Gerhard Schaden
email: gerhard.schaden@gmx.net

The Evolution of Lexical Usage Profiles in Social Networks

is paper investigates how network structure in uences the outcomes of reinforcement learning in a series of multi-agent simulations. Its basic results are the following: i) contact between agents in networks creates similarity in the usage patterns of the signals these agents use; ii) in case of complete networks, the bigger the network, the smaller the lexical di erentiation; and iii) in networks consisting of linked cliques, the distance between usage patterns re ects on average the structure of the network.

See the Trésor de la Langue française informatisé (http://atilf.atilf.fr), entry .

Jede Veränderung des Sprachusus ist ein Produkt aus den spontanen Trieben der einzelnen Individuen einerseits und den [. . . ] Verkehrsverhältnissen andererseits.

is was pointed out to me by Sylvain Billiard (p.c.). I would like to thank one of

Introduction

Lexical Variation, Lexical Change

Lexical variation and change are pervasive phenomena in natural languages. Contrary to grammatical change -o en assumed to be unidirectional, and predictable (see, e.g. Haspelmath, ) -lexical change is typically messy. It depends on speci c historical contexts, new technological inventions, and probably, to a certain degree, also on random events. is can be illustrated by one particular example of lexical shi and variation in French, namely voiture, which is today most commonly used to designate motorized vehicles for personal transportation. Notice that voiture is not a newly created lexical item; the word existed and referred in former times to (horse-drawn) carriages, a meaning that is still present in current French. A er a period of variation at the beginning of the th century, when self-propelled vehicles were referred to as voiture automobile, automobile or auto, Metropolitan French settled for the older, and shorter, voiture. German was confronted with the same problem and settled for Auto. e phenomenon was triggered by the introduction of a new technology, and is therefore an example of external change. e question arises as to whether this instance of lexical change should be considered a change in lexical meaning. A er all, even though the prototypical use in the speech community is clearly di erent today (shi ing from horse-propelled to self-propelled instances), it is not clear whether the meaning of the word as such has changed, since its former meaning remains available.

One may want to argue that initially, voiture had to extend its meaning, since it accommodated for a new referent. However, even this is far from clear: had something like horse-drawn been part of the original meaning, adding an adjective such as ''automobile'' should have led to a contradiction: no vehicle can be self-propelled and horse-drawn at the same time. Yet, be that as it may, it is clear enough that a semantic change may be under way, since horse-drawn carriages are extremely rare nowadays, and, should they disappear, the meaning of voiture would likely follow suit.

Summing up, the case of voiture illustrates a case that may very well not be a change in semantic meaning at all, triggered by a purely external cause, and possibly randomly.

e question is whether we should bother to investigate such instances at all, given the importance of all sorts of language-external noise involved in it. Linguists have mainly focused on regular types of linguistic change (such as grammaticalization), where random processes can be by and large neglected. Now, while it is true that individual cases of lexical meaning change o en seem random, and may well turn out to be random, there are patterns to lexical change as well. For instance, change is not saltationist (a word meaning horse today is very unlikely to mean pencil tomorrow), and change generally occurs along patterns of polysemy. Other factors that have been identi ed are the imitation of prestigious individuals (see Chudek et al., ). One of the main points that make such a pattern interesting and worthwhile to investigate is that, in order to ascertain what kinds of changes are not random, we need to understand the e ects of randomness in language use and change, for instance, when, where and how it in uences lexical change. In genetics, the e ect of genetic dri (random change, not a ected by natural selection) is recognized to be important, and it would be similarly important to know the e ects of random change on natural languages -a phenomenon that one may call linguistic dri . ere have been e orts modeling phenomena of cultural evolution in terms of dri (see, e.g., Han and Bentley, ; Reali and Gri ths, b; Gri ths and Reali, ; Bentley et al., ) , and the present paper aims to make a contribution towards furthering the comprehension of lexical dri .

Individually, instances of lexical meaning change may be anecdotic, but the phenomenon tells us something about the nature of language and how it is shaped: Language is a product of social consensus.

Learning as a Social Fact

Compared to our primate cousins, Humans are an intensely social and cooperative species. is has also consequences for language, and that on several levels: one basic fact on language is that it is acquired and used in social contexts (more precisely, in social networks).

e importance of social networks for natural language and its change has been recognized from early on. For instance, Hermann Paul wrote the following in his Prinzipien der Sprachgeschichte:

It is very tempting to interpret this quote in the light of recent theoretical developements, namely game theory (investigating the spontaneous drives of individuals) and network analysis (investigating the structure of lines of communication between individuals). In any case, linguists have started bringing these models together to study the interaction of language learning, change and di usion (see Smith et al., ; Benz et al., ; Mühlenbernd and Franke, ). Fagyal et al. (

) have shown that network structure is important for the uctuations of norms within a language; whereas Pierrehumbert et al. (

) provide a model showing that average-connected agents are the most likely source of successful innovation (as opposed to the highly connected members of an elite).

e basic aim of this paper is to investigate the implications of the fact that learning language necessarily takes place within a social setting. In order to do that, I will try to eliminate other potential in uences -like individual preferences of agents, etc. -as much as possible.

One major question will be whether learning depends on the structure and size of the network the learners are engaged in. I will investigate what the impact of learning is in a network with respect to di erenciation/homogeneity. e usual issue in research on learning in networks (e.g., DeGroot models, see Jackson, :

.) is the emergence of consensus in an initially diverse population (this is also true to some degree for the question of the emergence of norms in Fagyal et al., and Pierrehumbert et al., ). e isssue I am interested in here is rather the emergence of (lexical) di erenciation in an initially perfectly homogeneous population.

e study uses multi-agent simulations in circumstances where there is no right thing to learn, and thus, where there are no linguistic/social constraints on the use of variant forms that could alter the impact of pure randomness in a networked setting. All outcomes will be based on patterns of preferential use.

I will study not meaning change per se, but rather the changes in what I will call the Lexical Usage Pro les of networked agents. Assuming two words without any linguistic or social constraints that di erentiate them in a given context, the Lexical Usage Pro le is the probabilistic usage pattern associated by an Agent with these words (for instance, (s)he could use word with probability . , and word with probability . ). is notion of Lexical Usage Pro le will be made explicit below, in ( ), p. . In a sense, this pro le is about performance or pragmatics, and not about semantics or competence. However, it is easy to see that in a population where new agents enter the scene and old ones die, biased usage pro les might lead to the loss of one word, and therefore, in some con gurations considered below, to meaning change.

An important background issue of this paper is the question of the importance of usage-based factors on language and language change (frequency, etc.). While I will not directly provide an answer to this issue, the results presented here suggest that they indeed matter.

e methodology at work in this paper uses multi-agent simulations. As pointed out by Gilbert ( : ), ''[i]n most of the social sciences, conducting experiments is impossible or undesirable''. In order to see his point, consider the di culty of isolating a relevant subsystem of persons. Even if this could be resolved, we would still need to set up a control group. Controling and isolating the relevant variables would be di cult at best, and a real-world experiment dealing with the linguistic evolution of a population in a given setting might last far too long to be sustainable.

One possible solution to this problem is to experiment not on a group of people from the real world, but rather on a model. is has the advantages that the interaction of programmed agents does not pose ethical problems, and that properties of agents can be de ned as needed. For our case, it means that we can create agents without any preferences, and which act truly at random. However, multi-agent simulations are not without problems: rstly, we need to make sure that the model is close enough to the empirical phenomenon we are interested in, and secondly, that the model is simple enough to isolate causal factors. While ideally a model should conform to both requirements, these are also to some point inherently in con ict.

Let us now move to some required terminology with respect to social networks.

Social Networks

A social network is a structure representing agents and their interactions. Di erent kinds of networks model di erent types of interactions between agents. In some cases, we are only interested in the fact whether a link between two agents exists or not; in other cases, we want to compare the di ering strengths of links between agents (unweighted vs. weighted networks). In some cases, a link is symmetrical (for instance, in friendships), in some cases, it is not (which opposes symmetrical graphs and directed digraphs). e di erent combinations of these two properties are illustrated in gure .

Depending on the kind of interaction between agents one is interested in, di erent kinds of networks can be used. In our case, an act of communication between a speaker and a hearer is most easily modeled as a digraph, since it is an asymetrical kind of interaction, where participants have clearly de ned, and non-identical, roles. In what follows, I will mostly use weighted digraphs, since adding weights provides an easy way of representing turns of speaking.

Apart from the kind of links between agents, the overall structure of a network will also turn out to be important. For our purposes here, we will examine more closely two types of structure, namely complete networks and cliques.

A complete network is a network where all possible edges are present. In other words, every node is connected to every other node. is is illustrated for a graph on the le diagram in gure .

For a formal de nition, see Jackson ( : .). e second type of con guration we will study are cliques, which are maximal completely connected subnetworks of a given network. In gure , on the right side, nodes ABC form one clique, and nodes DEFG form another. One can imagine a clique as being a complete network that is a subpart of another network.

In this paper, we will study reinforcement learning in complete networks (of varying sizes), and in cliques connected to other cliques by bridges, that is, links whose absence would lead the graph to decompose into several, unconnected components.

