Lata Gangadharan
email: lata.gangadharan@buseco.monash.edu.au

Marianne Lefebvre
email: marianne.lefebvre@supagro.inra.fr

Sophie Thoyer
email: thoyer@supagro.inra.fr

Impacts of water rights security on water markets: Experimental evidence

Keywords:

Water markets are xpected to lead to ecient use of scarce water by re-allocating water from low value uses to high value uses. However a water allocation system must not only allocate specic volumes of water among users but also allocate the risk of supply shortages. The existence of both a market of water rights and a spot market of water allotments is necessary to allow users to manage better the risk of increased supply uncertainty. Whether the water rights market should be further sophisticated by oering dierent levels of security for rights is unclear. Indeed, increasing the complexity of water markets can eventually reduce eciency gains and cost-eectiveness of water trade. We propose an experimental design that captures the main characteristics of water markets. Farmers rst participate in the market for water rights while facing uncertainty on water allotments. . Once the water supply is known, they can trade their water allocation on the spot market. We examine two water right scenarios, one with a unique security level and another iwith two levels of security and we compare them in terms of allocation eciency, risk allocation and cost eectiveness. We vary transactions costs as a treatment variable and elicit risk preferences of subjects. By comparing the performance of the markets in each treatment, we can measure the benets of having two levels of security for water rights and test whether they are contingent on the characteristics of transaction costs and risk aversion.

Introduction

Water markets are acknowledged to allocate scarce water available eciently , by moving water from low to high value uses. Although there is now widespread adoption of trading mechanisms to re-allocate water, there is an ongoing debate on how to improve the trading processes. Most of the existing literature has focussed on the issue of transaction costs which reduce eciency gains [START_REF] Cason | Transactions costs in tradable permit markets: An experimental study of pollution market designs[END_REF] and third party impact when trade might aect other users who are not parties in the transaction [START_REF]Rural water use and the environment: The role of market mechanisms[END_REF][START_REF]Market mechanisms for recovering water in the murray darling basin[END_REF]. However, another important issue deserves attention: what is the role of water markets in the strategy of water users to manage risks of water shortage? The uncertainty of irrigation water supply, due to climatic variations, reduces farmers's benets because part of their production decisions are made before knowing the water availability for the coming season.This problem is particularly crucial for unregulated river systems where there is no water storage through reservoir dams. But it exists also for regulated systems because the probability of reserve replenisment from one year to another uctuates increasingly with climatic change. Water markets transform the risk on the availability of the water input into a risk on input prices. Calatrava and Garrido [START_REF] Calatrava | Spot water markets and risk in water supply[END_REF] demonstrate theoretically and empirically that allowing farmers to trade water can help to reduce their exposure to risk. However, an ecient risk management system should also enable the reallocation of risk from more risk-averse users to less-risk averse farmers ( [START_REF] Borch | Equilibrium in a reinsurance market[END_REF][START_REF]The theory of syndicates[END_REF][START_REF] Gollier Eeckhoudt | Economic and Financial Decisions under Risk[END_REF]).

Howitt [START_REF] Howitt | Spot prices, option prices and water markets: An analysis of emerging markets in california[END_REF] shows that pure spot markets, as well as right markets, have no risk-sharing properties. They cause all the risk to be born by one party.

The co-existence of both a market for water rights and a spot market for water is established in most countries where water can be traded. Farmers can thus obtain water from two sources. They can hold water rights which entitle them to a share of available water each year: for each right held, they get a volume of water, called an allocation 1 , which depends on the total water availability in the system for a given season. They can also buy water from the water spot market: when water right holders are told what their water allocation is for the year, they can either decide to use it entirely for production, or to sell (buy) excess (missing) quantities on the spot market [START_REF] Bjornlund | Can water markets assist irrigators managing increased supply risk? some australian experiences[END_REF]. Some countries have sophisticated the market by introducing water rights with dierent levels of security, low security water rights oering less guarantee that water be delivered than high security rights. The expectation is that such dierentiated water right system could contribute to improve further the eciency of water and risk allocation across farmers. However, increasing the complexity of water trading markets could also reduce 1 In the australian terminology, a water right is an entitlement. It gives the right to an allocation, ie a fraction of the total available water to be issued in the future. An allocation is a volume of water available in a given season.

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

eciency. This question is at the heart of a number of water market reforms. Under the riparian right law, as in Chile, Mexico and Australia, water rights are dened as a proportion of stream (or canal) ow or storage ( [START_REF] Rosegrant | Reforming water allocation policy through markets in tradable water rights: lessons from chile, mexico and california[END_REF]). The level of security is unique and identical for all water rights. If a dierentiated system is set-up, the available water is allocated to the high security rights rst. The water authority operates its storage so as to guarantee that the high security water rights can be supplied. Once provisions for high security water rights have been made, the remaining volume of water determines the low security allocations. As a result, low security water right owners bear the risk of low water supply. This is the basis of the prior appropriation doctrine, much in use in the Western states of United States: when shortage occurs, priority is given to the most senior rights, those which were historically appropriated rst. When a water right is sold, it retains its original appropriation date. The security of a water-right can thus be purchased by buying a senior right on the right market. In Australia, despite the riparian law, the recent water reforms introduced in some States have created a dierentiated water right system. Since 1994 in New South Wales and Victoria, farmers can thus constitute a portfolio of water rights of two security levels by trading on the right market. Such reforms are administratively complex and can lead to substantial transaction and learning costs for water users. Before encouraging a wider adoption, it is necessary to better understand whether they can lead to true eciency gains for water users.

The objective of this paper is to compare the performance of a market with two levels of security for water rights relatively to a market with a unique type of water rights, in terms of allocative eciency, cost-eectiveness, farmers' prots and prots variability. Field data are limited because water right markets are still thin [START_REF] Bjornlund | Farmer participation in markets for temporary and permanent water in southeastern australia[END_REF]. Moreover, dierences between countries or States in terms of hydrology and socio-economic environment are too important to compare the performance of both systems per-se. This paper therefore uses experimental data. It proposes an experimental design capturing the main characteristics of existing water markets. Subjects rst participate in a share market (corresponding to the water rights market) without knowing the allocation of coupons (corresponding to water allotment) they will get from their shares. In a second stage, they can trade their coupons on the coupon market (corresponding to the spot market for water allocation). The design is noteworthy in two respects. First, it is the rst experiment introducing dierent levels of security for shares. Second, it takes into account the role of transactions costs which are recognized as an important feature of water markets [START_REF] Bjornlund | Can water markets assist irrigators managing increased supply risk? some australian experiences[END_REF][START_REF] Freebairn | Water rights for variable supplies[END_REF]. We use a 2x2 design where the treatment variables are the number of levels of security for shares (1 or 2) and the presence of absence of transaction fees in the share and coupon market. By comparing the performance

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

of the market in each treatment, we can measure the benets of having two levels of security for water rights and test whether they are contingent on the characteristics of transaction costs and risk aversion. This paper is organized as follows. The second section summarizes the existing literature on the expected benets of a system with dierentiated security rights. The experimental design and corresponding theoretical predictions are presented in the third and fourth sections. The fth section analyses the experimental results and the last section concludes.

2 Expected advantages of water rights with dierentiated security levels

The interests of water trading are well understood theoretically and demonstrated em-

pirically. An increasing number of countries is adopting legislative reforms and necessary technical and administrative adjustments to allow water users to buy and sell water on a market. Most of them have also engaged into the creation -or the enhancementof water right markets, for example through the formal separation of water rights from land rights, mainly to facilitate real structural change within the irrigation industry.

Since water rights are a permanent entitlement providing access to a share of water from a uncertain-sized consumptive pool, they are considered as an asset. Freebairn and Quiggin rightly remind in their 2006 article on water rights that if the water market was perfectly competitive and transaction-cost free, and if water users are risk-neutral, then trading on the spot market is sucient to reach an ecient allocation of water amongst users [START_REF] Freebairn | Water rights for variable supplies[END_REF]. Therefore, in theory, trading on the water right market should not occur since all water users have the same expected value for water rights (expected value of the corresponding allocation on the spot market which is the same for all since there is a unique expected price for water) and thus display the same willingness to pay for rights. Under these assumptions, demand and supply of water rights can only be driven by long term speculation (related to the uncertainty on the level of future water supply) or saving motives (ref ). This eect has been experimentally conrmed by Godby et al [START_REF] Mestelman | Emissions trading with shares and coupons when control over discharges is uncertain[END_REF] who designed a market experiment mimicking the canadian emissions trading market, including both a share and a coupon markets. A coupon gives permission to discharge a unit quantity of waste. A share represents an entitlement to a specied fraction of the total available coupons to be issued in future periods. The share market corresponds to a market for ex-ante contracts. The coupon market is equivalent to the spot market. In a world of complete and perfect contingent future markets in coupons, share would be redundant. However, in the practical world of environmental regulation, shares may have some advantages in allowing more secure

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

long term planning for rms acquiring or selling coupons and in providing an explicit method for allocating any future variation in aggregate number of coupons [START_REF] Mestelman | Emissions trading with shares and coupons when control over discharges is uncertain[END_REF].

