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\DOI{10.5802/crgeos.216}
\datereceived{2023-02-08}
\dateaccepted{2023-05-02}
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\dateposted{2023-07-25}
\begin{document}

\begin{noXML}

%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{Geodynamics of continents and oceans - A tribute to Jean Aubouin}
%\def\cdr@specialtitle@french{G\'eodynamique des continents et des Oc\'eans - Hommage \`a Jean Aubouin}
%\makeatother

\title{The interplay of geology, climate and tectonics on river
incision: the example of the High Verdon Gorges, Southwestern French
Alps}

\alttitle{Impact de la g\'eologie, du climat et de la tectonique sur
l'incision fluviatile : l'exemple des Hautes Gorges du Verdon, Alpes du
Sud-Ouest}

\shortrunauthors

\author{\firstname{Thibaut} \lastname{Cardinal}\IsCorresp}
\address{Universit\'{e} C\^{o}te d'Azur, CNRS, Observatoire de la
C\^{o}te d'Azur, IRD, G\'{e}oazur, 250 rue Albert Einstein, Sophia
Antipolis 06560 Valbonne, France} 
\email[T. Cardinal]{cardinal@geoazur.unice.fr}

\author{\firstname{Carole} \lastname{Petit}\CDRorcid{0000-0002-8798-1168}}
\addressSameAs{1}{Universit\'{e} C\^{o}te d'Azur, CNRS, Observatoire de
la C\^{o}te d'Azur, IRD, G\'{e}oazur, 250 rue Albert Einstein, Sophia
Antipolis 06560 Valbonne, France} 
\email[C. Petit]{petit@geoazur.unice.fr}

\author{\firstname{Yann} \lastname{Rolland}\CDRorcid{0000-0001-9547-6092}}
\address{Universit\'{e} Grenoble Alpes, Universit\'{e} Savoie Mont
Blanc, CNRS, IRD, Universit\'{e} Gustave Eiffel, ISTerre, 38000
Grenoble, France}
\address{Universit\'{e} Savoie Mont Blanc, CNRS, P\^{o}le Montagne,
Edytem, F-73370 Le Bourget-du-Lac, France}
\email[Y. Rolland]{yann.rolland@univ-smb.fr}

\author{\firstname{St\'ephane} \lastname{Schwartz}\CDRorcid{0000-0001-7942-7071}}
\addressSameAs{2}{Universit\'{e} Grenoble Alpes, Universit\'{e} Savoie
Mont Blanc, CNRS, IRD, Universit\'{e} Gustave Eiffel, ISTerre, 38000
Grenoble, France}
\email[S. Schwartz]{stephane.schwartz@univ-grenoble-alpes.fr}

\author{\firstname{Pierre Gaston} \lastname{Valla}\CDRorcid{0000-0001-6525-5416}}
\addressSameAs{2}{Universit\'{e} Grenoble Alpes, Universit\'{e} Savoie
Mont Blanc, CNRS, IRD, Universit\'{e} Gustave Eiffel, ISTerre, 38000
Grenoble, France}
\email[P. G. Valla]{pierre.valla@univ-grenoble-alpes.fr}

\author{\firstname{Bruno} \lastname{Scalabrino}}
\addressSameAs{1}{Universit\'{e} C\^{o}te d'Azur, CNRS, Observatoire de
la C\^{o}te d'Azur, IRD, G\'{e}oazur, 250 rue Albert Einstein, Sophia
Antipolis 06560 Valbonne, France} 
\email[B. Scalabrino]{Bruno.SCALABRINO@geoazur.unice.fr}

\author{\firstname{Laurence} \lastname{Audin}\CDRorcid{0000-0002-4510-479X}}
\addressSameAs{2}{Universit\'{e} Grenoble Alpes, Universit\'{e} Savoie
Mont Blanc, CNRS, IRD, Universit\'{e} Gustave Eiffel, ISTerre, 38000
Grenoble, France}
\email[L. Audin]{laurence.audin@ird.fr}

\author{\firstname{Maxime} \lastname{Bertauts}}
\addressSameAs{2}{Universit\'{e} Grenoble Alpes, Universit\'{e} Savoie
Mont Blanc, CNRS, IRD, Universit\'{e} Gustave Eiffel, ISTerre, 38000
Grenoble, France}
\email[M. Bertauts]{maxime.bertauts@univ-grenoble-alpes.fr}

\author{\firstname{Swann} \lastname{Zerathe}\CDRorcid{0000-0002-4020-5823}}
\addressSameAs{2}{Universit\'{e} Grenoble Alpes, Universit\'{e} Savoie
Mont Blanc, CNRS, IRD, Universit\'{e} Gustave Eiffel, ISTerre, 38000
Grenoble, France}
\email[S. Zerathe]{swann.zerathe@ird.fr}

\author{\firstname{Denis} \lastname{Thi\'{e}blemont}\CDRorcid{0000-0002-0605-7150}}
\address{DGR/CGEO, BRGM, B.P. 6009, 45060 Orl\'{e}ans, Cedex, France}
\email[D. Thi\'{e}blemont]{d.thieblemont@brgm.fr}

\author{\firstname{R\'egis} \lastname{Braucher}}
\address{Universit\'{e} Aix-Marseille, CNRS-IRD-Coll\`{e}ge de
France-INRAE, UM 34 CEREGE, Technop\^{o}le de l'Environnement
Arbois-M\'{e}diterran\'{e}e, BP80, 13545 Aix-en-Provence, France}
\email[R. Braucher]{braucher@cerege.fr}

\author{\firstname{ASTER} \lastname{Team}}
\addressSameAs{5}{Universit\'{e} Aix-Marseille, CNRS-IRD-Coll\`{e}ge de
France-INRAE, UM 34 CEREGE, Technop\^{o}le de l'Environnement
Arbois-M\'{e}diterran\'{e}e, BP80, 13545 Aix-en-Provence, France}
\address{ASTER Team: Georges Auma\^{i}tre, Didier L.
Bourl\`{e}s$^{\dagger}$, Karim Keddadouche}

\begin{abstract}
Deciphering
the impact of short-term or long-term forcing on fluvial
incision, as well as understanding the influence of local (channel
lithology and morphology) and global (tectonic motions) parameters in
the spatial variation of incision efficiency, are ongoing
geomorphological research fields. To shed new light on these issues, we
chose to study the ``Hautes Gorges du Verdon'' (High Verdon Gorges or
HVG), located in the foreland of the Southwestern Alps. We collected
24 samples along three polished surfaces for Cosmic Ray Exposure (CRE)
$^{36}$Cl dating, which allowed us to constrain short-term
incision rates ranging from 0.06 to 0.2 mm/yr between 60 and 15 ka.
Compared to known regional uplift and denudation rates, incision rates
obtained in the HVG suggest tectonic or isostatic uplift as the main
driver of Verdon River incision in the Late Quaternary. This comparison
allows us to propose that the downcutting of the Verdon Gorges started
approximatively 1.5 to 2 Ma ago, even if the drainage network of the
Verdon catchment area could have been shaped earlier, during the
Messinian salinity crisis.
\end{abstract}

\begin{altabstract}
D\'echiffrer l'impact des for\c{c}ages \`a court ou long terme sur l'incision
fluviale, et comprendre l'influence des facteurs locaux (lithologie et
morphologie du lit de la rivi\`ere) et globaux (mouvements tectoniques)
sur la variation spatiale de l'efficacit\'e de l'incision, sont des
domaines de recherche en cours. Pour apporter un regard neuf sur ces
questions, nous avons choisi d'\'etudier les \guillemotleft{}~Hautes Gorges 
du Verdon~\guillemotright{}
(HGV), localis\'ees dans l'avant-pays des Alpes du Sud-Ouest. Nous avons
collect\'e 24 \'echantillons le long de trois surfaces polies pour la
m\'ethode de datation Cosmic Ray Exposure (CRE) $^{36}$Cl, qui nous a permis
de contraindre les taux d'incision \`a court terme allant de 0,06 \`a 
0,2~mm/an entre 60 et 15 ka. Compar\'es aux taux de soul\`evement et de
d\'enudation r\'egionaux connus, les taux d'incision obtenus dans les HGV
sugg\`erent que le soul\`evement tectonique ou isostatique est le principal
moteur de l'incision de la rivi\`ere DU Verdon au cours du Quaternaire
r\'ecent. Cette comparaison nous permet de proposer que l'incision des
Gorges du Verdon a commenc\'e il y a approximativement 2 Ma, m\^eme si le
r\'eseau de drainage du bassin versant du Verdon a pu \^etre form\'e plus
t\^ot, pendant la crise de salinit\'e messinienne.
\end{altabstract}

