Olivier ; Barreteau

Bruno Bonté

Yvan ; Caballero

Emmanuel ; Dubois

Coord. Stefano ; Farolfi

Patrice ; Garin

Cécile ; Hérivaux

Damien ; Jourdain

Philippe Le Coent

Julien Malard

B ; Bonte

M Montginoul

S Morardet

N Neverre

Analysing practices, social representations and behaviours of socio-hydro systems' actors

Keywords: Actors, Practices, Social representations, Behaviour, Water, Socio-Hydro systems, Hybrid methods

published or not. The documents may come

G-eau

Analysing practices, social representations and behaviours of socio-hydro systems' actors

Introduction and rationale

Water dynamics are closely linked to a wide set of intricate human uses, whether as a resource, a vehicle, a landscape feature or as a receptacle for waste, among other uses. These uses depend as well on various characteristics of water, including, availability, biological and chemical quality, reliability, and variability. Since indicators of water resource status will depend on the particular interest of the uses involved, this complexity of interactions between water and its uses complicates the task of characterising the current status of a given water resource. Understanding these complex webs of interaction is important, as water is key to the resilience of many social ecological systems (Falkenmark et al. 2019).

In the follow up to the literature on socio-ecological system, we name social-hydrological systems (or socio-hydro systems -SHS), those socio-ecological systems where water is a key factor of resilience. In practice, socio-hydro systems are a set of resources, actors, institutions and infrastructures. As specialisation of socio-ecological systems they comprise four main categories of components: [START_REF] Faysse | Participatory analysis for adaptation to climate change in Mediterranean agricultural systems: possible choices in process design[END_REF] users, [START_REF] Moreau | La justice sociale dans la construction du jugement d'acceptabilité. Analyse des réactions d'agriculteurs face à différentes règles de partage de l'eau souterraine[END_REF] governance systems, (3) resource units, and (4) resource settings [START_REF] Ostrom | A General Framework for Analyzing Sustainability of Social-Ecological Systems[END_REF]. As far as water plays a key role in their evolution, infrastructures are prominent components; engineering of water systems to control its availability has structured the fate of societies since antiquity (eg. [START_REF] Anderies | Robustness, institutions, and large-scale change in social-ecological systems: The Hohokam of the Phoenix Basin[END_REF], Wittfogel 1957). These human-made hardware infrastructures interact with the natural infrastructures water systems provide (e.g. wetlands) and with the human-made soft infrastructures (i.e. institutions') established to manage them. Socio-hydro systems face specific management challenges [START_REF] Brelsford | Developing a sustainability science approach for water systems[END_REF].

The study of socio-hydro systems is currently an active field of research, with emergence of domains such as sociohydrology [START_REF] Sivapalan | Socio-hydrology: A new science of people and water[END_REF] or hydrosocial cycles [START_REF] Wesselink | Socio-hydrology and hydrosocial analysis: Toward dialogues across disciplines[END_REF]. Beyond these scholarly fields specialising in water, the literature on coupled infrastructure systems and the robustness framework [START_REF] Anderies | A framework to analyze the robustness of social-ecological systems from an institutional perspective[END_REF][START_REF] Anderies | Refining the Robustness of Social-Ecological Systems Framework for comparative analysis of coastal system adaptation to global change[END_REF] enable us to understand the articulation between components with a focus on the role of infrastructures and infrastructure providers.

The analysis of socio-hydro systems pays particular attention to the concrete ways humans interact with the objects and living beings that make up these ecosystems, which we will qualify, for simplicity, as practices and behaviours. But it is equally interested in the consequences of these practices and behaviours for hydro systems and society, in a dynamic vision of these interactions. The mechanisms and determinants of these practices and behaviours constitute a central research object of the PRECOS team (Practices, Social Representations and Behaviours within Socio-Hydrosystems), which is part of the Joint Research Unit G-Eau2 . Schematically, the origin of these practices is sought in two complementary spheres of analysis: i) the logic of actions of each person, having the capacity to analyse his/her environment and sufficient independence to carry out choices according to individual preferences; ii) the various societal structures which will delimit these logics of individual actions: norms, institutions, values, incentives, knowledge and know-how, information. This duality of spheres of analysis leads to the mobilisation of a diversity of approaches and disciplines.

The central object of our analyses is therefore the individual behaviour of the actors within the sociohydro systems. Even if this behaviour takes place within groups, as it often does, we are interested in studying individual choices, how they evolve and the factors that influence them. We include in our analysis individual behaviours taking into account the strategies of other actors within the group (cooperative and non-cooperative equilibria in game theory models, for example) and the effect of collective rules established by (endogenous) or imposed on (exogenous) groups. We also study whether and under what conditions these individual choices influence the decisions taken by the groups and by the institutions that manage the systems within which the actors studied act and evolve.

The aim of this paper is to present and discuss a non-exhaustive body of methods and approaches that we 3 have put in place to analyse practices, social representations and behaviours of socio-hydro systems' actors in different geographical zones and to study various problems in connection with sociohydro systems over the last fifteen years.

We present four groups of methods: surveys/focus groups for the analysis of practices, social representations, preferences; stated preferences; experimental economics and field experiments; hybrid methods.

In Section 2, for each group of methods, we provide a short literature and the conceptual bases that underpin the methods, some examples of our application to the analysis of socio-hydro systems, a discussion about the particularity of their adoption in these systems, and a discussion about the advantages/limits of the methods.

Section 3 compares and discusses the groups of methods, referring particularly to their application to the analysis of socio-hydro systems' actors. It concludes that there is no ideal method for the proposed analysis and provides paths for further research in this field.

Methods

Practices, social representations and preferences on the regulation of water uses

Introduction: objectives and approaches

Adaptation to global change implies not only a change in collective rules, but also a change in individual practices (consumption, limiting the ecological footprint, involvement in collective action, etc.). These individual behaviours are based on social representations of the relationship between Humans and Nature. These representations allow people to justify their practices by using a set of arguments that combine economic, social, ecological and ethical considerations (Di Méo, 2008). The aim of our research is to characterise water use practices and the social representations underlying them in order to identify ways of transforming them for sustainable management. They combine the methods described above in a schematic way:

• Individual surveys on a representative sample of the population, 4 to identify behaviours, attitudes and associated social representations; • Individual semi-directive interviews and discussion groups to specify the components of social representations, the norms and values that drive them; • Discussion groups to discuss options for regulating these behaviours, using a variety of media depending on the context and the challenge: prospective scenarios, collective simulation (roleplaying games), discussions with experts, etc.; • The feedback of individual and collective preferences on the rules to be promoted.

Conceptual bases

This approach is inspired by the principle of methodological triangulation [START_REF] Caillaud | Triangulation méthodologique. Ou comment penser son plan de recherche[END_REF]. It is based on two main theoretical frameworks in social psychology. The first one, the theory of an individual's planned behaviour [START_REF] Ajzen | The theory of planned behavior[END_REF], postulates that behaviour results from a decision driven by personal intention, according to the following functional scheme:

Attitude characterises the positive or negative feelings about the feasible behaviour in a given situation. The subjective norm encompasses the set of beliefs shared with the social group(s) to which the individual is sensitive. The perception of a greater or lesser personal ability to adopt the behaviour, in terms of skills and control over the self and the action situation, also influences the intention to act and then the behaviour.

Figure 1. The theories of reasoned action and planned behaviour [START_REF] Ajzen | The theory of planned behavior[END_REF] All of these determinants result from the influence of socio-demographic factors, values, information sources, etc. The calibration of the parameters of this model in a given behaviour is carried out through quantitative surveys on a large panel representative of the population. The respondents register their degree of agreement or disagreement on Likert scales with propositions concerning these different beliefs and perceptions. Attitudes and behaviours towards wastewater reuse in Australia were analysed using this method by [START_REF] Nancarrow | What drives communities' decisions and behaviors in the reuse of wastewater[END_REF].

The second theoretical field focuses on the social roots of behaviour, through the theory of social representations [START_REF] Moscovici | 2è éd. La psychanalyse, son image et son public: étude sur la représentation sociale de la psychanalyse[END_REF]. Social representations are "organized and structured sets of information, beliefs, opinions and attitudes" [START_REF] Abric | L'approche structurale des représentations sociales : développements récents[END_REF], which guide perceptions of challenging situations, guide behaviour and are used to justify opinions. They are specific to each person, according to his or her experiences and knowledge. However, if the topic has been the subject of concerns and exchanges with others, individual representations are then integrated into social representations, influenced by the norms, values and knowledge developed and shared by the group or groups in which this individual has discussed them [START_REF] Jodelet | Les représentations sociales: regard sur la connaissance ordinaire[END_REF].

