Benoit Chèze
email: benoit.cheze@ifpen.fr

Maia David
email: maia.david@agroparistech.fr

Vincent Martinet
email: vin-cent.martinet@inra.fr.

Farmers' motivations to reduce their use of pesticides: a choice experiment analysis in France

Keywords: Discrete choice experiment, Pesticides, Agricultural practices. JEL Classification: Q12, Q18, Q51, Q57, C35

This article presents the results of a Discrete Choice Experiment (DCE) survey conducted among a hundred French farmers from June 2016 to February 2017. Respondents had to choose between conserving their actual farming practices or change towards a reduced use of pesticides. Thanks to this stated preference method, we analyze the factors influencing farmers' motivations to reduce -or not-their use of pesticides, we estimate the relative weight of these factors and we value the willingness to accept/willingness to pay for changes in each of these factors. Our contribution relies on including, besides other attributes, the role of the harvest-risk in farmers' decisions towars pesticides. Our results indicate that the most important attribute in the farmers' decisions making is the "risk of poor harvest" followed by the kind of "administrative commitment". Regarding the former attribute, farmers express high preferences for not bearing a risk of loss: they need to receive on average 100.89 euros (107.64 euros) per hectare and per year to compensate the utility loss associated with the risk of encountering one (two) additional year(s) of poor harvest.

Introduction

Reducing the use of pesticides has become a major challenge in developed countries' agriculture. As shown by the recent extremely rapid growth of organic farming (+ 20% of sales in France in 2016), consumers are now aware and demanding on this issue.

Public policies have developed for the last ten years to attempt to provide adequate incentives to change behaviors and boost research on this topic. Several farming practices have now proven efficient to maintain satisfactory yields while reducing the use of chemicals [START_REF] Lechenet | Reducing pesticide use while preserving crop productivity and profitability on arable farms[END_REF]). Reducing pesticides could reduce farmers' costs, improve their health and environment and prevent resistance ( [START_REF] Wilson | Why farmers continue to use pesticides despite environmental, health and sustainability costs[END_REF][START_REF] Bourguet | The hidden and external costs of pesticide use[END_REF]). However, up to now, results have been disappointing. Between 2008 and 2015, farmers' consumption of chemical inputs has increased in Europe (+10% in France over this period) and there is a lack of participation in agro-environmental schemes in this field. What are the main obstacles that prevent farmers from adopting low-pesticides practices that could be win-win strategies? There is a demand from researchers in ecology and agronomy towards economists to understand the socio-economic factors that explain farmers' behavior.

Our work contributes to this question by exploring the factors influencing farmers' choice to change their farming practices towards a reduced use of pesticides. Several socio-economic analyses have examined the motivations and obstacles to the adoption of environmentally friendly practices by farmers, using various methods.Contrarily to most of them, we use a quantitative approach, in order to estimate the relative weight of various decision factors and to provide farmers' willingness to pay (WTP)/ willingness to accept (WTA) for changes in these factors. Our methodology is based on non-market valuation, using a discrete choice experiment (DCE).

The DCE method has increasingly attracted the attention of environmental economists for the last ten years, as shown by their considerable recent use (see [START_REF] Hoyos | The state of the art of environmental valuation with discrete choice experiments[END_REF] for a survey). It is a stated preference method in which preferences are elicited through repeated fictional choices made by respondents. Compared to other non-market valuation methods, DCEs have the advantage of capturing the non-use value 1 and of taking into account several characteristics, or attributes, of the considered issue. It thus procures a WTP/WTA for each of these attributes rather than a global WTA/WTP as a contingent valuation would do. It is particularly useful to shed light on the trade-offs that occur in a problem or a decisionmaking. In our case, we wish to understand the factors influencing farmers' choice and the relative weight of these factors. We also wish to measure the WTA/WTP for changes in each of these factors. For these reasons, the DCE seems particularly appropriate to reach our objective.

Among the main drawbacks of the method, DCEs may induce some cognitive difficulties [START_REF] Hanley | Modelling recreation demand using choice experiments: Climbing in scotland[END_REF] as the questionnaire may be heavier than for a contingent valuation and it implies more complex econometric estimations. We kept vigilant on both these points.

The DCE approach has previously been used to examine farmers' choices to adopt environmentally friendly practices. Depending on the article, the adoption of the alternative practice can occur within ( [START_REF] Khuffus | Individual preferences and collective incentives: what design for agri-environmental contracts? The case of winegrowers' herbicide use reduction[END_REF][START_REF] Christensen | Determinants of farmers' willingness to participate in subsidy schemes for pesticide-free buffer zones -A choice experiment study[END_REF][START_REF] Broch | Using choice experiments to investigate the policy relevance of heterogeneity in farmer agri-environmental contract preferences[END_REF][START_REF] Espinosa-Goded | What do farmers want from agri-environmental scheme design? A choice experiment approach[END_REF][START_REF] Ruto | Investigating farmers' preferences for the design of agri-environmental schemes: a choice experiment approach[END_REF][START_REF] Hudson | Risk and transaction cost in contracting: results from a choice-based experiment[END_REF][START_REF] Peterson | Transaction costs in payment for environmental service contracts[END_REF]) or independently of [START_REF] Beharry-Borg | Evaluating farmers' likely participation in a payment programme for water quality protection in the UK uplands[END_REF][START_REF] Jaeck | Farmers' preferences for production practices: a choice experiment study in the Rhone river delta[END_REF][START_REF] Birol | Using a choice experiment to estimate farmers' valuation of agrobiodiversity on Hungarian small farms[END_REF][START_REF] Vidogbena | Control of vegetable pests in Benin -Farmers' preferences for eco-friendly nets as an alternative to insecticides[END_REF]) an agri-environmental contract with public authorities.

Regarding the specific issue of a reduced use of pesticides, to our knowledge, less than ten DCEs have been published. [START_REF] Christensen | Determinants of farmers' willingness to participate in subsidy schemes for pesticide-free buffer zones -A choice experiment study[END_REF], for example, analyze Danish farmers' motivation to sign subsidy schemes for pesticide-free buffer zones. They show that the contract's flexibility is a major decision criteria. [START_REF] Khuffus | Individual preferences and collective incentives: what design for agri-environmental contracts? The case of winegrowers' herbicide use reduction[END_REF] look into French wine-growers' decision to sign an agri-environmental scheme in which the payment is partly individual and partly based on a collective result (i.e. there is a bonus payment if the number of participants is above a given threshold). They show that farmers value positively the collective component of the contract. [START_REF] Jaeck | Farmers' preferences for production practices: a choice experiment study in the Rhone river delta[END_REF] study rice-grower's choice to reduce their use of chemical inputs in Camargue (France) and show how targeted contracts are needed given farmers' heterogeneity.

