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European Community policy concerning water is placing increasing demands on the acquisition of information about the quality of aquatic environments. The cost of this information has led to a reflection on the rationalization of monitoring networks and, therefore, on the economic value of information produced by these networks. The aim of this article is to contribute to this reflection. To do so, we used the Bayesian framework to define the value of additional information in relation to the following three parameters:
* initial assumptions (prior probabilities) on the states of nature, costs linked to a poor decision (error costs) and accuracy of additional information*. We then analyzed the impact of these parameters on this value, particularly the combined role of
*prior probabilities* and
* error costs* that increased or decreased the value of information depending on the initial uncertainty level. We then illustrated the results using a case study of a stream in the Bas-Rhin department in France.

Water quality monitoring can be defined as the acquisition of quantitative and representative information about the physical, chemical and biological characteristics of a water body over time and space [

Other studies have focused on the quantity of information provided by these networks, where information is defined as a reduction of the uncertainty concerning the intensity and transfer of pollutants. Harmanciogluand Apaslan [

Yokota and Thomson [

This method has been used for different types of additional information and different objectives: information providing the location of a school of fish or the best model to assess their population dynamics [

Concerning the value of information generated by water quality monitoring networks, Bouzit, Graveline and Maton [

In this article, we also address the Bayesian method to assess the economic value of additional information, as presented by Yokota and Thomson [

Let us assume an additional piece of information about the water quality provided by a monitoring network. This information can be obtained by adding measurement stations, by positioning them more carefully, by increasing the frequency of these measurements and the number of parameters observed, etc. The objective is to define the economic value of this additional information.

The aim of improving our knowledge about water quality is to be able to act more effectively upon it.

We can imagine two states of nature, one more unfavorable for the environment,

Two actions are possible for the decision maker:

We designate

The two error costs are positive. Therefore, neither of the two actions is preferable, regardless of the state of nature. This justifies our search for additional information about the states of nature to reduce the risk of error. The additional information can provide two types of messages,

The decision maker will rely on this information to implement his action:

We designate

The probability that this additional information will result in a wrong message is the likelihood function in Bayesian statistics.

Additional information only has a value if it allows us to modify the a priori decision (the decision made without additional information). This decision was based on prior probabilities on the states of nature, where p is the prior probability that the state of nature is the most unfavorable:

More precisely, without additional information, a risk-neutral decision maker chooses the action that minimizes the cost expectancy. Therefore,

In the case where

higher error cost due to the choice of

Some authors have attempted to estimate the prior probabilities in a subjective way [

The value of information will depend on the economic utility of modifying the decision in view of additional information. By designating

The value of information is written as the sum of utility expectations weighted by the occurrence probability of potential messages that can provide additional information.

According to Bayes’ theorem and our notations (Equation (3) and Equation (4)), we have:

The values of

* 1) For

maker modifies his action a posteriori, i.e., if it conveys the message,

The first two utilities,

* 2) For

maker modifies his action a posteriori, i.e., if it conveys the message,

In this scenario, and for the same reasons as those given in scenario (i), the first utility

In Section 2.3 above, we defined the value of information as follows:

If

Not surprisingly, we find that information has a higher value when it is more precise.

Initial assumptions or a priori probabilities can have a positive or negative influence on the value of information.

If the initial choice is action

In contrast, if the initial choice is

The derivative of

The costs linked to a poor decision or error cost can have a positive or negative influence on the value of information.

If the initial choice is the action

The same reasoning justifies the derivatives of

The derivatives of

maximal value of information (for

The contextualization of the preceding theoretical model will make it possible to illustrate the above results.

Water quality monitoring networks appeared in France in 1971. Many networks were created over time with different objectives. Some were created before the implementation of the European Water Framework Directive (WFD) in 2007: the National Pollution Survey (Inventaire National du degré de Pollution, INP), the National Basin Network (Réseau National de Bassin, RNB) and the National Complementary Basin Network (RéseauComplémentaire de Bassin, RCB). Others were created afterwards: the Control and Monitoring Network (Réseau de Contrôleet de Surveillance, RCS), the Operational Control Network (Réseau de Contrôle Opérationnel, RCO), the Reference Control Network (Réseau de Contrôle de Référence, RCR), the Survey Control Network (Réseau de Contrôled’ Enquête, RCE) and the Additional Control Network (Réseau de Contrôle Additionnel, RCA). Local networks can be added to these, including the Departmental Interest Network (Réseaud’ Intérêt Départemental) in the Bas-Rhin department (RID 67) that supplements the national networks.