\keywords{\kwd{Quaternary}
\kwd{Geomorphology}
\kwd{CRE $^{36}$Cl dating}
\kwd{Fluvial incision}
\kwd{Gorges}}

\altkeywords{\kwd{Quaternaire}
\kwd{G\'eomorphology}
\kwd{Datation par $^{36}$Cl}
\kwd{Incision fluviatile}
\kwd{Gorges}}

\maketitle

\vspace*{1.4em plus 1pt minus 1pt}

\twocolumngrid

\end{noXML}

\section{Introduction}\label{sec1}

Rivers, through their erosive power, play a key role in adjusting the
landscapes to multiple forcings such as tectonic uplift, sea-level
fluctuations or climate variations 
\citep{Whipple2004,WhippleTucker1999}. Indeed, bedrock channels set
the base level for adjacent hillslopes and thus control long-term
relief evolution and denudation rates 
\citep[e.g.,][]{Whippleetal2000}. Rivers not only control mass wasting by
undercutting hillslopes in mountainous areas \citep{Howardetal1994},
they also transport the resulting sediments towards depositional basins
in mountain forelands \citep{Gueritetal2016}.

The rate at which river incision shapes landscapes is highly variable
and is controlled by processes operating at different temporal and
spatial scales \citep{Daniels2008}. These processes interact with each
other, and the study of short-term (${<}$10$^{3}$ yr) processes may
allow to better understand their respective contributions together with
longer-term forcings (${>}$10$^{4}$ to 10$^{5}$ yr). For example, as
climate variations\unskip\break control water discharge in rivers 
\citep{Ely1997},
understanding how punctual flood events influence bedrock incision
rates can provide insights on the long-term landscape sensitivity to
climate changes [10$^{3}$--10$^{4}$ yrs, 
\citealp{Molnar2007,Hartshornetal2002,Lagueetal2005}]. 
Through the recurrence of
short-term processes (${<}$10$^{3}$ yr), rivers are irrevocably
adjusting their incision rates to long-term tectonic uplift rates in
order to achieve an ideal steady state in which vertical incision
equals to rock uplift \citep{WhippleTucker1999,Wobusetal2006}.
However, deciphering the dominant forcing if any (e.g., tectonic
{vs.} climate) remains difficult \citep{Hermanetal2013}.

The so-called ``external'' forcings control river erosion by providing
the necessary tools for bedrock incision: water discharge and sediment
availability. While the first provides the energy for sediment
transport, the latter acts as a ``mechanical tool'' for rivers to
incise their bedrock \citep{SklarDietrich2006,Jansenetal2011}.
However, several studies\unskip\break showed that an excessive amount of sediments
will, to the contrary, prevent incision by overloading the river,
raising the channel bed by aggradation and therefore temporarily
shielding the bedrock \citep{SklarDietrich2001,Hartshornetal2002}.
Furthermore, the efficiency of bedrock incision is controlled by
intrinsic morphological and geological features {{(}}lithology, slope,
with/depth ratio, local relief \citep{Schumm1977}. The degree of
jointing and the weathering state of the bedrock also influence river
incision rates \citep[e.g.,][]{Whippleetal2000}. These added elements
together act as a ``geological factor'' that dictates the locus of
erosion and its efficiency 
\citep{Cowieetal2008,Hartshornetal2002,Hermanetal2013,SklarDietrich2001}.

In fold-and-thrust belts, the folding of sedimentary layers with a
distinct resistance to erosion produces complex river network
geometries with alternating strike-parallel and perpendicular stream
sections defining a transverse drainage pattern 
\citep{Oberlander1965,Stokesetal2008,Twidale2004}. Beside these local
heterogeneities, large-scale regional horizontal tectonic movements can
be detected in the shape of the river network by systematic changes in
flow directions resulting from the planar deformation of the river
network with its substrate \citep{Gueritetal2016}. On the other hand,
vertical tectonic motions of the bedrock together with along-channel
variations in the rock resistance to erosion will affect both the river
longitudinal profile and the shape of surrounding hillslopes. The
complete understanding of interactions between such small- and
large-scale parameters and incision processes over large spatial and
temporal scales is not yet achieved \citep{Jansenetal2011}.

With the goal to shed some new light on the response of a river system
to internal and external factors, we chose to study the High Verdon
Gorges (HVG), located in the Southwestern Alps foreland (Figure~\ref{fig1}A). The
Verdon catchment presents the advantage of cross-cutting the whole
Meso-Cenozoic sedimentary sequence of the southern subalpine
fold-and-thrust belt, including highly resistant upper Jurassic
limestones in which the HVG were carved. The Verdon River headwaters
are located in an area previously covered by Quaternary glaciers 
\citep{Brissetetal2015}, while its outlet in the Durance river is near
the junction between the Alpine deformation front and the Valensole
foreland basin (Figure~\ref{fig1}B). In this paper, we present new, 
and use some
published \citep{Cardinaletal2022}, $^{36}$Cl Cosmic Ray Exposure
(CRE) datings of river-polished surfaces in the HVG and interpret them
for the recent (Late Quaternary) period, and discuss a long-term
(Pliocene to Quaternary) evolutionary scenario of the Verdon River in
its Alpine and Mediterranean context.


\begin{figure*}
%\vspace*{3pt}
\includegraphics{fig01}
%\vspace*{3pt}
\caption{\label{fig1}(A) Location of the Verdon Catchment in the
Southwestern Alps. (B) Simplified geological map of the study area. The
Verdon catchment area is underlined by brighter colours, corresponding
to the colours in the legend and on the cross-section. The High Verdon
Gorge (HVG) are highlighted along the river in pink. (C) Schematic
geological cross-section along the Verdon River longitudinal profile.
Black crosses indicate the beginning (B) and the end (E) of the river
profile. Note that in the profile; Cretaceous, Jurassic and Triassic
periods are distinguished from the more general term ``Mezosoic'' used
in the geological map B, as highlighted in the legend. The Black
outlined circles 1 to 3 on the map and on the profile indicate the
sampling sites. Thick red lines A, B, and C show the location of the
topographic profiles shown on Figure~\ref{fig10}. Locations numbered 
4 to 8 are
incision or uplift rates from literature which are discussed in 
Section~\ref{sec5}.}
%\vspace*{7pt}
\end{figure*}

\section{Context}\label{sec2}

\subsection{Structural context and drainage patterns of the Verdon 
River}\label{sec2.1}

The study area is located upstream of the foreland basin of the
Southwestern European Alps (Figure~\ref{fig1}A and B). The Castellane
fold-and-thrust belt (also called the ``Castellane Arc'') was first
formed during the Pyrenean collisional phase (Cretaceous to Eocene) and
underwent reactivation during the Oligocene due to the onset of Alpine
collision and SW propagation of the Penninic front, which resulted in
the development of an Oligocene foredeep filled with turbiditic
sequences \citep{Espurtetal2012,Jourdonetal2014}. During the Miocene,
compressional deformation propagated outwards and caused the uplift of
the sedimentary wedge together with the flexure and filling of the
Valensole molassic basin in the foreland (Figure~\ref{fig1}B). This deformation
phase ended with the underthrusting of Neogene molassic sequences below
the Digne Nappe during Late Miocene times \citep{Schwartzetal2017}.
The Valensole basin is filled with marine to continental conglomeratic
sequences, and erosional unconformities have been tentatively
correlated to the Mio-Pliocene transition marked by the Messinian
Salinity Crisis 
\citep{Clauzonetal1996,Clauzonetal2011,Hippolyteetal2011}. The last
marine sequences found in the Valensole basin are dated as Late
Tortonian and correspond to shallow water molasses 
\citep{Fordetal1999,FordLickorish2004}. Gravel deposits mark the end of
sedimentation in the Valensole basin, the upper surface of which has been
dated around 1.8 to 2 Ma; however, towards the Alpine front, alluvial
cones continue to prograde on the basin, ending with the Balene breccia
formation dated at 0.7 to 1 Ma \citep{Dubar1984,Dubaretal1998}. The
arrival of coarse, detritic deposits in the Valensole basin in the
early Quaternary (ca. 2.4 Ma) is interpreted as reflecting active
tectonics on the Castellane Arc and/or cooler climatic conditions 
\citep{Dubar1984,Dubaretal1998}.


