Alain Rapaport
email: alain.rapaport@inrae.fr

Robert David
email: r.david@technord.com

Denis Dochain
email: denis.dochain@uclouvain.be

Jérôme Harmand
email: jerome.harmand@inrae.fr

Thibault Nidelet
email: thibault.nidelet@inrae.fr

Consideration of maintenance in wine fermentation modeling

Keywords: Wine fermentation, mathematical modeling, population model, maintenance, variable yield

come

Introduction

The overall principle of wine fermentation consists in the conversion of sugar into ethanol by yeast. It has been observed from a long time that nitrogen consumed during the yeast growth is also playing an important role. The fermentation can be indeed modeled by a two-steps process where the yeast first grows on nitrogen as a limiting resource and then degrade the non-limiting sugar into ethanol and carbon dioxide. However, experimental observations have shown that the consumed nitrogen was not entirely converted into biomass. Several mathematical models have been proposed to take into consideration this characteristics. For instance, in [START_REF] Goelzer | Simulation and optimization software for alcoholic fermentation in winemaking conditions[END_REF][START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF], the biomass growth follows a logistic law whose carrying capacity depends on the initial quantity of nitrogen. In [START_REF] David | Nitrogen-backboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF], a model that distinguishes part of nitrogen used for yeast growth from another part responsible of the synthesis of proteins (hexose transporters [START_REF] Elbing | Role of hexose transport in control of glycolytic flux in saccharomyces cerevisiae[END_REF]) has been developed. Both models have been calibrated with experimental data and provide satisfactory fitting. However, both models present some drawbacks. The dependency of the dynamics on the initial condition of the first model makes it sensitive to the precise knowledge of the initial quantity of nitrogen (that needs to be "memorized" in the dynamical equations of the model). Moreover it does not allow to consider non-batch operations or continuous addition of nitrogen, such as in [START_REF] Clement | Use of a continuous multistage bioreactor to mimic winemaking fermentation[END_REF] for instance. The second model relies on the knowledge of the time-varying concentration of transporters, which is in general not easily accessible to experimental measurements, and several assumptions have been necessary to estimate it from biomass measurements.

The observation of the ratio of produced biomass over nitrogen consumption along the whole fermentation, determined on experimental database or numerical simulations of models [START_REF] David | Nitrogen-backboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF][START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF], shows that this ratio is non-constant and depends on the initial quantities. This highlights that the conversion of nitrogen into biomass can be viewed as a variable yield process. The experimental evidence that nitrogen is not entirely used for growth therefore advocates for the consideration of a maintenance term in the modeling (see for instance [START_REF] Goma | Comments on the "maintenance coefficient" changes during alcohol fermentation[END_REF]), without necessarily requiring a detailed representation of the internal mechanism or cells. The rationale of the results presented here is to test if the introduction of a maintenance term (see [START_REF] Pirt | The maintenance energy of bacteria in growing cultures. Proceedings of the Royal Society of London[END_REF][START_REF] Pirt | Principles of microbe and cell cultivation[END_REF][START_REF] Rapaport | About biomass overyielding of mixed cultures in batch processes[END_REF] or [START_REF] Beeftink | Maintenance requirements: energy supply from simultaneous endogenous respiration and substrate consumption[END_REF][START_REF] Heijnen | A macroscopic model describing yield and maintenance relationships in aerobic fermentation processes[END_REF][START_REF] Wang | A theoretical reassessment of microbial maintenance and implications for microbial ecology modeling[END_REF]) can improve the wine fermentation modeling. One of the originality of the proposed approach is to view the nitrogen consumption as a global consumption for growth by considering a variable yield. This allows to avoid to consider a specific structure to model the maintenance. The purpose of the present work is thus to investigate the ability of a simpler model with a maintenance term to reproduce and predict wine fermentation kinetics. It focuses mainly on the new modeling of the growth of yeast on nitrogen.

The proposed model

We denote by N , S, E, CO 2 and X the concentrations of (total) nitrogen, sugar, ethanol, dioxide carbon and biomass, respectively. For simplicity, we derive here a model under isothermal conditions.

For the first step N → X (yeast growth on nitrogen), we propose the following equations

dX dt =µ N (N, X)X (1)
dN dt = - µ N (N, X)X Y -m(N, X)X (2)
where Y is the growth yield, µ the Contois growth function

µ N (N, X) = µ max N N N + K N X
and m a maintenance function, which is positive for N > 0 and X > 0. We choose here a ratio-dependent kinetics function µ N to reproduce the observation that the growth is slowing down under an excess of yeast, with a Contois expression as in [START_REF] David | Nitrogen-backboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF]. In the literature, the maintenance m is often considered as constant [START_REF] Pirt | The maintenance energy of bacteria in growing cultures. Proceedings of the Royal Society of London[END_REF][START_REF] Pirt | Principles of microbe and cell cultivation[END_REF], which has been validated in continuous culture (chemostat). However, as already investigated in [START_REF] Wang | A theoretical reassessment of microbial maintenance and implications for microbial ecology modeling[END_REF], maintenance terms have to depend on the level of available resources, say R (N here). In particular, a constant maintenance in a batch model would imply dR dt < 0 when the resource is exhausted i.e. R = 0, and thus R could take unrealistic negative values, as underlined in [START_REF] Rapaport | About biomass overyielding of mixed cultures in batch processes[END_REF]. In [START_REF] Beeftink | Maintenance requirements: energy supply from simultaneous endogenous respiration and substrate consumption[END_REF][START_REF] Heijnen | A macroscopic model describing yield and maintenance relationships in aerobic fermentation processes[END_REF], the maintenance is directly related to the microbial activity which is stopped in absence of nutrients. This is why here we consider a maintenance function proportional to the growth activity, with a factor that might depend on the nitrogen concentration (one may expect that it decreases when the substrate N becomes rare)

m(N, X) = α(N )µ N (N, X)
where α is a positive function equal to zero for N = 0. Then one can consider the function y defined as follows

y(N ) := Y 1 + α(N )Y , N ≥ 0
Formally, model ( 1)-( 2) can be rewritten equivalently as

dX dt =µ N (N, X)X (3)
dN dt = - µ N (N, X)X y(N ) (4)
where the function y is playing the role of a variable yield. Identifying the function m or the function y is thus formally equivalent. However, we shall see in the next section that identifying the function y instead of m presents some practical advantages.

For the second step S → E + CO 2 , we follow the model proposed in the literature [START_REF] David | Nitrogen-backboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF]

dE dt = dCO 2 dt = µ N (N, X) + βν(E) µ S (S)X ( 5
)
dS dt = -k dE dt (6)
where µ S is a Monod function and ν E a function inhibited by the ethanol

µ S (S) = µ max S S K S + S , ν E (E) = 1 1 + K E E (7)
The inhibition by the consumption of sugar S by ethanol E has been reported many times in the literature [START_REF] Caro | Development of a kinetic model for the alcoholic fermentation of must[END_REF][START_REF] Cramer | Kinetic model for nitrogenlimited wine fermentations[END_REF][START_REF] Leao | Effects of ethanol and other alkanols on the glucose transport system of saccharomyces cerevisiae[END_REF][START_REF] Salmon | Sugar transport inhibition and apparent loss of activity in saccharomyces cerevisiae as a major limiting factor of enological fermentations[END_REF][START_REF] Viegas | Synergistic inhibition of the growth of saccharomyces bayanus by ethanol and octanoic or decanoic acids[END_REF]. The constant yield of production k of CO 2 and consumption of S follows a mass balance assumption, verified experimentally [START_REF] Haloui | Alcoholic fermentation in winemaking: On-line measurement of density and carbon dioxide evolution[END_REF] and that can be determined with thermodynamics considerations [START_REF] Vanbriesen | Evaluation of methods to predict bacterial yield using thermodynamics[END_REF].

Note that this model can be extended to anisothermal conditions, considering that the maximal specific rate parameters µ max N , µ max S and affinity constants K S , K E are temperature-dependent, as in [START_REF] David | Nitrogen-backboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF].

Calibration of the model

From model equation ( 1), the parameters of the function µ N can be identified independently of the yield and maintenance terms. To validate the hypothesis of ratio-dependency of the function µ N , one can first plot from experimental data the slope of the logarithm of X versus the ratio r = N/X and check if it follows qualitatively a function of the form

µ(r) = µ max N r K N + r
Then, a classical least-square method can be applied to fit parameters µ max N , K N on the data. Alternatively, one can plot the inverse of the slope of the logarithm of X versus the inverse of the ratio r to check if it follows qualitatively a linear dependency, as one get from equation ( 1)

d log X dt -1 = 1 µ max N + K N µ max N N X -1 (8)
However, for the accurate identification of the parameters µ max N , K N , a linear regression on equation ( 8) is expected to be less reliable than a non-linear least square optimization on the solution X(•) of (3), because

d dt log X -1 , N X -1
data might be far to be uniformly distributed.

Note from equations ( 1)-( 2) that one has lim t→+∞ N (t) = 0 (because the derivative of N cannot vanish when N is not exhausted). In absence of the maintenance term m, one gets dX dt + Y dN dt = 0 which implies that one should have

Y = X(+∞) -X(0) N (0) -N (+∞) = X(+∞) -X(0) N (0)
To test the validity of the model with maintenance, one can plot from experimental data the ratio X(+∞)-X(0)

N (0)
for different values of N (0) to check that it is not constant. If it is the case, one can then look for identifying a non-constant function y. For this purpose, we write from equations ( 3)-( 4)

X(+∞) -X(0) = - +∞ 0 y(N (t)) dN dt (t) dt
and as t → N (t) is a monotone decreasing function, one can make the change of variable n = N (t) in this last integral to obtain

X(+∞) -X(0) = N (0) 0 y(n) dn
Therefore, if one fits a differential function f such that f (0) = 0 that satisfies

X(+∞) -X(0) = f (N (0))
for experimental data with different values of N (0), then one simply get y = f ′ .

Let us underline that identifying the function y in this way can be done independently to the knowledge of the kinetics µ N , differently to the function m, what clearly presents some robustness advantages. Once the function µ N is identified, the maintenance function can then be determined as

m(N, X) = 1 y(N ) - 1 Y µ N (N, X)
where Y = y(0) (to fulfill α(0) = 0).

For model equations ( 5)-( 6), the coefficient k is kept from the literature, and the parameters β, µ max S , K S , K E are identified (with a least-square method) from experimental data of CO 2 production rate.

Validation of the model on synthetic data

We have used synthetic data generated by models of the literature that have been previously validated on experimental data [START_REF] David | Nitrogen-backboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF][START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF] for a certain range of initial conditions and operating conditions.

Validation on simulations of a model with transporter

We have considered the model with transporters developed in [START_REF] David | Nitrogen-backboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF], which is more complex with two additional state variables: the concentrations of hexose transporters and the nitrogen dedicated to these transporters. Data have been generated by simulating this model with the parameters given in [START_REF] David | Nitrogen-backboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF] and operating conditions given in Table 1.

X(0) 0.02 g.l -1 N (0) 0.071 -0.57 g.l -1 S(0) 200 g.l -1
time horizon 350 hours temperature constant equal to 24 • others no initial transporter no nitrogen addition Table 1 Operating conditions for the simulation of the model with transporters This model distinguishes explicitly two forms of nitrogen, one available for the yeast N X and the other one N tr for the transporters. To compare with the variable N of our model, we have considered the total nitrogen N = N X + N tr . 2.

