has been known for decades that degradation of mountain permafrost can lead to ground destabilisation, and ultimately generate landslides (e.g., Dramis et al., 1995; Lyle et al., 2004; Fischer et al., 2006; Geertsema et al., 2006; Gruber and Haeberli, 2007; Allen et al., 2009; Fischer et al., 2011; Kellerer‐Pirklbauer et al., 2012; Ravanel et al., 2017; Sæmundsson et al., 2018; Karjalainen et al., 2019; Patton et al., 2019; Magnin et al., 2023; Penna et al., 2023; Cathala et al., 2024). Hence, in a context of global climate change, landslides represent an increasing hazard for populations and infrastructures in mountain environments (e.g., Smith, 1990; Smith and Riseborough, 1996; Harris and Vonder Muhll, 2001; Lyle et al., 2004; Harris, 2005; Haeberli et al., 2010; Petley, 2012; Borgatti and Soldati, 2013; Haeberli et al., 2017; Morino et al., 2019; Hjort et al., 2022). It is thus crucial to predict the boundaries of permafrost, in order to be able to locate areas that present a landslide susceptibility.

2Predicting permafrost boundaries is enabled by numerical modelling of ground temperatures. Notably, statistical permafrost models are calibrated with topoclimatic data, and hence allow to model permafrost distribution at the regional or even global scale (e.g., Nelson, 1986; Gruber and Hoelzle, 2001; Guglielmin et al., 2003; Boeckli et al., 2012a, 2012b; Gruber, 2012; Gisnås et al., 2013, 2014 ; Magnin et al., 2015; Gisnås et al., 2016; Deluigi et al., 2017; Czekirda et al., 2019; Magnin et al., 2019; Obu et al., 2019; Wang et al., 2019). It should be noted that previous studies developed methods to downscale climatic data, which enables statistical modelling studies at a more local scale (e.g., Fiddes and Gruber, 2012, 2014; Fiddes et al., 2022; Filhol et al., 2023; Levavasseur et al., 2011; Stendel et al., 2007; Yin et al., 2021; Zhang et al., 2020). However, statistical permafrost models are unable to locate azonal permafrost (i.e., permafrost located beyond its climatic boundaries), as its presence depends on local physical processes (e.g., air circulation) that are not considered in statistical models.

3Physic-based permafrost models differ from statistical models in that they compute physical processes (e.g., heat transfer, hydrology, phase changes of water, air convection) in order to evaluate the presence of permafrost in a given context (e.g., Stocker‐Mittaz et al., 2002; Jafarov et al., 2012; Westermann et al., 2013; Zhang et al., 2013; Staub et al., 2015; Westermann et al., 2016; Magnin et al., 2017; Wicky and Hauck, 2017; Dagenais et al., 2020; Magnin and Josnin, 2021; Cathala et al., 2024; Wicky et al., 2024). Therefore, they are theoretically able to model the presence of azonal permafrost. Due to the numerical challenge that represents the modelling of such complex physical processes, physic-based models are often restricted to the local scale and simple case studies.

4In this scope, studying molards leads to a better understanding of the link between permafrost degradation and landslide generation. Molards are debris cones preserved in landslide deposits in periglacial areas. These landforms are remnants of ice-cemented sediment blocks that were transported within a landslide and then degraded in place (formally described in Morino et al., 2019; see also Lyle et al., 2004; Brideau et al., 2009; Milana, 2016). Molards are particularly useful in permafrost landslide studies, as they represent unequivocal evidence that both frozen and unfrozen material (hence a zone of degrading permafrost) was mobilised in a given landslide (Morino et al., 2019). It was notably observed that unpredicted molard-bearing landslides in Iceland originated from perched talus slopes – i.e., talus debris that accumulated at altitude, on intermediate local plateaus of structural or erosive origin, with an apical location. It suggests that azonal permafrost must be present within the concerned perched talus slopes, and that permafrost degradation could be among the destabilising factors for such landslides (Morino et al., 2019, 2021).

5However, dynamics of permafrost within perched talus slopes are currently poorly understood. Indeed, a talus slope is a complex system where the ‘chimney effect’ can take place. This air circulation effect was suggested to generate, at the base of the talus slope, a zone of maximum cooling in winter and of minimum warming in summer (fig. 1; e.g., Delaloye and Lambiel, 2005; Lambiel and Pieracci, 2008; Phillips et al., 2009; Morard et al., 2010; Millar et al., 2014; Popescu et al., 2017; Wicky and Hauck, 2017; Germain and Milot, 2024; Wicky et al., 2024). Hence, the chimney effect could allow ground ice to develop and persist beyond the predicted boundaries of permafrost. Talus slopes are thus especially good examples of areas that present a landslide risk, and that large-scale/coarse-resolution permafrost model cannot address. Some studies investigated the present state of permafrost within talus slopes, based on ground temperature measurements, geophysical measurements, and fieldwork observations (e.g., Jahn, 1984; Delaloye and Lambiel, 2005; Otto and Sass, 2006; Lambiel and Pieracci, 2008; Phillips et al., 2009; Morard et al., 2010; Scapozza et al., 2011; Bommer et al., 2012; Millar et al., 2014; Kneisel et al., 2015; Staub et al., 2015; Kenner et al., 2017; Popescu et al., 2017; Germain and Milot, 2024). However, only a handful of studies attempted to model numerically the thermal dynamics of talus slopes, at depth and on longer time scales (Tanaka et al., 2006; Wicky and Hauck, 2017; Myhra et al., 2019; Wicky et al., 2024; see Lan et al., 2024 for a review).

Fig. 1 – Schematic diagram of the cross-section of a talus slope, and the internal air circulation caused by the chimney effect a. in winter (Tair < Ttalus), and b. in summer (Tair > Ttalus).
Fig. 1 – Coupe schématique d’une pente d'éboulis et circulation d'air causée par l’effet de cheminée, a. en hiver (Tair < Ttalus), et b. en été (Tair > Ttalus).

Fig. 1 – Schematic diagram of the cross-section of a talus slope, and the internal air circulation caused by the chimney effect a. in winter (Tair < Ttalus), and b. in summer (Tair > Ttalus). Fig. 1 – Coupe schématique d’une pente d'éboulis et circulation d'air causée par l’effet de cheminée, a. en hiver (Tair < Ttalus), et b. en été (Tair > Ttalus).

‘T’ stands for ‘temperature’. Due to convective air circulation, in winter relatively hot air flows from the talus upward which draws in relatively cold air at the bottom of the talus. In summer, relatively cold air within the talus flows downward. The zone of maximum overcooling (winter) and minimum warming (summer) is located schematically with the white dashed box (schematic representation from Wicky and Hauck, 2017). On both panels the arrow indicates the direction of air circulation; its colour indicates the relative temperature gradient within the talus.
‘T’signifie ‘température’. En raison de la convection, en hiver, de l'air relativement chaud s'écoule vers le haut de l’éboulis, ce qui aspire de l'air relativement froid à la base de l’éboulis. En été, de l'air relativement froid s'écoule dans l’éboulis vers sa base. La zone de refroidissement maximal (hiver) et de réchauffement minimal (été) est située approximativement dans la boîte blanche en pointillés (représentation schématique d’après Wicky et Hauck, 2017). Sur les deux figures, la flèche indique la direction de circulation de l'air ; sa couleur indique le gradient de température relatif à l'intérieur de l’éboulis.

6Therefore, in this study we focus on the numerical modelling of the thermal dynamics of permafrost. More specifically, we investigate a perched talus slope that developed on an intermediate plateau, on the Hleiðargarðsfjall mountain. This perched talus slope – further referred to as ‘Gislá talus slope’ – has been the source area of an unpredicted debris avalanche – further referred to as ‘Gislá landslide’ – on October 6th 2020, in the Tröllaskagi peninsula (central northern Iceland), which threatened infrastructures and people. Notably, the presence of molards within the deposits of the Gislá landslide indicates the presence of ground ice within the Gislá talus slope at the date of the failure. Ice-cemented blocks of sediment were observed in the landslide deposits the day of the landslide (6th October 2020; Arnardóttir, 2023), which attests the permafrost origin of observed molards, and proves that the Gislá landslide mobilised ice-cemented sediment.

7We model heat transfer and phase changes of water using the finite element method (Courant, 1943) in two-dimensional (2D) cross-sectional models of the Gislá talus slope, for the past ~ 20,000 years, with thermal constraints obtained from field temperature measurements.

8We seek to answer the following questions: (i) can the occurrence of a chimney effect be characterised at the Gislá talus slope? (ii) Can permafrost be successfully maintained within the Gislá talus slope until the date of the failure? (iii) What was the state of permafrost within the Gislá talus slope at the date of the landslide? (iv) What thermal properties of the Gislá talus slope are required to maintain ice?

2. Study site

9The Gislá landslide (fig. 2a) occurred on October 6th 2020, on the flank of the Hleiðargarðsfjall mountain (65°24'23.60"N, 18°16'5.89"W; Tröllaskagi peninsula, central northern Iceland; fig. 2c). The detachment occurred in the Gislá perched talus slope, a debris accumulation with a slope of ~ 35°. Located on an intermediate plateau 750-800 m a.s.l. with an apical location, the talus slope accumulated over time from the degradation of the upper rock wall (summit around ~ 970 m a.s.l.), itself located within the Tertiary Basalt bedrock formation (Jóhannesson, 2014). The detachment zone of the Gislá landslide is a part of a longer perched talus slope, extending several kilometres north and south (fig. 2d, e). No grain size measurement was performed on the debris constituting the talus slope, but field photos show a diverse surface material, from silt/clay to cobbles/boulders. The landslide material travelled ~ 1800 m horizontally, stopping less than 100 m from a farm – causing no casualty and almost no damage to infrastructure (fig. 2d, e).

Fig. 2 – The Gislá landslide and its geographic context.
Fig. 2 – Le glissement de terrain de Gislá et son contexte géographique .

Fig. 2 – The Gislá landslide and its geographic context.Fig. 2 – Le glissement de terrain de Gislá et son contexte géographique .

a. photo of the Gislá landslide, taken on the day of the landslide, October 6th 2020 (courtesy of J.P. Jónsson, who obtained it from local police agents). Dashed lines indicate approximate altitude levels a.s.l., 750 m a.s.l. representing the elevation of the Gislá talus slope; b. Molard example (approximately 2 m high) within the deposits of the Gislá landslide (photo taken on July 2022); c. Location of the Gislá landslide (white dot; 65°24'24.90"N, 18°16'16.05"W) at the scale of the Tröllaskagi peninsula (central northern Iceland). White crosses locate the weather stations of Öxnadalsheiði (540 m a.s.l.) and Akureyri (31 m a.s.l.). Background: Google Earth – Landsat/Copernicus; d. The Gislá landslide from aerial view. Molards in the landslide deposits are located by white crosses (mapped from Arnardóttir, 2023); e. The local context of the Gislá landslide, with panel d. located by a white rectangle, houses by white dots, and waterways by light blue lines.
a. Photo du glissement de terrain de Gislá, prise le jour du glissement, 6 octobre 2020 (avec la permission de J.P. Jónsson, qui l’a obtenue des agents de police locaux). Les lignes en pointillés indiquent les altitudes approximatives a.s.l., 750 m a.s.l. représentant l’altitude de la pente de débris de Gislá. b. Exemple de molard (approximativement 2 m de haut) au sein des dépôts du glissement de terrain de Gislá (photo prise en juillet 2022) ; c. Localisation du glissement de terrain de Gislá (point blanc ; 65°24'24.90"N, 18°16'16.05"O) à l’échelle de la péninsule de Tröllaskagi (centre nord de l’Islande). Les croix blanches localisent les stations météorologiques de Öxnadalsheiði (col) et d’Akureyri (ville). Fond de carte : Google Earth – Landsat/Copernicus. d. Le glissement de terrain de Gislá en vue aérienne. Les molards présents dans les dépôts du glissement sont localisés par des croix blanches (cartographiés d’après Arnardóttir, 2023) ; e. Le contexte local du glissement de terrain de Gislá. Le panneau d. est localisé par le rectangle blanc, les bâtiments par des points blancs, et les cours d’eau par les lignes bleu clair.

10The Gislá talus slope is located close to the limit of discontinuous permafrost in the model from Obu et al. (2019) (one-kilometre resolution), and outside of the boundaries of permafrost predicted from regional, finer-scale models (Etzelmüller et al., 2007; Lilleøren et al., 2013; Czekirda et al., 2019; Etzelmüller et al., 2020). Molards located in the landslide deposits indicate that some of the mobilised material was ice-cemented (fig. 2b), suggesting that permafrost degradation was possibly among the destabilising factors of the Gislá landslide (Morino et al., 2019).