It is observed that water right trading is slowly picking up [START_REF] Michael | Environmental eectiveness and economic eciency of water use in agriculture: The experience of and lessons from the australian water reform programme[END_REF]. This growing interest of water users for the water right market reveal that trading water rights becomes strategic. Both transaction costs and risk attitudes can explain the willingness to trade in the rights market.

Firstly, it is well documented that water trading imposes transaction costs which are non negligible both for buyers and sellers: the need to nd an eligible trading partner at the rigt time, despite the existence of trade-facilitating solutions such as electronic market places or brokers can be costly ( [START_REF] Bjornlund | Farmer participation in markets for temporary and permanent water in southeastern australia[END_REF]). Freebairn and Quiggin [START_REF] Freebairn | Water rights for variable supplies[END_REF] thus argue that the existence of a market for water rights can improve the cost-eectiveness of water allocation by allowing water users to hold water rights which match better their water needs, thus reducing trade on the spot market and corresponding transaction costs. Farmers who are regular buyers on the spot market might nd more protable to increase the quantity of water rights they hold to limit their demand for spot market water and therefore reduce their exposure to transaction costs. Farmers who are regular sellers on the spot market will do the contrary. A system of dierentiated security rights allows to sophisticate the portfolio of rights held, therefore improving the matching with water needs under each climatic scenario. Freebairn and Quiggin result is nevertheless controversial because it relies on the assumption that transaction costs on the spot market are greater than transaction costs on the water right market. Australian markets seem to display greater transaction costs on the latter [START_REF] Brennan | Water policy reform in australia: lessons from the victorian seasonal water market[END_REF]. Dierential tax treatment and the administrative complexity and costs associated with markets for water rigihts are signicant factors which drive the preference for spot markets [START_REF] Bjornlund | Farmer participation in markets for temporary and permanent water in southeastern australia[END_REF]. If water rights' trading is costly, the costs may oset the gains from a portfolio of rights matching water needs (and thus limiting the need to trade in the spot market).

Secondly, farmers are not risk neutral and their willingness to manage risk also explains their interest for water rights. Interviews with farmers indicate that uncertainty on water allocation motivates farmers to hold more rights than necessary [START_REF] Brennan | Water policy reform in australia: lessons from the victorian seasonal water market[END_REF]. Water markets contribute to reduce the risk born by farmers by converting a quantity risk into a price risk [START_REF] Calatrava | Spot water markets and risk in water supply[END_REF], but they fail to share the remaining risk eciently. As underlined by Quiggin in [START_REF] Crase | Water Policy in Australia, the impact of Change and Uncertainty[END_REF], the quest to eliminate uncertainty is futile but uncertainty can be managed, allocated and sometimes mitigated . Howitt [START_REF] Howitt | Spot prices, option prices and water markets: An analysis of emerging markets in california[END_REF]shows that pure spot markets, as well as right markets, have no risk-sharing properties. They cause all the risk to be born by one party. On the spot market , the buyer bears all the risk as it has no fall-back source of supply. He bears both the uncertainty of supply in the spot market and the uncertainty on the resulting water price. On the water rights market, the seller bears

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

the burden of correctly valuing the current worth of future water . The principle of risk allocation (or risk sharing) is that risk should be allocated to the party best able to manage or accept it. In principle, this can be achieved through risk-sharing contracts such as options on the spot market or conditional leases of water: risk-averse users could then trade-o lower expected gains for lower variability of gains with more risk-tolerant users, willing to support a greater share of water variability. According to Bjornlund [START_REF] Bjornlund | Are the fundamentals emerging for more sophisticated water market instruments[END_REF], in Australian water market, the risk dierential between high value water users (mainly perenial crops) and producers of annual crops should be suciently large to enable sophisticated risk-sharing instruments to operate. Water rights with dierent levels of security can mimic these risk sharing contracts 2 . The agents willing to reduce their risk will pay more to buy secure water rights. The agents willing to bear risk can buy cheaper and less secure rights. Resource security being a zero-sum commodity, the more security is given to a group of users, the less there is for everybody else (Quiggin in [START_REF] Crase | Water Policy in Australia, the impact of Change and Uncertainty[END_REF]).

A dierentiated system displays thus two major advantages, compared to a single security system, but it signicantly complexies both the market management task and the trading decisions of buyers and sellers. The water administration will have to dene the ecient mix of entitlements (ratio between high and low security rights) in order to adjust best to farmers' preferences, under the constraint that the security levels can be respected [START_REF] Hughes | Management of irrigation water storages: carryover rights and capacity sharing[END_REF][START_REF] Shi | Simplifying complexity: Rationalising water entitlements in the southern connected river murray system, australia[END_REF] 3 .

Farmers must also be able to understand and to reap the benets of such system.

Overall, the benets of water rights dierentiation will depend on users' participation to the water rights market. Transaction costs on the water rights market (relatively to the spot market) and the heterogeneity in water users' willingness to bear risk are two essential drivers of participation in the water rights market. But higher prots 2 Australian National Water Initiative (2004) contains a set of risk assignment provisions that were intended to give entitlement holders greater certainty over who would bear the risks of future reductions in the quantity and security of water allocations. The risk of changes in the aggregate availability of water due to new knowledge about the hydrological capacity of the system are born by users, whereas the risk of reductions in water availability arising from changes in public policy will be born by the public, and water users will receive compensation for such reductions. Our approach is dierent as we study the possibility of sharing actual risk (vs future change) among agricultural users (vs between users and government). In our setting, compensation for higher risk is included in lower market prices for water rights of low security, and nanced by the higher market prices for high security rights.

3 The actual mix is a consequence of historical allocation of rights and sales water , where sales water was the excess water available in storage. It was made available to farmers, in proportion of their entitlements. During unbundling reform in 1994, sales water was converted into low security entitlements. In the recent years, State and Federal governments have buy-back water entitlements to return water systems to environmentally sustainable levels of extractions (implementation of the National Water Initiative of 2004). Governments need to select a suite of entitlements likely to deliver the required volume for the environment at the required time. A secondary objective could also be to take care that the remaining entitlements suit farmers' preferences in term of security. Of course, the more high security entitlements are bought-back, the higher the cost for the government.

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

and improved risk allocation can be only obtained if agents are capable to constitute the best portfolio of rights (minimizing need for trade). The next section describes the experimental design implemented to measure if such benets are observed in the laboratory.

Experimental design

Our experimental design captures the main characteristics of mature water markets where agricultural users participate both in the rights market and spot market

Terminology

To prevent their prior attitudes about environmental policy from inuencing their behavior, subjects are not told they will be trading water. We use a neutral terminology in the experiment where water rights are called shares and allocations are called

Game structure

Figure 1 represents the game structure. All subjects start stage 1 of each period with an equal number of shares they are given for free (table 1) and an equal initial endowment of 50 ECU. They know also the probability of occurrence of both scenarios and the number of coupons obtained from shares in each scenario (table 2). In stage 1, they can choose to modify the number of shares they hold by buying and selling in the share market. In stage 2, a random draw selects the scenario (blue or yellow). Subjects then know the number of coupons they get from their shares. Then can then trade coupons in the coupon market: they can either hold back their coupons, or sell them or buy more, provided they have sucient ECU to do so. At the end of stage 2, gains of subjects are calculated: it is the sum of ECU they hold after the trading stages plus the value in ECU of their coupons. They start next period with the initial number of shares and initial cash (no banking).

Number of shares

General security share 9

High security share 3

Low security share 12

Treatments

We use a 2x2 factorial design with 6 observations per cell to achieve the maximum information from our experimental budget (table 3). The treatment variables are the number of levels of security for shares (1 or 2) and the presence of absence of transaction fees in the share and coupon market. TFc stands for transaction fees in the coupon market and TFs transaction fees in the share market. Each subject participates in one of four treatments (between subject design).

One level of security Two levels of security The rst treatment dimension is the number of security levels. In treatment 1 and 3, there is only one type of shares called general security shares. In the two levels of security treatment (treatment 2 and 4), high security and low security shares are traded sequentially, with the high security shares being traded rst 6 .

5 This system is similar to the on-line electronic trading system that are used by farmers to trade water. In Australia, Watermove, Murray irrigation Exchange, Water Exchange, Water nd ... oer platforms that act as electronic clearing houses for water rights and spot trades where farmers post buy or sell bids for particular zone, which are then matched in ascending order for sellers and descending order for buyers to clear the market (Brooks and Harris (2008)). Most of these platforms work on the basis of posted sell and buy bids (a part from the largest (Watermove) where a pool price is calculated weekly) (Productivity Commission (2010)). We choose a CDA because multiple trading opportunities are important in experimental markets to generate increases in eciency (Cason and Friedman (2008)).

6 In the Australian context, both markets operate simultaneously but the high security market tends to be the most active. Traders try to buy high security water rights to secure a minimum water allocation (the minimum requirement in dry years), and then eventually buy low security shares.

