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\DOI{10.5802/crgeos.340}
\datereceived{2026-01-16}
\daterevised{2026-05-16}
\dateaccepted{2026-05-28}
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\section*{Declaration of interests}
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\COI{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.}

\begin{document}

\begin{noXML}

\CDRsetmeta{articletype}{research-article}

\TopicFR{G\'eomorphologie}
\TopicEN{Geomorphology}

\editornote{Article submitted by invitation}
\alteditornote{Article soumis sur invitation}

\title{Tracking recent climatic and anthropogenic perturbations of
surface processes in the French Massif Central from paired
\textsuperscript{14}C\textsubscript{\text{in\,situ}} and
\textsuperscript{10}Be analysis}

\alttitle{Suivi des perturbations climatiques et anthropiques
r\'ecentes des processus de surface dans le Massif central fran\c{c}ais
\`a partir de l'analyse coupl\'ee du
\textsuperscript{14}C\textsubscript{\textit{in situ}} et du
\textsuperscript{10}Be}

\author{\firstname{Vincent} \lastname{Godard}\CDRorcid{0000-0003-0143-5893}\IsCorresp}
\address{Aix Marseille Univ, CNRS, IRD, INRAE, CEREGE, Aix-en-Provence, France}
\address{Institut Universitaire de France, Paris, France}
\email[V. Godard]{godard@cerege.fr}

\author{\firstname{Sebastien J. P.} \lastname{Lenard}\CDRorcid{0000-0003-3358-7197}}
\addressSameAs{1}{Aix Marseille Univ, CNRS, IRD, INRAE, CEREGE, Aix-en-Provence, France}
\address{Institute of Arctic and Alpine Research, University of Colorado, Boulder, CO, USA}

\author{\firstname{Maarten} \lastname{Lupker}\CDRorcid{0000-0001-7609-6246}}
\address{D-EAPS, ETH Z\"urich, Switzerland}
\curraddr[M. Lupker]{SERI, Bern, Switzerland}

\author{\firstname{Irene}\nobreakauthor \lastname{Schimmelpfennig}\CDRorcid{0000-0001-8145-9160}}
\addressSameAs{1}{Aix Marseille Univ, CNRS, IRD, INRAE, CEREGE, Aix-en-Provence, France}

\author{\firstname{Cl\'ement} \lastname{Desormeaux}\CDRorcid{0000-0002-6852-0171}}
\addressSameAs{1}{Aix Marseille Univ, CNRS, IRD, INRAE, CEREGE, Aix-en-Provence, France}
\address{G\'eosciences Rennes, Universit\'e de Rennes, CNRS, Rennes, France}

\author{\firstname{Negar} \lastname{Haghipour}\CDRorcid{0000-0001-8223-0536}}
\addressSameAs{4}{D-EAPS, ETH Z\"urich, Switzerland}
\address{Laboratory of Ion Beam Physics, ETH Z\"urich, Switzerland}

\thanks{ANR TOPOEXTREME (ANR-18-CE01-0017), INSU/Tellus (Maraca) and
Radiate (20002215-ST-1.1).}

\shortrunauthors

\keywords{\kwd{Surface processes}
\kwd{Erosion}
\kwd{Cosmogenic nuclides}
\kwd{Geomorphology}
\kwd{Holocene}
\kwd{Transience}}

\altkeywords{\kwd{Processus de surface}
\kwd{\'Erosion}
\kwd{Nucl\'eides cosmog\'eniques}
\kwd{G\'eomorphologie}
\kwd{Holoc\`ene}
\kwd{\'Etat transitoire}}


\begin{abstract}
Understanding landscape evolution over Late Quaternary timescales
requires quantifying transient erosion responses to climatic and
anthropogenic forcings.  The paired cosmogenic nuclide system
\textsuperscript{10}Be--\textsuperscript{14}C\textsubscript{\text{in\,situ}}  offers unique insights into
surface process variations across 1--10 ka timescales owing to their
strongly contrasting half-lives.  We present new
\textsuperscript{14}C\textsubscript{\text{in\,situ}} measurements in
river sediment combined with existing \textsuperscript{10}Be data from
ten catchments along the southeastern margin of the French Massif
Central to investigate recent landscape dynamics.  All samples indicate
a state of temporal disequilibrium in the
\textsuperscript{10}Be--\textsuperscript{14}C\textsubscript{\text{in\,situ}} 
system, with
\textsuperscript{14}C\textsubscript{\text{in\,situ}}-derived denudation
rates being up to five times higher than \textsuperscript{10}Be-derived
rates.  This pattern suggests recent intensification of surface
processes.  The magnitude of disequilibrium varies spatially, with the
strongest signal in the steep catchments of the C\'evennes east of the
main drainage divide with the Rh\^one basin.  We employ a novel
inversion framework incorporating hilltop curvature measurements and
hillslope transport theory to reduce parameter space and account for
regional similarities in denudation dynamics.  Two transient scenarios
can explain the observations: an increase in denudation rate around
15--5 ka BP, possibly associated with the Pleistocene--Holocene
transition, or recent soil removal events within the last few centuries
linked to historical deforestation, although the available data do not
allow us to unambiguously discriminate between the two.  Our results
demonstrate the sensitivity of the
\textsuperscript{10}Be--\textsuperscript{14}C\textsubscript{\text{in\,situ}} 
system to recent landscape perturbations and highlight the complex
interplay between climatic transitions and anthropogenic forcing in
shaping temperate mid-elevation mountain landscapes. \end{abstract}

\begin{altabstract} 
Comprendre l'\'evolution des paysages \`a l'\'echelle de temps du
Quaternaire r\'ecent n\'ecessite de quantifier les r\'eponses
\'erosives transitoires aux for\c{c}ages climatiques et anthropiques.
Le syst\`eme de nucl\'eides cosmog\'eniques coupl\'es
\textsuperscript{10}Be--\textsuperscript{14}C\textsubscript{\textit{in\,situ}} 
offre un \'eclairage unique sur les variations des processus de surface
aux \'echelles de temps de 1 \`a 10 ka, en raison de leurs demi-vies
fortement contrast\'ees. Nous pr\'esentons de nouvelles mesures de
\textsuperscript{14}C\textsubscript{\textit{in\,situ}} dans des
s\'ediments de rivi\`ere, combin\'ees \`a des donn\'ees
\textsuperscript{10}Be pr\'eexistantes, pour dix bassins versants le
long de la marge sud-orientale du Massif central fran\c{c}ais, afin
d'\'etudier la dynamique r\'ecente des paysages. Tous les
\'echantillons r\'ev\`elent un \'etat de d\'es\'equilibre temporel dans
le syst\`eme
\textsuperscript{10}Be--\textsuperscript{14}C\textsubscript{\textit{in\,situ}}, 
avec des taux de d\'enudation d\'eduits du
\textsuperscript{14}C\textsubscript{\textit{in\,situ}} jusqu'\`a cinq
fois sup\'erieurs \`a ceux d\'eduits du \textsuperscript{10}Be. Cette
tendance sugg\`ere une intensification r\'ecente des processus de
surface. L'ampleur du d\'es\'equilibre varie spatialement, le signal le
plus marqu\'e s'observant dans les bassins versants escarp\'es des
C\'evennes, \`a l'est de la principale ligne de partage des eaux avec
le bassin du Rh\^one. Nous mettons en {\oe}uvre un nouveau cadre
d'inversion int\'egrant des mesures de courbure de cr\^ete et la
th\'eorie du transport sur les versants, afin de r\'eduire l'espace des
param\`etres et de tenir compte des similarit\'es r\'egionales dans la
dynamique de d\'enudation. Deux sc\'enarios transitoires permettent
d'expliquer les observations : une augmentation du taux de d\'enudation
autour de 15--5 ka BP, possiblement associ\'ee \`a la transition
Pl\'eistoc\`ene-Holoc\`ene, ou des \'ev\'enements r\'ecents d'\'erosion
des sols au cours des derniers si\`ecles, li\'es \`a la d\'eforestation
historique ; toutefois, les donn\'ees disponibles ne permettent pas de
trancher sans ambigu\"it\'e entre les deux. Nos r\'esultats
d\'emontrent la sensibilit\'e du syst\`eme
\textsuperscript{10}Be--\textsuperscript{14}C\textsubscript{\textit{in
situ}}  aux perturbations r\'ecentes des paysages et mettent en
\'evidence l'interaction complexe entre les transitions climatiques et
le for\c{c}age anthropique dans le fa\c{c}onnement des paysages
montagneux temp\'er\'es de moyenne altitude.
\end{altabstract}