The structural approach of representations distinguishes the core of representations, which determines its overall meaning and its organization, and is resistant to change [START_REF] Abric | L'approche structurale des représentations sociales : développements récents[END_REF]) from more peripheral elements, which define more personal attitudes, more likely to evolve under the effect of external influence [START_REF] Tafani | Attitude et approche structurale des représentations sociales: de l'ancrage psychologique à l'ancrage sociologique[END_REF]. Identifying these components may clarify why gaps persist between knowledge, attitudes and behaviours, or why people globally qualify a problem as important for society without recognizing its existence locally or adopting practices aimed at resolving it [START_REF] Michel-Guillou | La représentation sociale du changement climatique : enquête dans le sens commun, auprès de gestionnaires de l'eau[END_REF].

Many controversies over water issues were analysed using social representations theories : pollution (Michel-Guillou, 2011), vulnerability of water to climate change (Michel-Guillou, 2014), phytoremediation [START_REF] Amalric | L'ingénierie écologique face aux territoires: enjeux et représentations sociales d'une innovation dans le domaine du traitement de l'eau[END_REF], river ecological restoration (Germaine and Barraud 2013), water sharing in conflictual contexts [START_REF] Carrascal | Représentations sociales de l'eau dans un contexte de conflits d'usage : le cas de la Sierra Nevada de Santa Marta, Colombie[END_REF], risks of floods [START_REF] Baggio | La représentation sociale de l'inondation: influence croisée de la proximité au risque et de l'importance de l'enjeu[END_REF] and for health (Dos Santos, 2011), exchanges between surface and groundwater (Besteiro and Rivière-Honegger, 2018).

From an operational point of view, several complementary methods may be used:

• The structural analysis of the social representations of a topic required quantitative survey on a representative panel, using the associative method [START_REF] Abric | L'approche structurale des représentations sociales : développements récents[END_REF]. The respondents are asked to react to the statement of an inductive word by formulating and classifying word-pictures.

The most frequent and most important word-images form the core of representations common to a social group. This core composition can be confirmed by the calling into question technique (CIQ) [START_REF] Lo Monaco | Test d'indépendance au contexte (TIC) et structure des représentations sociales[END_REF]); • The spatial and territorial dimensions of water representations can be addressed by mobilising the production of commented handmade maps by a limited number of individuals [START_REF] Gieseking | Where We Go from Here: the Spatial Mental Mapping Method and Its Analytic Components for Social Science Data Gathering[END_REF]Girard et al., 2016) ; • Semi-structured interviews reveal the functional relationships that people establish between the different components of their representations; • Representations are transformed during social interactions where perceptions, attitudes, experiences and opinions are confronted. Participatory devices are similar to moments of reproduction of a thinking micro-society. In particular, focus groups [START_REF] Kitzinger | Qu'est-ce que les focus groups ?[END_REF], citizens' juries integrating debates with experts [START_REF] Barbier | Portée et limites du dispositif « jury citoyen[END_REF], serious game debriefings [START_REF] Hassenforder | Manuel d'observation des jeux sérieux[END_REF], and foresight events are opportunities for exchanges, especially when they offer social dilemmas as stimuli [START_REF] Caillaud | Représentations sociales et significations des pratiques écologiques : Perspectives de recherche[END_REF]. They reinforce objectification processes, making abstract concepts concrete. They help anchor new features, by integrating fresh knowledge, in order to make them familiar and transform the meaning of representations [START_REF] Pianelli | Rôle des représentations sociales préexistantes dans les processus d'ancrage et de structuration d'une nouvelle représentation[END_REF]. This anchoring process occurred in particular through the analogies and differences mobilised, the virtual dialogues (the "it is said that") when certain norms or value judgments are difficult to endorse publicly (Wibeck, Adelswärd et al., 2004). The virtual situation of a serious game accelerates the lived experience -through the trial and error of several options -and also favours a second learning loop necessary for the questioning of values and norms [START_REF] Medema | Multi-Loop Social Learning for Sustainable Land and Water Governance: Towards a Research Agenda on the Potential of Virtual Learning Platforms[END_REF], particularly when expressing disagreements (Duchesne and Haegel, 2008).

Advantages and drawbacks of the approach

This approach offers certain advantages in terms of improving knowledge:

• It reveals the reasons for preferences-refusals on behavioural regulation tools, based on values, dominant knowledge and beliefs, and perceptions of social justice, thus providing a point of view complementary to the standard cost and benefit analysis; • It is very effective in addressing the psychological distancing process (territorial, temporal or personal) of certain groups of actors towards the consequences of climate change, which is one of the major obstacles to climate change adaptation (Spence et coll. 2012); • It can help define an information strategy: which knowledge gap for which audience, which issues of concern, which political or ethical principle is at stake. 11

On the other hand, this approach requires a rigorous implementation, but also triangulation of the sources of analysis and therefore does not rely simply on the dominant voices of focus groups, which may carry a strategic message. This explains the two identified drawbacks:

• Being time-consuming and complex in the articulation of the different methods, which sometimes mobilise large representative samples, more qualitative approaches sometimes occurring in restricted groups; • Being limited in understanding and regulating water use practices anchored in daily routines, for which the behaviour is no longer the result of a conscious decision process (e.g. hygiene practices, eating habits, etc.) [START_REF] Spurling | Interventions in practice: reframing policy approaches to consumer behavior[END_REF].

Stated preferences methods

Literature review

Understanding the preferences of stakeholders for the environment, anticipating their responses to agro-environmental policies remains a challenge. This is because policies are established in complex and dynamic contexts and a great diversity of stakeholders is involved. Surveys based on hypothetical choices offered to stakeholders, often referred to as stated preference methods, can improve our ability to assess these preferences. Stated preference methods have been widely used in the environmental economics literature and their use in interdisciplinary research is increasing; this allows for the ex-ante estimation of people's preferences and the values they associate with new technologies, services, policies, or programs (e.g., [START_REF] Favre | Are Households Willing to Finance the Cost of Individual Water Supply? Case Study in Central Tunisia[END_REF][START_REF] Hérivaux | Valuing a diversity of ecosystem services: The way forward to protect strategic groundwater resources for the future?[END_REF][START_REF] Jourdain | A choice experiment approach to evaluate maize farmers' decision-making processes in Lao PDR[END_REF][START_REF] Mokaddem | Conception d'un paiement pour services environnementaux en pâturages collectifs. Une expérimentation des choix[END_REF] Contingent valuation methods allow for the direct elicitation of the stakeholders' willingness to pay for a hypothetical scenario of environmental improvement [START_REF] Mitchell | Using Surveys to Value Public Goods: The Contingent Valuation Method[END_REF]. The assumption is that the stated values reflect the benefits each respondent derives from the scenario. Discrete choice experiments (DCE) elicit respondents' preferences through controlled experiments also based on hypothetical scenarios [START_REF] Hensher | Applied choice analysis[END_REF][START_REF] Train | Discrete choice methods with simulation[END_REF]. Using a survey format, respondents are asked to make choices between different hypothetical versions of policy instruments and/or their environmental outcomes, which are described by their characteristics/attributes. The combinations of features/attributes are proposed to respondents according to a predefined experimental design that maximizes the reliability of respondents' calculations of trade-offs between the different attributes [START_REF] Rose | NGENE User Manual and Reference guide[END_REF].

Both methods are based on standard economic theory and assume that the decision maker is a rational utility-maximizing agent who will choose the alternative that provides him or her with the highest utility. In addition, DCEs also assume that respondents are willing and able to make trade-offs between the desirable and undesirable aspects of each alternative. Finally, DCEs assume that respondents consider all aspects or attributes of the alternatives in the same manner.

The application of stated preference methods to the study of socio-hydrosystems can include estimations of the value of water-related ecosystem services generated by policy interventions (e.g., [START_REF] Favre | Are Households Willing to Finance the Cost of Individual Water Supply? Case Study in Central Tunisia[END_REF][START_REF] Hérivaux | Introducing nature into cities or preserving existing periurban ecosystems? Analysis of preferences in a rapidly urbanizing catchment[END_REF][START_REF] Kanyoka | Households' preferences and willingness to pay for multiple use water services in rural areas of South Africa: An analysis based on choice modelling[END_REF][START_REF] Vivithkeyoonvong | Willingness to pay for ecosystem services provided by irrigated agriculture in Northeast Thailand[END_REF] or an estimation of the factors influencing stakeholders' willingness to participate in water-related policy instruments (e.g., [START_REF] Cottet | ViaRhôna : la valorisation du patrimoine rhodanien à l'épreuve des territoires, des acteurs et des usages. Rapport final du projet RhônaVel'eau, Plan Rhône[END_REF][START_REF] Manganyi | Preferences for index-based pasture insurance: a choice experiment in Limpopo Province, South Africa[END_REF] 5.

