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\DOI{10.5802/crgeos.297}
\datereceived{2025-03-02}
\daterevised{2025-05-21}
\dateaccepted{2025-05-23}
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\dateposted{2025-06-16}
\begin{document}

\begin{noXML}

\CDRsetmeta{articletype}{research-article}

\TopicFR{G\'eomorphologie}
\TopicEN{Geomorphology}
\TopicFR{Pal\'eoenvironnements, pal\'eoclimats}
\TopicEN{Paleoenvironments, paleoclimates}

\shortrunauthors

\title{Assessing climatic control on erosion dynamics in alpine glacial
cirques: evidence from the Neoglacial and Younger Dryas periods}

\alttitle{\'{E}valuation du contr\^{o}le climatique sur l'\'{e}rosion dans
des cirques glaciaires alpins : comparaison entre les p\'{e}riodes du
N\'{e}oglaciaire et du Dryas R\'{e}cent}

\author{\firstname{Quentin} \lastname{Portal}\CDRorcid{0009-0002-3837-537X}\IsCorresp}
\address{ISTerre, UMR 5275, Univ. Savoie Mont Blanc, Univ. Grenoble Alpes, 
CNRS, IRD, Univ. Gustave Eiffel, 73370 le Bourget-du-Lac, France}
\email[Q. Portal]{quentin.portal1@univ-smb.fr}

\author{\firstname{Jean-Fran\c{c}ois} \lastname{Buoncristani}\CDRorcid{0000-0001-5447-5640}}
\address{Biog\'{e}osciences, UMR/CNRS 6282, 
Univ. Bourgogne Europe, 6 Bd Gabriel, 21000 Dijon, France}
\email[J.-F. Buoncristani]{jfbuon@u-bourgogne.fr}

\author{\firstname{Benjamin} \lastname{Pohl}\CDRorcid{0000-0002-9339-797X}}
\addressSameAs{2}{Biog\'{e}osciences, UMR/CNRS 6282, 
Univ. Bourgogne Europe, 6 Bd Gabriel, 21000 Dijon, France}
\email[B. Pohl]{benjamin.pohl@u-bourgogne.fr}

\author{\firstname{Romain}\nobreakauthor\lastname{Delunel}\CDRorcid{0000-0001-7752-6498}}
\address{Univ. Lyon 2, CNRS, UMR 5600 EVS, 69576 Bron, France}
\email[R. Delunel]{romain.delunel@univ-lyon2.fr}

\author{\firstname{Jean-Louis} \lastname{Mugnier}\CDRorcid{0000-0002-3403-7747}}
\addressSameAs{1}{ISTerre, UMR 5275, Univ. Savoie Mont Blanc, Univ. Grenoble Alpes, 
CNRS, IRD, Univ. Gustave Eiffel, 73370 le Bourget-du-Lac, France}
\email[J.-L. Mugnier]{jean-louis.mugnier@univ-smb.fr}

\keywords{\kwd{Glacial cirques}
\kwd{Quantitative geomorphology}
\kwd{Paleogeography}
\kwd{Younger Dryas}
\kwd{Neoglacial}
\kwd{Alps}
\kwd{Erosion}}

\altkeywords{\kwd{Cirques glaciaires}
\kwd{G\'{e}omorphologie quantitative}
\kwd{Pal\'{e}og\'{e}ographie}
\kwd{Dryas R\'{e}cent}
\kwd{N\'{e}oglaciaire}
\kwd{Alpes}
\kwd{\'{E}rosion}}

\thanks{TelluS program of the Institut National des Sciences de
l'Univers, CNRS}

\begin{abstract}
Glacial cirques are key indicators of interactions between glaciers,
climate, and topography. Moraine formation in glacial cirques is mainly
influenced by periglacial and subglacial erosion processes, glacier
dynamics, and topography. The intensity and spatio-temporal variability
of erosion processes are climate-driven, yet climate is rarely
considered in moraine formation. In this study, moraines formed during
periods of glacier advances in several high-altitude cirques of the
Mont Blanc, Aiguilles Rouges, and Gran Paradiso massifs were used as
proxies for erosion to assess climate influence. We compared moraines
from two periods:  the Younger Dryas (cold and dry) and the Neoglacial
(temperate and humid). A PDD glacial model was used to calibrate
climate variations for these two periods relative to a reference period
(1979--2014). Denudation rates were calculated from moraine volumes
derived from high-resolution LiDAR DEM. Two extreme moraines
formation-time hypotheses allowed the calculation of minimum and
maximum values: 0.05 to  0.11 \tralicstex{mm\textperiodcentered a\textsuperscript{--1}}{$\mathrm{mm}{\cdot}\mathrm{a}^{-1}$} and
0.10 to  0.23 \tralicstex{mm\textperiodcentered a\textsuperscript{--1}}{$\mathrm{mm}{\cdot}\mathrm{a}^{-1}$} during the Younger
Dryas; 0.12 to  0.45 \tralicstex{mm\textperiodcentered a\textsuperscript{--1}}{$\mathrm{mm}{\cdot}\mathrm{a}^{-1}$} and 0.24 to 
0.90 \tralicstex{mm\textperiodcentered a\textsuperscript{--1}}{$\mathrm{mm}{\cdot}\mathrm{a}^{-1}$} during the Neoglacial.
Furthermore, denudation rates correlated positively with mean annual
temperature and precipitation in the studied cirques. These results
could highlight those climatic parameters exert both spatial and
temporal control on erosion in glacial cirques, with erosion being
significantly accentuated under more temperate and humid climates
compared to colder and dryer climates.
\end{abstract}

\begin{altabstract}
Les cirques glaciaires sont des indicateurs cl\'{e}s des interactions
entre glaciers, climat et topographie. La formation de moraines dans
les cirques glaciaires est principalement influenc\'{e}e par les
processus d'\'{e}rosion p\'{e}riglaciaire et sous-glaciaire, la
dynamique des glaciers et la topographie. L'intensit\'{e} et la
variabilit\'{e} spatio-temporelle des processus d'\'{e}rosion
d\'{e}pendent du climat, mais celui-ci est rarement pris en compte dans
la formation des moraines. Dans cette \'{e}tude, les moraines
form\'{e}es pendant des p\'{e}riodes d'avanc\'{e}e des glaciers dans
des cirques de haute altitude des massifs du Mont-Blanc, des Aiguilles
Rouges et du Grand-Paradis ont \'{e}t\'{e} utilis\'{e}es comme proxies
de l'\'{e}rosion pour \'{e}valuer l'influence du climat. Nous avons
compar\'{e} les moraines de deux p\'{e}riodes : le Dryas R\'{e}cent
(froid et sec) et le N\'{e}oglaciaire (temp\'{e}r\'{e} et humide). Un
mod\`{e}le glaciaire PDD a \'{e}t\'{e} utilis\'{e} pour calibrer les
variations climatiques de ces deux p\'{e}riodes par rapport \`{a} une
p\'{e}riode de r\'{e}f\'{e}rence (1979--2014). Les taux de
d\'{e}nudation ont \'{e}t\'{e} calcul\'{e}s \`{a} partir des volumes
des moraines obtenus en utilisant des MNT LiDAR \`{a} haute
r\'{e}solution. Deux hypoth\`{e}ses extr\^{e}mes de temps de formation
des moraines ont permis de calculer des valeurs minimales et maximales
: 0,05 \`{a} 0,11 \tralicstex{mm\textperiodcentered a\textsuperscript{--1}}{$\mathrm{mm}{\cdot}\mathrm{a}^{-1}$} et 0,10 \`{a} 
0,23 \tralicstex{mm\textperiodcentered a\textsuperscript{--1}}{$\mathrm{mm}{\cdot}\mathrm{a}^{-1}$} pendant le Dryas R\'{e}cent ;
0,12 \`{a} 0,45 \tralicstex{mm\textperiodcentered a\textsuperscript{--1}}{$\mathrm{mm}{\cdot}\mathrm{a}^{-1}$} et 0,24 \`{a} 
0,90 \tralicstex{mm\textperiodcentered a\textsuperscript{--1}}{$\mathrm{mm}{\cdot}\mathrm{a}^{-1}$} pendant le N\'{e}oglaciaire.
De plus, les taux de d\'{e}nudation sont positivement corr\'{e}l\'{e}s
avec les temp\'{e}ratures et pr\'{e}cipitations annuelles moyennes. Ces
r\'{e}sultats pourraient mettre en \'{e}vidence le contr\^{o}le
climatique sur l'\'{e}rosion dans les cirques glaciaires de haute
altitude avec une \'{e}rosion plus \'{e}lev\'{e}e pour des climats
temp\'{e}r\'{e}s et humides par rapport aux climats froids et secs.
\end{altabstract}