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\defcitealias{hippe2021cosmogenic}{ibid.}
\defcitealias{desormeaux2022investigation}{ibid.}
\defcitealias{richardson2019influences}{ibid.}
\defcitealias{slosson2022nonsteadystate}{ibid.}
\defcitealias{schaller200230}{ibid.}

\section{Introduction}\label{sec1}

Landscapes evolve primarily through the interplay of tectonics and
climatic forcings, which drive surface processes such as weathering,
erosion, and sediment transport
\citep{champagnac2012tectonics,kirby2012expression}.  While many
theoretical formulations conceptualize surface processes using a
steady-state framework, where these forcings balance each other,
widespread evidence points to ubiquitous transient changes in
surface-process intensity and topographic properties across natural
landscapes
\citep{mudd2016detection,prince2013evidence,godard2021transient}.  This
unsteadiness manifests across all spatial scales, from the response of
individual hillslopes to the reorganization of entire drainage systems,
and across a range of timescales spanning hundreds to millions of
years.  Understanding these transient responses is critical in
particular over Late Quaternary timescales, during which recent
climatic changes---notably associated with the Pleistocene--Holocene
transition---have strongly influenced landscape dynamics and set the
stage for the geomorphological systems as we observe them today
\citep{mariotti2021nonlinear,madoff2022global}. Nevertheless, the
precise nature and strength of the connection between climate change
and erosion remain subjects of active debate, hindering the analysis of
recent landscape evolution and its interactions with ecosystems and
societies.

To characterize these transient erosion responses and understand
landscape dynamics across timescales, researchers often rely on the
analysis of sedimentary archives.  These records form through the
progressive accumulation of erosion products and carry a wealth of
information on the conditions and processes acting in the contributing
catchment at various times
\citep[e.g.][]{kober2019postglacial,mariotti2021nonlinear}.   However,
several limitations exist: incomplete or disturbed records, sparse
sampling density, poor control on sediment provenance, and the
sometimes significant distance between sediment source area and
depositional sink. Furthermore, interpreting these records can be
challenging when deconvolving the distinct contributions of tectonic,
climatic and anthropogenic influences, which are often mixed and
blurred. These constraints underscore the need to develop complementary
approaches, especially those capable of documenting near-field erosion
dynamics, as close as possible to the active sites of surface processes
\citep{godard2025constraining}.

Terrestrial Cosmogenic Nuclides (TCN) have emerged as a highly
effective tool for investigating the dynamics of surface processes,
enabling quantitative estimations of past and present denudation rates
\citep{vonblanckenburg2005control,granger2014cosmogenic,schaefer2022cosmogenic,codilean2022octopus}. 
While a single TCN measurement only provides a single denudation rate,
the use of multiple TCN with distinct radioactive decay rates offers
invaluable insights into temporal changes in surface processes
\citep[e.g.][]{hippe2012quantifying,schimmelpfennig2022glacier,godard2024erosional}. 
Among these, paired measurements of the terrestrial cosmogenic nuclides
\tsup{10}Be and \tsup{14}C\tsub{\text{in\,situ}}, both produced
{in situ} within the quartz mineral, are particularly promising
for resolving Late Pleistocene and Holocene landscape dynamics, over 1
to 10~ka timescales
\citep{mudd2016detection,hippe2017constraining,skov2019detecting}.  The
very distinct half-lives of cosmogenic nuclides like \tsup{14}C
(5.7~ka) and \tsup{10}Be (1.39~Ma) make them ideally suited for
quantifying changes in denudation rates across these critical
timescales \citep{fulop2015quantifying,hippe2021cosmogenic}. Indeed,
the much longer-lived \tsup{10}Be is sensitive to landscape dynamics on
the 10--100~ka timescale, whereas the comparatively short-lived
\tsup{14}C\tsub{\text{in\,situ}} is mostly sensitive to recent events
on the 100~a--10~ka timescale, with no memory of older denudation
conditions. This pair is in particular sensitive to recent
perturbations, such as land cover changes, landslides, or fluctuations
in glacial extent, which can significantly shift the relative
concentrations of the two nuclides 
(\tsup{14}C\tsub{\text{in\,situ}}/\tsup{10}Be ratio) away from its
steady-state equilibrium value
\citep{hippe2017constraining,schimmelpfennig2022glacier}.  Despite its
considerable potential, very few datasets using the
\tsup{10}Be--\tsup{14}C\tsub{\text{in\,situ}} system to constrain
changes in denudation dynamics have been published to date, primarily
because of the limited number of specialized
\tsup{14}C\tsub{\text{in\,situ}} extraction facilities
\citep{lupker2019insitu,fulop2019ansto,lifton2023technical}, as well as
the more complex interpretations required by this system
\citep{skov2019detecting,hippe2017constraining}.

The Pleistocene--Holocene transition represents one of the most dramatic
recent environmental shifts, profoundly shaping the Earth's
contemporary landscapes and ecosystems
\citep[e.g.][]{shakun2010global,malhi2016megafauna,ellis2021land}. 
During this period, substantial increases in temperature and
modifications in precipitation regimes led to significant changes in
sediment production and transport mechanisms
\citep[e.g.][]{hughes2009increased,godard2025constraining}. 
Divergences in the apparent denudation rates derived from \tsup{10}Be and
\tsup{14}C\tsub{\text{in\,situ}} can serve as a diagnostic signal for
erosional transience during the Holocene, including periods of
significant anthropogenic influence.  Over the Late Pleistocene and
Holocene, landscapes experienced a conjunction of environmental and
cultural transformations, with climatic variability often coinciding
with the emergence, expansion and collapse of agropastoral societies
\citep[e.g.][]{ruddiman2007early,kirch2005archaeology}.  In many early
agricultural centers, accelerated soil thinning and erosion have been
directly linked to human activities such as widespread burning,
deforestation, intensive grazing, or cultivation, often exacerbated by
changing climatic conditions
\citep[e.g.][]{montgomery2007soil,owens2020soil}.  This entanglement of
factors poses a significant challenge to accurately discerning the
relative contributions of natural environmental change versus
anthropogenic forcing to long-term soil sustainability and landscape
evolution \citep{hippe2021cosmogenic}.  The idea of an ``Early
Anthropocene'' emphasizes the human and climate-driven impacts on
pre-industrial landscapes and highlights this complex and often
inseparable relationship \citepalias{hippe2021cosmogenic}.

To effectively address these questions, a careful selection of study
areas is required. Regions characterized by slow tectonic deformation
and low background denudation rates offer optimal conditions for
isolating, on 1--10~ka timescales, the influence of climatic variations
on surface processes from often overwhelming tectonic signals.  In this
context, the southeastern French Massif Central (FMC) presents an
interesting natural laboratory
\citep{olivetti2016cenozoic,desormeaux2022investigation}. This
mountainous region features a strong geomorphological gradient from its
incised eastern margin to the more subdued relief of the Massif
interior.  Focusing on small catchments in this type of context allows
us to minimize the complexities associated with extensive sediment
storage and long transport lags that often complicate the
interpretation of detrital TCN signals.

In this study, we present a new set of \tsup{14}C\tsub{\text{in\,situ}}
measurements in river sediment combined with existing \tsup{10}Be
concentrations from 10 catchments on the \mbox{eastern} margin of the French
Massif Central.  We analyze the denudation rates derived from these
nuclide concentrations and evaluate them against different
surface-process scenarios to explain the variations in disequilibrium
observed across the margin.  We explore in particular the impact of
instantaneous variations of denudation rates and soil thickness.