Examples of use within PRECOS

Uses of valuation methods based on stated preferences within the PRECOS team are very varied, in terms of purposes, surveyed population, themes, and application fields (Table 2). In our work, we can distinguish four main purposes of evaluation and four types of objects evaluated: • Analysis of motivations for riverrelated leisure choices and role of the river ecological restoration

Advantages and limitations

The advantages and limitations of stated preference valuation methods have been widely discussed in the economic literature (for recent review and discussion of good practices see [START_REF] Brouwer | A global meta-analysis of groundwater quality valuation studies[END_REF][START_REF] Johnston | Contemporary Guidance for Stated Preference Studies[END_REF]. With regard to their use in our research, we identify two main categories of limitations:

The first category includes technical difficulties related to the design of the survey questionnaire. Indeed, meta-analyses show that survey design characteristics (WTP elicitation format, payment vehicle, statistical estimation procedure, etc.) explain almost 10% of the variance across WTP estimates, highlighting the importance of methodological and survey design choices [START_REF] Brouwer | A global meta-analysis of groundwater quality valuation studies[END_REF]. Limiting possible biases, therefore, calls for a high degree of expertise and compliance with constantly evolving good practices. The construction of realistic hypothetical scenarios that are understandable to respondents is a difficult exercise, requiring the integration of different fields of knowledge, especially as the subject of the evaluation is complex. Meta-analyses also highlight the importance of the information provided to characterise the valued scenario, but also the reference scenario, as (i) WTP values are sensitive to scope and reference dependence; (ii) WTP values are sensitive to uncertainty in the baseline scenario; and (iii) the use of a single word with emotional overtone can influence the evaluation, e.g., mentioning "cancer" in the questionnaire significantly increases WTP for good groundwater quality [START_REF] Brouwer | A global meta-analysis of groundwater quality valuation studies[END_REF]. This becomes particularly important when valuing environmental goods and services that are unfamiliar to the respondents (e.g., groundwater ecosystems). The use of pictograms and pictures may help convey the changes to be valued, but could be misleading when designed by researchers unfamiliar with the cultural codes of the countries where they are conducting the survey. Finally, the size of the sample of respondents needed for a robust statistical analysis is important, especially if one of the objectives of the research is to analyse the heterogeneity of preferences. Surveys conducted in less developed countries and with target populations that are difficult to reach (e.g., farmers in remote areas as in Jourdain, Lairez, Striffler, et al. ( 2022)) seriously limit the number of respondents when compared to internet-based interviews conducted with respondents provided by professional panel providers. All this leads to significant costs and implementation.

The second category of limitations, in particular when analysing DCE results, relates to the differences between the hypotheses of the respondents' behaviour or way of reasoning and their real behaviour and choice heuristics: the use of these methods is based on the assumption that individuals make trade-offs between the different attributes of the subject of the evaluation (including the financial consequences for the respondents). It has, however, been shown that some people use different choice heuristics, e.g., elimination by aspect, ANA, etc. [START_REF] Hensher | Non-attendance and dual processing of common-metric attributes in choice analysis: a latent class specification[END_REF]Jourdain, Lairez, et al., 2022;[START_REF] Jourdain | Valuation of ecosystem services provided by irrigated rice agriculture in Thailand: a choice experiment considering attribute nonattendance[END_REF][START_REF] Scarpa | Modelling attribute non-attendance in choice experiments for rural landscape valuation[END_REF]. Prior surveys to identify subpopulations of preferences may help to solve this problem (e.g., [START_REF] Armatas | Applying Q-methodology to select and define attributes for non-market valuation: A case study from Northwest Wyoming, United States[END_REF][START_REF] Jensen | A Structured Approach to Attribute Selection in Economic Valuation Studies: Using Q-methodology[END_REF][START_REF] Mahlalela | Diverse stakeholder perspectives and ecosystem services ranking: Application of the Q-methodology to Hawane Dam and Nature Reserve in Eswatini[END_REF]. On the other hand, even if people do reason by making compromises, the high number of attributes and of attribute levels as well as the way they are presented to surveyed people increases the cognitive difficulty of choices, in particular for people with low levels of education. Furthermore, despite the precautions taken in designing the questionnaire, the possibility of a discrepancy between people's real and declared choices remains. Finally, on a more ethical and philosophical level, one may criticise the utilitarian and anthropocentric conception of values of the neo-classical framework on which these methods are based (Vatn, 2004;[START_REF] Kallis | To value or not to value? That is not the question[END_REF][START_REF] Parks | What have economists learned about valuing nature? A review essay[END_REF].

With the exception, perhaps, of the intrinsic complexity of our valuation subjects, whether they are public policy options or hydrosystem conditions, those limits are not specific to the application of stated preference methods to socio-hydrosystems.

Despite these various limitations, valuation methods based on stated preferences, and in particular the choice experiment, present several points of interest for our research: first, these methods can be adapted to a great diversity of subjects (hydrosystems, public policies). These are the only valuation methods that consider both the values that people attach to a hydrosystem or parts of it, because of their use, and non-use values (bequest value, intrinsic value), and research has shown that in the case of socio-hydrosystems the latter can be as important as the former [START_REF] Johnston | Modeling relationships between use and nonuse values for surface water quality: A meta-analysis[END_REF]. Compared with contingent valuation, choice experiment makes it possible to estimate the value placed on specific attributes of socio-hydrosystems or public policies and to propose more diverse scenarios of change.

Provided certain precautions are taken in the design of the questionnaire, sample size, and choice of econometric model [START_REF] Johnston | Contemporary Guidance for Stated Preference Studies[END_REF], it is possible to analyse the heterogeneity of preferences within the considered population. This may reveal potential conflicts between stakeholders or help take into account the attitudes of those concerned in the subsequent implementation of policies.

Specificity of our use of the method for the analysis of socio-hydrological systems

As a preamble, it is important to note that the PRECOS researchers are mainly "users" of stated preference methods: they adapt them to socio-hydrosystems issues, but they do not necessarily seek to develop new econometric models. Besides, they are often mostly interested in the analysis of the heterogeneity of preferences, motivations, attitudes, and decision-process (for example the conception of human-nature relationships, risk aversion, etc.). As such they do not always emphasise the WTP or WTA results but, instead, discuss the heterogeneity of the preferences in order to anticipate potential conflicts between stakeholders.

The purpose of the stated-preference research conducted by the PRECOS team is to support public policies and decision-making. Consequently, the research questions are co-constructed with the stakeholders involved in the management and use of the socio-hydrosystems at stake, such as ministries, water agencies, regions, chambers of agriculture, mixed syndicates, and water services. In the same way, the surveys are designed in consultation with them. The research results are used to help design public policy instruments or to conduct analyses to justify public policy choices. Therefore, the results are also shared with the stakeholders to increase the impact of the research.

An abundant literature describes the potential biases associated with the use of SP methods for valuing environmental goods [START_REF] Johnston | Contemporary Guidance for Stated Preference Studies[END_REF]. Our research suggests that there are additional problems related to the specific characteristics of socio-hydrosystems. They include:

1. Unfamiliarity with the goods and services evaluated by the respondents (e.g., groundwater ecosystems) and the important role (and bias) played by the information provided to the respondents. This task is even more complex when the information has to be conveyed via interpreters. 2. Complexity of the goods and services evaluated because of multiple uses and multiple scales (e.g., for the evaluation of the benefits of hydrosystems) 3. Uncertainties of the effects of proposed policies on socio-hydrosystems and the resulting uncertainty in the statements of the scenarios 4. Multiplicity of stakeholders and views, and the resulting issues for properly evaluating the preferences (e.g., the presence of ANA for some part of the respondents) 5. Non-monetary reasoning. Adapting the choice of payment vehicle or EC without a price and the necessity to adapt the payment vehicle to non-monetary equivalents On the first point, a major concern when applying SP methods to socio-hydrosystems is the very limited knowledge respondents may have of the environmental asset they are asked to value. In theory, SP methods should be used only when respondents have what Lazo et al. (1992) call "perfect information". Evidence from various surveys shows that this is rarely the case. People generally have very limited knowledge of groundwater resources and related management issues, even when they have a direct link to the resource through private wells. In such situations, SP specialists acknowledge that the method can still be used (Arrow et al. 1993). The burden of informing respondents then falls on the survey instrument. To avoid information bias, special attention should be paid to designing the survey protocol and questionnaire, especially to selecting the nature, format, and quantity of information provided to respondents [START_REF] Hérivaux | Integrated assessment of economic benefits of groundwater improvement with contingent valuation Integrated Groundwater Management[END_REF]. In that respect, when working in countries of the south, lower education levels of the population surveyed and the necessity to use interpreters render this task even more crucial. Factoring in the possibility of more uncertain respondent choices is also important [START_REF] Jourdain | Identify Lao farmers' goals and their ranking using bestworst scaling experiment and scale-adjusted latent class models[END_REF] On the second point, two types of observed embedding effects, closely related to the "mental model" of joint products highlighted by Schulze et al. ( 1998): respondents may have different mental models, often strongly held, which will replace whatever mental model the researcher intended to impose on the respondent. For example, in the case of groundwater, some respondents perceive groundwater as a uniformly distributed resource, rather than a collection of well-defined and spatially delineated reservoirs. These respondents are therefore not able to make a clear distinction between protecting groundwater in a broad sense on the one hand and protecting a specific aquifer on the other. The second embedding effect is linked to situations where actions to protect / restore groundwater also generate a wide range of environmental benefits (e.g., biodiversity, air quality regulation, positive landscape amenities…). Respondents may face difficulties in disentangling those benefits derived from groundwater protection from those of other environmental benefits [START_REF] Hérivaux | Integrated assessment of economic benefits of groundwater improvement with contingent valuation Integrated Groundwater Management[END_REF].

On the third point, another important concern is to develop credible scenarios. However, the potential outcome of projects aiming at modifying hydrosystems, or of policies, are indeed prone to many uncertainties. Recognizing these uncertainties and factoring them into the design of the surveys is also important [START_REF] Manganyi | Preferences for index-based pasture insurance: a choice experiment in Limpopo Province, South Africa[END_REF].

On the fourth point, water resources and the benefits of water-related ecosystems are often shared among stakeholders that have different views and different interests. While some stakeholders may value particular attributes of the ecosystems, others may value different ones. This may present some difficulties when designing the choice experiment, as some attributes may not be relevant to all respondents. In such a situation, some of the respondents may show a lack of interest in the survey, or develop various specific heuristics to make their choices. To minimize this possibility, some recent research argued that prior research to detect the diversity of views about the ecosystems may be warranted [START_REF] Armatas | Applying Q-methodology to select and define attributes for non-market valuation: A case study from Northwest Wyoming, United States[END_REF][START_REF] Jensen | A Structured Approach to Attribute Selection in Economic Valuation Studies: Using Q-methodology[END_REF][START_REF] Mahlalela | Diverse stakeholder perspectives and ecosystem services ranking: Application of the Q-methodology to Hawane Dam and Nature Reserve in Eswatini[END_REF].

On the fifth point, PRECOS researchers are sometimes working with communities and farmers who are not well connected to markets. In such cases, respondents may not respond to monetary incentives or may not reason in terms of monetary equivalent and then CE without specific monetary attributes may be used [START_REF] Jourdain | Farmers' preference for cropping systems and the development of sustainable intensification: a choice experiment approach[END_REF], or the use of other research methods may be required to evaluate the diversity of attitudes towards the services (e.g., [START_REF] Mahlalela | Diverse stakeholder perspectives and ecosystem services ranking: Application of the Q-methodology to Hawane Dam and Nature Reserve in Eswatini[END_REF].

Experimental economics in the lab and in the field

For a long time considered a non-experimental science [START_REF] Samuelson | Economics[END_REF], economics moved in the last decades of the 20 th Century towards a growing trend of experimental studies. The trend culminated in the Nobel prize awarded to V. Smith and D. Kahneman in 2002, for their work based on laboratory experiments involving market structures and agents' decisions under uncertainty.

Experimental economics consists of controlled experiments where the observed behaviour of the participants is a function of the environment (endowments, monetary rewards that motivate exchanges, etc.) and of an institution (instructions that describe the messages and the procedures of the market) [START_REF] Smith | Economics in the Laboratory[END_REF].

Conceptual foundations and literature review

By controlling the variables representing the environment and the institution, the participants' behaviour is observed when only one variable is changed at the time (ceteris paribus condition). The clear advantage of this method is the possibility of isolating one variable at the time that has an influence on the economic behaviour of agents and avoiding the 'noise' provoked by variables coexisting in other empirical studies based on data in uncontrolled setting.

Economic experiments are typically conducted in a laboratory, as this allows the control of environmental and institutional variable. Participants in these experiments are usually university students. This highly controlled setting allows the unbiased identification of exogenous treatments.

The external validity of this type of setting remains however limited unless one wants to insist a priori that those aspects of economic behaviour under study be perfectly general [START_REF] Harrison | Field experiments[END_REF]. Field experiments have been developed in complementarity with lab experiments in order to improve the external validity of economic experiments. Artefactual field experiments are the same as conventional lab experiments but with a nonstandard subject pool such as farmers or water users. A framed field experiment also includes in the environment and institutions a field context in either the task or information set that the subjects can use. Finally, in a natural field experiment the environment is one where the subjects naturally undertake these tasks and where the subjects do not know that they are part of an experiment [START_REF] Harrison | Field experiments[END_REF]. Recently, the terminology of Randomized Controlled Trials to designate natural experiments has gained momentum in the context of the "Nobel" prize awarded to Esther Duflo, Michael Kremer and Abhijit Banerjee.

Experimental economics has been used for several goals. [START_REF] Roth | Laboratory Experimentation in Economics -a Methodological Overview[END_REF] identifies three main objectives: 1) test theories; 2) produce facts to identify behavioural regularities still unknown and that can integrate economic models; 3) help decision-making, by testing the consequences and implications of the adoption of a new policy tool.

In the analysis of behaviour of actors in socio-hydro systems, the main goal of experimental economics is the third, looking for instance at the effectiveness or the acceptability of a local regulation tool for water allocation. Moreover, an economic experience can be used to elicit the risk and time preferences of local farmers when faced with a decision whether to invest in an innovative irrigation technique.

The experiments conducted in SHS in a scheme derived from a conceptual framework proposed by Ehmke and Shrogen (2008) might be placed to represent the experimental mindsets in social sciences (Figure 2). The scheme is composed of three broad and overlapping areas: Markets, Social preferences, and Environmental experiments. There are clear overlapping areas because people make their decisions within market and non-market contexts simultaneously, and this overlap of exchange institutions (i.e. institutions that allow transactions such as markets or agencies) can affect their decisions.

Socio-hydro systems, such as socio-ecological systems may easily be put in the area of Environmental experiments, where markets do exist, but are characterised by generalised market failure (common pool resources and absence of the excludability criterion for these economic goods). Experiments in this area are designed to evaluate: i) the rules that define new exchange institutions and incentive systems, ii) efficiency impacts of property rights and access to resources, iii) conventions creating conflicts and cooperation over resources.

However, experiments about socio-hydro systems seem particularly relevant in the overlapping areas between the Environmental experiments area and the other two.

The Markets -Environmental experiments overlap is where economists and environmental economists test policy instruments (taxes, subsidies, permits, etc.) to control environmental production [START_REF] Cason | A laboratory study of auctions for reducing non-point source pollution[END_REF]. The Social preferences-Environmental experiments overlap is where authors such as [START_REF] Ostrom | Rules, games, and common pool resources[END_REF] and [START_REF] Walker | Probabilistic Destruction of Common-Pool Resources -Experimental-Evidence[END_REF] apply experimental economics to the analysis of the common pool resource use and governance. Issues such as the consequences on the use of common pool resources of communication and participation in the design of management policies have been extensively studied. Studies of the role of non-monetary enforcement [START_REF] Masclet | Monetary and nonmonetary punishment in the voluntary contributions mechanism[END_REF] on the use of common pool resources was also analysed, and on the impact of trust, social capital, and social networks for the management of natural resources [START_REF] Ensminger | Reputation, trust, and the principal agent problem[END_REF] can also be put in this overlap area.

Finally, the Markets-Social preferences-Environmental experiments overlap area includes studies such as the rationality spill-over and the analysis of corruption, which seem to us currently less relevant to experiments in socio-hydro systems.

