Mariam Maki Sy

Hélène Rey-Valette

Charles Figuières

Monique Simier

Rutger De Wit
email: rutger.de-wit@umontpellier.fr

The Impact of Academic Information Supply and Familiarity on Preferences for Ecosystem Services

Keywords: preference elicitation, coastal lagoons, citizens' workshop, paternalism, cultural ecosystem services (CES), veil of ignorance

Preferences elicitation can be a challenging exercise for citizens participating in assessment surveys. It is even more challenging when it comes to complex and unfamiliar ecosystems and the threatened ecosystem services they provide. Making people aware of the characteristics of the ecosystem services being valued is determinant for the assessment process. We investigated the impact of familiarity and academic information supply on people's preferences for twenty selected ecosystem services of French Mediterranean coastal lagoons. The results show that regardless of familiarity and information supply, there is a strong consensus about the highest importance of regulation and maintenance ecosystem services as well as environmental education and research opportunity ecosystem services. By contrast, nine of the cultural ecosystem services, together with two provisioning ecosystem services showed heterogeneous preferences among the different citizen groups. Using a combination of descriptive and inferential statistics these eleven ecosystem services split up into three clusters characterized as (i) contemplative leisure, (ii) heritage, and (iii) consumptive activities. Familiarity and academic information supply had a strong impact on the preferences for these three clusters of ecosystem services.

Introduction

Ecosystems are essential for human well-being. Therefore, understanding the link between ecological processes of ecosystems and human welfare is critical for a wide range of decisionmaking contexts [START_REF] Fisher | Defining and classifying ecosystem services for decision making[END_REF]. Gathering information on complex ecosystem functioning and translating it into advantages society obtains from Nature has been widely carried out using the concept of ecosystem services (ESs) and through its economic valuation (see [START_REF] Costanza | The value of the world's ecosystem services and natural capital[END_REF][START_REF] Daily | Ecosystem services: benefits supplied to human societies by natural ecosystems[END_REF][START_REF] Dendoncker | Inclusive Ecosystem Services Valuation[END_REF][START_REF] Notte | An ecologicaleconomic approach to the valuation of ecosystem services to support biodiversity policy. A case study for nitrogen retention by Mediterranean rivers and lakes[END_REF]. ESs valuation includes assessing trade-offs among different options (e.g. ESs, ecological restoration projects, planning scenarios …). Hence, in general, it is based on assigning relative importance to nature's diverse benefits to humans [START_REF] Jacobs | A new valuation school: Integrating diverse values of nature in resource and land use decisions[END_REF], and this process could facilitate more adequate conservation choices [START_REF] Salles | Current issues in ecosystem services valuation (ESV)[END_REF].

In ecosystem goods and services related valuation practices, there is an ongoing debate about the process on how to achieve the preference elicitation (e.g. Dendonker et al., 2014;Kenter et al., 2015;2016;[START_REF] Jacobs | A new valuation school: Integrating diverse values of nature in resource and land use decisions[END_REF]2018). So far, little is known on how existing valuation methods actually elicit the different values [START_REF] Jacobs | The means determine the end -Pursuing integrated valuation in practice[END_REF]. In this area, increasing research attention is focused on the development of non-monetary valuation methods in favor of multi-criteria approaches allowing to better study the justification for compromises between objectives of efficiency, fairness and sustainability [START_REF] Costanza | Valuing natural capital and ecosystem services toward the goals of efficiency, fairness, and sustainability[END_REF]. Preferences elicitation can be a challenging exercise for citizens involved in assessment surveys especially when it comes to complex and unfamiliar goods or services. For instance, nature services like water purification or climate regulation are generated by a complex interplay of natural cycles [START_REF] Daily | Ecosystem services: benefits supplied to human societies by natural ecosystems[END_REF], which is often hardly understood by the majority of the citizens. Even many researchers, often highly specialized in their disciplines, may have difficulties in fully understanding the complex interplay. In Economics literature, the easiest-to-study situation is when individuals have preferences for goods and services with diverse characteristics about which they are well informed, and when their preferences are exogenous and reliable [START_REF] O'neill | Conceptions of Value in Environmental Decision-Making[END_REF]. This ideal situation is considered as the benchmark for which using a standard kind of rationality, it has been postulated that individuals maximize their correctly understood self-interest i.e. personal benefit [START_REF] Yamagishi | In Search of Homo 1064 economicus[END_REF].

However, many findings show that respondents involved in preference elicitation surveys are often not familiar and often do not hold appropriate information on the ecosystem goods and services being assessed [START_REF] Whitehead | Measuring Contingent Values for Wetlands: Effects of Information About Related Environmental Goods[END_REF][START_REF] Hanley | The Effects of Information in Contingent Markets for Environmental Goods: A Survey and Some New Evidence[END_REF][START_REF] Spash | Preferences, information and biodiversity preservation[END_REF][START_REF] Blomquist | Resource quality information and validity of willingness to pay in contingent valuation[END_REF][START_REF] Lewan | Knowledge and recognition of ecosystem services among the general public in a drainage basin in Scania, Southern Sweden[END_REF][START_REF] Lariviere | The value of familiarity: Effects of knowledge and objective signals on willingness to pay for a public good[END_REF][START_REF] Brahic | The impact of information on public preferences for forest biodiversity preservation: A split-Sample test with choice experiment method[END_REF][START_REF] Czajkowski | Controlling for the Effects of Information in a Public Goods Discrete Choice Model[END_REF][START_REF] Ami | When do social cues and scientific information affect stated preferences? Insights from an experiment on air pollution[END_REF][START_REF] Ville | Identification et évaluation des services écosystémiques rendus par les habitats coralligènes[END_REF]. Realistically, some ESs are clearly perceived by people while others are not [START_REF] De Groot | Global estimates of the value of ecosystems and their services in monetary units[END_REF]. In contrast, we assume that at least part of the relevant knowledge emanates from the citizens themselves, i.e. from their experience and the familiarity they have acquired with the natural environment. Hence, not only indigenous people [START_REF] Díaz | Assessing nature's contributions to people[END_REF], but also citizens in Western countries that are familiar with ecosystems have often acquired local knowledge that is complementary to the scientific knowledge. This may comprise both knowledge about their ecology, i.e. the local ecological knowledge (LEK) identified in ethnobiology [START_REF] Narchi | Marine ethnobiology a rather neglected area, which can provide an important contribution to ocean and coastal management[END_REF], and the knowledge of their benefits for society.

The citizens' preferences are based on perceptions, which sometimes hide a lack of knowledge about ecosystems and the services they provide. These perceptions could, nevertheless, change progressively as more information is provided. The external information that citizens often do not possess a priori [START_REF] Costanza | Value Theory and Energy[END_REF]) can be acquired either through increased familiarity with the ecosystems, or from academic information, or from a combination of both. Citizens who live in the proximity of the focal ecosystem or regularly visit it during holidays become familiar, meaning that they are well acquainted with this ecosystem. Personal appreciations may be based either on affection alone or on a combination of affection with increased knowledge [START_REF] Van Giesen | Affect and Cognition in Attitude Formation toward Familiar and Unfamiliar Attitude Objects[END_REF]. Depending on the individual, familiarity may result in increased affection for and cognitive knowledge of the ecosystem. In contrast, the supply of academic information only targets to increase the cognitive knowledge of the recipient citizens. For instance, [START_REF] Ami | When do social cues and scientific information affect stated preferences? Insights from an experiment on air pollution[END_REF] reported that the impact of scientific information about the effects of air pollution on respondents' preferences, expressed as their willingness to pay (WTP) values, was strong. A proportion of people (30%) receiving scientific information revised their WTP upwards relative to the mean WTP value. Similarly, presenting survey participants with objective signal regarding the accuracy of their knowledge about a public good caused a significant increase in their preferences (i.e., their WTP) for it [START_REF] Lariviere | The value of familiarity: Effects of knowledge and objective signals on willingness to pay for a public good[END_REF]. Also, [START_REF] Czajkowski | Controlling for the Effects of Information in a Public Goods Discrete Choice Model[END_REF] observed the effects of different information sets on subjects' preferences for a public good.

This study analyses the determinants of preferences for ESs of coastal lagoons related to the level and type of access to information. More precisely, the aim is to test the hypothesis according to which familiarity and academic information impact citizens' preferences for the relative importance of the different coastal lagoon ESs. This study of questions related to information strengthening the intrinsic motivations for ESs conservation allows us to integrate the issues of prioritizing measures of institutional, organizational and behavioral change. It is about studying the conditions of acceptance and the legitimacy of these changes following the logic of collective action and behavioral economics rather than public action based on financial incentives or technical measures. This represents a dynamic approach that emphasizes individual and collective learning within governance mechanisms and for which the role of perceptions and information is essential. We used the Palavas lagoons' complex, which comprises seven coastal lagoons on the Mediterranean coast close to the city of Montpellier (South of France), as our case study. Coastal lagoons are shallow water bodies located at the continent-sea interface. They are permanently or temporarily connected to the sea through inlets and are subjected to a flow of fresh water from the watershed. In addition to supporting a rich flora and fauna, lagoon areas have always been of great interest to humans [START_REF] Newton | An overview of ecological status, vulnerability and future perspectives of European large shallow, semi-enclosed coastal systems, lagoons and transitional waters[END_REF]. For instance, they are often used for recreational and commercial activities such as amateur fishing, bird watching, professional fishing, shellfish farming, etc. In most cases, lagoon systems face anthropogenic stressors such as the destruction of ecological habitats along the coastline, the discharge of wastewater, chemical contaminants, overfishing, invasive species introduced by human activity, intensive aquaculture, climate change or tourism [START_REF] Kennish | Drivers of Change in Shallow Coastal Photic Systems: An Introduction to a Special Issue[END_REF][START_REF] Turner | Ecological-economic analysis of wetlands: scientific integration for management and policy[END_REF].

