Numerical simulations of recent and future evolution of Monte Perdido glacier

Abstract

Glaciers are globally retreating due to climate change, and the Pyrenees Mountain range is no exception. This study uses the Open Global Glacier Model (OGGM) to explore the dynamics of the Monte Perdido glacier, one of the largest remaining glaciers in the Pyrenees. We explored three calibration approaches to assess their performances when reproducing observed volume decreases. The first approach involved mass balance calibration using terrestrial laser scanning data from 2011 to 2022 and climate data from a nearby weather station. The second approach used terrestrial laser scanning calibration with default climate data provided by OGGM (GSWP3-W5E5). The third approach used default geodetic mass balance calibration and default climate data. By comparing these calibration strategies and analysing historical data (terrestrial laser scanning and ground penetrating radar), we obtain insights of the applicability of OGGM to this small, mild conditions, Pyrenean glacier. The first calibration approach is identified as the most effective, emphasising the importance of selecting appropriate climate data and calibration methods. Additionally, we conducted future volume projections using an ensemble of General Circulation Models (GCMs) under the RCP2.6 and RCP8.5 scenarios. The results indicate a potential decrease in total ice volume ranging from 91.60% to 95.16% by 2100, depending on the scenario. Overall, this study contributes to the understanding of the Monte Perdido glacier’s behaviour and its response to climate change through the calibration of the OGGM, while also providing the first estimate of its future melting under different emission scenarios.

Full text

Cuadernos de Investigación Geográfica
Geographical Research Letters 2024 Nº 50 pp. xx-xx EISSN 1697-9540
Copyright © 2023, The authors. This work is licensed under
a Creative Commons Attribution 4.0 International License.
http://doi.org/10.18172/cig.5816
Please, cite this article as: Mateos-García, A., Santolaria-Otín, M., Sola, Y., Alonso-González, E., Otero, J., Del Rio, L.M.,
López-Moreno, J.I., Revuelto, J.2024. Numerical simulations of recent and future evolution of monte perdido glacier
Cuadernos de Investigación Geográfica 50. http://doi.org/10.18172/cig.5816
NUMERICAL SIMULATIONS OF RECENT AND FUTURE
EVOLUTION OF MONTE PERDIDO GLACIER
ANNA MATEOS-GARCÍA1,2*, MARÍA SANTOLARIA-OTÍN2,
YOLANDA SOLA2, ESTEBAN ALONSO-GONZÁLEZ3,1 ,
JAIME OTERO4, LUIS MARIANO DEL RIO5,
JUAN IGNACIO LÓPEZ-MORENO1, JESÚS REVUELTO1
1Instituto Pirenaico de Ecología (CSIC), Avda Montañana 1005, 50080 Zaragoza, Spain.
2Grup de Meteorologia, Departament de Física Aplicada, Facultat de Física,
Universitat de Barcelona, Martí i Franquès, 08028 Barcelona, Spain.
3Centre d’Etudes Spatiales de la Biosphère, Université de Toulouse,
CNRS–CNES–IRD–INRA–UPS, Toulouse, France.
4Departamento de Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones,
E.T.S.I. de Telecomunicación, Universidad Politécnica de Madrid,
Av. Complutense, 30, ES-28040 Madrid, Spain.
5Departamento de Física Aplicada. Escuela Politécnica,
Universidad de Extremadura, Cáceres 10071, Spain.
ABSTRACT. Glaciers are globally retreating due to climate change, and the Pyrenees Mountain range is no
exception. This study uses the Open Global Glacier Model (OGGM) to explore the dynamics of the Monte Perdido
glacier, one of the largest remaining glaciers in the Pyrenees. We explored three calibration approaches to assess
their performances when reproducing observed volume decreases. The first approach involved mass balance
calibration using terrestrial laser scanning data from 2011 to 2022 and climate data from a nearby weather station.