\maketitle

\vspace*{3pc}

\twocolumngrid

\end{noXML}

\section{Introduction}\label{sec1}
Glaciers exhibit highly variable erosion rates, ranging from $10^{-4}$
to $10^1~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$. This significant
variability results from various glaciological factors such as basal
temperature, subglacial topography, and flow velocity
\citep{SugdenJohn1976,Halletetal1996,Delmasetal2009,Hermanetal2015}. 
Analysis of catchments of valley glaciers spanning from Patagonia to
the Antarctic Peninsula has shown that glacial erosion rates vary from
1 to over $10~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ for temperate glaciers
and from 0.01 to less than $0.1~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ for
cold glaciers, highlighting latitudinal control and climate influence
\citep{Koppesetal2015,Fernandezetal2016}. Climate variations are
affecting glacial and periglacial erosion, which depends on
temperature, water availability, and freeze-thaw cycles 
\citep{Halletetal1996,Godonetal2013}. Glacial advances are linked to
cold and humid periods, but the impact of climatic conditions on
glacial erosion rates remains under debate, particularly regarding the
interactions between temperature, moisture, and glacier dynamic
\citep{Delmasetal2009,Hermanetal2021}.

Glacial cirques are highly sensitive to climate changes 
\citep{HussFischer2016,Schwatetal2023}. In these environments, two
erosive processes coexist: subglacial erosion over bedrock and
periglacial erosion processes in the cirque walls 
\citep{Guillonetal2015,Hermanetal2021}.  The moraines of cirque
glaciers are mainly composed of materials produced by periglacial
erosion processes, then transported and deposited by the glacier 
\citep{Smalletal1979,GomezSmall1985,Wetteraueretal2022}. A variable
proportion of subglacial sediment can also be deposited within moraines
\citep{Reheis1975,Anderson1978}. However, the finest part of the
materials produced by subglacial abrasion are generally exported into
proglacial streams 
\citep{HumphreyRaymond1994,Godonetal2013,Hermanetal2015,Hermanetal2021}.
As a result, determining the moraine volumes can serve as a proxy for
erosion within glacial cirques
\citep{Reheis1975,Anderson1978,LarsenMangerud1981,Crest2017}.
\looseness=-1

Since the Last Glacial Maximum, two periods when glaciers were more
extensive than today are particularly well-documented in the Alps: 
(1)~the 
\mbox{Little} Ice Age (LIA, 1250--1850), representing the final
Neoglacial advances  \citep{Solominaetal2016}, with temperatures
approximately 0.5~\textdegree C lower than 20th-century averages and
more humid conditions 
\citep{McDermottetal1999,MatthewsBriffa2005,Wanneretal2011,Magnyetal2012,Furlanettoetal2018,Kaufmanetal2020,Erbetal2022}; 
(2)~the Younger Dryas (12.9--11.7~ka BP)  \citep{Ivy-Ochs2015},
characterised by temperatures up to 6~\textdegree C below  20th-century
averages and drier conditions 
\citep{Ilyashuketal2009,ShakunCarlson2010,Samartinetal2012,Carlson2013,Renssen2020}.

In this context, this study aims to test the influence of climate
variations on erosion rates in glacial cirques by comparing the Younger
Dryas (YD) and Neoglacial (NG) periods. Our approach is based on
analysing moraines built during these glacial stages in high-altitude
cirques, with moraine volume serving as a proxy for erosion. We examine
moraines from these two periods across twelve glacial cirques  with
relatively homogeneous characteristics (i.e., exposure, lithology, and
geographic location) in the alpine massifs of the Gran Paradiso, Mont
Blanc, and Aiguilles Rouges. This analysis allows us to assess the
impact of climate parameters on erosion processes in glacial cirques
and to highlight the links between climate and erosion.

\begin{figure*}
\includegraphics{fig01}
\caption{\label{fig1}Location of the Mont Blanc and Aiguilles Rouges
(A) and Gran Paradiso (B) massifs within the context of the Western
Alps, and the studied cirques at the massif scale. (1)~Pendant and
Lognan; (2)~Nant Blanc; (3)~Drus; (4)~Nantillons;  (5)~Blaiti\`{e}re;
(6)~P\`{e}lerins; (7)~Remuaz; (8)~Invergnan;  (9)~Trajo; (10)~Timorion;
(11)~Gran Paradiso cirques (including from north to south the
Montandayne, Laveciau, and Gran Paradiso glaciers); (12)~Monciair.}
\end{figure*}

\section{Geological setting}\label{sec2}
This study focuses on glacial cirques located in the European alpine
massifs of the Gran Paradiso, Mont Blanc, and Aiguilles Rouges 
(Figure~\ref{fig1}). The Mont Blanc massif lies at the border between
France, Italy, and Switzerland. It belongs to the external crystalline
massifs and is primarily composed of Variscan gneiss and granite
\citep{Ayrtonetal1987}. The Aiguilles Rouges massif, located to the
west of Mont Blanc, is also part of the external crystalline massifs.
The Gran Paradiso massif (Italy) is one of the internal crystalline
massifs and is primarily composed of gneiss and granite with the
presence of schist  \citep{CompagnoniLombardo1974,Brouweretal2002}.  In
these two areas, moraine deposits record two periods of glacial
advances (available $\mbox{}^{10}$Be surface exposure dating for the
study area are presented in Supplement S1):  (1)~the YD moraines
\citep[][Agziou, personal communication]{Protinetal2019,
Protinetal2021,Baronietal2021,Serraetal2022a,Serraetal2022b},
which is the last cooling phase before the Holocene, and (2)~the NG
moraines, which spans the Late Holocene up to the end of the LIA
\citep{LeRoy2012,Gardent2014,LeRoyetal2015}.  In case moraines were not
directly dated using cosmogenic nuclides, their deposition age is
attributed to either YD or NG period based on PDD modelling results 
(Section~\ref{sec3.3}) and their relative position compared to other
dated moraines \citep{Nicoudetal2005}.\looseness=1

\begin{figure*}
\includegraphics{fig02}
\vspace*{5pt}
\caption{\label{fig2}(A)~View of the mapping of the surface of  a NG
moraine from the Laveciau glacier (Gran Paradiso) on a shaded DEM. 
(B)~Cross-section showing in yellow the volume of the moraine
calculated between the actual topography (black line) and the
interpolation (red line).}
\vspace*{6pt}
\end{figure*}