\section{Settings}\label{sec2}

The French Massif Central (FMC) belongs to a series of low- to
middle-elevation mountain ranges that represent the remnants of the
Hercynian orogeny across western and central Europe, such as the Vosges
or Bohemian Massif \citep{olivetti2020cretaceous}.  Due to significant
uplift and volcanic activity during the Late Cenozoic
\citep{seranne2002surrection,malcles2020determining}, the FMC stands as
a major topographic feature, and is characterized by a very steep
southeastern margin with topography rising from a few hundred metres
a.s.l. in the Rh\^one river valley, to more than 1000 m asl in the
interior of the FMC (Figure~\ref{fig:location}).

%fig1
\begin{figure*}
\includegraphics{fig01}
\caption{\label{fig:location}Location map of the studied basins along
the SE margin of the French Massif Central. Basins are colored
according to their average slope.  The three classes also correspond to
the three clusters that were defined independently from
cosmogenic-nuclide data, as explained in the Methods. The numbers used
for identification are the same as in
\citet{desormeaux2022investigation}, where the \tsup{10}Be data were
published. The red line indicates the drainage divide between the
Rh\^one basin to the east, and the Loire and Garonne basins to the
west.}
\end{figure*}

The topographic gradient is associated with a morphological contrast
between the Ard\`eche and C\'evennes Mountains with steep
near-threshold hillslopes and active river incision into bedrock, and
the gently rolling hillslopes observed farther west across the margin
edge, in the Margeride Mountains \citep{desormeaux2022investigation}.
This steep margin acts as a major topographic barrier for moisture
transport from the Mediterranean, and an orographic effect leads to
contrasting mean annual precipitation: ${>}$1500~mm at the margin and
${\sim}$500~mm in the interior of the Massif. The area is also subject to
intense storm events several times per year, leading to important
discharge variability along the streams that drain the margin
\citep{lelay2007exploring,desormeaux2022investigation}. Denudation
rates derived from \tsup{10}Be concentrations in river sediments also
highlight a strong spatial gradient across the margin. The Ard\`eche
and C\'evennes mountains are characterized by denudation rates in the
80--120 mm/ka range, whereas moving west beyond the Rhone catchment
divide, denudation rates are usually ${<}$40 mm/ka
\citep{olivetti2016cenozoic,desormeaux2022investigation}.

Like other middle-elevation Hercynian mountain domains in Europe, the
French Massif Central has been subject to limited glaciation during the
Late Quaternary, although several groups of glaciers and icefields have
been identified, notably in the central part of the FMC, in the Cantal,
Mont Dore and Aubrac mountains \citep{ancrenaz2022last}. Further east,
closer to the studied area, smaller glacier systems were also
recognized in the Margeride and Loz\`ere Mountains, with a limited
geomorphic imprint, both in terms of cumulative erosion and associated
deposits.     This is one of the key advantages of the study area, as
the TCN signal is unlikely to be strongly affected by glacial
shielding, glacial erosion or massive paraglacial sediment reworking in
the investigated basins. This limited influence of the Quaternary
Glaciations allows for a focused investigation into the impacts of
climatic and anthropogenic factors on weathering and hillslope
processes. 

\section{Methods}\label{sec3}

\subsection{Analytical approach}\label{sec31}

\citet{desormeaux2022investigation} sampled 34 medium-sized basins
along the southeastern margin of the FMC and measured \tsup{10}Be
concentrations. We selected 10 of these basins for
\tsup{14}C\tsub{\text{in\,situ}} analysis to investigate their recent
dynamics. The basins are affected by a large spectrum of surface
processes, due to varying mountainous landforms ranging from gently
rolling hillslopes of the FMC interior to the steep margin of the
Ard\`eche and C\'evennes Mountains. During the sample selection,
\citetalias{desormeaux2022investigation} took care to avoid areas impacted
by active landslides or dense human activity.

{In situ} \tsup{14}C extractions were performed at ETH Z\"urich on 5--6~g
aliquots of the 10 quartz samples (250--1000~$\upmu$m fraction) used for
the \tsup{10}Be analyses \citepalias{desormeaux2022investigation}.  The
extraction system and method outlined in \citet{lupker2019insitu}
allows degassing of all carbon species, including cosmogenic \tsup{14}C,
from the quartz at temperatures up to 1670~\textdegree C.  After
purification and quantification of the CO\tsub{2}, the \tsup{14}C/\tsup{12}C
ratios were measured at the gas ion source of the MICADAS accelerator
mass spectrometer at ETH Z\"urich
\citep{synal2007micadas,fahrni2013improving}.  The \tsup{14}C
concentrations were calculated following the method of
\citet{hippe2014calculating} (Table~\ref{tab:c14}).  Measurement
results of the inter-comparison quartz materials CRONUS-A and CRONUS-N
from the ETH extraction line used in this study are reported in
\citet{lupker2019insitu}. 

\begin{sidewaystable*}[p!]
\caption{\label{tab:c14}\tsup{14}C\tsub{\text{in\,situ}} analytical
results (see text for details)}
\tabcolsep 9pt
\begin{tabular}{cccccccc}
\thead                                                                                 
Sample & \parbox[t]{4.5pc}{\centering Quartz mass (g)}
& \parbox[t]{3pc}{\centering C Yield ($\upmu$gC/g)} & 
\parbox[t]{2pc}{\centering $\delta^{13}$C (\textperthousand)}
& Fraction modern &  
\parbox[t]{4pc}{\centering \tsup{14}C (${\times}10^6$~at.)}
&\parbox[t]{4.5pc}{\centering \tsup{14}C - bk corr.  ($\times10^6$~at.)}
& \parbox[t]{4pc}{\centering [\tsup{14}C] ($\times10^3$~at/g)}\vspace*{2pt}  \\
\endthead
CDX-CRN-02&5.7463& \02.2  & \0${-}$5.9 & 0.3035 ${\pm}$ 0.0030&0.5400 ${\pm}$ 0.0062&0.5240 ${\pm}$ 0.0078 & \091.181 ${\pm}$ 1.353   \\
CDX-CRN-04&6.9030& 13.8 & ${-}$13.9 & 0.0386 ${\pm}$ 0.0010&0.2545 ${\pm}$ 0.0091&0.2384 ${\pm}$ 0.0103 & \034.542 ${\pm}$ 1.487   \\
CDX-CRN-05&6.0447& 20.9 & \0${-}$9.9 & 0.0357 ${\pm}$ 0.0010&0.3033 ${\pm}$ 0.0108&0.2872 ${\pm}$ 0.0118 & \047.516 ${\pm}$ 1.951   \\
CDX-CRN-06&5.9356& 58.7 & ${-}$20.3 & 0.0158 ${\pm}$ 0.0010&0.3352 ${\pm}$ 0.0167&0.3191 ${\pm}$ 0.0173 & \053.762 ${\pm}$ 2.921   \\
CDX-CRN-08&4.5762& \01.1  & \0${-}$5.7 & 0.4728 ${\pm}$ 0.0000&0.6195 ${\pm}$ 0.0000&0.6034 ${\pm}$ 0.0047 & 131.859 ${\pm}$ 1.023 \\
CDX-CRN-09&5.9672& \03.6  & \0${-}$9.9 & 0.6048 ${\pm}$ 0.0050&1.3857 ${\pm}$ 0.0118&1.3697 ${\pm}$ 0.0127 & 229.532 ${\pm}$ 2.124  \\
CDX-CRN-12&6.5484& \03.4  & \0${-}$7.7 & 0.5876 ${\pm}$ 0.0050&1.3795 ${\pm}$ 0.0120&1.3635 ${\pm}$ 0.0129 & 208.213 ${\pm}$ 1.967  \\
CDX-CRN-15&4.3083& 94.8 & ${-}$22.7 & 0.0065 ${\pm}$ 0.0000&0.1598 ${\pm}$ 0.0000&0.1437 ${\pm}$ 0.0047 & \033.359 ${\pm}$ 1.087   \\
CDX-CRN-17&6.2913& \03.6  & \0${-}$9.3 & 0.3025 ${\pm}$ 0.0040 &0.7188 ${\pm}$ 0.0084&0.7028 ${\pm}$ 0.0096 & 111.705 ${\pm}$ 1.530 \\
CDX-CRN-19&4.6725& \03.0  & ${-}$10.3 & 0.1600 ${\pm}$ 0.0000&0.2959 ${\pm}$ 0.0000&0.2799 ${\pm}$ 0.0047 & \059.893 ${\pm}$ 1.002 
\botline
\end{tabular}
\tabnote{Note that on all figures the basins are labeled with the
number at the end of the sample name reported here. All indicated
uncertainties are ${\pm}1\sigma$. The process blank associated with this
series of sample contained 16038 ${\pm}$ 4682 atoms of \tsup{14}C. The
subtracted blank was averaged over 20 blank measurements obtained
between 06.01.2020 and 27.04.2021. \tsup{10}Be results and basin
properties are reported in \citet{desormeaux2022investigation}.}
\vspace*{-23pc}
\end{sidewaystable*}