The second approach used terrestrial laser scanning calibration with default climate data provided by OGGM
(GSWP3-W5E5). The third approach used default geodetic mass balance calibration and default climate data. By
comparing these calibration strategies and analysing historical data (terrestrial laser scanning and ground
penetrating radar), we obtain insights of the applicability of OGGM to this small, mild conditions, Pyrenean
glacier. The first calibration approach is identified as the most effective, emphasising the importance of selecting
appropriate climate data and calibration methods. Additionally, we conducted future volume projections using an
ensemble of General Circulation Models (GCMs) under the RCP2.6 and RCP8.5 scenarios. The results indicate a
potential decrease in total ice volume ranging from 91.60% to 95.16% by 2100, depending on the scenario. Overall,
this study contributes to the understanding of the Monte Perdido glacier’s behaviour and its response to climate
change through the calibration of the OGGM, while also providing the first estimate of its future melting under
different emission scenarios.
Simulaciones numéricas de la evolución reciente y futura del glaciar Monte Perdido
RESUMEN. Los glaciares están retrocediendo globalmente debido al cambio climático, y la cordillera de los Pirineos
no es una excepción. Este estudio utiliza el modelo Open Global Glacier (OGGM) para explorar la dinámica del
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glaciar Monte Perdido, uno de los glaciares actuales de mayor tamaño de los Pirineos. Se exploran tres enfoques de
calibración para evaluar sus rendimientos al reproducir las disminuciones de volumen observadas. El primer enfoque
consistió en calibrar el balance de masas utilizando datos de escaneo láser terrestre de 2011 a 2022 y datos climáticos
de una estación meteorológica cercana. El segundo enfoque utilizó la calibración de escaneo láser terrestre con datos
climáticos predeterminados proporcionados por OGGM (GSWP3-W5E5). El tercer enfoque manejó la calibración
geodésica predeterminada del balance de masas y los datos climáticos predeterminados. Al comparar estas estrategias
de calibración y analizar los datos históricos (escaneo láser terrestre y radar de penetración en el suelo), se obtiene
información sobre la aplicabilidad del OGGM a este pequeño glaciar pirenaico. Se considera que el primer método
de calibración es el más eficaz, haciendo hincapié en la importancia de seleccionar los datos climáticos y los métodos
de calibración adecuados. Además, se realizaron proyecciones de volumen futuras utilizando un conjunto de modelos
de circulación general (GCMs) bajo los escenarios RCP2.6 y RCP8.5. Los resultados indican una disminución
potencial en el volumen total de hielo que va del 91,60% al 95,16% para 2100, dependiendo del escenario. En general,
este estudio contribuye a la comprensión del comportamiento del glaciar Monte Perdido y su respuesta al cambio
climático a través de la calibración del OGGM, al tiempo que proporciona la primera estimación de su futura fusión
bajo diferentes escenarios de emisión.
Keywords: Mountain glacier, OGGM, in-situ surface observations, climate change.
Palabras clave: Glaciar de montaña, OGGM, observaciones superficiales in-situ, cambio climático.
Received: 11 August 2023
Accepted: 24 November 2023
*Corresponding author: Anna Mateos García and Jesús Revuelto, Instituto Pirenaico de Ecología (CSIC), Avda.
Montañana 1005, 50080 Zaragoza, Spain. E-mail: annamateosg@gmail.com; jrevuelto@ipe.csic.es
1. Introduction
Glaciers are highly sensitive indicators of recent climate variations (Beniston, 2003; Grunewald
and Scheithauer, 2010). Current assessments of the Intergovernmental Panel on Climate Change (IPCC)
have highlighted that changes in temperature and precipitation have resulted in global glacier retreat
since the 1950s that is unprecedented in the last 2000 years (IPCC, 2021).
Glaciers in the Pyrenees are currently in a critical situation, with clear evidence of very advanced
stages of degradation (Rico et al., 2017; Vidaller et al., 2021). Due to their small dimensions, glaciers
in the Pyrenees have minimal impact on water resources and global albedo feedback (López-Moreno et
al., 2020). However, they hold scientific and touristic value while carrying strong cultural heritage
(García-López et al., 2021; Moreno et al., 2021; Serrano Cañadas, 2023). Therefore, their melting
represents a significant event, symbolising the wider consequences of climate change.
Glaciers, characterized by compact, perennial ice, experience mass gain through snow
accumulation and mass loss during ablation, primarily through surface melting (van der Veen, 2013;
Eis, 2020). The balance between accumulation and ablation determines a glacier mass fluctuations, with
retreat occurring when ablation surpasses accumulation.