To test the role of information on preferences, a survey was carried out among two types of populations: inhabitants near the Palavas lagoons complex and a panel of citizens at the national level living in non-coastal areas. In order to disentangle the impact of academic information and familiarity on preferences, we controlled as much as possible the factors of change between these populations (e.g. demographic characteristics). Preferences were elicited using non-monetary ESs assessment through the Majority Judgement approach borrowed from Social choice literature [START_REF] Balinski | Majority Judgment -Measuring, Ranking and Electing[END_REF]. We carried out an analysis combining descriptive statistics and an econometric model to test our hypothesis. Section 2 details the material and methods used.

Sections 3 to 5 present, discuss, justify and conclude the main results.

Material and methods

Study area

The Palavas lagoons complex is located in the southern part of France bordering the Gulf of Lion in the Mediterranean Sea (see Figure 1). In addition to the lagoons, the study site comprises also peripheral riparian zones such as wetlands, pasture and other natural areas. Palavas lagoons are representative of shallow lagoons (mean depth < 2 m) nearby an urban area, predominantly natural while used in the same time for recreational and fishing activities. Water quality in the lagoons had been strongly impacted by human activities mainly due to nutrient over-enrichment which occurred during more than four decades since the 1960's [START_REF] De Wit | Restoration ecology of coastal lagoons: new methods for the prediction of ecological trajectories and economic valuation[END_REF][START_REF] Sy | Identifying Consensus on Coastal Lagoons Ecosystem Services and Conservation Priorities for an Effective Decision Making: A Q Approach[END_REF]. Climate change effects, in particular sea level rise, the increase in temperature or the variation in freshwater availability, could also have ecological consequences on the lagoons [START_REF] Kuhfuss | Evaluating the impacts of sea level rise on coastal wetlands in Languedoc-Roussillon, France[END_REF]. In response to these issues, ecological restoration targeting good water quality and good ecological status were initiated by decision makers [START_REF] De Wit | Restoration ecology of coastal lagoons: new methods for the prediction of ecological trajectories and economic valuation[END_REF][START_REF] Leruste | First steps of ecological restoration in Mediterranean lagoons: Shifts in phytoplankton communities[END_REF][START_REF] De Wit | A Multidisciplinary Approach for Restoration Ecology of Shallow Coastal Lagoons, a Case Study in South France[END_REF]. For instance, in 2005, the implementation of an 11-km offshore outfall system diverted the treated sewage effluents leading to a drastic reduction of anthropogenic inputs of nitrogen and phosphorus into the lagoons [START_REF] Leruste | First steps of ecological restoration in Mediterranean lagoons: Shifts in phytoplankton communities[END_REF][START_REF] De Wit | A Multidisciplinary Approach for Restoration Ecology of Shallow Coastal Lagoons, a Case Study in South France[END_REF]. Moreover, the area is a Natura 2000 site and also received the Ramsar designation as wetland of international importance in 2008 [START_REF] Sy | Identifying Consensus on Coastal Lagoons Ecosystem Services and Conservation Priorities for an Effective Decision Making: A Q Approach[END_REF]. The main characteristics of the Palavas lagoons are presented in Table 1 (adapted from [START_REF] Sy | Identifying Consensus on Coastal Lagoons Ecosystem Services and Conservation Priorities for an Effective Decision Making: A Q Approach[END_REF]. ./0*)1*2ℎ45 (6) to ℎ72/1)1*2ℎ45 (8) Environmental management measures Natura 2000 9:; (<) -6,600 ha (FR9101410); 9=> (?) -6,600 ha (FR9110042) Ramsar Since 2008

Survey characteristics and data collection process

The surveys were conducted among randomly selected local citizens near the Palavas lagoons and non-local citizens living in non-coastal municipalities in France (see Table 3). Local citizens encountered either in the urban centers or walking on footpaths along the littoral zone of the Palavas lagoons were invited to participate in citizen workshops. The invitation was often received with interest and a certain degree of enthusiasm. However, despite our phone call the day before the workshops, it turned out that only a small fraction of the people solicited accepted and showed up at the citizen workshops (N = 38 in total, approximatively 1 out 10 of the solicited individuals). We realized that this number represent a relatively small sample of the total population, although workable for an analysis. This is the consequence of requesting more time availability than in classical surveys. Therefore, we used Coarsened Exact Matching (CEM)

technique when this small sample was compared with the larger samples used for the internet survey (see section 2. Generally, the citizens participating in the workshops represented a sample representative of local populations of Villeneuve-lès-Maguelone and Lattes for gender, education and median income (see Table 2). However, there was a difference in the proportions associated with age groups between this sample and the populations of the two municipalities. This difference might be explained by the fact that these municipalities are suburban with relatively more active young workers. Similarly, the difference in the median incomes can be explained by the fact that we have in our sample only individuals whose income are taxable, contrary to those of the populations of the considered municipalities. The survey involving 803 non-local citizens was carried out online in June 2018. From the data set obtained, we retained the responses of two groups for the analysis. These groups were (i) a subsample of 115 non-local citizens that are familiar with the lagoons and (ii) a subsample of 289 non-local citizens that are unfamiliar with the lagoons. We introduced the notion of familiarity to indicate the proximity and frequency of visits of these lagoons. Non-local citizens who are familiar with the lagoons reported that they visit them very regularly (i.e. more than two times per year). Conversely, those who are unfamiliar with the lagoons never visited them. Hence, among the surveyed 803 non-local citizens, we did not include in our analysis those who only visited the lagoons once or twice.

Data were collected for both surveys using the same questionnaire (see the content of the questionnaire in Appendix A) which was composed of two series of questions as recommended in the literature on perceptions of ESs (see [START_REF] Blayac | Perceptions of the services provided by pond fish farming in Lorraine (France)[END_REF]: open and spontaneous as well as closed questions, mainly on perceptions of the activities and the characteristics of the lagoons area (see Table 3). Open, spontaneous and closed questions (37 questions) Categories of the questions Familiarity and use of the lagoons complex, preference elicitation questions for ecosystem services provided by the lagoons complex, level of knowledge of the lagoons complex and the services they provide, socio-demographic related questions A list of twenty ESs (see Table B in Responses of the local citizens were obtained during a workshop. Several workshop sessions were organized to vary the meeting places and facilitate discussions between participants (see Table 4). They were scheduled at the end of the day at 6.30 p.m. in order to allow the participation of people with a job. There were between 4 and 6 experts for each session, including three co-authors of the paper, so that they could easily facilitate and observe the discussions in the groups.

Table 4. Workshop organization

The course of the workshop sessions is shown in Fig. 2. After an introduction, the respondents completed, individually and unaided, the questionnaire on paper. This latter part lasted between 30 and 45 minutes. Subsequently, the academic information was provided by the experts in the form of oral presentations with the use of a PowerPoint support. A moment of conviviality around a drink closed each session by informally collecting the impressions of the participants regarding the interest of the session. In total the sessions lasted between 2:30 and 3 hours. The academic information supply session lasted about an hour. The presentations focused on ESs as well as aspects related to the ecological functioning, socio-economic dynamics and management of the Palavas lagoons and their immediate surrounding areas see Table 5.

Table 5. Details of the academic information provided

Data treatment process

The overall work flow for data collection and treatment is presented in Figure 3. First, disparities in sample sizes and characteristics of the different resident groups (see section 2.2) were corrected using Coarsened Exact Matching (CEM) (see section 2.3.1). The second step consisted of identifying ESs for which preferences were either homogeneous or heterogeneous among the different groups of respondents. Then, we assumed that there were no impacts of academic information and familiarity on those ESs for which preferences were homogeneous (see sections 2.3.2). The final step of the analysis consisted of identifying factors explaining the heterogeneity of preferences for the remaining ESs using a logit multinomial model (see section 2.3.3).

Information type Details Ecological functioning of the Palavas lagoons complex

General information on the lagoons: definition, Mediterranean lagoons, natural history Salinity, hydrogeological functioning, ecological interest Issues: global warming and sea level rise, eutrophication, artificialization of the coast, the costs of restoring the lagoons Some emblematic species of the Palavas lagoons complex Socio-economic dimensions of the Palavas lagoons complex management Definition of the concept of value The distinction between use and non-use values and the total economic value Evolution of the lagoons' management policies: the effects of the management policies, from causes at sectoral scales to ecosystem-based and concerted approaches Frameworks for analyzing interactions between nature and society: DPSIR (drivers, pressures, state, impact and response model of intervention) and ecosystem services Local well-being assessment frameworks The contributions of the lagoons to territorial well-being Ways to measure the connection and attachment to nature 3). This selection bias was corrected using the CEM approach introduced by Iacus et al. (2011). The main results are presented in the online supplementary material. The key goal of matching is to prune observations from the data so that the remaining data have better balance between the matching groups [START_REF] Iacus | Causal Inference without Balance Checking: Coarsened Exact Matching[END_REF]. The authors demonstrated how CEM generates matching solutions that are better balanced than methods under the older existing class based on propensity scores, Mahalanobis distance, nearest neighbors, and optimal matching [START_REF] Iacus | Multivariate Matching Methods That Are Monotonic Imbalance Bounding[END_REF].