\subsection{Steady-state interpretations of concentrations}

Steady-state denudation corresponds to the situation in which a
constant surface denudation rate has been applied long enough that the
TCN concentration depth profile no longer varies with time.  The
measured TCN concentrations $C$ (atoms/M), for \tsup{10}Be and
\tsup{14}C\tsub{\text{in\,situ}}, can be interpreted in terms of
steady-state denudation rates $\varepsilon$ (L/T),
{\begin{equation}\label{eq:ss}
C=\sum_i \frac{P_i}{\frac{\rho \varepsilon}{\Lambda_i}+\lambda},
\end{equation}}\unskip
with $\rho$ the rock density (M/L\tsup{3}), $\lambda$ the radioactive
decay constant (T\tsup{\tminus1}), $P_i$ the basin-averaged surface
production rates for the considered nuclide (atoms/M/T), computed for
each basin, and $\Lambda_i$ (M/L\tsup{\tminus2}) the attenuation
lengths for cosmic rays below the surface. The subscript $i$ refers to
the different production pathways for the TCN (\tsup{10}Be or
\tsup{14}C\tsub{\text{in\,situ}}), by neutrons, stopped muons and fast
muons.

Steady-state apparent denudation rates were calculated using the
Lal-Stone time-independent scaling scheme \citep{stone2000air}, with
the calibration dataset of \citet{borchers2016geological} for
spallation production rates and muon production properties from
\citet{braucher2013determination,braucher2003situ}. We use 160~g/cm\tsup{2}
for the effective neutron attenuation length in rock and a rock density
of 2.65~g/cm\tsup{3}. No shielding correction was considered.

To investigate the influence of soil mixing dynamics, we also use the
formalism proposed by \citet{foster2015hillslope} for a steady-state
mixed soil of thickness $H$ (L), where concentration $C$ (atoms/M)
can be calculated as,
{\begin{equation}\label{eq:foster}
C = \frac{\frac{\bar{P}H}{\varepsilon \beta} + C_b }{1+\frac{\lambda
H}{\varepsilon \beta}}.
\end{equation}}\unskip
$\bar{P}$ is the depth-averaged production rate in the soil
(atoms/M/T), including spallation and muogenic production, $\beta$ is
the rock-to-soil density ratio ($\beta=2$ in the following) and $C_b$
is the nuclide concentration in the bedrock at the interface with the
soil, which depends on both $H$ and $\varepsilon$. Under the
steady-state assumption, Equation~(\ref{eq:foster}) allows us to combine
the measurements of two nuclides, such as  \tsup{10}Be and
\tsup{14}C\tsub{\text{in\,situ}}, to determine both denudation rate
$\varepsilon$ and depth $H$.

\subsection{Hilltop curvature calculation}

Morphological data for the studied basins are reported by
\citet{desormeaux2022investigation}. In addition, we computed
basin-averaged  hilltop curvature $C_{\mathrm{HT}}$ (1/L), using open-access
2-m resolution lidar Digital Elevation Models
\citep[LIDAR~HD;][]{ign2026lidar}. Obtaining basin-averaged estimates
of hilltop curvature allows us to use the classical relationship in
transport-limited hillslopes between $C_{\mathrm{HT}}$ and denudation rate
$\varepsilon$ \citep{hurst2012using}.
{\begin{equation}\label{eq:cht}
\varepsilon =  \frac{K |C_{\mathrm{HT}}|}{\beta}.
\end{equation}}\unskip

This relationship involves the hillslope transport coefficient $K$
(L\tsup{2}/T), for which published compilations exist
\citep{richardson2019influences}, and will be used to analyze our
dataset.

\subsection{Transient dynamics modelling}

To study the possible disequilibrium associated with deviations from
steady state in the \tsup{10}Be--\tsup{14}C\tsub{\text{in\,situ}} system,
we also analyze the transient evolution of the concentrations in
response to perturbations and how they evolve from one steady-state
value toward another. We perform an inversion of the \tsup{10}Be and
\tsup{14}C\tsub{\text{in\,situ}} concentrations using a Markov chain
Monte Carlo (MCMC) sampler
\citep{vrugt2009accelerating,hartig2023bayesiantools}. For each model
we ran 8 chains in parallel, each $5\times10^5$ steps in length, with a
burn-in phase corresponding to the first 10\% of each chain.
Convergence was checked using the multivariate potential scale
reduction factor \citep{gelman1992inference}. The  likelihood
$\mathcal{L}$ was defined as,
{\begin{equation}
\ln \mathcal{L} = \sum_{i} \ln \left( \frac{1}{\sqrt{2\uppi} \,
\sigma_i} \right)  - \frac{1}{2} \sum_{i}
\frac{\left(C_i^{\mathrm{obs}} -
C_i^{\mathrm{mod}}\right)^2}{\sigma_i^2},
\end{equation}}\unskip
where $C_i^{\mathrm{obs}}$ is the measured concentration,
$C_i^{\mathrm{mod}}$ is the corresponding modeled concentration, and
$\sigma_i$ is the analytical measurement uncertainty on
$C_i^{\mathrm{obs}}$.

The inversions are constructed according to two distinct transient
scenarios inspired by those investigated in
\citet{hippe2021cosmogenic}. The first scenario considers a step change
in denudation rate at a fixed time $T$, synchronous for all basins.
Contrary to \citetalias{hippe2021cosmogenic}, we formulate the evolution in
terms of changes of the hillslope transport coefficient $K$, and
calculate denudation rates using Equation~(\ref{eq:cht}). The hillslope
transport coefficient is setting the pace of hillslope morphological
evolution and is modulated by climatic conditions and vegetation
\citep{richardson2019influences}. Following
\citet{hippe2021cosmogenic}, we consider a two-step scenario.  In
contrast to their approach, in which the change is specified directly
in terms of denudation rate, we instead impose a change in $K$ from
$K_1$ to $K_2$ at time $T$.

The coefficient $K$ is considered to be the same for all basins within
each of the clusters, which we define with $k$-means clustering
according to the values of denudation rates derived from the \tsup{10}Be
and \tsup{14}C\tsub{\text{in\,situ}} concentrations. We assume that
basins in each cluster share similar lithologies and climatic
conditions.  This approach has the advantage of reducing the dimension
of the problem to be solved. For example, in the case of a pair of
basins, for which we have determined the \tsup{10}Be and
\tsup{14}C\tsub{\text{in\,situ}} concentrations, we have a total of
four concentrations, in other words two concentrations per basin.
Formulating the problem as a step change in denudation rates at time
$T$ requires solving for five unknowns: the transition time $T$, the
denudation rate before the transition for each basin, and the
denudation rate after the transition for each basin. The problem is
under-determined in this case. Conversely, formulating the evolution in
terms of a step change in $K$ reduces the problem to three unknowns:
$T$, $K_1$ and $K_2$, because $K$ is a regional,
climatically-controlled parameter whose value at a given time is the
same for both basins. We use an exponential prior on the $K$
parameters, based on the compilation of
\citet{richardson2019influences}. The forward model for the prediction
of concentrations accounts for time variations in production rates
following the Lal-Stone time-dependent scaling scheme
\citep{lal1991cosmic,stone2000air,balco2008complete}, and the virtual
dipole moment reconstruction of \citet{muscheler2005geomagnetic}.

The second scenario considers an instantaneous soil removal event at a
time $T$, again synchronously for all basins. The thickness of soil
removed is identical for basins belonging to the same cluster, as is
the hillslope transport coefficient $K$, which does not change through
time.