Glacier dynamics of mass balance respond to climate fluctuations on longer time scales rather
than immediately (Huston et al., 2021). Consequently, the advance or retreat of a glacier is not only
determined by the weather of a single year but is a response to cumulative forcings from many years
(Huybers and Roe, 2009). Furthermore, there are other processes that influence glacier evolution such
as avalanches, being sheltered from dominant winds, debris cover thickness, slope of the ice surface, or
rocky outcrops that may appear and enhance incoming long-wave radiation (López-Moreno et al., 2019).
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Numerical simulations of evolution of Monte Perdido glacier
Given the urgency of climate change and glacier retreat, there is significant motivation to study
glacier dynamics through a modelling approach, allowing for predictions of future volume trends given
climatic and geographic inputs. Hence, this study aims to explore the performance of a glacier model
and its practical implementation for the Monte Perdido glacier, one of the largest remaining glaciers in
the Pyrenees (Vidaller et al., 2021), with noticeable thinning observed in recent years (López-Moreno
et al., 2019).
2. Study area
The Monte Perdido glacier, located in the Ordesa and Monte Perdido National Park in the
Central Spanish Pyrenees (42.6806°N, 0.0375°E), consisted of two ice bodies until 2021: the upper and
lower glaciers (Fig. 1). Both bodies are north facing and lie beneath the Monte Perdido Peak
(3355 m a.s.l.). The mean elevations of the upper and lower ice bodies are between 3110 and 2885 m
a.s.l., respectively (Julián and Chueca, 2007). In 2022, the lower Monte Perdido glacier experienced a
division, resulting in the formation of two separate ice bodies (Fig. 1).
Figure 1: (a) Location and extent of the Monte Perdido glacier in 2022 (coordinates in extended UTM zone
31 T). (b) View of Monte Perdido glacier on October 5, 2022.
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Mateos-García et al.
3. Data and methodology
3.1. Data analysis tools
To simulate and analyse the Monte Perdido glacier, we utilised the Open Global Glacier Model
(OGGM), which is a Python based open-source model (Maussion et al., 2019). We employed version
1.6.0 of OGGM, which was released on March 10, 2023 (Maussion et al., 2023). With the glacier
outlines, topographical data, and climate data at a reasonable resolution, the model can estimate the total
ice volume of the glacier and simulate its dynamic evolution in response to different climate forcings
(Maussion et al., 2019). To compute the ice thickness, the model uses an ice thickness inversion method
based on Farinotti et al., (2009).
OGGM is a flowline model that simplifies the glacier geometry by representing it as lines that
depict the central flow path. The flowlines are defined following the approach described by Kienholz et
al., 2014. The model employs the isothermal shallow ice approximation, assuming that the ice thickness
is small compared to its lateral extent, meaning that x-derivatives of stress and velocity are small
compared with the z-derivatives (Paterson, 2000). It is important to note that the shallow ice
approximation is primarily intended for large ice shelves and may not fully capture the complexities of
small mountain glaciers like Monte Perdido. For this glacier, it would be more appropriate to use a
model that solves the complete Stokes system, accounting for the three-dimensional nature of ice flow.
However, for the sake of simplicity and computational efficiency, we opted to use the OGGM model
for this study. Despite this limitation, the validation process supports its use for our specific objectives.
In addition, we used QGIS and CloudCompare software, both open-source platforms, to acquire
the outlines of the glacier derived from TLS and compare glacier surface differences between the TLS
and OGGM model.
3.2. Glacier observation dataset
The surface of the Monte Perdido glacier was derived from terrestrial laser scanning (TLS,
RIEGL LPM-321), following the methodology described by López-Moreno et al., (2016). This device
generates a 3D point cloud by measuring the distance to thousands of points of the target area with
LiDAR technology (Revuelto et al., 2014). TLS observations from 2011 to 2022, allowed us to diagnose
the current state of the Monte Perdido glacier and understand its recent evolution (López-Moreno et al.,
2019). By analysing the TLS data acquired over this period, we were able to track yearly changes in the
glacier’s surface elevation, thickness, and extent, providing crucial information about its dynamic
behaviour.