Based on these previous studies, twelve moraines corresponding to the
NG extension were analysed: the junction between the Pendant and Lognan
glaciers, the Nant Blanc, the Drus, the Nantillons, the Blaiti\`{e}re
and the P\`{e}lerins glaciers in the Mont Blanc massif; the Remuaz
cirque in the Aiguilles Rouges massif; the Invergnan, the Trajo, the
Timorion, the Monciair glaciers, and the junction between the
Montandayne, Laveciau and Gran Paradiso glaciers in the Gran Paradiso
massif  (Figure~\ref{fig1}). These moraines were selected due to their
well-preserved morphology, allowing us to determine their respective
volumes. To compare the results between the NG and the YD, we studied
three glaciers where YD moraines are clearly visible and preserved
downstream of the NG moraines  (Figure~\ref{fig1}): the junction
between the Nantillons and Blaiti\`{e}re glaciers and the junction
between the Pendant and Lognan glaciers in the Mont Blanc massif; the
junction between the Montandayne, Laveciau, and Gran Paradiso glaciers
in the Gran Paradiso massif. The limited number of NG and YD moraines
included in the study is due to the requirement for well-preserved
morphological features, ensuring that the moraines have not undergone
significant erosion and allowing reliable volume estimation (see 
Section~\ref{sec3.1}). However, this limited number of moraines is
located in a rather homogeneous context, characterised by crystalline
lithology and predominantly west- or northwest-facing slopes.

The YD is a cold event dated between 12.9 and 11.7~ka BP, well
documented in the Greenland ice stratigraphy (GS-1)
\citep{Rasmussenetal2006}.  In Europe, the YD is described as a period
that was 2 to 6~\textdegree C colder than the  20th-century averages
and characterised by reduced precipitation 
\citep{Ilyashuketal2009,Samartinetal2012,Carlson2013,Renssen2020}. In
the Swiss and Austrian Alps, the YD corresponds to the moraines of the 
``Egesen'' stadial  \citep{Maisch1982,Ivy-Ochsetal2009}. 

The NG period follows the climatic optima of the Middle Holocene
\citep{Davisetal2003,Wanneretal2008}. In Europe, it is characterised by
a return to cooler and wetter climatic conditions
\citep{McDermottetal1999,Vintheretal2009,Wanneretal2011,Magnyetal2012,Furlanettoetal2018,Erbetal2022}, which
fostered several periods of glacial advances (sometimes named LIATEs:
Little Ice Age Type Events), mainly the 4.2~ka advance, the L\"{o}bben,
the G\"{o}schenen I and II and the LIA \citep{MatthewsDresser2008}. 
Temperature anomalies during this period reach approximately
${-}$0.5~\textdegree C  compared to the averages of the second half of
the 20th-century 
\citep{MatthewsBriffa2005,Kaufmanetal2020,Erbetal2022}. Since
approximately 5.0 ka BP, alpine glaciers have experienced several
phases of advance, with the extent of these advances partly influenced
by glacier response times
\citep{MatthewsDresser2008,Ivy-Ochsetal2009,Solominaetal2015}. 

For our study area, we used two datasets to describe the current
climate. (1)~Due to the scarcity of data in high mountain regions, we
relied on compiled, controlled, and analysed data from 12
meteorological stations (daily temperature and precipitation) located
around the massifs, covering the period from 1979 to 2014 
\citep{Jolyetal2017}. These data allowed us to calculate altitudinal
gradients for temperature and precipitation (S2.1).  (2)~Interpolated
climate data from the CHELSA spatial database  \citep{Kargeretal2017},
with a resolution of approximately 1~km, were used to analyse spatial
variations in mean annual temperature and precipitation between 1981
and 2010 for the studied glacial cirques.

\section{Methods}\label{sec3}

\subsection{Calculation of moraine volume}\label{sec3.1} 
The boundaries of the moraines were mapped (Figure~\ref{fig2}A) using a
semi-automatic approach based on a convexity index calculated from a
LiDAR DEM with a resolution of 0.5 to 2~m, depending on the available
data (S3). This index utilises the Volumetric Obscurance (VO) method, a
recent DEM processing technique for characterising landform structures
\citep{Rollandetal2022,Daynacetal2024}. By calculating the VO and
applying a threshold, concave areas corresponding to the base of the
moraines and convex areas to the crests were identified. These
boundaries were verified using high-resolution aerial photographs
(\text{\textcopyright}ortho IGN) and, in some cases, through
direct field observations.

The mapped moraines edges were then used to calculate the moraine
volumes by reconstructing the bedrock surface beneath the moraines.
Along the moraine boundaries, elevation points were extracted every
2~m, and a spline interpolation method, ``thin plate splin'' of the
Saga toolbox in Qgis  \citep{DonatoBelongie2002}, was applied to
reconstruct the bedrock surface  \citep{Crest2017}. This method
generates a relatively flat surface  (Figure~\ref{fig2}B), representing
a topographic model of the bedrock. The volume between the LiDAR DEM
(corresponding to the moraines) and the reconstructed bedrock was then
calculated for each moraine (Tables~\ref{tab1} and~S6-1). This approach
is applicable to all studied moraines, as the geomorphology of the
bedrock surrounding the moraines shows no significant relief variation
because the moraines are located on glacial polished surfaces below the
Last Glacial Maximum (LGM) trimline 
\citep{CoutterandBuoncristiani2006,Salvatoreetal2021}. 

\begin{table*}
\caption{\label{tab1}Values of the constants used to calculate the
denudation rates in glacial cirques}
\begin{tabular}{cccccc}  
\thead
\parbox[t]{1.8cm}{\centering
Bedrock density $\rho_{\mathrm{b}}$} &amp; 
\parbox[t]{1.8cm}{\centering
Moraine density $\rho_{\mathrm{m}}$} &amp; 
\parbox[t]{1.8cm}{\centering
Maximum time NG} &amp; 
\parbox[t]{1.8cm}{\centering
Minimum time NG} &amp; 
\parbox[t]{1.8cm}{\centering
Maximum time YD} &amp; 
\parbox[t]{1.8cm}{\centering
Minimum time YD} 
\vspace*{2pt}\\ 
\endthead
$2700~\mathrm{kg}{\cdot}\mathrm{m}^{-3}$ &amp; 
$2025\pm135~\mathrm{kg}{\cdot}\mathrm{m}^{-3}$ &amp;
5000~years &amp; 2500~years &amp; 2400~years &amp; 1200~years
\botline 
\end{tabular}
\vspace*{8pt}
\end{table*}

To estimate the error between the calculated and real moraine volumes
and to select the most appropriate interpolation method, we simulated a
moraine surface on a large polished bedrock area in the Aiguilles
Rouges massif (S4). Several interpolation methods (kriging, IDW,
multilevel B-spline, and thin plate spline) were tested to generate an
interpolated bedrock model on the simulated moraine surface, following
the method described above. For each interpolation method, the volumes
above and below the real polished bedrock topography were computed by
multiplying the altitude difference (S4-1) between the two surfaces by
the cell resolution. The closer the two volume estimates are, the
better the bedrock modelling is. The smallest discrepancy,
approximately 7\%, was achieved using the  ``thin plate spline''
interpolation tool from the SAGA toolbox in QGIS
\citep{DonatoBelongie2002}. Therefore, this tool was selected to create
the bedrock model beneath all studied moraines, and the 7\% value was
adopted as the uncertainty associated with moraine volume calculations.