Having now introduced networks, the remainder of the paper is structured as follows. In section , we will introduce reinforcement learning and its e ects on lexical use and meaning. In section , we will consider what might change if learning takes place in a complete network, and section will investigate the outcome of reinforcement learning in the con guration of networks consisting of linked cliques.

Reinforcement Learning

Reinforcement Learning refers to a family of learning algorithms, and is one of the standard techniques in machine learning. It is modeled on behaviorist psychology, where learning is seen as the shi (typically: augmentation) of the probability of some behavior in a given agent.

Reinforcement Learning: Polya-Urns

Polya-urn processes provide a mathematical model of reinforcement learning. It corresponds to a random-draw from an urn. Contrary to other types of urns, if the answer is correct, not only is the ball returned into the urn, but some quantity of the same balls will be added to the urn. Let us consider an example: is is not the only possible model of reinforcement learning, but it happens to be one of the simplest, and one that does not drive one alternative into virtual oblivion too fast. URN t+ white: red:

At time t, corresponding to the beginning of the process, the urn contains one ball for each color. ese are the inclination weights. en, a ball is drawn at random (here, it happens to be the white ball). Assuming that white is the correct answer, white will be reinforced. is is done by adding an additional white ball -the reward -to the urn. e reward insures that the appropriate answers rises in probability. Whereas the initial probability of drawing white at t was only . , this probability has risen to . ˙ at t + .

e system will converge in the limit to a point where the appropriate answer is the only one. As gure shows, the speed of learning depends on the initial inclination weight (one may see higher inclination weights as higher con dence of the learner that both options are actually correct).

A general feature of reinforcement learning of this particular kind is that learning is initially fast, and then becomes gradually slower. at means that reinforcement learning obeys the Law of Practice, which is a general feature of human learning (see Skyrms, : ). e particular version of Polya-urn-based reinforcement learning used here has the additional advantage that it is variation-friendly, that is, it will not drive into extinction one alternative too fast.

Finally, reinforcement learning can provide a formalisation of priming and entrenchment. All these properties are desirable and can explain why reinforcement learning is popular, and why we want to adopt it in our simulations.

Although, in this setting, the initial weight of is never removed, as time progresses, and if reinforcement is consequent, the probability of drawing white will approach , since limn→∞ n n+ = . In other words, it has a bias against regularization.

Reinforcement Learning When There is Nothing To Learn

e setup I will consider here is a con guration where there is nothing to learn, that is, where both answers (or, more generally, all answers) are appropriate, and will be reinforced. is is something Skyrms (

) has explored in some detail. From a linguistic point of view, this might model a situation where two words are absolute synonyms. However, such a strong constraint is not necessary; it su ces that the context does not support a di erence between words (see Schaden, ). In such a case, the frequencies may shi around wildly, and chance (together with the impact of reinforcement learning) is the only in uence on the system.

As was shown in Schaden ( ), the outcome of the process is dependent on the ratio between inclination weights and the reward. e higher the inclination weights with respect to the reward, the more the probabilities of drawing one word or the other cluster around . -which means that both words are used with roughly equal frequency. Yet, the smaller the inclination weights with respect to the reward, the more probability mass will cluster towards and . is means that one or the other of the two words will have become dominant.

is pattern is interesting because the farther we move away from the area of the central . frequency, the more a word is fragile with respect to environmental changes or pragmatic reinterpretations.

Up to now, we have considered a word to be a monolithic entity, with a clear and uni ed sense. However, this may not be very realistic an assumption if we take into account polysemy, and it is not convenient for our simulations.

Simulating Change of Internally Differentiated Concepts

In what follows, I will assume internally di erentiated concepts, and more precisely, something like Pustejovsky's qualia-structure. Pustejovsky's basic assumption is that the (linguistic) meanings of words are far more complicated than what is o en assumed in (formal) semantics, and that many elements of what is o en thought of as encyclopedic knowledge are actually part of the linguistic meaning of a word. For instance, Pustejovsky assumes that words denoting objects have four qualia, or submeanings , which specify the denoted objects shape, material, function, etc. While one does not need to accept this speci c framework for dealing with polysemy, the basic ontological commitment my simulation requires is the existence of independently ponderable submeanings.

is move has several reasons: rstly, it considerably facilitates dealing with shi s of prototypical meaning. And secondly, from the empirical point of view, meaning shi s generally follow patterns of polysemy, and thus, some theory of polysemy (like the generative lexicon) is required anyway.

I will take a very simpli ed approach to polysemy. In the simulations, I will merely assume that every word consists of four independently ponderable lexical meanings, as illustrated in ( ):

As pointed out by one of the reviewers, such models are also related to the literature on regularization or absence of regularization of linguistic forms (see, e.g., Reali and Gri ths, a; Pijpops et al.,

). I will henceforth use the word ''quale'' as a synonym for submeaning. As far as I see, this commitment is not tied to a particular framework in the generative or functional tradition.

e precise number of submeanings has no real importance, and is rather a choice of convenience. I have adopted four submeanings because these are the number of qualias in Pustejovsky (

). Each submeaning forms an independent Polya-Urn. Nature chooses some submeaning at random, and a submeaning has to be matched by either Word or Word . e chosen word will then be reinforced at that particular submeaning/quale. e outcome of such processes is shown in gure , where I have plotted on the le side a sample outcome with an initial weight of . As one can see here, the speaker will use Word with a frequency of around . for submeanings , and , whereas with respect to submeaning , Word is dominant in about the same proportion. On the right side, I plotted a more global view in the simulation trials of what happens with di erent kinds of inclination weights with respect to the absolute di erences in weights in submeanings.

Quale1

I should stress once again that what has changed throughout these trials is not the lexical meaning in itself, but rather the frequency of usage associated with each word at a given submeaning. e outcome of reinforcement learning is an array of numbers, representing the (probabilistic) Lexical Usage Pro le of an agent. is is illustrated in ( ).

( )

W Q W Q W Q W Q W Q W Q W Q W Q Ag Ag Ag
e numbers in ( ) have been chosen for illustration purposes, and are extremely unlikely to show up in an actual simulation.

W1Q1 W 1 Q 2 W1Q3 W 1 Q 4 W2Q1 W 2 Q 2 W2Q3 W 2 Q 4 Agent 1 W1Q1 W 1 Q 2 W1Q3 W 1 Q 4 W2Q1 W 2 Q 2 W2Q3 W 2 Q 4 Agent 2 W1Q1 W 1 Q 2 W1Q3 W 1 Q 4 W2Q1 W 2 Q 2 W2Q3 W 2 Q 4
Agent 3 In order to get the probability of choosing a word for a speci ng submeaning (say Quale ), we need to compare the weights of that quale in Word , with the weight in Word . . Agent illustrates a case where all submeanings of both words have been reinforced exactly to the same degree. erefore, at the next turn, Agent will use any word for any submeaning with a probability of . . Agent illustrates the case where for submeanings -, Word has always been reinforced; whereas for submeaning , Word has been exclusively reinforced. erefore, Agent will choose near deterministically (with a probability of ≈ .

) Word for submeanings -, and with the same probability Word for submeaning .

A convenient way of plotting such Lexical Usage Pro les (which I will use below for comparison) are spiderplots, as illustrated in gure for the three agents in ( ).

Learning in Networks

So far, we have considered learning in isolation of a social setting. is might represent a single agent remaining all alone. Alternatively, it could also represent an agent in a network where all signaling is public, that is, where all communication is targeted to all other members in a network, and where the speaker reinforces himself just like all the other hearers do. ese are, however, very unrealistic assumptions, since not all communication is directed to the general public. erefore, the question arises whether the fact of agents being members of a network will change the dynamics and outcome of the learning -just as the inclination weight of the agents did before.

I will show that this is precisely the case.

Learning in Networks: General Algorithm

e algorithm used for the simulations in this paper is round-based. It can be illustrated as follows.

. Take some weighted digraph.

. Choose an edge uniformly at random.

More precisely, in order to know what the probability is to draw W for submeaning Q , we need to calculate

W Q W Q +W Q , which, for Agent in ( ), is: + = .
Agent e agent located at the tail node of the edge signals to the agent located at the head node of the edge, according to the signal chosen uniformly at random by Nature, and according to the tail node agent's weights for the chosen submeaning.

a) update the lexical representation of the head node agent. b) update the lexical representation of the tail node agent (if self-reinforcement is in place). . Decrease the weight of the edge by a) if the weight of the edge= a er decrementing, remove it; b) otherwise, repeat the procedure from step with the resulting network. . Repeat until no edge remains; end of turn. . Performk times on the weighted digraph Since this algorithm depends strongly on random elements (order of the edges, choice of the submeanings, probabilistic choice of the word by signaler), every simulation has been repeated times, in order to obtain a representative sample of possible outcomes.

Learning in Complete Networks

e rst setup we will consider is signaling in complete networks, where all edge-weights are the same. erefore, every agent will signal and receive signals exactly the same number of times.