Globally, the literature shows that the commitments' flexibility and the potential administrative burden are two major components of farmers' decision to change their practices. However, only very few contributions have looked into the role of risk in farmers' choices. Price-risk and harvest-risk are two factors that can drastically affect farmers revenues. In particular, a change in the use of pesticides can have major impacts on the stability of yields and many farmers actually use pesticides as a form of harvest insurance. As explained by [START_REF] Lechenet | Reducing pesticide use while preserving crop productivity and profitability on arable farms[END_REF], "the transition towards low-pesticides farming strategies might be hampered by the uncertainty behind any deep change (...). Risk aversion may be a hindering factor". [START_REF] Hudson | Risk and transaction cost in contracting: results from a choice-based experiment[END_REF] examines the role of the price-risk but the harvest-risk is even more at stake when considering the use of pesticides. Our analysis includes, besides other attributes, the role of the harvest-risk in French farmers' decisions to reduce -or not -their use of pesticides.

We first describe, in section 2, our methodology, including the experimental design and data collection. We then describe, in section 3, the econometric models associated to the DCE approach. Section 4 presents our main results and their interpretation. Conclusions and discussion are developped in section 5.

Methodology

The choice experiment approach relies on economic theory of consumer choice and non-market valuation. In a DCE survey, respondents have to make choices between several options defined by their attributes (i.e. fundamental characteristics of the respondents' situation). Several choice sets are typically presented to respondents, each composed of three options: the situation if nothing is changed (i.e. the satus quo) and two fictional options. Respondents then choose their favorite option among these three. An option is defined by a set of attributes taking different values according to the option. One of these attributes usually represents the monetary contribution of the respondents. Other attributes can include environmental or social implications of the considered issue. See [START_REF] Louviere | Stated choice methods : analysis and applications[END_REF] for a detailed description of the method.

The discrete choice modeling framework provides the advantage to vary simultaneously several attributes of the considered issue. By doing so, it reveals more detailed information than other stated preference methods such as contingent valuation. Especially, it allows to estimate the marginal rates of substitution between the different attributes. When one of the attributes is a cost (a price), these marginal rates of substitution can be interpreted as the WTP (or the WTA) for changes in the attributes' levels (see Section 4.3).

In our case, respondents were farmers who had to choose between conserving their actual farming practices or changing their practices towards a reduced use of pesticides.

Choice of the attributes and their levels

A first step was to choose the attributes composing the options, and their associated levels. As explained by [START_REF] Hanley | Modelling recreation demand using choice experiments: Climbing in scotland[END_REF], the number of attributes must be limited so as to avoid the cognitive burden of making too complicated choices. The selection of the attributes was based on the state of the literature, discussions with experts in agronomy, ecology and agricultural economists, focus groups with farmers and pre-tests of some choice sets.

As shown in Table 1, the chosen attributes are:

1. The farmer's yearly profit (or gross margin) per hectare: this attribute is given by the average profit per hectare and per year of the farm, in euro. This is the monetary attribute. The profit varies with a change of practice due to several factors including the impact on yields, on pesticides' expenses, on public aids, on the sales price, etc. It is expressed as a variation compared to the status quo, taking the following values: -50 e, +0e, +50e, +100e.

2. The risk of poor harvest: given by the number of years out of ten years for which the farm's harvest is drastically and exceptionally reduced (i.e. reduced by at least 30%) compared to a normal year. This poor harvest is due to diseases, pests, weeds, etc. This attribute is expressed in additional years with poor harvest with the new practice compared to the status quo: +0, +1 year, +2 years 3. The administrative framework of the change of practice: describing whether the change is coming along with any administrative commitment. This commitment can imply a public aid or higher sales price (included in the margin, i.e. first attribute) but may also bring some administrative burden. This attribute is qualitative and is expressed as the additional commitments compared to status quo: "no additional administrative framework", "signing an agri-environmental contract with public authorities" (with specification), "joining a Charter" (inducing no contractual specification and a flexible commitment), "entering a certification process" (associated with a specification, controls and a green label).

4. Impact on health and the environment: this attribute indicates how the exposure to harmful substances for health or the environment is reduced with the change in practice. It can take the following values: -0%, -20%, -50% -80% compared to the status quo.

The experimental design

The aim of the experimental design is to select the options (i.e. the combinations of attributes' levels) that are presented to respondents. With four attributes and three to four levels each, the questionnaire would be far too heavy if all the possible combinations of attributes' levels were submitted to respondents' choice. In order to choose the most relevant choice sets, that is those yielding maximum information on respondents' preferences, we use experimental design techniques (see [START_REF] Louviere | Stated choice methods : analysis and applications[END_REF] and [START_REF] Street | Quick and easy choice sets: constructing optimal and nearly optimal stated choice experiments[END_REF]) and the dedicated Ngene software, which is a reference in this field. It provides a statistically optimal sub-set of the possible combinations using a Bayesian D-optimal design, in our case a fractional factorial efficient design2 . This experimental design led to 16 different choice sets which were blocked into two groups in which respondents were randomly assigned, as is usual. As a result, the final questionnaire presented 8 choice sets to each respondent, which represents an acceptable cognitive load.

Presentation of the questionnaire and data collection

The questionnaire was designed to last less than 20 minutes. A first part was dedicated to general questions regarding the farmer's activity, the size of the farm, the use of pesticides and the actual level of the attributes in the respondent's case. The aim of the survey was then shortly described using illustrated slides and describing in detail the four attributes. We were very careful so as tho deliver an objective and neutral information.

The eight choice sets were then presented and the respondent was asked to pick his/her favorite option. The order of the choice sets was randomized so as to avoid having a potential declining concentration (last choices) always affecting the same choice set. The respondent could click on the i icon (see Figure 1) in order to obtain additional explanations. In order to detect protest answers, farmers choosing unchanged practices in all choice sets were asked the reasons of their choice.

After the choice sets came some final questions on the socio-demographic situation of the respondent (income level, gender, age, level of education) and on his/her understanding of the choice sets.

The survey was held from June 2016 to February 2017, taking two forms: face-to-face interviews directly on the farms and a websurvey. We were careful to give very similar information in both types of interviews. We obtained in total 100 answers from French farmers whose location, activities and main sociodemographic characteristics are described in section 4.1.

3 The choice experiment approach and the different econometric models

The choice experiment modeling framework relies on the characteristics theory of value [START_REF] Lancaster | A new approach to consumer theory[END_REF] and the random utility theory [START_REF] Mcfadden | Conditional logit analysis of qualitative choice behaviour[END_REF]. Different econometric models are used to analyze the discrete choice data, depending on the assumption made on the unobserved components of the random utility, i.e. the assumption on the distribution of its error terms.

Theoretical foundations of the choice experiment approach

Lancaster (1966) assumes that a good may be defined by its own characteristics.

The value of a good therefore consists of the sum of the value of all its characteristics. Applying this theory in a choice experiment approach, this means that each attribute is associated with a utility level and that the (indirect) utility of each respondent n for an alternative i in a choice set C, V n,i is derived from its K attributes, that is the sum of the utilities obtained from each of the K attributes.

Typically the representative utility of an alternative i for respondent n is specified to be a linear-in-parameters function:

(1)

V n,i = V (X i , Z n ) = K k=1 β ik x ik + A a=1
α an z an ∀n ∈ {1, . . . , N } ; ∀i ∈ {1, . . . , I} where V n,i is supposed to be a function of the observable i) K attributes of the alternative i, X i , and ii) the A characteristics of the n-th respondent, Z n .