With a length of 166.5 km and a catchment area of 2218 km$^{2}$, the
Verdon River is the main tributary of the Durance River. The Verdon
River and its catchment have their headwaters in the Helminthoid flysch
nappes (${\sim}$2500~masl) and run towards the south through the
unmetamorphosed Mesozoic sedimentary cover of the Alpine foreland. Near
the city of Castellane, the Verdon course takes a turn upon
encountering the outer folds and thrusts of the Castellane Arc and
consequently flows in a W--E direction, wandering around and cutting
across the fold axes \citep{Chardonnet1943,Jorda1975}. From this point,
the Verdon cuts its way through Jurassic limestones in which it dug one
of the most impressive European gorge, the High Verdon Gorges (HVG,
Figure~\ref{fig1}A). Downstream, the Verdon River meets the Valensole
Plateau and follows the Valensole conglomerate regular slope while
repeatedly crossing some Jurassic limestone outcrops 
\citep{Goguel1935}, until it reaches its outlet in the Durance River
(255 masl, Figure~\ref{fig1}B). The longitudinal profile of the Verdon
River reflects well lithological variations encountered along the
channel length. Indeed, significant convexity can be seen where the
river has incised the massive Tithonian limestone and formed the HVG,
whereas upstream and downstream, the river profile, although modified
by artificial dam lakes, is overall concave (Figures~\ref{fig1}C
and~\ref{fig2}).\looseness=-1

\begin{figure*}
\vspace*{1pt}
\includegraphics{fig02}
\vspace*{1pt}
\caption{\label{fig2}(A) Verdon River profile and location of the HVG
and dam lakes. (B) Longitudinal profile of the Verdon River along the
HVG, lithology schematic outcrop and location of the sampled sites.
Black crosses indicate the beginning (B) and the end (E) of the river
profile (see location of these point in Figure~\ref{fig1}B).}
\vspace*{2pt}
\end{figure*}

The origin of the Verdon River course is a matter of debate. Indeed,the
upstream portion of the river trends roughly parallel to the N--S
direction of tectonic structures \citep{Goguel1935,Jorda1975}. Further
its middle part crosscuts sub-perpendicularly the fold axes affecting
the Jurassic cover, while encompassing the upper part of the HVG and
the southern boundary of the Castellane Arc \citep{Chardonnet1943},
from the city of Castellane to the junction between the Verdon and
Artuby rivers (Figure~\ref{fig1}B). To explain these cross-cutting
relationships, many authors agree on the hypothesis that the Verdon
River course is, in the area, antecedent 
\citep{Blanchard1915,Chardonnet1943,Goguel1935,Nicod2004}. This
hypothesis implies that the Verdon River was originally flowing on a
rather low-relief peneplane and was then forced into incising the
underlying Tithonian limestones during a Cenozoic tectonic uplift
episode  \citep{Chardonnet1943}. 

\subsection{Catchment morphology}\label{sec2.2}

The overall ``L shape'' of the Verdon catchment suggests possible
drainage captures \citep{Blanchard1915} and/or a complex adaptation to
a deformed terrain  \citep{Goguel1935}. From a closer look, the Verdon
\mbox{catchment} and long river profile (Figure~\ref{fig1}) 
can be divided into three
portions:
\begin{itemize}
\item The upper Verdon Valley, from the headwaters to downstream of Castellane town;
\item The HVG, knickzone interrupting the overall concave profile (Figure~\ref{fig2}A);
\item The lower Verdon Valley, from the Sainte Croix Lake to its junction with the Durance River.\pagebreak
\end{itemize}
Regarding the upper section, the Verdon River catchment width decreases
downstream as a result of massive captures from the Asse and Bl\'{e}one
rivers to the West and from the Var River to the East 
\citep{Blanchard1915,Chardonnet1943,Jorda1975}. These authors
considered that the HVG constitutes a abnormally high local base level
for the upper Verdon. The HVG forms a limestone (Tithonic) lithological
knickpoint which likely mitigates the propagation of incision upstream,
as observed in several studies \citep{CrosbyWhipple2006, 
Jansenetal2010,BishopGoldrick2010,Cardinaletal2022}. 
Therefore, undergoing slower incision, the upper Verdon mean elevation
remains high, which makes it vulnerable to capture by the more
competitively erosive surrounding catchments. The high mean elevation
also allowed extensive glacier coverage in the upper Verdon catchment.
For comparison, the W\"{u}rmian glaciers extent reached a length of 40
km along the Verdon River, against only 20 km along the Var River. The
HVG therefore has a high impact on the morphological evolution of the
upstream catchment. Between the Sainte Croix and Castillon lakes, the
HVG course displays a complex pattern (Figure~\ref{fig1}B). Downstream, the
Verdon drainage area then considerably grows from the contribution of
the Artuby River (from 962 km$^{2}$ to 1300 km$^{2}$) and the
incorporation of the Valensole Plateau drainage\break network. 

\subsection{High Verdon Gorges morphology}\label{sec2.3}

The 26 km-long HVG (Figure~\ref{fig3}A) appears as a deep cut in the massive
limestones of the Mesozoic sequence. The cohesive nature of the bedrock
results in maintaining steep walls with mean height around 300~m
(Figure~\ref{fig3}B,~C), which makes it one of the most impressive mountain
gorges in western Europe. However, the limestones show different facies
along the gorges, from the compact late Jurassic to early Cretaceous
Tithonian bars with limited jointing, to middle--upper Jurassic
limestones and marls with a higher degree of bedding, fracturing and
weathering (Figure~\ref{fig2}).
The lithological variations are visible on the
river profile in the HVG, where Tithonian limestone outcrops are
highlighted by strong knickpoints (Figure~\ref{fig2}B). Furthermore, the gorge
transversal profile is alternatively wide and narrow (Figure~\ref{fig3}A), in
agreement with the successive outcropping of middle--upper Jurassic and
Tithonian limestones, respectively \citep{Martel1908}, demonstrating
the contrast in rock resistance along the gorges. 

\begin{figure*}
\vspace*{2pt}
\includegraphics{fig03}
\vspace*{2pt}
\caption{\label{fig3} (A) Aerial image (IGN) of the HVG with the main
topographic features and the location of the sampled sites and photos
point of view (B and C). (B) Samson Corridor and location of the
Collet-Baris anticline. (C) Location of the possible ancient Verdon
thalweg position.}
\vspace*{3pt}
\end{figure*}

A combination of rock falls, fluvial and karstic erosive processes
operates inside the gorges 
\citep{Chardonnet1943,Martel1908,Nicod2004}. The gorge walls are
affected by rock falls, creating scree slopes overgrown by vegetation
at the foot of weak lithology walls and large boulder accumulations in
the riverbed overlooked by resistant lithology walls. Intense fluvial
erosion is visible through the widespread presence of pot-holes and
polished surface, sometimes preserved high up in the steep walls but
especially along the riverbanks and within the boulder accumulation in
the river bed (Figure~\ref{fig4}). Locally, the development of karst network
results in open cavities and large overhangs (called ``baumes''; 
Figure~\ref{fig4}). These cavities in turn guide the course of the river and focus the
fluvial erosion. The karstic network is also intricated with the
current riverbed. Indeed, a part of the river flow is incorporated into
the subsurface karst system at ``La Mescla'' [Figure~\ref{fig3}A,
\citealp{Blanchard1915,FabreNicod1978}]. 


\begin{figure*}
\vspace*{2pt}
\includegraphics{fig04}
\vspace*{3pt}
\caption{\label{fig4} Field pictures of the High Verdon Gorges (at the
vicinity of the Samson sampling site) and highlight of the main
geomorphological erosion features.}
\vspace*{3pt}
\end{figure*}

\subsection{Incision of the High Verdon Gorges} \label{sec2.4}

The top of the HVG vertical walls are marked by a flat erosion surface
(Figure~\ref{fig3}A), possibly corresponding to a level of terraces as their
slope does not match that of the limestone bedding 
\citep{Chardonnet1943}. Located between 800--850~masl, the terraces
level is visible along the downstream part of the HVG, after La Mescla 
\citep{Martel1908}. The terraces are not present in the upstream part
of the HVG, but the numerous emergences of karstic network at the same
altitude (800--850 masl) suggest that this paleo-level is continuous
along the whole HVG  \citep{Chardonnet1943}. These terraces underline
an ancient and wider river channel (Figure~\ref{fig3}C), 
which is different from the present steep and narrow HVG. 