One of the clearest, and maybe, at rst sight, most surprising consequences of agents learning in a complete network is that it creates uniformity among the agents' lexical usage pro les. is is illustrated in gure for a complete network with agents. What the nal pro les look like cannot be predicted, since the process is guided by chance; however, the outcome that the members of a complete network all look alike is a constant pattern, regardless of the number of agents in the network.

Figure presents this in a rather intuitive way; we will look below for a way of better measuring similarity/dissimilarity across agents in a network. Interestingly, it turns out that there is an interaction between the size of the network and the degree of di erentiation that is created.

To start with, let us de ne the di erentiation of two words with respect to a given submeaning, or a ponderable lexical component (henceforth abbreviated as lc and subscripted with an index):

Decreasing the edge-weight by one (as well as removing -weighted edges) makes sure that an edge-weight of n corresponds to n interactions between the agents.

( ) Lexical di erentiation between Word and Word with respect to some ponderable submeaning l c i = def (lc i (Word ) -lc i (Word )) the absolute di erence between the ponderable lexical components of a word Let me repeat why lexical di erentiation is interesting for us in the context of lexical meaning change over time. While in our setup no (sub)meaning will ever be completely forgotten (because technically, no ball will ever be removed from the Polya-urn), the same is not true in real life.

Clearly, a word that is hardly ever used for some meaning is not very likely to make it into the next generation's lexicon. Let us now consider two extreme cases in relation with lexical di erentiation: rst, where lexical di erentiation is zero, and another one where it approaches in nity. A lexical di erentiation of zero means that both words have the same weight for the given submeaning, which means that they are equally likely to be chosen in order to describe the state of a airs corresponding to this submeaning. is corresponds to a situation where both words are used with the same frequency. erefore, transmission to the next generation for both words with respect to the submeaning can be taken for granted.

Let us consider the case where lexical di erentiation is very large. Under such circumstances, one word is chosen nearly all the time, and the other is hardly ever (or never) recruited to express that particular submeaning. is means that there is little chance for a new member of the language community to be ever exposed to that word for that meaning, and, therefore, to learn that it can be used to express this meaning. us, while lexical di erentiation does not directly correspond to meaning change, strong lexical di erentiation can be seen as a prerequisite or as a fore-runner for meaning change (that is, change not only a ecting performance-related aspects of language use, but competence).

We had seen above that -in a non-networked setting -the di erentiation between the two words depended on the inclination weights. It turns out that there is an impact of network size as well. If we keep stable the number of reinforcements per agent, the bigger the network, the less di erentiated the submeanings of Word and Word .

Furthermore, there is also a clearly discernable in uence of self-reinforcement: at constant network size, if the speaker reinforces his own lexical representation a er speaking, lexical di erentiation is bigger than without.

Why should this be so? Remember from what we have seen in section , that in cases of reinforcement learning, the initial tendency is very important, and in the beginning, the system quickly shi s away from the y-y initial conditions. Consider for instance a three-agent complete network, where speakers reinforce themselves. A er the rst signaling turn, two out of the three agents will have one word reinforced at the same submeaning. So, the next time that submeaning is drawn, there is a chance that the speaker has already been reinforced for one of the two words, and if one out of these two agents is drawn, the probability that the same word will be reinforced will be . On the other hand, there is a chance that the not-reinforced agent will be drawn, and then, the chance that the other word will be reinforced is .

Let us now consider the same process in a network with agents, and without self-reinforcement. A er one submeaning has been chosen for one word, there is only chance that the next time the submeaning is drawn, the speaker will already have been reinforced at this place. So, there are at means, if we consider cases where an agent invariably receives in one simulation run n reinforcements, whether he is in a network with other or other agents. e e ect of network size (and self-reinforcement) is thus the following: the bigger the network, and without self-reinforcement, the smaller the probability of choosing in all agents consistently the same word for a given submeaning. us, network size (in the case of complete networks) does in uence the kind of lexical di erentiation one can expect.

is also means that smaller-sized (complete) networks have a tendency to evolve faster, and to show bigger degrees of lexical di erentiation, while bigger networks show a tendency to maintain the initial status quo, and have less tendency to show extreme degrees of lexical di erentiation.

Can we extrapolate this result directly to human networks, and actual languages spoken in real-life communities? Although there are claims about (what one can interprete as) the relation between network structure and language structure (see, e.g., Kusters, , ), the present result does not carry over to existing human communities that easily, because these tend to have a di erent network structure.

According to Sutcli e et al. ( ), a typical human being is engaged in the following circles of network-relations (with their approximate basic sizes): (i) the active network of individuals that we know as persons and with whom we have reciprocated, personalized relationships that have a history (of about individuals; known in the ethnographic litterature as clan) (ii) the a nity group (or band, of around individuals) (iii) the sympathy group, with whom we have routine ties (numbering -individuals) (iv) the support clique, that is, people with which we have intimate ties ( -individuals). us, the overall network in which a human being evolves is not a complete network, which simply means that not all people that an individual has ties with are acquainted with each other.

Learning in Linked Cliques

While I will not investigate naturalistic networks, we can draw the conclusion that ''normal'' language communities are not built up as complete networks (at least for not acutely endangered languages). However, cliques are important subnetworks, and Mühlenbernd and Franke ( ) have shown that in language acquisition, they have an important role to play.

I have investigated a very simple setup, where two or three same-sized cliques are linked by bridges (see gure ). e edges within the clique are stronger than the edges between cliques.

is can be seen as the e ect of more costly interaction between cliques, than within cliques; one simple way of imagining this scenario are islands, where contact across islands is more limited than contact within islands.

In our setup, there is always only one agent that is in contact with the other clique(s). Now, the question is: does lexical di erentiation mirror the network structure?

We will rst look at cases with two linked cliques, and then, at three linked cliques.

Cases with Two Linked Cliques

Let us start by taking a very impressionistic rst look at the lexical usage pro les graphed as spiderplots, as in gure . Each line depicts a single simulation run, where the rst three agents belong to one clique, and the other three to another. It is quite obvious that within a clique, the agents always have very similar lexical usage pro les, whereas, if we compare two agents coming from di erent cliques, there is not necessarily any similarity. Notice however, that there is no intrinsic tendency to establish di erentiation across cliques; the pro les in simulation run n° are extremely similar in both cliques.

Yet, if we want to see the bigger picture, we need to have a better means of establishing a lexical proximity metric. We will take a very simple measure for the lexical distance between two words: we will simply add up the lexical di erentiation (i.e., the absolute di erence) for each pondered lexical component (or lc): Let us reexamine our rst two agents from ( ), on p. .

W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 1 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 2 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 3 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 4 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 5 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 6 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 1 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 2 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 3 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 4 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 5 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 6 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 1 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 2 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 3 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 4 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 5 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 6 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 1 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 2 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 3 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 4 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 5 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 6 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 1 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 2 W1Q1 W 1Q 2 W1Q3 W 1Q 4 W2Q1 W 2Q 2 W2Q3 W 2Q 4 Agent 3 W1Q1 W 1Q 2 W1Q3 W 1Q 4
( ) W Q W Q W Q W Q W Q W Q W Q W Q Ag Ag l ci (Ag ) -l ci (Ag )
Summing the numbers from the last line gives us LD(Ag , Ag ) = . Notice that this way of calculating distance is sensitive to the number of reinforcements an agent has received. For instance, if an agent A was identical to agent B, but if all its ponderations where ten times higher, there would be a great lexical distance, even though their observable behavior would be identical (at least, if ponderations are su ciently big not to be in uenced too much by the adding of ).

erefore, the ponderations need to be scaled in case of unequal number of reinforcements per agent.

In gure , we have represented the outcomes of simulation trials with two -agent cliques, e actual ponderation I used was to multiply each term of the formula by the minimum amount of global reinforcements an agent of the network had received, divided by the global amount of reinforcements that particular agent had received, or:

LD(Ag o , Ag p ) = k i= l ci (Ago) × mgr ∑ m i= l ci (Ag o ) -l ci (Agp) × mgr ∑ m i= l ci (Ag p )
, where

mgr = min ( m i= l ci (Ag ), . . . , m i= l ci (Ag j ))
is way, if the agent has received only the minimum amount of reinforcements, the number of reinforcements at his/her lexical components will not be altered; if (s)he has been reinforced more o en, that number will be scaled down. with an in-clique edge-weight of (the underlying network is depicted on the right). Di erent colors represent di erent types of distances between agents. e rst one, labeled PIC for Purely In-Clique, corresponds to the distances between agents in the same clique, and where no agent is in direct contact with a member of the other clique. e next category is labeled IWC -In-clique With Contact -and concerns agents in the same clique, but where one agent is in direct contact with the other clique. On average, the lexical distance is larger than in the PIC-group, but the distance is small, with little spread, compared to the remaining categories. e next category is DCA (or Direct Contact Agents, here Agent and Agent ), who belong to di erent cliques but who are in direct contact. eir lexical distance is much bigger, with much greater spread, but it is on average less than the distance between other cross-clique relationships. CCWC (Cross-clique With Contact) combines cases where agents belong to di erent cliques, do not have direct contact with one another, but where one of the agents is in direct contact with the other clique. On average, their lexical distance is greater than with direct contact agents, but it is less than if none of the two agents had any contact whatsoever with the other group (which is the category PCC, or Purely Cross-Clique).

e same picture obtains if we look at the outcome of simulation trials with two -agent cliques, with an in-clique edge-weight of , as in gure . We have the same pattern of small lexical distance within a clique, and greater distance across-cliques, with graduations given the amount of contact individual agents had.