We applied CEM using four main covariates which are age, gender, level of education and income. First, each covariate was coarsened using discrete values associated to the corresponding nominal categories. For instance, the covariate age was coarsened replacing the nominal categories 18 -39 years, 40 -59 years and 60 and over by 0, 1 and 2 respectively. Second, exact matching between the treated and control groups was applied using the values of the coarsened covariates. This step required sorting each observation into a stratum which includes unique values of the coarsened covariates. Finally, the selected strata were those containing at least one control and treated units. The strata with only control units were discarded. Treatment units that did match simultaneously with control units from both the non-local resident groups were also discarded. The control and treated groups are specified in Figure 4. 6.

Analysis of ecosystem services presenting heterogeneous preferences

The remaining ESs that did not present homogeneous preferences for ESs among the groups of respondents were analyzed separately. The aim was to identify explanatory factors that might explain heterogeneity in preferences for the considered ESs. More precisely, we tested the impact of several explanatory variables on the respondent choices for these ESs. The considered explanatory variables included the variable "population type" (informed, uninformed, familiar or unfamiliar), "age", "gender", "level of knowledge of Palavas lagoons" … (see Table 6). To this end we used a logit multinomial model as in [START_REF] Blayac | Perceptions of the services provided by pond fish farming in Lorraine (France)[END_REF]. The dependent variable that comprised different levels of ES categories was created through identifying different clusters (or categories) of these ESs using Principal Component Analysis (PCA) followed by Ward's hierarchical classification (HC) method. Hence this clustering of ESs, in contrast to the use of standard classification schemes (e.g. [START_REF] Liquete | Current Status and Future Prospects for the Assessment of Marine and Coastal Ecosystem Services: A Systematic Review[END_REF]Millenium Ecosystem Assessment, 2005;[START_REF] Teeb | The Economics of Ecosystems and Biodiversity Ecological and Economic Foundations[END_REF], emerged from the respondents' preferences, based on the attributed levels of priority. Only ESs within the identified clusters that contributed the most to the PCA axis were retained. The dependent variable was then constructed by calculating an average score for each cluster of ESs which were generated using Ward's HC method. The preference for a cluster of ESs for each respondent corresponded to the one with the maximum mean score.

A multinomial logit model was then used to estimate the preference for a cluster of ESs given a set of qualitative explanatory variables (see Table 6). The model corresponds to choice probabilities for the different ESs clusters [START_REF] Blayac | Perceptions of the services provided by pond fish farming in Lorraine (France)[END_REF]. Formally, the choice probabilities are: where Z is the coefficient vector including the intercept.

At first, we had a list of fourteen explanatory variables. To verify whether or not there was a multicollinearity (correlation within the explanatory variables), we performed the Cramer's V test. After the test, we retained eight explanatory variables (see Table 6) out of the fourteen previously listed. Moreover, interaction effects were observed for the retained variables 'population type' and 'donation to an environmental association' as well as both variables characterizing levels of knowledge. In addition, there were interaction effects between the variables 'donation to an environmental association' and both variables characterizing levels of knowledge. Finally, there was an interaction effect between both variables characterizing levels of knowledge. The overall quality of the multinomial logit model was verified using Akaike Information Criterion (AIC). The aim was to progressively remove interaction effects and single explanatory variables that have no significant impact on the dependent variable from the general model, until [START_REF] Hausman | Specification Tests for the Multinomial Logit Model[END_REF]. This hypothesis is tested to ensure that removing any alternative (here, a cluster of ESs) from the dependent variable does not affect the odds of the remaining alternatives.

Results

Coastal lagoon ESs: homogenous versus heterogeneous preferences of ESs among groups of respondents

Table 7 lists the results of the Fisher's exact tests, which allowed us to identify whether the preferences for these different ESs were homogeneous among the four groups (ESs marked in italics, 𝐻 D retained, p> 0.05) or heterogeneous (ESs marked in bold, 𝐻 D rejected, p < 0.05).

Eleven out of the twenty ESs presented heterogeneous preferences, and the remaining nine ESs presented homogeneous preferences. Interestingly, the latter included all five regulation and maintenance ESs as well as both environmental education and research opportunity ESs. Thus, regardless of familiarity and academic information supply, regulation and maintenance services as well as cognitive effects related services were judged as a priority by at least 90% of the respondents (see Table C in Appendix C). In addition, preferences of recreational hiking and walking ES and of fish resources ES were homogeneous, although both ESs were favored to a lesser degree compared to the former ones. The same results were also observed for the unmatched data (see Table C in Appendix C). Thus, preference elicitation of these services was very robust and did not change after applying CEM. Specific questions allowed to study the pertinence of possible factors explaining choices for those ESs presenting homogeneous preferences among the four groups of citizens (see Table 8). Hence, more than 98% of the respondents, who declared having either a good or a limited level of knowledge of the Palavas lagoons and the associated ESs, favor the regulation and maintenance ESs. The level of priority attributed to environmental education and research opportunity ESs increases with age. For instance, 70.6% of the respondents that are 18-39 years old favor these services against up to 90.6% for the 60 years and above. [START_REF] Liquete | Current Status and Future Prospects for the Assessment of Marine and Coastal Ecosystem Services: A Systematic Review[END_REF]

Table 7. The set of the twenty ecosystem services (ESs) used in this study. The ESs have been categorized according to the classification designed for coastal and marine ESs by

and currently included in CICES version 5.1 (Haines-Young and Potschin, 2018). Fisher's exact tests were performed to test for the homogeneity of preferences among the four groups of citizens (see section 2.2). Hence, ESs in italics presented homogeneous

preferences among the four groups of citizens. ESs in bold presented heterogeneous preferences among the four groups.

Descriptive and inference statistics for ESs showing heterogeneous preferences among groups of respondents

The clustering of the eleven ESs, for which preferences were heterogeneous among the respondents, resulted in the identification of three clusters i.e. three levels of the dependent variable (see Figure 5). We attributed descriptive qualifications to these three clusters based on the following interpretations. The cluster comprising two cultural ESs, i.e. historical site and local identity, is referred to as cultural heritage and was, therefore, named as 'Heritage'. The cluster comprising the cultural ESs 'aesthetic value of habitats or species', 'aesthetic value of landscapes', 'bird watching' and 'sentiment of relaxation' relates to leisure activities based on the contemplation of the lagoon ecosystem rather than on the consumption of its resources. Therefore, this cluster has been defined as 'contemplative leisure'. The cluster with the remaining five ESs all of which imply consumption of natural resources, either for provisioning or for leisure, has been defined as 'consumptive activities'.

Table 8. Factors explaining the level of priority attributed to ecosystem services presenting homogeneous preferences among groups of citizens. P, N and NP stand for "Priority", "Neutral" and "Not a priority" respectively.

Note: the rows of the table correspond to the factors explaining the level of priority attributed to ecosystem services presenting homogeneous preferences among groups of citizens. For the first row and first column for instance, the table is read as follow: up to 98.8% of the responds who already heard of the concept of ESs before the survey significantly consider regulation and maintenance services as a priority in terms of conservation. Likewise, 1.2% and 0% of these respondents are neutral about the conservation of regulation and maintenance services and consider them as not of a priority for conservation, respectively. The general logit multinomial model includes all the explanatory variables listed in Table 6. The reference variables are indicated in bold. Also, the 'heritage' cluster was used as the reference level of the independent variable. The final nested logit multinomial model was validated based on the results of the two hypotheses testing, i.e., the Likelihood ratio test and the IIA test. The econometric estimations are presented in Table 9. First, the choice for the nested model relative to the initial model was verified through the Likelihood ratio test. The null hypothesis consisted of choosing the final nested model. It was accepted based on the fact that the likelihood ratio test statistic (see "Chi2" in Table 9) was smaller than the theoretical chi-square with a margin of error of 5% and a degree of freedom (Df) of 54 in our case. Secondly, for the IIA assumption using the Hausman and McFadden test, the test statistic relative to the cluster consumptive activities was negative (-0.015, in Table 9). This is evidence that the IIA holds [START_REF] Hausman | Specification Tests for the Multinomial Logit Model[END_REF], P.1226cited in Franses and Paap, 2003).

Figure 5. Classification of the 11 ecosystem services (presenting heterogeneous preferences among the groups of respondents, in bold in

According to this final nested model (

Discussion

This study focused on the role of information and familiarity in the individual preferences of ESs in Mediterranean coastal lagoons with the aim of assisting the design of public policies.

Therefore, we studied how different variables impact the preferences of the respondents, using a logit multinomial model. We considered (i) the level of respondents' knowledge, i.e., whether they are informed and/or familiar or not, (ii) their behavior towards environment and (iii) their sociodemographic profile (see Table 6).

Identification of consensus and understanding of the heterogeneity of preferences

Surveys for ES assessments need to restrict the number of ESs under consideration for practical reasons. In our study, we used a list of 20 ESs selected from an original collection of 31 ESs [START_REF] Sy | Identifying Consensus on Coastal Lagoons Ecosystem Services and Conservation Priorities for an Effective Decision Making: A Q Approach[END_REF] [START_REF] Pendleton | A triage approach to improve the relevance of marine ecosystem services assessments[END_REF]. Nevertheless, a longer list without a priori judgments by the policy makers is needed to reveal the preferences based among the populations to respect their different worldviews and multiple values of nature (Diaz et al., 2019). The Qmethod, which as a serious card game is more ludic than questionnaires, easily allows considering a larger set of ESs under study without creating confusion (e.g. 31 ESs in the study of [START_REF] Sy | Identifying Consensus on Coastal Lagoons Ecosystem Services and Conservation Priorities for an Effective Decision Making: A Q Approach[END_REF]. However, such a Q-method cannot be easily implemented for an on-line survey.