{No geochronological constraint is available to precisely determine the timing of
incision and the formation of these terraces. However, some geological
indices can help estimating the period at which the incision started.
Indeed, continental deposits (conglomerates) from the Late Pleistocene,
corresponding to the latest period of filling of the Valensole Basin,
can be found at the same elevation as the terraces and karstic network,
i.e., between 800--850~masl \citep{Blanc1992,Chardonnet1943}. The
event responsible for the onset of the HVG formation is believed to be
the massive sea-level drop related to the Messinian Salinity Crisis 
\citep{Blanc1992,Nicod2004}, as proposed in surrounding areas 
\citep{Clauzonetal2011,Hippolyteetal2011}. However, some authors
suggest that the formation of the HVG is not older than the Pliocene 
\citep{Chardonnet1943}. From the elevation of the karstic network in
the Lower Verdon Gorges (downstream of the St Croix Lake), \citet{Blanc1992}
estimated an incision rate of 0.34--0.33 mm/yr since the
Pliocene-Quaternary boundary. However, no available data allows
constraining incision rates for the recent Quaternary period.}

\section{Methods} \label{sec3}

\subsection{Sampling strategy}\label{sec3.1}

In order to bring new insights on the incision history of the HVG,
three sites were selected and sampled for dating with the Cosmic Ray
Exposure (CRE) method. 

\begin{figure*}
\includegraphics{fig05}
\caption{\label{fig5} Field pictures of river-polished surface sampled
in the Samson Corridor and sample locations. Note the presence of
pot-holes attesting of the surface preservation since its exposure by
incision.}
{\vspace*{-2pt}}
\end{figure*}

Considering the size of the HVG, it seemed more adequate to sample
several sites along the gorges rather than one single wall as done
previously in neighbouring areas 
\citep{Vallaetal2010,Saillardetal2014,Rollandetal2017,Petitetal2019,Cardinaletal2021,Cardinaletal2022}. 
The main challenges in the HVG were the narrowness of the gorges and the
along-strike lithological variations. Indeed, the portions of the
gorges made of the most massive (Tithonian) limestones, in which
well-preserved river polished \mbox{surfaces} can be expected, are also the
narrowest ones, limiting exposure to cosmic rays due to strong
topographic shielding. Conversely, well-exposed surfaces were found in
portions of the gorges where the stratified limestones bedrock is very
fractured and was most likely impacted by post-incision erosion process
(mainly rock-falls). A compromise between gorge-wall preservation and
reasonable topographic shielding resulted in the selection of three
areas along the HVG (Figures~\ref{fig3}, and~\ref{fig5}--\ref{fig7})
located in:
\begin{itemize}
\item The downstream part of the Samson Corridor, at the upstream entrance 
of the\break gorge;
\item La Mescla, in the middle part of the gorges, at the junction with the 
Artuby River;
\item The Galetas bridge, at the gorges outlet.
\end{itemize}
\begin{figure*}
\includegraphics{fig06}
\caption{\label{fig6} (A) Field pictures of river-polished surfaces
sampled at La Mescla with sample location. Bedding (yellow dashed line)
is gently dipping southwards (5\textdegree). (B,~C) Details on 
Section~\ref{sec1} with overhanging walls. (D) Sketch map of the La Mescla 
site. (E,~F) Schematic topographic cross-sections of Sections~\ref{sec1} 
and~\ref{sec2}.}
\end{figure*}
\begin{figure*}
\vspace*{-2pt}
\includegraphics{fig07}
\vspace*{-2pt}
\caption{\label{fig7} (A) Aerial image (IGN) of Galetas area and
location of the three sampled river-polished surfaces. (B--D)
Details of the three sampled river-polished surfaces and sample
locations. Blue arrows show the river flow direction.}
\vspace*{-2pt}
\end{figure*}
While being very narrow but well-preserved, the Samson Corridor opens
up in its downstream part to a wide section of the gorge (Figure~\ref{fig3}A),
\mbox{corresponding} to a lithological change from massive to stratified
limestone (Figure~\ref{fig2}B). Sub-vertical polished surfaces showing good
preservation with the presence of pot-holes were sampled (Figure~\ref{fig5}). 

La Mescla, is characterized by a deep meander at the junction with the
Artuby River (Figure~\ref{fig3}). Fluvial incision focused on the south
flank by the tight curve of the meander has opened up this portion of
the gorges and created a much wider space than in the direct
surroundings, resulting in a more optimal exposure to cosmic rays.
Although this portion of the gorges is characterized by thin and
heavily fractured limestone beds, some river-polished features are
visible in the thickest strata (Figure~\ref{fig6}A--C). Two strikingly
different  polished surfaces were sampled (Figure~\ref{fig6}).
Section~\ref{sec1}  (Green area, Figure~\ref{fig6}A,~D) is directly
facing the entrance of the meander, while the second one is located
slightly downstream, at the centre of the meander (yellow area,
Figure~\ref{fig6}A,~D). The first section shows an overhanging profile,
with pot-holes in the lower part and underwater erosion pools at the
foot of the wall (Figure~\ref{fig6}B,~C,~E), while the second section
shows a smoother, nearly flat profile in its lower part
(Figure~\ref{fig6}A,~F). The site is also characterized by considerable
sediment aggradation, creating a pebble cordon growing towards the
Artuby River junction (Figure~\ref{fig6}D).\looseness=-1

At the Galetas bridge, we were confronted with the limit of
accessibility, both from above, because of the height of the gorge walls,
and below, because of the river depth. Therefore, instead of a vertical
profile along a single wall, we choose to sample a longitudinal profile
by sampling three polished surfaces at 8--10~m above the modern riverbed
along the massive Tithonian beds that form the outlet of the HVG
(Figure~\ref{fig7}). The samples were collected with a hammer and chisel and
their height above the river bed was measured with a tape measure.


\subsection{$^{36}$Cl CRE dating}\label{sec3.2}

$^{36}$Cl concentrations in collected limestone samples were quantified
in order to estimate Cosmic Ray\break Exposure (CRE) ages and unravel the
exposure history of the steep (almost vertical) bedrock gorge walls
that were theoretically gradually exposed through river incision 
\citep{Schalleretal2005, Ouimetetal2008}. 
$^{36}$Cl concentrations were
determined by accelerator mass spectrometry (AMS) measurements
performed at ASTER, the French national AMS facility (CEREGE,
Aix-en-Provence) \citep{Arnoldetal2010}. A sea-level and high-latitude
$^{36}$Cl production rate for calcium spallation of 42.2~${\pm}$~3.4
atoms $^{36}$Cl~g$^{-1}$~a$^{-1}$ 
\citep{Schimmelpfennigetal2009,Braucheretal2011} was used and scaled
following \citet{Stone2000} and corrected for topographic shielding (TS),
constrained from field measurement data and using the online tool
CRONUS-Earth from \citet{Balcoetal2008}. For more details on the
dating method and the analytical protocol, the reader is referred to
several previous studies 
\citep{Zeratheetal2014,Cardinaletal2021,Cardinaletal2022}. All exposure
ages are indicated according to before present (BP) nomenclature. 

\subsection{Incision rate computation}\label{sec3.3}

The numerical code developed by \citet{Glotzbachetal2011}, originally
designed for thermochronology age-elevation relationships, was used to
determine temporal variations in incision rates from the CRE data. The
code defines the regression segments that best fit the CRE ages data
and the associated uncertainties with elevation distribution. As in
\citet{Glotzbachetal2011}, a Monte Carlo approach was used to randomly
divide the data into 1, 2 or 3 successive time intervals in order to
define regression segments by weighted linear regression, and to select
the best-fitting ones according to their $R^{2}$ value. The following
criteria were applied: no negative incision rate was allowed; regression
segments constrained by less than 3 data points were rejected; the
intersection between two curve segments must correspond to the
intersection between the two sets of data that were used to calculate
them.