Cases with Three Linked Cliques

In the cases with two linked cliques, the main di erence was between intra-clique and inter-clique relations. Does this carry over to cases with three linked cliques? Figure shows that the crossclique category no longer behaves in a homogeneous way, and that there is another factor that has to be taken into account, namely distance between the cliques.

e key observation is the following: the clique formed by Agents -is in direct contact with the clique formed by Agents -, but they are in touch with the clique of agents -only through Agent . Once we order by clique distance and by the type of contact, things fall into place, and we DiffAg5Ag17 What could be the reasons for this outcome? My guess would be as follows.

e more agents per clique, the smaller the impact of the cross-clique contacts. erefore, the impact of the contact with another clique simply gets swamped by the mass of reinforcements that happen within the clique. It is probably this (limited, but continuous) cross-clique contact that reduces the lexical distance between adjacent cliques. If agents live forever, and clique size becomes very big, I would therefore expect adjacency between cliques to get less and less important.

e pattern obtained in this section for smaller clique-sizes seems to be able to account for phenomena like the development of dialect continua, where linguistic di erences are small in adjacent populations, but get more and more important as populations become separated. But can we extrapolate this result to human societies? Arguably, clique size is not unlimited in human agents (see Sutcli e et al.,

), and we are clearly not immortal. erefore, the basic results obtained in the simulations should carry over to real populations. However, I should iterate once again the central nding when studying complete networks: while contact creates similarity, absence of contact does not create per se dissimilarity; it only makes it improbable that, in the absence of selectional processes, two populations develop in the same direction. erefore, even if the simulations predict that actual populations that are connected by bridges should be divergent at opposite ends of a network most of the time, this is not a necessary outcome.

To conclude this section, let us take stock of what this paper has shown, and to what degree this is relevant for the sociology and long-term consequences of agents learning a language in a social network. e experimental set-up is highly idealized, and has considered agents without desires, aims, or preferences, whose lexical choices are exclusively determined by the result of reinforcement learning, and are random.

e experimental conditions also investigated only highly simpli ed types of network con gurations, which do not apply to humans living ''in the Ideally, if we could study the limit-behavior of this system mathematically, this issue would be simply a matter of calculation. However, as it stands, the simulation has properties which make it di cult to deal with mathematically, the most severe being that it is not a Markov-chain process. is means that the future state of the system cannot be wholly determined from the current state alone, and without knowing how the present state has been attained. As pointed out by Sylvain Billiard (p.c.), there is a way of transforming the experimental setup into a Markov-chain process, and preliminary results indicate that at least for complete networks, the outcomes are the same. However, it is not clear as of yet whether this identity of outcomes carries over to arbitrary networks.

wild''. Yet, these idealizations provided us with a way of examining the impact of network structure, which was the only element that varied through the di erent experimental conditions. us, this paper has shown that the following patterns obtain in relation with linked cliques: i) within-clique di erences are smaller if none of the agents involved has direct contact with members of other cliques; ii) within-clique di erences with a contact agent are smaller if the contact agent is in contact with only one member of another clique; iii) cross-clique di erences are smallest when both agents are in direct contact with one another; and iv) cross-clique di erences increase with the distance between the cliques the agents belong to.

Conclusions and Perspectives

In this paper, I have studied the importance of network structure in acquisition and use of lexical items. We have seen that the size of complete networks has an impact on the outcome of learning, and more precisely, on lexical di erentiation. We have also seen that network structure and distance have a direct repercussion on the similarity pro les of the agents in the network (dialect continua, etc.).

As such, this paper has tried to provide a contribution to the phenomenon of lexical dri , that is, lexical change that is not caused by any type of functional or adaptive pressure, as driven by the structure of the social network the learners are engaged in. Other kinds of in uences are certainly at work as well, as for instance production and learning biases. erefore, the results obtained here can provide us with a benchmark against which we can evaluate the claims that some other in uence had an impact on certain types of historical developments, and which are not reducible to mere randomness.

An important limitation of the present paper concerns the types of network investigated, which were of a highly idealized sort. In future work, it will have to be checked whether and to what degree these results carry over to networks satisfying the characteristics of standard real-life Human communication networks (as investigated by Sutcli e et al.,

).

Figure :

 : Figure : Di erent Kinds of Social Networks (from le to right): unweighted graph, weighted graph, unweighted digraph, weighted digraph

Figure :

 : Figure : Structural Con gurations of Networks: Complete Network and Cliques within a Network

  Figure : Speed of learning depends on Inclination Weights

  Figure : Outcomes of Reinforcement Process

Figure :

 : Figure : Spiderplots of the Lexical Usage Pro les of the Agents in ( )

Figure :

 : Figure : Increasing Network Size and Decreasing Lexical Di erentiation

Figure :

 : Figure : Cliques of Equal Size, Linked by Bridges

Figure :

 : Figure : Agents Within Cliques Look Alike; Agents in Di erent Cliques Mostly Di er

Figure :

 : Figure : Linked Cliques -Lexical Distance and Network Distance

Acknowledgements

I had the opportunity to present preliminary versions of this paper at the Séminaire des linguistes of the UMR STL, and at the Yearly Meeting of the Belgian Linguists' Association, and I would like to thank the organizers and the audience for their feedback and criticism. I would also like to thank the two anonymous reviewers, as well as Sylvain Billiard and Cédric Patin for their comments on previous versions of this paper. Finally, Katia Paykin helped me with my English. None of them should be assumed to agree with anything I wrote in this paper; all errors and omissions are mine alone.

e simulations have been performed with sbcl Common Lisp, using the graph-library by Eric Schulte (https://github.com/eschulte/graph). Networks have been drawn with graphviz (Gansner and North, ). Data analysis has been performed with GNU R.

DiffAg1Ag3 DiffAg1Ag4 DiffAg1Ag5 DiffAg2Ag3 DiffAg2Ag4 DiffAg2Ag5 DiffAg3Ag4 DiffAg3Ag5 DiffAg4Ag5 DiffAg7Ag8 DiffAg7Ag9 DiffAg7Ag10 DiffAg7Ag11 DiffAg8Ag9 DiffAg8Ag10 DiffAg8Ag11 DiffAg9Ag10 DiffAg9Ag11 DiffAg10Ag11 DiffAg13Ag14 DiffAg13Ag15 DiffAg13Ag16 DiffAg13Ag17 DiffAg14Ag15 DiffAg14Ag16 DiffAg14Ag17 DiffAg15Ag16 DiffAg15Ag17 DiffAg16Ag17 DiffAg1Ag6 DiffAg2Ag6 DiffAg3Ag6 DiffAg4Ag6 DiffAg5Ag6 DiffAg7Ag12 DiffAg8Ag12 DiffAg9Ag12 DiffAg10Ag12 DiffAg11Ag12 DiffAg13Ag18 DiffAg14Ag18 DiffAg15Ag18 DiffAg16Ag18 DiffAg17Ag18 DiffAg6Ag12 DiffAg12Ag18 DiffAg1Ag12 DiffAg2Ag12 DiffAg3Ag12 DiffAg4Ag12 DiffAg5Ag12 DiffAg6Ag7 DiffAg6Ag8 DiffAg6Ag9 DiffAg6Ag10 DiffAg6Ag11 DiffAg7Ag18 DiffAg8Ag18 DiffAg9Ag18 DiffAg10Ag18 DiffAg11Ag18 DiffAg12Ag13 DiffAg12Ag14 DiffAg12Ag15 DiffAg12Ag16 DiffAg12Ag17 DiffAg1Ag7 DiffAg1Ag8 DiffAg1Ag9 DiffAg1Ag10 DiffAg1Ag11 DiffAg2Ag7 DiffAg2Ag8 DiffAg2Ag9 DiffAg2Ag10 DiffAg2Ag11 DiffAg3Ag7 DiffAg3Ag8 DiffAg3Ag9 DiffAg3Ag10 DiffAg3Ag11 DiffAg4Ag7 DiffAg4Ag8 DiffAg4Ag9 DiffAg4Ag10 DiffAg4Ag11 DiffAg5Ag7 DiffAg5Ag8 DiffAg5Ag9 DiffAg5Ag10 DiffAg5Ag11 DiffAg7Ag13 DiffAg7Ag14 DiffAg7Ag15 DiffAg7Ag16 DiffAg7Ag17 DiffAg8Ag13 DiffAg8Ag14 DiffAg8Ag15 DiffAg8Ag16 DiffAg8Ag17 DiffAg9Ag13 DiffAg9Ag14 DiffAg9Ag15 DiffAg9Ag16 DiffAg9Ag17 DiffAg10Ag13 DiffAg10Ag14 DiffAg10Ag15 DiffAg10Ag16 DiffAg10Ag17 DiffAg11Ag13 DiffAg11Ag14 DiffAg11Ag15 DiffAg11Ag16 DiffAg11Ag17 DiffAg6Ag18 DiffAg1Ag18 DiffAg2Ag18 DiffAg3Ag18 DiffAg4Ag18 DiffAg5Ag18 DiffAg6Ag13 DiffAg6Ag14 DiffAg6Ag15 DiffAg6Ag16 DiffAg6Ag17 DiffAg1Ag13 DiffAg1Ag14 DiffAg1Ag15 DiffAg1Ag16 DiffAg1Ag17 DiffAg2Ag13 DiffAg2Ag14 DiffAg2Ag15 DiffAg2Ag16 DiffAg2Ag17 DiffAg3Ag13 DiffAg3Ag14 DiffAg3Ag15 DiffAg3Ag16 DiffAg3Ag17 DiffAg4Ag13 DiffAg4Ag14 DiffAg4Ag15 DiffAg4Ag16 DiffAg4Ag17 DiffAg5Ag13 DiffAg5Ag14 DiffAg5Ag15 DiffAg5Ag16