The high-resolution topography of the glacier’s surrounding area was obtained from the Centro
Nacional de Información Geográfica (CNIG) (CNIG, 2023) (Fig. 2). Specifically, we utilised the Digital
Elevation Model (DEM) with a 5 m grid resolution. This data allowed us to accurately represent the
terrain and its influence on the glacier’s behaviour. The glacier outlines were derived from the 2011
TLS (first year with observations), combining this information with topographical variables (Revuelto
et al., 2022). Additionally, GPR measurements were obtained in 2016 to capture the ice thickness of the
Monte Perdido glacier along several observation transects with an uncertainty of 5 m (López-Moreno et
al., 2019).
We specifically focused on analysing the lower Monte Perdido glacier due to the higher
availability of TLS and GPR (ground-penetrating radar) data.
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Figure 2: Outlines and DEM of glacier’s surrounding area in 2011 (WGS84 coordinate system).
3.3. Climate data
We used long-term (1982-2022) monthly mean temperature and precipitation data obtained
from a weather station located at the Góriz refuge (42.66335°N, 0.01501°E). This meteorological data,
managed by the Spanish Meteorological Service (AEMET), was collected approximately 2.5 km from
the glacier and at an elevation of 2195 m a.s.l. To adapt the data to the glacier region, we applied a lapse
rate of 6.5 °C/km and a precipitation correction factor, which will be further explained in detail.
To ensure a continuous climate dataset, we addressed missing data from the weather station by
utilising ERA5 reanalysis data (Hersbach et al., 2023). Prior to filling the gaps, we evaluated the Góriz
and ERA5 data during overlapping periods and applied the appropriate multiplication factor to
precipitation and temperature. This approach was necessary to maintain data continuity for the OGGM.
Furthermore, we have also used the GSWP3- W5E5 data set (Lange and Büchner, 2020), which is the
default OGGM climate data. GSWP3-W5E5 dataset is a merge between the GSWP3 (Global Soil
Wetness Projected phase 3) dataset (Dirmeyer et al., 2006; Kim et al., 2017) and the W5E5 (bias-
adjusted ERA5 reanalysis) dataset (Lange, 2019; Cucchi et al., 2020) at 0.5°x 0.5° spatial resolution.
For future projections, we selected a list of 10 global climate models from the Coupled Model
Intercomparison Project Phase 5 (CMIP5) ensemble (Taylor et al., 2012) (Table 1). By considering
multiple GCMs, we aimed to capture a range of potential future climate scenarios and assess their impact
on the glacier.
For CMIP5, four Representative Concentration Pathways (RCPs) have been formulated that
provide insights into the expected levels of radiative forcing in the year 2100 when compared to
preindustrial conditions (Taylor et al., 2012). These pathways serve as estimations for the impact of
greenhouse gas concentrations on the Earth’s energy balance. Radiative forcing represents the net
change in the energy balance of the Earth system, determined at the top of the atmosphere or the
tropopause, due to natural or human-induced perturbations (Myhre et al., 2013). For our analysis, we
focused on the RCP2.6 and RCP8.5 scenarios, as they represent the two extremes within the RCP
framework. RCP8.5 stands as the “high” scenario, projecting a continuous rise in radiative forcing
throughout the twenty-first century until it reaches approximately 8.5 W/m2 by the end of the century.
Conversely, the RCP2.6 scenario assumes strong mitigation efforts with a radiative forcing of 2.6 W/m2
by 2100 (Taylor et al., 2012).
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Table 1. CMIP5 models used in this study.
Model name
Resolution
Originating Group(s)
References
CCSM4
0.9°×1.2°
NCAR
Gent et al., 2011
CNRM-CM5
1.4°×1.4°
CNRM-CERFACS
Voldoire et al., 2013
CSIRO-Mk3-6-0
1.8°×1.8°
CSIRO-QCCCE
Rotstayn et al., 2009
CanESM2
2.8°×2.8°
CCCMA
Arora et al., 2011
GFDL-CM3
2.5°×2.0°
NOAA, GFDL
Donner et al., 2011
GFDL-ESM2G
2.5°×2.0°
NOAA, GFDL
Dunne et al., 2012
GISS-E2-R
2.5°×2.0°
NASA, GISS
Miller et al., 2014
IPSL-CM5A-LR
3.7°×1.9°
IPSL
Hourdin et al., 2006
MPI-ESM-LR
1.8°×1.8°
MPI-M
Zanchettin et al., 2013
NorESM1-M
1.8°×2.5°
NCC
Bentsen et al., 2013
3.4. Model calibration
To determine the volume evolution of our glacier, it is important to know how melt in a given
period relates to the climate in the same period. This relationship is established by analysing a period in
which we have available both climate data and thickness change, i.e., from 2011 to 2022. Once this
calibration is done, we can predict glacier evolution applying future climate forcing to our glacier,
assuming that the glacier response to climate forcing remains constant in the future.