Examples in the PRECOS team

Table 3 includes some examples of studies about the behaviour of actors in socio-hydro systems that have been approached by the PRECOS team through experimental economics. [START_REF] Farolfi | Fourniture d'information et consentement à payer l'eau d'irrigation dans les groupements de développement agricole tunisiens. Une étude par l'économie expérimentale[END_REF] studied to what extent information provided to users on the functioning of the system ("institutional" information) and/or on the decisions taken by other users ("social" information) can affect their WTP. The analysis was twofold. A field survey first revealed the farmers' demand for better information provision. A laboratory experiment then allowed isolating the impact of the two types of information on subjects' decisions through a framed game, with properties similar to those observed in the field. Data collected in the lab confirmed the existence of a causality relation between information provided to users and their WTP for a common resource such as irrigation water. External validity of the results obtained in the laboratory should be tested by a lab-in the field experiment with real stakeholders. This work would fit in the Environmental experiments-markets overlap in Figure 2. 2019) studied the impact of social comparison information on farmers' irrigation decisions. Although social norms and social comparison nudges have proved to have a significant impact on a variety of behaviour, it is questionable whether this type of information may have an impact in real-life socio-hydro systems, especially for decisions that involve large economic stakes such as irrigation decisions. In order to test this hypothesis in a real-life context, the authors conducted a randomised controlled trial among 200 farmers equipped with irrigation smart meters in South-West France. Treated farmers received weekly information on individual and group irrigation water use over four months. Our results rule out medium to large average effect-sizes of the nudge. They nevertheless suggest that the social comparison was effective at reducing the consumption of those who irrigate the most, although it appears to backfire and reduce the proportion of those who do not consume water at all. This work would fit into the Environmental experiments-markets overlap in Figure 2.

The goal of the [START_REF] Brugnach | Relational quality and uncertainty in common pool water management: An exploratory lab experiment[END_REF] paper was to understand if and how the socio relational environment in which decisions are made shapes decision-making under uncertainty in common pool water resource management. The aim of this paper was twofold: methodological and analytical. It consisted in designing experiments for carrying out uncertainty analysis to explore the influence that the relationships established among decision actors have in making decision choices under uncertainty in management processes. To this end, the authors developed one experimental game protocol, representing a typical water management scenario: irrigation, in which they tested three different conjectures about the combined effects of uncertainty and relationships. In doing so, authors played close attention to the quality of relationships developed among players (acting as water managers), and how these relationships were structured and organised. Initial laboratory tests, to be confirmed through lab in the field experiments, initially confirmed the importance that the relationships established among players have for coping with uncertainty in managing water resources. This work would fit in the Environmental experiments-Social preferences overlap in Figure 2.

Specific features of experimental protocols in socio-hydro systems

It is important to ask ourselves at this stage whether there is a particular specificity in the use of economic experiments for the analysis of socio-hydro systems. The following characteristics require in our opinion particular attention in designing the protocols adopted in the analysis of socio-hydro systems (Table 4).

The Complexity of the system, both in the social and in the hydrological components. Interdependency among the various components of the system is an immediate consequence of complexity. The Asymmetry of access to the resource: in an irrigation system for instance, farmers are placed in a sequence where head-enders are privileged over tail-enders in the access to water. Water is also a dynamic resource, which flows through the system. The latter are two quite specific (while not exclusive) characters of socio-hydro systems compared to socio ecosystems. The multiple facets of water as natural resource represent another characteristic of SHS (for instance water is characterised by its quantitative availability, but also by the quality of the resource). Water also has multiple uses, and is a particular economic good, which can, in different contexts, assume different economic values (private good, public good, common pool resource, or even club good). Uncertainty in the availability and the difficulty to observe (particularly groundwater) the resource are two additional characteristics of SHS. Important aspects concerning the management of SHS are the crucial role of institutions for the governance of the resource and the relevance of information provision and communication for water management. As is often the case, the results of our research have direct policy implications so there is a pressing need to verify the external validity of our analyses. Finally, in this not exclusive list of characteristics of the SHS, we cite the relevance of the analysis of interrelations (relational quality, presence of social capital) among the members of the social component of our systems.

Within PRECOS, we analyse several of the mentioned aspects in socio-hydro systems using experimental economics. For instance, in addition to the case studies presented above (Table 2), Figureau et al. (2012) analysed different instruments for groundwater management combining economic incentives and social preferences. [START_REF] Chabé-Ferret | Can we nudge farmers into saving water? Evidence from a randomised experiment[END_REF] studied the influence of social information on the water use decisions of farmers. [START_REF] Dubois | Contrasting effects of information sharing on common-pool resource extraction behavior: Experimental findings[END_REF] studied the influence of information sharing by CPR users on the resource management.

We consider that framing matters in economic experiments on SHS. Several authors state [START_REF] Laury | Altruism spillovers: Are behaviors in context-free experiments predictive of altruism toward a naturally occurring public good?[END_REF][START_REF] Michel-Guillou | Commitment of farmers to environmental protection: From social pressure to environmental conscience[END_REF][START_REF] Cooper | The impact of meaningful context on strategic play in signaling games[END_REF]) that context in an economic experiment is essential to facilitate the understanding of the problem by players and their explication of behavioural variables otherwise masked by an abstract experimental protocol. The work of our team, such as [START_REF] Farolfi | Influence of Context on Player Behavior[END_REF], therefore tests the effects of framing and confirmed the effects of the water contexts on players' behaviour. What can be observed at this stage is that SHS have some specific characteristics (while not exclusive) and many other characteristics common to all socio-eco systems that are already widely studied in experimental economics through the research on CPR [START_REF] Walker | Rent Dissipation in a Limited-Access Common-Pool Resource -Experimental-Evidence[END_REF]. We may then conclude that there is no need for a specific method or approach to study socio-hydro systems through economic experiments. On the other side, there are some specificities in socio-hydro systems that characterise these systems. These specificities, namely the asymmetry of access to the resource, the dynamic and flowing nature of water, and the difficulty of observing the resource (limited to groundwater) require particular attention in the use of experimental economics to analyse the socio-hydro systems. [START_REF] Janssen | Head-enders as stationary bandits in asymmetric commons: Comparing irrigation experiments in the laboratory and the field[END_REF] develop an experimental set-up for irrigation water that takes into consideration these characteristics, and that is so framed that the so-called 'micro-situational variables' can play their role. Some of our more recent studies (Bonte et al., 2019;[START_REF] Brugnach | Relational quality and uncertainty in common pool water management: An exploratory lab experiment[END_REF] use experimental set-ups in line with the work by [START_REF] Janssen | Head-enders as stationary bandits in asymmetric commons: Comparing irrigation experiments in the laboratory and the field[END_REF]. Other studies in our group [START_REF] Farolfi | Fourniture d'information et consentement à payer l'eau d'irrigation dans les groupements de développement agricole tunisiens. Une étude par l'économie expérimentale[END_REF][START_REF] Dubois | Contrasting effects of information sharing on common-pool resource extraction behavior: Experimental findings[END_REF] are based on more 'conventional' experimental economic protocols (not framed, considering water as a CPR with symmetric access by users, etc.), particularly when we want to go deeper into some specific aspects of the observed behaviours that emerged from previous analysis.

Advantages and limitations

Some final considerations may be necessary about the advantages and limits of the use of experimental economics methods to approach the research questions presented.

A clear advantage comes from the possibility of isolating the effect of specific variables on the actors' behaviour and testing, through a rigorous protocol and with quantitative indicators, the hypotheses made. Another important advantage, with respect to the stated preferences methods, resides in the fact that subjects participating in an experiment reveal their 'real' economic preferences by making their choices as they act, knowing that their performance will be remunerated immediately after the experiment. Conversely, stated preference methods are biased by the fact that subject declare their preferences without a corresponding payment, and therefore are more prone to 'lie' for many reasons. Hypothetical bias arises in stated preference valuation studies when respondents report a willingness to pay (WTP) that exceeds what they actually pay using their own money in laboratory or field experiments [START_REF] Loomis | What's to Know About Hypothetical Bias in Stated Preference Valuation Studies[END_REF]. Experiments nevertheless usually require reductionist approaches that do not allow for accounting for the multiple specificities of SHS. This may limit the so-called external validity, or generalisation of results of the experiments [START_REF] Levitt | What do laboratory experiments measuring social preferences reveal about the real world?[END_REF].

One of the main constraints of the use of experimental methods is their applicability to exploring the various contexts of SHS. Indeed, practical limits still exist in the implementation of lab experiments in the field, due to the difficulty of recreating laboratory conditions (lack of electric power, internet network, etc.) particularly in southern fields. Also, in several communities, the use of monetary incentives is seen with scepticism and sometimes distrust, while NGOs and development agencies are reticent in the use of monetary incentives as they 'spoil' the stakeholders. Consequently, alternatives to the use of monetary incentives (ex. seeds, food, etc.) are often to be found.