\section{Results and local interpretations}\label{sec4}

The sample characteristics are reported in Table~\ref{tab1}. CRE ages
determined from the $^{36}$Cl concentrations are reported in the CRE
age vs. height plots (Figure~\ref{fig8}). The term ``riverbed'' used
here refers to the bedrock, which corresponds to the bottom of the
river channels. It was measured in few locations. The actual geometry
of the river thalweg is therefore poorly constrained.

\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig08}
{\vspace*{2pt}}
\caption{\label{fig8} CRE age vs. height (left $y$-axis) plot and
associated incision rates (right $y$-axis) of (A) Samson, (B) La Mescla
with Section~\ref{sec1} (continuous line) and Section~\ref{sec2} 
(dashed line), and (C)
Galetas. Black lines corresponds to linear regressions, blue lines
corresponds to the incision rates inferred from those regressions and
corresponding uncertainties (light grey rectangles). (D) Inferred
incision rates variations over time for the studied sites, and
corresponding uncertainties.}
{\vspace*{2pt}}
\end{figure*}

\begin{table*}
%\vspace*{-2pt}
\caption{\label{tab1}$^{36}$Cl CRE sample characteristics and
geochronological results}
\tabcolsep=2pt
\fontsize{9.3}{11.3}\selectfont
\begin{tabular}{cccccccccc}
\thead
Sample & 
\parbox[t]{2cm}{\centering Height above river bed (m)} & 
\parbox[t]{1.5cm}{\centering Samp. thick. (cm)} & 
\parbox[t]{1cm}{\centering TS\break factor} & 
\parbox[t]{2cm}{\centering Spallation scaling} & 
\parbox[t]{1cm}{\centering $^{35}$Cl\break (ppm)} & 
Ca (\%) & 
\parbox[t]{1.5cm}{\centering Atoms\break $^{36}$Cl (at/g)} & 
\parbox[t]{2cm}{\centering Atoms\break $^{36}$Cl ${\pm}$ (at/g)} & 
\parbox[t]{1.5cm}{\centering CRE\break age (ka)}\vspace*{2pt} \\ 
\endthead
\multicolumn{10}{c}{{Samson} (lat: 43.7842\textdegree{}; long: 6.3936\textdegree{}; mean elevation: 606 masl)}\vspace*{2pt} \\ 
S01 & 2 & 1 & 0.16 & 1.67 & 37.3 & 40.7 & \083,944 & \0\,6349 & 15.9~${\pm}$~1.2 \\ 
S02 & 2.4 & 1 & 0.16 & 1.67 & 29.9 & 40.7 & \089,670 & \0\,8452 & 17.2~${\pm}$~1.6 \\ 
S03 & 3.3 & 1 & 0.16 & 1.67 & 32.5 & 40.8 & \091,776 & \0\,5730 & 17.5~${\pm}$~1.1 \\ 
S04 & 3.7 & 1 & 0.16 & 1.67 & 35.0 & 40.7 & 118,596 & \0\,7068 & 22.7~${\pm}$~1.4 \\ 
S05 & 4.6 & 1 & 0.16 & 1.67 & 31.5 & 40.6 & 136,006 & \0\,8988 & 26.4~${\pm}$~1.7 \\ 
S06 & 5.8 & 2.5 & 0.16 & 1.67 & 32.0 & 41.7 & 188,287 & \0\,9862 & 36.0~${\pm}$~1.9 \\ 
S07 & 6.8 & 1 & 0.16 & 1.67 & 28.1 & 40.8 & 187,869 & \0\,9775 & 36.9~${\pm}$~1.9 \\ 
S08 & 7.1 & 1 & 0.16 & 1.67 & 28.6 & 40.8 & 205,363 & 13,024 & 40.4~${\pm}$~2.6 \\ 
S09 & 7.7 & 1.5 & 0.16 & 1.67 & 23.4 & 40.7 & 205,909 & 11,192 & 40.9~${\pm}$~2.2 \\ 
S10* & 8 & 1.5 & 0.16 & 1.67 & 33.1 & 40.6 & 190,457 & 16,417 & 37.3~${\pm}$~3.2 \\ 
S11* & 11 & 1 & 0.16 & 1.67 & 24.5 & 40.4 & 110,890 & \0\,8575 & 21.6~${\pm}$~1.7\vspace*{6pt} \\ 
\multicolumn{10}{c}{{La Mescla} (lat: 43.7399\textdegree{}; long: 6.3794\textdegree{}; mean elevation: 564 masl)}\vspace*{2pt} \\ 
M01 & 1.1 & 1 & 0.39 & 1.61 & 43.1 & 40.5 & 388,057 & 38,470 & 32.5~${\pm}$~3.2 \\ 
M02 & 2.0 & 1 & 0.39 & 1.61 & 47.3 & 40.5 & 568,763 & 36,811 & 48.2~${\pm}$~3.1 \\ 
M03 & 2.8 & 1 & 0.39 & 1.61 & 33.5 & 40.6 & 677,155 & 29,949 & 59.0~${\pm}$~2.6 \\ 
M04 & 3.9 & 1 & 0.39 & 1.61 & 36.5 & 40.5 & 386,654 & 34,273 & 32.6~${\pm}$~2.9 \\ 
M05* & 4.7 & 3 & 0.39 & 1.61 & 37.8 & 41.1 & 184,681 & 13,407 & 15.0~${\pm}$~1.1 \\ 
M06* & 5.6 & 2.5 & 0.39 & 1.61 & 43.7 & 41.1 & 198,667 & 26,792 & 16.1~${\pm}$~2.2 \\ 
M07 & 6.3 & 2 & 0.39 & 1.61 & 43.0 & 40.7 & 669,682 & 32,058 & 57.4~${\pm}$~2.7 \\ 
M08 & 6.2 & 1.5 & 0.39 & 1.61 & 49.3 & 40.6 & 651,036 & 29,465 & 55.4~${\pm}$~2.5\vspace*{6pt} \\ 
\multicolumn{10}{c}{{Galetas} (lat: 43.7972\textdegree{}; long: 6.2576\textdegree{}; mean elevation: 475 masl)}\vspace*{2pt} \\ 
G01 & 10 & 1 & 0.20 & 1.49 & 16.2 & 40.5 & 288,596 & 13,927 & 53.2~${\pm}$~2.6 \\ 
G02 & 8.0 & 1 & 0.54 & 1.50 & 26.9 & 40.5 & 423,770 & 18,845 & 28.0~${\pm}$~1.2 \\ 
G03* & 10 & 1 & 0.54 & 1.50 & 19.5 & 40.6 & 308,352 & 15,745 & 20.3~${\pm}$~1.0 \\ 
G04 &  8.9 & 1 & 0.67 & 1.49 & 48.6 & 40.5 & 356,756 & 18,990 & 18.3~${\pm}$~1.0 \\ 
G05 & 9.0 & 2.5 & 0.67 & 1.49 & 49.4 & 41.1 & 596,356 & 29,548 & 31.6~${\pm}$~1.6 
\botline
\end{tabular}
\tabnote{Sample field information, topographic shielding (TS) factor of
the sampled surfaces, samples thickness (Samp. thick.), natural
chlorine contents, calcium, cosmogenic $^{36}$Cl contents in the
limestone samples, resulting $^{36}$Cl CRE ages are indicated. Samples
with an asterisk correspond to CRE ages identified as outliers and
discarded for incision rate computation.}
\vspace*{-2pt}
\end{table*}

\vspace*{-2pt}
\subsection{Samson Corridor}\label{sec4.1}

A total of 11 samples were collected along a 12 m-high polished surface
in the Samson Corridor, which gave CRE ages ranging from 15 to 45 ka.
These data were already presented by \citet{Cardinaletal2022}, where
the authors made a conservative choice to consider only one regression
line for deriving incision rates. As in the present study, to constrain
more precisely the timing of incision in the HVG, the code was allowed
to use three regression lines in order to obtain incision rate
variations. Apart from two samples (S10 and S11) that clearly
demonstrate the occurrence of rock-falls 
\citep[as seen in][]{Cardinaletal2021},
the rest of the data shows a consistent
history of progressive incision with three incision rate trends:
\begin{itemize}
\item 0.25~${\pm}$~0.17 mm/yr from 45 to 30 ka;
\item 0.18~${\pm}$~0.03 mm/yr from 30 to 16 ka;
\item 0.90~${\pm}$~0.53 mm/yr from 16 to 15 ka.
\end{itemize}
Considering the large uncertainties associated with the calculated
incision rates, and relatively similar estimates, it can be concluded
that the first two periods are difficult to distinguish from each other
and that incision in the Samson Corridor underwent only one major incision
rate change after ca. 16 ka. The lack of CRE data does not allow us to
constrain an incision rate for the remaining 2 m of the surface,
corresponding to the last 15 ka (Figure~\ref{fig8}A). 