3. Data and Methods

11In this section, we detail the acquisition and processing of data (i.e., 2D-geometry of the study site and temperature time series) that serve as inputs for the numerical models, and our modelling approach.

3.1. Data

12In order to perform our model runs, we have to characterise the 2D cross-sectional geometry of the Gislá talus slope, and reconstruct surface temperature time series to be used as forcing data.

3.1.1. Site geometry

13Our numerical models require a 2D cross-sectional geometry to be functional; hence, we need: (i) a topographic profile of the talus slope prior to the landslide, and (ii) an estimation of the bedrock topography below the talus.

14To characterise the topography of the Gislá talus slope, we acquired 470 drone photos seven days after the landslide, on October 13th 2020 (equipment: DJI Matrice 600 Pro; Nikon D850 camera; Zeiss Distagon 35 mm lens) to generate a digital elevation model (DEM) and an orthophoto of the study site, with the Structure from Motion photogrammetry method (software: Agisoft Metashape; e.g., Westoby et al., 2012; Fonstad et al., 2013). The final DEM has a resolution of 32 cm/pixel. As the landslide was triggered in 2020, the DEM represents the post-landslide morphology of the Gislá talus slope. To model the thermal dynamics of the talus slope prior to the landslide, we perform a reconstruction of the pre-landslide topography with the semi-automatic method described in Guimpier et al. (2022), using a GIS software (QGIS version 3.28.15). The reconstruction method summarises as follows (fig. 3):

  • generation of contour lines at an interval of 2 metres;

  • delineation of the affected talus slope, based on contour lines and orthophoto;

  • cut-out of the contour lines based on the talus slope delineation (fig. 3a);

  • generation of points every 2 metres along the remaining contour lines (fig. 3b);

  • extraction of elevation values within each point;

  • interpolation of the pre-landslide DEM from the points containing elevation data with the Triangulated Irregular Network method.

Fig. 3 – Main steps of the pre-landslide topographic reconstruction.
Fig. 3 – Principales étapes de reconstitution de la topographie pré-glissement.

Fig. 3 – Main steps of the pre-landslide topographic reconstruction. Fig. 3 – Principales étapes de reconstitution de la topographie pré-glissement.

a. Contour lines cut out according to the delineation of the talus slope (10-metres interval, elevation given every 50 m). Sensors used further in the studies are located by white crosses, and their respective name indicated in italic font; b. Points generated along the contour lines; c. Topographic profile (grey line) selected for defining the surface geometry of the talus slope. Points A and B located on the profile locate the profile shown in panel d; d. Reconstructed pre-landslide topography (black line), measured post-landslide topography (grey line), and estimated bedrock topography (black dashed line) obtained by extrapolation of the bedrock topography around the talus. The extent of this profile is located on the full profile in panel c. In all panels, the white area represents the extent of the studied talus slope, the white crosses in a., b. and c. locate the thermal sensors (Section 3.1.2.), and north is up. White arrows indicate overall slope direction. Background (panels a., b., c.): drone orthophoto.
a. Courbes de niveau découpées selon l’emprise de l’éboulis (intervalle de 10 m, altitude donnée tous les 50 m). Les capteurs utilisés dans la suite de l’étude sont localisés par des croix blanches, et leur nom indiqué en italique ; b. Points générés le long des courbes de niveau ; c. Profil topographique (ligne grise) sélectionné pour définir la géométrie de la surface de la pente d’éboulis. Les points A et B situés sur le profil localisent le profil montré dans le panneau d ; d. Topographie pré-glissement reconstruite (ligne noire), topographie mesurée après le glissement de terrain (ligne grise), et topographie estimée du substratum rocheux (ligne pointillée noire) obtenue par extrapolation de la topographie du substratum autour de l’éboulis. L'emprise de ce sous-profil est localisée sur le profil complet dans le panneau c. Dans tous les panneaux, la zone blanche représente l'étendue de l’éboulis, les croix blanches localisent les capteurs thermiques utilisés (Section 3.1.2.), et le nord est en haut. Les flèches blanches indiquent la direction générale de la pente. Arrière-plan (panneaux a., b., c.) : orthophoto drone.

15We then extract topographic data of the pre-landslide DEM along a selected profile parallel to the slope, located approximately in the middle of the talus slope, and crossing the detachment scarp of the landslide (fig. 3c, d).

16To estimate the bedrock topography below the talus, we extract topographic data from the post-landslide DEM along the selected profile. At the bottom of the talus, we extrapolate upslope the average slope of the bedrock exposed by the landslide; at the top of the talus, we extrapolate downslope the average slope of the bedrock located right above the talus (fig. 3d). In both cases we consider approximately 15 m (horizontally) of bedrock to calculate the average slopes. We consider that the bedrock topography below the talus follows the extrapolated profiles and includes a slope break where the two extrapolations intersect (fig. 3d), forming a terrace on which the talus sits.

3.1.2. Temperature time series

17In order to create temperature time series to be used as boundary conditions in our models, we: (i) measured temperature for about one year at the Gislá talus slope; (ii) compute correlations between our measured data and air temperature datasets that go further back to year 1881; and (iii) compute modelled temperature time series back to -20,000 years based on Etzelmüller et al. (2020). Our approach for reconstructing temperature time series is summarised in a schematic workflow (fig. 4a).

18We installed 18 thermal sensors in the Gislá talus slope and in the surrounding rock wall, that measured temperature with an hourly time step between August 1st 2021 and July 9th 2022. We inserted rock wall sensors into 10 cm depth drilled holes in the bedrock, and we placed talus sensors at various depths (surface to 80 cm deep, in boreholes). Two sensors were placed at each sensor location, to prevent data loss in case one sensor malfunctioned. In some locations, we installed chains of sensors between the surface and the close subsurface. Therefore, the 18 sensors are spread over six sensor locations (fig. 4a).

Fig. 4 – Schematic workflows of our methodological processes.
Fig. 4 – Diagramme workflow de nos processus méthodologiques.

Fig. 4 – Schematic workflows of our methodological processes. Fig. 4 – Diagramme workflow de nos processus méthodologiques.

a. Generation of temperature time series. Input datasets are identified by a regular font, result datasets by a bold font, and processes by an italic font. ‘TS’ stands for ‘time series’; b. Modelling approach for the creation and parametrisation of the numerical models. The main steps are identified by a bold font. The dashed square identifies the steps that are done outside of FEFLOW. ‘BC’ stands for ‘boundary conditions’, ‘TC’ stands for ‘thermal conductivity’.
a. Création des séries temporelles. Les données d’entrée sont identifiées par une police normale, les données résultantes par une police en gras, et les processus par une police italique. ‘TS’ signifie ‘série temporelle’ ; b. Méthode de modélisation de la création et paramétrisation des modèles numériques. Les étapes principales sont identifiées par une police en gras. Le carré en pointillé identifie les étapes se faisant en-dehors de FEFLOW. ‘BC’ signifie ‘condition aux limites’, ‘TC’ signifie ‘conductivité thermique’.

19To compute thermal gradients along the rock wall and talus (Section 3.2.3.), we use four of the 18 sensors – two in the rock wall and two in the talus. In the rock wall, we use one sensor above the talus and one below the talus (the ‘RW sensors’, named respectively ‘RW_top’ and ‘RW_bot’; Geoprecision® M-Log5W-ROCK, accuracy ± 0.1 °C, resolution 0.01 °C, fig. 4a). In the talus, we use one sensor in its highest part and one in its lower part (the ‘talus sensors’, named respectively ‘Talus_top’ and ‘Talus_bot’; model: Mouser® ibutton DS1925L-F5#, accuracy ± 0.5 °C, resolution 0.065 °C). Talus sensors were wrapped in tape in order to increase their protection against potential damages and to waterproof them, with negligible insulating effects. Elevation and installation depth of the sensors are summarised in Table 1.

Tab. 1 – Elevation (m a.s.l.), depth and geological setting of the emplacements of the four thermal sensors installed in the Gislá talus slope and surrounding bedrock.
Tab. 1 – Altitude, profondeur et cadre géologique des emplacements des quatre capteurs thermiques installés dans la pente d’éboulis d'Eyjafirði et le substrat rocheux environnant.

Tab. 1 – Elevation (m a.s.l.), depth and geological setting of the emplacements of the four thermal sensors installed in the Gislá talus slope and surrounding bedrock.Tab. 1 – Altitude, profondeur et cadre géologique des emplacements des quatre capteurs thermiques installés dans la pente d’éboulis d'Eyjafirði et le substrat rocheux environnant.

20From the measured data, we compute daily temperature averages for all four sensors. We also obtain air temperature time series from nearby weather stations from the Icelandic Meteorological Office (IMO). We then compute correlations (i.e., linear regression and R-squared value) between daily averages of both RW sensors, and daily averages from weather stations on the measurement period (August 1st 2021 to July 9th 2022). We select the two weather stations that show the best correlations (i.e. maximum R-squared values), here the automatic weather stations of Öxnadalsheiði (measurement period: July 29th 1995 to present; elevation: 540 m) and Akureyri (January 1st 1949 to present; 31 m). The equations of linear regression we compute are as follows (station/sensor):

  • Öxnadalsheiði/RW_top:

  • Akureyri/RW_top:

  • Öxnadalsheiði/RW_bot:

  • Akureyri/RW_bot:

21Based on those equations, we then reconstruct daily temperatures of RW sensors back to January 1st 1949 (earliest available air temperature data), for each sensor. The Öxnadalsheiði weather station is preferred as it shows the best correlation with measured data; the Akureyri weather station is used when Öxnadalsheiði data are missing (e.g., prior to July 29th 1995). Statistics on correlations are given in Section 4.1.

22We then compute monthly averages of RW sensors for the period January 1st 1949 to present. Furthermore, we obtained monthly air temperature time series from the Akureyri manned weather station (measurement period: November 1881 to December 2015) from the IMO. As above, we compute correlations (i.e., linear regression and R-squared values) between monthly average temperatures of both RW sensors, and monthly average temperatures from the Akureyri manned weather station, for the period January 1949 to December 2015 (in both cases, R-squared > 0.99). We then reconstruct monthly temperatures for RW sensors between November 1881 and December 1948, based on the following equations of linear regressions:

  • Talus_top:

  • Talus_bot:

23Contrary to the RW sensors, which are located on sub-vertical outcrops, talus sensors are affected by the winter snow cover. Therefore, air and ground surface temperature are decoupled during the snow cover period (Namias, 1985; Zhang, 2005; Mote, 2008). From data indicating the presence of a snow cover at the Akureyri automatic weather station (qualitatively between 0 = no snow and 4 = continuous snow cover), we calculate the average start and end date of the continuous snow cover based on the period 1998 to 2022. With this method, we approximate the ‘summer’ as a period with no snow cover, between May 7th and October 13th; and we approximate the ‘winter’ as a period with a continuous snow cover, between October 13th and May 7th (standard deviation: ± 17 days).

24In the absence of local measurements of air temperature, we reconstruct the talus temperature time series based on the RW reconstructed time series. We thus compute daily averages for both talus sensors, and compute correlations between their summer data and summer data from both RW sensors. As RW_top shows the best correlations, we use its equations of linear regression to reconstruct temperature of talus sensors, daily (to January 1st 1949) and monthly (to November 1881). For winter periods, as talus sensors are affected by the snow cover, we multiply the results of the temperature reconstruction by their respective n-factor (Klene et al., 2001a, 2001b; Riseborough et al., 2008). With Talus_top as an example, it gives the following formula:

  • Talus_top (summer):

  • Talus_top (winter): n-factor

25The n-factor is a parametric representation of the insulating effect of the snow cover on a given sensor. It is calculated based on the freezing degree days (FDD), which are the sum of negative daily temperatures for a given sensor over the measurement period. In practise, the n-factor calculates as a ratio [FDDtalus sensor / FDDRW sensor] (Klene et al., 2001a, 2001b; Riseborough et al., 2008). In our case, talus sensors are affected by the snow cover; hence, its insulating effect maintains temperatures around 0 °C, which reduces the number of days with negative temperatures, and ultimately reducing the FDD of talus sensors. On the contrary, RW sensors are not affected by the snow cover and serve as proxies for air temperature; hence, their FDD are relatively high, and equal to that of the local air temperature. Statistics on n-factors and FDD used in the reconstruction of Talus sensor time series are provided in Section 4.1.

26Therefore, the n-factor takes values between 0 (no negative daily temperatures measured at a talus sensor, i.e., perfect insulation from the snow cover) and 1 (equal negative daily temperatures measured at the talus and RW sensors, i.e., no snow cover). In our case, for a given talus sensor, a value close to 0 indicates that temperatures reconstructed from RW_top are strongly attenuated, and thus closely maintain around 0 °C. On the contrary, a value close to 1 indicates that reconstructed temperatures are virtually not attenuated, and thus are nearly equal to temperatures of RW_top.