For his part, [START_REF] Mcfadden | Conditional logit analysis of qualitative choice behaviour[END_REF] proposes to consider that individuals make choices according to a deterministic part along with some degree of randomness. Combining theories of both [START_REF] Lancaster | A new approach to consumer theory[END_REF] and [START_REF] Mcfadden | Conditional logit analysis of qualitative choice behaviour[END_REF], we assume that the random utility of the i-th alternative for each individual n, U n,i , is composed of a deterministic component,V n,i = V (X i , Z n ), and a stochastic element, n,i :

(2)

U n,i = V (X i , Z n ) + n,i
where the error term n,i is a random variable that captures the unsystematic and unobserved random element of individual n's choice [START_REF] Hanley | Price vector effects in choice experiments: an empirical test[END_REF][START_REF] Holmes | Feature based methods[END_REF][START_REF] Louviere | Stated choice methods : analysis and applications[END_REF].

Assuming the rationality of individuals, respondents are thus supposed to associate each alternative i with a utility level U n,i and choose the option that provides them with the greatest utility. It comes that an agent n will choose an alternative i from a finite set of alternatives C if its indirect utility of i,U n,i , is greater than the indirect utility he could have derived from any other alternative j, U n,j :

(3)

U n,i > U n,j ⇒ V n,i + n,i > V n,j + n,j ∀ j = i; i, j ∈ C
The probability that an individual chooses alternative i is the same as the probability that the utility of alternative i is greater than the utility of any other alternative of the choice set [START_REF] Adamowicz | Stated preference approaches for measuring passive use values: Choice experiments and contingent valuation[END_REF]. Following [START_REF] Train | Discrete choice methods with simulation[END_REF], the probability that an agent n chooses alternative i in a choice set C is:

P n,i = P {U n,i > U n,j ∀ j = i; i, j ∈ C} (4) ⇔ P n,i = P {V n,i + n,i > V n,j + n,j ∀ j = i; i, j ∈ C} (5) ⇔ P n,i = P { n,j < V n,i -V n,j + n,i ∀ j = i; i, j ∈ C} (6)

The different econometric models

Different discrete choice models are obtained from different assumptions about the distribution of the random terms.

The conditional logit (CL) model

If we suppose that unobserved components, the error terms n,i , all independently, among the N agents and between the I alternatives, follow a standard Gumbel distribution3 , we have specified a conditional logit model (or multinomial logit model).

Since the unobserved components are independent, we can multiply Eq. ( 6) to obtain the probability of individual n choosing alternative i, conditional on n,i :

P n,i | n,i = j =i P { n,j < V n,i -V n,j + n,i } (7) = j =i e -e -(V n,i -V n,j + n,i ) (8)
P n,i is then obtained with the integration of P n,i | n,i over the distribution of the unobserved components:

(9) P n,i = j =i e -e -(V n,i -V n,j + n,i ) e -n,i e -e -n,i d n,i
Calculations then lead this expression to simplify in (10)

P n,i = e V n,i j e V n,j
where P n,i only depends on observable components.

An important drawback to this model is that β is considered fixed across all individuals, while we can expect the preferences to vary among the respondents. Two other important drawbacks are the hypothesis of independence of irrelevant alternatives (IIA) and uncorrelated unobserved components.

The random parameter logit (RPL) model

The random parameter logit model [START_REF] Mcfadden | Mixed MNL models for discrete response[END_REF][START_REF] Train | Discrete choice methods with simulation[END_REF], also called the mixed logit model, solves these three issues. In this model, the preferences parameters β are allowed to vary across individuals; only their distribution needs to be known. As such, for a given β we can define the logit probability :

(11) L n,i (β) = e V n,i (β) j e V n,j (β) If f (β)
is the density function describing the distribution of preferences over individuals, we get back to (12)

P n,i = L n,i (β)f (β)dβ
which is the probability of interest.

Results and interpretation

Recall that we want to analyze farmers' motivations to reduce their use of pesticides and to estimate the monetary value associated with the farmers' various decision factors. The DCE presented in the previous section has been conducted among a hundred farmers who had to choose between conserving their actual farming practices or changing their practices towards a reduced use of pesticides. After removing protest answers, we finally obtained 1992 choices elicited from 83 respondents. We first describe this sample in Section 4.1 and then analyze in Section 4.2.2 the discrete choice data collected by estimating two types of econometric models: the conditional logit (CL) and the random parameter logit (RPL).

Descriptive Statistics

Table 3 and Table 2 present some descriptive statistics for the final sample composed of 83 respondents (39% of women). The respondents' ages range from 23 to 68 years, with an average of 46 years. The mean area of their agricultural exploitations is about 117 hectares but there is a great disparity among them, as showed by the standard errors of the annual turnover and gross margin per hectare. Some other descriptive statistics are presented in the Appendix.

Econometric models

The results of both the CL and RPL estimates for the sample are presented in Table 4 andTable 5

Model specifications

According to Eq. ( 2), the random utility of the i-th alternative for each individual n, U n,i , is composed of a deterministic component,V n,i = V (X i , Z n ), and a stochastic element, n,i . It has already been explained how the econometric models (CL and RPL) actually depends on the assumption on the distribution of error terms n,i . Before estimating these models, one also need to specify the deterministic part of the utility function, V n,i = V (X i , Z n ). The linear specification is often chosen in the literature as it is the most simple one to work with.

Moreover, an Alternative Specific Constant (ASC) term is included to capture the (systematic) effect of unobserved influences (omitted variables) on the utility function. The ASC is modelled as a dummy that takes the value 0 if one of the hypothetical alternatives is chosen and 1 if 'none of these', i.e. the status quo alternative, is chosen. Thus, the ASC defines a situation with "no variation of the farmer's yearly gross margin per hectare", "no additional years with poor harvest", "no additional administrative framework" and "no reduction of the exposure to harmful substances for health or the environment". A positive and statistically significant ASC would indicate strong preferences for no additional conservation. It would suggest the existence of some omitted variables that have a positive effect on the farmers' utility of choosing to keep their actual farming practices.

Hence, the model is specified so that the probability of selecting a particular farming practice scenario i is a function of attributes of that alternative and of the alternative specific constant. We thus assume that the utility V n,i is an additive function. Eq. (2) becomes:

(13) U n,i = ηASC + β i,1 x i,1 + β i,2 x i,2 + β i,3 x i,3 + β i,4 x i,4 + A a=1 α an z an + n,i
where Z n = (z 1n , . . . , z an , . . . , z an ) represents the vector of the A socio-demographic characteristics of the n-th respondent. x i,1 , x i,2 , x i,3 and x i,4 correspond to the different level taken by the attributes "Gross margin", "Risk of poor harvest", "Administrative commitment" and "Health and environmental impacts", respectively. Note that in our case, "Gross margin" is the payment attribute. Thus specified, β = (β i,1 , β i,2 , β i,3 , β i,4 ) coefficients quantify the influence which the various levels of the four attributes exert over the utility that farmers associate with the I different alternatives available, relative to the utility of the "status quo" option that appeared on every choice card.