Estimation of the Contois function

µ max N 0.103 h -1 K N 0.0381 g.l -1

Estimation of the variable yield function

On Figure 2, data X(T ) -X(0) versus N (0) from the model with transporters have been plotted for T = 350 hours (we have checked that N is quasi-null at T and that X does no longer increase after T ). One can see that the points are aligned but the line that passes through these points does not touch 0, which is not possible for a constant yield (for a constant yield, the points have to be aligned on a line that passes through 0 because when N (0) = 0 there is no biomass production). Then we have fitted a C 2 function f such that f (0) = 0 with the following expression

f (N ) =      aN + b 1 - N † -N N † 3 , N < N † aN + b, N ≥ N †
whose parameters are given in Table 3. N † 0.176 g.l -1 Table 3 Parameters of the variable yield function y Then, we obtain the variable yield function y as the C 1 function

y(N ) = f ′ (N ) =    a + b 3(N † -N ) 2 N † 3 , N < N † a, N ≥ N †
and the function α which describes the maintenance as

α(N ) = 1 y(N ) - 1 y(0) =      N 3 † aN 3 † +3b(N † -N ) 3 - N † 3b+aN † , N < N † 3b a(3b+aN † ) , N ≥ N †
that are both depicted on Figure 3. Note that the model with transporters has been validated only for N (0) in the interval [0.071, 0.57] g.l -1 , and that we have no a priori information about the behavior of the yield for values of N (0) smaller than 0.071 g.l -1 . The threshold parameter N † has been simply chosen so that the simulations of the variables X and N of the model ( 3)-( 4) were the closest from the ones of the transporter model.

Estimation of the other parameters and comparison of the models

For the model of the second step S → E +CO 2 , the stoichiometric parameter k has been taken for the literature, while the other parameters β, µ max S , K S , K E have been estimated with a least-square optimization on the CO 2 chronicles only (the CO 2 production rate being a variable that is usually measured in experiments), starting from values in [START_REF] David | Nitrogen-backboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF]. Values are given in Table 4. Finally, we present on Figures 4,5,6 simulations of the new model for three largely different initial values of nitrogen from 0.170 g.l -1 to 0.567 g.l -1 . The evolution of the ethanol concentration E has not been reproduced as it is proportional to the CO 2 concentration.

µ max S 0.197 h -1 K S 21.1 g.l -1 K E 72.7 g.l -1
These simulations shows the ability of the new model to reproduce, with a single set of parameters, close simulations to the model with transporters, in terms of production of biomass and dioxide carbon, estimation of the peak of the CO 2 production rate and depletion of (total) nitrogen and sugar. Fig. 6. Comparison with the model with transporters (in dashed) for N (0) = 0.567 g.l -1

Validation on the SOFA model

The model proposed in [START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF] does not consider explicitly transporters with an additional state variable as the previous model, and present instead more complicated expressions of the dynamics that depend on the initial condition, with an additional latency term at the beginning of the simulations. Therefore, this is not a Markovian model. It has been validated on different operating conditions, and has been encoded into the SOFA software exploited for decision making [START_REF] Goelzer | Simulation and optimization software for alcoholic fermentation in winemaking conditions[END_REF]. We have launched simulations of this model for the same operating conditions than for the previous model (Table 1). Although simulations look qualitatively similar, they do not overlap, especially for the biomass chronicle. This could be explained by the fact that this model is intended to predict a number of cells and not precisely a biomass (an average number of 4.15 10 9 cells for one g of biomass has been used to have X expressed in g.l -1 as for the previous model). We have proceeded to a new validation of our model on these data.

Estimation of the Contois function

Figure 7 shows that the data N X , dX dt

X

do not follow precisely the graph of a function (this is most probably due to the fact that the model is not Markovian). Indeed, this happens mainly for large value N 0 of the initial nitrogen. We believe that this could be explained by the dynamics of the biomass X of this model, which is a logistic law with a carrying capacity given by an heuristic expression that depends on N 0 , and not a dynamics coupled with the dynamics of N (indeed the interval of tested values of N 0 might be larger than the validity of this model). However, we have fitted the graph of a Contois function to these data with the parameters given in Table 5, which has been able to reproduce satisfactorily the trajectories of the model for a large amplitude of values of N 0 , as we shall see later on. As one can see on Table 5, the values of µ max N and K N are significantly larger and smaller (respectively) than in Table 2, which is consistent with the observation that this model predict a faster convergence of the biomass to its maximal value, despite the latency term (compare Figures 4,5,6 with Figures 10,[START_REF] Heijnen | A macroscopic model describing yield and maintenance relationships in aerobic fermentation processes[END_REF][START_REF] Leao | Effects of ethanol and other alkanols on the glucose transport system of saccharomyces cerevisiae[END_REF].

µ max N 0.270 h -1 K N 0.00952 g.l -1

Estimation of the variable yield function

Data X(T ) -X(0) from the simulation of the SOFA model have been plotted on Figure 8 at T = 350 hours, for different values of N (0) in the interval [0.071, 0.57] g.l -1 (here also we have checked that the fermentation was quasiended at T ). On can see that the points follows an increasing concave curve and further increase very slowly, quite differently to the model with transporters (see Figure 2). We have then fitted a C 2 function f with f (0) = 0 for the expression

f (N ) =    bN -aN 2 , N < N † bN -aN 2 + bN + A B e -BN † -e -BN N < N † with A = (b -2aN † )e BN † , B = 2a b -2aN †
and parameters a, b, N † given in Table 6. Then, we obtain the expression of the variable yield function

y(N ) = f ′ (N ) =    b -2aN, N < N † Ae -BN , N ≥ N † as well as the function α α(N ) = 1 y(N ) - 1 y(0) =    1 b-2aN -1 b , N < N † e b(N -N † ) b-2aN † -1 b , N ≥ N †
whose graphs are drawn on Figure 9. Figures 10,[START_REF] Heijnen | A macroscopic model describing yield and maintenance relationships in aerobic fermentation processes[END_REF][START_REF] Leao | Effects of ethanol and other alkanols on the glucose transport system of saccharomyces cerevisiae[END_REF] show the comparison between the SOFA model and our calibrated model for the same initial condition than for the former comparison with the model with transporters. Here also, we see that the proposed model reproduces quite faithfully the simulations of the SOFA model, with the advantage of being a simpler Markovian model. Indeed, the difference between the model with transporters and the SOFA model can be translated into different maintenance terms (see Figures 3 and9): for large values of nitrogen, the model with transporters behaves like a model with a maintenance proportional to the growth, while the SOFA model amounts to have a strongly increasing maintenance. Recall that the simulations for the largest value of N (0) showed the most differences between these two models (for N (0) = 0.567 g.l -1 , the model with transporters predicts a biomass production of 5.11 g.l -1 , while the SOFA model predicts 3.88 g.l -1 ; see Figures 6 and12). While the model with transporters has been validated experimentally for N (0) in the interval [0.170, 0.567] g.l -1 , we believe the validation of the SOFA model for initial concentrations of nitrogen larger than 0.4 g.l -1 might need to be revisited (although our model once calibrated is able to reproduce the SOFA simulations). K E 71.9 g.l -1 Table 8 Parameters fitted on the experimental data

Conclusion

In this work, we have demonstrated that the consideration of a maintenance term, or equivalently a variable yield, in wine fermenting modeling can satisfactorily replace more sophisticated models with a simpler structure. Indeed, the effects of the underlying mechanisms of transporters, which are difficult to capture experimentally, are translated into a variable yield between biomass and nitrogen. We have shown that this variable yield, as a function of the nitrogen concentration, can be estimated from experimental data of biomass growth and nitrogen depletion. This consideration brings a flexibility to suit to different kind of models or experimental data (once calibrated) with a single common structure, that could correspond to different operating conditions or hypotheses in wine fermentation. This new approach opens new perspectives of control of fermentation with nitrogen addition, based on a simple Markovian model, as well as model extensions with aromatic compounds [START_REF] Mouret | Prediction of the production kinetics of the main fermentative aromas in winemaking fermentations[END_REF] or multi-strains [START_REF] Conacher | The ecology of wine fermentation: a model for the study of complex microbial ecosystems[END_REF].

Figure 1

 1 Figure 1 shows a good fitting of the Contois function µ N on data N X , dX dt X

Fig. 1 .

 1 Fig. 1. Fitting of the Contois function on data of the model with transporters

Fig. 2 .

 2 Fig. 2. Fitting the function f on data of the model with transporters

Fig. 3 .

 3 Fig. 3. The variable yield function y and the function α

Fig. 4 . 1 Fig. 5 .

 415 Fig. 4. Comparison with the model with transporters (in dashed) for (0) = 0.170 g.l -1

Fig. 7 .

 7 Fig. 7. Fitting of the Contois function on data of the SOFA model

Fig. 8 .

 8 Fig. 8. Fitting the function f on data of the SOFA model

Fig. 9 .

 9 Fig. 9. The variable yield function y and the function α

Fig. 10 .

 10 Fig. 10. with the SOFA model (in dashed) for N (0) = 0.170 g.l -1

Fig. 11 . 1 Fig. 12 .

 11112 Fig. 11. with the SOFA model (in dashed) for N (0) = 0.283 g.l -1

Fig. 14 .Fig. 15 .Fig. 16 .

 141516 Fig. 14. Simulation for N (0) = 0.170 gl -1 (experimental data in blue)

Table 2

 2 Parameters of the Contois function µ N

Table 4

 4 Parameters for the second step S → E + CO 2 model

Table 5

 5 Parameters of the Contois function µ N

Table 6

 6 Parameters of the variable yield function y

Table 7

 7 ).

	k	2.17
	β	3.22
	µ max S	0.197 h -1
	K S	17.6 g.l -1
	K E	36.4 g.l -1

Table 7

 7 Parameters for the second step S → E + CO 2 model

Calibration of the model on real data

We have considered data from experiments conducted at SPO Lab (INRAE, Montpellier, France) in 2004, that have been used to calibrate the model with transporters and the SOFA model (see [START_REF] David | Nitrogen-backboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF][START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF]). These data consist in a set of three experiments with the same operating conditions given in Table 1 and different initial concentrations N (0) of nitrogen, exactly as for the simulations of Sections 4.1 and 4.2. For each experiment, one has -height measurement points for X, -no measurement point for N , S or E, -about 400 measurement points for CO 2 and dCO 2 /dt, We have first calibrated a function f (•) to the data (N (0), X(T ) -X(0)), with the same expression than in Section 4.2, to determine a yield function y(•) (see Figure 13). As we not have measurements of N over the time, we cannot estimate the Contois parameters independently of the CO 2 measurements, as we did with the synthetic data. All the parameters of the model have been fitted simultaneously with a least square method (values are given in Table 8), excepted for the sugar conversion yield for which we have used the value of the literature k = 2.17, as before. Figures 14,[START_REF] Pirt | The maintenance energy of bacteria in growing cultures. Proceedings of the Royal Society of London[END_REF][START_REF] Pirt | Principles of microbe and cell cultivation[END_REF] show the results of the fitting for the three experiments. One can appreciate the goodness of fit for a unique set of parameters. In particular, the production of biomass and CO 2 , as well as the height and date of the peak of dCO 2 /dt are well predicted with this model.