For this calibration process, several steps using OGGM were involved. Firstly, we set up the
geographical input data for the glacier, such as outlines and local topography. Then the climate data was
processed from a user-defined climate file, and later the glacier flowlines were determined (Maussion
et al., 2019). Afterwards, we proceeded with the mass balance calibration process. For this, we employed
OGGM’s standard mass-balance (MB) model, which utilises a temperature index approach (Maussion
et al., 2019; Vlug, 2021). The basic assumption of these models is that the melt is proportional to the
positive temperature in a certain period of time (Braithwaite and Zhang, 2000; Hock, 2003). This
calibration determines specific glacier simulation parameters: the temperature bias, the precipitation
factor and the degree-day factor (Maussion et al., 2019; Schuster et al., 2023).
The monthly temperature index model can be calibrated on any mass balance product. The
default is the geodetic MB data from Hugonnet et al., 2021, which consists of comparing the glacier
surface, obtained from satellite elevation datasets, over two dates (Belart, 2018). This global geodetic
glacier dataset provides a mean specific glacier MB estimate between 2000 and 2019 for almost every
glacier on Earth (more than 200,000) (Schuster et al., 2023). However, these geodetic estimates do not
capture interannual variations and its spatial resolution is moderate when compared to TLS data.
Alternatively, in situ mass balance measurements can be employed to capture the year-to-year changes.
The monthly mass balance  at elevation  is computed as follows:
()=

 ()−  max(()− , 0) (1)
Where monthly solid precipitation 
 is multiplied by the precipitation correction factor
. As there
is no precipitation lapse rate in the model, 
can be seen as a global correction factor for orographic
precipitation, avalanches, and wind-blown snow (Vlug, 2021). The precipitation is assumed as liquid
above 2°C, solid below 0°C, and the fraction of solid precipitation is linearly interpolated between these
two boundary values.  is the monthly mean air temperature at 2 m and  is the monthly mean air
temperature above which ice melt is assumed to occur (-1°C per default according to OGGM standard
due to ice pressure). The temperature lapse rate is set by default to 6.5 °C/km. The parameter  is the
degree-day factor indicating the temperature sensitivity of the glacier (van der Laan et al., 2022;
Schuster et al., 2023).
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Numerical simulations of evolution of Monte Perdido glacier
We conducted three simulations (each with a specific calibration of three parameters:
precipitation factor, temperature bias, and degree-day factor) to analyse the behaviour of glaciers under
different configurations (Fig. 3, Table 2):
Figure 3: Comparison of TLS-derived mass balance (and its standard deviation (SD) and (a) modelled mass
balance with in situ MB calibration and Góriz weather station climate data, (b) modelled mass balance with in situ
MB calibration and GSWP3-W5E5 climate data, and (c) modelled mass balance with geodetic MB calibration.
Table 2. Data sources used for mass balance calibration and climate data in different simulations
Data used for MB calibration
Climate data
Simulation 1
TLS
Góriz weather station
Simulation 2
TLS
GSWP3-W5E5
Simulation 3
Geodetic MB
GSWP3-W5E5
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- Simulation 1: This simulation involved calibrating the mass balance using in situ data obtained
from TLS for the years 2011 to 2022. The precipitation factor was estimated by comparing the
total water equivalent of snow during the accumulation period (from October to April) at the
glacier location (López-Moreno et al., 2019) with the precipitation data recorded at the Góriz
weather station for the same period. Analysis of specific years (2013-14, 2014-15, and 2016-
17, which are the only periods with glacier surface observations during the accumulation period)
revealed a maximum mean snow accumulation in late April of 3.25 m, with an average snow
density of 454 kg/m3 (López-Moreno et al., 2019). This indicated a total water equivalent of
1475.5 mm for the accumulation period. Considering that the mean precipitation observed at
the Góriz weather station during the same period was 1089.6 mm, a precipitation factor of 1.3
was estimated and used for the mass balance calibration. Then, the model adjusted the degree-
day factor and the temperature bias to minimise the difference between the model outputs and
observed data, ensuring a better fit between the simulated and the actual mass balance.