Figure : Linked Cliques -Lexical Distance Mirrors Network Distance get once again the familiar, ascending pattern: in-clique distance is lowest; agents that are in direct contact, but belong to adjacent cliques have relatively lower lexical distance than those that have no contact at all. While the picture seems rather clear in cliques with few agents, the bigger the number of agents per clique, the less clear the di erence in distance between di erent cliques that are or are not directly adjacent. is is illustrated for a network consisting of cliques with agents per clique in gure .

e e ect would be more pronounced with even more agents per clique. However, there are limits to reasonable visualisation. Since we are doing pair-wise comparison (excluding comparisons of agents with themselves, which would trivially yield a distance of ), for a network of n agents, we have n(n-) comparisons.

is increase is exponential, and would mean that for a network of agents ( agents per clique in cliques), we would have * = pair-wise comparisons to plot.


Isabelle Braud
email: isabelle.braud@irstea.fr

Pierre-Alain A Ayral

Christophe Bouvier

Flora Branger

Guy Delrieu

Guillaume Dramais

Jérôme Le Coz

Etienne Leblois

Guillaume Nord

Jean-Pierre P Vandervaere

Advances in flash floods understanding

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

The Mediterranean area is prone to intense rainfall events triggering flash floods, characterized by very short response times that sometimes lead to dramatic consequences in terms of casualties and damages as shown by Gaume et al. [START_REF] Gaume | A compilation of data on European flash floods[END_REF] for Europe. Recent examples in France include the events in Nîmes (1988), Vaison-la-Romaine (1992), Aude (1999), Gard (2002Gard ( , 2005)), Draguignan (2010), Alpes-Maritimes (2015) or the series of events that affected the south-east of France in 2014. Flash floods often occur over very short time and spatial scales [START_REF] Gaume | A compilation of data on European flash floods[END_REF][START_REF] Braud | Multi-scale hydrometeorological observation and modelling for flash flood understanding[END_REF] with a sudden onset and a rapid rising time. These events can affect large territories, but their impact may be very local in catchments that are generally ungauged. As an example, the analysis of the 8-9 September 2002 event in the Gard region (France) showed that many casualties occurred in less than 20 km² catchments that were ungauged [START_REF] Ruin | Human exposure to flash-floods-relation between flood parameters and human vulnerability during a storm of September 2002 in Southern France[END_REF]. Larger catchments (up to 1000 km²) suffered important economic damage (urban zones and main transportation network). Several studies and projects have addressed the questions of processes triggering flash floods. They showed that the spatial and temporal rainfall variability, landscape E3S Web of Conferences characteristics and soil humidity are influential factors on flash flood generation but their respective role still remains unclear [START_REF] Borga | Flash flood forecasting, warning and risk management: the HYDRATE project[END_REF] and the predictability of such events remains low due to high non-linearity in the hydrological response related to threshold effects and structuredheterogeneity at all scales. In addition, flash floods are difficult to monitor using operational rain gauge and discharge networks and a high spatial and temporal resolution is required [START_REF] Borga | Surveying flash floods: gauging the ungauged extremes[END_REF]. Indeed, gauging flash-flooding rivers with classical techniques remains a challenge due to practical and security reasons and the difficulty to be at the right place at the right moment. Weather radar data proved to be valuable for characterizing the space and time variability of rainfall [START_REF] Creutin | Radar hydrology modifies the monitoring of flash-flood hazard[END_REF], although the radar signal interpretation is more difficult in complex terrain and/or over urbanized areas, which are the most prone to such events.

To progress in flash flood understanding and modelling, it is necessary to progress on two fundamental questions in hydrology [START_REF] Sivapalan | Prediction in ungauged basins: a grand challenge for theoretical hydrology[END_REF]: 1/ the change of scale problem or how to transfer knowledge acquired at a given scale to another scale; 2/ the prediction in ungauged basin (PUB) problem, in order to assess the risk everywhere over a given region, requiring models able to provide reliable prediction at various scales (from a few km 2 to 1000 km 2 ). To go into that direction, Kirchner [START_REF] Kirchner | Getting the right answer for the right reasons: linking measurements, analyses, and models to advance the science of hydrology[END_REF] advocated for field experiments, specifically designed to advance the science of hydrology and address the change of scale problem in order "to get the right answer for the right reasons" The strategy is based on experiments on nested catchments, allowing the sampling of spatial heterogeneity at all scales. These recommendations formed the basis of the experimental and modelling strategies set up in the framework of the FloodScale project [START_REF] Braud | Multi-scale hydrometeorological observation and modelling for flash flood understanding[END_REF], aiming at increasing flash flood understanding and simulation.

In this paper, we first (section 2) present the observation and modelling strategy set up during the FloodScale project [START_REF] Braud | Multi-scale hydrometeorological observation and modelling for flash flood understanding[END_REF] that contributed to the HyMeX (Hydrological cycle in the Mediterranean Experiment) [START_REF] Drobinski | HyMeX, a 10-year multidisciplinary program on the Mediterranean water cycle[END_REF]. The observation strategy combines a four year multiscale data collection in two meso-scale catchments in south-east France with opportunistic measurements during the autumn season, when flash floods are more likely to occur. The modelling strategy follows the suggestion of Clark et al. [START_REF] Clark | Pursuing the method of multiple working hypotheses for hydrological modeling[END_REF] where models are used for process understanding and hypotheses testing. In section 3, we highlight the main findings derived from the observations and data analysis in terms of major active processes during flash floods and their space and time variability. In section 4, we present innovative methods to gauge rivers during flash floods and to improve the rainfall fields' description as well as methods for quantifying rainfall fields and discharge uncertainty. In section 5, we show how the knowledge derived from observation can be incorporated into models for hypothesis testing. This is conducted at various spatial scales from small to regional scales catchments. Finally, in section 6, we highlight how the knowledge acquired during the project can be useful for operational services and can contribute to improve models used in operational forecasting.

Observation and modelling strategies 2.1 Observation strategy

The observation was focused on two meso-scale catchments located in south-east France (Gard and Ardèche catchments) (Figure 1), with a multi-scale observation strategy including both continuous measurements during four years (Enhanced Observation Period -EOP) and opportunistic measurements during the four autumn seasons of 2012 to 2015.

Three scales were considered for data collection: 1/ the hillslope scale for process understanding; 2/ the small to medium-sized catchment scale (1-100 km 2 ) to document the change of scale and the spatial variability of landscape characteristics and processes; 3/ the regional scale (100-2000 km 2 ) that is the scale of interest for flash flood warning and management (Figure 2). At the hillslope scale, the experimental set up aimed at characterizing the dominant processes during and between floods for different types of Mediterranean hillslopes, the final objective being the definition of a hillslope typology, allowing a transposition of the results to non-monitored catchments. For this purpose, various hillslopes, typical of the Mediterranean environment in terms of spatial variability of soil depth, soil hydraulic properties, pedology, vegetation and geomorphology were selected and instrumented. The instrumented hillslopes were located in three small catchments (Valescure, Tourgueille, Gazel, see locations in Figure 1), corresponding to different geologies: granite, schist, marl and limestones respectively (see details in [START_REF] Braud | Multi-scale hydrometeorological observation and modelling for flash flood understanding[END_REF] and in Section 3).