27For all four sensors, we calculate the average temperature for the reference period 1961-1990. We then apply to each sensor the temperature linear deviation modelled in Etzelmüller et al. (2020), with the intermediate scenario of a Holocene Thermal Maximum (HTM) at + 0.5 °C. This linear deviation model was calculated specifically for Iceland (Etzelmüller et al., 2020), and is based on oxygen-isotope data from an ice core acquired in northern Greenland (North Greenland Ice Core Project members, 2004). The linear deviation model allows to reconstruct, for each sensor, temperatures with a 10-years timestep back to the end of the Last Glacial Maximum (LGM) at -20,000 years, until 100 years before present.

28No temperature data are available for the plateau upslope of the Gislá talus slope. Nevertheless, the plateau is included in the selected topographic profile. Therefore, we create an artificial temperature time series for the plateau, assuming that the thermal regime of this part of the site has negligible influence on the talus slope. In summer the synthetic plateau time series takes the temperature values of the sensor with the highest elevation (i.e., RW_top). To account for the snow cover, in winter the plateau time series takes the temperature values of RW_top multiplied by the lowest n-factor we calculated in the talus (i.e., ~ 0.10, for Talus_top).

29Ultimately, we create five time series covering the period from -20,000 years to December 13th 2022: RW_top, RW_bot, Talus_top, Talus_bot, and Plateau time series. A summary of the temporal resolution and sources of data for the temperature time series is provided in Figure 5. As the computation time step of the numerical simulations is automatic (Section 3.2.4.), FEFLOW interpolates linearly in-between temperature values of the time series when the data time step is larger than the computation time step.

Fig. 5 – Schematic diagram of the resolution and sources of temperature data along the time series.
Fig. 5 – Diagramme de la résolution et des sources des données de température le long de la série temporelle.

Fig. 5 – Schematic diagram of the resolution and sources of temperature data along the time series.Fig. 5 – Diagramme de la résolution et des sources des données de température le long de la série temporelle.

30As a comparison, we model temperatures at the Talus_bot sensor over the year of measurement with the Cryogrid community model (Westermann et al., 2023; see also Aga et al., 2023; Ben-Asher et al., 2023; Cathala et al., 2024). Cryogrid is a one-dimensional energy-balance model that uses downscaled topoclimatic data for simulating ground thermal dynamics and water/ice balance (Gisnås et al., 2013; Westermann et al., 2013; Westermann et al., 2016). As input air temperature data, we use ERA5 global reanalysis data (Hersbach et al., 2020) downscaled at the measurement point-scale with the methods described in Filhol et al. (2023).

3.2. Modelling

31We use the commercial software FEFLOW version 7.2 (for Finite Element subsurface FLOW and transport system; DHI-WASY GmbH; DHI, 2017; Diersch, 2014) to model the thermal dynamics of permafrost within the Gislá talus slope. FEFLOW uses the finite element method (Courant, 1943; see also Strang, 1973; Holland, 1974; Argyris et al., 1979; Williamson, 1980; Bathe, 2008) to model heat transfer, mass transport and groundwater flow in various case scenarios (e.g., 2D or 3D, variably porous medium, saturated or not, transient or steady flow); its plug-in piFreeze (DHI, 2017) accounts for phase changes of water. Details on the mathematical approach of FEFLOW are given in Section 3.2.2. FEFLOW with piFreeze was used for less than a decade in geological studies, which investigated various scenarios: rock walls in contexts of rock avalanche events (Magnin et al., 2017; Magnin and Josnin, 2021; Cathala et al., 2024), degrading permafrost plateau (Langford et al., 2020), thermal effect of hot buried pipeline in permafrost ground (Nagare et al., 2021), or heat transport within multi-layered compacted clay (Dalla Santa et al., 2022).

32Our approach of creation and parametrisation of the numerical is summarised in a schematic workflow (fig. 4b).

3.2.1. Site geometry and discretisation

33We import in FEFLOW the topographic data (surface and underlying bedrock) described in Section 3.1.1. to create a 2D cross-sectional model of the Gislá study site. For technical purposes, we consider that the surface topography of the study site remains stable over the modelling time period. Additionally, we create a 5 km-deep layer below the Gislá model, following the methodology in Magnin et al. (2017) and Magnin and Josnin (2021). The geometry hence contains three polygons (fig. 6): talus, surface bedrock, and deep bedrock (the 5 km-deep layer). We mesh the geometry with the Triangulated Irregular Network (TIN) method, which discretises all polygons into triangular elements which have a node at each vertex (fig. 6). We use FEFLOW default parameters (notably maximum element angles = 30°), and refine the meshing at polygon edges to accommodate the computational complexity of the transition zone between talus and bedrock. The modelling spatial resolution required is, relatively speaking, high for the talus; intermediate for the surface bedrock; low for the deep bedrock. Therefore, we manually increase or decrease the relative meshing density for each polygon in order to match the required differential modelling resolution. Final relative meshing densities and number of elements per polygon are:

  • deep bedrock: 1 (292 elements);

  • surface bedrock: 25 (487 elements);

  • talus: 2000 (222 elements).

34Proceeding this way optimises the ratio (modelling resolution/processing time) of our numerical model runs.

Fig. 6 – Geometry of the Gislá study site, divided into three polygons (talus, surface bedrock, deep bedrock), each one discretised in triangular elements at various spatial resolutions.
Fig. 6 Géométrie du site d'étude d’Eyjafirði, divisé en trois polygones (éboulis, substratum superficiel, substratum profond), chacun discrétisé en éléments triangulaires à différentes résolutions spatiales.

Fig. 6 – Geometry of the Gislá study site, divided into three polygons (talus, surface bedrock, deep bedrock), each one discretised in triangular elements at various spatial resolutions. Fig. 6 – Géométrie du site d'étude d’Eyjafirði, divisé en trois polygones (éboulis, substratum superficiel, substratum profond), chacun discrétisé en éléments triangulaires à différentes résolutions spatiales.

Thermal boundary conditions are indicated in italics. Arrows indicate the nodes where the base thermal boundary condition (geothermal heat flux of -0.1 W.m-2) is applied. Crosses indicate the nodes where the sensor time series (RW_top, RW_bot, Talus_top, Talus_bot) are applied. The solid black line spans the nodes where the Plateau time series is applied. The dashed black lines span the nodes where values of sensor time series are extrapolated or interpolated. The surface of this cross section corresponds to the topographic profile presented in Figure 3.
Les conditions aux limites thermiques sont indiquées en italique. Les flèches indiquent les nœuds où la condition aux limites de température de base (flux de chaleur géothermique de -0,1 W.m-2) est appliquée. Les croix indiquent les nœuds où les séries temporelles des capteurs (RW_top, RW_bot, Talus_top, Talus_bot) sont appliquées. La ligne noire continue s'étend sur les nœuds où la série temporelle du Plateau est appliquée. Les lignes noires en tireté couvrent les nœuds où les séries temporelles des capteurs sont extrapolées ou interpolées. La surface de cette coupe correspond au profil topographique présenté sur la Figure 3.

3.2.2. Numerical approach

35We assume the Gislá study site (bedrock and talus) as constituted entirely of basalt. Only porosity varies between the bedrock and talus. Bedrock and talus are individually considered homogeneous and isotropic. As we work in saturated conditions, the medium is composed of a solid (rock and ice) and a liquid phase (water). As in Magnin et al. (2017), we do not simulate water flow but heat transfer only. Therefore, heat transfer is by conductin only, and the energy conservation equation writes as follow (Diersch, 2014; DHI, 2017):

36with the porosity of the medium; and are the volumetric heat capacities of the liquid and solid phases respectively (J.m-3.K-1, with the phase density and its specific heat capacity); is the flow velocity (set to 0 m.s-1 in our study case, as we do not consider water flow); is the temperature (K); is the hydrodynamic thermal dispersion tensor (J.m−1.s−1.K−1; which includes the thermal conductivity, W.m-1.K-1).

37The piFreeze plugin then accounts for the presence of ice in the solid phase, by computing the ice bulk volumetric fraction as (with the bulk volumetric fractions of air, water, rock and ice respectively; as we work in saturated conditions, in our study case). Then, the freezing function (DHI, 2017) is computed as:

38with and the volumetric bulk fractions and densities of the corresponding phase respectively (water or ice). This equation links the bulk mass of unfrozen water to the total bulk mass of water (frozen and unfrozen), and decreases with increasing presence of ice. Ice forms gradually within a temperature interval we define, which is

39with the freezing point of water (set at -1 °C; Magnin et al., 2017; Magnin and Josnin, 2021), and the length of the temperature interval (set at 2 °C; Magnin et al., 2017; Magnin and Josnin, 2021).

40Finally, values of thermal conductivity and heat capacity of the solid phase in Equation 1 are modified by the ice bulk volumetric fraction and the freezing function , respectively as follows:

41and

42with the latent heat of ice formation.

3.2.3. Thermal parameters, initial conditions and boundary conditions

43The thermal parameters of the material the user can set in FEFLOW are: porosity, volumetric heat capacity of solid (i.e., the rock phase), thermal conductivity (TC) of solid, volumetric heat capacity of water, and TC of water. piFreeze adds the possibility to set: water density, ice density, volumetric heat capacity of ice, TC of ice, latent heat, and freezing function (freezing temperature, temperature range of the phase change, and residual liquid fraction). The values of thermal parameters we use are detailed in Table 2, with the associated reference(s) for each parameter value.

44Notably, the thermal parameter that plays the most important role in the modelling of thermal dynamics is the TC of the rock phase. We perform model runs with values of 0.75, 1.1, and 1.75 W.m-1.K-1. Values of ~ 1.75 W.m-1.K-1 are commonly found in the literature for Icelandic basalts (1.6 to 1.9 in Flóvenz and Sæmundsson, 1993; 1.5 to 2.0 in Oxburgh and Agrell, 1982; 1.7 in Pálmason and Sæmundsson, 1979). A more recent work suggests a value of ~ 1.1 W.m-1.K-1 (Ruether, 2011), from 810 measurements made on Icelandic basalts. For reasons detailed in Section 5.1.3., we decided to perform model runs with a lower value than those typically found in the literature (i.e., 0.75 W.m-1.K-1). Nevertheless, the lowest TC value Ruether (2011) measured on Icelandic basalts is 0.62 W.m-1.K-1, which gives us credibility in using a TC value of 0.75 W.m-1.K-1.

45For the talus, we use porosity values of 0.5 (as in Wicky and Hauck, 2017) and 0.8. We chose to investigate a porosity value as high as 0.8, as fieldwork observations revealed the possibility of excess ice within the talus (see Section 2).

46All model runs have a temperature initial condition of -3 °C applied at all nodes – i.e., homogeneous frozen conditions. Setting an initial temperature below the freezing temperature (-1 °C) ensures that no ice melting occurs in the talus during the first part of the runs (that serves as an initialisation of the models, Section 3.2.4.), when boundary conditions in surface temperatures are themselves several degrees below zero. Using frozen initial conditions is justified by the fact that our model runs start at the end of the LGM, before the northern hemisphere deglaciation (19,000 to 20,000 years before present; Clark et al., 2009). Depending on the model run, the initial ice bulk volumetric fraction within the talus varies between 0.5 (when porosity = 0.5) and 0.8 (when porosity = 0.8). It should be noted that some natural processes (e.g., snow avalanche deposits) could incorporate ice inside the talus slope; however, for technical purposes we consider that no ice is added to the system during the model runs. Details on initial conditions are given in Table 2.

Tab. 2 – Summary of thermal parameters, initial conditions, and boundary conditions used to perform model runs.
Tab. 2 – Résumé des paramètres thermiques, des conditions initiales et des conditions aux limites utilisés pour effectuer nos simulations.

Tab. 2 – Summary of thermal parameters, initial conditions, and boundary conditions used to perform model runs. Tab. 2 – Résumé des paramètres thermiques, des conditions initiales et des conditions aux limites utilisés pour effectuer nos simulations.

Associated reference is provided (when applicable). Letters in brackets indicate the phase (‘s’ for solid, ‘w’ for liquid, ‘i’ for ice) the parameter applies to.
Les références associées sont fournies (le cas échéant). Les lettres entre parenthèses indiquent la phase (s pour solide, w pour liquide, i pour glace) à laquelle le paramètre s'applique.