Rosine Cartier
email: rosine.cartier@geol.lu.se

Laurence Vidal

Florence Sylvestre

Corinne Sonzogni

Frédéric Guiter

Elodie Brisset

Cécile Miramont

Paleohydrological history of Lake Allos (2200 m a.s.l) since 13 500 cal a BP in the Mediterranean Alps inferred from an ostracod δ 18 O record

Keywords: Lateglacial/Holocene, Mediterranean Alps, ostracods, oxygen isotopes, paleohydrology

This paper presents the first Lateglacial/Holocene (the last 13 500 cal a BP) ostracod δ 18 O record to infer hydroclimate variability in the Southern French Alps. Cytherissa lacustris (δ 18 O sp ) shells extracted from the sediments of Lake Allos allowed a reconstruction of δ 18 O lake water (δ 18 O lw ) except for the interval 5800-2800 cal a BP. The shape of the Younger Dryas (YD) clearly differed from records documented in the northern Alps. First, δ 18 O lw values remained close to modern values before a marked drop ca. 12 000 cal a BP. Then, after several oscillations, δ 18 O lw values increased, reaching the highest value of the record ca. 6100 cal a BP during a thermal optimum for this latitude. Finally, low δ 18 O lw values occurred from 450 to 100 cal a BP during the Little Ice Age (LIA) following the Medieval Climate anomaly. At the beginning of the YD, δ 18 O lw probably reflected changes in local glacier dynamics and precipitation sources. The following decrease in δ 18 O lw values was associated with higher freshwater inputs during the second half of the YD. During the LIA, the low δ 18 O values are consistent with a higher torrential activity and lower air temperatures.

Introduction

The Alpine climate has changed significantly during the past century, with temperatures increasing by 2 °C [START_REF] Auer | HISTALPhistorical instrumental climatological surface time series of the Greater Alpine Region[END_REF], i.e. more than twice the global average. In the Southern French Alps, local climate conditions such as temperature, precipitation and wind are highly influenced by altitude, topography, and the relative contribution of air masses from the Atlantic Ocean and the Mediterranean Sea. For each of the most recent decades, the surface of the Mediterranean Sea has warmed by around 0.4 °C and sea level has risen by about 3 cmcomparable to global trends, but in part due to decadal variability related to the North Atlantic Oscillation (NAO) [START_REF] Cramer | Climate change and interconnected risks to sustainable development in the Mediterranean[END_REF]. The diversity of alpine environmental contexts requires a better understanding of local hydroclimate responses to climate change to improve regional climate prediction.

Climate variability exerts a strong control on regional alpine weather and local-scale environmental processes that are well recorded in past environmental studies [START_REF] Blenckner | Large-scale climatic signatures in lakes across Europe: A meta-analysis[END_REF][START_REF] Arnaud | Erosion under climate and human pressures: an alpine lake sediment perspective[END_REF][START_REF] Cartier | Diatom-oxygen isotope record from high-altitude Lake Petit (2200 m a.s.l.) in the Mediterranean Alps: shedding light on a climatic pulse at 4.2 ka[END_REF][START_REF] Regattieri | Holocene Critical Zone dynamics in an Alpine catchment inferred from a speleothem multiproxy record: disentangling climate and human influences[END_REF]. Lake sediment deposits are excellent archives to study climate evolution because of the acute sensitivity of lakes to environmental change and multi-scale processes throughout the hydrological cycle [START_REF] Schwander | Oxygen isotopes of lake marl at Gerzensee and Leysin (Switzerland), covering the Younger Dryas and two minor oscillations, and their correlation to the GRIP ice core[END_REF]. Therefore, producing oxygen isotope records from alpine lacustrine sediments allows a better understanding of high-altitude hydroclimate variability to compare with mid-European and Mediterranean records (von [START_REF] Von Von Grafenstein | A mid-European decadal isotope-climate record from 15,500 to 5000 years[END_REF][START_REF] Zanchetta | Enhanced rainfall in the western Mediterranean during deposition of sapropel S1: stalagmite evidence from Corchia cave (Central Italy)[END_REF][START_REF] Magny | Holocene climate changes in the central Mediterranean as recorded by lake-level fluctuations at Lake Accesa (Tuscany, Italy)[END_REF][START_REF] Magny | Holocene hydrological changes in south-western Mediterranean as recorded by lake-level fluctuations at Lago Preola, a coastal lake in southern Sicily, Italy[END_REF][START_REF] Regattieri | Holocene Critical Zone dynamics in an Alpine catchment inferred from a speleothem multiproxy record: disentangling climate and human influences[END_REF]). These regional comparisons can reveal local climate specificities through time as well as synchronicities and time lags in hydrological and environmental responses to global climate events [START_REF] Lauterbach | Environmental responses to Lateglacial climatic fluctuations recorded in the sediments of pre-Alpine Lake Mondsee (northeastern Alps)[END_REF].

In the Southern French Alps, long-term paleoclimate records remain scarce and/or do not cover the entire Lateglacial/ Holocene periods (Harrison et al., 1993;[START_REF] Digerfeldt | Reconstruction and paleoclimatic interpretation of Holocene lake-level changes in Lac de Saint-Léger, Haute-Provence, southeast France. Palaeogeography[END_REF][START_REF] Drysdale | Late Holocene drought responsible for the collapse of Old World civilizations is recorded in an Italian cave flowstone[END_REF][START_REF] Wilhelm | 1400 years of extreme precipitation patterns over the Mediterranean French Alps and possible forcing mechanisms[END_REF][START_REF] Wirth | Holocene flood frequency across the Central Alpssolar forcing and evidence for variations in North Atlantic atmospheric circulation[END_REF][START_REF] Cartier | Diatom-oxygen isotope record from high-altitude Lake Petit (2200 m a.s.l.) in the Mediterranean Alps: shedding light on a climatic pulse at 4.2 ka[END_REF][START_REF] Regattieri | Holocene Critical Zone dynamics in an Alpine catchment inferred from a speleothem multiproxy record: disentangling climate and human influences[END_REF]. Climate, environmental changes and vegetation succession that have occurred since the last glaciation are not entirely documented and understood [START_REF] Brisset | Lateglacial/Holocene environmental changes in the Mediterranean Alps inferred from lacustrine sediments[END_REF][START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF]. In the Mercantour Massif, deglaciation of cirque-glacier catchments occurred between 14 000 and 13 500 cal a BP, i.e. during the Lateglacial Interstadial [START_REF] Brisset | Lateglacial/Holocene environmental changes in the Mediterranean Alps inferred from lacustrine sediments[END_REF]. In the same area, several moraines suggest glacier advances during the Younger Dryas (YD) associated with wet conditions, a different signature from elsewhere in the Alpine region and indicative of a regional specificity [START_REF] Pauly | Subfossil trees suggest enhanced Mediterranean hydroclimate variability at the onset of the Younger Dryas[END_REF][START_REF] Spagnolo | Glacier extent and climate in the Maritime Alps during the Younger Dryas[END_REF]. The last retreat of a cirque glacier following deglaciation goes back to the beginning of the Holocene (ca. 11 000 cal a BP). Later, relatively wet conditions occurred during the Early and Late Holocene bracketed by drier conditions from ca. 7000 to 3000 cal a BP as suggested by lake level reconstructions and speleothem records (Harrison et al., 1993;[START_REF] Digerfeldt | Reconstruction and paleoclimatic interpretation of Holocene lake-level changes in Lac de Saint-Léger, Haute-Provence, southeast France. Palaeogeography[END_REF][START_REF] Regattieri | Holocene Critical Zone dynamics in an Alpine catchment inferred from a speleothem multiproxy record: disentangling climate and human influences[END_REF]. Even though the literature has indicated glacier advances during the Holocene (Subboreal and Little Ice Age, LIA; [START_REF] Federici | Glacial history of the Maritime Alps from the Last Glacial Maximum to the little ice age[END_REF], no clear pattern is seen in lake sediment records [START_REF] Brisset | Lateglacial/Holocene environmental changes in the Mediterranean Alps inferred from lacustrine sediments[END_REF]. The watershed of Lake Allos (also in the Mercantour Massif) contains moraines which could be attributed to the Neoglacial period (ca. 4500 cal a BP) or the LIA [START_REF] Jorda | Les montagnes du Haut Verdon, Etude géomorphologique[END_REF][START_REF] De Beaulieu | Contribution pollenanalytique à l'histoire tardiglaciaire et holocène de la végétation des Alpes méridionales françaises[END_REF]. In summary, questions remain regarding the local hydroclimate evolution in the Southern French Alps and its specificities at key periods of environmental changes.

In this paper, we present the first δ 18 O record covering the end of the Lateglacial, and Early and Late Holocene for the Mediterranean Alps, based on the analysis of ostracods buried in sediments from Lake Allos (2200 m a.s.l). The δ 18 O signal in lake carbonates is a function of lake water oxygen isotope composition and temperature [START_REF] Stuiver | Oxygen and carbon isotope ratios of fresh-water carbonates as climatic indicators[END_REF][START_REF] Leng | Palaeoclimate interpretation of stable isotope data from lake sediment archives[END_REF]. This relationship with lacustrine conditions has led to successful reconstructions of past δ 18 O lake water (δ 18 O lw ) for Mediterranean lakes [START_REF] Develle | Controlling factors on a paleo-lake oxygen isotope record (Yammoûneh, Lebanon) since the Last Glacial Maximum[END_REF][START_REF] Roberts | Oxygen isotopes as tracers of Mediterranean climate variability: an introduction[END_REF]. δ 18 O lw provides a regional paleoclimate proxy, not influenced by local human activities, allowing a comparison with environmental and geomorphological studies (glacier advances, [START_REF] Holzhauser | Glacier and lake-level variations in west-central Europe over the last 3500 years[END_REF][START_REF] Rea | Atmospheric circulation over Europe during the Younger Dryas[END_REF]torrential activity, Brisset et al., 2017;pollen assemblages, Cartier et al., 2018) and large-scale climate oscillations in Europe (e.g. Younger Dryas, Medieval Climate Anomaly (MCA), LIA). Finally, the hydrological response of Lake Allos is compared to a large set of records from central Europe, the Northern/Southern Alps and the Mediterranean basin to highlight the specificities of the region.

Watershed and lake properties

Lake Allos (44°14′N, 6°42′35″E) is characterized by a 40-mdeep basin located in the subalpine zone at 2230 m a.s.l in the Mercantour national park 'Massif du Mercantour' in the Southern French Alps (Fig. 1). Lake Allos is the largest (1 km long and 700 m wide; 54 ha) natural mountain lake in Europe at an altitude above 2000 m. The lake is located in a karstic dissolution basin shaped by Quaternary glaciers [START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF]. The watershed of 520 ha culminates at 2740 m a.s.l. It consists, upstream, of sandstones of Triassic to Cretaceous age building the highest parts, and carbonate conglomerates south of the lake. The watershed is covered by scratched grasslands associated with larches. Lake Allos is composed of two basins constrained by lithology. In the south, the deeper basin (46 m water depth) basement is composed of limestone and karstified calcareous marls; north, a carbonate conglomerate unit constrains a shallower basin (20 m water depth) (Fig. 2). The lower limit of these conglomerates corresponds to a Paleocene erosional surface and Late Cretaceous limestones. Precipitation and snowmelt in the drainage basin feed three major torrents (Laus, Lac and Source). There is no surface outlet and tidal range can reach 13 m on an annual cycle [START_REF] Onema | Annual monitoring of Lake of Allos[END_REF]. A natural underground outlet in the northern part of the lake feeds the downstream torrent (Chadoulin), which stops flowing during dry summers when the lake level is below the outlet level. The surface of Lake Allos is generally frozen from November to May and lake waters are stratified during summer. Annual water temperature in the epilimnion varies between 8 and 15 °C. In the hypolimnion (below 15 m depth), water temperature varies between 3.6 and 4.3 °C (annual monitoring between June and September in 2013; ONEMA; Supporting Information Material S1).