\vspace*{-3pt}
\subsection{La Mescla}\label{sec4.2}

Eight samples were collected along the two sections described above,
and gave CRE ages ranging from 60 to 15 ka for Section~\ref{sec1} and 60 to 
30 ka for Section~\ref{sec2}. Both sections are located along the concave 
banks of the meander. The data collected from La Mescla indicate a much more
contrasted incision history, which seems in agreement with the complex
morphology of the site. Indeed, as described above, the sampled site
can be seen as two distinct sections; an upstream part with an
overhanging high wall, and a downstream part with a nearly flat
surface. The top of each \mbox{section} corresponds to the top of a limestone
bed: St04 for the highest portion and St01 for the lowest portion
(Figure~\ref{fig6}A). Three observations can be made:
\begin{itemize}
\item Samples collected at the top of each of the two sections (03:
Section~\ref{sec1}; 07 and 08, Section~\ref{sec2}) show similar exposure 
ages (55--60~ka), despite different heights above river bed (2.8~m for 
sample 03 and 6.2--6.3 m for samples 08 and 07);
\item  Samples 01 and 04, collected 2 m below the highest samples of
their respective portion but at different heights above river bed 
(1.1~m for sample 01, 3.3 m for sample 04), have a similar exposure age 
(32~ka); 
\item Intermediate samples 05 and 06 (height above river bed: 4.7 m for
sample 05 and 5.6~m for sample 06) both have a very similar age of
15--16~ka, much younger than the rest of the data, despite being located
in an intermediate position relative to the river bed.\looseness=-1
\end{itemize}
To understand these contrasted CRE ages, the evolution of this specific
portion of the HVG must be reconstructed. The samples 08, 07 and 03,
although located at different heights above the present river bed, have
similar exposure ages and could therefore represent a paleo-riverbed
with a steeper slope than the present one (Figure~\ref{fig9}A). The CRE age of
samples 01 and 04 could then represent a second paleo-riverbed at ca.
30 ka, 2 m below the first one, but with a similar slope (Figure~\ref{fig9}B).
The CRE ages would therefore indicate that between 60 and 30 ka,
incision occurred at a rate of 0.06--0.1~mm/yr. 

\begin{figure*}
\includegraphics{fig09}
\caption{\label{fig9} Sketch (not to scale) of the proposed evolution
and incision history of the La Mescla sampled site at (A) 55--60 ka, (B)
32 ka and (C) 15--16 ka. Paleo-rb: proposed slope of paleo-riverbed;
Present-rb: estimated present riverbed slope; St: limestone strata.
The term ``riverbed'' used here refers to the bedrock, which
corresponds to the channel bottom.}
\end{figure*}

However, Section~\ref{sec1} of La Mescla site seems to have undergone a more
focused and intense incision, since the above mentioned tilted
paleo-riverbed seems to have been flattened to match the modern
riverbed. Indeed, Section~\ref{sec1} is directly facing the upper part of the
meander, while Section~\ref{sec2} is located more deeply in the inside of the
meander curve (Figure~\ref{fig6}D). Hence, the upstream portion is more exposed
to the direct impact of the river flow, while the downstream portion
may be shielded from the shear strength and turbulence of the flow, as
most of it is absorbed in the upstream section of the meander. Such a
focused lateral erosion could have destabilized the bedrock wall by
undercutting its foot, creating an overhanging cliff. Indeed, Samples
05 and 06 show similar young exposure ages of ${\sim}$16~ka, which can
be interpreted as rock falls. Indeed, although probably smoothed by
dissolution, the shallow cavity scarred by a vertical fracture, in
which samples 05 and 06 are located, could be indicative of a rock fall
(Figure~\ref{fig6}C) and therefore could explain the much younger CRE age of
those samples compared to the surrounding ones. The CRE data agree with
an acceleration of incision at the same time for the Samson area
(Figure~\ref{fig8}A), suggesting a period of enhanced incision occurring around
16 ka (age of the possible rock falls). Such an incision wave could
have flattened, very locally and by a combination of vertical incision
and lateral erosion, the riverbed by erasing what could have been a
small lithological knickpoint at La Mescla that did not propagate
upstream, as observed in other studies \citep[][and
references therein]{Johnsonetal2010}.


\subsection{Galetas}\label{sec4.3}

A total of 5 samples was collected along three river polished surfaces
at the outlet of the HVG. The CRE ages range between 55 and 15 ka. The
compilation of these data suggest a low and yet poorly constrained
incision rate of 0.07~${\pm}$~0.04 mm/yr between the 15--55~ka period. 

\section{Discussion}\label{sec5}

\subsection{Short-term incision}\label{sec5.1}

The code was allowed to calculate incision rates with relatively few
points, permitting to highlight rapid variations in incision rates. The
disadvantage of this approach is that these incision rates are not
always well constrained from the CRE data. This strategy allows us to
infer an acceleration of incision from 0.2 to 0.9 mm/yr between 17 and
15 ka in the Samson Corridor (Figure~\ref{fig8}C), but with too few points 
to really constrain it. At the same period, a sequence of rock falls in 
the La Mescla site can be inferred, suggesting a period of increased
downcutting at that time. Following the regional interpretation
proposed by \citet{Cardinaletal2022}, several rivers connected to the
Last Glacial Maximum (LGM) glaciation in the SW French Alps underwent a
period of enhanced fluvial incision following the main glacier retreats
[19--17 and 14 ka; \citealp{Rollandetal2019}]. From these results, it
seems that the Verdon River may have undergone the same evolution, but
since only three ages younger than 20 ka are obtained in the entire
dataset, it remains difficult to infer any detailed post-glacial
history of the HVG with confidence.

\subsection{Long-term incision} \label{sec5.2}

Our results yield two ranges of slow but steady incision rates for the
HVG: 0.06--0.07 mm/yr in the downstream parts of the HVG (Galetas and La
Mesla Section~\ref{sec2}), a roughly similar value of 0.1 mm/yr in the area 
of focused incision (La Mescla Section~\ref{sec1}) between 60 and 15 ka 
(Figure~\ref{fig8}C), and a larger value around 0.2 mm/yr on average in the 
upstream part (Samson Corridor) of the HVG. 

Based on these estimates and on data obtained on the HVG by CRE dating,
the following questions can be subsequently explored: (1) What is the
onset time of HVG formation? (2) What is the main driver for the
long-term incision? (3) What is the respective contribution of
glacial/interglacial phases in lowering or enhancing these long-term
incision rates? 

\subsubsection{What is the onset time of HVG formation?}\label{sec5.2.1}

From the CRE data, the long-term Verdon River incision rates can be
bracketed between 0.06 and 0.2~mm/yr on scales up to several 10's of ka
(neglecting the brief, less constrained, 0.9 mm/yr incision rate
${\sim}$at 15 ka obtained in the Samson Corridor). These incision rates
are lower than those inferred by \citet{Brocardetal2003}
in the neighboring Buech river (0.8 mm/yr over the last 190 ka). If these
results are extrapolated from the bottom of the gorge to the first
level of terraces, up to 300~m above the present riverbed near La
Mescla \mbox{(Figure~\ref{fig10}),} \mbox{computed} 
\mbox{first-order} ages estimates range between
1.5 and 5 Ma, which would thus represent the onset of the main incision
period that dug the HVG up to 300~m.\looseness=-1

\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig10}
{\vspace*{2pt}}
\caption{\label{fig10}\fontsize{9.8}{12}\selectfont Topographic
profiles drawn from the IGN DEM with corresponding surface abandonment
ages. (A) across the Valensole Plateau near Moustier Sainte Marie;
after \citet{Dubaretal1998}, (B) along the lower Verdon channel; after
\citet{Dubaretal1998} and (C) in the HVG near the La Mescla site (this
study). See location profiles on  Figure~\ref{fig1}B. Note that the
vertical and horizontal scales are different between each panel.}
{\vspace*{2pt}}
\end{figure*}

The last deposits of the Valensole basin are dated around 1.8 to 2 Ma 
\citep{Dubar1984,Dubaretal1998,Hippolyteetal2011}, except for local
clastic deposits of the Balene breccia formation, which are dated
around 0.7 to 1 Ma \citep{Dubaretal1978,Dubaretal1998}. This
continental formation is presently incised by tributaries of the Verdon
River. The upstream position of this formation suggests that
downcutting of the lower Verdon River may have started before 1 Ma 
\citep{Dubaretal1998}. In that case, the maximum height of the HVG
(${\sim}$300~m) would correspond to a long-term incision rate of 0.3
mm/yr, which is higher but of the same order of magnitude than
short-term rates deduced from CRE data.