47We use two types of temperature boundary conditions (fig. 6). First, we apply at all nodes at the base of the model a geothermal heat flux of -0.1 W.m-2 (Jóhannesson et al., 2020, from Hjartarson, 2015). Second, we force temperatures at the surface of the models with the temperature time series we reconstructed (Section 3.1.2.; fig. 6). We apply the Plateau time series uniformly at all surface nodes on the plateau. We apply the RW_top time series at the first surface node above the talus; we apply the RW_bot time series at the first surface node below the talus. We use the 1D linear interpolation FEFLOW tool to compute interpolated (between RW_top and RW_bot nodes) and extrapolated time series (above RW_top and below RW_bot) at all surface nodes, based on the values of RW_top and RW_bot time series. We apply the Talus_top time series at the first surface node at the top of the talus; we apply the Talus_bot time series at the first surface node at the bottom of the talus. We use the 1D linear interpolation to compute interpolated time series at all surface nodes on the talus. Details on boundary conditions are given in Table 2.

48In the present study, we seek to investigate only the heat transfer within the Gislá talus slope; hence we are not considering groundwater flow in our model runs. To ensure that meltwater from ice degradation does not flow, we apply at all nodes a hydraulic head of ~ 975 m (i.e., the highest elevation value of the topographic profile) and at all elements a hydraulic conductivity of 0 m.s-1.

3.2.4. Simulation process & scenarios

49We run numerical models on a computer with two processors (Intel® Xeon® CPU E5-2640 v4; 2.4 GHz) of 10 cores each, and 256 Go RAM. Each model runs from -20,000 years to December 13th 2022, with an initial time step of one day, which adapts automatically to accommodate the simulation complexity that can arise during the model runs (e.g., when temperatures are around the freezing point and phase changes occur). The temporal resolution of temperature time series is shown in Figure 5. Each model run takes approximately four to five hours to complete. All simulation parameters (e.g., distribution of temperatures or ice bulk volumetric fraction) are automatically recorded at specific time steps we selected prior to all model runs.

50The first part of the simulations (from -20,000 to -100 years) serves as an initialisation of the model, i.e., generates a plausible temperature distribution before simulating contemporary temperature distributions (further referred to as the ‘LGM-initialisation’ method). In Magnin et al. (2017) and Magnin and Josnin (2021), the initialisation is performed individually by running models with the geothermal heat flux as the base boundary condition, and the first time steps of surface time series as the surface boundary conditions, until a thermal equilibrium is reached (further referred to as the ‘equilibrium-initialisation’ method). These two methods giving similar results in our study case (Section 4.2), we choose to use the LGM-initialisation method as it reduces computation time.

51Apart from a test run (Section 4.2.), we dedicate six simulation scenarios to the investigation of the sensitivity of our model to the initial porosity/ice content of the talus (Section 4.4.), and the thermal conductivity (TC) of the rock phase (Section 4.5.). We investigate those two parameters as they have the greatest effect on the simulation results. Therefore, we perform: (i) three runs with a fixed TC (1.1 W.m-1.K-1) and an initial porosity/ice content varying between 0.3, 0.5 and 0.8; (ii) three runs with a fixed initial porosity/ice content (0.8) and a TC varying between 0.75, 1.1 and 1.75 W.m-1.K-1.

52For each parameter (initial porosity/ice content and TC), we investigate values consistent with the literature (tab. 2), as well as extreme values that show the boundary behaviours of our model.

4. Results

4.1. Analysis of temperature data

53The correlations between RW sensors and the Öxnadalsheiði and Akureyri weather stations, used for the reconstruction of RW temperature time series, have R-squared values between 0.81 and 0.88, with the Öxnadalsheiði weather station showing the best correlation with both RW sensors (tab. 3). The correlation between Talus sensors and RW_bot for the summer period, used for the reconstruction of Talus temperature time series, have R-squared values of 0.82 and 0.87. By comparison, the R-squared values of correlations for the winter period are 0.18 and 0.57 (tab. 3). We also provide FDD and n-factor values used for the reconstruction of Talus temperature time series, as well as FDD and n-factor computed for RW sensors (not used for the reconstruction of RW temperature time series, for information purposes only). We illustrate with the example of sensor Talus_top the result of time series modelling (-20,000 to present time; fig. 7a) and time series statistical reconstruction (1881-2022; fig. 7b).

Tab. 3 – Summary of statistics calculated for temperature reconstruction back to January 1st 1949, for all four sensors.
Tab. 3 - Résumé des statistiques calculées pour la reconstitution de la température depuis le 1er janvier 1949, pour les quatre capteurs.

Tab. 3 – Summary of statistics calculated for temperature reconstruction back to January 1st 1949, for all four sensors. Tab. 3 - Résumé des statistiques calculées pour la reconstitution de la température depuis le 1er janvier 1949, pour les quatre capteurs.

For RW sensors, the n-factor is calculated with the Öxnadalsheiði weather station. For talus sensors, R-squared values are calculated based on the summer period; by comparison, we also provide the R-squared values for the winter period. ‘FDD’ stands for ‘freezing degree days’.
Pour les capteurs RW, le n-factor est calculé avec la station d'Öxnadalsheiði. Pour les capteurs d'éboulis, les valeurs de R-carré sont calculées sur la base de la période estivale ; à titre de comparaison, nous fournissons également les valeurs de R-carré pour la période hivernale. ‘FDD’ signifie ‘freezing degree days’.

Fig. 7 - Illustration example of the temperature time series resulting from a. the modelling approach (-20,000 to present time), and b. the statistical reconstruction with annual average, minimum and maximum temperatures (calculated from monthly averages), over the period 1881-2022.
Fig. 7 - Exemple illustratif des séries temporelles de température résultant a. de la méthode de modélisation (de -20,000 à l’Actuel), et b. de la reconstitution statistique (1881-2022).

Fig. 7 - Illustration example of the temperature time series resulting from a. the modelling approach (-20,000 to present time), and b. the statistical reconstruction with annual average, minimum and maximum temperatures (calculated from monthly averages), over the period 1881-2022. Fig. 7 - Exemple illustratif des séries temporelles de température résultant a. de la méthode de modélisation (de -20,000 à l’Actuel), et b. de la reconstitution statistique (1881-2022).

Both temperature curves represent the Talus_top sensor time series.
Les deux courbes de température représentent la série temporelle de température du capteur Talus top.

54Temperature measurements we acquired during approximately one year show that talus sensors are affected by snow cover, which maintains temperatures around 0 °C at those sensors for part of the winter due to a zero-curtain effect (Outcalt et al., 1990; see also Hanson and Hoelzle, 2004; fig. 8a). In addition, snow cover in mountains is considered continuous between September 27th 2021 and May 15th 2022 in data from the Akureyri weather station. However, in the middle of winter (i.e., between ~ November and April), both talus sensors show temperature oscillations. Those oscillations reflect the temperature oscillations measured by RW_top (which serves as a proxy for air temperature), despite being significantly attenuated. Additionally, temperatures measured by the Talus_bot sensor are also lower than the temperatures measured by the Talus_top sensor (fig. 8a). Temperatures we modelled with Cryogrid adequately match measured temperatures in summer (fig. 8b). However, winter modelled temperatures do not show temperature oscillations that appear on measured data (fig. 8a, b). As a comparison, we provide the daily average, minimum and maximum temperature curves over the year of measurement (August 1st 2021 and July 9th 2022), for the Öxnadalsheiði (fig. 8c) and Akureyri (fig. 8d) weather stations.

55Curves of the daily average, minimum and maximum temperatures over the year prior to the landslide (October 7th 2019 - October 6th 2020) are provided for the Öxnadalsheiði (fig. 9a) and Akureyri (fig. 9b) weather stations. The annual average, minimum and maximum temperatures over the period 1881 - 2021 (i.e., the full temporal record) is also provided (fig. 9c, d), with data from the Akureyri manned station (1881-1948) and automatic station (1948-2021). The temperature curve shows a general temperature increase over the last ~ 40 years (fig. 9d), of ~ 0.4 °C/decade. The average air temperatures measured at the Öxnadalsheiði and Akureyri weather station for the year prior to the landslide (7th October 2019 - 6th October 2020) are respectively of +0.3 °C and +4.1 °C.

56The average temperatures for each sensor and over different periods (1961-1990, 1991-2020, year of measurement) are given in Table 4. We see from that table that, in the talus, average temperatures were above 0 °C for both reference periods (1961-1990 and 1991-2020); and that, despite being higher in altitude, temperatures reconstructed for Talus_top (824 m) are higher than temperatures reconstructed for Talus_bot (719 m) for all three time periods: +0.73 °C (1961-1990), +0.66 °C (1991-2020), +1.04 °C (year of measurement).

Fig. 8 – Daily temperatures measured and modeled for the study and recorded by nearby weather stations between August 1st 2021 and July 9th 2022.
Fig. 8 - Températures journalières mesurées et modélisées pour le site d'étude et relevées par les stations météo proches, entre le 1er août 2021 et le 9 juillet 2022.

Fig. 8 – Daily temperatures measured and modeled for the study and recorded by nearby weather stations between August 1st 2021 and July 9th 2022.Fig. 8 - Températures journalières mesurées et modélisées pour le site d'étude et relevées par les stations météo proches, entre le 1er août 2021 et le 9 juillet 2022.

a. Daily average temperatures, measured by RW_top (black line), Talus_top (red line) and Talus_bot (green line). The approximate summer period for this year is greyed out. Example periods showing the effect of the snow cover and air coupling on temperatures measured by talus sensors are located; b. Measured temperatures and modelled temperatures (with Cryogrid) at the Talus_top sensor, on the same period as panel a. Modelled data do not show temperature oscillations in winter; c. Daily average, minimum and maximum temperatures from the Öxnadalsheiði weather station, between August 1st 2021 and July 9th 2022; d. Daily average, minimum and maximum temperatures from the Akureyri weather station, between August 1st 2021 and July 9th 2022.
a. Températures moyennes journalières, mesurées par RW_top (ligne noire), Talus_top (ligne rouge) et Talus_bot (ligne verte) entre le 1er août 2021 et le 9 juillet 2022. La période estivale approximative pour cette année est grisée. Des exemples de périodes montrant l'effet de la couverture neigeuse et du couplage de l'air sur les températures mesurées par les capteurs de l’éboulis sont localisés ; b. Températures mesurées et modélisées par Cryogrid au capteur Talus_top, sur la même période de temps que le panneau a. Les données modélisées ne montrent pas d'oscillations de température en hiver ; c. Températures journalières (moyenne, minimum et maximum) mesurées à la station météorologique d’Öxnadalsheiði, entre le 1er août 2021 et le 9 juillet 2022 ; d. Températures journalières (moyenne, minimum et maximum) mesurées à la station météorologique d’Akureyri, entre le 1er août 2021 et le 9 juillet 2022.

Fig. 9 – Temperature data from weather stations. Daily average, mini-mum and maximum temperatures between 7th October 2019 and 6th October 2020.
Fig. 9 – Données de température des stations météorologiques. Tempé-ratures journalières (moyenne, minimum et maximum) entre le 7 oc-tobre 2019 et le 6 octobre 2020.

Fig. 9 – Temperature data from weather stations. Daily average, mini-mum and maximum temperatures between 7th October 2019 and 6th October 2020.Fig. 9 – Données de température des stations météorologiques. Tempé-ratures journalières (moyenne, minimum et maximum) entre le 7 oc-tobre 2019 et le 6 octobre 2020.

a. From the Öxnadalsheiði weather station, and b. The Aku-reyri weather station; c. Annual average, minimum and maximum tem-peratures over the period 1881-2021, from the Akureyri manned (1881-1948) and automatic (1949-2021) weather stations; d. Zoom on panel c, with a vertical axis stretched between 0 °C and 6 °C. Temperatures data shown in c. and d. are calculated from the monthly averages.
a. Mesurées à la station météorologique d’Öxnadalsheiði, et b. A la station météorologique d’Akureyri ; c. Températures annuelles (moyenne, minimum et maximum) sur la période 1881-2021, mesurées à la station météorologique habitée d’Akureyri (1881-1948) et la station automatique d’Akureyri (1949-2021) ; d. Zoom du panneau c, avec une échelle verticale étirée entre 0 °C et 6 °C.
Les températures des panneaux c. et d. sont calculées à partir des moyennes mensuelles.

Tab. 4 – Back-calculated average, minimum and maximum temperatures over time periods 1961-1990, 1991-2020 and year of measurement, for all four sensors and for the Öxnadalsheiði and Akureyri weather stations.
Tab. 4 – Températures moyennes, minimum et maximum sur différentes périodes de temps (1961-1990, 1991-2020, année de mesure), pour les quatre capteurs ainsi que pour les stations météorologiques d’Öxnadalsheiði et d’Akureyri.

Tab. 4 – Back-calculated average, minimum and maximum temperatures over time periods 1961-1990, 1991-2020 and year of measurement, for all four sensors and for the Öxnadalsheiði and Akureyri weather stations.Tab. 4 – Températures moyennes, minimum et maximum sur différentes périodes de temps (1961-1990, 1991-2020, année de mesure), pour les quatre capteurs ainsi que pour les stations météorologiques d’Öxnadalsheiði et d’Akureyri.