Hybrid methods

Literature review

As illustrated in the other sections of the paper, our group mobilises several methods to carry out our research. It is sometimes necessary to use methods from distinct scientific disciplines and this brings us to inter / multi / trans disciplinary studies. This section is dedicated to such approaches, ones that we have considered as hybrid methods. Based on Alvargonzalez (2011), we use the following definitions: a multi-disciplinary study consists in a study using several disciplines jointly but staying within the boundaries of each discipline; an inter-disciplinary study consists of analysis and synthesis coordinated as a coherent whole; and a trans-disciplinary study consists of integrated natural, social and health science in a humanities context transcending the traditional boundaries of each discipline. The disciplines and approaches on which we focus here, in the context of analysing behaviours of individuals involved in SHS questions, are developed in this section, divided into four categories of hybridization.

1. Combining behavioural economics together with social psychology: Actors enrolled in socioenvironmental contexts, such as common pool resource (CPR) dilemmas, are faced with economical behavioural choices (e.g., self-interest, altruistic) that may influence their cognition (e.g., attitudes, opinions, economical preferences). Hence, it seems useful to address research questions, and consequently to develop hybrid methods relative to the interaction between behavioural economics and social psychology. We develop methods using experimental CPR dilemmas (e.g., [START_REF] Ostrom | Rules, games, and common pool resources[END_REF] ; literature related to strategic behavioural choices in game theory research (e.g., [START_REF] Cox | How to identify trust and reciprocity[END_REF] and field experiment research (e.g, Cardenas et al., 2000 ;Fehr and Fischbacher, 2002 ;[START_REF] Velez | What motivates common pool resource users? Experimental evidence from the field[END_REF] ; literature related to attitude change (e.g., Festinger, 1959), explicit attitude measures (e.g., [START_REF] Krosnick | Attitude measurement. Handbook of attitudes and attitude change[END_REF], implicit attitude measures (e.g. [START_REF] Greenwald | Measuring individual differences in implicit cognition: the implicit association test[END_REF] and to relations between explicit and implicit attitude changes (e.g., Gawronski et Bodenhausen, 2006).

2. Combining social psychology theories with social simulation: In our research unit, we use participatory methods, such as role-playing games, to support natural resource management.

However, we need to be aware of the influence of game settings on participants' behavioural patterns and attitudes, before fine tuning the design and use of the games. To this end, we developed a method to assess the framing induced by the conditions of implementation of a game. Our methodology was first to formalize theories from social psychology on attitude change and attitude-behaviours relationships (Glasman and Albarracin, 2006 ;Azjen, 1991Azjen, , 2004 ; ;Albarracin, 2000). And, second, to implement them into an agent-based model representing a role-playing game, in accordance with the literature on opinion dynamics (e.g., Holley and Liggett, 1975 ;Galam, 2002 ;Sznajd-Weron and Snajd, 2000 ;Latané, 1981 ;Deffuant et al., 2000 ;Hegselmann and Krause, 2002).

3. Combining participatory modelling together with agent-based modelling and experimental economics: Although Agent Based Modelling (ABM) is a very powerful tool for integration of disciplines in interdisciplinary or transdisciplinary studies [START_REF] Bousquet | Simulating the interaction between a society and a renewable resource[END_REF][START_REF] Bousquet | Multi-agent simulations and ecosystem management : A review[END_REF], they have, in this research group, more the role of a method that we want to hybridize with others.

We use them for their ability to formalise the situation of an economic agent, in relation to other agents and to their environment.

4. Combining economic modelling together with water-resource modelling: in our team, we developed several multi-model couplings integrating economical and water-resource dimensions. Researche is aimed at using these models as computational tools for different purposes, such as helping water managers with their adaptation strategy to global change, or with understanding the sustainability trade-offs of subsistence versus market-based agriculture. Regarding the PRECOS team focus, we aim at integrating these models into experimental frameworks to support the economical behavioural choices of participants. The models we develop in order to couple them with economical modelling include hydrological / hydrogeological modelling, that consists in using mathematical equations to simulate the way precipitation over a given river basin / territory is transformed into river flow and infiltration to recharge aquifers, using several different computation methods (Semenova and Beven, 2015;Refsgaard et al., 2012). Water demand modelling methods mobilise the mathematical combination of economic, social, demographic and environmental variables at the scale of the territory that depends on surface and/or groundwater resources (Collet et al., 2013;Terrasson et al., 2014). Climate change modelling consists in handling complex mathematical models able to describe the land surface and atmosphere dynamics and interactions (O'Neill et al., 2016). Note that hybrid methods generally do not carry out climate models that are too computational costly, but rather use future projections of the climate variables they provide to force hydrological and water demand models. As an integrative modelling and simulation approach, we can cite System Dynamics (SD) modelling (Forrester, 1961); originally developed for the business consulting field, it consists in representing a complex system through a series of stocks, flows, and auxiliary variables that complete feedback loops. While the dynamic behaviour of agent-based models stems from the interaction between many individual agents interacting according to (generally simple) set rules, in the case of SD modelling, dynamic behaviour emerges from the structure of the feedback loops incorporated into the model. Since its conception, SD modelling has been applied to many fields outside of business management, in particular hydrology (Mirchi et al., 2012) and natural resource management more generally (e.g., Arshad et al., 2015).

Examples from the PRECOS team

We illustrate these hybrid approaches through five case studies presented in Table 5, illustrating our four categories of hybridization explained in Section 2.4.1. (the fourth and fifth case studies being part of the fourth category).

1. We designed an experimental protocol based on a CPR dilemma inspired by [START_REF] Ostrom | Rules, games, and common pool resources[END_REF] and representing appropriation of water during periods of drought in the Aude watershed (France). We set two treatments, the first one representing the actual state (at the time of the experiment) of the water management at the political level in the area, and the second introducing a new political measure aimed at reducing the lack of water during periods of drought. Our objective was to identify and discriminate between the behavioural strategies used by the participants in the two treatments, and analyse the impacts of those behaviours on the attitude change of participants toward the sharing of water.

2. We designed an agent-based model representing the dynamics occurring in a role-playing game developed to support the management of runoff issues in the Pays de Caux (Normandie, France). The agent-based model is focused on the exploration of framings caused by game design and implementation of attitude dynamics occurring through successions of negotiations within the game. Mechanisms of attitude change were formalised with regard to social psychology theories and implemented in the model. Results of simulations bring possible explications of the underlying mechanisms of the framings caused by design and implementation choices, such as giving feedback to participants about the consequences of their actions.

3. This study attempts to gain knowledge of participatory modelling for natural resources management but this time using experimental economics combined with an ABM converted to an on-line game for the sake of experimental economics. In this case, we formalise our approach from a modelling and simulation perspective.

4. This example is devoted to the exploration of the interest of using the framework of interdisciplinary water resources and demand and econometric modelling to help water managers develop their adaptation strategy to global change at the river-basin scale. To that end, climate modelling projections are applied to hydrological and water uses modelling methods and the results are combined with ecological, economics, agronomical and civil engineering factors to build adaptation strategies through participative methods. The framework was tested on the Orb river basin, a Mediterranean basin in southern France, where global change is expected to exacerbate the difficulties of meeting the growing water demands and the WFD environmental in-stream flow requirements. It showed that optimisation models for the least-cost allocation of measures to satisfy all the constraints at the river basin scale may help to design global change adaptation strategies. It was also shown that it was useful to prioritize the type of actions to be implemented (for instance some conservation measures must be systematically implemented) in the adaptation strategy plan. Finally, the proposed modelling framework can help evaluate possible trade-offs between development of water uses, environmental objectives and costs of water management.

5. This example is similar to the fourth one in the sense that it uses a modelling and simulation approach to combine knowledge from various disciplines in an interdisciplinary framework. It uses system dynamics modelling to combine a micro-economic approach with physically-based crop modelling in the context of policy analysis for Indigenous food systems in Guatemala. In this case study, the main aim was to test the resilience of self-subsistence and market-oriented small-scale agriculture to climate change and socioeconomic shocks. The SD model was initially built from causal loop diagrams generated with stakeholders during (mostly) individual interviews before quantification with survey data, and it contains local microeconomic dynamics of labour and land allocation (agricultural versus salaried work for labour; agricultural, forest or shrubland for land use) based on the expected economic yield of each activity. Agricultural yield, in turn, was predicted with an external model (PCSE) that combined different climatic scenarios and soil conditions to predict the frequency and agronomic severity of droughts. Both models were then coupled with Tinamït software (Malard et al., 2017) to predict the reciprocal effects of drought impacts, vulnerability and societal (economic) response in the two different study cases.