- Simulation 2: As in the first simulation, this one involved mass balance calibration using TLS
data. However, instead of using weather station climate data, we used the default climate data
(GSWP3-W5E5) provided by the OGGM framework. The three parameters (precipitation
factor, temperature bias, and degree-day factor) were adjusted accordingly.
- Simulation 3: In this simulation, the mass balance was calibrated with the default average
geodetic observations from January 2000 to January 2019 of Hugonnet et al., 2021, and the
default climate data (GSWP3-W5E5) provided by OGGM.
All the calibration alternatives have at least the three free parameters mentioned above (Schuster
et al., 2023). Without these parameters, the observed glacier MB often cannot be reproduced by the model.
Once the mass balance calibration is performed, a standard geometry evolution model, which is
a depth-integrated flowline model, is responsible to compute the change in glacier geometry. Before
running this simulation, stable glacier conditions are required at the beginning of the study period. To
ensure this, we performed a spin-up process, where the geometry and evolution of the glaciers were
initialised from a given year. We selected a fixed geometry spin-up year of 2000, approximately 10
years before the date of the outline (2011). This year (2011) represents the point at which the glacier is
expected to reach equilibrium (Maussion et al., 2019).
Using the flowline model, an estimate of the ice flux along each glacier grid point cross-section
is computed by making assumptions about the shape of the cross-section (parabolic, rectangular or
trapezoid) and relying on mass-conservation consideration (Maussion et al., 2019). Using the physics
of ice flow and the shallow ice approximation, the model then computes the thickness of the glacier
along the flowlines and the total volume of the glacier.
After performing the historical climate run, we used the ten GCMs described in Table 1 to
project future volume of the Monte Perdido glacier. We employed an ensemble of GCMs to represent
the temperature and precipitation variability in climate projections. To downscale global climate data to
a regional level, we obtained precipitation and temperature data for each GCM from the OGGM server
hosted by the University of Bremen and we applied the precipitation and temperature biases, to the
baseline local climatology, which was defined using the Góriz weather station climate dataset. The
model then uses the interpolated climate data for each GCM to calculate glacier mass balance.
Using this climate data, we ran the simulation for each GCM and scenario from 2020 to 2100.
To initiate this task, we inputted the GCM climate data and utilised the spun up geometry and mass
balance conditions from the historical run as initial conditions within the model.
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Numerical simulations of evolution of Monte Perdido glacier
Finally, we compiled the 20 simulations generated from the ensemble of GCMs and merged
them into two datasets, one for each RCP scenario. This allowed us to calculate the median values and
plot the evolution of glacier volume (Fig. 7).
4. Results and discussion
4.1. Evaluation of climate data
We first evaluate the GSWP3-W5E5 dataset from the OGGM repository against the data
measured at the Góriz weather stations.
Figure 4a represents the historical annual temperature data measured at the Góriz weather
station, along with the GSWP3-W5E5 dataset. The data reveals long-term temperature variations in the
region, and a notable temperature rise on both datasets. The 30-year rolling average highlights this
increase smoothing out short-term variations. The slope of 0.04°C/year and the p-value < 0.05 on both
datasets, confirm a statistically significant positive trend in temperature.
Figure 4: (a) Annual mean temperature and (b) total annual precipitation obtained from Góriz weather
station (grey) and GSWP3-W5E5 dataset (green). The 30-year rolling average is depicted in dashed lines.
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Mateos-García et al.
In addition, Figure 4b shows the historical total annual precipitation data obtained from the
weather station and the GSWP3-W5E5 dataset. The data provides the interannual variability of
precipitation over time. Unlike the temperature, there is no significant change in precipitation over time
(p-value > 0.05). Furthermore, we observed a mean temperature difference of 0.4°C between the Góriz
weather station, situated at 2195 m a.s.l., and the GSWP3-W5E5 dataset, located at 1756 m a.s.l.