The logic of our survey is consistent with the socio-cultural approach developed by Martin-Lopez et al. (2014). Our results show in the first place a large consensus for 9 of the 20 studied ESs,

shown by homogeneity of preferences (see Table 7). These nine ESs included all 5 ESs of the category Regulation and maintenance services, 1 out of 3 provisioning services (i.e., fisheries)

and only 3 out of 12 cultural ESs. This pattern of preferences was thus independent of familiarity and information supply and appeared to be accepted a priori by an overwhelming majority. This may reflect that nowadays, particularly within the French society, a large majority (85 %) of the general public attaches a high importance to biodiversity and is convinced of the need for its conservation [START_REF] Croutte | L'opinion des Français sur la participation des citoyens à une agence pour la biodiversité[END_REF]. But while recognizing the importance of biodiversity for supporting life on earth, knowledge of biodiversity and awareness of its importance for well-being is less developed among the general public [START_REF] Croutte | L'opinion des Français sur la participation des citoyens à une agence pour la biodiversité[END_REF]. It appears that, even when possessing little precise knowledge, the general public trusts and supports the messages delivered by the biodiversity experts. The latter may explain that the ESs research opportunities and environmental education were also homogeneously perceived as relatively very important (see Table 7). Similar results were obtained according the socio-economic approach in the study of [START_REF] Martín-López | Trade-offs across value-domains in ecosystem services assessment[END_REF], which also showed that comparably their monetary assessments tended to underestimate most of the regulating ESs and the ESs research opportunities and environmental education. A study using Q-methodology among highly-involved stakeholders, including different experts, in Palavas lagoons also showed a strong consensus concerning the major relative importance of regulation and maintenance ESs [START_REF] Sy | Identifying Consensus on Coastal Lagoons Ecosystem Services and Conservation Priorities for an Effective Decision Making: A Q Approach[END_REF]. Hence, concerning biodiversity and the regulation and maintenance ESs of emblematic ecosystems, there is no major conflict of preferences and opinions between the general public and the experts.

In contrast, the concept of Cultural ESs (CES) has been subjected to a large debate and controversy in the literature. Some authors suggest revising and broadening the standard frameworks of the concept or discarding the term "cultural" itself (Chan et al., 2012a(Chan et al., , 2012b;;[START_REF] Winthrop | The strange case of cultural services: Limits of the ecosystem services paradigm[END_REF][START_REF] Fish | Conceptualising cultural ecosystem services: A novel framework for research and critical engagement[END_REF][START_REF] Small | The challenge of valuing ecosystem services that have no material benefits[END_REF] or even abandoning the concept [START_REF] Kirchhoff | Abandoning the Concept of Cultural Ecosystem Services, or Against Natural-Scientific Imperialism[END_REF]. One of the main criticism is that it tries to combine all notions of cultural value (e.g. moral, religious, aesthetic) under a single term [START_REF] Small | The challenge of valuing ecosystem services that have no material benefits[END_REF]. In addition, [START_REF] Díaz | Assessing nature's contributions to people[END_REF] insisted on the role of culture and local knowledge in the way people understand the importance of all ESs, including those that have been classically categorized as provisioning and regulating services. Indeed, the notion of nature's contribution to people (NCP), which is one of the more recent key elements of the IPBES conceptual framework, recognizes the central and pervasive role that culture and local knowledge play in defining and understanding all links between people and nature (Diaz et al., 2018). Therefore, the cultural background strongly determines how people assess the need for ESs conservation. The paramount role of these cultural factors justifies understanding the preferences and levels of knowledge. This involves psychological and sociological approaches in order to explain determinants of these preferences. The anthropocentric nature of ES is often put forward for its ability to rally individuals more easily in favor of their conservation, while the link between well-functioning ecosystems and their ability to provide ESs is not always well understood. Furthermore, this relationship is not necessarily equivalent depending on the type of ESs, the contexts or the state of conservation of the ecosystems [START_REF] Barnaud | Deconstructing ecosystem services: Uncertainties and controversies around a socially constructed concept[END_REF]. In addition to the lack of information on ecological processes, individuals have a limited ability to process information. And the instability of their preferences over time and the varying context should also be taken into account.

Our interpretation of the results of this study gave rise to an original typology of CES. The distinction among those CES refers to different motivations regarding conservation depending on whether they are hedonic (i.e. motivations that fulfill personal pleasure or benefit) or stemming from a broader interest in favor of the quality and the identity of the territory. Inductive approaches have been used to empirically study people's preferences about CES [START_REF] Dou | Assessing the influences of ecological restoration on perceptions of cultural ecosystem services by residents of agricultural landscapes of western China[END_REF][START_REF] Maraja | Perceptions of cultural ecosystem services from urban green[END_REF][START_REF] Pike | The assessment of cultural ecosystem services in the marine environment using Q methodology[END_REF][START_REF] Stålhammar | Recreational cultural ecosystem services: How do people describe the value? Ecosyst[END_REF]. Comparably, we used such an inductive approach for the 11 ESs with heterogeneous preferences, which indicated that the 9 CES split up into 3 main clusters based on people's preferences. The eleven remaining

ESs were clustered through a PCA followed by Ward's hierarchical classification method. A multinomial logit model was then developed to determine factors explaining the choice for the identified clusters issued from these eleven ESs. Thus, our results propose a categorization of CES according to whether they imply individual or collective benefits, and whether these are consumptive (implying consumption of natural resources and often creating a higher level of disturbance) or contemplative (enjoyment of nature based on observation and sensitivity for surroundings causing only minor disturbance). Interestingly, the two provisioning services (biomass for grazing, shellfish farming) were grouped together with consumptive leisure ESs to constitute the cluster 'consumptive activities'.

We assume that hedonic motivations (i.e. motivations that fulfill personal pleasure or benefit) for

ESs are directly related to the use of the lagoons and therefore to familiarity. On the other hand, we assume that the heritage services and the impacts of the uses on the lagoons involve cognitive knowledge which can be acquired through academic information. Thus, our results show that local residents strongly favored contemplative leisure compared to the unfamiliar citizens (see Table 9). However, this trend decreased with academic information supply which led the local citizens to prioritize more the collective services (heritage services) at the expense of the selfcentered ESs (i.e. those ESs that contribute to personal well-being, here contemplative leisure).

Interestingly, consumptive leisure (hunting and recreational fishing) as well as provisioning services, grouped together in the cluster 'consumptive activities', were relatively less favored by the respondents (see Table 9). This is probably related to the fact that these ESs benefit only a limited number of practitioners in the Palavas lagoons site. Also, their activities often induce disturbances to the natural system and nuisance to other people.

Role of information for public policies focusing on learning and engagement of users and residents

As mentioned in the introduction, several studies have shown the role of intrinsic motivations on the personal engagement of individuals with respect to conservation issues, beyond the sociodemographic variables and specific knowledge levels [START_REF] Wilson | Biophilia[END_REF]. In addition to the positive impact of nature on health [START_REF] Capaldi | The relationship between nature connectedness and happiness: a meta-analysis[END_REF][START_REF] Sandifer | Exploring connections among nature, biodiversity, ecosystem services, and human health and well-being: Opportunities to enhance health and biodiversity conservation[END_REF], several studies show the role of positive feelings, attachment and bonding with nature on the intrinsic motivations in favor of nature conservation [START_REF] De Young | Encouraging Environmentally Appropriate Behavior: The Role of Intrinsic Motivation[END_REF][START_REF] Kollmuss | Mind the Gap: Why do people act environmentally and what are the barriers to pro-environmental behavior?[END_REF][START_REF] Mayer | Why Is Nature Beneficial?[END_REF][START_REF] Mackerron | Happiness is greater in natural environments[END_REF][START_REF] De Bell | The importance of nature in mediating social and psychological benefits associated with visits to freshwater blue space[END_REF][START_REF] Lapointe | Urbanization alters ecosystem service preferences in a Small Island Developing State[END_REF][START_REF] Pereira Lima | Understanding landowners' intention to restore native areas: The role of ecosystem services[END_REF][START_REF] Kaltenborn | Can cultural ecosystem services contribute to satisfying basic human needs? A case study from the Lofoten archipelago, northern Norway[END_REF]. Hence different situations need to be identified for designing the measures in public policies, particularly those enhancing learning processes.

Our assessments of the role of information from academic and empiric sources aim at contributing to develop pro-environmental behavior of citizens based on their intrinsic motivations. These can be influenced by a better knowledge by the citizens of the ecosystems.

This way, our approach is opposed to an attitude of paternalism (for a philosophical study, see [START_REF] Dworkin | Paternalism[END_REF] adopted by some scientists and public authorities who plead for a predominating role of experts in environmental decision making. Such paternalism reflects the belief that public policies ought to be grounded on scientific-based assessments, rather than on citizens' perceptions that could lead to "erroneous" preferences. This paternalistic approach clearly conflicts with the democratic ideal. However, hybrid forms do exist as in the work of [START_REF] Thaler | Nudge: Improving Decisions about Health, Wealth and Happiness[END_REF] on nudges falls halfway between paternalism and liberalism. It exploits the most recent advances of behavioral economics to design an architecture of choices in a way that preserves freedom of choice and at the same time navigates people towards the goals that are considered socially desirable. However, [START_REF] Thaler | Nudge: Improving Decisions about Health, Wealth and Happiness[END_REF] underline the need for information, highlighting that "people make good choices in contexts in which they have experience, good information, and prompt feedback". Moreover, they emphasized conversely that "people are most likely to need nudges for decisions that are difficult, complex, and infrequent, and when they have poor feedback and few opportunities for learning". The procedure adopted during the citizen workshops, allowed a respect for freedom of choice with the engagement of a dialogue with experts and that the information thus supplied could be used as nudges.