Specific features of our hybrid methods in the landscape of socio-hydro systems studies

Hybridization of methods in general is of course not restricted to socio-hydro systems studies. In sociohydro systems studies, we note that several dynamics co-exist in interdisciplinary work about social and hydrological systems (or hydrological territories according to the groups) such as socio-hydrology [START_REF] Sivapalan | Socio-hydrology: A new science of people and water[END_REF][START_REF] Wesselink | Socio-hydrology and hydrosocial analysis: Toward dialogues across disciplines[END_REF] that includes social dynamics into hydrological models (and to which our fourth case could refer) or hydro-sociology [START_REF] Massuel | Inspiring a Broader Socio-Hydrological Negotiation Approach With Interdisciplinary Field-Based Experience[END_REF] trying to combine points of view from natural and social science in order to understand more profoundly the dynamics observed on a territory. Researchers from all these integrative approaches acknowledged the benefits of their combined approaches even though these are expensive in terms of time and effort because of the intricate nature of social and hydrological dynamics. We are not at the point where we can propose a clear view of hybrid methods for analysing practices, social representations and behaviours of sociohydro systems' actors but we hope that we are, through these works, contributing to building bridges that are needed for the study of socio-hydro-systems in general.

The formal quantification presented in the fourth example, through the modelling methods of the flows and balances between the different compartments of the socio-hydrosystems makes it possible to communicate in a concrete manner about their relative importance. This facilitates the prioritisation of the problems to be addressed when building adaptation strategies for climate change.

In the case of coupled SD modelling (fifth example), while there are no limitations to the nature of the external biophysical model (hydrological, cropping, ecological), the majority of published studies have used either a cropping or a hydrological model. This may be due to the fact that these model types are particularly complex and that many well-established and well-tested models already exist for these fields; this adds to the advantage of adopting a coupled modelling approach when dealing with sociohydro systems.

Advantages and limitations

Considering that our use of hybrids methods within the team is substantially different across the studies, we list the advantages and limitations regarding each example of case study:

1. Advantage: the development of a protocol integrating economical and psychological features allowed us to show relationships between two intra-disciplinary objects, i.e., strategic behaviours and attitudes, and then gives us a better understanding of the effects of a new political measure for water management on individuals.

Limitation: This kind of interdisciplinary study is very specific, which hinders us from enrolling in an existent scientific literature that fits our global approach to the research questions. Limitation: Subjective assumptions are still needed to model attitude changes occurring in a roleplaying game. This is due to the yet unknown mechanisms if human behaviour and cognitions. 3. Advantage and limitation: Using complex models, initially designed for participatory modelling, in experimental economics can bring "noise" to the protocols. However, it raises new kinds of research questions.

4. The type of optimisation framework proposed in the fourth example has the advantage of the integrative approaches that force participants to enter into dialogue and share their conceptual and methodological choices, which stand in contrast to multidisciplinary research where various disciplines may follow their priorities in parallel. Among the limitations associated with the fourth example, it may be mentioned that the type of optimisation framework adopted makes it difficult to quantify uncertainties. Indeed, they are of different types depending on the processes or factors considered (physical behaviour of the systems versus behaviour of the populations in terms of water use for example) and are too complicated to extrapolate from future situations. 28 5. In the case of Guatemala, the use of a hybrid (coupled modelling) approach allowed for the use of the most appropriate models for each of the socioeconomic and hydrological domains. While some efforts have been made to translate hydrological or cropping models to SD language, these efforts are time-consuming and result in less efficient models that are inflexible and computationally expensive to run. The coupling approach used here allows us to keep the hydrological and other biophysical aspects of the socio-environmental system within the framework of specialist models that have already been developed and well tested. At the same time, the use of a SD framework for the socioeconomic part of the system allows for the representation of these processes in a clear and visual form that is easy for stakeholders to understand. The coupling of the two systems then leads to the emergence of dynamic behaviour and feedback between the two. Such approaches facilitate the use analysis of the interactions between economic and hydrological (as well as other environmental) processes from a system dynamics point of view. At the same time, the use of SD as opposed to agentbased modelling precludes the representation of the behaviour of individual agents, meaning that economic processes must instead be modelled at the village or regional scale.

Discussion and conclusion

Analysing practices, social representations and behaviours of socio-hydro systems' actors is a complex task, as the system's object of study are complex ones, where individual subjects interact with other subjects (socio systems) and with the biophysical and ecological components of the hydro system. These interactions create multiple consequences and feedbacks, making it very difficult to isolate the relations of causality at the origin of the impacts that humans' actions have on the hydro systems and on other humans.

To study those complex interactions and try to represent practices, social representations and behaviours of socio-hydro systems' actors, our team PRECOS proposes the groups of methods presented in the previous section, and illustrated in the table below (Table 6), where a comparison is presented in terms of several criteria. These groups of methods are surveys/focus groups for the analysis of practices, social representations, preferences and stated preferences, experimental economics and field experiments, and hybrid methods.

Table 6. Comparison of the presented groups of methods Stated preferences methods and experimental economics produce more quantitative results, and are less adapted to the use of participatory approaches and procedures for their implementation than surveys and focus groups (although new developments in stated preferences have recently allowed some flexibility in the introduction of more participatory approaches). Surveys and stated preferences methods are usually implemented in field contexts, while experimental economics and hybrid methods can take place in both laboratory and field situations.

Following the examples presented in Section 2, surveys and focus groups have a higher tendency towards hybridisation and transdisciplinary approaches, even though stated preferences and experimental economics are progressively moving in this direction.

Stated preferences and experimental economics move from the same neoclassic mainstream economics foundations (economic rationality), while the analysis of practices, social representations and preferences based on survey and focus groups are rooted in other references, such as theories of planned action and of social representations.

Hybrid methods are influenced by the methods and approaches that constitute them, and this is true for all the criteria presented in the table.

All methods have advantages and limitations in terms of applicability to the studied systems and capacity to isolate the observed phenomena.

The analysis of practices, social representations and preferences through surveys and focus groups allows for depicting the emergence of preferences (or refusals) of regulation tools based on values and beliefs and on social justice perception; they are to be compared and put into perspective with the usual benefit-cost analysis. For these reasons, these methods inform managers and decision makers about the right information to disseminate and the best media to favour. On the other hand, these methods are relatively complex, take time to put in place, and sometimes require large samples that require expensive surveys.

Stated preferences are a well-established method that benefits from an extensive literature and from thousands of applications around the world, including in situations where socio-hydro systems are studied. These methods allow for eliciting both use and non-use values, the latter being particularly important in the case of socio-hydro systems. Choice modelling allows for estimating the value placed on specific attributes of socio-hydro systems and it is possible through them to analyse the heterogeneity of preferences within the considered population. On the other hand, these methods are relatively complex to put in place, and require a high level of technical skills, not often found in the field, and particularly not in developing countries. Another limit of the method is represented by the main hypotheses behind it (choice heuristics, neoclassical individualistic rationality), that are the targets of criticism from a large community of scientists that consider these hypotheses too 'restrictive' and not fully representative of human behaviour. Finally, stated preferences often do not fully reflect the real behaviour of economic agents. This 'hypothetical' bias favours the use of other methods complementary to those based on stated preferences.

Experimental economics and field experiments have their main strength in the capacity to analyse economic subjects' behaviour in controlled environments (laboratory or lab-in-the field) and in economically incentivised situations. Therefore, the hypothetical bias resulting from declarative methods such as the stated preferences ones is minimized. The possibility of isolating the variables at stake in specific treatments allows a precise analysis of the causality in the observed phenomena. On the other hand, laboratory experiments are questioned in terms of generalisation of the results obtained (external validity), and for this reason field experiments (lab-in-the-field) are often required, especially when the experiments aim at supporting decision making about public policies. The complexity and technicality of these methods are common to the stated preferences ones, and practical limits in the field, such as the difficulty to implement a lab, economically incentivised, protocol in rural areas of developing countries need to be mentioned. Randomised field trials require large samples and therefore are expensive and complicated to implement.

Hybrid methods have the advantage of their adaptation to a specific situation at stake and benefit from the complementarity of the original methods that constitute them. The main inconvenience is represented by the lack of seminal studies and texts for reference, as hybrid methods are crafted 'on the spot' based on the specific needs of the case study, and each case is 'unique.'