\subsection{Definition of erosional surfaces and\newline  
calculation of denudation rates}\label{sec3.2} 
The catchment corresponding to each moraine (NG or YD) was calculated
by delineating water flow lines from the DEM (``channel network'' of
the Saga toolbox in Qgis). Then, the ridge lines separating the flow
lines were precisely extracted by thresholding the convexity index
calculated using the VO method on the DEM. For each catchment,
geomorphological and climatic parameters were extracted: real surface
area (taking slope into account), minimum, maximum, and average
altitudes, relief (difference between maximum and minimum altitude)
median slope, as well as average annual temperature and precipitation 
(Tables~S5-1 and~S5-2). The sediment source area corresponds to the
entire catchment, considering that the sediments stored in the moraines
can result from both periglacial erosion processes and glacial erosion
processes  \citep{Reheis1975,Anderson1978,BennettGlasser2011}. 

The denudation rates were calculated from the volume of the moraines,
the production area, and the time of moraine formation
(Equation~(\ref{eq1})).
{\begin{equation}
D = [(\rho_{\mathrm{m}}\times V_{\mathrm{m}})/
(\rho_{\mathrm{b}}\times S_p\times t)]\times
10^3\label{eq1}
\end{equation}}\unskip
With  $D$ representing the denudation rate in
$\mathrm{mm}{\cdot}\mathrm{a}^{-1}$;  $\rho_{\mathrm{m}}$ and
$\rho_{\mathrm{b}}$ representing the densities of the moraine material
and the bedrock, respectively, in $\mathrm{kg}{\cdot}\mathrm{m}^{-3}$;
$V_{\mathrm{m}}$ the volume of the moraines in  $\mathrm{m}^{3}$; $S_p$ the
sediment source area in  $\mathrm{m}^{2}$; and  $t$ the duration of
moraine formation in years.

The surface used for this calculation is the real surface area of the
catchment, obtained from the DEM using the cosine of the slope for each
cell. This volumetric approach does not account for the suspended and
bed loads exported in proglacial streams; thus, the calculated
denudation rates represent minimum values for the studied glacial
cirques and may underestimate the actual denudation. 

We estimated the bulk density of the moraine material and the time of
formation of the moraines (Table~\ref{tab1}). The Gran Paradiso and
Mont Blanc massifs consist predominantly of granite and gneiss, leading
us to choose a bedrock density of $\rho_{\mathrm{b}}=
2700~\mathrm{kg}{\cdot}\mathrm{m}^{-3}$.  Moraine density is often
estimated by accounting for a porosity of 20 to 30\% 
\citep{Smalletal1984,Curryetal2006},  resulting in densities ranging
from 1890 to  $2160~\mathrm{kg}{\cdot}\mathrm{m}^{-3}$. A density of
moraine sediments of $1926~\mathrm{kg}{\cdot}\mathrm{m}^{-3}$ was
measured by  \citet{Altmannetal2020}  in the Kauner Valley (Austrian
Alps, crystalline rocks). Based on these values, we adopted a mean
moraine density value  of $\rho_{\mathrm{m}}=
2025\pm135~\mathrm{kg}{\cdot}\mathrm{m}^{-3}$.

During the YD and often during the Early Holocene (EH), glaciers
experienced phases of advance or stagnation with some minor
fluctuations  \citep{Ivy-Ochsetal2009,Braumannetal2021}. Moraines from
these periods are documented in the Gran Paradiso and Mont Blanc
massifs through  $\mbox{}^{10}$Be surface exposure dating
\citep{Protinetal2019,Protinetal2021,Baronietal2021,Serraetal2022b} 
but not all studied moraines were precisely dated. Consequently, two
extreme hypotheses were considered to calculate maximum and minimum
denudation rate values from moraines volume:  (1)~the formation time of
the YD moraines corresponds solely to the YD duration, spanning
1200~years  \citep{Ivy-Ochsetal2009};  (2)~the formation time of the YD
moraines corresponds to the total duration of the YD and the EH,
spanning approximately from 12.9 to 10.5~ka BP
\citep{Ivy-Ochsetal2009,Ivy-Ochs2015,Solominaetal2015}, and
corresponding to a period of 2400~years. 

For the moraines of the NG, two extreme scenarios were also considered
to provide minimum and maximum values of denudation rates. (1)~The
moraines may correspond solely to the materials eroded during the five
phases of glacial advance similar to the Little Ice Age (LIATEs)
\citep{MatthewsBriffa2005,MatthewsDresser2008}. Summing the duration of
these five phases  \citep{Ivy-Ochsetal2009,LeRoy2012}  yields a minimum
formation time of 2500~years.  (2)~Alternatively, the moraines may
include all erosion products deposited during the NG, if the materials
eroded during retreat phases were subsequently transported by the
glacier during the following advance phases. Considering this scenario,
the formation time of the moraines would span 5000~years, corresponding
to the maximum duration of the NG in the Alps 
\citep{MatthewsDresser2008,Ivy-Ochsetal2009,Solominaetal2015}. 
\looseness=1

As a result, denudation rates vary by a factor of two for both periods
between the two extreme assumptions.

\subsection{PDD glaciological model used for\newline 
paleoclimate calibration}\label{sec3.3} 
The respective extents of the YD and NG periods for the glaciers were
mapped in both massifs using a chronological framework derived from
$\mbox{}^{10}$Be surface exposure dating 
\citep{Protinetal2019,Protinetal2021,Baronietal2021,Serraetal2022b} 
and geomorphological studies  \citep{Ayrtonetal1987,Gardent2014}. Using
high-resolution LiDAR DEMs (S3) from the Mont Blanc massif, we
synthesized the geomorphological 
{mapping} of moraines representing the
glacial \mbox{extents} of the YD and NG periods onto a DEM with a greater
precision than previous studies, resulting in a new geomorphological
map that improves upon previous reconstructions 
\citep{PortalBuoncristiani2024}.\looseness=1

\begin{figure*}
\includegraphics{fig03}
\caption{\label{fig3}PDD modelling of glacier-covered areas during the
Neoglacial (A) and Younger Dryas (B) periods, example from the Mont
Blanc massif. The black lines correspond to the moraines from the
respective periods.}
\vspace*{4pt}
\end{figure*}

The PDD (Positive Degree Day) glacier model calculates a glacier's mass
balance based on annual positive temperatures, using specific melting
factors for snow and ice, while incorporating constraints related to
basal ice shear on the topography (S2.2) 
\citep{Paterson1994,HarperHumphrey2003,Blardetal2007,Heymanetal2013,Protinetal2019}. The parameters of the PDD model were calibrated using current
climatic data from 1979 to 2014 (S2.1) \citep{Jolyetal2017} and
present-day glaciological data (S2.3) 
\citep{SixVincent2014,Reveilletetal2017,Protinetal2019}. The following
climatic variables were incorporated in the model: monthly mean
temperatures and their standard deviation, monthly altitudinal
gradients of temperature, monthly mean precipitation, and the annual
altitudinal gradient of precipitation. In the PDD model, spatial
variations in temperature and precipitation, as well as temperature and
precipitation gradients, are assumed to remain constant over time.
Calibration parameters for these climatic variables were differentiated
between the Mont Blanc and Aiguilles Rouges massifs, and the Gran
Paradiso massif, reflecting regional climatic variations. The
glaciological parameters to incorporate into the model include the
Degree Day Factors (DDF) for snow and ice, also assumed to remain
constant over space and time. Using this calibrated PDD model, we
determined the optimal combination of precipitation and temperature
conditions associated with the glacial extents of the NG period 
(Figure~\ref{fig3}A) and the YD period (Figure~\ref{fig3}B) by applying
variations to the reference climate data. The most relevant
precipitation and temperature combinations to obtain the best possible
fit with the moraines for each period were chosen by following
literature proxies and climate modelling 
\citep{McDermottetal1999,MatthewsBriffa2005,Rasmussenetal2006,Ilyashuketal2009,ShakunCarlson2010,Wanneretal2011,Magnyetal2012,Samartinetal2012,Carlson2013,Furlanettoetal2018,Protinetal2019,Kaufmanetal2020,Renssen2020,Erbetal2022}.
However, the glacial extents obtained from PDD modelling do not
perfectly match the moraine crests corresponding to the considered
periods (Figure~\ref{fig3}). This discrepancy can be attributed to
several limitations inherent to this simple modelling approach: (1)~the
Degree Day Factors (DDF) for snow and ice were calibrated using the Mer
de Glace and Argentiere glaciers  (Section~S2.3), both located on the
northern slopes of the Mont Blanc massif. These values may therefore be
less accurate for glaciers exposed to the south in the Mont Blanc
massif and for those in the Gran Paradiso massif; (2)~the poorly
constrained ice flow modelling, based on thresholding basal shear
stress as a function of slope variations, may overly favor ice flow
over steep areas;  (3)~the DEM used was not corrected for recent
surface modifications, such as\unskip\break
landslides.