%fig2
\begin{figure*}
\includegraphics{fig02}
\vspace*{5pt}
\caption{\label{fig:2nuclides}(A) Normalized two-nuclide plot for the
\tsup{10}Be--\tsup{14}C\tsub{\text{in\,situ}} system.  The
concentrations are normalized according to the individual production
rates of the basins.  Samples are colored according to the
denudation-derived cluster they belong to. Ellipses represent 2$\sigma$
confidence intervals. The solid and dashed curves correspond to the
prediction for steady-state denudation or constant exposure of the
surface, that is absence of denudation. (B) Comparison of steady-state
denudation rates derived from the \tsup{10}Be and
\tsup{14}C\tsub{\text{in\,situ}} measured concentrations (error bars
are ${\pm}2\sigma$). The solid line indicates equal \tsup{10}Be and
\tsup{14}C\tsub{\text{in\,situ}} denudation rates, and dashed lines
correspond to  \tsup{14}C\tsub{\text{in\,situ}} denudation rates higher
by factors of 2, 5 and 10.}
\end{figure*}

\section{Results}

\subsection{Analysis of concentrations and steady-state predictions}

The measured \tsup{14}C\tsub{\text{in\,situ}} concentrations range from
$33\pm1\times10^3$ to $230\pm2\times10^3$~at/g of quartz 
(Table~\ref{tab:c14}). The lowest concentration is at least one order of
magnitude above the ${+}1\sigma$ analytical blank value. When combined
with the \tsup{10}Be data of \citet{desormeaux2022investigation}, all our
samples plot below the steady-state denudation curve on a two-nuclide
plot (solid line, Figure~\ref{fig:2nuclides}A).  This curve corresponds
to the predicted surface concentrations in the case of a constant
denudation through time. This position indicates that the measured TCN
concentrations cannot be explained by a steady-state denudation history
nor by a constant exposure of samples at the surface. We observe that
the amplitude of deviation from the steady-state denudation curve is
highly variable, and samples do not cluster as a single group.  Some
samples are close to steady-state denudation conditions, whereas most
samples are distant from the steady-state curve and appear to be very
depleted in \tsup{14}C\tsub{\text{in\,situ}}. Most of these samples
with very low \tsup{14}C\tsub{\text{in\,situ}}/\tsup{10}Be are located
east of the drainage divide, where topographic gradients are the
highest (Figure~\ref{fig:location}). We computed steady-state
denudation rates based on the measured \tsup{14}C\tsub{\text{in\,situ}}
and \tsup{10}Be concentrations (Figure~\ref{fig:2nuclides}B). These
steady-state rates for the two nuclides are clearly different in most
cases, with up to ${>}$5-fold differences, the 
\tsup{14}C\tsub{\text{in\,situ}}-derived denudation rates being
systematically higher than their \tsup{10}Be equivalent. This
difference can be considered as a clue for an intensification of
surface processes in the recent past, within the sensitivity time
window of \tsup{14}C.


The $k$-mean clustering based on the apparent denudation rates
(Figure~\ref{fig:2nuclides}B) yielded 3 clusters. Cluster 1 corresponds
to basins located in the interior of the FMC with low \tsup{10}Be-derived
denudation rates and a moderate disequilibrium between \tsup{10}Be and
\tsup{14}C\tsub{\text{in\,situ}}. Cluster 2 corresponds to basins on
the topographic margin, mostly in the C\'evennes east of the divide,
with both high \tsup{10}Be-derived denudation rates and the strongest
disequilibrium. Cluster 3 corresponds to basins on the topographic
margin and east of the divide with high \tsup{10}Be-derived denudation
rates and a lower \tsup{10}Be--\tsup{14}C\tsub{\text{in\,situ}}
disequilibrium. Even though the average slope of the basin was not used
for the TCN-based clustering, the three resulting clusters are
consistent with the slope classes used in Figure~\ref{fig:location} and
correspond to a geomorphic gradient of increasing slopes.

We observe a clear correlation ($R^2 = 0.82$) between \tsup{10}Be-derived
denudation rates and hilltop curvature ($C_{\mathrm{HT}}$), except for basin 6,
which has the highest curvature (Figure~\ref{fig:cht}). This correlation
suggests the importance of transport-limited hillslope dynamics over
long time scales, and the obtained transport coefficient
$K=0.009\pm0.001$~m\tsup{2}/a is within the range reported by
\citet{richardson2019influences} for comparable settings. Basin 6 is
also the steepest basin, and its deviation from the observed linear
trend may result from a transition from transport- to
weathering-limited conditions on its hillslopes
\citep{godard2016weatheringlimited}.

%fig3
\begin{figure}
\includegraphics{fig03}
\caption{\label{fig:cht}Relationship between \tsup{10}Be steady-state
denudation rate (error bars are ${\pm}2\sigma$) and the absolute value
of hilltop curvature extracted from a LiDAR DEM, for the studied
basins. Black line is a linear regression ($R^2=0.82$ and $p<0.001$)
and the envelope denotes its 95\% confidence interval. Basin 6 was
excluded from the regression (justification in text). The slope of the
regression corresponds to a hillslope transport coefficient of
$0.009\pm0.001$ m\tsup{2}/a.}
\end{figure}

As a single, basin-wide steady-state denudation rate over the period of
resolution cannot explain the concentrations observed for each of our
paired \tsup{10}Be--\tsup{14}C\tsub{\text{in\,situ}} samples, we explore
other processes.  Specifically, we investigate steady-state soil mixing
and \mbox{associated} dynamic burial, which has been shown to induce apparent
disequilibrium in other paired nuclide systems
\citep{makhubela2019effects,knudsen2019timeintegrating,hippe2021cosmogenic,godard2024erosional}.
For each basin, we use the formalism proposed by
\citet{foster2015hillslope} to compute the denudation rates and
soil-mixing thicknesses that explain both the observed \tsup{10}Be and
\tsup{14}C\tsub{\text{in\,situ}} concentrations
(Figure~\ref{fig:ss_soil}). The modeled denudation rates range from 20
to 120 mm/ka, with mixing thicknesses reaching more than 10 meters for
some basins.  We did not observe such thick soils in the studied area,
even in the low relief interior of the FMC. Furthermore, the fact that
the thickest predicted soils are associated with the steepest basins
(Figure~\ref{fig:ss_soil}B) suggests that this process of soil mixing
is unlikely to be the main factor explaining the observed
disequilibrium.

%fig4
\begin{figure*}
\includegraphics{fig04}
\vspace*{-3pt}
\caption{\label{fig:ss_soil}(A) Relationship between steady-state soil
mixing depth and denudation rate computed according to the formalism of
\citet{foster2015hillslope}, using both \tsup{10}Be and
\tsup{14}C\tsub{\text{in\,situ}} data. Ellipses correspond to 2$\sigma$
confidence intervals. (B) Relationship between the steady-state mixing
depth and basin average slope (error bars are ${\pm}2\sigma$).}
\vspace*{-3pt}
\end{figure*}

We also use a simple mixing budget to test the idea that the
\tsup{14}C\tsub{\text{in\,situ}}--\tsup{10}Be disequilibrium  results from
a dilution by the tapping of sources of old (${>}$50 ka) and shielded
sediments (Figure~\ref{fig:dead_sed}). Deposits such as deep fluvial,
glacial or lacustrine fills, can have very low 
\tsup{14}C\tsub{\text{in\,situ}} concentrations and their mixing with
the active sediments transiting in the river network could
substantially affect the measured concentration. For basins where the
disequilibrium is low, a moderate amount (on the order of 10\%) of
material derived from old and shielded sediments could explain the
observed \tsup{14}C\tsub{\text{in\,situ}}/\tsup{10}Be ratios.
However, for many catchments, the estimated amount is higher than 50\%,
and no field evidence indicates the existence of reservoirs large
enough to be a source of such sediments. We also note that the
proportion of these old sediments is highest in the steepest
catchments, where intermediate storage of material is least likely.
Finally, the existence of such large reservoirs of completely shielded
sediments is also highly unlikely from a geomorphological point of
view, as any transient deposit would immediately start to accumulate
cosmogenic nuclides over depths of several meters.