In this context, our research aims to better understand the types of knowledge needs in terms of ESs and individual profiles in order to propose learning processes, which, by improving this knowledge, generate greater motivation to preserve ESs. As such, this type of survey comprises a way to associate the general public, the local populations in public policies and develop participative scenarios allowing for a better management for the conservation and ecological restoration of protected areas as recommended by the IPBES global assessment report assessment of biodiversity and ecosystem services of 2019. Accordingly, this should lead to better managing the trade-offs between social objectives that represent different worldviews and multiple values of nature (Diaz et al., 2019). The learning processes thus lead to understand the involvement of populations in ecosystem management as a co-evolution process Delagado et al. (2019). And, knowing that collective learning through participatory approaches combining experience and expertise [START_REF] Pendleton | A triage approach to improve the relevance of marine ecosystem services assessments[END_REF][START_REF] Beaumont | Practical application of the Ecosystem Service Approach (ESA): lessons learned and recommendations for the future[END_REF] promote the creation of new values in favor of ESs conservation [START_REF] Strokosch | Co-experience, co-production and co-governance: an ecosystem approach to the analysis of value creation[END_REF]. The issue is then to question learning processes, which, may be the result of single or double loop processes [START_REF] Argyris | Organizational learning II: Theory, method and practice Reading[END_REF].

Single loop refers to learning that is applied straightforwardly, while double loop refers to learning that provokes a profound change in the reference systems of individuals and their understanding of the subject (definitions adapted from [START_REF] Argyris | Organizational learning II: Theory, method and practice Reading[END_REF]).

The central questions we addressed concerned the impact of information on preferences taking into account how the information was acquired by the citizens. Information acquired by familiarity with a natural environment according to the frequency of visits can be differentiated from those resulting from academic trainings or those that are more contextualized and are offered as awareness-raising measures. Hence, information supply can reduce bias by making individual choices more informed and may lead to the reorganization of preferences. This may even lead to changing the value systems of the citizens (i.e., double loop processes). In the case of knowledge related to the functioning of ecosystems and the contribution of ESs to the wellbeing of society in general, individuals' preferences are influenced by cultural dimensions that must be taken into account. These include the links of individuals to nature as well as their cultural proximity to ESs (i.e. these ESs are part of their culture). Hence, the fact that unfamiliar populations attributed a greater consideration for heritage services is striking. We think that this is because these populations are neither directly concerned by the direct consumptive nor by the contemplative benefits of these ecosystems and therefore not influenced by their own interest and affection for these natural areas. This lack of concernment can be linked to the notion of veil of ignorance popularized by Rawls [START_REF] Rawls | A theory of justice[END_REF]. According to the ethics suggested by Rawls, parties who judge policy and management options are supposed to adopt a veil of ignorance. This implies a thought experiment for the participants, which purpose is to fully neutralize the influence of their specific individual interests. Under such a veil of ignorance, the parties will hopefully tend to evaluate the options only on the basis of considerations of general interest [START_REF] Rawls | A theory of justice[END_REF]). It appears that the unfamiliar populations, that might not be aware of how the various alternatives will affect their own particular case, seem to evaluate the ESs spontaneously in accordance with this veil of ignorance. This observation advocates the interest to involve diverse populations in preference elicitation surveys. Indeed, mobilizing only local knowledge when carrying out ESs assessment might present a risk of favoring particular individual and local interests.

In terms of public policy, the splitting up of the CES and the differential impacts of familiarity and information supply on preferences for the different CES raises the question on the mechanisms which allow the citizens to perceive and value these CES. Information economists dealing with goods traded on markets have adopted a classification scheme based on the difficulty with which consumers can assess their quality or obtain the pertinent information.

Accordingly, at least three types of goods have been identified i.e. (i) search goods, (ii)

experience goods and (iii) credence goods. The search goods category [START_REF] Nelson | Information and Consumer Behavior[END_REF] comprises the goods for which the attributes can be ascertained prior to consumption, i.e. by inspection and information gathering. This category comprises most products and typical examples include clothing and staple food. Experience goods [START_REF] Nelson | Information and Consumer Behavior[END_REF] can be accurately evaluated only after they have been used or consumed (e.g. restaurant, holiday). Finally, credence goods [START_REF] Darby | Free Competition and the Optimal Amount of Fraud[END_REF] are difficult or impossible to evaluate even after consumption has occurred. That is, the consumer might lack the knowledge or the expertise, or because the information is too costly to acquire compared to its expected benefits (e.g. medical treatments). This approach may be inspiring when assessing ESs. To our knowledge, non-market goods and services and particularly

ESs have never been investigated through the lens of this typology. We propose that future studies could be useful to develop a similar typology for ESs. For example, it appears obvious that the sentiment of relaxation can be considered as an experience ESs. Many of the maintenance and regulation ESs, for which most citizens lack the detailed ecological knowledge, can perhaps been categorized as credence ESs. However, for the ESs microclimate regulation and flooding and other extreme event regulation the situation is more ambivalent. Most people living in the coastal zone experience how the lagoons contribute to temper the climate (lower maximum and higher minimum temperatures than in more continental settings), which means that microclimate regulation could also be considered as an experience ES. Some people that live in the coastal area since a long time may recall disastrous extreme flash floods from rivers and have experienced how coastal lagoons can store large quantities of water and thus prevent dangerous submersions. Their experience of such dramatic events often has a long-lasting impact on their preferences. Finally, for some ESs it will be easier for the citizens to search for information, e.g. particularly for several provisioning services which could therefore be categorized as search ESs.

Hence, the development of a comparable classification of ESs will allow to consider the access to information and knowledge (familiarity and academic) for the different ESs in order to better target programs and forms of awareness raising.

Conclusion

In this study, we assumed that local populations are familiar with the focal ecosystem and that they possess knowledge about their ecology and benefits for society. The main results that emerged from our analysis show that there is a high interest for regulation and maintenance as well as environmental education and research opportunity services regardless of population type.

By contrast, nine of the cultural ESs (CES) together with two provisioning ESs showed, however, heterogeneous preferences among the different groups of citizens. These eleven ESs were split up into three clusters comprising (i) contemplative leisure, (ii) heritage and (iii) consumptive activities.

We addressed two main questions: (i) does familiarity impact citizens' preferences of the relative importance of the different coastal lagoon ESs? and (ii) do the preferences of familiar citizens change after receiving academic information? Familiarity with the ecosystem particularly impacted the CES. Thus, familiar local citizens valued the contemplative leisure much more than others, presumably because of their hedonic self-centered approach based on personal pleasure or benefit. This effect was attenuated by academic information supply. Finally, non-locals who never visited Palavas lagoons attribute greater priority to heritage services compared to consumptive activities and contemplative leisure. Hence, our hypothesis about the impact of academic information supply and familiarity on preferences is supported by our observations for heritage services, contemplative leisure and consumptive activities.

The analysis of perceptions of the ESs provided by ecosystems is increasingly demanded by environmental policy managers. Therefore, the surveys reported in this article were designed in collaboration with local managers. The perceptions revealed by the surveys represent a proxy allowing a better understanding of the demand for ESs that, so far, has been poorly addressed compared to the supply of ESs. For example, the MAES working group (Mapping and Assessment of Ecosystems and their Services - [START_REF] Burkhard | Mapping Ecosystem Services, Mapping Ecosystem Services[END_REF][START_REF] Burkhard | An operational framework for integrated Mapping and Assessment of Ecosystems and their Services (MAES)[END_REF] produced maps of ESs supply that allow identifying trade-offs and links among ESs, using the concept of ES bundles. The combination of these ES supply maps with land use maps in territorial planning documents is increasingly practiced for a better integration of development policies and ecosystem conservation policies (Le [START_REF] Clec | Spatialiser des services écosystémiques, un enjeu méthodologique et plus encore[END_REF]Furst et al., 2014;Maes et al., 2015). These maps strengthen the ability to identify strategic areas for integrated territorial management. Nevertheless, this approach in spatial planning, which often results in zoning, does not a priori accommodate the questions about the social acceptability of conservation measures.

To increase the social acceptability, information about the perceptions of the populations of ESs and their demands is of paramount importance for spatial planning. Taking into account the plural forms of access to ES knowledge [START_REF] Nelson | Information and Consumer Behavior[END_REF], familiarity with ecosystems, when based on a reasoned use of these ecosystems, appears to be a determining factor for reinforcing the intrinsic motivations for pro-environmental behavior (Kollmuss and Ageyman, 2002).

o "The Palavas lagoons complex prevents the runoff of flood water" o "The Palavas lagoons complex plays an important role in the cycle of nutrients (nitrogen and phosphorus) which are essential for the maintenance of aquatic life". o "The Palavas lagoons complex is an essential habitat for bird nesting and the life cycle of many species". o Etc. D. Finally, the 'sociodemographic profile' category included questions about, for instance, the respondents' age, gender, and behavior towards environment (whether she or he is a member or donates to an environmental association for instance, respondents' connectedness to nature …).

Appendix C. Levels of priority of ecosystem services presenting homogeneous preferences among the groups of respondents according to familiarity and academic information supply

  Note: (1) The Palavas lagoons complex comprises 7 different lagoons that were created by compartmentalization of a historic large lagoon; (2) Grec and Arnel lagoons; (3) Prévost lagoon; (4) Ingril lagoon; (5) Méjean and Grec lagoons; (6) FR9101410 -SCI = Site of Community Interest (Habitats Directive); (7) FR9110042 -SPA = Special Protection Area (Birds Directive). Note: the total area of the Natura 2000 site includes the Estagnol nature reserve.