The end of sediment deposition in the Valensole basin is ascribed to
Early Quaternary climate cooling, and was supposed to correspond to the
onset of river network entrenchment in the Valensole plateau and its
surroundings \citep{Dubar1984}. While global cooling started in the
late Pliocene for the Northern hemisphere 
\citep{SucZagwijn1983,Haugetal2005}, evidence for increased incision
and valley downcutting in the Alps seem to have occurred later, around
0.9--1 Ma \citep{Muttonietal2003,Vallaetal2011}, hence around the
mid-Pleistocene transition between the glacial/interglacial cycles
periodicity of 40-ka to 100-ka \citep{Lisiecki2010}. Therefore, the
onset of the Valensole basin deposits incision can be bracketed between
1 and 2 Ma, which is consistent with the younger age estimate (ca. 1.5
Ma) of gorge entrenchment and the higher bound of incision rates
(${\sim}$0.2 mm/yr) estimated from our CRE datings and extrapolation
along the HVG. 

\subsubsection{What is the main driver for the long-term incision?}\label{sec5.2.2}

The present 
total incision of the Balene breccia formation, located in
the Valensole Basin, is of 50 to 70 m, leading to a mean incision rate
of 0.07 to 0.1 mm/yr over the last 0.7--1 Ma. Between the Valensole
abandonment surface dated at 1.8 to 2 Ma and the Verdon thalweg around
the Sainte Croix Lake, it can estimated that the Verdon River has
incised about 220 m, which gives a mean incision rate of 0.1 mm/yr
since that time. This estimate is consistent with the above mentioned
estimation obtained from the Balene breccia formation (Table~\ref{tab2}). From
morphological analysis and CRE dating of the Durance terraces,
\citet{Siameetal2004} inferred a similar incision rate for the Durance
River on its eastern side, with rates of 0.1 mm/yr since 2 Ma. The
value of 0.1 mm/yr can therefore be assumed to constitute a good
estimate for the long-term (i.e., since 1.8 to 2 Ma) average incision
rate of rivers in the Valensole plateau. Such an incision rate is
possibly driven by large-scale isostatic and/or tectonic uplift 
\citep{Champagnacetal2008}, although local tectonic structures might
have also played a role  \citep{HippolyteDumont2000,Siameetal2004}.

\begin{table*}
\caption{\label{tab2}Synthesis of incision and uplift measurements
estimates in the study area\vspace*{-3pt}}
\tabcolsep=2pt\fontsize{9}{10.2}\selectfont
\begin{tabular}{cccccccc}  
\thead
\parbox[t]{1.7cm}{\centering Time\break interval (ka)} &
\parbox[t]{1.8cm}{\centering Uncertainty\break (ka)} &
\parbox[t]{1cm}{\centering Height\break (m)} &
\parbox[t]{1.8cm}{\centering Uncertainty\break (m)} & {Observation} &
Site name &
\parbox[t]{1.3cm}{\centering Site\break number} & {Reference}\vspace*{2pt} \\ 
\endthead
{\0\020} & \0\01 & 1.4 & 0.5 & Incision & Galetas & 1 & This study \\ 
{\0\030} & \0\05 & 2 & 0.5 & Incision & Mescla & 2 & This study \\ 
{\0\050} & \0\05 & 10 & 0.5 & Incision & Samson & 3 & This study \\ 

{\0850} & 150 & 60 & 10 & Incision & Balene breccia & 4 &
\parbox[t]{2cm}{\centering \citep{Dubar1984}\break and this study}\vspace*{2pt} \\ 

{1900} & 100 & 200 & 10 & Incision & Valensole surface & 5 &
\parbox[t]{2.5cm}{\centering \citep{Dubaretal1998}\break and this
study}\vspace*{2pt} \\ 

{2000} & 100 & 200 & 50 & Uplift & East Durance & 6 & \citep{Siameetal2004} \\ 

{1450} & 100 & 290 & 10 & Incision & Samson & 3$_{\mathrm{ext}}$ &
\parbox[t]{2cm}{\centering This study\break (extrapolated)}\vspace*{2pt} \\ 

{3000} & 400 & 345 & 5 & Uplift & Digne nappe & 7 & \citep{Hippolyteetal2011} \\ 

{3000} & 400 & 645 & 5 & Uplift & Digne nappe & 7$_{\mathrm{corr}}$ & 
\parbox[t]{3cm}{\centering \citep{Hippolyteetal2011}\break (corrected)}\vspace*{2pt} \\ 

{6000} & 500 & 3500 & 500 & Denudation & Velodrome & 8 & \citep{Schwartzetal2017}
\botline
\end{tabular}
\tabnote{Site numbers and location refer to Figure~\ref{fig11}.}
\vspace*{-4pt}
\end{table*}

This mean incision rate of 0.1 mm/yr is roughly consistent with the
higher range of incision rates inferred for the medium part of the HVG:
``La Mescla'' site and, considering its large uncertainties, and the
Galetas site in the lower part of the HVG. It is also consistent with
contemporary average denudation rates ranging between 0.04 and 0.12
mm/yr computed from topographic analysis and $^{10}$Be CRE data on the
Valensole Plateau hillslopes \citep{Godardetal2020}. Incision rates in
the Samson Corridor (0.2~mm/yr) is twice as high, as in neighbouring
catchments for the recent period covering the last ca. 40 ka [ranging
from 0.15 and 0.28 mm/yr; \citealp{Cardinaletal2022}]. This can be
ascribed either to differential tectonic motions (with respect to the
lower Verdon Gorges and Valensole plateau) or to delayed incision of a
steep, disequilibrium river profile that might have accumulated between
several glacial cycles \citep{Rollandetal2017}. The tectonic
hypothesis argues for the role of Pliocene to Quaternary faults,
accommodating Plio-Quaternary shortening along the Digne--Castellane
arcs \citep[e.g.,][]{Sanchezetal2010,Bauveetal2014}. These structures
could locally consist of EW trending blind thrusts and folds
responsible for the measured incision rates in the Samson Corridor. For
instance, in the Samson Corridor, the Verdon River cuts across a
topographic dome corresponding to an anticline axis cored by lower
Jurassic limestones (the Collet-Barris anticline), instead of flowing
in the neighbouring, lower-altitude syncline to the west 
(Figures~\ref{fig1}C and~\ref{fig3}B). 
This can be {interpreted} as an antecedence assisted by the network
of N--S and E--W faults \citep{Nicod2004} and suggests a \mbox{possible,} very
slow differential uplift between the Mesozoic sedimentary cover units
of the \mbox{Castellane} arc and the Valensole basin of 0.1 mm/yr since the
incision onset of the HVG. This value is consistent with previously
obtained estimates of differential uplift rates on Quaternary canyons
in the Digne Nappe, although the age of the canyons are only indirectly
constrained \citep{Hippolyteetal2011}. The contractional deformation
is still ongoing, as shown by the seismicity observed south of the
Castellane area [see \mbox{\citealp{LePichonetal2010,Larroqueetal2021}} for a
\mbox{synthesis].}