Regional climate and oxygen isotope composition of precipitation

Climate in the Southern French Alps is temperate. Winter snow depths average 122 cm at 2700 m a.s.l. and snow cover duration is about 182 days at 2100 m a.s.l. (Durand et al., 2009a). Mean annual temperature in the Southern French Alps at 1800 m a.s.l. is 4.8 °C, varying from -0.1 °C in winter to 9.6 °C in summer, and mean annual precipitation is 944 mm, mainly in spring and autumn (Durand et al., 2009b). The precipitation regime is characterized by a strong seasonality mainly determined by a north-westerly atmospheric flow and by the northward penetration of Mediterranean flows in the Southern Alps. The source et al., 1999); (b) Lake Ghirla [START_REF] Wirth | Plant-wax D/H ratios in the southern European Alps record multiple aspects of climate variability[END_REF]; (c) Corchia Cave [START_REF] Zanchetta | Enhanced rainfall in the western Mediterranean during deposition of sapropel S1: stalagmite evidence from Corchia cave (Central Italy)[END_REF]; (d) Lake Accesa [START_REF] Magny | Holocene climate changes in the central Mediterranean as recorded by lake-level fluctuations at Lake Accesa (Tuscany, Italy)[END_REF]; (e) Lake Preola [START_REF] Magny | Holocene hydrological changes in south-western Mediterranean as recorded by lake-level fluctuations at Lago Preola, a coastal lake in southern Sicily, Italy[END_REF]. The blue star shows the location of Lake Allos. areas of alpine precipitation can be traced with oxygen isotopes because precipitation of Mediterranean origin has a mean weighted oxygen isotope composition of δ 18 O p = -4.3 ‰ VSMOW (SD = 1.7 ‰), whereas those of Atlantic origin, which supply a large amount of rainfall during winter months (Bolle, 2003), have a δ 18 O p = -8.5 ‰ VSMOW (SD = 3.51‰) (Fig. 1; [START_REF] Gonfiantini | Oxygen-18 variations of rainwater during precipitation: application of the Rayleigh model to selected rainfalls in Southern France[END_REF].

Figure 3 shows monthly weighted means of δ 18 O p from GNIP stations around Lake Allos (IAEA/WMO, 2019 Thononles-Bains: 46°22′N, 6°28′E; Draix: 44°13′N, 6°33′E; Malaussène: 43°92′N, 7°13′E; Monaco: 43°73′N, 7°42′N). For Thonon-les-Bains (385 m a.s.l) and Draix (851 m a.s.l), two stations North-East of Lake Allos, mean δ 18 O p is -7.4 ‰ during summer months and -11.3 ‰ during winter months. South of Lake Allos and closer to the Mediterranean Sea, the mean δ 18 O p at Malaussène station (359 m a.s.l) is -5.8 ‰ during summer months and -4.9 ‰ during winter months; -2.18 ‰ and -5.85 ‰ for Monaco (2 m a.s.l), respectively (Fig. 3). At these stations, δ 18 O p values are not a function of the amount of precipitation but rather vary according to the season. δ 18 O p follows a linear relationship with air temperature (IAEA/WMO, 2019) and is lower during periods of lower air temperatures influenced by air masses from the Atlantic.

Methods

The long sediment sequence of Lake Allos was sampled in July 2011 (name: ALO11) in the deep (45 m), southern basin (44°14′N, 6°42′29″E) using a UWITEC piston-coring device mounted on a floating platform (laboratory EDYTEM). Four sites were cored (sites I to IV). The cored sediment sequences reached the geological basement at a coring depth of 14 m in sites 01 and 04, and at 13.5 m in site 03. In addition, a short core (ALO11-P1) was sampled using a UWITEC gravity corer to preserve the sediment interface. All the 18 core sections are presented in supplementary material in [START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF] and are available at https://doi.org/10.1016/j.quascirev.2018. 02.016. Extensive figures are presented in [START_REF] Brisset | Données nouvelles sur la chronologie de la déglaciation dans la vallée du Haut-Verdon (lac d'Allos, Alpes françaises du Sud). Quaternaire[END_REF] in open access at https://tel.archives-ouvertes.fr/tel-01095721. The chronology of core ALO11 is based on 23 accelerator mass spectrometry (AMS) 14 C dates [START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF] from terrestrial macro-remains measured by the Poznan Radiocarbon Laboratory and 210 Pb accumulation rate constrained by 137 Cs measured in the underground laboratory of Modane [START_REF] Etienne | Influence of sample location and livestock numbers on Sporormiella concentrations and accumulation rates in surface sediments of Lake Allos, French Alps[END_REF]. Considering temporal deposition differences between continuous and instantaneous sediment layers, age-depth modeling was performed after removing flood layer thicknesses (see details in [START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF].

Lake water sampling and measurements of δD and δ 18 O lw Lake water samples were collected directly after spring snowmelt and following the drier summer season to evaluate the effect of summer evaporation on δ 18 O lw . Water sampling was performed at Lake Allos from the shore using 50-ml polyethylene dark bottles fully filled at the following dates: 23 September 2019, 9 June 2020 and 12 October 2020.

Measurements of δD and δ 18 O lw were performed in two laboratories because of logistic difficulties during the coronavirus pandemic. The sample collected in 2019 was measured at CEREGE (France) on a Picarro L2140i analyser coupled with a high-precision A0211 vaporizer and an A0325 autosampler. Standard deviation on routine measurements was ±0.023 ‰ for δ 18 O and ±0.078 ‰ for δD. The two water samples taken in 2020 were measured at the BGS (British Geological Survey, UK). Oxygen isotope (δ 18 O) measurements were made using the CO 2 equilibration method with an Isoprime 100 mass spectrometer plus an Aquaprep device. Deuterium isotope (δD) measurements were made using an online Cr reduction method with a EuroPyrOH-3110 system coupled to a GVI IsoPrime mass spectrometer [START_REF] Morrison | On-line high-precision stable hydrogen isotopic analyses on nanoliter water samples[END_REF]. Standard deviation was ±0.05 ‰ for δ 18 O and ±1.0 ‰ for δD.

Extraction and preparation of ostracods for δ 18 O analysis

Directly after coring (autumn 2011), the entire 14-m-long sequence (half cores of the sections 'OUT' correlated to the master core ALO11 at a maximum error range of 5 mm; see supplementary material in [START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF] was sliced continuously every 5 cm (270 samples in total). Each sample covers on average 30 years ([min;max] = [5;63], see the accumulation rate in [START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF]. The sample volume was 170 cm 3 above 564 cm and 77 cm 3 below. Samples were kept in closed bottles at low temperatures to maintain their humidity. All the 270 samples were analysed. Most samples were sieved from February to April 2012 and the remaining samples during autumn 2012. As the sediment was fresh and humid, hand-sieving with water was soft, allowing complete removal of detrital particles without mechanical or chemical actions. The sieved material was retrieved from 200and 100-µm meshes with water, and ostracods were handpicked with a fine brush using a stereo binocular microscope and Petri dishes. The ostracod valves were well preserved without any signs of mechanical stress or dissolution. Adhering sediments were removed using distilled water, fine needles and brushes. Then, carapaces were rinsed with ethanol and dried in ambient air [START_REF] Caporaletti | Ostracods and stable isotopes: proxies for palaeoenvironmental reconstructions[END_REF]. All ostracods were counted and identified using a specific flora of Western and Central Europe [START_REF] Meisch | Freshwater Ostracoda of Western and Central Europe[END_REF] to identify changes in ostracod abundances and ecology. These results have already been published in [START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF].

According to [START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF], Cytherissa lacustris valves are present in the sediments during periods of oligotrophic and oxic deep waters, whereas soil acidification and long-term cation release may have limited the calcification reaction from 5800 to 2800 cal a BP. C. lacustris is absent from the last centimetre of sediment and is replaced by the more eutrophic species Cypria ophthalmica.

Analysis of oxygen isotopes in C. lacustris (δ 18 O sp ) and reconstruction of δ 18 O lw Cleaned valves of C. lacustris were counted and weighed. The measurement of oxygen isotopes was performed on a minimum of three valves having a total mass >50 µg. Oxygen isotopes (δ 18 O sp ) were measured using a Kiel III Carbonate Device coupled to a Thermo Finnigan Delta Plus IRMS (in the CEREGE laboratory, Aix-en-Provence) and expressed in ‰ relative to VPDB. Based on NBS-19 measurements, the analytical precision for δ 18 O is 0.06 ‰. For the reconstruction of δ 18 O lw , δ 18 O sp values were corrected for various effects such as isotopic fractionation at equilibrium (expressed relative to SMOW; [START_REF] Coplen | Calibration of the calcite-water oxygen-isotope geothermometer at Devils Hole, Nevada, a natural laboratory[END_REF] and the vital effect. The vital effect of C. lacustris has been studied in two lakes, Starnberger See and Ammersee, at different stages of development and different depths [START_REF] Von Von Grafenstein | A mid-European decadal isotope-climate record from 15,500 to 5000 years[END_REF] and in [START_REF] Devriendt | Ostracod calcite records the 18 O/ 16 O ratio of the bicarbonate and carbonate ions in water[END_REF]. Since the freshwater environment of Lake Allos is similar to that of Lake Ammersee, the vital effect calculated in von [START_REF] Von Von Grafenstein | A mid-European decadal isotope-climate record from 15,500 to 5000 years[END_REF] was used in this paper. Based on this study, adults of C. lacustris are in average enriched by +1.49 ± 0.16 ‰ VPDB relative to equilibrium calcite. The isotopic enrichment of waters by evaporation is considered negligible at Lake Allos (see Results and interpretation).

The oxygen isotope composition of lake waters (δ 18 O lw ) was then calculated as follows [START_REF] Kim | Temperature dependence of 18 O[END_REF]: All reconstructed oxygen isotope values were corrected by -0.89 ‰ to account for the δ 18 O difference between inorganic calcite precipitation according to [START_REF] Kim | Temperature dependence of 18 O[END_REF]

∆ ∆ ∆ δ δ = - - ( - °) - Ow Osp Ovo O C H O C O

Results and interpretation

Modern variability in δ 18 O lw and hydrological functioning of Lake Allos The modern oxygen and deuterium isotope compositions of Allos' lake waters at different seasons of the year were compared to δ 18 O and δD values in Lake Petit waters located nearby, and δ 18 O p values from weather stations in the region (Fig. 3). The values at Allos plot near the global meteoric water line and were slightly heavier than at Lake Petit during spring 2011 (Fig. 3).

In June 2020, δ 18 O lw (‰ VSMOW) at Allos was -11.1 ‰ (SD = 0.01 ‰) and δD (‰) was -75.1‰ (SD = 0.71 ‰). In September 2019, δ 18 O lw (‰ VSMOW) was -10.4 ‰ (SD = 0.06 ‰, two replicates) and δD (‰ VSMOW) was -72.6 ‰ (SD = 0.29 ‰, two replicates). The following year in October 2020, δ 18 O lw (‰ VSMOW) at Allos was -10.5 ‰ (SD = 0.01 ‰) and δD (‰ VSMOW) was -71.6 ‰ (SD = 0.43 ‰). Both samples in September and October plot on the global meteoric water line, showing no effect of lake water evaporation on the δ 18 O and δD values of lake waters.