Thus, the PDD modelling approach enabled us to estimate a cooling of
0.8~\textdegree C for the NG period and 4.5~\textdegree C for the YD
period compared to the 1979--2014 reference period. The precipitation
change factor, calibrated against the same reference period, was
determined to be 1.2 for the NG and 0.5 for the YD. Our climate
calibration indicates a temperature difference of 3.7~\textdegree C
between the YD and NG, representing a slightly greater cooling than
that calibrated by  \citet{Serraetal2022b} using a similar glacial
modelling approach on the Gran Paradiso massif. They suggested a
cooling of 3.1~\textdegree C between the two periods when considering
half the current precipitation levels for the YD. This discrepancy
likely stems from differences in both the models and input climatic
data. While our climatic reconstructions rely on more detailed local
datasets (see above and  Section~S2.1), our ice flow dynamic model is
based on more simple assumptions.

To assess the spatial variation of temperatures and precipitation
during the NG and YD periods, we utilized spatial climate data from the
CHELSA database  \citep{Kargeretal2017} for the period 1981--2010. By
applying the previously calculated cooling values and precipitation
factors to these spatial datasets, we inferred the spatial variations
in temperature and precipitation during the NG and YD periods in the
Mont Blanc and Gran Paradiso massifs, under the assumption that the
present-day spatial distribution mirrored that of the NG and YD, which
is probably an approximation  \citep{Dumas2013}. 

\begin{table*}
\caption{\label{tab2}Main results of the erosion calculation in the
glacial cirques during the NG (moraine volumes and denudation rates)}
\begin{tabular}{cccc} 
\thead
Cirque (massif)  &amp;
\parbox[t]{2.5cm}{\centering
Moraine volume $(10^{6}~\mathrm{m}^{3})$} &amp;
\parbox[t]{2.5cm}{\centering
Maximum denudation rate 
$(\mathrm{mm}{\cdot}\mathrm{an}^{-1})$} &amp; 
\parbox[t]{2.5cm}{\centering
Minimum denudation rate 
$(\mathrm{mm}{\cdot}\mathrm{an}^{-1})$}
\vspace*{2pt}\\ 
\endthead
Nant Blanc (MB) &amp; $5.22\pm0.37$ &amp; $0.36\pm0.03$ &amp; $0.18\pm0.03$ \\ 
Nantillons (MB) &amp; $5.81\pm0.41$ &amp; $0.90\pm0.09$ &amp; $0.45\pm0.09$ \\ 
Blaiti\`{e}re (MB) &amp; $3.72\pm0.26$ &amp; $0.41\pm0.04$ &amp; $0.20\pm0.04$ \\ 
P\`{e}lerins (MB) &amp; $7.62\pm0.53$ &amp; $0.38\pm0.04$ &amp; $0.19\pm0.04$ \\ 
Drus (MB) &amp; $1.35\pm0.09$ &amp; $0.27\pm0.03$ &amp; $0.13\pm0.03$ \\ 
Pendant and Lognan (MB) &amp; $4.51\pm0.32$ &amp; $0.54\pm0.05$ &amp; $0.27\pm0.05$ \\ 
Remuaz (AR) &amp; $1.69\pm0.12$ &amp; $0.86\pm0.08$ &amp; $0.43\pm0.08$ \\ 
Gran Paradiso (GP) &amp; $12.95\pm0.91$ &amp; $0.41\pm0.04$ &amp;  $0.21\pm0.04$ \\ 
Monciair (GP) &amp; $4.54\pm0.32$ &amp; $0.62\pm0.06$ &amp; $0.31\pm0.06$ \\ 
Trajo (GP) &amp; $4.00\pm0.28$ &amp; $0.24\pm0.02$ &amp; $0.12\pm0.02$ \\ 
Invergnan (GP) &amp; $4.06\pm0.28$ &amp; $0.60\pm0.06$ &amp; $0.30\pm0.06$ \\ 
Timorion (GP) &amp; $2.39\pm0.17$ &amp; $0.49\pm0.05$ &amp; $0.24\pm0.05$ 
\botline 
\end{tabular}
\tabnote{Minimum denudation:  $t = 5000$~years. Maximum denudation:  $t
= 2500$~years. Uncertainties take into account the estimated error in
moraine volume and the uncertainty in moraine density. MB ${=}$ Mont
Blanc; AR ${=}$ Aiguilles Rouges; GP  ${=}$ Gran Paradiso.}
\vspace*{8pt}
\end{table*}

\section{Results}\label{sec4} 

\subsection{Volume of moraines during Neoglacial and Younger Dryas
periods}\label{sec4.1}
The volumes of the NG moraines for the 12 studied glacial cirques vary
between  $12.95\pm0.91$ and  $1.35\pm0.09~\mathrm{Mm}^{3}$
(Tables~\ref{tab2} and~S6-1).  The 
\mbox{smallest} moraine volume is recorded
in the Drus glacier (Mont Blanc massif) and the largest moraine volume
is observed in the Gran Paradiso area, encompassing the catchments of
the current glaciers of Montandayne, Laveciau, and Gran Paradiso. For
the YD period, calculated moraine volumes range from 
$3.57\pm0.25~\mathrm{Mm}^{3}$ for the Pendant and Lognan glaciers to 
$2.65\pm0.19~\mathrm{Mm}^{3}$ for the Gran Paradiso glacier
\mbox{(Table~\ref{tab3}).}

\begin{figure*}
\includegraphics{fig04}
\vspace*{5pt}
\caption{\label{fig4}Comparison of the denudation rates calculated for
the NG (blue) and the YD (purple) in the three relevant cirques for
minimum time hypothesis (A) and maximum time hypothesis (B).}
\vspace*{14pt}
\end{figure*}

\begin{table*}
\caption{\label{tab3}Main results of erosion calculations in the
glacial cirques during the YD (moraine volumes and denudation rates)}
\begin{tabular}{cccc} 
\thead
Cirque (massif) &amp; 
\parbox[t]{2.5cm}{\centering
Moraine volume
$(10^{6}~\mathrm{m}^{3})$} &amp; 
\parbox[t]{2.5cm}{\centering
Maximum denudation rate
$(\mathrm{mm}{\cdot}\mathrm{an}^{-1})$} &amp;
\parbox[t]{2.5cm}{\centering
Minimum denudation rate 
$(\mathrm{mm}{\cdot}\mathrm{an}^{-1})$}
\vspace*{2pt}\\ 
\endthead
Nantillons and Blaiti\`{e}re (MB) &amp; 
$2.88\pm0.20$ &amp; $0.23\pm0.02$ &amp; $0.11\pm0.02$ \\ 
Pendant and Lognan (MB) &amp; 
$3.57\pm0.25$ &amp; $0.35\pm0.03$ &amp; $0.18\pm0.03$ \\ 
Gran Paradiso (GP) &amp; 
$2.65\pm0.19$ &amp; $0.10\pm0.01$ &amp; $0.05\pm0.01$ 
\botline
\end{tabular}
\xxtabnote{Minimum denudation:  $t = 2400$~years. Maximum denudation:  $t
= 1200$~years. Uncertainties take into account the estimated error in
moraine volume and the uncertainty in moraine density. MB ${=}$ Mont
Blanc; GP ${=}$ Gran Paradiso.}
\vspace*{8pt}
\end{table*}