Figure 1 .

 1 Figure 1. Palavas lagoons complex. Satellite images from IGN-Géoportail.

  Appendix B) was selected before by focus groups of scientists and lagoon managers. These ESs was considered as the relatively most important ESs, in terms of conservation, provided by Palavas lagoons based on an original selection of 31 ESs (see[START_REF] Sy | Identifying Consensus on Coastal Lagoons Ecosystem Services and Conservation Priorities for an Effective Decision Making: A Q Approach[END_REF]. The general definition of the ESs was adapted from[START_REF] Liquete | Current Status and Future Prospects for the Assessment of Marine and Coastal Ecosystem Services: A Systematic Review[END_REF], who provided a classification of coastal ES that is now integrated in CICES 5[START_REF] Haines-Young | Common International Classification of Ecosystem Services (CICES) V5.1 and Guidance on the Application of the Revised Structure[END_REF]. The twenty selected ESs were presented in a randomized order in the survey, without any reference to ES categories. Preferences were elicited for the different ESs using the Majority judgment (MJ), a voting method introduced by Balinski and Laraki (2010). We borrowed MJ from Social Choice theory and to our knowledge it has never been used in research related to environmental issues. Our MJ for ESs ranking is an absolute non-monetary method in the sense that each ES is judged by its merit or grade in a common language independently from the other services. According to work in the field of Social Choice, this type of ranking is considered to offer a more robust selection basis[START_REF] Balinski | Majority Judgment -Measuring, Ranking and Electing[END_REF].The respondents indicated their individual preferences for the different ESs by answering the following question: "What do you think are the most important roles of the Palavas lagoons in terms of conservation priority? Please check the box associated with each role according to its level of conservation priority". The list of the considered ESs (i.e. the roles) was presented in the rows of a table and the columns presented different levels of conservation priority i.e. 'high priority', 'priority', 'neutral', 'low priority', 'not a priority'.

Figure 2 .

 2 Figure 2. The course of the workshop session.

Figure 3 .

 3 Figure 3. The work flow for data collection and treatment processes

Figure 4 .

 4 Figure 4. Coarsened Exact Matching (CEM) of the control and treated groups

  (𝑍 𝐶𝑙𝑢𝑠𝑡𝑒𝑟 1 ) + 𝑒𝑥𝑝 (𝑍 𝐶𝑙𝑢𝑠𝑡𝑒𝑟 2 )

  the final model with the lowest AIC criterion was reached. The obtained final nested model was then validated based on two hypotheses testing i.e. the Likelihood ratio test and the Hausman and McFadden test. First, the choice for the nested model relative to the initial model was verified through the Likelihood ratio test. The null hypothesis consisted of choosing the final nested model. Secondly, the final nested model was validated through the independence of irrelevant alternatives (IIA) assumption using the Hausman and McFadden test

Table 1 .

 1 Main characteristics of Palavas lagoons' complex.

Table 2 .

 2 Demographic characteristics of the surveyed local residentsNote: the difference in the median incomes can be explained by the fact that we have in our sample only individuals whose incomes are taxable, contrary to those of the populations of Villeneuve-lès-Maguelone and Lattes.

Table 3 .

 3 Characteristics of the surveys and the surveyed population types

	Population type	Non-Local Residents	Local Residents
		Unfamiliar	Familiar	Local	Local bis
	Number of surveyed individuals	289	115	38
	Familiarity with the study site	Never visited	Regularly visit	Familiar
	Data collection method	On line	Workshop
	Survey period	June 2018	May-June 2017 and 2018
	Perception type	Existing	Existing	Constructed
	Information supply		None	None	Academic
	Questionnaire type

Table 6 .

 6 Factors explaining preferences for ecosystem services. The referent levels are indicated in bold.

Table 7

 7

) based on the results of the principal component analysis (PCA). The underlined ecosystem services are the ones that contributes the most to the two axes. See Table

B

in Appendix B for the definitions of the corresponding ecosystem services.

Table 9

 9

), compared to the unfamiliar non-local residents, the local residents are 5.8 times more likely to choose the 'contemplative leisure' ESs over 'heritage' ESs. However, this odds ratio decreased to 2.8 after academic information supply during the citizens' workshops. In other words, relative to the 'heritage' ESs cluster and after receiving academic information, local residents' preferences of the level of priority towards 'contemplative leisure' ESs decreased. Moreover, unfamiliar non-local residents were 0.23 and 0.21 times less likely to choose contemplative leisure ESs and 'consumptive activities' ESs, respectively.

Table 9 .

 9 The final nested model issued from the econometric analysis. It explains the choices for the three clustered categories of ecosystem services that presented heterogeneous preferences among the groups of citizens.

  based on preference elicitation, is a major issue to facilitate the use of these assessments in public policies. Thus, it has been invoked that ES assessments should concentrate only on a limited number of ESs by selecting those that are most susceptible to variations induced by the different management options

	Variable	Contemplative leisure vs. Heritage	Consumptive activities vs. Heritage
		Estimate	Odds	Z value Pr (>|Z|)	Estimate	Odds	Z value Pr (>|Z|)
		(SE)	Ratio			(SE)	Ratio
	Type
	Unfamiliar	Ref.				Ref.
	Familiar	0.014	1.014	0.029	0.9771	-0.054	0.947 -0.1084 0.9136
		(0.471)				(0.502)
	Informed local	1.055	2.872	2.217	0.0265*	-0.584	0.557 -0.7309 0.4648
	residents	(0.476)				(0.791)
	Local residents	1.759	5.807	3.817	p < 0.001***	-7.281	0.001 -0.3163 0.7517
		(0.461)				(23.018)
	_intercept	-1.490	0.225	-5.386	p < 0.001***	-1.555	0.211 -5.4725 p < 0.001***
		(0.277)				(0.284)
	Final nested model	Df	Chi2	P-
	validation tests			value
	Likelihood ratio test	54	62.544	0.199
	Independence of
	irrelevant alternatives
	(IIA) assumption
	Heritage	1	< 0.001 0.999
	Contemplative leisure	1	< 0.001 0.999
	Consumptive activities	4	-0.015

under the guidance of a focus group. A longer list in these questionnaires could introduce confusion and fatigue. Hence, the selection of ESs for ES assessments, including those

Table C .

 C Levels of priority of ecosystem services presenting homogeneous preferences among the groups of respondents according to familiarity and academic information supply. The corresponding level of priorities are indicated in the table as P, N and NP which stand for "Priority", "Neutral" and "Not a priority", respectively.

	Ecosystem services	P-Value Level of	Local residents	Matched		Initial observations
	presenting	priority		observations	for non-local
	homogeneous			for non-local	residents
	references			residents
			Local Informed	Matched	Matched	Familiar Unfamiliar
			Local	Familiar	Unfamiliar
	Regulation and	0.431
	maintenance	P	93.3% 100.0%	96.2%	92.2%	95.7%	93.4%
		N	6.7% 0.0%	3.8%	7.8%	4.3%	6.6%
		NP	0.0% 0.0%	0.0%	0.0%	0.0%	0.0%
	Fish resources	0.264
		P	26.7% 26.7%	51.9%	36.9%	47.0%	25.6%
		N	50.0% 50.0%	30.8%	41.7%	30.4%	43.6%
		NP	23.3% 23.3%	17.3%	21.4%	22.6%	30.8%
	Recreational hiking	0.288
	and walking	P	53.3% 46.7%	67.3%	62.1%	76.5%	61.6%
		N	26.7% 36.7%	19.2%	29.1%	15.7%	31.1%
		NP	20.0% 16.7%	13.5%	8.7%	7.8%	7.3%
	Environmental	0.741
	education and research	P	93.3% 90.0%	92.3%	90.3%	96.5%	91.7%
	opportunity	N	3.3% 10.0%	7.7%	8.7%	3.5%	7.6%
		NP	3.3% 0.0%	0.0%	1.0%	0.0%	0.7%

Acknowledgments

Mariam Maki Sy benefitted from a PhD fellowship from the DRIIHM LabEx (ANR-11-LABX-0010_DRIIHM), "Device for Interdisciplinary Research on human-environments Interactions" within the framework of the Human-environment observatory "Mediterranean coastline". The authors thank the members of the former Syndicat Mixte des Etangs Littoraux (SIEL) for their support and advice during the data collection process. Mylène Farge and Nicole Lautrédou-Audouy are thanked for their help in organizing the citizen workshops. We are most thankful to the thirty-eight citizens who participated in the citizens' workshop on a voluntary basis and genuinely provided their time for this study. We also acknowledge the participation of the respondents in the internet survey. All data have been treated anonymously in compliance with the EU General Data Protection Regulation (GDPR).

Appendix A: The content of the survey The questionnaire was composed of open, spontaneous and closed questions (37 questions). It included four main categories:

A. The 'Familiarity and use of the lagoons complex' category included questions like:

• What is your city of residence and for how long have you been living there?

• Approximately how often do you go near the lagoons? (Never, 1 or 2 times a year, About once a week except winter, About once a week all year long, More often), • What activities do you do, frequently, from time to time or never, around the lagoons?

Check each activity according to the frequency. The activities listed were, among others: jogging, horse riding, water sports…

B. The 'preference elicitation' category included one question which was formulated as follow:

'What do you think are the most important roles of the Palavas lagoons in terms of conservation priority'? Please check the box associated with each role according to its level of conservation priority.

The roles (i.e. the list of the ecosystem services considered in the study) was presented in the rows of a table and the columns presented different levels of conservation priority i.e. 'high priority', 'priority', 'neutral', 'low priority', 'not a priority'.