%fig5
\begin{figure*}
\includegraphics{fig05}
\vspace*{-3pt}
\caption{\label{fig:dead_sed}(A)  Steady-state denudation rate ratios
between \tsup{10}Be and \tsup{14}C\tsub{\text{in\,situ}} as a function
of the estimated fraction of total flux from old sediments.  (B)
Fraction of the total flux from old sediments as a function of the
basin slope.}
\vspace*{-3pt}
\end{figure*}

\subsection{Transient dynamics modelling}
As steady-state solutions do not provide acceptable explanations for
the observed concentrations, we investigate the impact of transient
perturbations. As suggested by previous studies
\citep{hippe2021cosmogenic}, the low 
\tsup{14}C\tsub{\text{in\,situ}}/\tsup{10}Be ratios could be explained
by a transient response to recent changes in surface processes, either
through an increase in denudation rates or through a discrete
soil-removal event \citepalias{hippe2021cosmogenic}.  Indeed, both
hypotheses contribute to rapidly bringing rocks with lower 
\tsup{14}C\tsub{\text{in\,situ}}/\tsup{10}Be ratios to the surface, and
this disequilibrium can persist for hundreds to thousands of years
(Figure~\ref{fig:examples}).

%fig6
\begin{figure*}
\includegraphics{fig06}
\vspace*{-3pt}
\caption{\label{fig:examples}Examples of two possible transient
scenarios explaining the observed \tsup{10}Be and
\tsup{14}C\tsub{\text{in\,situ}} concentrations for two samples in our
dataset (CDX-CRN-02 and CDX-CRN-19). Both scenarios correspond to a
perturbation in the past, starting from steady-state conditions.
Scenario 1 (orange curves) considers an instantaneous increase in
denudation rate, driven by an increase of the hillslope transport
coefficient $K$. Scenario 2 (pink curves) considers an instantaneous
removal of a given thickness of soil with no change in the hillslope
transport coefficient. The parameters used here are for illustrative
purpose and do not correspond to best fitting values from an
optimization procedure.  The ellipse color corresponds to the cluster
the sample belongs to.} 
\vspace*{-3pt} 
\end{figure*}


In Scenario 1, we consider the implications of a step change in
denudation rate at a given transition time $T$, occurring synchronously
in all basins.  As explained above, we do not express this change
directly in terms of a shift in denudation rate from $\varepsilon_1$ to
$\varepsilon_2$, but rather in terms of a change in the hillslope
transport coefficient $K$, from $K_1$ to $K_2$. The values of $K_1$ and
$K_2$ are defined for each cluster independently of the others. We
perform a MCMC inversion to obtain the marginal posterior distributions
for $T$ and the various $K$, and assess the likelihood of the scenario
(Figure~\ref{fig:acc_ero}). We have excluded basin 6 from the analysis,
as it displays a clear outlier behavior in the relationship between
denudation rate and hilltop curvature (Figure~\ref{fig:cht}), which is
likely due to a transition from transport- to weathering-limited
conditions, as noted above.

%fig7
\begin{figure*}
\includegraphics{fig07}
\vspace*{-3pt}
\caption{\label{fig:acc_ero}Scenario 1: results of an inversion of the
\tsup{10}Be and \tsup{14}C\tsub{\text{in\,situ}} data assuming a step
change in the hillslope transport coefficient $K$ (from $K_1$ to
$K_2$).  Each cluster has different values of $K_1$ and $K_2$, but the
timing of the change is synchronous.  The different clusters, from 1 to
3, are identified by the colors blue, red and yellow, respectively. (A)
Cumulative probability density curves for $K_1$ and $K_2$, for each
cluster, before (solid line) and after (dashed line) the transition. 
The black line corresponds to the compilation of $K$ values from
\citet{richardson2019influences}. (B) Joint posterior distribution of
$K_1$ and $K_2$. The black contours correspond to the probability
density of the compilation of $K$ values from
\citet{richardson2019influences}. The thick solid grey line corresponds
to $K_1=K_2$. Thin grey solid and dashed lines correspond to various
values of the ratio $K_2/K_1$, and the corresponding increase in
denudation rate, from ${\times}2$ to ${\times}100$. (C) The orange
distribution corresponds to the transition time between $K_1$ and
$K_2$, which is common for all basins. The blue curve is the Greenland
oxygen-isotope ice record of \citet{grootes1993comparison}, shown for
reference. (D)~Comparison of observed and predicted \tsup{10}Be and
\tsup{14}C\tsub{\text{in\,situ}} concentrations. The black line
indicates equality between the observed and predicted concentrations,
and grey bands indicate deviations by ${\pm}20$\% and ${\pm}50$\%.}
\end{figure*}

Scenario 1 implies an order-of-magnitude variation in $K$ and
denudation rates for clusters 1 and 2, and a more subdued evolution for
cluster 3 (Figure~\ref{fig:acc_ero}A,B). Such large-amplitude changes
in denudation rates have been reported by \citet{hippe2021cosmogenic};
however, in our modelling framework, they imply very high $K_2$ values,
outside the range reported by \citet{richardson2019influences}. This
shift would have occurred after 30 ka BP, and most likely between 15
and 5 ka BP (orange colored distribution in \mbox{Figure~\ref{fig:acc_ero}C}).
The inverted parameters predict most of the \mbox{concentrations} to within
20\% of the observed values for both nuclides, with up to 6 catchments
deviating more, but still within 50\% of the observed values
(Figure~\ref{fig:acc_ero}D). The very high values of $K_2$ for two of
the clusters imply that a variation in denudation through
climatically-driven modulation of the diffusive hillslope transport
coefficient $K$ is not likely to fully explain the observed
disequilibrium, and suggest that mass-wasting processes might be
involved. However, we did not observe widespread recent landsliding in
the studied basins.

In Scenario 2, we explore the instantaneous removal of a given
thickness of soil $H$ occurring at a given time $T$
(Figure~\ref{fig:soil_remove}). Background denudation rates are set by
using a constant value of the hillslope transport coefficients $K$,
which are the same before and after the perturbation, and applying
Equation~(\ref{eq:cht}). The values of $H$ and $K$ are defined for each
cluster independently of the others. This inversion yields transport
coefficients $K$ which are within the range of the compilation by
\citetalias{richardson2019influences}. The soil removal event is predicted
to have occurred very recently, most likely during the last centuries
(Figure~\ref{fig:soil_remove}C). The amplitude of removal is variable
across clusters, with a depth up to 3 m at cluster 2, but ${<}$1 m for
the others (Figure~\ref{fig:soil_remove}B). The removal of several
meters of material may not be realistic, but it should be noted that
the calculation uses a regolith density of 1.3~g/cm\tsup{3}, which may be
an underestimate depending on the nature of the cover and the type of
process involved. Scenario 2 is also successful at reproducing the
observed concentrations (Figure~\ref{fig:soil_remove}D).

%fig8
\begin{figure*}
\includegraphics{fig08}
\caption{\label{fig:soil_remove}Scenario 2: results of an inversion of
the \tsup{10}Be and \tsup{14}C\tsub{\text{in\,situ}} data based on the
scenario considering instantaneous soil removal at a given time. Each
cluster has a different value of the thickness of soil removed. Each
cluster has a different value of the hillslope transport coefficient
$K$, which is constant through time and does not change at the
transition in this scenario. The different clusters, from 1 to 3, are
identified by the colors blue, red and yellow, respectively. (A)
Cumulative probability density curves for $K$, for each cluster.  The
black line corresponds to the compilation of $K$ values from
\citet{richardson2019influences}. (B)~Distribution of removed soil
thickness for each cluster. (C) Distribution of the joint soil removal
time. The blue curve is the Northern Hemisphere temperature anomaly
from \citet{briffa2000annual}, for reference. (D) Comparison of
observed and predicted \tsup{10}Be and \tsup{14}C\tsub{\text{in\,situ}}
concentrations. The black line indicates equality between the observed
and predicted concentrations, and grey bands indicate deviations by
${\pm}20$\% and ${\pm}50$\%.}
\end{figure*}