Theoretically, the order of the two markets will not impact the equilibrium of both markets. Experimentally, some order eect may be observed. To limit the number of treatments, we stick to empirical reality and we choose to run the experiment with the high security share market rst then the low security market.

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

The second treatment dimension is the transaction fees. There is empirical evidence of signicant transaction costs in water markets (Carrey and al (2002), Allen Consulting group ( 2006)). [START_REF] Freebairn | Water rights for variable supplies[END_REF] suggest that spot trading is likely to be associated with larger transaction costs, and thus will be less ecient than water rights trades over the long term. They show under this assumption that dierentiated markets for rights improves the eciency and cost-eectiveness of water allocation. This treatment with transaction costs in the coupon market only is not empirically relevant.

Nevertheless, it is necessary as a baseline because the benets from having two types of shares are theoretically higher in this case (treatment 1 and 2). Alternatively, Brennan 7 . We could have run complementary treatments with no transaction fees at all (T F s = T F c = 0) or equal transaction fees in both markets (T F s = T F c = 2) but these treatments are theoretically equivalent to T3 and T4. Indeed, there is no gains from share trading if trading in the coupon market is not costly, or if it's not more costly than trading shares. The justication of the treatments will appear more clearly in the section with the theoretical predictions.

Subject types

We have two types of subjects. The only dierence between types if the the marginal benets from each coupon (table 4). In the lab, we can induce participants' preferences in order to mimic eld water users. Type 1's marginal benets mimic a mixed crop producer, with relatively low value of water and elastic water demand. Parameters are 7 Reported to the market price, this fee is high compare to the fees in water trading platforms.

We set a high monetary transaction fee to capture all the transaction costs born by farmers in the eld that cannot be captured in the lab. Costs of writing contracts, search cost of locating and identifying trading partners ... are time consuming but not necessarily nancially costly. In the eld, buyer and seller don't pay the same transaction fee to participate in the water market but theoretically, the burden of the fee is shared between the buyer and the seller so we set them equal in the experiment. Moreover, transaction costs on the water rights market are higher than on the spot market for allocation. However, the purchase of water entitlements is amortized over several years. In the experiment we set the transaction fee equal for coupons and shares for simplicity, having in mind that the annualized transaction costs for rights may not be much higher than the annual transaction costs for allocation trading.

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

chosen so that type 1 does not use water in the dry scenario at equilibrium: because water is too expensive compared to the low value of his crops, type 1 is better o selling water than using it. On the contrary, farmers with high-value crops such as orchards or vineyard are highly sensitive to reductions of water volumes available. They need a minimum quantity of irrigation water to protect the long term productivity of their plantations. For example, horticulturist are prepared to pay very high prices for water during dry periods to limit potential catastrophic losses to perennial planting caused by insucient irrigation

Experimental procedure

The experiment was conducted at LEMM (University of Montpellier) in september 2010. We conducted two sessions of each of the four treatment, with 18 participants per session, for a total of 144 participants. Each session lasted 3 hours. Each session was conducted in the following manner. We rst ask subjects to participate in a lottery game (a slightly modied Holt and Laury lottery game, described in Gangadharan and

Nemes [START_REF] Gangadharan | Experimental analysis of risk and uncertainty in provisioning private and public goods[END_REF]) in order to control for risk aversion of individual subject 9 . Subjects were 8 For [START_REF] Brennan | Water policy reform in australia: lessons from the victorian seasonal water market[END_REF], the risk of losses to perennial plantings has not been so far a driver of water markets. Indeed, the market prices observed are lower than the gross margin of horticulturist. The situation where they are willing to pay water at a very high price has not happened yet because long-term equilibrium between capital investment decisions and dam reservoir yields ensure than investments in perennial agriculture are secure from catastrophe . In our experiment, the equilibrium of the coupon market in the dry scenario is such that type 2 holds the minimum 4 coupons. This means that type 2 is not at threat of catastrophic losses at equilibrium. A catastrophic loss will happen if he had less than 4 coupons.

9 Participants had to indicate their preferences between two options: a safe option that yielded 3.5

Euros with certainty or a risky option. The risky option has a probability of winning 6 Euros changing from 10% in the rst lottery to 100% in the 10th lottery or correspondingly the probability of winning 1 Euro changing from 90% in the rst lottery to 0% in the 10th lottery. One of the games was played at the end of each session. Subjects received an additional 1, 3.5 or 6 Euros, depending on their choice and the outcome of the lottery game. In order to control for wealth eects, the lottery was played and subjects' gains were only revealed to the subjects at the end of the session.

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

then invited to read the instructions of the experiment explaining the dierent stages of the game, the trading software and the monetary incentives. They also lled up a quizz to verify their understanding of the game. Subjects played two practice periods, which did not count toward subjects' earnings, followed by a series of between 9 and 12 periods which could potentially be selected for payment. The practice periods used the same parameters as the rest of the periods. At the end of each session, qualitative and quantitative information were collected in the form of questionnaires from the participants. Subjects were also asked to describe their strategies.

Participants are compensated according to their gains in one period, randomly chosen.

Gains in one period are equal to the net revenues from buying and selling the shares and coupons in the markets and the benets from holding coupons. They get an additional payment for the lottery game. Subjects made an average of 18.50 euros for a 3 hours sessions.

Theoretical predictions

In this section, we measure the eect of uncertainty on the decisions of agents to participate in the right and/or the spot market. The two markets dier in the way uncertainty is present: decisions about the number of rights users want to hold must be taken before knowing what the water allocation is. The uncertainty is resolved (the water allocation is known) before the spot market opens. We compute the market equilibria of the two markets. We apply input demand theory under uncertainty to a situation where water input is available from both the spot and the right market. We solve the model for two agents under risk neutrality and risk aversion, with agent i being a type 1 agent and agent j being a type 2 agent. For a market of 6 participants (3 type-1 agents and 3 type-2 agents), the price predictions are the same and the traded quantities simply multiplied by 3. We solve the model by backward induction: the equilibrium of the coupon market is computed rst, then the equilibrium on the share market is deduced. In the experiment, the share trading takes place rst, followed by the coupon trading, once the scenario is drawn.

A risk neutral agent will choose the number of shares as well as his number of coupons in order to maximize his net expected benet from coupons and trading.

M ax

S i ,c i,t E [B(c i ) + pc. (W.S i -c i ) -T F c . |W.S i -c i |] + p S . (Q i -S i ) -T F S . |Q i -S i | (1)
Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. ( 2010 pc t is the equilibrium price of a coupon.

Transaction fees

T F c is the transaction fee to buy and to sell in the coupon market. T F s is the transaction fee to buy and to sell in the share market.

dc i is the net position of agent i in the coupon market (1 for a net seller, -1 for a net buyer). ds i is the net position of agent i in the share market (1 for a net seller, -1 for a net buyer).

10 We do not model the gradual allocation during the season. We assume that the season is one point in time where farmers know the quantity of water they receive from their water rights and then trade on the allocation market with no uncertainty on quantity. Uncertainty is only before the season, at the time of buying rights. With such an interpretation, we do not study intra seasonal allocation risk management strategies.

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

Equilibrium in the coupon market

Trading in the coupon market will occur until marginal benets from coupon, net of transaction fees are equalized between agents. In the presence of TC in the coupon market (treatment 1 and 2), the number of coupons held is increased (decreased) for a net seller (buyer) because he has to pay TC if he sells (buys) in the coupon market (table 5 and6). Type 1 is a net seller of coupons and type 2 a net buyer at equilibrium because type 1 marginal benets from coupons are lower. When the scenario is yellow, type 1 does not hold any coupon as the price is too high compare to his marginal benets from coupons (see proof in Appendix A).

Blue scenario Yellow scenario

Coupons held by Type 1 at equilibrium 0 7

Coupons held by Type 2 at equilibrium 6 11

Equilibrium price 13.33 5.33 Equilibrium in the share market

The maximum price an agent is willing to pay for a share (to sell a share) is equal to the expectation of the coupon price (net of transaction costs) multiplied by the number of coupons obtained from one share. The marginal benets of coupons have no impact on the WTP for share because agents can buy more or sell extra coupons in the coupon market.

An agent is willing to buy a share if

p S < E [W (pc -T F c .dc i )] + T F S .ds i (2)
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An agent is willing to sell a share if

p S > E [W (pc -T F c .dc i )] + T F S .ds i (3)
In the absence of transaction fees in the coupon market (treatment 3 and 4), under rational expectation and risk neutrality hypothesis, the expected value of a share is equal for all agents. As a result, no trade should happen in the share market because of the transaction fees in the share market. When there are transaction fees in the coupon market (treatment 1 and 2), there is heterogeneity in the value of a share across subjects if they anticipate they will have a dierent position in the coupon market. As a result, shares' trading happens at equilibrium in treatment 1 and 2. Type 2 being net buyers in the coupon market, they will be willing to pay more for shares than type 1 subjects. As a result, type 1 will sell shares to type 2.