C. The 'level of knowledge of the lagoons complex and the services they provide' category included questions as:

• Have you ever heard of the term "ecosystem service" before this survey?

• How would you rate your level of knowledge regarding the ecological functioning and the services provided by the Palavas lagoons complex? • Which of the following statements are true or false for the Palavas lagoons complex?

Please answer "I don't know" for neither case. [There was a total of twelve statements] o "The Palavas lagoon complex provides a natural environment for many activities such as fishing, non-motorized water sport, discovery of natural spaces, waterfowl hunting, ..." o "The Palavas lagoons complex is the property of the French Department of Hérault" o "The Palavas lagoons complex provides natural resources (fish, shellfish, fodder, etc.) necessary for the functioning of many economic activities such as professional fishing, tourism, etc". o "Shellfish farming is the most important economic activity of the Palavas lagoons complex area" Appendix B: the list of the ecosystem services used in the study


André Paquier
email: andre.paquier@irstea.fr

Quentin Royer
email: quentin.royer@irstea.fr

Christine Poulard
email: christine.poulard@irstea.fr

Pascal Billy
email: pascal.billy@developpement-durable.gouv.fr

Defining uncertainty for a simplified

Keywords: Flood mapping, uncertainty sources, hydraulic calculation, Rhône River, Gardons River

come

INTRODUCTION

Extreme floods assessment is necessary for flood management. For vulnerable facilities that do not resist to any flooding, it appears as a compulsory requirement. For usual stakes, it is part of the useful data for building a relevant management plan and dimensioning measures for flood damages reduction. Particularly, the 2007 European Flood Directive requires to identify Areas with Potential Significant Flood Risk and map on these areas three levels of floods. In France, the three levels concern [START_REF]Circulaire du 16 juillet 2012 relative à la mise en oeuvre de la phase[END_REF]:

• a flood between 10 and 30 years return period;

• a flood between 100 and 300 years return period;

• a flood of at least 1000 years return period.

As such extreme floods are very rare, their hydraulic modelling cannot rely on calibration on floods of equivalent magnitude. Thus, calibration is carried out for more ordinary floods and the calibration is then extrapolated to higher discharges, which means that uncertainty will increase with the flood return period. A recent research project Flowres [START_REF] Proust | Projet ANR-14-CE03-0010 Flowres[END_REF] shows that the use of a relevant model is necessary to reduce the uncertainty generated by the extrapolation. However, even with a well selected and well calibrated model, it is difficult to obtain an accuracy of less than 10% while the accuracy on the peak flow discharge is typically above 20% for a 10000 years return period. Then, it is expected that any acceptable hydrodynamic model should be more accurate than this range of 20%.

In France, for more than twenty years, flood hazard has been reported in the PPRI (plans for prevention of flood risks) which relied on the mapping of the 100 years flood or a historical flood if higher. Then, for a lot of rivers, detailed maps of such floods exist and can be considered as a reference of the rare but not extreme floods. One can use the knowledge of the flooding processes contained in these maps in order to build more accurate extreme floods maps. A method was developed to obtain such a map rapidly but the question stands in the uncertainty linked to the simplified method and whether the final map is accurate enough for various purposes.

Here below, after the description of the method, of the software and of the two case studies, the effects of the various factors of uncertainty are estimated.

THE ADDITIONAL DEPTHS METHOD

Description of the method

The method was named "Additional Depths Method" ("méthode des surcotes" in French language) because it aims at providing the difference between the water elevation accurately calculated for a known flood (typically the 100 years flood), and the water elevation to be estimated for an extreme flood (typically the 1000 years flood).

The method is based on several assumptions. The first one is the one-dimension feature of the flood flow, which can be translated into a calculation of the water elevation in a river cross section. The second assumption is the possibility to calculate the additional depth only from the additional cross section, as if the two flows (respectively below and above the known flood elevation) were separated. The third assumption can be summed up in the use of a Manning Strickler equation [START_REF]Circulaire du 16 juillet 2012 relative à la mise en oeuvre de la phase[END_REF].

Q=AKsS 1/2 R 2/3 (1)
in which Q is the additional flow discharge, A is the additional wetted area, S the slope, Ks the Strickler coefficient and R the hydraulic radius related to the additional wetted area. Energy losses are included in a linear bottom friction, assuming that the influence of the hydraulic structures or other singularities is relatively weak, which can be the case for extreme floods except if there are large structures (bridges or dams generally) that can be considered individually. Because the additional flow is essentially in the flood plain, the Strickler coefficient to be used for calculating additional water depth can be determined from (an average of) the land use of the flood plain (a usual value of 15 m 1/3 s -1 is recommended implying additional uncertainty that it is discussed here below). The second important parameter of Eq. 1 is the slope: in case of uniform flow, the energy slope is equal to the bottom slope; to be as close as possible from uniform flow, the slope should be calculated in a homogeneous reach in which the flow is nearly uniform; then, two possibilities exist either the bottom slope or the slope of the free surface for the known flood. If the flow is influenced by a large structure, the slope of the known flood will be obviously a better choice considering that the slope of the known flood is already influenced by the large structure; however, a minimum slope of 0.01% is requested. The fourth assumption is the decrease of water elevation in the downstream direction; although it seems obvious, it is not the best solution to reduce error [START_REF] Paquier | Quick estimate of extreme floods water levels[END_REF] because such a constraint is likely to accumulate errors if not carried out cautiously; however, it is applied to favour easy interpolation inside one reach and as a factor of control at the junction of two homogeneous reaches.

Three alternatives are selected for the calculation of the additional depth:

1. the more obvious one (called "M2" in the tool) requires to extract the topography of the additional cross sections and solving Eq.1 applying friction on bottom and banks; 2. a simplified version of M2 one (called "M1" in the tool) considers that the additional cross section is a trapeze; it permits avoiding to look for an additional topography that might be finally not representative; 3. using the information about the topography of the main channel if available in order to calculate the water elevation for the whole cross section. The known flood elevation is used to estimate the Strickler coefficient of the known flood area. Then, an average of the Strickler coefficient (between the known flood coefficient and the added flooded area coefficient estimated from land use) is used in Eq.1 (method called "M3" in the tool). In order to calculate the average, the Einstein equation [START_REF] Einstein | Der hydraulische oder profil-radius[END_REF] is used (average on the wetted perimeter multiplied by the Strickler coefficient at the power 3/2).

Methods M2 and M3 are using the same topography for the added flooded area and should provide similar results if the topography is accurate; however, in this latter case, method M3 appears to be preferred because it represents the flow resistance in a better way except in the rare cases in which the flow in the added area is separated from the flow for the known flood.

Description of the tool

To permit an easy application of the method, a software was developed in python language and was integrated in Q-Gis as a plug-in called "surcotes" that one can integrate in one's version of QGis in the same way as usual plug-in.

The first step of the tool requires the definition of the following data:

1. A digital topographic model (DTM) that will be used in any case a more detailed topography is not provided (for instance, in France, IGN topographic data basis); 2. The hydraulic axis of the valley (for instance, in France, the BD Carthage hydrographic network); 3. The cross sections that will define the homogeneous reaches (at least two sections for every reach); these cross sections can be defined by two points only if they are straight and if the topography is provided by the DTM; if the topography of the cross sections is known, it could be used instead of the DTM topography which is often less accurate in the main channel; 4. The extent of the know flood as a set of polygons; 5. Eventually the water elevation of the known flood in the cross sections.

The first step of the calculation is the assessment of the Strickler coefficients for the known flood. For M1 and M2 methods, this value is not used but it permits to check that the value of the known water elevation is coherent with the topography of the cross sections. In case the known water elevation is not provided, the user should select one of the values proposed by the software that are coming from the estimate of the elevation of the points in which the boundary of the known flood extent cuts the cross section. In that step, the user can reduce the cross section (if levees or secondary branches not involved in the flow capacity) to match the known flood extent.

The second step of calculation is calculating the extreme flood water elevation by one of the method. Then, this value is used to estimate the extreme flood extent crossing these values at the user cross sections and at interpolated cross sections (linear interpolation of water elevation at a constant space step) with the DTM.

THE CASE STUDIES

The Rhône case

The Rhone case is a 18 kilometres long reach about 50 kilometres downstream from Lyon. The reach was shared in two homogeneous sub-reaches. In the upstream one, the presence of a channel (parallel to the main river and joining it downstream) that is used for hydropower complicates the modelling. However, because the channel is rather narrow if compared to the width of the full flood plain, a simple method to take it into account consists in deducting the full capacity of the channel to the discharge to the flood discharge and compute in the natural topography of the flood plain.

For this reach, the extent of the floods for various return periods were investigated in a detailed way and can be used for references. We will use the 100 years flood as starting and will compare the result of our simplified method for the 1000 years flood with the reference for the same return period. Knowing the discharges for the two return periods and the water elevation for the 100 years return period, we can also compare the water elevations for the 1000 years return period.

A detailed DTM exists in this case but it does not cover fully the extent for the extreme floods. Thus, the procedure was: using the detailed cross sections and DTM to obtain the topography of the cross sections as far as possible and then complete (if necessary) by the 1 m IGN topographic basis; then using the 1m IGN topographic basis for mapping because it permits to cover the whole area homogenously.