The small to medium sized catchments appear in orange in Figure 1. They were chosen to document various geologies: granite, schist, marls, limestones and basalt, and land use: forest and agricultural areas. To document the landscape spatial variability, high resolution information was acquired to document topography (1 m Digital Elevation Model (DTM) from LiDaR measurements); land use (5 to 10 m resolution land use maps derived from Quickbird or Pleiades images); as well as collection of existing data about geology and pedology (1/ 250 000 resolution). In those catchments, nested water level, discharge and soil moisture measurement networks were set up, documenting as much as possible, homogeneous subcatchments in terms of geology and land use. This was associated with the collection of high resolution rainfall data. Soil hydraulic properties were also documented from the collection of existing data base or the set-up of dedicated field campaigns (see details in [START_REF] Braud | Multi-scale hydrometeorological observation and modelling for flash flood understanding[END_REF] and [START_REF] Nord | A high space-time resolution dataset linking meteorological forcing and hydrosedimentary response in a mesoscale Mediterranean catchment (Auzon) of the Ardèche region, France, Earth Systems Sciences Data[END_REF]). [START_REF] Braud | Multi-scale hydrometeorological observation and modelling for flash flood understanding[END_REF]) At the regional scale, the focus was mainly on the collection of operational rainfall and discharge data. Nevertheless, during HyMeX first Special Observation Period (SOP1) [START_REF] Ducrocq | HyMeX-SOP1, the field campaign dedicated to heavy precipitation and flash-flooding in the northwestern Mediterranean[END_REF] and EOP periods, research radars were deployed in the Gard and Ardèche catchments to refine the rainfall estimation. In addition, the Claduègne catchment in Ardèche (see location in Figure 1) was equipped with a high density of rain gauges (Hpiconet a network composed of 19 to 21 gauges in about 100 km 2 with a 1-5 minute time step). In the Ardèche catchment, a network of Large Scale Particule Image Velocimetry (LS-PIV) stations [START_REF] Coz | Performance of image-based velocimetry (LSPIV) applied to flash-flood discharge measurements in Mediterranean rivers[END_REF] was also set up to continuously monitor discharge in particular during high flows.

The opportunistic measurements included the sampling of flood events for geochemistry analysis, gauging of flooding rivers, soil moisture measurements, field observations of runoff. The deployment of teams in the field was possible thanks to a continuous analysis of weather forecasts available on the HyMeX SOP website by on-duty scientist staff and the availability of real time a http://mistrals.sedoo.fr/?editDatsId=656&datsId=656&project_ name=HyMeX&q=hpiconet information on the http://sop.hymex.org web site. This included meteorological forecasts provided by Météo-France, real time rain gauges and radar rainfall observations and reanalysis of soil moisture state over the area of interest. Adopting this EOP strategy for flashflood observations was very relevant. Indeed, autumn 2012 that corresponded to the first HyMeX SOP [START_REF] Ducrocq | HyMeX-SOP1, the field campaign dedicated to heavy precipitation and flash-flooding in the northwestern Mediterranean[END_REF] did not led to significant events in those catchments whereas during autumn 2014, about 10 significant events hit the Cévennes-Vivarais region, amongst which several concerned our studied catchments. As an illustration, about 45 river gaugings during high floods were performed in the Ardèche catchment in 2014. The strategy of EOP aiming at reinforcing research observatory and operational observations during four years for flash-floods was thus a very successful proofof-concept for such rare events over specific Mediterranean watersheds.

Modelling strategy

The modelling strategy is detailed in Braud et al. [START_REF] Braud | Multi-scale hydrometeorological observation and modelling for flash flood understanding[END_REF] and relies on an iterative process where models are used, as much as possible, without calibration in order to apply the hypothesis testing framework and be able to relate model parameters with physical hypotheses. The iterative process includes the following steps:

1/ A first modelling approach is built from existing knowledge and data and from first hypotheses about dominant processes; 2/ The model results are compared with observations and the analysis focuses on discrepancies that can be due to problems in model forcing data; parameters specification; process representation or missing processes; 3/ New data are collected or additional analyses are performed to understand the discrepancies; 4/ A new version of the model is set up and new hypotheses are tested; 5/ The process is continued until sufficient agreement between model and observation is obtained. This strategy was applied at the various documented scales in order to progress in process understanding and simulation. The results are illustrated in Section 5.

Main results from the hillslope and small scale catchments observation and modelling

The experimental set-up at the hillslope and small to medium catchment scale was designed to address the following questions:

1/ What is the storage capacity of soils in the studied area? 2/ In which conditions do we observe sub-surface lateral flow or direct surface runoff and can we quantify the speed of sub-surface lateral flow? 3/ What is the respective part of surface, subsurface and deeper layers flow in the discharge at the outlet of the catchments?

4/ Is the impact of land use larger than the impact of soil texture on soil surface hydraulic properties? 5/ What is the impact of active river network extension on the efficiency of the hydrological response? 6/ What is the respective role of rainfall, soil moisture, geology, land use variability on the hydrological response?

The effort of the past four year was mainly dedicated to data acquisition, data validation and data provision to the HyMeX data base b . A complete analysis of the whole data set has not yet been achieved. Nevertheless, the results obtained up to now already provide interesting insight into some of the questions listed above. They are briefly reviewed below. In the agricultural area of the Ardèche catchment, flow was thought to be mainly due to surface runoff and related to land use. Field observations showed that near saturated hydraulic conductivity was low due to high clay contents and that infiltration excess runoff was initiated in less permeable areas (including the crest) with saturated areas progressively connected to the hydrographic network. Soil moisture sensors (Decagon 10HS) installed in various land uses between 10 and 50 cm depth showed that, during rainfall events, only the top soil (30 cm) was affected by significant change in soil moisture. The differences between fields also appeared larger than the differences between different land uses (Figure 3). Hydraulic properties of the soil surface were characterized in situ using a new device called "saturometer" which allows the quantification of the time needed to reach saturation under artificial rainfall [START_REF] Vandervaere | The use of ponding time to determine soil hydraulic properties during infiltration prior to runoff[END_REF]. Results show a lower hydraulic conductivity in vineyards than in grassland sites, but a time to saturation longer due to a lower initial soil moisture in vineyards, which can be explained by a higher evaporation within the 0-5 cm top layer between events, not visible at 10 cm depth. Data b http://mistrals.sedoo.fr/HyMeX/ analysis will be continued and complemented with modelling in order to analyze more deeply the complex interplay between initial conditions, land use and rainfall.

In the forested area of the Gard catchment, runoff was thought to be dominated by sub-surface flow and questions had been raised about the soil storage capacity and imperviousness of the underlying weathered horizons. The experimental set up was mainly devoted to study those questions.

Six transects in granite (Valescure) and schist (Tourgueille) were instrumented with soil moisture sensors (ten locations) with 2 depths at each site. The continuous measurement lasted about one hydrological year at each site. Soil hydraulic conductivity was characterized using disk infiltrometers [START_REF] Reynolds | Determination of hydraulic conductivity using a tension infiltrometer[END_REF]. Soil depth was measured from direct pedological pits or a method based on the analysis of electrical resisitivity (ERT) signal along the transects. This allowed the determination of the statistical distribution of soil hydraulic conductivity, soil water retention and soil depth for each transect. Although the intra-transect spatial variability is quite large, the inter-transect distribution appears quite stable (Figure 4). For soil depth, the average is around 30 cm, and the spatial variability in this area can be considered as following a log-normal distribution, with parameters -1.14 and 0.72 respectively for the mean and the standard deviation of the soil depth logarithm. Soil moisture data were analyzed to derive the soil retention and hydraulic conductivity curves for the surface horizon, but also the deeper horizon using the HYDRUS-1D software and an inverse modelling technique detailed in [START_REF] Bourgeois | Inverse modeling of soil water content to estimate the hydraulic properties of a shallow soil and the associated weathered bedrock[END_REF]. The method reveals, consistently with in situ measurements, high value of hydraulic conductivity in the top horizon (several hundreds of mm hr -1 ), but more interestingly, also large values of hydraulic conductivity towards deeper soil horizons. The same kind of observations was also conducted on "infiltration fields" of about 10 m 2 with natural and artificial rainfall. This allows to document the hydrological response from normal to extreme conditions The sites were equipped with soil moisture sensors, piezometers, tensiometers, and electrode lines to perform multi-temporal resistivity (ERT) surveys (see details in [START_REF] Braud | Multi-scale hydrometeorological observation and modelling for flash flood understanding[END_REF]). It was also possible to inject tracers upstream the field and to follow its dispersion using ERT. The example in Figure 5 shows that although rocky horizons are present, fluxes are mainly vertical in the first 2 m of soil. In addition, artificial rainfalls of about 500 mm (100 mm hr -1 in 5 hours) occurring on semi-saturated soil can be completely infiltrated, confirming that infiltration in the weathered horizon is possible and that storage capacity is about twice that of the surface horizon [START_REF] Adamovic | Assessing hydrodynamic properties of soils under natural and artificial rainfalls at the plot scale in the Valescure catchment[END_REF]. Geochemistry sampling performed during some rainfall and flood events allowed to go towards a quantification of the fraction of water coming from the surface and sub-surface. A large panel of elements including physico-chemistry, trace elements, stable water isotopes and organic carbon were analyzed. During floods, Ca, Sr and electrical conductivity analyses show a contribution of about 60-80% of rain water to the peak, and only 20-40% of pre-existing water. However, at the scale of the event, these proportions are inverted. At the small catchment scale, but also for the whole Cévennes-Vivarais region, a synthesis of infiltration tests performed by [START_REF] Desprats | Cartographie de la perméabilité des sols pour l'aide à la prévision des crues ; cas d'étude sur le Gardon d'Anduze[END_REF] and of the data collected during the project [START_REF] Braud | Analysis of infiltration tests and performed in the Claduègne catchment in May-June 2012, contribution to WP3.4 "Documentation and mapping of soil hydraulic properties, soil geometry and vegetation cover of small catchments[END_REF] showed that land use and geology were significant controlling factor of surface hydraulic conductivity (significant differences between natural/cultivated and forest/crops and between different geologies, Figure 6) and that pedo-transfer functions, based only on texture or porosity data failed to reproduce the range of observed values.