The equilibrium allocation of shares in treatment 1 and 2 is such that the need of costly trade in the coupon market is minimized (table 7). When only general security shares are avaiilable (treatment 1), the equilibrium number of shares is such that trade of coupons is required only in the yellow scenario. Shares are allocated according to the need of coupons in the blue scenario. Simple calculation show that any other allocation of shares is less ecient as it will require more trade in the coupon market. When two levels of security for shares are available (treatment 2), the experiment is parametrized such that, by constituting an ecient portfolio of shares, no trade is required in the coupon market is both scenarios. High security shares A are bought to cover the need for coupons in the yellow scenario when shares B give no coupons. Low security shares B are bought to complement the allocation from high security shares A in the blue scenario.

The equilibrium price will be equal to the average between the seller's minimum price is willing to sell and the buyer's maximum price is willing to buy. We assume subjects can be risk averse and predict the eect of risk aversion on the Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

behavior in the dierent markets. Risk aversion and uncertainty on the coupon allocation impact both markets because subjects are less willing to participate in the coupon market, thus it modies their behaviors in the share market. The number of shares held at equilibrium under risk aversion depends on the anticipation of agents on their position in the coupon market. The equilibrium price in the share market will be higher under risk aversion if subjects all anticipate they will have to buy in the coupon market.

On the contrary, if all subjects expect they can speculate and buy extra shares in order to sell part of their allocation in the coupon market, the price of shares will decrease under risk aversion (see appendix B for an intuition of the proof ).

From these theoretical prediction, one can draw some hypothesis to be studied with experimental data.

Hypotheses

Hypothesis 1: The price of shares is equal to the average of the coupon price (net of transaction costs) multiplied by the number of coupons the share yields 11 .

Hypothesis 2: Less trade happens in the share market in T3 and T4 (compare to T1 and T2)

The presence of transaction fees in the coupon market creates an opportunity for share trading in T1 and T2. In T3 and T4, the value of a share is theoretically identical among agents, thus there is no scope for shares trading. Moreover, the transaction fees for share trading in treatment 3 and 4 reenforce the disincentive to trade shares.

Hypothesis 3: There is less trade in the coupon market when there are two levels of security for shares. This is the argument of Freebairn and Quiggin [START_REF] Freebairn | Water rights for variable supplies[END_REF]. With the parameter of the experiment, in T1, the equilibrium number of shares is such that trade is required only in the yellow scenario. When two levels of security for shares are available (T2), the experiment is parametrized such that a perfect mapping of subjects preferences is possible by 11 In the literature on water markets, Bjornlund and Rossini [START_REF] Bjornlund | Fundamentals determining prices in the market for water entitlements: An australian case study[END_REF]observe a relation between the price of water rights and the prices of water allocation. The price of rights increases with the price of water allocation. The market for water rights seems to lead the market for allocations in the cyclical movements until January 1997. Since then the market for allocations has been leading the market for water rights, as rational economic behaviour would dictate. The magnitude of the cyclical uctuations in the allocation market is much higher than it is in the right market.

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constituting an ecient portfolio of shares, such that no trade is required in the coupon market in both scenarios (table 8). Hypothesis 4: The number of coupons traded is equal in T3 and T4.

Yellow scenario

Hypothesis 3 is veried only if subjects can constitute an ecient portfolio of shares in order to minimize the need to trade in the coupon market. If hypothesis 2 is veried, there is less trade in the share market in T3 and T4. As a result, more trade of coupons is required to reach the equilibrium allocation of coupons in T3 and T4.

Hypothesis 5: The total prots are higher in T2 than T1. Total prots are equal in T3 and T4.

If hypothesis 3 is veried for T1 and T2, higher prots are due to the cost savings in terms of transaction fees. If hypothesis 4 is veried, such eect does not happen in T3 and T4. The total prots have thus no reason to be dierent between T3 and T4 (table 9). Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

Hypothesis 6: Type 2 (type 1) have less (more) variable gains in the treatment with two levels of security for share (see proof in appendix C). The allocation of risk is thus improved in treatment 2 compare to treatment 1 if type 2 is more risk averse 12 .

Results

We compare the prices, the quantities traded and the eciency of all markets in the dierent treatments. We also analyze the determinants of the number of coupons and shares held by a subject and determine some recurrent trading strategies. We can then validate or invalidate our hypotheses drawn from the theoretical predictions.

We conduct conservative, nonparametric Wilcoxon's signed-rank tests with exactly one summary statistic value per group (in order to satisfy the statistical independence required for this kind of a test). These tests are valuable as they require a minimum of statistical assumptions. In addition, we report results from multivariate regression models. The regression models evaluate the contribution of dierent factors on the decisions made by subjects.

Only part of the statistical analysis is presented here. We will intergrate further analyzis in the future versions.

Rk: We compute all statistics as average of the last 4 periods played in each treatment (periods 6 to 9).

Aggregate maket performance

We assess market performance under four headings: system eciency, price convergence and stability and trading volumes.

Eciency

Eciency is dened as the actual gains from trade expressed as a percentage of the potential maximum gains. The point of reference is the share and coupon allocation that would minimize transaction costs and maximize prots given the institutions available in each treatments. We nd high eciency ratio (table 10). The eciency ratio are in 12 Thanks to randomization, there is no reason for type 2 subjects to be more risk averse than type 1 subjects in the lottery game. Nevertheless, because of their marginal benet function, type 2 subjects may be less willing to bear risk in the experiment. We want to study the interaction between risk aversion elicited in the lottery game and type. Risk averse behaviors observed in the experiment can be explained by the elicited risk aversion or by the type.

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average lower in T1 than T2 and higher in T3 than T4. Pairwise mann witney tests (using one observation per group: the eciency ratio over periods 6 to 9) between T1 and T2 does not conrm that eciency is lower in T1 than T2. One cannot reject the hypothesis that eciency is the same in both treatments (two-tailed p-value =0.24).

However, the same mann witney test between T3 and T4 show that one can reject the hypothesis that eciency is the same when two levels of security for share are available (right-tail p-value =0.02)

We also compare the observed prots to the theoretical prots if subjects don't trade at all 13 (no-trade-eciency). The no-trade-eciency ratio are higher than 100%, which in- dicates that subject achieve to increase their prots by trading in the dierent markets, even if they don't reach maximum potential gains (eciency). The no-trade-eciency ratio are in average lower in T1 than T2 and higher in T3 than T4. . We also run mann-witney tests on no-trade-eciency ratio (using one observation per group: the average no-trade-eciency ratio over period 6 to 9). One can reject the hypothesis that no-trade-eciency is the same when two levels of security for share are available.

No-trade-eciency is lower in T1 than T2 (T1-T2: left-tail p-value =0.004) and higher in T3 than T4 (T3-T4: right-tail p-value =0.02). It suggests that having access to more levels of security for rights, can not only increase theoretical prots, but also eciency ratio. This is the case in T2 but not in T4, because there are gains from trading shares only in the former treatment.

Price convergence and stability

One measure of the performance of the market institution is the extent to which the prices converge toward the theoretical equilibrium. The continuous double auction is known to have the property that transaction prices and quantities converge over time to the equilibrium. We do not observe convergence over time in both markets. Median prices of coupons and shares are not closer to the equilibrium level at the end of the session than at the beginning. Prices are relatively stable. Median coupons prices are in 13 Even if agents don't trade at all during the experiment (they keep their their initial allocation of shares and coupons obtained from it), they can reach an eciency of more than 85% (T1: 89.16%, T2:87.58%, T3:86.62%, T4:86.62%).

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average 41% higher than the equilibrium prices in the blue scenario and 10% lower than equilibrium prices in the yellow scenario (average over period 6 to 9). Shares prices are higher than equilibrium prices.

Trading volumes

The eciency of the dierent market institutions can be assessed with the number of trades realized compared to the theoretical predictions of the minimum number of trades required to maximize total surplus. There are more trade than required to maximize social surplus in quasi all the markets and scenarios (table 12 and13) 15 . As a result, transaction fees paid are higher than minimum transaction fees predicted in all treatments (see table 14). Nevertheless, we observe learning as average transaction fees paid by a subject decrease over time in gure 2. 15 The high security share market is less active than at equilibrium, as well as the coupon market in treatments 3 and 4. This is due to the more than optimal activity in the share market in these treatments.

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

Number of shares traded

Evidence supporting hypothesis 2:

The number of shares traded is higher in T1 than T3 and higher in T2 than T4 (table 12). Mann-Whitney tests (using one observation per group: the mean number of trades hapenning in a group in the share market over periods 6 to 9) reject the null hypothesis of no impact of treatment on quantities traded (T1 compare to T3 (right-tail p-value=0.09) and T2 compare to T4 (right tail p-value=0.07 for high security shares, right tail p-value=0.02 for low security shares) ). One cannot reject the hypothesis that trade of shares is signicantly higher in treatments with no transaction fees on shares (T1 and T2). In treatments with no gains from trade (T3 and T4), theory predicts no trading activity in the share market.