These results suggest that Lake Allos behaves like an open system with high dilution and fast discharge due to an underground outlet in the karstic depression. Considering an average Chadoulin flux of ~275 L s -1 [START_REF] Carzon | Monographie hydrologique du Verdon[END_REF] and a volume of Lake Allos of ca. 9 × 10 6 m 3 based on the bathymetric data, the estimated water residence time is close to 1 year. Recent data (SAGE, 2014) provide a mean value of 112 L s -1 of the flux of Chadoulin over a 5-year survey. This gives a mean residence time of <2.5 years, similar to the estimation based on less recent data. In systems with a relatively short residence time of water, it is expected that δ 18 O values of lake waters are primarily influenced by the δ 18 O signature of direct precipitation (depending on air temperature at the time of precipitation formation and precipitation origin) and the δ 18 O composition of the main water inflows from the watershed (i.e. snowmelt) (Roberts et al., 2008). The lake level of Allos can temporarily drop below the underground outlet during dry summers, meaning that an effect of evaporation could play a role only during exceptional years. Annual lake water mixing occurs twice, once during spring snowmelt and once in late autumn, as in other deep lake systems such as Lake Ammersee in southern Germany [START_REF] Von Grafenstein | A 200 year mid-European air temperature record preserved in lake sediments: an extension of the δ18Op-air temperature relation into the past[END_REF].

Significance of the C. lacustris δ 18 O signal Cytherissa lacustris (Cytherideidae) is an endobenthic species and inhabits sublittoral and profundal zones of cold, deep lakes and the littoral zones of high-altitude alpine lakes [START_REF] Meisch | Freshwater Ostracoda of Western and Central Europe[END_REF]. C. lacustris is very sensitive to oxygenation conditions prevailing at the sediment-water interface and maximum abundance is found in waters between 4 and 15 °C throughout the year. Adults and juveniles of C. lacustris are found together without seasonal changes in relative abundance, meaning that C. lacustris reproduces continuously throughout the year [START_REF] Von Von Grafenstein | A mid-European decadal isotope-climate record from 15,500 to 5000 years[END_REF]. Therefore, variations in δ 18 O sp represent annual deep water variability.

According to annual monitoring (see Study site section and Supporting Information Material S1), deep lake waters of Lake Allos (below 15 m depth) where C. lacustris develops remained at 4 °C throughout 2013. Seismic surveys show that the lake sediment infill is well stratified with no evidence of sediment reworking [START_REF] Wilhelm | 1400 years of extreme precipitation patterns over the Mediterranean French Alps and possible forcing mechanisms[END_REF]. Layers of sediment are continuous between the shallow basin and the deep basin, suggesting that the lake level did not drop by more than 20 m over the study period. As lake water temperature is close to 4 °C below 15 m, we consider that temperature at the bottom of the deep basin remained relatively constant. Therefore, δ 18 O sp variations are assumed to be representative of δ 18 O lw variations. Note that samples cover a longer period (ca. 30 years) compared to the C. lacustris calcification timespan.

Reconstruction of past δ 18 O lw

Thick and strongly calcified valves of C. lacustris are well preserved in the sediments and show no signs of dissolution (Fig. 4). C. lacustris is almost the only species of ostracods found in the sediments. Valves of Cypridopsis vidua, Candona candida and Cypria ophthalmica are present in sediments from the last 1500 years [START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF]. Abundance of C. lacustris is variable along the core. Ostracod valves are absent in the sediments from 5800 to 2800 cal a BP during a period with high diatom concentrations (data published in Cartier et al., 2018; Figure 5). Mean C. lacustris abundance in core sediment slices 5 cm long is 3.1 valves from the bottom to 5800 cal a BP and 2.8 valves from 2800 cal a BP to the top of the record [START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF]. Concentrations in valves cm -3 are presented in Fig. 5. The highest concentrations, up to 0.35 valves cm -3 , are observed at the end of the YD and from 10 000 to 8500 cal a BP. C. lacustris valves were sufficiently numerous to allow 73 oxygen isotope measurements.

Over the entire study period, minimum and maximum values of δ 18 O sp range from -8.4 ‰ VPDB (11 900 cal a BP) to -6.3 ‰ VPDB (6100 cal a BP) (Fig. 5). Mean δ 18 O sp along the core is -7.1 ‰ VPDB (SD = 0.4‰). The highest variability in δ 18 O sp is observed during the YD (12 700-11 500 cal a BP). A drop in δ 18 O sp is present at 11 900 cal a BP and followed by an increase in δ 18 O sp at the transition with the Holocene. After a peak, values decrease again until ca. 8500 cal a BP. High δ 18 O sp values are present from 7200 to 6100 cal a BP, ca. 2800 cal a BP and ca. 1000 cal a BP during a thermal optimum for mid-northern latitudes and during the MCA. δ 18 O sp drops again to low values from 500 cal a BP during the LIA before a rise in the topmost sample representing sub-modern conditions (Fig. 5). Unfortunately, C. lacustris is absent from the first top centimetre of sediments, preventing measurement of modern δ 18 O sp values. After correcting the δ 18 O sp for the vital effect and isotope fractionation between calcite and water at 4 °C, the reconstructed δ 18 O lw ranges between -12.8 and -10.6 ‰ VSMOW. Mean δ 18 O lw is -11.5 ‰ VSMOW (SD = 0.4 ‰) for the entire record (Fig. 5). The reconstructed oxygen isotope value in the top sample (-11.3 ‰) is consistent with the modern δ 18 O lw range (-11.1 ‰ to -10.4 ‰) for 2019 and 2020.

Discussion

Major factors influencing the δ 18 O signal at Lake Allos The δ 18 O signal in lake carbonates is primarily a function of the lake water oxygen isotope composition and water temperature [START_REF] Stuiver | Oxygen and carbon isotope ratios of fresh-water carbonates as climatic indicators[END_REF][START_REF] Leng | Palaeoclimate interpretation of stable isotope data from lake sediment archives[END_REF]. The lake water oxygen isotope composition itself is a product of (i) the δ 18 O value of the seawater from which it originally derived; (ii) rain-out history, seasonality and air-mass trajectory; and (iii) oxygen isotope fractionation of lake water compared to mean meteoric precipitation, primarily by evaporation but also by groundwater flux [START_REF] Develle | Controlling factors on a paleo-lake oxygen isotope record (Yammoûneh, Lebanon) since the Last Glacial Maximum[END_REF][START_REF] Roberts | Oxygen isotopes as tracers of Mediterranean climate variability: an introduction[END_REF]. According to the modern oxygen isotope composition of Lake Allos' waters, δ 18 O lw plots along the global meteoric water line, showing no effect of evaporation after the summer season (Fig. 3). δ 18 O in precipitation entering the lake varies according to the season, due to changes in air temperatures and differential contribution in vapor of Atlantic and Mediterranean origin. Therefore, a lowering in δ 18 O lw is expected to reflect an increasing contribution of water inflow from snowmelt, a higher contribution of precipitation of Atlantic origin, and/or precipitation occurring primarily during colder seasons [START_REF] Gonfiantini | Oxygen-18 variations of rainwater during precipitation: application of the Rayleigh model to selected rainfalls in Southern France[END_REF]. In contrast, increasing δ 18 O lw is interpreted as a higher contribution of water inflow from rain versus snowmelt preferentially of Mediterranean origin and/or precipitation occurring mainly during warmer periods. In the catchment area, sources of signal change are evapotranspiration by vegetation, water losses by percolation into soils and delayed flows (stored in the ice, snow or soils). However, the δ 18 O value of waters having percolated into soils might be considered as the average δ 18 O value of local rainfall over several months (McDonnell [START_REF] Mcdonnell | Effect of catchment-scale subsurface mixing on stream isotopic response[END_REF][START_REF] Tang | The effect of soil hydrology on the oxygen and hydrogen isotopic compositions of plants' source water[END_REF]. At Lake Allos, a low but permanent flow of water currently persists from the remains of a rock glacier. Four phases of glacial advances have been identified in the Allos watershed [START_REF] Jorda | Les montagnes du Haut Verdon, Etude géomorphologique[END_REF][START_REF] De Beaulieu | Tardiglaciaire et postglaciaire des Alpes de Haute-Provence. Le glaciaire de la Blanche[END_REF]. Stages 1 and 2 (respectively at 1850-1900 and 2265 m a.s.l) pre-date the formation of Lake Allos and are attributed to the early Lateglacial [START_REF] Brisset | Données nouvelles sur la chronologie de la déglaciation dans la vallée du Haut-Verdon (lac d'Allos, Alpes françaises du Sud). Quaternaire[END_REF]. Stage 3, located at 2310 m a.s.l., is attributed to the YD, indicating a glacier advance near Lake Allos during this period [START_REF] Brisset | Données nouvelles sur la chronologie de la déglaciation dans la vallée du Haut-Verdon (lac d'Allos, Alpes françaises du Sud). Quaternaire[END_REF]. Finally, stage 4 is attributed to the last cooling period during the Late Holocene that might be related to the Neoglacial period (4500 cal a BP) or the LIA [START_REF] Jorda | Les montagnes du Haut Verdon, Etude géomorphologique[END_REF][START_REF] Brisset | Données nouvelles sur la chronologie de la déglaciation dans la vallée du Haut-Verdon (lac d'Allos, Alpes françaises du Sud). Quaternaire[END_REF].

The comparison between the δ 18 O lw signal, vegetation evolution and the potential presence of a glacier, in particular during the YD, provides additional clues to identify factors influencing oxygen isotope variability. The marked drop in δ 18 O lw ca. 12 000 cal a BP (2σ error = 360) probably occurred during the second half of the YD. Pollen analysis shows the presence of open vegetation from the base of the record to 1150 cm depth (ca. 11 700 cal a BP). A high percentage (30 %) of steppic taxa is consistent with the dominance of runoff processes in a sandur-type outwash plain at the glacier snout during massive deglaciation of the Allos cirque. Then, steppic taxa (Artemisia, Chenopodiaceae, Caryophyllaceae) increased again during the YD (Fig. 5). A similar vegetation is recorded during the YD in other paleoenvironmental studies of the Mediterranean Alps [START_REF] De Beaulieu | Contribution pollenanalytique à l'histoire tardiglaciaire et holocène de la végétation des Alpes méridionales françaises[END_REF][START_REF] Finsinger | Late Glacial to Holocene Deglaciation of the Colle Del Vei Del Bouc-Colle Del Sabbione Area (Argentera Massif, Maritime Alps, Italy-France)[END_REF][START_REF] Ponel | Late-glacial and Holocene high-altitude environmental changes in Vallée des Merveilles (Alpes-Maritimes, France): insect evidence[END_REF][START_REF] Gandouin | Late Glacial and Holocene chironomid assemblages in Lac Long Inférieur (southern France, 2090 m): palaeoenvironmental and palaeoclimatic implications[END_REF]. It is difficult to precisely define the onset of the YD based solely on the pollen diagram as steppic taxa progressively decrease from the base of the record. Nevertheless, the end of the YD probably corresponds to the end of the Artemisia period, associated with a decrease in steppic taxa and the extension of tree cover (black line on Fig. 5).