Regarding X i = (x i,1 , x i,2 , x i,3 , x i,4 ), the attributes can be specified as discrete or continuous variables and it is possible to combine qualitative and quantitative attributes in the same model specification.

CL and RPL models results

Two models specifications has been chosen here. Table 4 presents the results for the CL (column (1)) and the RPL model (column ( 2)) when all attributes are specified as continuous variables whereas in Table 5, only the payment attribute (Gross margin) and the "Health and environmental impacts" attribute are modelled as a continuous variable. The two other attributes ("Risk of poor harvest" and "Administrative commitment") are modelled as effect-coded dummy variables. In both Tables, the RPL model is preferred to the CL model according to its highest value of the log-likelihood function. Moreover, recent applications of the Table 5: Results of the CL and RPL models (second models specification) RPL model have shown that this model is superior to the CL model in terms of overall fit and welfare estimates [START_REF] Lusk | Demand for beef from cattle administered growth hormones or fed genetically modified corn: a comparison of consumers in France, Germany, the United Kingdom and the United States[END_REF]. For all these reasons, we focus our interpretations on the results of the RPL models in both Table 4 andTable 5. According to [START_REF] Mcfadden | Mixed MNL models for discrete response[END_REF], the RPL is a highly flexible model that can approximate any discret choice model. Compared to the CL model, it relaxes the independence from irrelevant alternatives (IIA) hypothesis of the multinomial logit by allowing the random components of the alternatives to be correlated, while maintaining the assumption that they are identically distributed [START_REF] Greene | Econometric Analysis[END_REF]. Hence, some parameters of the vector β are assumed to be randomly distributed in the population rather than fixed as in the usual multinomial logit model.

Here, all the parameters except the payment attribute4 are specified to be normally distributed, and distribution simulations are based on 1000 draws to estimate their respective mean and standard deviation. The assumed normal distribution of the random parameters is one way to model heterogeneity in preferences. The normal distribution is symmetric and unbounded. So the use of this distribution means that we make a priori no assumption on farmers' preferences: positive as well as negative parameter values may be taken, in order to capture the heterogeneity in the population. Fixing the payment attribute coefficient, on the contrary, ensures that all respondents have a positive coefficient, in our case, so that the estimated WTA will be normally distributed (see Section 4.3 for more details).

Regarding the results of the RPL estimations, standard deviations of a majority of the coefficients are significant, indicating that a RPL provides a significantly better representation of the choices than a CL5 as it shows that there is heterogeneity among respondents around the mean. This indicates that the data supports choice specific unconditional unobserved heterogeneity for these attributes and some respondents might prefer lower levels of these.

Except for the "Health and environmental impacts" attribute, all the coefficients of the RPL model presented in both Tables 4 and5 are statistically significant and have the expected sign. To our great astonishment, the coefficient of "Health and environmental impacts" attribute, even though negative, is not statistically significant at the 10 % level in both RPL models. The reduction of exposure to harmful substances for health or the environment seems to have no effect on the farmers' utility. The coefficient of the ASC is negative but not statistically significant in Table 4. In Table 5 however, its coefficient becomes statistically significant at the 10% level and remains negative. Combined with the latter result on the non-significance of "Health and environmental impacts" coefficient, it indicates that there are some variables that are not included in the model, which induce farmers to prefer to change their actual practices to reduce their use of pesticides rather than conserving their actual farming practices.

In Tables 4 and5, the sign of the payment attribute coefficient (Gross margin) in both RPL models is statistically significant at the 10% level and the 5%, respectively. Its positive sign was expected as it indicates that the effect on respondents' utility of choosing from a finite choice set an alternative with a higher average yearly profit per hectare is positive.

In the first model specification (Table 4), the "Risk of poor harvest" and "Administrative commitment" attributes are modelled as continuous variables. Both coefficients are negative, meaning that an increase in harvest risks or in administrative commitments reduce the repondents' utility. Interestingly, respondents associate any additional administrative framework coming with a change of practice as higher administrative burden rather than as a beneficial accompanying measure.

In Table 5 on the contrary, the two latter-mentioned attributes are modelled as dummy coded variables: attributes are encoded using i) two dummy-coded variables per level ("+ 1 year" and "+ 2 years") for the "harvest risks" attribute and ii) three dummy-coded variables per level ("Charter", "Contract" and "Certification") for the "administrative commitments" attribute6 . All dummy variables are statistically significant and negative, confirming estimate results obtained for the first model specification (see Table 4). However, this second model specification tends to indicate that there are no linear effect in the "administrative commitments" attribute. In Table 5, the coefficients of "Charter", "Contract" and "Certification" correspond to the variation in utility due to an additional administrative framework taking the form of these three kinds of commitments, respectively, compared to the status quo situation, i.e. "no additional administrative framework". In absolute terms, the coefficient of "Contract" (-0.527) is superior to the "Charter" coefficient (-0.431) but inferior to the "Certification" one (-0.519). Curiously, "signing an agri-environmental contract with public authority", such as a MAEC contract, is actually perceived by respondents as worse than "entering a certification process" (yet associated with a specification, controls and a green label).

Willingness to accept estimates

As mentioned in Section 2, welfare measures can be determined in the form of marginal WTP/WTA, by estimating the marginal rate of substitution between the change in an attribute under consideration and the marginal utility of income represented by the coefficient of the payment attribute, β pay . The latter is assumed constant as is common in the literature [START_REF] Hensher | The mixed logit model: the state of practice[END_REF].

Table 6 reports the marginal WTA values for each of the attributes estimated in both RPL models using the Wald procedure (Delta method). The Delta method stipulates that the WTA for a unit change of a given attribute can be computed as the marginal rate of substitution between the quantity expressed by the attribute in question and the payment attribute [START_REF] Louviere | Stated choice methods : analysis and applications[END_REF]. Since utilities are modelled as linear functions of the attributes, the marginal rate of substitution between two attributes is the ratio between the coefficients7 :

(14) W T A k = - dx pay dx k = - dU/dx k dU/dx pay = - ∂V /∂x k ∂V /∂x pay = - β k β pay
When attributes are modelled as effect-coded dummy variables, but the payment attribute, the WTA associated with each attribute k and each level l becomes:

(15) W T A l k = - β l k β pay
where β l k are the estimated parameters, which measure the variation of the utility associated with a variation of the attribute k from the status quo level to the level l. W T A l k then represents the willingness to accept to move from the status quo level of attribute k to a level l.

Since the RPL model assumes i) the payment attribute is a fixed parameter and ii) other attributes' coefficients are normally distributed, W T A are then normally distributed, as linear combinations of normal random variables. We then have the convenient result that:

(16) E[W T A k ] = - E[β k ] β pay (17) E[W T A l k ] = - E[β l k ] β pay
For comparisons, estimates presented in Table 6 were calculated using both RPL models. The first lines correspond to WTAs computed from the RPL model estimates presented in Table 4 whereas the last lines correspond to WTAs computed from the RPL model estimates presented in Table 5. The estimated standard deviations and confidence intervals around the mean of the WTA estimates are obtained using the Krinsky and Robb parametric bootstrapping method [START_REF] Krinsky | On approximating the statistical properties of elasticities[END_REF].