We compared volumes of moraines between the YD and the NG periods
across three glacial catchments. In the cirques of Gran Paradiso, the
moraine volume is $2.65\pm0.19~\mathrm{Mm}^{3}$ during the YD, compared
to $12.95\pm0.91~\mathrm{Mm}^{3}$ during the NG. Merged catchments of
the Blaiti\`{e}re and Nantillons glaciers yield a moraine volume of 
$2.88\pm0.20~\mathrm{Mm}^{3}$ for the YD, with corresponding NG volumes
of  $5.22\pm0.37~\mathrm{Mm}^{3}$ and  $5.81\pm0.41~\mathrm{Mm}^{3}$,
respectively. Finally, the Pendant and Lognan glaciers present a
moraine volume of $3.57\pm0.25~\mathrm{Mm}^{3}$ for the YD and 
$4.51\pm0.32~\mathrm{Mm}^{3}$ for the NG. In all cases, the moraine
volumes calculated for the YD are smaller than those of the NG, despite
the larger catchments surface areas.

\subsection{Denudation rates}\label{sec4.2} 
Using the previously discussed data and the calculated volumes of the
moraines (see  Sections~\ref{sec3.1} and~\ref{sec3.2}), denudation
rates for the 12 glacial cirques were calculated
(Equation~(\ref{eq1})). During the NG, denudation rates ranged from 
$0.12\pm0.02$ to $0.45\pm0.09~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ based
on the maximum formation time and from  $0.24\pm0.02$ to
$0.90\pm0.09~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ for the minimum
formation time (Table~\ref{tab2}).

For the YD, the calculated denudation rates for the three glacial
cirques range between  $0.05\pm0.01$ and
$0.18\pm0.03~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ based on the maximum
formation time and between  $0.10\pm0.01$  and for 
$0.35\pm0.03~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ based on the minimum
formation time (Table~\ref{tab3}).

When comparing denudation rates for the YD and NG periods in the three
glacial cirques where both glacial advances are recorded
(Figure~\ref{fig4}), YD denudation rates are lower than those
calculated for the NG. The differences are the same when considering
minimum or maximum denudation rates, since there is a factor of two
between these values for each period. In the Blaiti\`{e}re and
Nantillons glacial cirques, the YD denudation rate is approximately two
or four times lower than NG rates, with a value of 
$0.11\pm0.02~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ compared to
$0.20\pm0.04$ and  $0.45\pm0.09~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ for
minimum values. For the Pendant and Lognan glacial cirques, the
difference between the YD denudation rate and the NG denudation rate is
smaller, i.e.\ $0.18\pm0.03~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ compared
to  $0.27\pm0.05~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ for the minimum
values, respectively. Finally, in the Gran Paradiso cirque, the YD
denudation rate is around four times lower than that of the NG, with
minimum values of  $0.05\pm0.01$ and
$0.21\pm0.04~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$, respectively.

\begin{figure*}
\includegraphics{fig05}
\vspace*{3pt}
\caption{\label{fig5}Denudation rates plotted against climatic
parameters. (A)~Maximum denudation rates against mean annual
temperature. (B)~Minimum denudation rates against mean annual
temperature. (C)~Maximum denudation rates against mean annual
precipitation. (D) Minimum denudation rates against mean annual
precipitation. RHO ${=}$ Spearman's rho value.} 
\vspace*{6pt}
\end{figure*}

\subsection{Climatic  parameters correlation with\newline 
denudation rates}\label{sec4.3}
The temperature and precipitation values calibrated using PDD modelling
for the NG and YD were averaged for each catchment (Table~S5-1) using
the CHELSA climate spatial database  \citep{Kargeretal2017}.
Non-parametric rank correlation tests (Spearman's rho) were then
performed to examine the relationship between climatic parameters,
successively, the volumes of the moraines, and the denudation rates. No
significant correlation was identified between moraine volumes and
climatic parameters. However, a significant positive correlation at the
95\% confidence level was observed between climatic parameters
(temperature and precipitation) and denudation rates
(Table~\ref{tab4}). Spearman's rho value is 0.69 for the correlation
with average temperature (Figure~\ref{fig5}A,~B) and 0.52
for the correlation with average precipitation (Figure~\ref{fig5}C,~D).
These results remain consistent across both extreme
hypotheses (minimum and maximum timeframes), despite the two-fold
variation in\unskip\break 
timeframes.

\begin{table*}
\caption{\label{tab4}Results of the Spearman correlation tests between
the volumes of the moraines and the denudation rates and the climatic
parameters}
\begin{tabular}{ccc} 
\thead
Climatic parameter &amp; 
Moraine volumes &amp;
Cirques denudation \\ 
\endthead
Temperature &amp; 0.01 &amp; 0.69$^*$ \\ 
Precipitation &amp; 0.15 &amp; 0.52$^*$
\botline
\end{tabular}
\xxxtabnote{Asterisks indicate significant correlations at the 95\%
confidence level.}
\vspace*{-2pt}
\end{table*}

\subsection{Correlation between Neoglacial\newline 
morphological parameters and denudation rates}\label{sec4.4}
Spearman's non-parametric correlation tests were conducted successively
between the moraine volumes and the denudation rates with the
geomorphological parameters of the catchments for the NG period
(Table~\ref{tab5}).

\begin{figure*} 
\includegraphics{fig06}
\caption{\label{fig6}Denudation rates (here minimum values but maximum
values would show the same trend) plotted against geomorphological
parameters: (A)~moraine volumes against cirque area; (B)~denudation
rates against cirque area;  (C)~denudation rates against maximum
altitude of the cirques; and  (D)~denudation rates against relief of
the cirques.}
\end{figure*}

\begin{table*}
\caption{\label{tab5}Results of the Spearman correlation tests between
the volumes of the NG moraines or the denudation rates of the NG and
the geomorphological parameters}
\begin{tabular}{ccc} 
\thead
Geomorphological parameter &amp; 
Moraine volumes &amp;
Cirques denudation \\ 
\endthead
Surface area &amp; 0.69$^*$ &amp; ${-}$0.52$^*$ \\ 
Minimum altitude &amp; ${-}$0.27 &amp; 0.37 \\ 
Maximum altitude &amp; 0.38 &amp; ${-}$0.78$^*$ \\ 
Average altitude &amp; 0.34 &amp; ${-}$0.22 \\ 
Relief &amp; 0.39 &amp; ${-}$0.79$^*$ \\ 
Median slope &amp; ${-}$0.04 &amp; ${-}$0.21
\botline
\end{tabular}
\xxxxtabnote{Asterisks indicate significant correlations at the 95\%
confidence level.}
\end{table*}

The volume of the moraines only shows a significant positive
correlation with the size of the catchment, with a Spearman rho of 0.69
(Figure~\ref{fig6}A).