To the Northwest of the HVG, thermochronology data from Miocene
sediments underthrusted below the Digne Nappe yielded long-term
exhumation rates of about 0.5 to 0.6 mm/yr since ca. 6 Ma [Figure~\ref{fig11}C;
\citealp{Schwartzetal2017}]. These higher values are possibly due to
the activity of a crustal-scale, ``thick-skin'', thrust located below
the Barles half-window \citep{Nouibatetal2022,Schwartzetal2017}. Here,
NNW--SSE to NW--SE trending thrust wedges (Esclangon and Tanaron horse
structures) have accommodated N70\textdegree{}E-trending compressional
deformation and are responsible for the Plio-Quaternary uplift of
Barles area \citep{Hippolyteetal2011}.
In addition, based on balanced
and restored cross-sections through southwestern Subalpine and Central
Provencal zones, \citet{Balansaetal2022} suggested that the relative
northeastward migration of buried basement highs contributed to the
observed Pliocene-Quaternary contractional deformation and uplift of
the central and northern extremity of the Valensole area. It is likely
that this contractional deformation continued to migrate to the NNE
until reaching the Barles half-window. The above mentioned local
exhumation rates are consistent with the preservation of late Pliocene
to early Quaternary canyons in the Digne Nappe, as denudation can have
been more focused and more intense in the Barles half-window than in
the surrounding area, where the nappe is preserved and well visible
today. Moreover, the late stage denudation history since 1--2 Ma is too
recent and too shallow to be precisely recorded  by apatite
fission-track (AFT) and (U--Th)/He (AHe) thermochronology~data.
\looseness=-1

\begin{figure}
\includegraphics{fig11}
{\vspace*{-5pt}}
\caption{\fontsize{9.5}{11}\selectfont\label{fig11} Compilation of
incision and uplift rates at different time scales. (A) Incision rates
in the HVG from CRE dating (this study) over 20 to 50~ka. (B) Same data
as on A with additional incision or uplift rate estimates from the
literature (sites 4, 5, 6 and 7). Point 3$_{\mathrm{ext}}$ corresponds
to the extrapolation of the recent 0.2 mm/yr incision rate (site~3) to
the actual gorge height measured in the Verdon canyon. Points
7$_{\mathrm{corr}}$ corresponds to the uplift of the Digne Nappe in the
Esquichiere canyon relative to the Valensole basin 
[\citealp{Hippolyteetal2011}, point~7], to which is added an uplift of
0.1 mm/yr of the Valensole basin relative to the base level, in order to
allow comparison with the other points. (C) Same as B (B corresponds to
the grey-dashed rectangle on the bottom left) with long-term AFT/AHe
exhumation rate estimates from \citet{Schwartzetal2017} interpreted as
uplift estimates. The Messinian Salinity Crisis (MSC) period is
indicated (transparent blue rectangle). See Table~\ref{tab1} for
details.}
\end{figure}


Considering all these values together, and assuming that recent
(${<}$60 ka) incision rates in the HVG can be extrapolated to the
overall Quaternary\break period, it can be proposed that: (i) there is a very
slow (0.1 mm/yr) uplift of the whole region since the last 1.5 to 2 Ma,
encompassing the Valensole basin and the Digne Nappe--Castellane Arc
units, which is possibly the result of late Alpine tectonics or
isostatic uplift \citep[e.g.][]{Champagnacetal2008}; (ii) there might be
an additional, although very slow, thin-skin deformation (0.1 mm/yr of
uplift) of the sedimentary cover of the Castellane Arc relative to the
Valensole basin; (iii) the situation is different in the Barles
half-window, where higher rock exhumation rates occurred in the Late
Miocene (ca. 6 Ma) in response to the activity of a crustal-scale
thrust [recognized on crustal-scale geophysical images;
\citealp{Nouibatetal2022}] and/or northeastward migration of a basement
high \citep{Schwartzetal2017,Balansaetal2022,Nouibatetal2022}. Whether
this activity was constant during the last 6 Ma, or was initially very
fast and progressively slowed down to reach the observed
uplift/incision rates for the last 1.5--2 Ma further south is difficult
to quantitatively assess. Vertical GPS motions in the study area are
poorly constrained, with present-day uplift rates of 0.41~${\pm}$~0.58~mm/yr 
at the nearest station at Moustier-Saint-Marie 
\citep{Sternaietal2019}, so it is impossible to compare our long-term
uplift estimates values with modern and almost instantaneous uplift
rates from geodesy \citep[e.g.,][]{Pina-Valdesetal2022}.

\subsection{What is the respective contribution of glacial/interglacial phases in lowering or enhancing incision?}\label{sec5.3}

In this framework, and comparing our results with long-term incision
rates estimated in the Valensole Plateau and in the Verdon Gorges, the
higher (up to 0.9 mm/yr at 15--16 ka, Figure~\ref{fig8}A) incision rates obtained
in the Samson Corridor can be tentatively ascribed to its upstream
position in the HVG. The Samson Corridor is located at the boundary
between two erosion regimes during the late-Quaternary period. Incision
is mainly controlled by the influence of glaciation in the high Verdon
Valley, while the lower Verdon Valley is only under a fluvial incision
regime. Therefore, the higher incision rates estimated over a short
period (${\sim}$0.9 mm/yr from 16 to 14 ka) could be the result of a
paraglacial crisis in the Verdon River posterior to the LGM. The same
timing of enhanced incision is observed in neighbouring catchments\break
following post-LGM deglaciation \citep{Cardinaletal2022}. Furthermore,
increased incision after 16 ka could have triggered rock falls in the
La Mescla site of the HVG (Section~\ref{sec4.2}). However, it is also possible
that rockfall might solely be related to freezing and thawing effects,
as observed by \citet{Cardinaletal2021} in a similar periglacial gorge
setting. Therefore, the enhanced incision in the higher part of HVG
could {result} from an increased interaction with the High Verdon Valley,
where glacial incision has been efficient. The effect of enhanced
incision \mbox{following} glaciers melting could have been hindered and
buffered in the rest of the gorges, due to the resistance of the
Tithonian limestones to such influences. 

\section{Conclusions}\label{sec6}

We sampled three 10 m-high river-polished walls within the High Verdon
Gorge, in order to apply the Cosmic Ray Exposure dating approach and
derive incision rates. These data are used to discuss the gorge origin
and both short-term and long-term dynamics. Each site shows local
complexities related to the intricate course of the Verdon River and,
except for the upstream boundary of the HVG (Samson corridor), no
significant variations in incision rates with time are evidenced. It
remains therefore difficult to relate the HVG downcutting to the
post-LGM paraglacial incision crisis, as it is more likely the case in
other rivers also connected to the LGM glacial extent in the region
\citep[e.g.][]{Cardinaletal2022}. The relatively steady incision rates
(0.06--0.2 mm/yr) obtained from our CRE data cover a time window between
60 and 15 ka and are comparable to long-term regional uplift,
exhumation and denudation rate estimates. This leads us to propose that
tectonic and/or isostatic uplift are the main drivers for the Late
Quaternary incision of the Verdon River. Finally, this long-term
incision, when extrapolated to the rest of the vertical 300~m-high
gorge walls and to other estimated incision heights from the Valensole
basin, is consistent with a Mid- to Early Quaternary (${\sim}$1.5 to 2
Ma) onset of incision for the HVG. This age estimate could reasonably
fit with the beginning of Alpine glaciations; although the general
pattern of the river network was probably already present in Late
Miocene times, intense downcutting responsible for the initial
entrenchment of the Verdon River can be ascribed to the Quaternary
climate cooling.

\section*{Conflicts of interest}

Authors have no conflict of interest to declare.

\section*{Acknowledgments} 

This study has been funded by the French Geological Survey (Bureau de
Recherches G\'{e}ologiques et Mini\`{e}res; BRGM) through the national
program ``R\'{e}f\'{e}rentiel G\'{e}ologique de France'' (RGF-Alpes).
This work has also been supported by the French Government, through the
UCA-JEDI Investments in the Future project managed by the National
Research Agency (ANR) with the reference number \mbox{ANR-15-IDEX-01.} The
$^{36}${Cl measurements were performed at the ASTER AMS national
facility (CEREGE, Aix en Provence) which is supported by the INSU/CNRS,
the ANR through the ``Projets th\'{e}matiques d'excellence'' program for
the ``Equipements d'excellence'' ASTER-CEREGE action and IRD. This
manuscript benefitted from constructive reviews by two anonymous
reviewers and efficient editorial handling by O. Fabbri.}

\CDRGrant[ANR]{ANR-15-IDEX-01}

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