Table 6: WTA estimates

In calculating a WTA, it is important that both parameters used in the calculation be statistically significant, otherwise no meaningful WTA measure can be established. Recall that in both RPL models, the coefficient of "Health and environmental impacts" attribute is not statistically significant at the 10 % level. Not surprisingly, estimated coefficients and standard deviations lead to negative lower bounds of the confidence intervals for this attribute.

Regarding the other attributes, mean WTA estimates are systematically lower for the first model specification (Table 6, first lines) than for the second one (Table 6, last lines). Moreover, whatever the model specification retained, when the payment attribute is used as the normalizing variable, the most important attribute is the "risk of poor harvest" followed by the kind of "administrative commitment". Indeed, the mean WTA of the former and the latter attributes are respectively equal to 56.82 and 29.24 in the first model specification and are ranging from 100.89 to 107.64 and from 70.48 to 86.20 respectively in the second model specification.

Focusing on the second model specification, a second lesson is obtained from the comparison of the "Risk of poor harvest" attribute dummy coded levels. According to our results, farmers need to receive on average 100.89 euros per hectare and per year to compensate the utility loss associated with the risk to encounter one additional poor harvest. In the meantime, they need "only" to receive seven euros more than this amount (107.64 euros per hectare and per year) to compensate the utility loss associated with a risk multiplied by two. Actually, farmers express high preferences for not bearing a risk of loss. One or two additional year(s) out of ten of poor harvest are equivalent, meaning it is having a risk of loss that is important in their decision.

Concluding remarks and discussion

This article proposed to investigate farmers' motivations to reduce their use of pesticides and to evaluate the willingness to pay and/or to accept (WTP/WTA) to change their actual farming practice.

To better understand farmers' decision factors and the relative weight of these factors, we chose to apply a discrete choice experiment (DCE) approach. Globally, the literature shows that the flexibility of their decisions and the administrative burden are two major components of farmers' decision to change their practices. However, only very few contributions have looked into the role of risk in farmers' decisions. Price-risk and harvest-risk are two factors that can drastically affect farmers revenues. In particular, a change in the use of pesticides can have major impacts on the stability of yields and many farmers actually use pesticides as a form of harvest insurance. Regarding the specific issue of a reduced use of pesticides, to our knowledge, very few studies proposed to examine the role of the risk in farmers' decision making. Our contribution offers to fill this gap by including, besides other attributes, the role of the harvest-risk in French famers' decisions to reduce -or not -their use of pesticides.

A DCE survey has thus been conducted among a hundred farmers from June 2016 to February 2017. Respondents had to choose between conserving their actual farming practices or changing their practices towards a reduced use of pesticides. After removing protest answers, we finally obtained 1992 choices elicited from 83 respondents. Each alternative of the choice set was a function of four attributes; namely "Gross margin", "Risk of poor harvest", "Administrative commitment" and "Health and environmental impacts".

Two models specifications have been specified. In the first model specification, all attributes are specified as continuous variables. In the second model specification, only the payment attribute (Gross margin) and the "Health and environmental impacts" attribute are modelled as a continuous variable. The two other attributes ("Risk of poor harvest" and "Administrative commitment") are modelled as effect-coded dummy variables. Both model specification are estimated using Conditional Logit (CL) and Random Parameter Logit (RPL) econometric models.

Except for the "Health and environmental impacts" attribute, all the coefficients of the RPL models are statistically significant and have the expected sign. Regarding other attributes, both "Risk of poor harvest" and "Administrative commitment" attributes' coefficient are negative, meaning that an increase in harvest risks or in administrative commitments reduce the repondents' utility. Interestingly, respondents associate any additional administrative framework coming with a change of practice as a higher administrative burden rather than as a beneficial accompanying measure.

When looking at the WTA estimates, the use of the payment attribute as the normalizing variable shows that the most important attribute in the farmers' decisions making is the "risk of poor harvest" followed by the kind of "administrative commitment". Regarding the former attribute, our results indicate that farmers express high preferences for not bearing a risk of loss. One or two additional year(s) out of ten of poor harvest are equivalent8 , meaning it is having a risk of loss that is important in their decision.

Last but not least, to our great astonishment, the coefficient of "Health and environmental impacts" attribute is not statistically significant at the 10 % level in both RPL models. The reduction of exposure to harmful substances for health or the environment seems to have no effect on the farmers' utility. The coefficient of the ASC however, in the second specification estimated thanks to a RPL model, shows that there are some variables that are not included in the model, which induce farmers to prefer to change their actual practices to reduce their use of pesticides rather than conserving their actual farming practices. Combined with the latter result on the non-significance of "Health and environmental impacts" coefficient, it indicates that we have to go further in the analysis. One solution may be to include interactions of respondent-specific social, economic and attitudinal characteristics with choice specific attributes and/or with ASC in the utility function. Another solution would be to estimate a Latent Class Model as an alternative model for accounting for preference heterogeneity.

Figure 1

 1 Figure1shows an example of a choice set (in French) where the first column gives the attribute's title and short definition and the three following columns represent the three options among which the respondent must choose (the last column being the status quo).

Figure 1 :

 1 Figure 1: Example of a choice set

Table 2 :

 2 Descriptive Statistics

	. Before presenting these results in Section 4.2.2, we have to specify
	10

Table 3 :

 3 Descriptive Statistics the model specifications which have been retained to estimate the econometric models.

Table 4 :

 4 Results of the CL and RPL models (first models specification)

The non-use value of non-market goods is the existence value or bequest value. It is for instance useful when valuing issues linked to biodiversity.

Details on the characteristics of the efficient design used and the associated program are available upon request.

The n,i are supposed to be Independent and Identically Distributed (IID) and to follow a type I extreme-value distribution. Then the cumulative distribution function and the density function of each n,i are F ( n,i ) = e -e -n,i and f ( n,i ) = e -n,i e -e -n,i , respectively.

And those associated with socio-demographic variables.

Recall that a CL assumes that coefficients are the same for all respondents.

Thus defined, the excluded levels for each variable -which are tied to the ASC -are "no additional years with poor harvest" and "no additional administrative framework", respectively.

It should be noted that the derivative of the unobserved part of the utility function is supposed to be zero with respect to both attributes.

According to our results, farmers need to receive on average 100.89 euros (107.64 euros) per hectare and per year to compensate the utility loss associated with the risk to encounter one (two) additional years of poor harvest.