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10). 16 This is coherent with Angrisani and al [START_REF] Steen Hick | No trade in the laboratory[END_REF]. They ran side-by side markets with an without gains from trade. By comparing trading activity under the two conditions, they assessed how eectively and through which channels, the no-trade logic is incorporated to the behavior of experimental subjects.

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

Coupon market Number of coupons traded

Evidence supporting hypothesis 3 and invalidating hypothesis 4: In average, there is more trade of coupons in T1 than T2, thus supporting hypothesis 3. But hypothesis 4 is not supported because this is also the case for T3 compare to T4 (table 12). Using Mann-Witney tests based on one observation per group (average number of coupons traded in a group over period 6 to 9), the data reject the hypothesis that number of coupons traded are the same with one or two levels of security for shares (right-tail p-value = 0.02 for pairwise comparison between T1 and T2 and right-tail p-value = 0.07 for pairwise comparison between T3 and T4).

Prots

Evidence suporting hypothesis 5: Both type 1 and type 2 prots are higher when two types of shares are available (T2 compare to T1) in both scenarios. When there is no gains from shares trading (T3 and T4), the total prots are lower when there is two levels of security for shares (T4 compare to T3) (table 16). Using Mann-Witney tests based on one observation per group (average total prots over period 6 to 9), the data reject the hypothesis that prots are the same with one

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

or two levels of security for shares (left-tail p-value = 0.03 for pairwise comparison between T1 and T2 and right-tail p-value = 0.04 for pairwise comparison between T3 and T4). We also compute a robust-rank order test as the samples dispersions might be dierent between treatments (FELTOVICH, 2003, Exp economics vol6). We reject the hypothesis of equal medians of total prots in T1 and T2 with a left-tail alpha risk of 0.5% (U = -6.25) and in T3 and T4 with a right-tail alpha risk of 2.5% (U = 2.55).

Evidence invalidating hypothesis 6: Nevertheless, using Mann-Witney tests based on one observation per group (average standard deviation of prots over period 6 to 9), the data fail to reject the hypothesis that the prots are equally variables with one or two levels of security for shares (Type1 prots: two-tailed p-value = 0.13 for pairwise comparison between T1 and T2 , twotailed p-value = 0.24 for pairwise comparison between T3 and T4; Type2 prots: twotailed p-value = 0.48 for pairwise comparison between T1 and T2 , two-tailed p-value = 0.30 for pairwise comparison between T3 and T4). The robust-rank order tests also fail to reject the hypothesis of equal variability prots. (Type1 prots: U=-1.64 for pairwise comparison between T1 and T2 , U=-1.33 for pairwise comparison between T3 and T4; Type2 prots: U=0.68 for pairwise comparison between T1 and T2 , U=1.06 for pairwise comparison between T3 and T4).

Summary

More work should be done. We will complete our results by parametric regressions to verify the validity of the hypotheses. Moreover, we'll look at trading strategies of subjects and check if risk aversion explains trading patterns. Table 18 summarizes the hypothesis and the evidence of their validity or invalidity.

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10). The economic gains expected from water markets depends on the characteristics of the market design and how participants react to the design in the eld. In this paper we focus on two design details relevant for water market performance: the eect of having dierent level of security for water rights, and transaction costs. This can provide the rst steps towards designing more optimal water market regulations to achieve an ecient allocation of water and risks with limited transaction costs.

While most policy discussions of water markets plans envisage the development of future markets in allocation, no previously reported laboratory experiments have implemented any form of trading future entitlements to allocation (rights). Godby and al [START_REF] Mestelman | Emissions trading with shares and coupons when control over discharges is uncertain[END_REF] have shown than the introduction of shares improve the performance of the emission trading markets. This result certainly holds for water markets, as illustrated by the increasing activity on water rights market [START_REF] Michael | Environmental eectiveness and economic eciency of water use in agriculture: The experience of and lessons from the australian water reform programme[END_REF]. We have shown that dierentiating shares in terms of security can further increase eciency. Our results suggest that formal trading of dierent types of future entitlements to water allocation improve the eciency of water markets if trading shares is less costly than trading coupons. However, as soon as spot market trading is ecient and costless, there is no gains from shares trading, thus no gains from a complexied water rights market. We do observe in the lab that the costs of trading shares oset the gains from a portfolio of shares matching coupon needs.

In the short term, we could run other treatments and test what is the transaction costs conguration which increases the gains from a dierentiated system. Further research could include eld experiment with farmers trained in water trading to see if they take better advantage of a dierentiated system than non-experimented students.

We acknowledge nancial support from the ANR project "RISECO", ANR-08-JCJC-0074-01

  to modify the quantity and security of water rights he holds by trading in the right market. Water rights give a right to a share of the available water, wich varies stochastically (with a known distribution) and water allocated can be traded on the spot market. The design precludes trading motives associated to longterm strategies such as savings and speculation on the future value of water rights. It enables to observe trading strategies associated with the need to reduce transaction costs and manage risk better, and to compare them for a general security right system and for a dierentiated right system.. The objective is to measure the gap between observed market equilibria and theoretical equilibria and, if any, analyse how and why individual trading strategies are dierent from predictions. The results will help to conrm whether a dierentiated right system can contribute to improve resource allocation eciency.

  coupons . A share represents an entitlement to a specied fraction of the total available coupons to be issued. Shares A are shares with high level of security and shares B are low security shares. When only one level of security of shares is available, the shares are simply called shares . In the paper, we'll use the general term goods to mention both shares and coupons. The dierent goods are linked: shares are converted into coupons after the share trading stage according to the draw of a scenario. Coupons are converted into experimental monetary units (ECU) at the end of a period according to a benet function. The scenarios are a simplied representation of the climatic 4 No existing experiment on water markets consider both markets. Cristi and Alevy (2009) and Garrido (2007) only focus on the spot market. Hansen and al (2007) experiment includes the spot market and an option market but no rights market. Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

  variability. A wet season is described by blue scenario whereas a dry season is called yellow scenario . Both scenario are equally likely. The blue scenario was drawn in periods 1,2,5,7,8 and 12 and the yellow scenario in 3,4,6,9,10,11. The distribution of scenarios is equal for all treatments and sessions (drawn in advance).

Figure 1 :

 1 Figure 1: Game structure

(

  2006) suggests that the nancial and administrative costs of spot trade are small. Field interviews we have conducted in Northern Victoria (Australia) largely provide evidence of higher transaction costs on the water rights market. If there is quasi no transaction fees to trade in the spot market and positive transaction fees in the share market (treatment 3 and 4), as observed in the elds, no trade should happen in the share market, dierentiated shares yielding therefore less benets.(see theoretical predictions for more details). The transaction fee T F s,c are set to two ECUs per coupon traded for both the buyer and the seller in T1 and T2 and two ECUs per share traded for both the buyer and the seller in T3 and T4

Figure 2 :Figure 3 :

 23 Figure 2: Average transaction fees paid by a subject

Table 1 :

 1 Initial endowment of shares per subject

		Blue scenario	Yellow scenario
	General security share	1	0.33
	High security share (A)	1	1
	Low security share (B)	0.5	0

Table 2 :

 2 Number of coupons received per share

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Table 3 :

 3 Treatments

Table 4 :

 4 8 . Type 2 represents this type of farmer, with high marginal value of water, rather inelastic water demand, and a minimum water requirement.The rst 3 coupons have no value for Type 2 because they are insucient to ensure production, but the fourth unit yields a high marginal value. Marginal benet (in ECUs) for coupons held at the end of a period

	Unit	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	>=16
	Type 1	10	9	8	7	6	5	4	3	2	1	0	0	0	0	0	0
	Type 2	0	0	0	24	22	20	18	16	14	12	10	8	6	4	2	0

Table 5 :

 5 Coupon market equilibrium Treatment 1 and 2

	Blue scenario	Yellow scenario

Table 6 :

 6 Coupon market equilibrium Treatment 3 and 4

Table 7 :

 7 Share market equilibrium Treatment 1 and 2

	Treatment 1	Treatment 2
	General security	High security	Low security

Table 8 :

 8 Number of coupons allocated and traded for each agent (if the share market is at equilibrium) Treatment 1 and 2

	Blue scenario

Table 9 :

 9 Equilibrium prots

	T1	T2	T3	T4

Table 10 :

 10 Eciency ratio(average over all groups and over all periods 6 to 9)

		T1	T2	T3	T4
	Eciency	94.14	96.95	95.80	91.96
	no-trade-eciency	104.26	109.31	107.60	103.28

Table 11 :

 11 Table 11 gives the deviation in ECU of shares prices Deviation of shares median price from equilibrium price in ECU (average by treatment over period 6 to 9)

	from equilibrium price	14 . One should try to explain why subjects are willing pay high
	prices for shares. According to our theoretical predictions, risk aversion can increase
	the equilibrium price of shares if all subjects anticipate they will be net buyers in the
	coupon market.
			T1	T2	T3	T4
	General security shares	3.17		6.75
	High security shares		2.29	14.31
	Low security shares		0.17	2.88

Table 12 :