At the scale of the whole Cévennes-Vivarais area, several studies focused on the analysis of recessions in order to gain insight into catchment characteristics that could be useful for improving flash flood simulation. Vannier et al. [START_REF] Vannier | Regional estimation of catchment-scale soil properties by means of streamflow recession analysis for use in distributed hydrological models[END_REF] showed that soil storage capacity estimated from existing data bases was underestimated, as compared to results obtained from discharge recession analysis. They used this method to derive probable depth and hydraulic conductivity of the weathered bedrock, which was found to be dependent on geology. They also showed that the storage capacity of the weathered layer was much larger than that of the upper soil, described in soil data bases. The results of this large scale analysis are consistent with those of the experiments conducted at the hillslope and small catchment scales, which underlines the interest of the multi-scale approach. The major role of geology in modulating the hydrological response has also been shown. The black line is the envelope curve proposed by [START_REF] Gaume | A compilation of data on European flash floods[END_REF].

The nested catchments monitoring strategy also allowed documenting discharge at spatial scales that were seldom sampled by the operational networks, but also by post-event field survey aiming at documenting peak discharge [START_REF] Gaume | Post-flood field investigations in upland catchments after major flash floods: proposal of a methodology and illustrations[END_REF] as shown by the red points in Figure 7.

The figure shows that the network allowed documenting small spatial scales that were not documented before, even during post-event surveys. No exceptional event was recorded at those scales. Nevertheless values of specific discharge of about 10 m 3 s -1 km -2 were recorded, which is already quite high.

Progress in rainfall and high discharge estimation and quantification of their uncertainty

In terms of rainfall, the objective was to progress in rainfall spatial and temporal variability description, as well as in the quantification of uncertainty. A 1 km²rainfall reanalysis over the Cévennes-Vivarais region (32 000 km²), was produced for the 2007-2014 period and is available on the HyMeX database c . For the 133 most intense rain events, an hourly rain product based on radar -raingauge merging was produced for two types of geographical supports: 1/ 1-km² raster maps and; 2/ spatial divisions of the main Cévennes watersheds into hydrological meshes of almost constant size in the range of 5 -300 km². The methods and their comparison to other rainfall products are described in Delrieu et al. [START_REF] Delrieu | Geostatistical radar-raingauge merging: A novel method for the quantification of rain estimation accuracy[END_REF] and Boudevillain et al. [START_REF] Boudevillain | A high-resolution rainfall re-analysis based on radar-raingauge merging in the Cévennes-Vivarais region, France[END_REF], indicating a systematic superiority of the merging method (Kriging with External Drift) over Ordinary Kriging (OK). Additional reanalyses at higher resolution were also conducted using research observation networks. The error model indicates that the added-value of the radar network in terms of Quantitative Precipitation Estimate (QPE) with respect to the hourly raingauge network is larger for localized convection rain events as well as for the smallest space-time scales (Figure 8) which are those of interest for flash-flood prediction in the region. Another way to account for rainfall spatial variability and uncertainty is to use stochastic rainfall simulators. The SAMPO stochastic rainfall simulator [START_REF] Leblois | Space-time simulation of intermittent rainfall with prescribed advection field: Adaptation of the turning band method[END_REF] was improved 1/ to make a key technical component (a Gibbs Sampler) able to efficiently handle up to ~1500 conditioning data points where available, as broader conditioning chunks make the conditional simulations smoother in both time and space 2/ to be able to simulate rainfall fields in mild non-homogeneous conditions such as the presence of an orographic gradient [START_REF] Ollagnier | Climatologie des pluies en région Cévennes-Vivarais : caractérisation des situations pluvieuses à l'échelle régionale, Juin 2013, M2R[END_REF], using gradually variable point distribution parameters -a technique initially tested within the PhD of D. Penot [START_REF] Penot | Cartographie des événements hydrologiques extrêmes et estimation SCHADEX en sites non jaugés[END_REF]. From this a set of several realizations, conditioned on observations at rain gauges [START_REF] Caseri | Generating precipitation ensembles for flood alert and risk management[END_REF], was used to provide plausible rainfall fields in the Cévennes-Vivarais region catchment. An example of such field is provided in Figure 9. More drastic heterogeneity has also been studied, focusing on mosaic simulations where sharply contrasting subdomains are handled separately. This is a technique of primary importance for free (climatological) simulations without conditioning, but results are mixed as far as rainfall reanalysis is concerned.

In terms of discharge estimation of flooding rivers, several non-contact techniques were tested and compared. They allow a safe (for the equipment and the operators) gauging, in conditions when traditional methods are not applicable. This includes the use of fixed video cameras, analyzed using LS-PIV (Large Scale Particle Image Velocimetry) techniques [START_REF] Ducrocq | HyMeX-SOP1, the field campaign dedicated to heavy precipitation and flash-flooding in the northwestern Mediterranean[END_REF][START_REF] Hauet | Application de la méthode LSPIV pour la mesure de champs de vitesse et de débits de crue sur modèle réduit et en rivière[END_REF] and the use of portable surface velocimetry radars (SVR) [START_REF] Dramais | Jaugeage par radar mobile, protocole et résultats[END_REF][START_REF] Welber | Field assessment of non-contact stream gauging using portable surface velocity radars (SVR)[END_REF]. Algorithms were also developed to use videos of flooding rivers from the internet for the estimation of discharge, based on the same principles as those used with LS-PIV [START_REF] Boursicaud | Gauging extreme floods on YouTube: application of LSPIV to home movies for the post-event determination of stream discharges[END_REF]. In the framework of the Enhanced Observation Period, distributed and multi-scale hydrometry was set up and tested. This includes the setup of dense networks of water level monitoring for catchments ranging from 0.2 to 12 km 2 [START_REF] Nord | A high space-time resolution dataset linking meteorological forcing and hydrosedimentary response in a mesoscale Mediterranean catchment (Auzon) of the Ardèche region, France, Earth Systems Sciences Data[END_REF] allowing discharge measurements at scales much smaller than currently available for flash floods (see Figure 7).

FLOODrisk 2016 -3 rd European Conference on Flood Risk Management For the establishment of the stage-discharge relationships, a Bayesian framework aiming at including prior knowledge of hydraulic controls and gauging uncertainty was developed [START_REF] Le Coz | Combining hydraulic knowledge and uncertain gaugings in the estimation of hydrometric rating curves: A Bayesian approach[END_REF]. The BaRatin d software implements the method and is freely available. BaRatin determinates the most probable stage-discharge relationship and the associated uncertainty. The application of BaRatin to the FloodScale stations showed that the added value of the non-contact gaugings is high. First, uncertainties, especially for high discharge where the curves were generally extrapolated, are significantly reduced. Second, the stage-discharge relationship can be established in only a few years of operation. Operational protocols and training sessions have been provided to French operational services and some of them use the tools developed in the project. New developments have been also performed to propagate the stage-discharge uncertainties to hydrographs and water balance components (Figure 10) [START_REF] Horner | Accounting for stage measurement errors in the uncertainty of streamflow records[END_REF]. This will allow including observation uncertainty in the calibration and evaluation of hydrological models.

Modelling at various scales

At the various scales, the hypotheses testing framework highlighted in section 2.2 was applied. The hillslopes and small catchment scale observations in the granite and schist catchments were used to set up a distributed, event-based model, based on the experimental findings that lateral flow and deep infiltration are the dominant processes in those catchments [START_REF] Bouvier | Hydrological processes generating flash floods in a small mountainous Mediterranean French catchment[END_REF]. It was tested with success on the available rainfall-runoff events on the small Valescure catchment [START_REF] Bouvier | Hydrological processes generating flash floods in a small mountainous Mediterranean French catchment[END_REF] (see also an example in Figure 11). The extension of this model to a medium size catchment (Gardons catchment) also provided satisfactory results. At the various scales, the hypotheses testing framework highlighted in section 2.2 was applied. The hillslopes and small catchment scale observations in the granite and schist catchments were used to set up a distributed, event-based model, based on the experimental findings that lateral flow and deep infiltration are the dominant processes in those catchments [START_REF] Bouvier | Hydrological processes generating flash floods in a small mountainous Mediterranean French catchment[END_REF]. It was tested with success on the available rainfall-runoff events on the small Valescure catchment [START_REF] Bouvier | Hydrological processes generating flash floods in a small mountainous Mediterranean French catchment[END_REF] (see also an example in Figure 11). The extension of this model to a medium size catchment (Gardons catchment) also provided satisfactory results. CVN-p (green), the CVN (orange) and the SIMPLEFLOOD (black) models (taken from [START_REF] Braud | Multi-scale hydrometeorological observation and modelling for flash flood understanding[END_REF]) At the regional scale, Vannier et al. [START_REF] Vannier | Investigating the role of geology in the hydrological response of Mediterranean catchments prone to flash floods: regional modelling study and process understanding[END_REF] used the results obtained in [START_REF] Braud | Analysis of infiltration tests and performed in the Claduègne catchment in May-June 2012, contribution to WP3.4 "Documentation and mapping of soil hydraulic properties, soil geometry and vegetation cover of small catchments[END_REF] about soil water storage to upgrade the CVN model [START_REF] Anquetin | Sensitivity of the hydrological response to the variability of rainfall fields and soils for the Gard 2002 flash-flood event[END_REF], by adding the altered bedrock layer to the soil description in the model (CVPp). The drainage flow at the bottom of the soil columns was added to the river flow as base flow. They showed improvement in simulated discharge, both at the annual and event scale [START_REF] Vannier | Investigating the role of geology in the hydrological response of Mediterranean catchments prone to flash floods: regional modelling study and process understanding[END_REF]. The improvement was larger for granite dominated catchments than for schist dominated catchments. An example is provided in Figure 12 for a granite sub-catchment.