Additionally, the Góriz weather station records a greater total annual precipitation compared to the
GSWP3-W5E5 dataset, with a difference of 590 mm.
4.2. Comparison of modelled and TLS-derived volume differences
The comparison of TLS volume evolution (surface decrease multiplied by glacier extent) and
modelled volume evolution provides insights into the accuracy of the model in replicating the observed
glacier volume changes (Fig. 5). The root mean square error (RMSE), correlation coefficient, and p-
value were calculated to evaluate the model performance (Table 3).
Figure 5: Monte Perdido glacier volume (and SD) since 2011 derived from TLS data compared with the three
simulations.
Table 3. Comparison of TLS-Derived Volume with the three simulations from 2011 to 2020
Corr.
p-value
RMSE (m3)
Simulation 1
0.93
<0.01
279435.16
Simulation 2
0.92
<0.01
280778.70
Simulation 3
0.91
<0.01
418856.88
The results indicate that both simulations with in situ mass balance calibration, namely
simulation 1 and 2, exhibit a higher correlation with the TLS-derived volume compared to simulation 3.
This suggests that the calibration process with TLS data improves the agreement between the model and
the observed data. Furthermore, simulation 1 with Góriz climate data shows slightly improved
performance compared to the one with GSWP3- W5E5 climate data, as evidenced by a lower RMSE
value and higher correlation coefficient (Table 3).
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Numerical simulations of evolution of Monte Perdido glacier
The incorporation of TLS data into the calibration process helps to account for the interannual
variation of the glacier mass balance. This, in turn, enhances the accuracy of the model’s predictions.
Furthermore, Góriz climate data might provide a better representation of the local climate conditions
and their influence on the glacier, resulting in a more accurate estimation of mass balance parameters.
It is important to note that simulation 3, despite exhibiting a slightly lower correlation and higher
RMSE, still demonstrates a reasonable agreement with the TLS derived volume. This suggests that the
calibration process, even with GSWP3-W5E5 climate data and geodetic mass balance calibration, can
provide valuable insights into the glacier’s behaviour. However, the differences in performance between
simulation 3 and the other simulations highlight the importance of selecting appropriate climate data
and calibration methods to improve the accuracy of glacier volume projections.
4.3. Comparison of modelled and GPR thickness
The GPR measurements, taken in 2016, offer a direct assessment of the glacier’s ice thickness
at specific locations on the Monte Perdido glacier (López-Moreno et al., 2019). The comparison of
modelled and GPR thickness provides additional insights into the accuracy of the model’s representation
of the spatial distribution of ice (Fig. 6).
Figure 6: Difference between the modelled ice thickness and the GPR measurements taken in 2016 at specific
locations of Monte Perdido glacier. WGS84 coordinate system.
It has to be noted that the GPR measurements were influenced by the presence of water, causing
a very low signal to noise ratio leading to ± 5 m of uncertainty in estimations of ice thickness, which
should be taken into account when interpreting the results.
The mean difference between the modelled and GPR thickness is 6.4 m, with a maximum
difference of 32.7 m, indicating a certain level of variability and uncertainty in the model’s ability to
capture the ice thickness distribution. Furthermore, the average discrepancy between the two datasets is
provided by the RMSE of 8.7 m. While there is some level of agreement between the model and the
GPR data, there are still considerable differences between them.
However, it is important to note that GPR measurements provide localised information and may
not fully represent the entire glacier’s ice thickness distribution. Additionally, accurately modelling ice
thickness is challenging without precise knowledge of the topography below the glacier.
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Mateos-García et al.
Moreover, the weather station used for collecting meteorological data for the Monte Perdido
glacier is situated about 2.5 km away from the glacier and on the south face, while the glacier itself is
on the north face. This spatial difference introduces uncertainty in representing local climate conditions,
despite applying temperature and precipitation correction factors. The use of a fixed lapse rate of
6.5°C/km to adjust weather station data to the glacier region simplifies temperature variations with
elevation. Additionally, the estimation of the precipitation factor based on comparing data from the
glacier location and a weather station may overlook variations in snowfall patterns, snow density, or
liquid precipitation during the accumulation period.