 12 Number of shares traded in a group (average over period 6 to 9) and theo-

		T1	T2	Prediction	T3	T4	Prediction
	General security	8.33		6	5.42		0
	High security		6.29	9		4.62	0
	Low security		9.08	6		4.00	0
	retical predictions
	14 One cannot calculate deviation in % as the equilibrium prices of shares in T3 and T4 is nulle

Table 13 :

 13 Number of coupons traded in a group (average over period 6 to 9) and

		T1	Prediction	T2	Prediction	T3	Prediction	T4	Prediction
	Blue scenario	2.83	0	3.17		0	9.42	12	5.75	12
	Yellow scenario	4.08	6	2.17		0	5.75	12	3.92	12
	theoretical predictions
					T1	T2	T3	T4
		Total TF paid		27.66	21.34	21.67	34.50
		Theory : Minimum TF	24.00	0.00	0.00	0.00

Table 14 :

 14 Total transaction fees paid in a group and theoretical prediction 6.2 Share market

	Price of shares
	Evidence invalidating hypothesis 1:
			T1	T2	T3	T4
		General security shares	53.31		17.38
		High security shares		29.88	47.89
		Low security shares		30.55	102.44
	Table 15:	Deviation in percentage of median price of shares from E[median
	pCoupon.W](average over period 6 to 9)

The price of shares is not equal to the average of the coupon price (net of transaction costs) multiplied by the number of coupons the share yields. Price of shares are between 29% and 102% higher than the expected value of a share (table

15

).

Table 16 :

 16 Number of coupons traded in a group (average over period 6 to 9)

	T1	T2	T3	T4

Table 17 :

 17 Prot in ECUs(average over periods 6 to 9)

			T1	T2	T3	T4
		Total Prots (group)	625.54	655.88	655.29	629.00
		Total Prots (group)	796.25	836.33	839.33	814.92
	Blue scenario	Prot Type1 Prot Type2	109.61 155.81	118.28 160.50	112.28 167.50	117.11 154.53
		Total Prots (group)	454.83	475.42	471.25	443.08
	Yellow scenario	Prot Type1 Prot Type2	84.56 67.06	85.31 73.17	84.83 72.25	82.67 65.03

Table 18 :

 18 Type 1 prots are more variables when two types of shares are available (T2 and T4) whereas type 2 prots are less variable. Standard deviation of Prot (period 6 to 9)

		T1	T2	T3	T4
	Type 1	18.58	21.05	17.79	21.27
	Type 2	52.33	50.81	55.69	52.66

Table 19 :

 19 Summary of hypothesis 7 Conclusion

	Hypotheses	Comparison	Support of the hypothesis
	H1	Price of shares = expected value of shares	not supported >
	H2	Number of shares traded T1>T3 T2>T4	supported*
	H3	Number of coupons traded T1>T2	supported**
	H4	Number of coupons traded T3=T4	not supported**
	H5	Average Prots T1<T2 T3=T4	supported**
	H6	Variability of prots	not supported

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

Appendix A: Equilibrium coupon market Trading in the coupon market will occur until marginal benets from coupon, net of transaction fees are equalized between agents. The equilibrium number of coupons held by an agent is:

Because agents have the opportunity to trade in the coupon market, the equilibrium number of coupons held does not depend on the number of rights S i . In the presence of TC in the coupon market, the number of coupons held is increased (decreased) for a net seller (buyer) because he has to pay TC if he sells (buys) in the coupon market.

The equilibrium price of an allocation clears out the market:

The equilibrium price of coupon decreases with the total quantity of coupons allocated W t .(S i + S j ) and increases with the marginal benet from coupons. Transaction fee in the coupon market increases coupon price because b i > b j , dc j = -1, dc i = 1.

Appendix B: Eect of risk aversion in the share market

We assume subjects can be risk averse and predict the eect of risk aversion on their behaviors in the dierent markets. Risk aversion and uncertainty on the coupon allocation impact both markets because subjects are less willing to participate in the coupon market, thus it modies their behaviors in the share market.

Eect of risk aversion on the number of shares held by agent

An agent anticipating she will be net buyer in the coupon market (E [W.S i -c i ] < 0) will hold more shares in order to increase her allocation and reduce the need to buy more coupons in the coupon market. A net buyer in the share market (S i > Q i ) will buy more shares and net seller in the share market (S i < Q i ) will sell less shares under risk aversion.

An agent anticipating she will be net seller in the coupon market (E [W.S i -c i ] > 0) will reduce the number of shares he holds (to reduce her allocation and to reduce the need to sell extra-allocations). A net buyer in the share market (S i > Q i ) will buy less shares and net seller in the share market (S i < Q i ) will sell more shares under risk aversion.

Comment citer ce document : Gangadharan, L., Lefebvre, M., Thoyer, S. (2010). Impacts of water rights security on water markets: experimental evidence. In: 4èmes journées de recherches en sciences sociales INRA-SFER-CIRAD (p. 31 p.). Presented at 4. Journées de recherches en sciences sociales, Rennes, FRA (2010-12-09 -2010-12-10).

Eect of risk aversion on the shares' price

If all the agents anticipate they will be net buyer in the coupon market , the price of shares will increase as buyers are willing to pay a markup as a risk premium and sellers are not willing to sell unless the price is increased of the risk premium. Their expected utility is maximized when the price is higher than the value of the share.

If all the agents anticipate they will be net seller in the coupon market , the price of shares will decrease as buyers are not willing to buy unless the price is reduced due to the uncertainty on the value of a share and sellers are willing to sell even if the price is lower than the expected value of the share. Their expected utility is maximized when the price is lower than the value of the share.

Eect of risk aversion on the trading activity in both markets

Risk aversion reduces the trading activity in the coupon market. The eect of risk aversion on the number of trades in the share market depends on the heterogenity among agents. If they all have the anticipation on their net position in the coupon market, and all have the same risk aversion, no trade is possible in the share market (when one is willing to sell, the other is not willing to buy and vice versa) 17 .

Appendix C: Proof of hypothesis 6

In T1, at equilibrium, the number of shares held is such that trade of coupons is required only in the yellow scenario. One can compute prots and the dierence between prots in the blue and in the yellow scenario. The existence of two levels of security for shares reduces the variability of prots between scenarios for type 2 but it increases it for type 1. To assess the performance of the dierentiated system concerning allocation of risks, one should know which type is the more willing and able to bear risk.


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 2010-04-24 -2010-04-27).

Opportunities of genetic association studies in pepper: estimation of the genetic structure and linkage disequilibrium in a germplasm sample

Mélissa Cantet, Stéphanie Mallard, Maryse Nicolaï, Anne-Marie Sage-Palloix, Véronique Lefebvre Institut National de la Recherche Agronomique (INRA), UR 1052 Génétique et Amélioration des Fruits et Légumes (GAFL), Montfavet, France Genetic association studies permit to dissect complex traits, but the resolution depends on the extent of the linkage disequilibrium (LD). When LD declines rapidly around a target locus, locus scans help to identify candidate genes. To avoid false positive associations, the germplasm genetic structure has to be considered. To evaluate opportunities of genetic association in pepper (Capsicum spp.), we investigated the LD extent and the genetic structure in a germplasm sample, at two levels: the wholegenome and a 1-Mb target locus. INRA maintains a pepper collection of 1322 accessions from 5 cultivated and 6 wild species. We randomly sampled 381 accessions from the 5 cultivated species (C. annuum, C. chinense, C. frutescens, C. baccatum, C. pubescens) and one wild species (C. eximium). We genotyped them with 7 SSR markers from 7 chromosomes and 6 SNP markers within the target locus. The genetic diversity of the sample was higher at the genome-wide level (He=0.48, expected heterozygosity, Nei, 1973) than at the target locus (He=0.39). However, SNPs are generally less polymorphic than SSRs. The SSR data revealed that the sample was structured into two major groups. Group1 mostly contained C. annuum accessions, while group2 consisted in a mixture of the other species. As expected, group2 presented more allelic diversity than group1. Group2 was itself structured into 3 sub-groups, roughly splitting the accessions from C. pubescens, C. baccatum and C. frutescens. At the whole-genome level, the LD was high (r²mean=0.28) compared to other species (0.06 for potato). This is favourable for genome-wide association studies. A high LD could be due to the sample structure or related to the limited number of markers. At the target locus, the LD extended up to 300 kb (r²mean=0.9) in group1, and was also high compared to other species (7 kb for maize, 200 kb for lettuce). But it was specifically low (r²mean=0.09) in group2. A high LD is unfavourable for locus-specific association studies. To highlight genotype-phenotype fine associations on pepper, we will focus on haplotype analysis with more markers and within a larger germplasm sample, in considering especially accessions from group2. Session: 3; Presentation: poster

  Opportunities of genetic association studies in pepper: estimation of the genetic structure and linkage disequilibrium in a germplasm sample Melissa Cantet, Stephanie Mallard, Maryse Nicolaï, Anne-Marie Sage-Palloix, Véronique Lefebvre To cite this version: Melissa Cantet, Stephanie Mallard, Maryse Nicolaï, Anne-Marie Sage-Palloix, Véronique Lefebvre. Opportunities of genetic association studies in pepper: estimation of the genetic structure and linkage disequilibrium in a germplasm sample. 2. International Symposium on Genomics of Plant Genetic Resources, Apr 2010, Bologne, Italy. hal-02751906 Comment citer ce document : Cantet, M., Mallard, S., Nicolai, M., Sage-Palloix, A.-M., Lefebvre, V. (2010). Opportunities of genetic association studies in pepper: estimation of the genetic structure and linkage disequilibrium in a germplasm sample. In: Final Program & Abstracts (p. 122). Presented at 2. International Symposium on Genomics of Plant Genetic Resources, Bologne, ITA (


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Somatic embryogenesis of forest trees in

By comparison, it was interesting to make the point of advances made in Europe. Therefore, in the frame of the European project Treebreedex (http://treebreedex.eu), a review has been made on somatic embryogenesis in both Angiosperm and Gymnosperms forest tree species, results that will be presented today.