Other studies, such as the study of Lake Mondsee sediments in the north-eastern Alps, have shown that cooling at the onset of the YD is simultaneously reflected in ostracod δ 18 O and vegetation [START_REF] Lauterbach | Environmental responses to Lateglacial climatic fluctuations recorded in the sediments of pre-Alpine Lake Mondsee (northeastern Alps)[END_REF]. A similar synchronicity in the response of isotope and vegetation records is shown in a European synthesis by [START_REF] Reinig | Precise date for the Laacher See eruption synchronizes the Younger Dryas[END_REF], recording the onset of the YD at 12 800 cal a BP (130 years earlier than thought). Therefore, the later drop in δ 18 O values observed at Allos (ca. 12 000 cal a BP) could be related to the influence of a local glacier in the watershed rather than temperatures, at least during the YD interval. Following this hypothesis, an increasing glacier/snowmelt contribution could explain decreases in δ 18 O lw when the presence of a glacier is suspected. During the mid-Holocene, vegetation starts to be highly influenced by humans, leading to an opening up of forests at lower altitudes, which limits the use of cross-comparison with the δ 18 O signal [START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF]Figure 5). However, it can be seen that intervals with low δ 18 O lw values during the Late Holocene and in particular during the LIA correspond to occurrences of Ephedra sp., supporting the presence of cooler periods [START_REF] Cartier | Multiproxy analyses of Lake Allos reveal synchronicity and divergence in geosystem dynamics during the Lateglacial/Holocene in the Alps[END_REF].

Paleohydrology in the Mediterranean Alps and comparison with other climate reconstructions

Beginning of lake infilling and the climate reversal of the YD (i.e. from 13 350 to 11 500 cal a BP)

The first period of lake infilling of Lake Allos (13 350-12 700 cal a BP) can be attributed to the end of the Allerød considering the oldest 14 C date, giving an age of 13 070-12 800 cal a BP (2σ) at 1260 cm depth. As only one 14 C date predates the onset of the YD, uncertainties remain regarding the chronology but climatic conditions must necessarily have been relatively warmer than previous periods to allow the massive deglaciation of the cirque of Allos. Additional information can be obtained from the pollen diagram, which documents an open landscape characteristic of the pre-Holocene period from the base of the record to 1150 cm depth (ca. 11 700 cal a BP; min: 11 570, max: 11 920; 95 %) (Fig. 5). The corresponding age for this depth is consistent with recognized boundaries of the YD, i.e. 12 800-11 500 cal a BP from the Greenland ice-core (GS-1) and mid-European isotope records [START_REF] Reinig | Precise date for the Laacher See eruption synchronizes the Younger Dryas[END_REF] (Fig. 6).

In the Northern Alps, the δ 18 O record of lake Leysin (1255 m a.s.l., Switzerland), [START_REF] Schwander | Oxygen isotopes of lake marl at Gerzensee and Leysin (Switzerland), covering the Younger Dryas and two minor oscillations, and their correlation to the GRIP ice core[END_REF] shows quasisimultaneous temperature changes between Greenland and Europe during the YD. Records from the northern Alps or its foreland display consistent shapes of the YD, similar to the Ammersee record (533 m a.s.l.) (Fig. 6). In addition, oxygen isotope records from Lake Mondsee (481 m a.s.l., [START_REF] Lauterbach | Environmental responses to Lateglacial climatic fluctuations recorded in the sediments of pre-Alpine Lake Mondsee (northeastern Alps)[END_REF], Lake Gerzensee (603 m a.s.l., von Grafenstein et al., 2013), Hölloch cave (700 m a.s.l., [START_REF] Li | A high-resolution speleothem proxy record of the Late Glacial in the European Alps: extending the NALPS19 record until the beginning of the Holocene[END_REF] and the TEX86 temperature record from Lake Lucerne (434 m a.s.l., [START_REF] Blaga | A TEX 86 lake record suggests simultaneous shifts in temperature in Central Europe and Greenland during the last deglaciation[END_REF] also document synchronous changes during the YD.

Located at higher altitudes, the δ 18 O lw record from Lake Allos (2230 m a.s.l.) in the Southern French Alps clearly differs from those documented in the Northern Alps. According to the age-depth model, the beginning of the YD is marked by relatively high δ 18 O values compared to the second half of the YD (ca. after 12 000 cal a BP; Fig. 5). Several hypotheses might explain the persistence of high δ 18 O values during this period, including (i) water storage induced by the presence of a local glacier in the watershed, (ii) a lower temperature shift at the Allerød-YD transition in the Southern French Alps and (iii) a greater influence of precipitation of Mediterranean origin to counteract a large cooling. Several factors could also have played a simultaneous role in the changes observed. The first hypothesis, i.e. water storage induced by the presence of a glacier, agrees with datings of moraines in the Southern French Alps [START_REF] Darnault | Timing of the last deglaciation revealed by receding glaciers at the Alpine-scale: impact on mountain geomorphology[END_REF]; Figure 6). A meltwater flux during summer is not excluded but was probably of less importance to the lake budget than during the second half of the YD. Concerning a lower temperature shift (hypothesis 2), the study of paleo-extents of the Argentière glacier close to the study site Figure 6. Estimated δ 18 O (δ 18 O lw , ‰ VSMOW) in the lake waters of Lake Allos compared to other records: oxygen isotope ratios in precipitation (δ 18 O p , ‰ VSMOW) based on the record of Lake Ammersee (Germany; von [START_REF] Von Von Grafenstein | A mid-European decadal isotope-climate record from 15,500 to 5000 years[END_REF]; Lake Ghirla plant wax (δD, ‰ SMOW) at the foot of the Southern Alps [START_REF] Wirth | Plant-wax D/H ratios in the southern European Alps record multiple aspects of climate variability[END_REF]; oxygen isotope record (δ 18 O, ‰ VPDB) of Corchia Cave CC26 (Northern Italy; [START_REF] Zanchetta | Enhanced rainfall in the western Mediterranean during deposition of sapropel S1: stalagmite evidence from Corchia cave (Central Italy)[END_REF]; lakelevel fluctuations (m) at Accesa (Italy; [START_REF] Magny | Holocene climate changes in the central Mediterranean as recorded by lake-level fluctuations at Lake Accesa (Tuscany, Italy)[END_REF]; lake level reconstruction at Preola (Southern Italy; [START_REF] Magny | Holocene hydrological changes in south-western Mediterranean as recorded by lake-level fluctuations at Lago Preola, a coastal lake in southern Sicily, Italy[END_REF] [START_REF] Protin | Climatic reconstruction for the Younger Dryas/Early Holocene transition and the Little Ice Age based on paleo-extents of Argentière glacier (French Alps)[END_REF] invalidates this hypothesis as reconstructed temperature shifts (ΔT varying between 3.6 and 5.5 °C compared to modern temperatures) are in the same range as temperature reconstructions from the Northern Alps (e.g. ΔT of 3.9 °C at the YD-Holocene transition in the Swiss Alps; [START_REF] Samartin | Lateglacial and Early Holocene summer temperatures in the southern Swiss Alps reconstructed using fossil chironomids[END_REF]. Finally, the third hypothesis (a higher influence of precipitation of Mediterranean origin) is in accordance with the hydrogen isotope record of plant waxes from Lake Ghirla in the Southern Alps showing unexpectedly high δD wax values during the YD [START_REF] Wirth | Plant-wax D/H ratios in the southern European Alps record multiple aspects of climate variability[END_REF]. This signal was interpreted as a shift from a northern North Atlantic to a southern North Atlantic/western Mediterranean Sea source due to a southward migration of the westerlies with climate cooling. Assuming a temperature shift (YD-modern conditions) varying between 3.6 and 5.5 °C [START_REF] Protin | Climatic reconstruction for the Younger Dryas/Early Holocene transition and the Little Ice Age based on paleo-extents of Argentière glacier (French Alps)[END_REF], an altitudinal effect of -0.2 ‰ per 100 m (e.g. [START_REF] Schürch | Observation of isotopes in the water cycle?the Swiss National Network (NISOT)[END_REF] and a correlation between δ 18 O in precipitation and air temperatures of 0.33 ‰ per °C (Draix station; r 2 = 0.54; Supporting Information Fig. S1), the precipitation reaching Allos at the beginning of the YD may have been the result of a mixture of 50 % Atlantic -50 % Mediterranean (30 % / 70 %, respectively) to counteract the effect of cooling on the δ 18 O record.

At a broader scale, a higher contribution of Mediterranean precipitation in the Southern French Alps would fit a recent study published in [START_REF] Rea | Atmospheric circulation over Europe during the Younger Dryas[END_REF] based on glacier, pollen and chironomid assemblages, showing that the YD was certainly characterized by the presence of a positive Scandinavia (SCAND) climate configuration pushing storm tracks south and east. To summarize, while the temperature hypothesis can be excluded, glacier storage and a Mediterranean precipitation source remain plausible explanations for high δ 18 O values during this period.

During the second half of the YD, the isotopic record of Lake Allos also presents an original shape. The δ 18 O record is marked by a sharp drop to low δ 18 O values corresponding to the lowest values of the record (-12.8 ‰ VSMOW) ca. 12 000 cal a BP. These changes are probably the result of large freshwater inputs to the lake due to glacier melting. This implies a large influence of glacier dynamics in the watershed on the isotopic signal, as suggested by the comparison with the pollen diagram. Alternatively, the presence of humid conditions would fit the regional geomorphological studies from the Maritime Alps, indicating the presence of glacier advances ca. 12 500-12 300 cal a BP [START_REF] Pauly | Subfossil trees suggest enhanced Mediterranean hydroclimate variability at the onset of the Younger Dryas[END_REF][START_REF] Spagnolo | Glacier extent and climate in the Maritime Alps during the Younger Dryas[END_REF].

The Holocene period from 11 500 cal a BP to the present day Isotope records covering the transition from the Lateglacial to the Holocene are very sparse in the Alps, and almost nonexistent in the Southern French Alps. A moraine dating to the Preboreal period in the Maritime Alps (Fig. 6; [START_REF] Federici | Exposure age dating and Equilibrium Line Altitude reconstruction of an Egesen moraine in the Maritime Alps, Italy[END_REF] suggests new glacial advances at the beginning of the Holocene. Although supported by only a few samples, a drop in δ 18 O lw in the record of Allos (from -11 to -12 ‰ VSMOW) ca. 10 800 cal a BP seems to follow the cold and humid Preboreal oscillation ca. 11 300 cal a BP [START_REF] Ilyashuk | Lateglacial environmental and climatic changes at the Maloja Pass, Central Swiss Alps, as recorded by chironomids and pollen[END_REF].