The denudation rates of the cirques exhibit three significant negative
correlations with geomorphological parameters: surface area, maximum
altitude, and relief of the cirque. The Spearman rho values are
${-}$0.52, ${-}$0.78, and  ${-}$0.79, respectively (Figure~\ref{fig6}B--D). 

\section{Discussion}\label{sec5}

\subsection{Potential issues on denudation rates\newline
calculations}\label{sec5.1}

\subsubsection{Proglacial stream exports}\label{sec5.1.1}
As discussed by  \citet{Delmasetal2009}, the fraction of sediment
exported via proglacial streams introduces significant underestimation
in the interpretation of absolute denudation rates calculated using
volumetric approaches. Denudation rates estimated from suspended and
bed loads measurements in proglacial streams can span several orders of
magnitude \citep{Halletetal1996,Hermanetal2015,Koppesetal2015,
Guillonetal2018,Jenkin2024}, including those presented
in this study. Consequently, the volume of exported sediment may
account for a substantial portion of the total eroded material in
glacial cirques. However, estimating average values over millennial
timescales remains highly challenging. The 
\mbox{absolute} denudation rates
reported in this study may therefore be significantly underestimated.
Nonetheless, relative relationships between denudation rates and other
quantitative parameters, such as temperature or precipitation, are
likely to remain robust, unless the respective proportions of sediment
exported via proglacial streams and that retained in moraines varies
markedly among cirques. Such variability may be limited, given the
relatively homogeneous characteristics of the studied cirques (i.e.,
exposure, lithology, and geographic location). 

\subsubsection{Risk of double counting}\label{sec5.1.2}
Another potential source of error in the calculation of denudation
rates is the overestimation of sediment volumes due to the inclusion of
material that was originally eroded during an earlier period, left
during glacier retreat, and subsequently reworked and redeposited in
moraines during a later advance. In our study context, the amount of
such reworked older material stored in the analysed moraines appears to
be quite limited. The moraines are deposited on polished bedrock, and
there are no substantial till deposits within the cirques that could
have been remobilized by subsequent glacial advances. Moreover, the
maximum time formation hypothesis used to calculate minimum denudation
rates assumes that the moraines were formed from material eroded over
several advance-retreat cycles, particularly in the case of the NG.
This approach implicitly accounts for the possible reworking of
previously deposited sediments in the denudation estimates.

\subsubsection{Time of moraines formation and paraglacial
response}\label{sec5.1.3}
To account for chronological uncertainties in the moraine record, we
considered two contrasting time scenarios. The minimum time corresponds
to the duration of the YD for YD-related deposits, and to the
successive glacier advance episodes of the NG for the NG-related
moraines. The maximum time corresponds to the combined duration of the
YD and the EH, as several dated YD moraines yield both YD and EH ages.
Moreover, the maximum time scenario allows the denudation rate
calculations to account for the issue of double counting (see 
Section~\ref{sec5.1.2}) and paraglacial adjustment post-retreat. In
small cirques, such paraglacial responses are typically rapid 
\citep{ChurchSlaymaker1989,Ballantyne2002}, and our maximum scenario
likely encompasses this effect. However, this approach does not capture
potential paraglacial responses acting over longer timescales (e.g.,
since the Last Glacial Maximum, LGM). If part of the NG headwall
destabilization reflects delayed geomorphic adjustments inherited from
broader deglaciation, this could partly explain the higher denudation
rates calculated for this period compared to the YD. While the maximum
time scenario is likely more realistic, using both extreme endmembers
provide bounded estimates for denudation rates.

\subsection{Climate control on glacial cirques\newline
denudation rates}\label{sec5.2}

\subsubsection{Correlation between climatic parameters and denudation
rates}\label{sec5.2.1}
For the three glacial cirques where denudation rates could be
calculated for both the NG and the YD, denudation rates were 1.5 to 4.2
times lower than the minimum NG denudation rates. These findings could
suggest that erosion in Alpine glacial cirques was more intense during
the temperate and humid NG period  (${-}$0.8~\textdegree C and 1.2 times
higher calibrated precipitation relative to the 1979--2014 period) than
during the cold and dry YD period  (${-}$4.5~\textdegree C and half the
calibrated precipitation relative to the 1979--2014 period).  They also
could reflect a long-term effect of the paraglacial response of the
post-LGM deglaciation (see  Section~\ref{sec5.1.3}).  Similar results,
indicating more efficient erosion during temperate periods compared to
glaciated periods, have been observed in glacial cirques using
alternative denudation rate estimation methods, such as cosmogenic
nuclides \citep{Crestetal2017}, although without explicit climatic
parameters quantification. This type of approach also shows similar
results on shorter timescale with increasing erosion rates in glaciated
alpine catchments since the LIA
\citep{Wetteraueretal2022,WetterauerScherler2023,Courtial-Manentetal2025}. 

These erosion patterns likely reflect contrasting subglacial and
periglacial dynamics, controlled by glacial thermal regimes and
frost-cracking processes. During the cold, dry YD climate, glaciers
likely developed extensive cold-based surfaces due to a significant
lowering of the ELA  \citep{Protinetal2019}, thereby reducing
subglacial erosion processes and protecting the bedrock from erosion
\citep{Godonetal2013,Hermanetal2015}. Conversely, during the NG,
glaciers had a temperate-type thermal regime, facilitating subglacial
erosion processes. Periglacial erosion processes, such as
frost-cracking, may also be more limited during the YD compared to the
NG in the cirque walls. The altitudinal zone most affected by intense
frost-cracking depends on temperature gradient and freeze-thaw cycles
within the rock, and the availability of liquid water. This zone varies
with climatic conditions and is linked to the state of permafrost
\citep{HalesRoering2009,Deluneletal2010,Savietal2015,Ravaneletal2020,Draebingetal2022}. During the YD, this
zone of active frost-cracking activity may have shifted to lower
altitudes than those of the studied cirques, potentially leading to
reduced denudation rates in these cirques. This could explain the
decrease in denudation rates observed between the NG and the YD in this
study. Considering the annual altitudinal temperature gradients used
for the PDD modelling (Table~S2-3), which are  5.99~\textdegree
C/1000~m for the Mont Blanc massif and 6.12~\textdegree C/1000~m for
the Gran Paradiso massif, and the mean annual temperature difference
calibrated between these two periods (3.7~\textdegree C), the lowering
of the frost-cracking window can be roughly estimated at approximately
620~m for the Mont Blanc massif and 600~m for the Gran Paradiso massif.
Conversely, current climate change is causing the frost-cracking window
to rise. It also affects related processes, such as the frequency of
frost occurrence and the altitudes exposed  \citep{Pohletal2019}, and
the degradation of mountain permafrost  \citep{Magninetal2017}.
Consequently, increasing destabilization of high-altitude rock walls in
the Mont Blanc massif is already being observed\unskip\break 
\citep{Courtial-Manentetal2025}. 