  Europe: what's going on? An overview Marie-Anne Lelu-Walter, Luc Pâques, David Thompson, Luc Harvengt To cite this version: Marie-Anne Lelu-Walter, Luc Pâques, David Thompson, Luc Harvengt. Somatic embryogenesis of forest trees in Europe: what's going on? An overview. IUFRO Working Party 2.09.02 : Somatic Embryogenesis of Forest Trees Conference, Aug 2010, Suwon, South Korea. hal-02751970 Comment citer ce document : Lelu-Walter, M.-A., Pâques, L., Thompson, D., Harvengt, L. (2010). Somatic embryogenesis of forest trees in Europe: what's going on? An overview. In: Advances in Somatic Embryogenesis of Trees and Its Application for the future forests and plantations. Conference Program (p. p. 20). Presented at IUFRO Working Party 2.09.02 : Somatic Embryogenesis of Forest Trees Comment citer ce document : Lelu-Walter, M.-A., Pâques, L., Thompson, D., Harvengt, L. (2010

embryogenesis of forest trees in Europe: what's going on? An overview

  MA Lelu-Walter(1) , Luc Pâques(1) , David Thompson(2) , Luc Harvengt(3) (1) Research Unit on Breeding, Genetic and Physiology of Forest Trees, France; of clonal propagation methods, such as somatic embryogenesis, has potentially numerous applications and advantages over conventional rooted cuttings(Klimaszewska et al. 2007). The speed at which a new material can be produced, the high potential of amplification make somatic embryogenesis a powerful and flexible tool for the release of improved varieties. Indeed, this efficient method of plant regeneration constitutes a tool for research (study of gene function) and for species improvement (production of a large number of genetically improved plants). Somatic embryogenesis can contribute to increase selection efficiency and facilitate deployment of improved varieties. Somatic embryogenesis has in many instances become the method of choice for clonal propagation of conifers(Sutton 2002). Its deployment is now achieved in Canada (CellFor, JD Irving), United States (Arborgen, Weyerhaeuser) where millions of emblings are routinely produced (Picea sp., Pinus sp., Pseudotsuga menziesii).

	Leluwa@orleans.inra.fr
	(2) COILLTE TEORANTA, Ireland; David.Thompson@coillte.ie
	(3) FCBA Technological Institute, France; Luc.HARVENGT@fcba.fr
	Invited Oral presentation MA Lelu-Walter

). Somatic embryogenesis of forest trees in Europe: what's going on? An overview. In: Advances in Somatic Embryogenesis of Trees and Its Application for the future forests and plantations. Conference Program (p. p. 20). Presented at IUFRO Working Party 2.09.02 : Somatic Embryogenesis of Forest Trees Somatic Development


Magdalena Kristiawan

Tomáš Jirout

Vaclav Sobolik
email: vsobolik@univ-lr.fr

Tomas Jirout

Spatial mapping of wall velocity gradients for wavy Taylor-Couette flow

Keywords: Wavy vortices, electrodiffusion method, three-segment probes

I. Introduction

Several techniques can be used for the measurements of velocity gradients at the solid-liquid interface. Using dissolution of substances like benzoic acid [START_REF] Gogoi | Empirical approach to solid-liquid mass transfer in a three-phase sparged reactor[END_REF] or copper [START_REF] Gruber | Mixed convection in the copper dissolution technique of studying mass transfer[END_REF]Melin 2003, Raguin et al. 2001) the time mean values can be estimated. A little more information can provide visualisations by dye chemisorption at polymers [START_REF] Kuhnel | Visualization and determination of local mass transfer at solid walls in liquid flow[END_REF]. The measurement of the current of an electrochemical reaction, i.e. the electrodiffusion (polarographic) method [START_REF] Cognet | Utilisation de la polarographie pour l'étude de l'écoulement de Couette[END_REF][START_REF] Lebouché | Relation entre les fluctuations pariétales du transfert massique et du gradient de vitesse dans le cas d'un nombre de Schmidt grand[END_REF], is the only method able to follow the space distribution and time evolution of wall velocity gradients. This method is based on the measurement of the electric current limited by the transfert of actives species to the working electrode. Using a redox reaction, repetitive measurements can be carried out with a system which does not require addition of active compounds as in the case of the above mentioned method. The measurements are confined to the diffusion boundary layer which is very thin (several micrometers) in the electrolyte solutions (high Schmidt number). This fact distinguishes the electrodiffusion method from the other methods like laser Doppler anemometry, hot film anemometry and particle image velocimetry. The three-segment probes (see Fig. 1) are composed of three insulated circular sectors that act as working electrodes [START_REF] Sobolik | Method of manufacture of segmented probe with circular cross-section[END_REF]. For the evaluation of flow direction, we make use of the non-linear dependence of the limiting current density on the distance from the forward electrode edge, i(x) ~ x -1/3 [START_REF] Lévêque | Les lois de la transmission de la chaleur par convection[END_REF]). The forward sector has higher current than the sector that lies in his shade. Hence, velocity gradient and its components can be calculated from the limiting diffusion currents passing through the three segments [START_REF] Wein | Theory of direction sensitive probes for electrodiffusion measurement of wall velocity gradients[END_REF]. In this work, the electrodiffusion method with a three-segment and simple micro-electrodes was used for the study of the axial (γ z ) and azimuthal (γ θ ) components of velocity gradient at the outer wall of Taylor-Couette flow.

Nomenclature

A

: Amplitude of vortices (s

II. Experimental Facility

Experiments were carried out in the flow between concentric cylinders with the inner cylinder rotating and outer cylinder fixed. The inner cylinder was driven by a stepper motor with electronically controlled rotation rate. The diameters of the outer and inner cylinders were equal to 62 and 49.6 mm, respectively. This corresponds to the radius ratio, R 1 /R 2 = 0.8. The aspect ratio was about 44. For simultaneous observation of flow pattern and measurement of velocity gradient and vortex characteristics a Kalliroscope solution was added to the electrolyte. The flow regime with wavy Taylor vortices, i.e. vortices with steady azimuthal waves was studied. The vortices were swept past the electrodes by a slow axial flow. Using three-segment probe, see Fig. 1, complete maps of axial and azimuthal components of velocity gradient and their fluctuations at the wall of the outer cylinder were obtained as a function of axial co-ordinate and time. The vortex size (height) and the number and celerity of azimuthal waves were measured by an array of simple electrodes mounted in the wall of the outer cylinder. The arrangement of the electrodiffusion probes along the perimeter of the outer cylinder is shown in Fig. 2. The azimuthal (γ θ ) and axial (γ z ) components of the velocity gradient (γ) were measured by the three-segment probe 3s with a diameter of 0.5 mm. Simple probes e4, e5 and e6 were formed by circular electrodes with the same diameter (0.5 mm). The celerity of azimuthal waves was calculated from the time lag (correlation) of currents delivered by e4 and e5. The wave period was obtained from autocorrelation of the current through the electrode e4. The wavelength was calculated from wave period and celerity. The vortices were driven by a slow axial flow (z-direction) along the probes. The drifting vortex velocity was calculated from the time necessary for a vortex to cover the distance between e5 and e6. The height of vortices was obtained from their period and drifting velocity. The correlations and fast Fourier transformation of measured currents were calculated using Scilab software.

III. Results and discussions

The limiting diffusion current histories measured by the three-segment probe (I 1 , I 2 , I 3 ) and three simple probes (I 4 , I 5 , I 6 ) at Ta=323 are shown in Fig. 3. The measurements were taken over about one and half vortex pairs with a sampling frequency of 40 1/s. The vortex drifting velocity was 0.14 mm/s. Knowing the drifting velocity, the time axis can be transformed to the axial coordinate z. The time t d55 corresponds to the passage of a vortex pair along the probe e5 in axial direction, whereas the time t d56 indicates the passage of vortex crest between the probes e5 and e6. The time t d56 was used for calculation of vortex drifting velocity and t d55 for calculation of vortex height. The azimuthal waves manifest themselves in the signal oscillations. These waves were studied by means of the current correlations R 4i , calculated with respect to I 4 .