4.4. Future volume projections
Across both RCP scenarios, the projected total ice volume for the Monte Perdido glacier shows
a consistent decrease from 2020 to 2100. Figure 7 shows a faster decline in volume between 2020 and
2060, followed by a deceleration in the rate of decrease.
Figure 7: Multi-GCM ice volume for RCP2.6 and RCP8.5 scenarios from 2020 to 2100 with the historical
simulation from 2000 to 2020 in a dashed line and the calibrated period in a solid black line. Volumes for
each GCM run of RCP2.6 are plotted in blue and for RCP8.5 in red, with multi-GCM medians represented in
thicker lines. Plot (a) displays the full projection, while (b) zooms the 2020 - 2080 period.
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Numerical simulations of evolution of Monte Perdido glacier
The total median volume exhibits minimal variation between the RCP scenarios. For the RCP8.5
scenario, the ice volume experiences a significant decrease of 95.2% by the year 2100, 88.6% by 2060,
and 66.0% by 2040. Similarly, under the RCP2.6 scenario, there is a decrease of 91.6% by 2100, 82.8%
by 2060, and 59.6% by 2040.
The observed decreasing trend in the volume of the Monte Perdido glacier is not unexpected;
many studies have documented similar decreases in glacier volume worldwide (Ma et al., 2010;
Zekollari et al., 2019; Khadka et al., 2020), including in the Pyrenees (Chueca Cía et al., 2005; López-
Moreno et al., 2016; Campos et al., 2021; Vidaller et al., 2021). Given that Monte Perdido is one of the
largest glaciers of the Pyrenees, situated at higher altitudes and facing north, it suggests that other
glaciers might experience even more pronounced losses.
5. Conclusions
We employed the Open Global Glacier Model to simulate and analyse the Monte Perdido glacier
recent and future evolution. We utilised the OGGM to estimate the total ice volume of the glacier and
simulate its evolution in response to different climate forcings.
The calibration process of the OGGM involved three simulations: one using in situ mass balance
calibration and weather station climate data, another with in situ mass balance calibration using default
climate data, and a third with uncalibrated mass balance and default climate data. Through these
simulations, we evaluated the performance of the model when replicating the observed volume changes
of the glacier. The simulations with in situ mass balance calibration exhibited a higher correlation with
TLS-derived volume compared to the default MB geodetic calibration, indicating the importance of
exploiting in-situ observations on the calibration to improve model accuracy.
Furthermore, we projected the future volume of the Monte Perdido glacier using an ensemble
of ten GCMs under the RCP2.6 and RCP8.5 scenarios. The results showed a consistent decrease in total
ice volume from 2020 to 2100, with a faster decline between 2020 and 2060 followed by a deceleration
in the rate of decrease. The projected volume reductions were substantial, ranging from 91.6% to 95.2%
by the year 2100, depending on the scenario. These findings align with the global trend of glacier volume
decrease and are consistent with previous studies in the Pyrenees region.
In addition, as we look ahead, it's worth considering future directions that could further enhance
our understanding of glacier behaviour and its interaction with climate. While our study primarily
focused on the Monte Perdido glacier's response to climate forcing, we acknowledge the need for future
investigations into the potential consequences of climate change on avalanche triggering and its
subsequent impact on glacier evolution. Moreover, new approaches like ODINN.jl (Bolibar et al., 2023)
and MuSA (Alonso-González et al., 2022) demonstrate promising paths to enhance glacier modelling
by incorporating advanced data assimilation techniques.
Acknowledgements
The authors are grateful for the OGGM community for developing and maintaining the OGGM
model, AEMET, ISIMIP and the World Climate Research Programme’s Working Group on Coupled
Modelling for providing the necessary climate data and CNIG for granting access to their geospatial
data. J. Revuelto is supported by a “Ramón y Cajal” postdoctoral fellow of the Spanish Ministry of
Science, Innovation and Universities (RYC2021-033859-I). This work was partly supported by the
project “MeltingIce: La desaparición de los últimos glaciares Pirenaicos” of the “Convocatoria 2023 de
BECAS LEONARDO a Investigadores y Creadores Culturales Fundación BBVA”.
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