D Hurther
email: david.hurther@hmg.inpg.fr

U Lemmin

Multistatic acoustic Doppler profilers for fine-scale studies of velocity and particle flux processes

Multistatic acoustic Doppler profilers for fine-scale studies of velocity and particle flux processes

David Hurther, Ulrich Lemmin

Introduction

Acoustic Backscattering Systems (ABS) such as Acoustic Doppler Current Profilers (ADCP) and Acoustic Doppler Velocimeters (ADV) are intensively used among the oceanographic, coastal and nearshore research as versatile measuring tools for a wide range of studies addressing bio-geochemico-physical processes [START_REF] Hamilton | Acoustic backscatter measurements of estuarine suspended cohesive sediment concentration profiles[END_REF][START_REF] Gilboy | An intercomparison of current measurements using a vector measuring current meter, an acoustic Doppler current profiler, and a recently developed acoustic current meter[END_REF][START_REF] Kim | Estimating bottom stress in a tidal boundary layer from acoustic Doppler velocimeter data[END_REF][START_REF] Elgar | Quality control of acoustic Doppler velocimeter data in the surfzone[END_REF][START_REF] Betteridge | Evaluation of a Triple-Axis Coherent Doppler Velocity Profiler for Measuring Near-Bed Flow: A Field Study[END_REF]). More recently, these instruments are increasingly employed in river, channel flow, lake and reservoir studies [START_REF] Lane | Three-dimensional measurement of river channel flow processes using acoustic Doppler velocimetry[END_REF], Lopez and Garcia 1999[START_REF] Hurther | Shear stress statistics and wall similarity analysis in turbulent boundary layers using a high-resolution 3-D ADVP : Ocean current measurement[END_REF][START_REF] Nikora | Flow turbulence over fixed and weakly mobile gravel beds[END_REF], Blanckaert and DeVriend 2004, 2005[START_REF] Bricault | Rétrodiffusion acoustique par une suspension en milieu turbulent: application à la mesure de profils de concentration pour l'étude de processus hydro-sédimentaires[END_REF], Hurther et al. 2007) for which current speed, discharge, suspended sediment concentration, water-depth or bedtopography information are aimed. The main advantage of acoustical devices is their ability to measure the flows characteristics in high turbidity conditions where optical tools can not be employed. Furthermore, unlike LDV or PIV systems, acoustical devices can be easily deployed in the field as autonomous instruments. Finally there is a tendency to choose ABS for suspension flow studies [START_REF] Thorne | A review of acoustic measurement of small-scale sediment processes[END_REF] as the backscattered intensity can be inverted for sediment concentration estimations [START_REF] Hamilton | Acoustic backscatter measurements of estuarine suspended cohesive sediment concentration profiles[END_REF][START_REF] Shen | Application of an acoustic particle flux profiler in particle-laden open-channel flow[END_REF][START_REF] Admiraal | Laboratory measurement of suspended sediment concentration using an Acoustic Concentration Profiler (ACP)[END_REF][START_REF] Fugate | Determining Concentration and Fall Velocity of Estuarine Particle Populations using ADV, OBS and LISST[END_REF][START_REF] Hurther | Turbulent particle flux and momentum statistics in suspension flow[END_REF][START_REF] Bricault | Rétrodiffusion acoustique par une suspension en milieu turbulent: application à la mesure de profils de concentration pour l'étude de processus hydro-sédimentaires[END_REF]. This capability can be combined with velocity measurements in order to provide sediment flux profile estimates. The present study proposes improvements in pulse-to-pulse coherent velocity profiling and sediment concentration profiling at turbulent scales using a single emitter combined with a versatile hardware system. This system allows for quasi-simultaneous multi-frequency profiling in a co-located sample volume. The ability to perform erosion flux profiling in the benthic region of highly turbulent suspension flows is validated.

Acoustic intensity inversion for fine-scale suspension concentration profiling

We start from the expression of the output signal I(r) of a monostatic ABS that is proportional to the acoustic intensity backscattered by a cloud of suspended particles located at a distance r from the transducer [START_REF] Thorne | A review of acoustic measurement of small-scale sediment processes[END_REF]. This expression is valid under the assumption of incoherent and first order (multiple scattering is neglected) scattering processes:

∫ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = - - r s w dr r C r s s m s r t o o v e r C a f a e c r ka r P RT r I 0 ' ) ' ( ) ' ( 4 3 2 2 4 2 ) ( 16 . 3 05 . 1 ) ( ζ α ρ τ ψ (1)
Where R, T v , P 0 , r 0 , k, a t , ψ, r, τ, α w , ζ s , a s , f m , ρ s , C, are the transducer constant, the hardware constant, the reference pressure at a reference distance, the reference distance, the wavenumber of the emitted ultrasound, the radius of the transducer, the transducer directivity function, the distance from the transducer, the duration of the emitted pulse train, the water attenuation constant, the sediment attenuation constant, the mean radius of the insonified particles, the mass concentration of the particle suspension. In order to simplify the previous expression, we define three new variables as follows:

∫ = - j r S dr r C r j S j j e C A A I 0 ) ( ) ( 4 ζ With ∫ = = - j r S dr r C r j S j j j e C A A I J 0 ) ( ) ( 4 ζ (2)
Where j is the index of the gate located at r=r j . A j is the range dependent system parameter, A s is the acoustic sediment parameter and J j is the desired local sediment mass concentration affected by the non-linear sediment attenuation effect along the travel path of the acoustic pulse train. As will be shown below, this effect is at the origin of significant instabilities in the estimated concentration profile [START_REF] Thorne | A review of acoustic measurement of small-scale sediment processes[END_REF].

In this study we consider that A s is independent of range, since the studied suspension flows are all constituted of particles with mono-dispersed size distributions. Also note that I(r) corresponds to the ABS output signal that is proportional to the mean square backscattered pressure. In section 4 we will investigate whether this expression can be applied to estimate suspension concentration at turbulent flow scales. In the following two subsections we discuss the principles and performances of different inversion methods of Eq. ( 2) in order to extract the suspension concentration in benthic regions of highly turbulent suspension flows.

Iterative inversion method: principle and limitations

The iterative inversion method has been proposed by [START_REF] Soulsby | Dynamics of Marine Sands, a manual for practical applications[END_REF]. In order to invert the normalized intensity J j (see Eq. ( 2)) at a given point j, it is necessary to know the sediment concentration profile between the transducer and this point. Therefore, an iterative resolution from one point to the consecutive one is necessary: knowing the concentration at the first measuring point of the profile, the intensity attenuation between this point and the next one can be deduced. This implies a negligible attenuation between the transducer and the first point in order to determine the concentration at this first point, i.e.: 1 1 J C = . This boundary condition is a source of significant inversion errors when measuring in highly turbulent benthic suspension regions. The point to point iterative procedure becomes:

∫ = + + + 1 ) ( 4 1 1 j r j r S dr r C j j j j e J J C C ζ ( 3 )
Another difficulty in Eq. ( 3) is the incapacity to determine the exact value of the attenuation integral between two consecutive points in the profile. The integral can only be approximated by a numerical scheme. Using a rectangular method for the integral approximation, Eq. ( 3) becomes :

r C j j j j j S e J J C C Δ + + = ζ 4 1 1 ( 4 )
As a result the iterative inversion method relies on the assumptions of negligible intensity attenuation due to the suspension between the transducer and the first point of the profile, and the discrete numerical estimate of the attenuation integral between consecutive points. In most cases errors linked to these two assumptions are cumulative. Indeed, if the concentration profile is monotonic along the transducer axis, the sign of the error in the estimation for each integral will be the same. This leads to an increase of the error with distance from the transducer. Furthermore, the integral estimate error propagates with the iteration steps. Thus even the smallest error at one point generates errors at all following points in the profile. This is particularly severe when an error is made at the first point where attenuation is assumed to be negligible, because it will cause errors over the entire profile. The estimated suspension concentration will tend towards zero or infinity when the error is negative or positive, respectively. Therefore, this method is not well suited for attenuating media found in highly turbulent benthic suspension flows.