The time lag t w45 between the autocorrelation of R 44 and correlation R 45 (see Fig. 4) corresponds to the passage of a selected wave point between e4 and e5, and t w44 to the passage of one wave past e4. The time t w45 was used for the calculation of azimuthal wave celerity and the wave period t w44 for calculation of wavelength. The number of azimuthal waves was obtained by dividing the perimeter of the outer cylinder by the wavelength. The velocity gradient components calculated from currents I 1 , I 2 , I 3 are shown in Fig. 5a. The z-coordinate concerns the height of vortices but it is irrelevant for the wavelength of azimuthal waves. The period of azimuthal waves shown in Fig. 5a is a function of number of waves, angular velocity of waves and drifting velocity of vortices. The amplitude of the velocity gradient components at different position z is given by the envelope of the oscillations which is not shown. The meaning of different symbols is also shown in this figure. The notion of filtered velocity gradient is introduced. This means velocity gradient or its components where the azimuthal waves were filtred out by a Butterworth filter, see γ θf and γ zf in Fig. 5a. The course of filtered wall velocity gradients and their components is similar to the wall velocity gradients in Taylor-Couette non wavy flow (Sobolik et al.). From the point of view of the axial velocity, the outflow creates a forward critical point on the outer cylinder, see Fig. 5a. The azimuthal component of velocity gradient exhibits a maximum at this point and a minimum at the rear critical point (inflow). The axial component of velocity gradient is zero at these points. In fact, there is a small finite value of axial velocity gradient due to the drifting velocity of vortices. The amplitude of azimuthal waves, given by the envelope of oscillations, has azimuthal a θ , and axial component a z . The azimuthal component is zero in forward and rear critical points. The axial component has a maximum in forward critical point and it is very small at the extremes of γ zf . Like in the classical forward critical point, the amplitude of axial oscillations, a z , exhibits maxima and the variation of  γ zf is steep and almost linear. It is much steeper than in the inflow. The outflow has the form of a narrow jet with a high radial and azimuthal velocity. Even if the amplitude of the axial component of velocity gradient has its maximum at the forward critical point, the oscillations of absolute value velocity gradient are very small, see Fig. 5b. It is due to the high value of azimuthal velocity gradient which is steady at this point. We observed the transition from Taylor vortex flow into wavy vortex flow at Ta= 80.5. This value is much higher than the values calculated by Jones 1985. From his Fig. 3, we deducted values of 55.0, 57.6 and 64.5 for set-up of 1, 2 and 3 waves, respectively. We found always three waves at the transition which is in agreement with the simulations carried out by Jones. The components of wall velocity gradient measured at different rotational rate are shown in Figs 6, 7 and8. The rate of data acquisition was equal to 40 1/s. At the lowest rotational rate, Ta=97 (Fig. 6), the regime of three azimuthal waves was stable. The amplitude of wall shear rate and its azimuthal component was almost zero at the critical points. The amplitude of axial component exhibited maximum at the forward critical point and a small value at the rear critical point. Minima of the axial amplitude are located at the crest of γ θf . At these points, the azimuthal amplitude exhibited maxima. This scenario did not change with increasing rotational rate. The only exception was that the axial amplitude had an almost constant value in the outflow region. The characteristic values of the vortices are shown in Table 1 The axial component of the wall shear rate can be compared to the wall shear rate in classical impinging jet even if the azimuthal component in the forward stagnation point exhibits a maximum. According to Prandtl's boundary theory [START_REF] Schlichting | Boundary Layer Theory[END_REF]), it holds for the stagnation region of an impinging jet that the wall shear rate is proportional to the distance from the stagnation point. The maximum of the wall shear rate is at the transition from the stagnation zone to the wall jet region. The spatial distribution of the wall shear rate fluctuations depends on the jet Reylnolds number and the distance of the orifice from the plate (Alekseenko and Markowich 1994). It can have a maximum or minimum in the stagnation point or a constant value in the jet region. At Ta=97, the amplitude of γ z had maximum at the forward stagnation point and with increasing Ta the amplitude became almost constant in the outflow zone. [START_REF] Jones | The transition to wavy Taylor vortices[END_REF] concluded that the strong azimuthal jets at the outflow region destabilize the flow making the vortices wavy. [START_REF] Coughlin | Modulated waves in Taylor-Couette flow Part 2. Numerical simulation[END_REF] supposed that the both radial and azimuthal jets and axial gradient of the azimuthal velocity are responsible for the waviness. The strong azimuthal jet manifests itself by the maxima of γ θf in Figs 6-8. It increases with the Taylor number. The strength of radial jet can be deduced from the axial gradient of γ  zf . Its maximum value is also in the forward critical point. [START_REF] Akonur | Three-dimensional velocity field for wavy Taylor-Couette flow[END_REF] estimated the mean value of the azimuthal shear stress from the PIV measurements for a radius ratio of 0.81. The values were normalized by the shear stress at transition to the Taylor vortex flow τ rθ / τ rθ,tr . As the shear stress is a linear function of velocity gradient with viscosity as a multiplication constant, these values can be compared with our values of γ θ /  γ θ,tr , see Table 2. Our values are about 40 % higher than that of Akonur and Lueptow. This is caused by the inability of PIV to measure close enough to a wall. Due to this fact, the data on shear stress of Akonur and Lueptow exhibit a discontinuity close to the walls.

0 1 2 -1 0 1 R 4i R 4 R 42 R 41 R 45 R 46 R 44 t w45 t w44 t, s

Akonur and Lueptow

This work Ta The velocity gradients and their components were calculated from the measured limiting diffusion currents using the quasi-steady approach, i.e. the Lévêque solution. Taking into account the inertia of the diffusion boundary layer, the amplitudes of oscillations will be even higher.

IV. Conclusions

The three-segment ellectrodiffusion probes are convenient for the mapping of the velocity gradient components on the wall of the wavy Taylor-Couette flow.

The form of the axial distribution of filtered wall shear rate components is similar to the distribution in steady Taylor vortices. However, the maximal values are more important.

Jet like outflow characterised by forward critical point was identified. The oscillations of axial component of velocity gradient exhibit maximum oscillations whereas the oscillations of the azimuthal component are negligible in the forward critical point. The effect of the inertia of the boundary layer on the oscillation amplitudes should be studied in the future.

Fig. 1 :Fig. 2 :

 12 Fig. 1: Three-segment probe with a diameter of 0.5 mm.

Fig. 3 :

 3 Fig. 3: Current histories: I 1 , I 2 , I 3 -three-segment probe; I 4 , I 5 , I 6 -simple electrodes; Ta =323

Fig. 4 :

 4 Fig.4: Correlations with respect to the current I 4

  Tab. 2: Comparison of normalize mean values of wall shear stress and velocity gradient.

Fig. 5 :Fig. 7 :Fig. 8 :

 578 Fig. 5 : Characteristic values of velocity gradient (b) at its components (a) at Ta = 323, h= 12 mm.

Simple electrodes C8. Topic A 2 nd International Conference on Energy Conversion and Conservation; 22 to 25 April 2010. Hammamet, Tunisia -2-

	a	-1 ) : Amplitude of azimuthal waves (s	-1 )
	d	: Entrefer between cylinders (m)
	h	: Vortex height (m)
	I i	: Electric current (A) : Density of electric current (A.m -2 )
	n	: Number of azimuthal waves
	L	: Distance between electrodes (m)
	R 1	: Radius of inner cylinder (m)
	R ij Ta	: Correlation coefficient (-) : Taylor number = Ω R 1 1/2 d	3/2 /µ (-)
	t v	: Time, time lag (s) : Velocity (m.s -1 )
	x	: Distance from the forward electrode edge
	z	: Axial co-ordinate (m)
	Greek letters
	φ γ k	: Flow angle (deg) : Velocity gradient = dv k /dr (s	-1 )
	µ Ω	: Viscosity (Pa.s) : Rotational rate of inner cylinder (rad.s	-1 )
	τ ij	: Shear stress (Pa)
	Subscripts
	d	: Vortex
	f	: Averaged over azimuthal wave
	max	: Maximum
	min	: Minimum
	θ	: Azimuthal
	r	: Radial
	tr	: Transition to Taylor vortex flow
	w	: Azimuthal wave
	z	: Axial
	1,2,3 : Segments of three-segment probe
	4,5,6 :

  .

	Ta	n	Az	az	a θ	γ θmax	h.10	3
	97	3	4.8	4.1	2.4	13.7	11.2
	202	4	21.1	14.3	7.5	46.3	11.1
	483	2	60.4	74.4	52.9	194	11.1
	Tab. 1: Parameters of wavy vortex flow shown in Figs 6 -8.

nd International Conference on Energy Conversion and Conservation; 22 to 25 April 2010. Hammamet, Tunisia -4-

nd International Conference on Energy Conversion and Conservation; 22 to 25 April 2010. Hammamet, Tunisia -5-

Acknowledgements

This work was supported by the "Agence National de la Recherche", France, by the grant number ANR-08-BLAN-0184-01.