4.2. Initialisation methods

57The LGM-initialisation and the equilibrium-initialisation methods (Section 3.2.4.) give similar final temperature distribution (fig. 10), justifying the use of the one requiring less computation time (i.e., LGM-initialisation method) for all further models presented in this study.

Fig. 10 – Temperature distribution at the date of the Gislá landslide (October 6th 2020), with a. the LGM-initialisation method, and b. the equilibrium-initialisation method, with a TC of the rock phase of 1.1 W.m-1.K-1 and an initial porosity/ice bulk volumetric fraction of 0.8.
Fig. 10 – Distribution de la température à la date du glissement de terrain d'Eyjafirði (6 Octobre 2020), avec a. la méthode d'initialisation du LGM, et b. la méthode d'initialisation à l’équilibre, avec une TC de la phase rocheuse de 1,1 W.m-1.K-1 et une porosité/fraction volumétrique de glace initiales de 0,8.

Fig. 10 – Temperature distribution at the date of the Gislá landslide (October 6th 2020), with a. the LGM-initialisation method, and b. the equilibrium-initialisation method, with a TC of the rock phase of 1.1 W.m-1.K-1 and an initial porosity/ice bulk volumetric fraction of 0.8.Fig. 10 – Distribution de la température à la date du glissement de terrain d'Eyjafirði (6 Octobre 2020), avec a. la méthode d'initialisation du LGM, et b. la méthode d'initialisation à l’équilibre, avec une TC de la phase rocheuse de 1,1 W.m-1.K-1 et une porosité/fraction volumétrique de glace initiales de 0,8.

4.3. Ground temperature evolution over the Holocene

58All model runs follow the same temperature dynamics (fig. 11): surface temperatures rise from -20,000 years to the HTM (between -10,000 to -8000 years), leading to an onset of ground ice degradation within the talus during the HTM around -11,000 years (fig. 11a, b); ground ice entirely melts around -9500 years. Temperatures then decrease and stabilise slightly above 0 °C at the surface of the talus from -8000 years to the end of the modelled time series (i.e., -100 years), maintaining the inside of the talus unfrozen (fig. 11c, d). The water within the talus then freezes again before the start of contemporary time series (i.e., November 1881). From the beginning of contemporary time series surface temperatures steadily increase, causing ground ice within the talus to degrade progressively (1950: fig. 11e, f), hence reaching a minimum ice content at the date of the Gislá landslide (fig. 11g, h).

Fig. 11 – Evolution of the temperature distribution and the ice bulk volumetric fraction over a model run, with a TC of the rock phase of 1.1 W.m-1.K-1 and an initial porosity/ice bulk volumetric fraction of 0.8.
Fig. 11 – Evolution de la distribution de la température et de la fraction volumétrique de glace au cours d'une exécution du modèle, avec une TC de la phase rocheuse de 1,1 W.m-1.K-1 et une porosité/fraction volumétrique de glace initiales de 0,8.

Fig. 11 – Evolution of the temperature distribution and the ice bulk volumetric fraction over a model run, with a TC of the rock phase of 1.1 W.m-1.K-1 and an initial porosity/ice bulk volumetric fraction of 0.8. Fig. 11 – Evolution de la distribution de la température et de la fraction volumétrique de glace au cours d'une exécution du modèle, avec une TC de la phase rocheuse de 1,1 W.m-1.K-1 et une porosité/fraction volumétrique de glace initiales de 0,8.

a. Temperature distribution and b. Ice bulk volumetric fraction at -11,000 years; c. Temperature distribution and d. Ice bulk volumetric fraction at -8000 years; e. Temperature distribution and f. Ice bulk volumetric fraction on 01/01/1950; g. Temperature distribution and h. Ice bulk volumetric fraction on the date of the Gislá landslide (06/10/2020).
a. Distribution de la température et b. Fraction volumétrique de glace à -11 000 ans ; c. Distribution de la température et d. Fraction volumétrique de glace à -8 000 ans ; e. Distribution de la température et f. Fraction volumétrique de glace au 01/01/1950 ; g. Distribution de la température et h. Fraction volumétrique de glace à la date du glissement de terrain d’Eyjafirði (06/10/2020).

4.4. Sensitivity to porosity/ice content

59Increasing the porosity and initial ice bulk volumetric fraction within the talus decreases the final temperatures at the base of the talus, leading to a larger zone where ground ice persists, with an overall higher ice bulk volumetric fraction (fig. 12).

Fig. 12 – Temperature distribution and ice bulk volumetric fraction at the date of the Gislá landslide (October 6th 2020) with a TC of the rock phase of 1.1 W.m-1.K-1.
Fig. 12 – Distribution de la température et fraction volumétrique de glace à la date du glissement de terrain d'Eyjafirði (6 Octobre 2020) avec une TC de la phase rocheuse de 1,1 W.m-1.K-1.

Fig. 12 – Temperature distribution and ice bulk volumetric fraction at the date of the Gislá landslide (October 6th 2020) with a TC of the rock phase of 1.1 W.m-1.K-1. Fig. 12 – Distribution de la température et fraction volumétrique de glace à la date du glissement de terrain d'Eyjafirði (6 Octobre 2020) avec une TC de la phase rocheuse de 1,1 W.m-1.K-1.

a. temperature distribution and b. ice bulk volumetric fraction, for an initial porosity/ice bulk volumetric fraction of 0.3; c. temperature distribution and d. ice bulk volumetric fraction, for an initial porosity/ice bulk volumetric fraction of 0.5; e. temperature distribution and f. ice bulk volumetric fraction, for an initial porosity/ice bulk volumetric fraction of 0.8.
a. distribution de la température et b. fraction volumétrique de glace, pour une porosité/fraction volumétrique de glace initiales de 0.3 ; c. distribution de la température et d. fraction volumétrique de glace, pour une porosité/fraction volumétrique de glace initiales de 0,5 ; e. distribution de la température et f. fraction volumétrique de glace, pour une porosité/fraction volumétrique de glace initiales de 0,8.

4.5. Sensitivity to the thermal conductivity

60Decreasing the TC of the rock phase also decreases the final temperatures at the base of the talus, leading to a larger zone where ground ice persists (fig. 13). Notably, the core of persisting ground ice seems to shift toward the edge of the talus with decreasing TC of the rock phase.

Fig. 13 – Temperature distribution and ice bulk volumetric fraction at the date of the Gislá landslide (October 6th 2020) with an initial porosity/ice bulk volumetric fraction of 0.8.
Fig. 13 – Distribution de la température et fraction volumétrique de glace à la date du glissement de terrain d'Eyjafirði (6 octobre 2020) avec une porosité/fraction volumétrique de glace initiales de 0,8.

Fig. 13 – Temperature distribution and ice bulk volumetric fraction at the date of the Gislá landslide (October 6th 2020) with an initial porosity/ice bulk volumetric fraction of 0.8. Fig. 13 – Distribution de la température et fraction volumétrique de glace à la date du glissement de terrain d'Eyjafirði (6 octobre 2020) avec une porosité/fraction volumétrique de glace initiales de 0,8.

a. Temperature distribution and b. Ice bulk volumetric fraction, for TC of the rock phase of 1.75 W.m-1.K-1; c. Temperature distribution and d. Ice bulk volumetric fraction, for TC of the rock phase of 1.1 W.m-1.K-1; e. Temperature distribution and f. ice bulk volumetric fraction, for TC of the rock phase of 0.75 W.m-1.K-1.
a. Distribution de la température et b. Fraction volumétrique de glace, pour une TC de la phase rocheuse de 1,75 W.m-1.K-1 ; c. Distribution de la température et d. Fraction volumétrique de glace, pour une TC de la phase rocheuse de 1,1 W.m-1.K-1 ; e. Distribution de la température et f. Fraction volumétrique de glace, pour une TC de la phase rocheuse de 0,75 W.m-1.K-1.

5. Discussion

5.1. Thermal regime of the Gislá talus slope

5.1.1. Holocene temperatures and permafrost dynamics

61The total disappearance of ice within the Gislá talus slope (around -9500 years; fig. 11) happens during the HTM – as considered by Etzelmüller et al. (2020), from which our temperature time series (-20,000 to present) are derived. The HTM is characterised by a continuous period of above-zero average air temperatures from around -10,000 to -6000 years, from when average air temperature drops sub-zero again and decrease steadily until present times (North Greenland Ice Core Project members, 2004). Such a pattern is consistent with a total thawing followed by a period of freezing within the Gislá talus slope, as highlighted by the numerical models we provide (fig. 11). For Iceland specifically, previous studies indeed reported relatively high temperature (several degrees above the 1961-1990 reference period), glacial retreat, and sometimes even overall ice-free conditions during the HTM (e.g., Gudmundsson, 1997; Geirsdóttir, 2004; Caseldine et al., 2006; Norðdahl et al., 2008; Geirsdóttir et al., 2009; Etzelmüller et al., 2020; Benediktsson et al., 2024).

62At a more recent temporal scale, air temperatures have been generally increasing over the last ~ 40 years (fig. 9c, d). Moreover, the presence of ice-cemented blocks (Arnardóttir, 2023) and subsequent molards in the deposits of the Gislá landslide indicate that degrading permafrost was present in the Gislá talus slope at the time of the landslide. Therefore, we suggest that permafrost degradation was possibly among the destabilising factors of the landslide (Section 2; Morino et al., 2019). However, the year prior to the landslide (October 7th 2019 to October 6th 2020) was not particularly warm compared to the 1991-2020 reference period (respectively +4.1 °C and +4.2 °C). Therefore, in case permafrost degradation was indeed among the destabilising factors for the Gislá landslide, it suggests a longer-term climatic control over the stability of the ice within the Gislá talus slope (i.e., the general temperature increase measured over the last 40 years).

63It should be noted that, if permafrost degradation was among the trigger factors of the Gislá landslide, particular attention should be devoted to the whole perched talus slope (fig. 2d, e). Indeed, more destabilisations could happen along this talus slope in the future, representing a serious threat to houses disseminated within the valley, at the base of the slope. Moreover, waterways also flow at the base of the slope. Future landslides could reach the water and block the flow, creating a dam lake and a potential subsequent dam burst that would have considerable impact on the people and infrastructure in the valley.

64Overall, we acknowledge that the triggering of a landslide is multifactorial (e.g., water supply from the active layer, rain or snowmelt, freeze-thaw processes, seismic activity). Hence, the purpose of the present study is less to discuss the exact destabilising factors of the Gislá landslide than to provide primary suggestions.

5.1.2. Persistence of permafrost within the Gislá talus slope

65The temperatures we measured at talus sensors over the period August 1st 2021 to July 9th 2022 show oscillations over a continuous period during winter (fig. 8), despite the presence of snow cover. Such oscillations can be explained by the onset of air circulation inside the talus slope – i.e., the occurrence of a chimney effect (fig. 1; Sawada et al., 2003; Delaloye and Lambiel, 2005; Lambiel and Pieracci, 2008; Phillips et al., 2009; Morard et al., 2010; Millar et al., 2014; Popescu et al., 2017; Wicky and Hauck, 2017; Germain and Milot, 2024; Wicky et al., 2024). Moreover, temperatures measured by the Talus_bot sensor are generally lower than the temperatures measured by the Talus_top sensor, over the measurement period as well as on longer timescales (tab. 4; fig. 8). Lower measured temperatures at the base of the talus also support the contemporary occurrence of a chimney effect within the Gislá talus slope.

66Our modelling approach is simplified, in the sense that we do not explicitly model the air convection (i.e., the chimney effect) within the talus. Nevertheless, we consider that the simulations model successfully the expected permafrost occurrence in the Gislá talus slope. Indeed, the evolution of temperature distribution shows a zone with sub-zero temperature that maintains perennially at depth, at the base of the talus slope (fig. 11, 12). The direct consequence of such temperature distribution is that ground ice also maintains at the base of the Gislá talus slope (fig. 11, 12), as observed in previous studies (e.g., Delaloye and Lambiel, 2005; Lambiel and Pieracci, 2008; Phillips et al., 2009; Morard et al., 2010; Popescu et al., 2017), which is consistent with geomorphological observations of molards within the Gislá deposits. Moreover, the average air temperature reconstructed at the RW_bot sensor (proxy for the air temperature close to the talus slope) is positive for the reference periods 1961-1990 (+0.20 °C) and 1991-2020 (+1.47 °C). We suggest that reproducing the cooling effect of air convection is enabled in our simulations by the combination of our field temperature measurements (i.e., lower temperature measured by Talus_bot compared to Talus_top) and thermal parameters we use in the simulations (i.e., particularly low TC; Section 5.1.3.).