Between 9800 and 8400 cal a BP, δ 18 O lw at Lake Allos increased, reaching a maximum of -10.7 ‰ VSMOW, and then decreased to -11.8 ‰ VSMOW. The millennial-scale change in the δ 18 O values is assumed to be related primarily to changes in air temperature and precipitation regime rather than to glacier influence. To the best of our current knowledge [START_REF] Brisset | Données nouvelles sur la chronologie de la déglaciation dans la vallée du Haut-Verdon (lac d'Allos, Alpes françaises du Sud). Quaternaire[END_REF][START_REF] Brisset | Lateglacial/Holocene environmental changes in the Mediterranean Alps inferred from lacustrine sediments[END_REF], it seems unlikely that the upper moraines date back to this time interval in the watershed of Allos; however, remaining moraines not yet sampled are under investigation. Increasing δ 18 O values might then be the result of a higher contribution of precipitation occurring during warmer seasons and/or preferentially of Mediterranean origin. Indeed, the Early Holocene in the northern mid-latitudes is characterized by the highest summer and lowest winter solar insolation [START_REF] Laskar | A long-term numerical solution for the insolation quantities of the Earth[END_REF]. Therefore, higher summer temperatures are recorded in the Eastern Alps [START_REF] Ilyashuk | Holocene temperature variations at a high-altitude site in the Eastern Alps: a chironomid record from Schwarzsee ob Sölden, Austria[END_REF]. In the Southern Alps, a high-resolution δ 13 C isotopic signal highlights an early Holocene warming and/or a climate oscillation called the '9.3 ka' dry climate event [START_REF] Audiard | Identifying Short-Term Climatic Changes Through Isotopic Charcoal Analyses Early Holocene Warming and the '9.3 Ky' Event at the Mesolithic Site of la Baume de Monthiver[END_REF].

In contrast, the period 9200-8400 cal a BP suggests a higher contribution of snowmelt, precipitation of Atlantic origin and/ or the presence of colder conditions. More broadly, the northwestern Mediterranean region at the beginning of the Holocene generally experienced a long-term trend towards humid conditions from 9200 to 6800 cal a BP, as evidenced in lake isotope records (Roberts et al., 2008), caves (Rio Martino and Corchia Cave, [START_REF] Regattieri | Holocene Critical Zone dynamics in an Alpine catchment inferred from a speleothem multiproxy record: disentangling climate and human influences[END_REF][START_REF] Zanchetta | Enhanced rainfall in the western Mediterranean during deposition of sapropel S1: stalagmite evidence from Corchia cave (Central Italy)[END_REF]) and lake level reconstructions [START_REF] Harrison | European lakes as palaeohydrological and palaeoclimatic indicators[END_REF][START_REF] Jalut | Holocene circum-Mediterranean vegetation changes: climate forcing and human impact[END_REF][START_REF] Magny | North-south palaeohydrological contrasts in the central Mediterranean during the Holocene: tentative synthesis and working hypotheses[END_REF] (Fig. 6).

At the transition from the Early to Mid-Holocene (8200 cal a BP), low data resolution limits our ability to assess fine variations in the δ 18 O record. However, we observe a general trend towards increasing δ 18 O lw culminating ca. 6100 cal a BP, representing the highest value of the sequence (-10.6 ‰ VSMOW), followed by an abrupt decrease at 5700 cal a BP, unfortunately supported by only one data point. During that time period, precipitation reconstruction [START_REF] Brayshaw | Changes in Mediterranean climate during the Holocene: insights from global and regional climate modelling[END_REF] and paleoclimate data from lake isotope records [START_REF] Roberts | Climatic, vegetation and cultural change in the eastern Mediterranean during the mid-. Holocene environmental transition[END_REF] indicate drier conditions from 8000 to 6000 cal a BP in both Western and Eastern Mediterranean regions. This period also represents a thermal optimum in the Northern Hemisphere between 30 and 60°N [START_REF] Kaufman | Holocene global mean surface temperature, a multi-method reconstruction approach[END_REF].

For the last 2800 cal a BP, our results suggest major paleohydrological changes near Lake Allos. A shift from high δ 18 O lw to low δ 18 O at 2300 cal a BP is concomitant with increasing torrential activity at Lake Allos [START_REF] Brisset | The overlooked human influence in historic and prehistoric floods in the European Alps[END_REF] and in the Southern French Alps during the Iron Age time interval interpreted as a cooler and more humid period [START_REF] Jorda | Morphogenèse et fluctuations climatiques dans les Alpes françaises du Sud de l'Age du Bronze au haut Moyen Age. Nouvelles de l'archéologie. Paper presented at the Round Table "Le climat à la fin de l'Age du Fer et dans l'Antiquité (500 BC-500 AD): méthodes d'approche et résultats[END_REF][START_REF] Sivan | Rythmes de la sédimentation et interprétations paléoclimatiques lors du Postglaciaire (Alpes du Sud) 14c et dendro-géomorphologie, deux chronomètres complémentaires[END_REF]; however, the low resolution limits further interpretation (Fig. 7). Then, at the beginning of the Roman Period ca. 1900-1800 cal a BP, higher δ 18 O lw suggests the presence of higher air temperatures and/or a higher contribution of rain to the lake (versus snowmelt) preferentially of Mediterranean origin. A drier period at lower altitudes in the valleys is illustrated by human occupation closer to or within current riverbeds [START_REF] Bravard | Le climat d'après les informations fournies par les enregistrements sédimentaires fluviatilis étudiés sur des sites archéologiques[END_REF][START_REF] Jorda | Morphogenèse et fluctuations climatiques dans les Alpes françaises du Sud de l'Age du Bronze au haut Moyen Age. Nouvelles de l'archéologie. Paper presented at the Round Table "Le climat à la fin de l'Age du Fer et dans l'Antiquité (500 BC-500 AD): méthodes d'approche et résultats[END_REF]. From 1800 to 1300 cal a BP, low δ 18 O lw values suggest lower air temperatures and/or a higher contribution of precipitation (mostly snow) of Atlantic origin to the lake. The Late Antiquity also coincides with higher torrential activity both at high altitude at Allos [START_REF] Brisset | The overlooked human influence in historic and prehistoric floods in the European Alps[END_REF] and in lowlands [START_REF] Sivan | Rythmes de la sédimentation et interprétations paléoclimatiques lors du Postglaciaire (Alpes du Sud) 14c et dendro-géomorphologie, deux chronomètres complémentaires[END_REF], negative temperature anomalies in tree ring records [START_REF] Büntgen | European tree-ring data and the Medieval Climate Anomaly[END_REF] and glacier advances in the European Alps [START_REF] Holzhauser | Glacier and lake-level variations in west-central Europe over the last 3500 years[END_REF] (Fig. 7). Higher δ 18 O lw occurs again from 1300 to 500 cal a BP, which might correspond to the MCA also seen in the tree ring record of [START_REF] Corona | Long-term summer (AD 751-2008) temperature fluctuation in the French Alps based on treering data[END_REF] (Fig. 7). Regarding our results, the MCA shows several oscillations in the δ 18 O record with three peaks ca. 1200, 850 and 600 cal a BP. The transition between the MCA and LIA at 500 cal a BP is very sharp with δ 18 O lw highly depleted during two low excursions. These δ 18 O values are similar to the values obtained in the second part of the YD. This abrupt decrease might be explained by lower air temperatures and/or higher freshwater inputs from snowmelt to the lake preferentially of Atlantic origin. During the LIA, sedimentological studies show increasing fluvial activity in the Southern French Alps, at Allos [START_REF] Wilhelm | 1400 years of extreme precipitation patterns over the Mediterranean French Alps and possible forcing mechanisms[END_REF][START_REF] Brisset | The overlooked human influence in historic and prehistoric floods in the European Alps[END_REF] and downstream [START_REF] Miramont | Évolution historique de la morphogenèse et de la dynamique fluviale d'une rivière méditerranéenne: l'exemple de la moyenne durance (France du sud-est)[END_REF][START_REF] Sivan | Rythmes de la sédimentation et interprétations paléoclimatiques lors du Postglaciaire (Alpes du Sud) 14c et dendro-géomorphologie, deux chronomètres complémentaires[END_REF], a water level rise in the Jura [START_REF] Magny | Quantitative reconstruction of Younger Dryas to mid-Holocene paleoclimates at le Locle, Swiss Jura, using pollen and lake-level data[END_REF], and glacial tongue advances in both the Northern and Southern Alps [START_REF] Holzhauser | Glacier and lake-level variations in west-central Europe over the last 3500 years[END_REF][START_REF] Ivy-Ochs | Latest Pleistocene and Holocene glacier variations in the European Alps[END_REF]; Figure 7). Overall, two moraines in the Maritime Alps showing glacial advances during the Iron Age ca. 2400 cal a BP [START_REF] Ribolini | Relationships between glacier and rock glacier in the Maritime Alps, Schiantala Valley, Italy[END_REF] and the LIA ca. 450 cal a BP [START_REF] Federici | Abhandlungen-Evidence and chronology of the Little Ice Age in the Argentera Massif (Italian maritime alps)[END_REF] are coherent with low δ 18 O values at Allos (Fig. 6). The fourth stage of glacial advance at Allos described in [START_REF] Jorda | Les montagnes du Haut Verdon, Etude géomorphologique[END_REF] could then be linked to the LIA given the intensity of the event in the δ 18 O record. However, the sequence discontinuity and low periodic resolution require further isotopic studies for the Mediterranean Alps.

Finally, comparing oxygen isotope records from Northernmid and Southern Europe (Fig. 6) with the δ 18 O record at Lake Allos allows a better understanding of how air temperatures and hydrology have responded to climate change during the end of the Lateglacial and Holocene periods. The record of Allos shows an alternation of glacier growth and melting during the YD and a general high variability in freshwater inputs (as in [START_REF] Bakke | Rapid oceanic and atmospheric changes during the Younger Dryas cold period[END_REF] while air temperature proxies [START_REF] Von Von Grafenstein | A mid-European decadal isotope-climate record from 15,500 to 5000 years[END_REF][START_REF] Schwander | Oxygen isotopes of lake marl at Gerzensee and Leysin (Switzerland), covering the Younger Dryas and two minor oscillations, and their correlation to the GRIP ice core[END_REF] show similar boundaries with Greenland ice cores. During the Holocene, the record of Lake Allos highlights a general trend towards drier conditions from the Early to mid-Holocene (ca. 6000 cal a BP) followed by wetter conditions from 2800 cal a BP to the present day. Unfortunately, the resolution of the record prevents further interpretations for the mid-Holocene, and other events might have occurred (see [START_REF] Cartier | Diatom-oxygen isotope record from high-altitude Lake Petit (2200 m a.s.l.) in the Mediterranean Alps: shedding light on a climatic pulse at 4.2 ka[END_REF]. This trend is the opposite of lake water level variations in Southern Europe recorded at Lake Preola in Southern Italy [START_REF] Magny | Holocene hydrological changes in south-western Mediterranean as recorded by lake-level fluctuations at Lago Preola, a coastal lake in southern Sicily, Italy[END_REF]Figure 6) but in agreement with local lake water level reconstructions (Harrison et al., 1993;[START_REF] Digerfeldt | Reconstruction and paleoclimatic interpretation of Holocene lake-level changes in Lac de Saint-Léger, Haute-Provence, southeast France. Palaeogeography[END_REF] and isotope cave records [START_REF] Regattieri | Holocene Critical Zone dynamics in an Alpine catchment inferred from a speleothem multiproxy record: disentangling climate and human influences[END_REF]. Whereas changes in global air temperatures in the Northern Hemisphere were relatively smooth during the Holocene with a progressive increase in air temperatures until 6000 cal a BP followed by a decreasing trend until the 19th century [START_REF] Kaufman | Holocene global mean surface temperature, a multi-method reconstruction approach[END_REF], local hydroclimate records from the Mediterranean Alps show a higher variability with centennial and millennial climate oscillations.