The results show that from the 100 years flood to the 1000 years flood, the flooded area is not strongly increased (for a flow discharge passing from 4970 to 6710 m 3 /s upstream). Figure 1 shows that some discrepancies exist. The three main ones (river main channel, secondary channel for hydropower and flooded area north east of the secondary channel) are only a question of representation; on Figure 1, one can see that the secondary channel can be included or not in the calculation (and thus in the flooded area) depending of the user's choice. The other discrepancies show that the calculation provides nearly always a larger extent of the extreme flood with differences that can be considered as relatively high due to the small differences between the two reference flooded areas. In terms of additional water depth, the result (for the M3 method) is 0.08 m too high with a mean of the absolute value of the error of 0.2 m for a mean additional depth of 0.91 m; the relative error ranges from 0 to 98% with an average of 26%. The discrepancies in the flooded area are coming from a discrepancy between the water elevations provided and the topography used as shown on Figure 2a on which the map of the 100 years flood extent is drawn from the water elevation and the DTM. Selecting different water elevations for the 100 years flood, on can fit the reference flood extent (Figure 2b) and thus will change also the extreme flood extent and water elevation. For the flood extent, the improvement is verified, particularly, permitting to avoid spurious extensions due to interpolation of water elevations during mapping; however, the differences in water elevation introduced to match the reference flood map are kept for the extreme flood, which means that the calculated extreme water elevations will be wrong reflecting again the discrepancies between the two information (table of water elevation and DTM).

The Gardons case

The Gardons study area is about 10 kilometres long and includes the city of Alès and the Gardon d'Alès River till it joins the Gardon d'Anduze River. Three sub-reaches were distinguished separated by the confluence of two tributaries. A third tributary in Alès was not fixed as boundary between two sub-reaches but a step in the peak flow discharges was considered. The topography was based on the 5 m IGN data base and on detailed cross sections that similarly to the Rhone case should be sometimes extended from the 5 m data base in order to cover the 1000 years flood extent. In that case, there is no reference for the extreme flood extent but the PPRI map can be used as the reference for the known flood. Peak flow discharges were provided for both floods and are used to calculate a reference water elevation at the various cross sections.

Using the 1D model RubarBE [START_REF] El Kadi Abderrezzak | One-dimensional numerical modelling of dam-break waves over movable beds: application to experimental and field cases[END_REF], several calculations were performed for both peak discharges in order to find some kind of references for the flood extent and water elevations: first with the same sections as the ones used in the tool (called "same" with a standard set of Strickler frictions of 30 m 1/3 s -1 in main channel and 15 m 1/3 s -1 in flood plain and "KS" with a more varied set of frictions), second with the detailed original sections (called "original" before simplification and extension by the tool, applying the standard set of frictions), third with another set of cross sections that should be more recent (called "other" applying the standard set of frictions). Figures 3 and4 show that the results obtained are very different. Then, a 2-D model using the software Rubar 20 [START_REF] El Kadi Abderrezzak | Modelling flash flood propagation in urban areas using a two-dimensional numerical model[END_REF] was also used on the original cross sections and with the standard set of friction coefficients. The differences in water elevation are also important included with the 1D model ("original") with the same topography. The comparison of the 2D calculation with the reference map (Figure 5) shows also that the 2D model is not well calibrated or that the reference map was not established with the same topography that the one used for our study. Then, it was not surprising that the 2D model does not provide the same extreme map as the calculation by the additional depths method (Figure 6). On Figure 6, one can see also that even if the water elevations are not exactly the same, M1 (or M2 not shown as nearly identical to M1) and M3 methods provide similar maps except downstream Alès. Finally, as the tool is only calculating the additional water depths, it is important to evaluate if these additional depths are estimated correctly. Figure 7 shows that except for the first kilometre, M3 method provides an acceptable estimate of the additional water depths, particularly if compared with 2D model results, while it is the opposite for M1 and M2 methods. The narrowing of the flood plain at the crossing of the town of Alès that reduces the free surface slope explains that M3 calculation that keeps the mean slope of the reach (and a uniform flow) provides a too low additional depth (the different geometries enhancing the discrepancy).

DISCUSSION ABOUT UNCERTAINTY ASSESSMENT

Previous results

[3] summed up previous studies on the Additional Depths Method. The authors recommended to use the method included in the tool as M3 method except that the constraint of a decreasing water elevation going downstream was not considered as the better solution because, if only one cross section, it may lead to a generalized error on the upstream reach. However, this default can be avoided checking the latter cross section (which is easy in the plugin that indicates the sections on which the correction is modifying the water elevation). On those previous tests, the error on the flooded area (additional flooded areas and erroneously not flooded areas over the total flooded area) was then estimated to about 10% corresponding to a mean error in water elevations between 1 and 2 metres (about 50% of the additional water depth). The higher deviations in water elevation were located in narrow valleys with nearly no consequences for flooded areas while the main discrepancies in the flooded area were in the reaches in which the flood plain is very flat (except levees) and thus also places in which the 1-D flow hypothesis can be strongly discussed. The causes of error were identified in the topography, the assessment of the Strickler coefficient in the additional area and the estimate of the slope. However, the main errors were coming from using a local slope and the recommendation was to use a slope at reach scale, either the one of the free surface or the average bottom slope of the valley. The plugin "Surcotes" integrates this recommendation basing the calculation on homogeneous sub-reaches for which the user can define the slope, the default value being the average bottom slope.

Uncertainty for the Rhône case

The default calculation with the method M3 of the plugin provided an error of less than 10% on the water depths. With M3 method, these results are very stable to changes in friction coefficients and slopes and can be even improved (2% of error) making smoother the topography at the interface of the detailed data and the usual DTM. However, the mapping show large differences with an error of about 70% in the additional flooded area (if defined as the ratio of the sum of the wrongly flooded area ("not flooded" against "flooded" or "flooded" against "not flooded") to the total flooded area) because the method produces a too large 100 years flood map crossing DTM and reference water elevations. If the 100 years map is corrected by changing the water elevations (average of 0.7 m necessary), the error in mapping is reduced to about 40% (and the error in the average additional water depth is about 15%). This value should be compared to the 30% increase of the additional flooded area if the 1000 years flow is increased by 10%.

As the topography of the bottom inside the reference flood area is well known, the Rhone case is typically a case in which M1 and even M2 methods should not be recommended. Using them, the error is increased with a rising of water elevation by about 1.2 m which means an additional flooded area more than doubled. It can be explained that the flow width does not increase a lot leading to a too large friction overestimated at the interface between the 100 years flow and the additional flow.

Uncertainty for the Gardons case

For the Gardons case, no reference for the extreme flood was used. The reference for the 100 years flood shows a flooded area strongly larger than what is obtained by a 2-D model, which reveals a problem of accuracy of the DTM or any other error. The use of various geometries in the 1D model solving de Saint Venant equations shows differences up to 5 metres reminding the importance of an accurate topography for hydrodynamic modelling.

In such a case, only the additional water depths can be compared guessing that similar values will mean a same mapping if one starts from the reference map. The mean increase of the water elevation was 1.14 m for the 2D model and 1.43 m for the 1D model with the same geometry but only 0.8 m if the cross sections used in the plugin are used in a 1D de Saint Venant model that generally underestimates the water elevation. The plugin with the M3 method provides an average increase of water elevation of 1.2 m (1.85 m for M1 and 2.02 m for M2), which agrees with 2D model. However, if the M3 method is further compared to the 2D, the absolute values of the differences in the local additional water depths reach an average of 0.4 m, which means about 30% of the mean increase of the water elevation; this value reflects the uncertainty that can be expected from the use of the plugin and should be compared to an increase by about 0.6 m if the flow is increased by 20% which is a usual uncertainty range for the estimate of a 1000 years discharge. Note that using as reference map, the 2D mapping of the 100 years flood, one provides similar mean increase of water elevation (1.13 m for M3 method) but eventually higher local differences because of the local discrepancies in the topography.

CONCLUSIONS

The additional depths method guesses that the reference flood map agrees with the topographical data used for extending the flood mapping to the extreme floods. In the two study areas described here above, it was not the case and, thus, it was difficult to evaluate the own accuracy of the method. Because the widening of the flooded area is limited between the reference flood and the extreme flood, the M3 method of the plugin "Surcotes" is the best solution. It can provide a mean additional water depth at less than 10% but, because locally the difference can be up to 100%, even if the reference map is well reproduced by the plugin, the error in the additional flooded area can be as high as 40%.

Then, it can be recommended to use the plugin "surcotes" only if the flow is mainly 1D and if the DTM used for mapping agrees with the topography used for the establishing the map (the plug in permitting to evaluate that point). Of course, the accuracy of the results will depend on the accuracy of the DTM but also on the selection (by the user) of the more relevant slopes and friction coefficients. The use of the M1 and M2 methods of the plugin should be limited to the cases in which the flooded area increases a lot between the reference and the extreme flood.

Figure 1 :

 1 Figure 1: Rhône case -Upstream part of the flooded area (100 years extent with 1000 years extent (reference in violet and calculated in pink)).

Figure 2 :

 2 Figure 2: Rhône case -Downstream part of the flooded area: referenced 100 years extent as black line, calculated 100 years and 1000 years extent (respectively in violet and in pink); a (left): initially; b (right): after adjustment of the 100 years extent on the cross sections.

Figure 3 :

 3 Figure 3: Water elevation along the Gardons reach for the reference flood.

Figure 4 :

 4 Figure 4: Water elevation along the Gardons reach for the extreme flood.

Figure 5 :

 5 Figure 5: Map of the reference flood calculated using 2D model with the reference extent of the reference flood (black line).

Figure 6 :

 6 Figure 6: Map of the extreme flood calculated using 2D model with the M1 (black line) and M3 (green line) extent.

Figure 7 :

 7 Figure 7: Additional water depths along the Gardons reach between the extreme flood and the reference flood.

ACKNOWLEDGEMENTS

The development of the "Additional Depths Method" was partly funded by the French Ministry of Environment (MTES).