67Note that the models we propose show that permafrost maintains within the Gislá talus slope although it is located outside of the predicted boundaries of permafrost at the regional scale (Etzelmüller et al., 2007; Lilleøren et al., 2013; Czekirda et al., 2019; Etzelmüller et al., 2020). Indeed, such permafrost distribution maps are estimated from topoclimatic data, which are unable to predict azonal permafrost maintained by local physical processes (e.g., the air circulation due to the chimney effect).

5.1.3. Thermal parameters of the Gislá talus slope

68Brideau et al. (2009) estimated that observed molard initial blocks are constituted of ~ 50 % of ice. However, at the time of the Gislá landslide, none of the model scenarios, even the most ice-conservative one (initial porosity/ice content = 0.8; TC = 0.75 W.m-1.K-1; fig. 13e, f), is able to reach this 50 % ice content. Therefore, we can assume that, at the time of the landslide, the actual temperature distribution shows a larger zone with sub-zero temperature, and that the actual ground ice content is higher at the base of the talus – compared to our most ice-conservative scenario (initial porosity/ice content = 0.8; TC = 0.75 W.m-1.K-1; fig. 13e, f).

69We obtain this ice-conservative scenario with a TC of the rock phase of 0.75 W.m-1.K-1, which is significantly lower than the TC values for Icelandic basalt usually found in the literature (~ 1.75 W.m-1.K-1 in Pálmason and Sæmundsson, 1979; Oxburgh and Agrell, 1982; Flóvenz and Sæmundsson, 1993). To our knowledge, only Ruether (2011) reported TC values as low as 0.75 W.m-1.K-1, but in less than 1 % of their 810 TC measurements. Note also that, although the thermal effect of the chimney effect can be identified in the temperature records of our talus sensors (fig. 8; Section 5.1.2.), air convection itself is not simulated in our model runs. Wicky and Hauck (2017) and Wicky et al. (2024), who specifically modelled convective heat transfer within talus slopes, observed from sensitivity tests that air circulation between the inner talus and the outside plays a major role in (or even is necessary for) the persistence of permafrost in talus slopes. Air convection should theoretically enhance persistence of ground ice within the Gislá talus slope, compared to our model results. Therefore, we assume that decreasing the rock-phase TC to a value considered as very low with respects to the literature (which seems to be necessary in our model runs for significant amounts of ground ice to persist closer to the surface; fig. 13) might have partly compensated for the effect of air convection, enhancing the persistence of ground ice within the talus.

5.2. Limitations of the temperature model runs

70The present study is a continuation of previous work done by Magnin et al. (2017) and Magnin and Josnin (2021), which used FEFLOW/piFreeze to investigate permafrost dynamics in rock walls within the Mont Blanc massif (European Alps). Notably, they found that the results of their numerical models match with borehole temperature and electrical resistivity data (Magnin et al., 2017) – validating the use of FEFLOW/piFreeze to study natural permafrost contexts. However, we acknowledge several limitations in the modelling approach we propose here.

71First, the contemporary temperature time series (Section 3.1.2.) we use as boundary conditions in the models are not measured, but reconstructed from the air temperature measured by two automatic weather stations (Öxnadalsheiði and Akureyri), both located at ~ 30 km from the Gislá study site. Hence, neither weather station represents perfectly the air temperature conditions in Gislá, which is reflected in the imperfection of the correlations between temperatures measured at our sensors and at weather stations (R-squared values between 0.81 and 0.88; tab. 2). Moreover, the Holocene temperature time series (i.e., from -20,000 to present times) are inherently inaccurate: we modelled them based on a simple temperature shift, and at a 10-year time step only (Etzelmüller et al., 2020). Overall, the reconstructed time series represent inaccurately the actual surface temperature dynamics at the Gislá talus slope. However, forcing data for such long-term numerical modelling studies necessarily have to be reconstructed or modelled, and thus are inherently subject to such inaccuracies.

72Second, we do not take into account the dynamics of snow cover in our reconstruction method for temperature time series, as we consider the snow cover as a binary state only (present/not present). Such a method does not account for variations in snow depth, which lead to varying insulation effects depending on the snow depth (e.g., Zhang, 2005; Luetschg et al., 2008; Ge and Gong, 2010; Rödder and Kneisel, 2012; Park et al., 2015). The timing of snow cover in our temperature time series is also an approximation, as we calculate its average based on the period 1998-2022 and consider the resulting winter period as constant over the contemporary part of the temperature time series. This timing may not be representative of the whole time series. Nevertheless, different timings of snow cover imply different durations of its insulating effect, and can lead to ground cooling or warming depending on complex factors (e.g., Goodrich, 1982; Ling and Zhang, 2003; Stieglitz et al., 2003; Zhang, 2005). Additionally, the n-factors that are applied to every winter period all over the contemporary part of the time series are calculate based on the year of measurement only. However, we have no mean to know whether the calculated n-factors are representative of the average conditions at the Gislá talus slope over the whole reconstruction period; reconstructed temperature data may then be under- or over-attenuated during winter periods. Note that the effect of snow cover insulation on surface temperatures is more adequately taken into account in energy-balance models (e.g., Cryogrid). However, we show that such models cannot reproduce the temperature oscillations due to the onset of the chimney effect in winter (fig. 8b).

73Third, we use a simple semi-automatic method to reconstruct the pre-landslide surface topography of the Gislá talus slope (Section 3.1.1.; Guimpier et al., 2022). It was proved that this method gives results that are less accurate than other reconstruction methods (Guimpier et al., 2022), but also that it is supposed to be adapted to a landslide with a relatively smooth detachment surface. It should be the case with the Gislá study site, as talus slopes are debris that lie at their angle of repose. For the underlying bedrock topography, we also use a simplistic estimation based on geometrical extrapolations. These topographic reconstructions may not represent perfectly the reality of the Gislá talus slope. However, the methods we use have the advantage of being systematic, hence being easily reproducible from one site to another, and reducing to a minimum biases arising from methods requiring more user intervention (e.g., the two other pre-landslide reconstruction methods shown in Guimpier et al., 2022).

74Fourth, our numerical models do not represent the complexity of a natural talus slope. We consider a material that is homogeneous on the whole talus (e.g., in terms of porosity and initial ice bulk volumetric fraction), when natural talus slopes are constituted of debris of varying grain size, heterogeneously distributed within the talus (e.g., Hinchliffe et al., 1998; Curry and Black, 2003; Sanders, 2010). Such heterogeneous debris distribution has implications not only for the thermal parameters of the bulk talus slope, but also on the potential air circulation itself. As our modelling approach considers the talus slope as a bulk, it cannot account for such heterogeneous debris distribution. However, we expect that the tests of sensitivity to the initial porosity/ice content, with extreme values of 0.3 and 0.8, sweep across a wide range of natural configurations. In addition, we also run models in saturated conditions, and only heat transfer by conduction is considered (i.e., no water flow). However, the present study is innovative with respects to previous modelling studies (Tanaka et al., 2006; Wicky and Hauck, 2017; Myhra et al., 2019; Wicky et al., 2024), as our contemporary temperature time series are based on field measurements and have a relatively high temporal resolution (one month to one day; fig. 5); and as the geometry of the talus is constrained by topographic observations and measurements. Therefore, considering a simplified geological setting allows to evaluate the sensitivity of the model to other parameters (e.g., thermal conductivity; Section 5.1.3.).

75Additionally, the fact that our model runs do not simulate air convection (i.e., the chimney effect) also represents a limitation: temperature is certainly lower at the base of the talus compared to our model results, enhancing the persistence of permafrost (Section 5.1.3.).

76Finally, a perched talus slope is a dynamic system with debris that accumulates over time. As our modelling approach requires a fixed geometry, we are unable to consider topographic variations of the Gislá talus slope – either through accumulation or previous destabilisations. It should also be noted that snow avalanche deposits can also accumulate on the talus slope. It would represent an input of ice from the surface, which our models are unable to consider.

6. Outlook

77Our study also leads to several key points for future work. First, thanks to the unconventional approach we used, we showed that the thermal properties of the Gislá talus slope (more specifically the thermal conductivity) that allow the persistence of permafrost differ significantly from the values that can typically be found in the literature. For future modelling studies, such unconventional approaches, based on ground-truth evidence, can help in defining additional modelling scenarios with significantly different results. Overall, such approaches highlight the occurrence of physical phenomena other than those modelled in our case, reducing the thermal conductivity may have partly compensated for the effect of air convection. Hence, future studies could investigate the sensibility of this assumption and compare the results of models with air convection vs. models without air convection and with reduced thermal conductivity. The results of such a study could make easier future numerical modelling studies of talus slopes, by providing a quantitative way to compensate for the effect of air convection.

78Additionally, we provided all the necessary information to easily reproduce our workflow (reconstruction of pre-landslide topography, reconstruction of temperature time series, numerical modelling). Therefore, similar studies could emerge on different study sites. Notably, Iceland has other talus-sourced landslides that bear evidence for the mobilisation of degrading permafrost, and an inventory of molards around the globe will provide additional study sites in periglacial regions worldwide.

79Overall, the greatest challenge in realising more similar studies is logistics for temperature data acquisition. A way to overcome this challenge lies in energy-balance models (e.g., CryoGRID), which can produce ground temperature time series, downscaled from climatic data in order to match the scale of a site-specific study. However, we showed in the present study that energy-balance models are not suitable to study talus slopes specifically – and more generally sites where air convection influences the near-surface temperatures. We suggest that an interesting outlook would be to perform a comparative study between model runs forced with time series based on measured data and model runs forced with time series modelled by energy-balance models. Such a study would question the need for forcing field data in numerical modelling studies. Comparing the results of energy-balance models that include freeze/thaw processes (like CryoGRID) to the results of 2D heat transfer models (such as ours) for a given study site could shed light on the pros and cons of those two methods. Using ground-truth evidence for the presence of permafrost could highlight physical processes that are challenging to model for energy-balance models, and potentially ways to compensate it – similarly to our approach with the Gislá talus slope.

7. Conclusions

80In the present study, we investigated the permafrost dynamics at the Gislá talus slope (Tröllaskagi peninsula, Iceland) through numerical modelling. This talus slope was the source area of a landslide which mobilised degrading azonal permafrost. We sought to understand the conditions under which permafrost could persist within the Gislá talus slope. Our study leads to the following conclusions:

  • one-year near-surface temperature measurements characterise the occurrence of a chimney effect in the Gislá talus slope, and provide relevant data to build forcing time series to model permafrost dynamics within this talus;

  • with a simplistic approach that does not explicitly model air convection, we successfully modelled the expected permafrost occurrence within the Gislá talus slope. Notably, although the average air temperature over the reference period 1991-2020 is +1.47 °C, the models account for the contemporary persistence of permafrost at the base of the talus;

  • field observations of ice-cemented sediment blocks and subsequent molards in the landslide deposits gave additional constraints on the ground ice content within the Gislá talus slope at the time of the landslide (i.e., 50 % ground ice content). Therefore, we adopted an unconventional modelling approach where we sought for the combination of parameters that allow ground ice to persist;

  • the most ice-conservative model scenario (i.e., lowest rock phase TC) is required to only approach the constraint on ground ice content given by the observation of ice-cemented sediment blocks and subsequent molards. However, all model scenarios enable persistence of ground ice within the Gislá talus slope (porosity/initial ice content from 0.3 to 0.8; TC from 0.75 to 1.75 W.m-1.K-1).

*Auteur correspondant : Tel : +33 6.38.55.15.13, Mail : meven.philippe@uni-smb.fr (M. Philippe)

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Annexe

Version française abrégée

La dégradation du permafrost de montagne due au changement climatique actuel déstabilise les versants, ce qui peut provoquer des glissements de terrain qui représentent un risque important en milieu montagneux (e.g., Gruber and Haeberli, 2007 ; Magnin et al., 2023 ; Cathala et al., 2024). Connaître les limites précises du permafrost de montagne est donc crucial afin de prévenir les futurs glissements de terrain et protéger les populations vulnérables en conséquence. Pour cela, la modélisation numérique des limites du permafrost est un outil indispensable.

Parmi les modèles numériques, ceux dits « à base physique » modélisent explicitement des processus physiques (e.g., transfert thermique, convection de l’air ; Wicky and Hauck, 2017 ; Magnin and Josnin, 2021 ; Cathala et al., 2024). Les modèles à base physique permettent donc de modéliser la présence de permafrost azonal, c’est-à-dire le permafrost persistant au-delà de ses limites climatiques par l’action de processus physiques locaux. Notamment, le permafrost peut persister au sein des pentes d’éboulis lorsqu’une circulation d’air particulière survient, appelée « l’effet cheminée » (fig. 1).

Dans cette étude, nous nous intéressons à la pente d’éboulis perchée de Gislá (65°24'23.60"N, 18°16'5.89"W ; péninsule de Tröllaskagi, Islande ; fig. 2), qui a été la source d’un glissement de terrain le 6 octobre 2020. Malgré le fait qu’elle soit située en-dehors des limites climatiques du permafrost, des molards observés dans les dépôts du glissement indiquent que du matériel riche en glace a été mobilisé (teneur en glace proche de 50 % ; Brideau et al., 2009).