Our review of the groups of methods revealed that there are some specificities in socio-hydro systems that need to be considered with particular attention when designing and implementing the protocols for the analysis of practices, social representations and behaviours of socio-hydro systems' actors. These specificities, namely the asymmetry of access to the resource, the dynamic and flowing nature of water, and the difficulty of observing the resource (limited to groundwater), while not requiring a radical recrafting of the methods used in other contexts of socio-eco systems, suggest their adjustment to the specific cases.

Our position, in conclusion, is that there is no 'ideal' method for the study of practices, social representations and behaviours of socio-hydro systems' actors, and every case study deals with a very specific situation where the choice of the method to be applied is a new challenge. What we suggest in this paper is to proceed in two parallel directions:

1) Adapting as much as possible the proposed groups of methods to the specificities of SHS;

2) Moving in the direction of transversality and interdisciplinarity, by producing hybrid methods able to take into account the complexity of the systems at stake and benefit from the complementarity of different methods.

The main limitation of this study resides in the incomplete review of methods and tools proposed for the analysis of the practices, social representations and behaviours of socio-hydro systems' actors. We chose to present in this paper only the methods used by the PRECOS team. This choice was driven by the aim to provide the reader with a panel of methods that have proved their effectiveness and utility in real contexts and with real actors. On the other side, there are certainly more methods for realising the aims described in the text that have not been presented here. A future research pathway is represented by a larger methodological review for the analysis of the practices, social representations and behaviours of socio-hydro systems' actors, followed by a reasoned comparison between the methods presented in this work and those included in the review.

Figure 2 .

 2 Figure 2. Experimental mindsets (Adapted from: Ehmke and Shrogen, 2008)

Table 4 .

 4 Characteristics of socio-hydrosystems in relation to the use of experimental

2 .

 2 Advantages: Developing an agent-based model of attitude change based on social psychological theories enables us to give more realism to the mechanisms underlying the dynamics observed through the simulation of the model. Using an agent-based model as a virtual laboratory instead of laboratory experiments enables us to explore multiple variations of parameter values, as well as to catch the equilibriums of the dynamics only visible on large time scales.

Table 1 .

 1 Methods for the analysis, practices, social representations and preferences used within the PRECOS team

	Goals	Themes	Targeted	Tools	Results
			population

Table 2 .

 2 Stated preferences methods within the PRECOS team

	Goals	Themes (location of case	Targeted	Tools	Results	Refer
		studies)	population			ences
	Design of	Preferences for weather	Small scale farmers Choice Experiment and	Identification of potential barriers to	7
	incentive-based	index-based drought		analysis of farmers' risk	insurance take-up related to
	agricultural policy	insurances (RSA)		aversion	preferences and risk aversion
	instruments
		Type of erosion control	Farmers	Choice experiment	A combination of individual and	8
		measures and Payment for			collective conservation measures
		Environmental Services			under individual subscription, and
		(Morocco)			incentives in the form of technical
					assistance to improve production
					performances may facilitate the
					implementation of PES and encourage
					collective action for the conservation
					of pastures as a common good
		Type of agri-environmental		Choice experiment	Behavioural analysis of preferences	9
		contract (France: Vistre		(mixed logit model with	for an agri-environmental contract
		river)		interactions between	(mix of CE and behavioural economics)
				attitudes and preferences
				for environmental
				contracts)
	Preferences for	Preferences/WTP for	Users and non-users	Choice experiment	Preferences for water services for	10
	water-related environmental	different improvements of the service of provision of	of drinking water supply services	Contingent valuation	different subgroups (with/without individual access, water collection	and 11
	policies	good quality water (South			methods, price, income level, cultural
		Africa, Tunisia)			preferences)
		Preferences for	Inhabitants living on	Contingent valuation	• WTP for groundwater protection	12
		groundwater protection	the groundwater		and restoration

Table 3 .

 3 Economic experiments on Socio-hydro systems within the PRECOS team

	Goals	Topics	Targeted population	Tools	Results	References
	Understand the	Influence of	Farmers	Experimental	Existence of a	17
	influence of	social and	(preliminary	Economics in	causality relation
	information on	institutional	survey),	the Laboratory.	between
	decision-making in	information on	University	A non-linear	information
	socio-hydro systems.	the willingness	Students (Lab	Public Good	provided to users
	This can foster	to pay water in	experiment)	game framed to	and their WTP for
	policies towards	Tunisian water		represent the	a common
	more or different	users'		irrigation water	resource such as
	information available	associations		context was	irrigation water
	to water users			used.
	Understand whether	Influence of	University	Experimental	Initial tests	18
	the relational links in	relational links in	Students (Lab	Economics in	confirmed the
	a group (social	a group on the	experiment)	the Laboratory.	importance that
	capital) influence	perception of		An asymmetric	the relationships
	common pool	uncertainty and		game including	established
	resource use and	on the use of		a Public Good	among players
	uncertainty	common pool		component and	have for coping
	perception. This can	resources,		a Common Pool	with uncertainty
	foster policies	particularly		Resource one	in managing
	facilitating the	water		was used. It was	water resources.
	establishment of			framed to
	better relations and			represent an
	improved social			irrigation
	capital among water			system.
	users
	Test the impact of	Influence of	Farmers	Randomized	No significant	19
	social comparison	social		controlled trial	effect on average
	information on	comparison		with 200	water use by
	decisions with high	information on		farmers	farmers but
	economic stakes in	irrigation			reduction of
	socio-hydro-systems	decision of			water use of
		farmers in South			largest users and
		West France			increase of the
					lowest users.
	Chabé Ferret et al. (

Table 5 :

 5 Hybrid methods within the PRECOS team

	Hybrid methods and type of inter-pluri-	Goals	Topics	Targeted	Tools	Results	Refer
	trans-disciplinarity			population			ences
	1. Behavioural economics and	-Understand the effects	Influence of the	-University	-Experimental	Treatments underway	20
	social psychology	of water supply political	implementation of a	students (lab	Economics in the laboratory.
	-Interdisciplinarity between two experimental sciences where the coherence is ensured by a common experimental protocol for answering the question of the relation between attitude and behaviour -Transdisciplinarity concerning the question of the influence of the new water supply in Aude	measures on pure Nash behavioural strategies of participants included in a Common Pool Resource dilemma. -Understand the effects of pure Nash behavioural strategies on implicit and explicit attitude change of	water supply system in the Aude watershed (France) on behaviours and attitude of farmers towards irrigation during periods of drought	experiment), -Farmers (mobile lab experiment)	A CPR dilemma game framed to represent appropriation of water during periods of drought was used. -Psychological measures of attitudes. A questionnaire based on Likert scales was used to grasp explicit attitudes. An Implicit
		participants			association Test was used to
					grasp implicit attitudes.
	2. Social psychology and social	Understand how the	Influence on attitude	Stakeholders	Multi-agent system. An	Results showed how game	21
	simulation	game design and use of	dynamics of the design	of a	agent-based model of	design of RPGs can lead to
	Multi-disciplinary	role-playing games (RPGs) used as	and use of the RPG CauxOpération	watershed (farmers,	attitude/behaviour dynamics was used within	different shaped outcomes. The relative simplicity of the
		participatory simulation	(Souchère and al.,	mayors,	which hypotheses at the	model enabled us to
		methods for	2010), aiming to	agricultural	individual level are based on	understand the underlying
		environmental	facilitate coordinated	watershed	psychological theories	processes responsible for
		management influence	management of a	advisors)		those shaped outcomes
		attitudes of participants	watershed which is
			prone to erosive runoff
			in Normandie (France)
	3. Agent-Based-Modelling / Role Playing	Analyse experimentally	Common pool resource	Academic	Experimental economics,	In the laboratory,	22
	Games and experimental economics.	the effect of	management,	research.	laboratory of experimental	participatory modelling
		participatory modelling	Companion modelling,	Students	economics, Agent-Based	fosters water users
		on water users'	lab experiments	and other	Modelling (NetLogo), INI-	'cooperation in a situation
		cooperation when they		people	Wat-A-Game Role Playing	of common pool resources.

This collective paper was designed and discussed within the PRECOS Team of the Joint Research Unit G-Eau (http://www.geau.fr/index.php/en/umr-g-eau/teams/item/416-practices-social-representations-and-behaviours-within-sociohydrosystems-precos). The members of the Team appearing as authors contributed written texts to the paper.

http://g-eau.fr/index.php/fr/

'We' in this paper refers to the PRECOS team.

Examples: 1 out of

irrigators in a survey of the Louts, in another, 845 consumers in the Pic Saint Loup community.

The list of references for all tables is presented after the general reference list.