\subsubsection{Correlation between geomorphological\newline 
parameters and denudation rates}\label{sec5.2.2}

{\vspace*{-2pt}}

In glacial cirques, we observed a negative correlation between NG
denudation rates and cirque areas (Figure~\ref{fig7}). However, several
studies suggest a positive relationship between catchment size and
glacial erosion rates  \citep{Halletetal1996,KoppesMontgomery2009}.
This difference could be explained by varying processes between small
and large glacial systems, such as importance of subglacial erosion
depending on ice sliding velocity and subglacial hydrology, and
distinct temporal scales, ranging from a few years to several millennia
\citep{Halletetal1996,KoppesMontgomery2009,Hermanetal2021}.
Furthermore, the catchment surface areas are positively correlated with
maximum altitude and relief, with Spearman's rho values of 0.76 and
0.72, respectively, and could reflect the same trend here.
\looseness=-1

\begin{figure*}
\includegraphics{fig07}
\caption{\label{fig7}Comparison of denudation rates calculated in
glacial cirques based on moraine volumes against: (A)~catchment area
(logarithmic scale on both axes); (B)~latitude (logarithmic scale on
the ordinate axis). These calculations assume moraine formation
occurred continuously throughout the entire NG period. Data for
glaciated catchments of Patagonia and Antarctica have been added for
visualization.}
\end{figure*}

NG denudation rates show a negative correlation with maximum cirque
altitudes (Figure~\ref{fig5}C), suggesting that lower-altitude cirques 
rock walls experienced more intense erosion during the NG. Assuming a
negative altitudinal temperature gradient and a positive altitudinal
precipitation gradient (a first-order approximation), our results
suggest that temperature exerts a stronger control on denudation rates
than precipitation. Additionally, the strong  negative correlation
between maximum cirque altitude and denudation rates could also
indicate that periglacial erosion processes dominate over glacial
erosion in forming the studied moraines. This could be due to the
altitude-dependent variation of the maximum frost-cracking zone, which
is controlled by temperature \citep{Savietal2015}.

Our results show that denudation rates decrease as cirque relief
increases. While this may seem unexpected at first, our analysis shows
that the cirques with the highest relief also have the highest maximum
altitudes, with these two parameters being strongly correlated (rho ${=}$
0.84). This suggests that maximum altitude is the primary
geomorphological factor influencing erosion in the studied cirques,
likely due to its relationship with
temperature.

{\vspace*{-2pt}}

\subsubsection{Latitudinal variation of cirque denudation
rates}\label{sec5.2.3}

{\vspace*{-2pt}}

To evaluate latitudinal controls on cirque denudation, we compare
moraine-derived erosion rates across a climatic gradient, from
temperate to polar regions. Our synthesis includes: the Rocky Mountains
\citep[${\sim}$40\textdegree\ N,][]{Reheis1975}, Pyrenees
\citep[${\sim}$43\textdegree\ N,][]{Crest2017}, and Alps
(${\sim}$45\textdegree\ N, this study) as mid-latitude
benchmarks, contrasted with Arctic conditions on Baffin Island
\citep[${\sim}$66\textdegree\ N,][]{Anderson1978}. This
${\sim}$26\textdegree\ latitudinal span captures stark
differences in glacial/periglacial regime efficiency between temperate
and high-latitude  environments. The assumptions in these studies align
with those used to calculate the minimum denudation rates in this work,
considering the moraines formation time to span the entirety of the NG.
This duration varies slightly depending on the study area. While cirque
areas were calculated by accounting for slope in  \citet{Crest2017},
\citet{Reheis1975} and \citet{Anderson1978}  likely used projected
areas, although this is not explicitly stated. If slope had been
considered, the calculated denudation rates would have been slightly
lower. Across all these datasets, NG denudation rates range from 
$0.01~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ to over 
$1~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ (Figure~\ref{fig7}, Table~S6-1).

This comparison leads to two main observations. First, the negative
correlation between denudation rates and catchment areas is further
strengthened by incorporating additional data, with a Spearman's rho
value of ${-}$0.76. Second, denudation rates at high latitudes are one to
two orders of magnitude lower than those at mid-latitudes for
catchments of comparable surface area (Figure~\ref{fig7}A). At
mid-latitudes, NG denudation rates range from 
$0.12~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ for the Trajo cirque (Alps) to
$1.65~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ for the Arapaho cirque (Rocky
Mountains), whereas at high latitudes, they range from 0.01 to 
$0.07~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ (Canadian Arctic).
Furthermore, Wilcoxon tests show that all latitudinal groups are
statistically distinct at the 95\% confidence level, except for the
single cirque in the Rocky Mountains (Figure~\ref{fig7}B).
\looseness=-1

These results, observed over time scales of several thousand years,
highlight variations in denudation rates within glacial cirques that
are linked to latitude, potentially reflecting a climate-controlled
process. Similar mechanisms as proposed in  Section~\ref{sec5.2.1} may
also explain the latitudinal variation in denudation rates in glacial
cirques. However, other factors influencing denudation rates between
these groups, such as lithology, were not tested here and could also
play a role.  On comparable time scales, similar latitudinal trends
have been identified using geophysical data to estimate marine glacial
sediment volumes in fjords and bays across Patagonia and Antarctica
\citep{Fernandezetal2016}, spanning approximately  45\textdegree\ S to
65\textdegree\ S. These trends have also been observed over shorter time
scales (decades to a century), based on sediment yields from 15
glaciated catchments in the same region  \citep{Koppesetal2015}
(Figure~\ref{fig7}B).\looseness=-1

\section{Conclusion}\label{sec6} 
This study investigated the impact of climate on erosion in glacial
cirques within the Gran Paradiso, Mont Blanc, and Aiguilles Rouges
massifs. Denudation rates were quantified based on moraine volumes and
the real surface areas of the cirques. The analysis focused on moraines
from two distinct periods: the cold and dry Younger Dryas (YD) and the
\mbox{temperate}
and humid Neoglacial (NG). A total of three YD moraines and
twelve NG moraines were 
\mbox{examined.}

The main source of uncertainty was the duration of moraine formation.
To address this, two extreme hypotheses were considered, allowing for
the estimation of minimum and maximum denudation rates. For each
period, the results from both \mbox{hypotheses} differed by a factor of two,
demonstrating that the relative ranking of denudation rates remained
consistent regardless of the time assumption. During the YD, denudation
rates ranged from 0.05 to  $0.11~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ for
minimum values and from 0.10 to 
$0.23~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ for maximum values. During the
NG, denudation rates ranged from 0.12 to 
$0.45~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ for minimum values and from
0.24 to  $0.90~\mathrm{mm}{\cdot}\mathrm{a}^{-1}$ for maximum values. A
positive correlation was observed between denudation rates in the
studied cirques and mean annual temperature and precipitation. In the
three cirques where denudation rates were calculated for both periods,
denudation rates were systematically lower during the YD than during
the NG.  These results highlight those climatic 
{parameters} that exert
both spatial and temporal control on erosion in glacial cirques, with
erosion being significantly accentuated under more temperate and humid
climates compared to rather cold and dry climates.\looseness=-1

Further investigations could help link these results to the glacial and
periglacial erosion processes operating in these environments. For
example, the \mbox{altitudinal} shift in the zone of most intense
frost-cracking in rock walls may partly explain the differences in
denudation rates observed between the two studied periods.

\section*{Declaration of interests}
The authors do not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and have
declared no affiliations other than their research organizations.

\section*{Acknowledgments}
This research is part of the MORCLIM project, which received funding
from the TelluS program of the Institut National des Sciences de
l'Univers, CNRS.  The authors thank Florence Magnin for her answers
about mountain permafrost.  The authors thank the anonymous reviewer
for their valuable feedback, which helped improve the quality of this
publication.

\back{}

\section*{Supplementary data}
Supporting information for this article is available on the journals
website under \printDOI\ or from the author.

\CDRsupplementaryTwotypes{supplementary-material}{\cdrattach{crgeos-297-suppl.pdf}}

\printbibliography
\refinput{crgeos20250192-reference.tex}

\end{document}
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