Dans cette étude, nous utilisons donc un modèle à base physique modélisant le transfert thermique et les changements de phase de l’eau, afin de mieux comprendre la dynamique thermique des pentes d’éboulis et d’évaluer la présence de permafrost au sein de la pente d’éboulis de Gislá au moment du glissement de terrain.

Pour créer ces modèles numériques, nous avons caractérisé le profil topographique de la pente d’éboulis de Gislá et reconstruit sa morphologie pré-glissement, à partir d’un modèle numérique de terrain créé à partir de photos acquises par un drone (fig. 3).

Nous avons également placé des capteurs thermiques au niveau du talus et de la paroi rocheuse (fig. 3a), qui ont mesuré la température de surface pendant près d’un an entre l’été 2021 et l’été 2022. Nous avons utilisé quatre de ces capteurs : deux à la base et au sommet du talus, deux à la base et au sommet de la paroi rocheuse. Leurs caractéristiques sont fournies dans le Tableau 1. À partir des mesures de ces capteurs et de données de température de l’air, nous avons reconstruit quatre séries temporelles de température jusqu’en 1881 (statistiques sur la reconstruction fournies dans le Tableau 3). Nous avons également modélisé les séries temporelles pour ces quatre capteurs jusqu’à – 20,000 ans BP (Etzelmüller et al., 2020). Le processus de reconstruction et modélisation des séries temporelles est détaillé en Figure 4a ; le résumé de la résolution et de la source des températures le long de la série temporelle est fourni en Figure 5 ; et un exemple de série temporelle complète est fourni en Figure 7.

Nous avons ensuite implémenté la géométrie en deux dimensions de notre site d’étude dans le logiciel commercial FEFLOW, qui utilise la méthode des éléments finis pour résoudre les équations de transfert thermique et modéliser les changements de phase de l’eau au sein des modèles. Nous avons utilisé les séries temporelles de température précédemment créées pour contraindre nos modèles, et avons défini leurs conditions initiales (e.g. température, teneur en glace) et paramètres physiques (e.g. porosité, conductivité thermique, capacité thermique volumétrique ; tabl. 2). Le processus de création et de paramétrisation des modèles est détaillé en Figure 4b.

Chaque modèle tourne depuis -20 000 ans BP jusqu’à la date du glissement de terrain ; la période -20 000 ans BP jusqu’à -100 ans BP sert à initialiser le modèle. Nous avons étudié l’impact sur nos modèles de deux paramètres : la conductivité thermique de la roche, et la porosité/teneur en glace initiale de la pente d’éboulis.

Sur la période de mesure, les températures au sommet de la pente d’éboulis de Gislá sont globalement supérieures aux températures à sa base (fig. 8). Les données de températures de l’air utilisées dans cette étude sont présentées en Figure 9, et les températures moyennes, minimum et maximum pour différentes périodes de temps sont fournies dans le Tableau 4.

La Figure 10 illustre la validation de notre méthode d’initialisation (i.e., en utilisant la période -20 000 ans BP jusqu’à -100 ans BP) en comparaison à la méthode d’initialisation classique des modèles numériques.

Au cours de chaque simulation, la glace commence à dégeler vers -11 000 ans BP, et fond totalement vers -9 500 ans BP. De -8 000 ans BP à -100 ans BP, l’intérieur du talus est dégelé. La glace se reforme totalement avant le début de la période contemporaine (i.e., avant 1881), puis dégèle progressivement jusqu’à atteindre une teneur minimum au moment du glissement de terrain (fig.  1).

Les modèles sont particulièrement sensibles à deux paramètres : la porosité/teneur en glace initiale du talus, et la conductivité thermique de la roche. En augmentant la porosité/teneur en glace initiale (0,3 ; 0,5 ; 0,8 ; fig. 12) et en diminuant la conductivité thermique de la roche (1,75 ; 1,1 et 0,75 W.m-1.K-1 ; fig. 13), on observe que le permafrost persiste dans une plus large zone à la base du talus, avec des teneurs en glace globalement plus élevées.

Les températures plus élevées au sommet de la pente d’éboulis par rapport à sa base, et les oscillations thermiques observées durant l’hiver malgré la couverture neigeuse indiquent qu’un effet cheminée a bien lieu dans la pente d’éboulis de Gislá.

Malgré des températures de l’air nettement au-dessus de 0 °C au cours des dernières décennies, nos modèles parviennent à modéliser la persistance du permafrost au sein de la pente d’éboulis.

Nous avons adopté une approche de modélisation non-conventionnelle, cherchant une combinaison de paramètres (porosité/teneur en glace initiale, conductivité thermique de la roche) permettant d’approcher la contrainte de teneur en glace donnée par la présence de molards (~ 50 % ; Brideau et al., 2009). Néanmoins, la teneur en glace maximum de nos modèles est nettement inférieure à cette contrainte (~ 25 %). Nous suggérons donc que les valeurs extrêmes que nous avons utilisées pour la porosité/teneur en glace initiale et la conductivité thermique de la roche ont permis de compenser partiellement le manque de modélisation explicite de la convection de l’air, et que modéliser ce processus pourrait augmenter la teneur en glace maximum de nos modèles.