Conclusions

Sediments from Lake Allos have allowed for the analysis of oxygen isotope ratios in valves of Cytherissa lacustris, a species encountered in deep lakes. Variation in δ 18 O covers the end of the Lateglacial and the Holocene (except from 5800 to 2800 cal a BP). δ 18 O lw was estimated after correcting ostracod δ 18 O values with the vital effect of C. lacustris and the effect of isotope fractionation at equilibrium between calcite and water at 4 °C. The main factors influencing the isotopic record are estimated to be: variation in air temperatures, freshwater inputs through melting glacier/snowmelt contribution, and meteoric precipitation sources (West from the Atlantic and South from the Mediterranean region). Despite only one 14 C date before the Holocene, our data indicate the persistence of a steppic vegetation during the YD. Relatively high δ 18 O lw values at that time could be related to glacier water storage and Mediterranean precipitation source. Then, during the second half of the YD, the large drop in δ 18 O lw might be the result of higher freshwater inputs to the lake budget. During the Holocene, the highest δ 18 O lw value of the record was reached ca. 6100 cal a BP during a thermal optimum at this latitude, suggesting a potential role of climate in large vegetation succession in the Southern French Alps. Finally, the Late Holocene (from 2800 cal a BP to the present day) shows several oscillations in δ 18 O lw following major climate phases recognized at the European scale and glacier advances/retreat in the Western Alps: a higher contribution of ice/snowmelt inputs to the lake and/or lower temperatures during the Late Antiquity and LIA and a reverse trend during the Roman Warm Period and MCA. Therefore, the fourth stage of glacial advance in the watershed of Allos could be linked to the LIA given the intensity of the event in the δ 18 O record. However, new studies on hydroclimate in high-altitude environments are required to fully understand these questions due to the discontinuity of the sequence. [START_REF] Mann | Global signatures and dynamical origins of the little ice age and medieval climate anomaly[END_REF], glacial advances at Aletsch in Switzerland [START_REF] Holzhauser | Glacier and lake-level variations in west-central Europe over the last 3500 years[END_REF], torrential deposits in Southern French Alps [START_REF] Sivan | Rythmes de la sédimentation et interprétations paléoclimatiques lors du Postglaciaire (Alpes du Sud) 14c et dendro-géomorphologie, deux chronomètres complémentaires[END_REF] and temperature anomalies reconstructed from dendrochronological data [START_REF] Corona | Long-term summer (AD 751-2008) temperature fluctuation in the French Alps based on treering data[END_REF]. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 1 .

 1 Figure 1. Location map of Lake Allos and other paleohydrological records discussed in the text: (a) Lake Ammersee (von Grafenstein et al., 1999); (b) Lake Ghirla (Wirth and Sessions, 2016); (c) Corchia Cave (Zanchetta et al., 2007); (d) Lake Accesa (Magny et al., 2007); (e) Lake Preola (Magny et al., 2011). The blue star shows the location of Lake Allos. White arrows indicate weighted mean δ 18 O of rain from the Mediterranean region(-4.3 ‰) and the Atlantic (-8.5 ‰) (Celle-Jeanton et al., 2004). [Color figure can be viewed at wileyonlinelibrary.com]

  Figure 1. Location map of Lake Allos and other paleohydrological records discussed in the text: (a) Lake Ammersee (von Grafenstein et al., 1999); (b) Lake Ghirla (Wirth and Sessions, 2016); (c) Corchia Cave (Zanchetta et al., 2007); (d) Lake Accesa (Magny et al., 2007); (e) Lake Preola (Magny et al., 2011). The blue star shows the location of Lake Allos. White arrows indicate weighted mean δ 18 O of rain from the Mediterranean region(-4.3 ‰) and the Atlantic (-8.5 ‰) (Celle-Jeanton et al., 2004). [Color figure can be viewed at wileyonlinelibrary.com]

Figure 2 .

 2 Figure 2. Bathymetry of Lake Allos (in meters) and location of the coring site (ALO11). Dark blue corresponds to deeper waters. The dashed line corresponds to a low lake level recorded in summer 2006. Arrows represent water inflows to the lake and the outlet is represented by a black dot. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 3 .

 3 Figure 3. On the left, location map of meteorological stations (black squares) and lakes (stars). On the right, δ 18 Oand δD (in ‰ VSMOW) in lake waters of Allos (in blue LA: 23 September 2019; 9 June 2020 and 13 October 2020) compared to other sites: Lake Petit (in green LP: 17 May 2011 and 17 September 2011; Cartier et al., 2019); Mean δ 18 O and δD in precipitation from meteorological stations (in yellow Station 1 Thonon-les-Bains 1999-2016, Station 2 Draix 2004-2013, Station 3 Malaussène 1997-1999 and Station 4 Monaco 1999-2016; IAEA/WMO, 2019). Thered line represents the global meteoric water line (GMWL). [Color figure can be viewed at wileyonlinelibrary.com]

A

  monitoring program of δ 18 O p carried out between 2004 and 2009 by the IAEA/WMO in 2015 was performed at Draix station (44°08′00″N, 006°20 ′00″E), located 25 km from Lake Allos (Supporting Information Material S1). Mean annual values of δ 18 O p varied between -7.0 ‰ (in 2006) and -10.4 ‰ (in 2009). Mean δ 18 O p for the 6 years of monitoring was -8.32 ‰.

Figure 4 .

 4 Figure 4. Scanning electron micrograph of a valve of Cytherissa lacustris (Aix-Marseille University, Saint Charles).

  et

Figure 5 .

 5 Figure 5. Oxygen isotope ratios (δ 18 O) in ostracods (in ‰ VPDB) and lake water (δ 18 O lw in ‰ VSMOW, the blue dashed line represents average modern δ 18 O lw calculated from the three samples available) according to ages, concentrations in ostracods and diatoms (valves cm -3 ), percentages of pollen of P. sylvestris, Artemisia sp. and the sum of steppics (Artemisia, Chenopodiaceae, Caryophyllaceae) from Cartier et al. (2018). The dashed line represents the onset of the Younger Dryas (YD) based on the oldest 14 C date and the black line represents the end of the YD according to ages and the pollen diagram, together with worldwide accepted limits for the Lateglacial and Holocene periods (Walker et al., 2018). [Color figure can be viewed at wileyonlinelibrary.com]

  Figure6. Estimated δ 18 O (δ 18 O lw , ‰ VSMOW) in the lake waters of Lake Allos compared to other records: oxygen isotope ratios in precipitation (δ 18 O p , ‰ VSMOW) based on the record of Lake Ammersee (Germany; von[START_REF] Von Von Grafenstein | A mid-European decadal isotope-climate record from 15,500 to 5000 years[END_REF]; Lake Ghirla plant wax (δD, ‰ SMOW) at the foot of the Southern Alps[START_REF] Wirth | Plant-wax D/H ratios in the southern European Alps record multiple aspects of climate variability[END_REF]; oxygen isotope record (δ 18 O, ‰ VPDB) of Corchia Cave CC26 (Northern Italy;[START_REF] Zanchetta | Enhanced rainfall in the western Mediterranean during deposition of sapropel S1: stalagmite evidence from Corchia cave (Central Italy)[END_REF]; lakelevel fluctuations (m) at Accesa (Italy;[START_REF] Magny | Holocene climate changes in the central Mediterranean as recorded by lake-level fluctuations at Lake Accesa (Tuscany, Italy)[END_REF]; lake level reconstruction at Preola (Southern Italy;[START_REF] Magny | Holocene hydrological changes in south-western Mediterranean as recorded by lake-level fluctuations at Lago Preola, a coastal lake in southern Sicily, Italy[END_REF]. Locations of the sites are shown on Fig. 1. Ages of endmoraine and polished bedrock (Maritime Alps) dated by 10 Be and 14 C methods are from: (1) Spagnolo and Ribolini (2019); (2) Darnault et al. (2012); (3) Federici et al. (2008); (4) Ribolini et al. (2007); and (5) Federici and Stefanini (2001). [Color figure can be viewed at wileyonlinelibrary.com]

Figure 7 .

 7 Figure 7. Estimated δ 18 O (δ 18 O lw , ‰ VSMOW) in Allos' lake waters for the last 3000 years compared to global signatures of the Medieval Climate Anomaly (MCA) and Little Ice Age (LIA)[START_REF] Mann | Global signatures and dynamical origins of the little ice age and medieval climate anomaly[END_REF], glacial advances at Aletsch in Switzerland[START_REF] Holzhauser | Glacier and lake-level variations in west-central Europe over the last 3500 years[END_REF], torrential deposits in Southern French Alps[START_REF] Sivan | Rythmes de la sédimentation et interprétations paléoclimatiques lors du Postglaciaire (Alpes du Sud) 14c et dendro-géomorphologie, deux chronomètres complémentaires[END_REF] and temperature anomalies reconstructed from dendrochronological data[START_REF] Corona | Long-term summer (AD 751-2008) temperature fluctuation in the French Alps based on treering data[END_REF]. [Color figure can be viewed at wileyonlinelibrary.com]

  18 O sp values (‰ VPDB) were converted to the SMOW scale using the equation of[START_REF] Coplen | Comparison of stable isotope reference samples[END_REF]

	e where δ 18 O δ 2 ;4 18 18 18 18 18 where Δ 18 O e is the enrichment by evaporation (considered δ ( )= * ( )+ O VSMOW O VPDB 1, 0309 30.9 18 18 negligeable at Lake Allos) and Δ 18 O (C-H 2 O; 4 °C) is the isotope fractionation equilibrium between calcite and water at 4 °C = 32.635 on the SMOW scale, calculated from the following equation with T = temperature in K (Kim and O'Neil, 1997): ∆ α ( -°) = ( ) = O C H O C ln 2 ; 4 1000 18.03 18 ( ) * -T 32.42 10 3

w is the oxygen isotope ratio in lake waters (‰ VSMOW), δ 18 O sp is the oxygen isotope ratio in ostracods and Δ 18 O vo is vital offset; ostracods enriched by +1.49 ± 0.16 ‰ compared to an equilibrium calcite. After subtraction of the vital effect, δ

  (used by von Grafenstein et al., 1999 to calculate the vital effect of C. lacustris) and[START_REF] Friedman | Compilation of stable isotope fractionation factors of geochemical interest[END_REF] (Decrouy et al., 2011).

Acknowledgements. We thank C. Vallet-Coulomb (CEREGE, France) and the British Geological Survey (UK) for the oxygen isotope analysis of modern waters. Thanks go to D. Sabatier (CEREGE, France) for providing material for picking ostracods and to H. Bruneton for her valuable help with ostracod determination. Many thanks to O. Laurent and M.-F. Leccia from the National Park of Mercantour for their support and sampling of modern waters. Thanks to R. Pickering for rereading the manuscript. The PhD thesis of R. Cartier (Aix-Marseille University) was funded by the 'Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation'. Several projects supported the research work: Programme d'Intérêt Transfrontalier (Parc National du Mercantour, France) led by F. Suméra (SRA-PACA) entitled 'Etude de l'usage et de l'occupation du sol et du territoire Mercantour', and the project LADICIA, 'Quand l'homme et le climat façonnent la montagne méridionale: le Lac d'Allos, une histoire du Détritisme, des Instabilités Climatiques et des Impacts Anthropiques' (Région PACA, ref. 2010_08_012) led by C. Miramont (IMBE).

Abbreviations. LIA, Little Ice Age; MCA, Medieval Climate Anomaly; NAO, North Atlantic Oscillation; YD, Younger Dryas..

Supporting information

Additional supporting information can be found in the online version of this article.This article includes online-only Supplemental Data.