Adamovic et al. [START_REF] Adamovic | Assessing the simple dynamical systems approach in a Mediterranean context: application to the Ardèche catchment (France)[END_REF] and Coussot [START_REF] Coussot | Assessing and modelling hydrological behaviours of Mediterranean catchments using discharge recession analysis[END_REF] used discharge recession analysis to characterize the catchment behavior as a simple dynamical system following the approach of Kirchner [START_REF] Kirchner | Catchments as simple dynamical systems: Catchment characterization, rainfall-runoff modeling, and doing hydrology backward[END_REF]. They found that such a simple model was applicable to Mediterranean catchments, mainly during low-vegetation periods (when deciduous trees have lost their leaves) and under humid conditions. This led to a simple model (3 parameters), mainly representing rapid sub-surface flow. Adamovic et al. [START_REF] Adamovic | Development of a data-driven distributed hydrological model for regional scale catchments prone to Mediterranean flash floods[END_REF] proposed a distributed model, SIMPLEFLOOD, based on this approach, using parameters regionalized according to geology [START_REF] Adamovic | Assessing the simple dynamical systems approach in a Mediterranean context: application to the Ardèche catchment (France)[END_REF][START_REF] Adamovic | Development of a data-driven distributed hydrological model for regional scale catchments prone to Mediterranean flash floods[END_REF]. In the Ardèche catchment, satisfactory performances were obtained for floods and continuous simulations, although discharge was generally underestimated in summer. An example of simulation appears in Figure 12. Adamovic [START_REF] Adamovic | Development of a data-driven distributed hydrological model for regional catchments prone to Mediterranean flash floods[END_REF] also tested a coupling of the SIMPLEFLOOD model with a 1D hydrodynamic model for flood propagation in the downstream river channel, without significant improvement of discharge estimation in the simulated cases.

Synthesis of the main results and interest for operational purposes

The main outcome of the FloodScale project is the unique data set it assembled and the demonstration that the proposed observation strategy mixing continuous measurements over a four-year period and opportunistic measurements during four autumns was adapted to capture flash floods. In addition, effort was made to quantify uncertainty at all levels. All those elements render the collected data set unique given the variety of sampled space and time scales, which are much finer than those captured by operational networks. The project also demonstrated the importance of high quality discharge date, even at low flow, as it was shown that recession data were containing useful information for understanding and simulating flash floods. The whole data set is available for the international research community through the HyMeX data base portal.

In terms of process understanding and innovative measurements, the following points can be highlighted:

1/ A method for merging radar and rain gauges data was proposed and validated and error on the estimated rainfall fields was quantified; 2/ A method for quantifying rainfall field uncertainty in non-homogeneous areas has also been proposed (use of a stochastic rainfall generator); 3/ Various non-contact measurements techniques for flooding discharge have been proposed and validated and are already used in operational services; 4/ An objective method for quantifying stagedischarge uncertainty and its propagation to discharge times series has been validated and a software implementing this method is freely available; 5/ Geology was highlighted as an important factor in modulating the hydrological response and the soil water storage, with the necessity to include storage capacity of the weathered soil horizons in the modelling; 6/ Lateral sub-surface flow must be taken into account even when surface runoff is important; 7/ The iterative modelling strategy mixing observation and modelling for hypothesis testing proved to be successful and allowed building simulation models that are consistent with observations.

There is still work to do to fully exploit the collected data sets, but some results can already be useful for operational services. These data sets can serve as reference for the evaluation of research or operational models. Rainfall field can also be useful for the evaluation of satellite products or the evaluation of rainfall simulated by meteorological models.

Lessons learnt about soil water storage and its modulation by the geology, as well as the results in terms of surface hydraulic conductivity can be directly incorporated into forecasting models. The simulation models developed during the project can form the basis for simplified versions that could be used in the next generation of forecasting models.

Figure 1 :

 1 Figure 1: Location and elevation map of the study area. The two main studied catchments: Gard (2062 km 2 ) and Ardèche (2388 km 2 ) appear in bold black. The small research catchments are shown with orange boundaries (from [2])

Figure 2 :

 2 Figure 2: Diagram showing the characteristic spatial scales of the processes considered in the study (black, diagonal) and the associated typical observation time scales; the required data characterizing the catchments physical properties at each scale (purple, top left); the modelling approaches (red, bottom right). Interactions between scales and how the change of scale problem is addressed are shown with the blue arrows for the model meshing and orange arrows for the processes representation. HRU means Hydrological Response Unit.(taken from [2])

Figure 3 :

 3 Figure 3: Average of 0-5 cm depth soil moisture for several events in 2013 and different land uses in the Claduègne subcatchment.

Figure 4 :

 4 Figure 4: Top: Hydraulic conductivity curves of the top horizon at transect 1 in Valescure Bottom: Hydraulic conductivity curves derived from median parameter of the top horizon for each transects 1 to 5.

Figure 5 :

 5 Figure 5: Example of soil resistivity multi-temporal monitoring after salt injection.

Figure 6 :

 6 Figure 6: Average and standard deviation of the logarithm of soil surface hydraulic conductivity estimated using all the available data in the Cévennes-Vivarais region, showing that geology and land use are discriminant factors to explain the spatial variability

Figure 7 :

 7 Figure 7: Specific peak discharge as function of catchment area for the operational network in the Gard and Ardèche catchment (black), post-event survey (IPEC) in the region in 2002, 2008 and 2014 (blue and green), and the continuous nested measurement network set up during FloodScale (red points).The black line is the envelope curve proposed by[START_REF] Gaume | A compilation of data on European flash floods[END_REF].

Figure 8 :Figure 9 :

 89 Figure 8: Normalized standard deviation of the rain rate error over a range of spatial and temporal scales using rain gauges alone (ordinary kriging-OK) top) and radar-rain gauge merging ( kriging with external drift -KED-bottom) for all studied events (left) and localized convective events (right). Green (resp. pink) values correspond to low (resp. high) errors. The error model was parameterized using a cross validation technique

Figure 10 :

 10 Figure 10: Example of propagation of stage-discharge uncertainty on a measured hydrograph for the flood of November 4 2014 at the Vallon Pont d'Arc gauging station. The colors correspond to uncertainties in the stage-discharge relationship when only a priori hydraulic knowledge (blueconfig 0), traditional gauging (pink-config 1) and all gauging including SVR opportunistic measurements (green-config 2) are taken into account

Figure 11 :

 11 Figure 11: Comparison of the observed discharge with calculated discharge at the event scale. The model either simulates the total discharge and the discharge due to exfiltration of the sub-surface flow, occurring at convergent sub-surface path flows which lead to soil saturation.

Figure 12 :

 12 Figure 12: Observed (red points) and simulated discharge at Ardèche at Meyras in 2008 (top) and from October 21 to November 06 2008 (bottom) using the CVN-p (green), the CVN (orange) and the SIMPLEFLOOD (black) models (taken from [2])

FLOODrisk 2016, 3rd European Conference on Flood Risk Management, Innovation, Implementation, Integration Lyon, France, 18 -20 October 2016

Acknowledgements

The FloodScale project was funded by the French National Research Agency (ANR-2011 BS56 027) and received complementary funding from the MISTRALS/HYMeX program, the Rhône-Alpes region, Montpellier 2 University, Alès School of Mines, Irstea, CNRS, CNR, Schapi, SINTEF. We also thank the following data providers: Météo-France, SPC Grand Delta and EDF-DTG. The Ardèche and Languedoc-Roussillon data bases come from the « Inventaire et Gestion des Sols/ Référentiel Pédologique Régional » program. Pleiades images were made available by the CNES/TOSCA CALVADOVS project. We thank the HyMeX (ESPRI/IPSL et SEDOO/Observatoire Midi-Pyrénées) data base for their help in access and processing the data and Météo-France for the access to the http://sop.hymex.org / site during autumn campaigns. The study catchments are part of Observatoire HydroMétéorologique Cévennes-Vivarais (OHM-CV) funded by INSU/CNRS, OSUG/Grenoble, and Allenvi. The Pôle Risques helped in the organization of the final workshop. We also thank all the colleagues and the numerous students who contributed to data collection and analysis, in particular the four Ph D students that worked in the project: M. Adamovic, O. Le Bourgeois, O. Vannier and A. Wijbrans.