\section{Discussion}
\vspace*{-3pt}

\subsection{Multi-nuclide dataset analysis approach}
\vspace*{-3pt}

Our reconstruction of the denudation history from the 
\tsup{14}C\tsub{\text{in\,situ}} and \tsup{10}Be concentrations is
inspired by the scenarios proposed by \citet{hippe2021cosmogenic}, with
the difference that we incorporate information about the catchment
morphology in our inversion, by using measured hilltop curvature and
inverting for changes in the hillslope transport coefficient. We follow
the method proposed by
\citet{godard2021transient,godard2024erosional,godard2025constraining},
which consists in formulating the time variations of surface processes
in terms of efficiency parameters instead of individual denudation
histories for each basin or site. This approach relies on the idea that
denudation variations are strongly correlated, both in their timing, as
was considered by \citet{hippe2021cosmogenic}, and in their amplitude,
so that, for example, a twofold increase in the denudation rate of one
catchment is likely to have affected nearby catchments with similar
relative changes in intensity. Our approach uses a linear relationship
between denudation rates and a morphological characteristic of the
basin to decrease the dimension of the inversion problem. In our case
we use Equation~(\ref{eq:cht}) with a hillslope transport coefficient
considered common to all basins belonging to the same cluster. We could
have used other geomorphological laws that express denudation rates as
a function of a quantifiable morphological variable and an efficiency
parameter setting the intensity of the considered process. In addition,
our approach allows us to compare the inversion results with published
values of $K$ \citep{richardson2019influences}.

Scenarios 1 and 2 consider one single event of either denudation
acceleration or soil removal. Several sites in the FMC suggest various
stages of surface processes as a response to climatic or anthropic
perturbations, in particular over the Holocene
\citep[e.g.][]{surmely2009occupation,chassiot20187000year,chassiot2022anthropogenic}.
Assuming a single event forces the inversion to maximize the amplitude
of the surface process response, and the summation of a sequence of
lower intensity events through time, either denudation acceleration or
soil removal, might yield similar TCN signals. Such a sequence may be
more likely than a single very intense event, but \mbox{constraining} its
detailed timing would dramatically increase the number of parameters in
our inversion, to the point of rendering it intractable. Additionally,
the two scenarios we consider are not mutually exclusive, and we could
speculate that the measured TCN signal results both from a change in
\mbox{denudation} rates at the Pleistocene--Holocene climatic transition and
from a recent, anthropogenically driven soil-removal event.

Our approach directly relies on the conditions of applicability of
Equation~(\ref{eq:cht}), which include continuous hillslope transport. 
Consequently, Equation~(\ref{eq:cht}) cannot account for processes such
as mass wasting and the discontinuous denudation of hillslope material,
which may occur during drastic climatic changes. This might be a reason
for the abnormally high recent transport coefficient ($K_2$) obtained
through the denudation change scenario (Figure~\ref{fig:acc_ero}), when
compared with the range of values reported by
\citet{richardson2019influences}.

We considered basins distributed across a geomorphic gradient with a
strong contrast in relief and soil cover, but no differential in
tectonic rock uplift. The $k$-mean clustering allowed us to identify
subsets of catchments with comparable characteristics. This choice was
guided by the diversity of observed 
\tsup{14}C\tsub{\text{in\,situ}}/\tsup{10}Be ratios in our dataset
suggesting contrasted dynamics and responses to environmental changes.
Basins with relatively low hillslope angles (${<}$20\textdegree,
clusters 1 and 3) clearly display the lowest amount of deviations
between the two nuclides, with some catchments almost at equilibrium
(Figures~\ref{fig:location}  and~\ref{fig:2nuclides}). The interior
basins (cluster 1) show very limited impacts of climatically driven
changes in hillslope dynamics, with almost no $K$ variation in Scenario
1 (denudation-rate change; Figure~\ref{fig:acc_ero}) and very limited
soil stripping in Scenario 2 (Figure~\ref{fig:soil_remove}). In
contrast, cluster 2 in the C\'evennes displays the largest variations,
highlighting the sensitivity of this steep landscape to perturbations.
This observed spatial gradient in sensitivity contrasts with some of
the modeling results of \citet{mudd2016detection}, who showed that, on
the contrary, slowly eroding landscapes should display the highest
response. We note that the catchments along the margin are also subject
to a drastically different hydro-climatic regime compared with the
interior of the massif, with occurrences of extreme rainfall events and
large discharge variability \citep{desormeaux2022investigation}. The
contrast in sensitivity between the two domains is then not only
controlled by the intrinsic dynamics of the
\tsup{14}C\tsub{\text{in\,situ}}--\tsup{10}Be system, but also by
changes in the nature of surface processes through time with a possible
intensification of extreme precipitation and discharge events along the
topographic margin associated with the onset of a wetter climate during
the Holocene \citep[e.g.][]{peyron1998climatic,ponel2022lateglacial}.

\subsection{Comparison with other \tsup{14}C\tsub{\text{in\,situ}} datasets}

Only a limited number of previous studies using the
\tsup{14}C\tsub{\text{in\,situ}}--\tsup{10}Be system in detrital sediments
have been published, providing a glimpse into changes of Earth surface
processes over the Late Quaternary 
\citep[e.g.][]{kober2019postglacial,hippe2017constraining}. Due to this
limited number of previous studies and the geomorphic and climatic
diversity of the settings they investigated, there is no single
analysis framework for such datasets, which complicates the
generalization of the results. We also note that these studies almost
systematically observe significant deviations from steady-state ratios,
which probably reflects the major variations in environmental
parameters over the last tens of millennia
\citep{godard2025constraining}, even though the actual processes
invoked in each case are very different in nature and timing.  In some
cases, this combination of processes make the signal very difficult to
interpret \citep{schmidt2026quantifying}.

\citet{hippe2021cosmogenic} showed a major disequilibrium of the
\tsup{14}C\tsub{\text{in\,situ}}--\tsup{10}Be system in catchments of the
Altiplano, which could be explained either by punctual events of
denudation acceleration or soil removal. All these events occurred
after 5 ka BP and \citetalias{hippe2021cosmogenic} suggest that they could
be related to wetter conditions over the area and coeval changes in
agricultural practices, highlighting the connections between climatic
variability and human activities.  Our study converges towards similar
interpretations but with different timings, as we observe a variable
degree of disequilibrium in our basins that seems to be driven by how
basins respond to perturbations depending on their hillslope gradient.
For example, we could postulate that steep basins of the margin are
close to threshold hillslope conditions and will display a shorter and
non-linear response to changes in transport coefficient, whereas basins
with lower slopes are more likely to stay in the linear domain, with
more subdued responses \citep{godard2021influence}.

\citet{slosson2022nonsteadystate} observed similar low ratios and a
strong disequilibrium of the \tsup{10}Be--\tsup{14}C\tsub{\text{in\,situ}}
system in large basins draining the eastern flank of the Argentinian
Andes, which they interpret as the manifestation of cumulated storage
events on hillslopes within these basins. However, the setting of
\citetalias{slosson2022nonsteadystate} is very different from the area we
investigate: our basins are smaller, the glacial imprint is weak if not
absent, and there are no active tectonics.  We cannot directly compare
their results with ours, as we have only a limited number of plausible
processes, and transient storage is not realistic in our \mbox{setting}.

\citet{fulop2020millionyear} also obtained detrital
\tsup{10}Be--\tsup{14}C\tsub{\text{in\,situ}} data in SE Australia, on
basins much larger than the ones investigated in our study.  They
observe low ratios of variable amplitude which in their setting
indicate complex sediment reworking in large-scale fluvial systems. 
Such processes are not relevant for the type of landscape and basins of
our study.  A recent study by \citet{towers2025denudation} focuses
exclusively on \tsup{14}C\tsub{\text{in\,situ}} to investigate
denudation processes in the postglacial landscape of the Scottish
Highlands. They infer a significant contribution of paraglacial
deposits in the studied catchment to the present-day sediment flux in
the main channel, and thus highlight the lasting impact of glaciation
on these processes. Because of a different setting without major
glacial impact and different methods, we cannot conduct a meaningful
comparison of their results with ours, but their study underscores the
interest of \tsup{14}C\tsub{\text{in\,situ}} as a tracer of Holocene
processes.