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Table des illustrations

Titre Fig. 1 – Schematic diagram of the cross-section of a talus slope, and the internal air circulation caused by the chimney effect a. in winter (Tair < Ttalus), and b. in summer (Tair > Ttalus). Fig. 1 – Coupe schématique d’une pente d'éboulis et circulation d'air causée par l’effet de cheminée, a. en hiver (Tair < Ttalus), et b. en été (Tair > Ttalus).
Légende ‘T’ stands for ‘temperature’. Due to convective air circulation, in winter relatively hot air flows from the talus upward which draws in relatively cold air at the bottom of the talus. In summer, relatively cold air within the talus flows downward. The zone of maximum overcooling (winter) and minimum warming (summer) is located schematically with the white dashed box (schematic representation from Wicky and Hauck, 2017). On both panels the arrow indicates the direction of air circulation; its colour indicates the relative temperature gradient within the talus.‘T’signifie ‘température’. En raison de la convection, en hiver, de l'air relativement chaud s'écoule vers le haut de l’éboulis, ce qui aspire de l'air relativement froid à la base de l’éboulis. En été, de l'air relativement froid s'écoule dans l’éboulis vers sa base. La zone de refroidissement maximal (hiver) et de réchauffement minimal (été) est située approximativement dans la boîte blanche en pointillés (représentation schématique d’après Wicky et Hauck, 2017). Sur les deux figures, la flèche indique la direction de circulation de l'air ; sa couleur indique le gradient de température relatif à l'intérieur de l’éboulis.
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Titre Fig. 2 – The Gislá landslide and its geographic context.Fig. 2 – Le glissement de terrain de Gislá et son contexte géographique .
Légende a. photo of the Gislá landslide, taken on the day of the landslide, October 6th 2020 (courtesy of J.P. Jónsson, who obtained it from local police agents). Dashed lines indicate approximate altitude levels a.s.l., 750 m a.s.l. representing the elevation of the Gislá talus slope; b. Molard example (approximately 2 m high) within the deposits of the Gislá landslide (photo taken on July 2022); c. Location of the Gislá landslide (white dot; 65°24'24.90"N, 18°16'16.05"W) at the scale of the Tröllaskagi peninsula (central northern Iceland). White crosses locate the weather stations of Öxnadalsheiði (540 m a.s.l.) and Akureyri (31 m a.s.l.). Background: Google Earth – Landsat/Copernicus; d. The Gislá landslide from aerial view. Molards in the landslide deposits are located by white crosses (mapped from Arnardóttir, 2023); e. The local context of the Gislá landslide, with panel d. located by a white rectangle, houses by white dots, and waterways by light blue lines.a. Photo du glissement de terrain de Gislá, prise le jour du glissement, 6 octobre 2020 (avec la permission de J.P. Jónsson, qui l’a obtenue des agents de police locaux). Les lignes en pointillés indiquent les altitudes approximatives a.s.l., 750 m a.s.l. représentant l’altitude de la pente de débris de Gislá. b. Exemple de molard (approximativement 2 m de haut) au sein des dépôts du glissement de terrain de Gislá (photo prise en juillet 2022) ; c. Localisation du glissement de terrain de Gislá (point blanc ; 65°24'24.90"N, 18°16'16.05"O) à l’échelle de la péninsule de Tröllaskagi (centre nord de l’Islande). Les croix blanches localisent les stations météorologiques de Öxnadalsheiði (col) et d’Akureyri (ville). Fond de carte : Google Earth – Landsat/Copernicus. d. Le glissement de terrain de Gislá en vue aérienne. Les molards présents dans les dépôts du glissement sont localisés par des croix blanches (cartographiés d’après Arnardóttir, 2023) ; e. Le contexte local du glissement de terrain de Gislá. Le panneau d. est localisé par le rectangle blanc, les bâtiments par des points blancs, et les cours d’eau par les lignes bleu clair.
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Titre Fig. 3 – Main steps of the pre-landslide topographic reconstruction. Fig. 3 – Principales étapes de reconstitution de la topographie pré-glissement.
Légende a. Contour lines cut out according to the delineation of the talus slope (10-metres interval, elevation given every 50 m). Sensors used further in the studies are located by white crosses, and their respective name indicated in italic font; b. Points generated along the contour lines; c. Topographic profile (grey line) selected for defining the surface geometry of the talus slope. Points A and B located on the profile locate the profile shown in panel d; d. Reconstructed pre-landslide topography (black line), measured post-landslide topography (grey line), and estimated bedrock topography (black dashed line) obtained by extrapolation of the bedrock topography around the talus. The extent of this profile is located on the full profile in panel c. In all panels, the white area represents the extent of the studied talus slope, the white crosses in a., b. and c. locate the thermal sensors (Section 3.1.2.), and north is up. White arrows indicate overall slope direction. Background (panels a., b., c.): drone orthophoto.a. Courbes de niveau découpées selon l’emprise de l’éboulis (intervalle de 10 m, altitude donnée tous les 50 m). Les capteurs utilisés dans la suite de l’étude sont localisés par des croix blanches, et leur nom indiqué en italique ; b. Points générés le long des courbes de niveau ; c. Profil topographique (ligne grise) sélectionné pour définir la géométrie de la surface de la pente d’éboulis. Les points A et B situés sur le profil localisent le profil montré dans le panneau d ; d. Topographie pré-glissement reconstruite (ligne noire), topographie mesurée après le glissement de terrain (ligne grise), et topographie estimée du substratum rocheux (ligne pointillée noire) obtenue par extrapolation de la topographie du substratum autour de l’éboulis. L'emprise de ce sous-profil est localisée sur le profil complet dans le panneau c. Dans tous les panneaux, la zone blanche représente l'étendue de l’éboulis, les croix blanches localisent les capteurs thermiques utilisés (Section 3.1.2.), et le nord est en haut. Les flèches blanches indiquent la direction générale de la pente. Arrière-plan (panneaux a., b., c.) : orthophoto drone.
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Titre Fig. 4 – Schematic workflows of our methodological processes. Fig. 4 – Diagramme workflow de nos processus méthodologiques.
Légende a. Generation of temperature time series. Input datasets are identified by a regular font, result datasets by a bold font, and processes by an italic font. ‘TS’ stands for ‘time series’; b. Modelling approach for the creation and parametrisation of the numerical models. The main steps are identified by a bold font. The dashed square identifies the steps that are done outside of FEFLOW. ‘BC’ stands for ‘boundary conditions’, ‘TC’ stands for ‘thermal conductivity’.a. Création des séries temporelles. Les données d’entrée sont identifiées par une police normale, les données résultantes par une police en gras, et les processus par une police italique. ‘TS’ signifie ‘série temporelle’ ; b. Méthode de modélisation de la création et paramétrisation des modèles numériques. Les étapes principales sont identifiées par une police en gras. Le carré en pointillé identifie les étapes se faisant en-dehors de FEFLOW. ‘BC’ signifie ‘condition aux limites’, ‘TC’ signifie ‘conductivité thermique’.
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Titre Tab. 1 – Elevation (m a.s.l.), depth and geological setting of the emplacements of the four thermal sensors installed in the Gislá talus slope and surrounding bedrock.Tab. 1 – Altitude, profondeur et cadre géologique des emplacements des quatre capteurs thermiques installés dans la pente d’éboulis d'Eyjafirði et le substrat rocheux environnant.
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Titre Fig. 5 – Schematic diagram of the resolution and sources of temperature data along the time series.Fig. 5 – Diagramme de la résolution et des sources des données de température le long de la série temporelle.
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Titre Fig. 6 – Geometry of the Gislá study site, divided into three polygons (talus, surface bedrock, deep bedrock), each one discretised in triangular elements at various spatial resolutions. Fig. 6 Géométrie du site d'étude d’Eyjafirði, divisé en trois polygones (éboulis, substratum superficiel, substratum profond), chacun discrétisé en éléments triangulaires à différentes résolutions spatiales.
Légende Thermal boundary conditions are indicated in italics. Arrows indicate the nodes where the base thermal boundary condition (geothermal heat flux of -0.1 W.m-2) is applied. Crosses indicate the nodes where the sensor time series (RW_top, RW_bot, Talus_top, Talus_bot) are applied. The solid black line spans the nodes where the Plateau time series is applied. The dashed black lines span the nodes where values of sensor time series are extrapolated or interpolated. The surface of this cross section corresponds to the topographic profile presented in Figure 3.Les conditions aux limites thermiques sont indiquées en italique. Les flèches indiquent les nœuds où la condition aux limites de température de base (flux de chaleur géothermique de -0,1 W.m-2) est appliquée. Les croix indiquent les nœuds où les séries temporelles des capteurs (RW_top, RW_bot, Talus_top, Talus_bot) sont appliquées. La ligne noire continue s'étend sur les nœuds où la série temporelle du Plateau est appliquée. Les lignes noires en tireté couvrent les nœuds où les séries temporelles des capteurs sont extrapolées ou interpolées. La surface de cette coupe correspond au profil topographique présenté sur la Figure 3.
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Titre Tab. 2 – Summary of thermal parameters, initial conditions, and boundary conditions used to perform model runs. Tab. 2 – Résumé des paramètres thermiques, des conditions initiales et des conditions aux limites utilisés pour effectuer nos simulations.
Légende Associated reference is provided (when applicable). Letters in brackets indicate the phase (‘s’ for solid, ‘w’ for liquid, ‘i’ for ice) the parameter applies to.Les références associées sont fournies (le cas échéant). Les lettres entre parenthèses indiquent la phase (s pour solide, w pour liquide, i pour glace) à laquelle le paramètre s'applique.
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Titre Tab. 3 – Summary of statistics calculated for temperature reconstruction back to January 1st 1949, for all four sensors. Tab. 3 - Résumé des statistiques calculées pour la reconstitution de la température depuis le 1er janvier 1949, pour les quatre capteurs.
Légende For RW sensors, the n-factor is calculated with the Öxnadalsheiði weather station. For talus sensors, R-squared values are calculated based on the summer period; by comparison, we also provide the R-squared values for the winter period. ‘FDD’ stands for ‘freezing degree days’.Pour les capteurs RW, le n-factor est calculé avec la station d'Öxnadalsheiði. Pour les capteurs d'éboulis, les valeurs de R-carré sont calculées sur la base de la période estivale ; à titre de comparaison, nous fournissons également les valeurs de R-carré pour la période hivernale. ‘FDD’ signifie ‘freezing degree days’.
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Titre Fig. 7 - Illustration example of the temperature time series resulting from a. the modelling approach (-20,000 to present time), and b. the statistical reconstruction with annual average, minimum and maximum temperatures (calculated from monthly averages), over the period 1881-2022. Fig. 7 - Exemple illustratif des séries temporelles de température résultant a. de la méthode de modélisation (de -20,000 à l’Actuel), et b. de la reconstitution statistique (1881-2022).
Légende Both temperature curves represent the Talus_top sensor time series.Les deux courbes de température représentent la série temporelle de température du capteur Talus top.
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Titre Fig. 8 – Daily temperatures measured and modeled for the study and recorded by nearby weather stations between August 1st 2021 and July 9th 2022.Fig. 8 - Températures journalières mesurées et modélisées pour le site d'étude et relevées par les stations météo proches, entre le 1er août 2021 et le 9 juillet 2022.
Légende a. Daily average temperatures, measured by RW_top (black line), Talus_top (red line) and Talus_bot (green line). The approximate summer period for this year is greyed out. Example periods showing the effect of the snow cover and air coupling on temperatures measured by talus sensors are located; b. Measured temperatures and modelled temperatures (with Cryogrid) at the Talus_top sensor, on the same period as panel a. Modelled data do not show temperature oscillations in winter; c. Daily average, minimum and maximum temperatures from the Öxnadalsheiði weather station, between August 1st 2021 and July 9th 2022; d. Daily average, minimum and maximum temperatures from the Akureyri weather station, between August 1st 2021 and July 9th 2022.a. Températures moyennes journalières, mesurées par RW_top (ligne noire), Talus_top (ligne rouge) et Talus_bot (ligne verte) entre le 1er août 2021 et le 9 juillet 2022. La période estivale approximative pour cette année est grisée. Des exemples de périodes montrant l'effet de la couverture neigeuse et du couplage de l'air sur les températures mesurées par les capteurs de l’éboulis sont localisés ; b. Températures mesurées et modélisées par Cryogrid au capteur Talus_top, sur la même période de temps que le panneau a. Les données modélisées ne montrent pas d'oscillations de température en hiver ; c. Températures journalières (moyenne, minimum et maximum) mesurées à la station météorologique d’Öxnadalsheiði, entre le 1er août 2021 et le 9 juillet 2022 ; d. Températures journalières (moyenne, minimum et maximum) mesurées à la station météorologique d’Akureyri, entre le 1er août 2021 et le 9 juillet 2022.
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Titre Fig. 9 – Temperature data from weather stations. Daily average, mini-mum and maximum temperatures between 7th October 2019 and 6th October 2020.Fig. 9 – Données de température des stations météorologiques. Tempé-ratures journalières (moyenne, minimum et maximum) entre le 7 oc-tobre 2019 et le 6 octobre 2020.
Légende a. From the Öxnadalsheiði weather station, and b. The Aku-reyri weather station; c. Annual average, minimum and maximum tem-peratures over the period 1881-2021, from the Akureyri manned (1881-1948) and automatic (1949-2021) weather stations; d. Zoom on panel c, with a vertical axis stretched between 0 °C and 6 °C. Temperatures data shown in c. and d. are calculated from the monthly averages.a. Mesurées à la station météorologique d’Öxnadalsheiði, et b. A la station météorologique d’Akureyri ; c. Températures annuelles (moyenne, minimum et maximum) sur la période 1881-2021, mesurées à la station météorologique habitée d’Akureyri (1881-1948) et la station automatique d’Akureyri (1949-2021) ; d. Zoom du panneau c, avec une échelle verticale étirée entre 0 °C et 6 °C. Les températures des panneaux c. et d. sont calculées à partir des moyennes mensuelles.
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Titre Tab. 4 – Back-calculated average, minimum and maximum temperatures over time periods 1961-1990, 1991-2020 and year of measurement, for all four sensors and for the Öxnadalsheiði and Akureyri weather stations.Tab. 4 – Températures moyennes, minimum et maximum sur différentes périodes de temps (1961-1990, 1991-2020, année de mesure), pour les quatre capteurs ainsi que pour les stations météorologiques d’Öxnadalsheiði et d’Akureyri.
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Titre Fig. 10 – Temperature distribution at the date of the Gislá landslide (October 6th 2020), with a. the LGM-initialisation method, and b. the equilibrium-initialisation method, with a TC of the rock phase of 1.1 W.m-1.K-1 and an initial porosity/ice bulk volumetric fraction of 0.8.Fig. 10 – Distribution de la température à la date du glissement de terrain d'Eyjafirði (6 Octobre 2020), avec a. la méthode d'initialisation du LGM, et b. la méthode d'initialisation à l’équilibre, avec une TC de la phase rocheuse de 1,1 W.m-1.K-1 et une porosité/fraction volumétrique de glace initiales de 0,8.
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Titre Fig. 11 – Evolution of the temperature distribution and the ice bulk volumetric fraction over a model run, with a TC of the rock phase of 1.1 W.m-1.K-1 and an initial porosity/ice bulk volumetric fraction of 0.8. Fig. 11 – Evolution de la distribution de la température et de la fraction volumétrique de glace au cours d'une exécution du modèle, avec une TC de la phase rocheuse de 1,1 W.m-1.K-1 et une porosité/fraction volumétrique de glace initiales de 0,8.
Légende a. Temperature distribution and b. Ice bulk volumetric fraction at -11,000 years; c. Temperature distribution and d. Ice bulk volumetric fraction at -8000 years; e. Temperature distribution and f. Ice bulk volumetric fraction on 01/01/1950; g. Temperature distribution and h. Ice bulk volumetric fraction on the date of the Gislá landslide (06/10/2020).a. Distribution de la température et b. Fraction volumétrique de glace à -11 000 ans ; c. Distribution de la température et d. Fraction volumétrique de glace à -8 000 ans ; e. Distribution de la température et f. Fraction volumétrique de glace au 01/01/1950 ; g. Distribution de la température et h. Fraction volumétrique de glace à la date du glissement de terrain d’Eyjafirði (06/10/2020).
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Titre Fig. 12 – Temperature distribution and ice bulk volumetric fraction at the date of the Gislá landslide (October 6th 2020) with a TC of the rock phase of 1.1 W.m-1.K-1. Fig. 12 – Distribution de la température et fraction volumétrique de glace à la date du glissement de terrain d'Eyjafirði (6 Octobre 2020) avec une TC de la phase rocheuse de 1,1 W.m-1.K-1.
Légende a. temperature distribution and b. ice bulk volumetric fraction, for an initial porosity/ice bulk volumetric fraction of 0.3; c. temperature distribution and d. ice bulk volumetric fraction, for an initial porosity/ice bulk volumetric fraction of 0.5; e. temperature distribution and f. ice bulk volumetric fraction, for an initial porosity/ice bulk volumetric fraction of 0.8.a. distribution de la température et b. fraction volumétrique de glace, pour une porosité/fraction volumétrique de glace initiales de 0.3 ; c. distribution de la température et d. fraction volumétrique de glace, pour une porosité/fraction volumétrique de glace initiales de 0,5 ; e. distribution de la température et f. fraction volumétrique de glace, pour une porosité/fraction volumétrique de glace initiales de 0,8.
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Titre Fig. 13 – Temperature distribution and ice bulk volumetric fraction at the date of the Gislá landslide (October 6th 2020) with an initial porosity/ice bulk volumetric fraction of 0.8. Fig. 13 – Distribution de la température et fraction volumétrique de glace à la date du glissement de terrain d'Eyjafirði (6 octobre 2020) avec une porosité/fraction volumétrique de glace initiales de 0,8.
Légende a. Temperature distribution and b. Ice bulk volumetric fraction, for TC of the rock phase of 1.75 W.m-1.K-1; c. Temperature distribution and d. Ice bulk volumetric fraction, for TC of the rock phase of 1.1 W.m-1.K-1; e. Temperature distribution and f. ice bulk volumetric fraction, for TC of the rock phase of 0.75 W.m-1.K-1.a. Distribution de la température et b. Fraction volumétrique de glace, pour une TC de la phase rocheuse de 1,75 W.m-1.K-1 ; c. Distribution de la température et d. Fraction volumétrique de glace, pour une TC de la phase rocheuse de 1,1 W.m-1.K-1 ; e. Distribution de la température et f. Fraction volumétrique de glace, pour une TC de la phase rocheuse de 0,75 W.m-1.K-1.
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Meven Philippe, Florence Magnin, Jean-Yves Josnin, Costanza Morino, Nicolas Monzie et Skafti Brynjólfsson, « Modelling the thermal dynamics of perched permafrost talus slopes: insights from a recently destabilised site (Gislá landslide, October 6th 2020, Iceland) »Géomorphologie : relief, processus, environnement [En ligne], vol. 30 - n° 3 | 2024, mis en ligne le 20 janvier 2025, consulté le 11 février 2025. URL : http://journals.openedition.org/geomorphologie/19138 ; DOI : https://doi.org/10.4000/134ad

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Auteurs

Meven Philippe

EDYTEM, Université Savoie Mont-Blanc, CNRS UMR 5204, Le Bourget-du-Lac, France.

Florence Magnin

EDYTEM, Université Savoie Mont-Blanc, CNRS UMR 5204, Le Bourget-du-Lac, France.

Articles du même auteur

Jean-Yves Josnin

EDYTEM, Université Savoie Mont-Blanc, CNRS UMR 5204, Le Bourget-du-Lac, France.

Articles du même auteur

Costanza Morino

University of Padova, Department of Land, Environment, Agriculture and Forestry, Padova, Italy.

Nicolas Monzie

EDYTEM, Université Savoie Mont-Blanc, CNRS UMR 5204, Le Bourget-du-Lac, France.

Skafti Brynjólfsson

Icelandic Institute of Natural History, Borgum Norðurslóð, Is-600 Akureyri, Iceland.

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