Explicit inversion method: principle and limitations

This method has been proposed by Lee and Hanes (1993). It relies on the analytical solution to Eq. ( 2) starting from the natural logarithm of this equation. After operating an adequate change of variable, its derivative with range r can be integrated and becomes:

∫ - = j r r S j j dr r J J C 1 ) ( 4 1 ζ ( 5 )
As for the iterative inversion method it is assumed that intensity attenuation due to sediments between the transducer and the first point in the profile is negligible, i.e. that:

1 1 J C = .
Furthermore, the integral of the normalized intensity J(r) also has to be approximated by a discrete numerical scheme. However, in this method, the numerical resolution of Eq. ( 5) will remain explicit for any type of numerical scheme that approximates the integral (rectangular or trapezoidal methods). It has to be noted that inversion instability problems are similar for all type of numerical scheme. Adopting the same rectangular scheme for the integral approximation in both inversion methods, the local suspension concentration becomes:

∑ - = Δ - = 1 1 4 1 j i i S j j J r J C ζ ( 6 )
The problems here arise from the error affecting the denominator of Eq. ( 6). Both terms in the denominator are subject to errors. The error in the denominator term originates from the assumption 1 1 J C = whereas the error in the second denominator terms is caused by the integral approximation.

When the assumption 1 1

J C =
is not valid at the first gate, the application of Eq.( 6) will lead to underestimated concentrations whereas the errors in the approximations of the normalized intensity J(r) will induce a singularity in the estimated concentration profile. Before the singularity, the inverted concentration will be overestimated. After the singularity it will become negative before reaching zero asymptotically with distance r from the transducer. The previous analysis considered both effects separately. When both are taken into account the prediction of the total effect on the estimated concentration profile becomes impossible. Finally, as for the iterative inversion method, the error propagates via the integral of the normalized intensity J(r) between the second gate and the gate j. Thus a perturbation at one any gate of the profile will affect the subsequent concentration estimates.

A novel bi-frequency inversion method

In order to reduce the instabilities in the estimated concentration profiles we propose a bi-frequency inversion method. Starting from the following relation:

( ) ( ) ( ) i S k S i S k S j j k j i C J J ζ ζ ζ ζ - = , , ( 7 )
The concentration profile can be estimated from :

( ) ( ) i S k S k S i S j k j i j J J C ζ ζ ζ ζ - - = 1 1 , 1 1 , ( 8
)
Where j i J , corresponds to the normalized intensity at frequency i for r=r j . The advantages of this inversion are immediate. First, the boundary condition 1 1

J C =

at the first gate is no longer necessary to perform the inversion. The absence of integrals eliminates the errors caused by their numerical estimates. The propagation of the local errors via the integrals disappears. As a result, the local concentration estimations are independent from all others.

Results

Figure 1 shows an example of the inverted suspension concentration profile in an Oscillating Grid Turbulence (OGT) experiment conducted at LEGI Grenoble. The suspension is constituted of fine sand particles of mean diameter equal to 126μm. The vertically oscillating grid is located at 35cm from the transducer. The generated suspension is in a steady equilibrium state meaning that the mean particle settling flux is in balance with the mean ascendant turbulent erosion flux. The transducer is aligned with the vertical direction being normal to the grid plane. The three inversion methods have been applied to the acquired mean profiles of normalized intensity. Previously, all system and acoustical parameters have been determined by a rigorous calibration procedure [START_REF] Bricault | Rétrodiffusion acoustique par une suspension en milieu turbulent: application à la mesure de profils de concentration pour l'étude de processus hydro-sédimentaires[END_REF]. The acoustically determined suspension profiles have been compared to local measurements obtained with a calibrated OBS (D&A instruments). All three of the above inversion methods were applied to the acquired mean profiles of normalized intensity after all system and acoustic parameters were determined by a rigorous calibration procedure [START_REF] Bricault | Rétrodiffusion acoustique par une suspension en milieu turbulent: application à la mesure de profils de concentration pour l'étude de processus hydro-sédimentaires[END_REF]. The results for the iterative and explicit methods are calculated for a carrier frequency of 2 MHz. The bi-frequency inversion uses the frequencies of 1.67MHz and 2Mhz obtained quasisimultaneously with the same wide-band transducer. The same transducer has been used for the iterative and explicit inversions. The spatial resolution in the vertical direction is set to 3mm with a Pulse Repetition Frequency of 1KHz. 32 consecutive pings (or shots) are averaged together for one incoherent acoustic intensity estimate. This setting allows the resolution of the Taylor micro-scale in the investigated suspension flow (Hurther and Lemmin 2007). For the results obtained from iterative and explicit methods (Eqs (4) and ( 6)), the increasing divergence of the estimated concentration profiles from the OBS measurements is obvious (Fig. 1). These trends confirm the previously discussed limitations of the standard inversion methods for highresolution profiling in highly turbulent suspension flows. The bi-frequency inversion results (Eq.( 8)) and the OBS measurements are in good agreement over the entire profile. The bi-frequency inversion results into stable concentration profiles even when intensity attenuation by the suspension is significant throughout the water column.

Improving high-resolution velocity estimations using bi-frequency Doppler noise suppression

Velocity profile estimations based on the pulse-to-pulse coherent Doppler phase shifts between the emitted and backscattered acoustic pulse trains are subject to important errors due to inherent Doppler noise in the phase of the backscattered wave (Hurther and Lemmin 2007). The effect on the mean velocity estimation is negligible whereas mean turbulent quantities such as the normal turbulent intensities, the TKE, the turbulent velocity spectra, TKE dissipation rate, are particularly affected [START_REF] Garbini | Measurement of fluid turbulence based on pulsed ultrasound techniques. Part 1. Analysis[END_REF][START_REF] Voulgaris | Evaluation of the acoustic Doppler velocimeter (ADV) for turbulence measurements[END_REF], Hurther and Lemmin 2001[START_REF] Blanckaert | Means of noise reduction in acoustic turbulence measurements[END_REF]. Starting from the expression of the velocity corresponding to the time derivative of the phase shift between emitted and backscattered acoustic pulse trains (Hurther and Lemmin 2007):

[ ]) ( ) ( ) ( ) ( 2 t n t V t t r dt d k V c + = + = γ π ( 9 )
the phase can be decomposed into the term ( ) t rˆ representing the instantaneous spatially average particle displacement within the sample volume, added to the undesired Doppler phase noise term ) (t γ . The contribution of the noise term in the turbulent spectrum is shown in Fig. 2 (circles) for a carrier frequency at 1.25 MHz in the highly turbulent oscillating grid experience described in section 1.4. The measurement location is at z/z 0 =0.67 (i.e. 8 cm from the center of the grid) using the reference distance for OGT defined by [START_REF] Matsunaga | Quantitative properties of oscillating-grid turbulence in a homogeneous fluid[END_REF]. The velocity spectra are calculated from the Fourier transform of the temporal autocorrelation function of the velocity signal:

∫ +∞ ∞ - - = τ τ π τ d f i R f S VV VV ) 2 exp( ) ( ) ( ( 1 0 )
The parameter npp in Fig. 2 indicates the number of samples over which the consecutive velocity estimations are averaged using the pulse-pair algorithm described in Hurther and Lemmin (2001). As can be seen in Fig. 2 for f > 3Hz, the slope of the velocity spectra presented by the circles deviates from the expected -5/3 slope (dashed line). The lower decay with frequencies above 3 Hz is due to the Doppler noise effect represented by the term γ in Eq. ( 9). When integrated over the frequency band of the system, this undesired effect results into a velocity variance added to the variance of the particle velocity averaged over the sample volume:

2 2 2 σ + = V V ( 1 1 )
This undesired effect is the principal for the limited TKE and TKE dissipation rate measurements in field studies [START_REF] Garbini | Measurement of fluid turbulence based on pulsed ultrasound techniques. Part 1. Analysis[END_REF][START_REF] Voulgaris | Evaluation of the acoustic Doppler velocimeter (ADV) for turbulence measurements[END_REF][START_REF] Blanckaert | Means of noise reduction in acoustic turbulence measurements[END_REF], Hurther and Lemmin 2001). As will be shown below, the bi-frequency method reduces this effect and at the same time allows high temporal resolution necessary for reliable TKE dissipation estimations. The bi-frequency method consists of estimating the quasi-instantaneous velocities with two different carrier frequencies at the same time (for the turbulent scales under investigation) and in co-located same sample volume:

) ( ) ( ) ( ) ( ) ( ) ( 2 2 1 1 t n t V t V t n t V t V + = + = ( 1 2 )
where V 1 and V 2 are the instantaneous velocities measured nearly simultaneously with the carrier frequencies, f c =f 1 and f c =f 2 , respectively. Each velocity component is composed of the sum of the same spatially averaged velocity and the respective noise contributions. The time-averaged noise contributions are negligible and therefore

V V V = = 2 1
. The white noise characteristics induce the following simplification in the crossed spectrum:

V V n n V V V V S d f i R d f i R S ∫∫ +∞ ∞ - +∞ ∞ - = - + - = τ τ π τ τ τ π τ ) 2 exp( ) ( ) 2 exp( ) ( 2 1 2 1 (13)
The associated normal Reynolds stress term can be estimated from the covariance as:

2 2 2 2 2 2 1 0 2 1 2 1 V V V df S V V V V = - = - = = ∫ +∞ σ σ ( 1 4 )
where the Doppler noise effect is suppressed. If the above reasoning is correct, the crossed-velocity spectrum should decay with a -5/3 slope over a much wider frequency band than the auto-velocity spectra presented in Fig. 2. The -5/3 slope should be constant until it reaches a frequency limit beyond which it should decay faster because of spatial averaging effects. The turbulent cross-spectrum is represented by triangles in Fig. 2 for comparison with the turbulent auto-spectrum. Both spectra are in good agreement up to 3 Hz. The corrected cross-spectrum preserves a -5/3 slope in the inertial subrange until a frequency close to 20Hz. For frequencies above this limit, the spectrum decays with a rate higher than the typical Kolmogorov trend due to spatial averaging effects. The effect of the bi-frequency Doppler noise suppression method on the mean TKE profile and the TKE dissipation rate is shown in Figs. 3a and3b, respectively. The bi-frequency method can be compared to the Doppler noise suppression method proposed by [START_REF] Garbini | Measurement of fluid turbulence based on pulsed ultrasound techniques. Part 1. Analysis[END_REF] where the crossed spectrum is calculated from the velocity signals at two consecutive locations in the profile:

1 1 1 1 + + = z z z z V V V V S S assuming 0 1 1 1 = + Z Z n n S
. The bi-frequency method is tested for frequency shifts of 180KHz and 240KHz between the two carrier frequencies. All measurements are compared to the semi-theoretical models for normalized TKE and TKE dissipation rate valid in highly turbulent OGT [START_REF] Matsunaga | Quantitative properties of oscillating-grid turbulence in a homogeneous fluid[END_REF].

For both quantities (Figs. 3a and3b), good agreement is found between the theoretical model (black line) and the two corrected profiles using bi-frequency suppression. The Garbini method underestimates the quantities, because the TKE contained in the isotropic turbulent flow scales of size smaller than the distance separating two consecutive sample volumes is also suppressed. The standard mono-frequency estimate based on the auto-spectrum reveals important noise contributions throughout the profile.

Acoustic profiling of turbulent erosion flux

In order to test the capabilities of the ABS in simultaneous and co-located velocity and suspension concentration measurements at turbulent scales (settings at 32 Hz and 3mm), mean turbulent erosion flux versus mean sediment concentration were calculated from data collected in a fully turbulent openchannel suspension flow at EPFL Lausanne [START_REF] Bricault | Rétrodiffusion acoustique par une suspension en milieu turbulent: application à la mesure de profils de concentration pour l'étude de processus hydro-sédimentaires[END_REF]. For the same particles, the flow conditions were varied over a wide range of flow discharge, Reynolds number, Shields number and relative bed roughness. The slope of the obtained curves has been compared to the settling velocity calculated by the modified Stokes formula valid in turbulent flows (Soulsby 1998). Figs. 4a, 4b and4c show the results for three different flow conditions. We obtained a good linearity between ascendant mean erosion flux and the mean sediment concentration for all the points in the three profiles and the slopes of the fitted curves are in very good agreement for all flow conditions. Finally, the correspondence with the theoretical value of 3.9 mm/s for the settling velocity is encouraging.

Conclusion

This study proposes two novel bi-frequency methods to perform quasi-simultaneous and co-located velocity and suspension concentration profiling at turbulent scales using Acoustic Backscattering Systems working in the MHz range. The first method improves the stability of the inverted suspension concentration profile in situation where intensity attenuation due to sediments cannot be ignored such as found in highly turbulent benthic regions. However, the method is currently still limited to suspensions with mono-dispersed size distributions. The second method allows for an effective suppression of the Doppler noise contribution in the turbulent inertial subrange using the decorrelation of the Doppler noise at two slightly different ultrasound frequencies. As a result, profiles of mean turbulent quantities such as normal intensities, TKE, turbulent spectra, TKE dissipation rates can be estimated more accurately. Finally, the ABS ability to combine velocity and concentration profiling is demonstrated by estimating turbulent erosion flux in highly turbulent suspension flows.

Fig. 1

 1 Fig.1 Inverted sediment concentration profiles

Acknowledgements

This study has been supported partially by the European commission (FP6) under the grant HYDRALAB III-SANDS and the French national program LEFE-IDAO. The technical assistance of J.-M. Barnoud, and C. Perrinjaquet is greatly appreciated.