\subsection{Comparison with existing constraints on \mbox{recent}
climatic and anthropic forcings in the FMC}

Although we selected our study area and the sampled basins to minimize
the direct impact of glacial shielding and erosion during the Late
Pleistocene, periglacial conditions were present in the landscape, with
localized gelifraction and associated slope deposits. In many places,
the development of periglacial formations on hillslopes was actually a
key factor of sensitivity to later erosion events triggered by Holocene
climatic fluctuations or anthropogenic land occupation changes
\citep{dendievel2015environmental}. An extensive cover of clasts
recently produced by gelifraction could be a factor promoting intense
regolith removal during climatic changes, and could correspond to the
major increase in denudation in Scenario 1.

\citet{schaller200230} provided the only \tsup{10}Be-based
paleo-denudation dataset in the Massif Central, from terraces of the
Allier and Dore rivers, located northwest of our study area. While
their 30-ka record presents some minor fluctuations through time, they
do not observe major changes in denudation rates between glacial and
inter-glacial conditions. In particular, all their paleo-denudation
rates are within the range of observed modern detrital \tsup{10}Be
denudation rates at similar locations \citepalias{schaller200230}.
Crucially, such sequences based solely on \tsup{10}Be often display
limited sensitivity to short period variations, in particular in slowly
erosive settings \citep{schaller2006limits}, and thus their results are
not incompatible with ours, as we take advantage of short-lived
nuclides such as \tsup{14}C\tsub{\text{in\,situ}} to detect
fluctuations of potentially larger amplitude.

Human occupation has also been recognised, with scattered settlements
and a variable imprint on vegetation throughout most of the Holocene
\citep{cubizolle2014vegetation}, although anthropogenic pressure
increased markedly during the historical period
\citep{surmely2009occupation,lavrieux20136700,jacob-rousseau2014torrential}.
Notably, the eastern part of the FMC was largely deforested in the
XVIII$^{\mathrm{th}}$ and XIX$^{\mathrm{th}}$ centuries, facilitating
soil erosion \citep{astrade2011detailed}. The extent of this
deforestation and the recognition of the associated geomorphological
crisis triggered a massive restoration program in French mountainous
areas in the second half of the XIX$^{\mathrm{th}}$ century and into
the XX$^{\mathrm{th}}$ century. A recent, historical, major increase in
sediment fluxes associated with human-induced changes in vegetation
cover is also well documented in lakes of the FMC
\citep{macaire1997sediment,ballut2008environmental}.   The recent
erosion history of the eastern FMC seems to be influenced by the
general patterns of climatic evolution over western Europe, with
episodic interference from human activities.  As proposed by
\citet{defive2013response}, both forcings act in conjunction, with
their timing mostly dictated by climate but their spatial expression
controlled by human land use.

The two types of forcings could correspond to the end-member scenarios
we consider in our inversion of the dataset. In the hypothesis of a
single increase in denudation rates (Scenario 1), the timing of the
associated event appears to be restricted to the 15--5 ka BP interval. 
Within this time frame, one candidate is the Pleistocene--Holocene
transition, whose impact on the acceleration of TCN-derived denudation
rates worldwide has recently been proposed by
\citet{godard2025constraining}. Some lacustrine records of the eastern
part of the FMC extend into the Pleistocene and display evidence for an
increase in sedimentation rates around 10 ka \citep{martin2019impact}.
However, the limited number of sites prevents us from concluding
whether this is a regional pattern, and changes in the nature of the
sediments make the interpretation of this signal ambiguous.  Other
records suggest instead a stabilizing influence of the Holocene
expansion of vegetation \citep{degeai2009environmental} or a decrease
in sedimentation rates \citep{thouveny1994climate}. At other sites in
the Ard\`eche mountains, pulses of non-organic matter in the sediment
record are unambiguously associated with climatic perturbation phases
during the Late Pleistocene and Early Holocene
\citep{dendievel2015environmental}. While an increase in denudation
rates (Scenario 1) around this transition could explain our observed
concentrations, the associated increase in the transport coefficient is
too high to be compatible with our assumption of continuous hillslope
diffusive transport. The response we observe cannot derive solely from
changes in this transport coefficient, as has been proposed for some
systems \citep{hughes2009increased}, and we expect a contribution from
discontinuous, stochastic mass wasting.

The FMC sites that provide various records of Holocene environmental
changes suggest variable erosion impacts from anthropic pressure, with
changes connected to climatic and socio-economic factors
\citep[e.g.][]{chassiot2022anthropogenic,lavrieux20136700}. The two
forcings are highly interconnected, and their respective contributions
are usually difficult to deconvolve, hindering identification of the
impact of individual climatic events such as the 8.2~ka cold and wet
event \citep{magny2003contrasting}.  Climatic and anthropogenic
perturbations can contribute to the exhumation of deep soil and bedrock
and deliver material with lower
\tsup{14}C\tsub{\text{in\,situ}}/\tsup{10}Be  ratios in the fluvial
system. We note, however, that the soil thicknesses required to explain
these ratios are ${>}$2~m in one of the clusters, corresponding to the
C\'evennes area. Although deforestation was intense in parts of this
landscape, such a substantial soil removal depth is clearly
unrealistic.  Conversely, this scenario is permissible for the other
clusters, with soil-removal thicknesses ${<}$1 m.  In the end, both
end-member scenarios are probably too extreme to independently explain
the depressed ratios we observe, and we suggest a combination of
different processes, such as the activation of hillslope processes
around the Pleistocene--Holocene transition and the recent
anthropogenic disturbances related to the
XVIII$^{\mathrm{th}}$--XIX$^{\mathrm{th}}$ deforestation.

\section{Conclusion}
We presented a new dataset of \tsup{14}C\tsub{\text{in\,situ}}
concentrations in river sediments complementing existing \tsup{10}Be data
for 10 basins along the eastern margin of the French Massif Central. We
observe varying degrees of disequilibrium between the two nuclides,
which point to a transient evolution of surface processes over the
Holocene or the Late Glacial period. The diversity in
\tsup{14}C\tsub{\text{in\,situ}}/\tsup{10}Be ratios suggests complex
spatial variations in the nature and timing of these changes, and
different responses across our study area, in part related to the
contrasting geomorphological contexts of the steep margin and the
low-relief interior of the Massif.   We explored various scenarios to
reproduce the observed concentrations, including a recent increase in
denudation rates and a soil-removal event.

Among previous studies that have highlighted a disequilibrium in the
\tsup{10}Be--\tsup{14}C\tsub{\text{in\,situ}} system for river sediments,
our work is the first to incorporate topographic information into the
inversion of TCN concentrations.  This approach accounts for
similarities in denudation dynamics between adjacent basins while
reducing the number of inferred parameters. A scenario implying an
increase in denudation rates around 10 ka can explain most of the
observed concentrations, but would suggest hillslope transport
coefficients that are outside the range of the values reported in the
literature. Alternatively, a very recent (within the last few
centuries) removal of soil or regolith could also explain the observed
concentrations and disequilibrium, with variable depths of removal
across the studied area. A combination of both processes---variations
in background denudation and soil removal---most likely involving
multiple events, is probably driving the transient evolution of surface
processes in this area. 

\mbox{}
{\tsup{14}C\tsub{\text{in\,situ}}} is now an analytically mature TCN
system with robust systematics, even if the low number of extraction
facilities limits its broader use. Interpreting the widely observed
disequilibrium of the \tsup{10}Be--\tsup{14}C\tsub{\text{in\,situ}}
remains very challenging and \mbox{context-specific,} as the system is highly
sensitive to recent changes in surface processes, even over very short
timescales of a few centuries. In our study and others, such as
\citet{hippe2021cosmogenic}, a panel of different scenarios can be
invoked to explain the observed deviations in isotopic ratios.
Addressing these ambiguities requires methodological developments in
interpretating this signal and also integration of other constraints on
the recent evolution of surface processes in a unified analysis
framework.

\section*{Acknowledgments}
This research was supported by ANR TOPOEXTREME (ANR-18-CE01-0017),
INSU/Tellus (Maraca) and Radiate (20002215-ST-1.1) grants. We thank two
anonymous reviewers for constructive and insightful comments.

\CDRGrant[ANR]{ANR-18-CE01-0017}
\CDRGrant[INSU/Tellus]{20002215-ST-1.1}

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