The modification of these networks in 2007 when the WFD was implemented corresponded to a change in the way these networks were designed. Until then, they mainly fulfilled a time-oriented objective, i.e., to measure water quality at a regular frequency at a specific number of measurement stations (generally located on rivers over 10 km long) in order to observe water quality. With the WFD, the objective became space-oriented since information about the quality of each specific water body then became a necessity. This finer spatial grid is accompanied by a rationalization of the measurement frequency that is now linked to observed qualitative problems. A water body that has difficulty in achieving good status will be more closely monitored.

The Steinbach is a stream in the Bas-Rhin department of France. It is 8 km long and flows into the Sauer River, passing through the towns of Dambach, Lembach, Niedersteinbach and Obersteinbach. It is considered to be a water body according to the definition of the European Water Framework Directive and, as a result, has a water quality measurement station that is part of the RID 67, station n˚02045160, located within the city limits of Lembach.

In 2013, a wastewater treatment plant with a population equivalent (PE) of 740 was built in Niedersteinbach in order to collect and treat the effluents of the neighboring communities before discharging them into the Steinbach. Two purification techniques were studied for this treatment plant: activated sludge, which is a biological treatment technique that uses wastewater treatment microorganisms, and a natural lagoon-based wastewater treatment system that uses a bacterial culture to break down organic matter. The activated sludge technique is more costly but more effectively treats the nutrients that can lead to eutrophication when they are discharged into the stream. Eutrophication, which is produced by the proliferation of plants, can have an impact on the fauna and flora by depriving them of oxygen, and generates additional costs to produce drinking water.

When choosing a treatment technique, it is therefore important to know if the environment is sensitive to nutrients and, consequently, if the risk of eutrophication is real. Is it better to use the more costly activated sludge technique to avoid all risks of eutrophication, or the natural lagoon-based system at the risk of having to assume the ecological damage linked to the eutrophication of the water body?

The Steinbach measurement station made it possible to provide information about the sensitivity of the environment so that a well-informed decision could be made.

To calculate the value of this information, we identify:

-two states of nature:

-and two possible actions concerning the choice of the technique to be used at the wastewater plant:

The use of activated sludge will eliminate the risk of eutrophication, regardless of the state of nature:

The use of a natural lagoon-based system will lead to damage linked to eutrophication E of the stream if the environment is sensitive to nutrients:

The costs of a poor decision (Equation (2)) can be expressed as follows:

The Rhin-Meuse Water Agency produces technical datasheets [

Investment cost for lagoon-based system = 676.3 × (740) − 93,858 = ?06,604

Operating cost for lagoon-based system = 3.6501 × (740) + 1117.3 = ?,818/year

Investment cost for activated sludge = 11,023 × (740)^{0.6159} = ?44,851

Operating cost for activated sludge = 14.454 × (740) + 6433.8 = ?7,130/year

By calculating the constant annuity with a discount rate of 4% and a lifespan of 25 years, we have:

Estimating the damage linked to eutrophication is complicated because it is closely linked to the local context. The water from the Steinbach is not used to produce drinking water, whereas fish farming and recreational fishing could be affected, and the fauna and flora could be subjected to environmental damage. Sutton et al. [

The Steinbach goes through four villages: Dambach (809 inhabitants), Obersteinbach (241 inhabitants), Niedersteinbach (155 inhabitants) and Lembach (1730 inhabitants), with 6%, 77%, 76% and 14% of the municipalities, respectively, located on the water body. We can therefore estimate the number of inhabitants affected by the quality of the water body at 594. With an average household size of 2.3 in France, this means that 258 households are affected, resulting in damage costs of ?8,082 to ?06,647/year basing ourselves on the figures of Söderqvist and Hasselström [

In order for the information provided by the monitoring station to have value, the damage must be greater than

The aim of this article is not to precisely estimate the damage and, consequently, the value of information, but to instead understand how the parameters influence this value. We illustrate our model with the two upper bounds of the estimates found in the literature, ?1,662 and ?06,647/year.

The error costs (Equation (8)) then become:

Taking the equations used to express the value of additional information described in Equation (6), the error costs given in Equation (9), and the inaccuracy, Equation (3), of 1%, 5% and 10%,

We can see in

In fact, if the damage is high (low) and its probability of occurrence is also high (also low), the value of information is low because the choice of opting a priori for activated sludge (natural lagoon-based system) appears to be more appropriate. Additional information in this case therefore provides little information.

In this example, the use of additional information can even lead to a negative value when the additional information is not accurate. In fact, there is a non-null probability that additional information may lead to the modification of a decision that was appropriate a priori.

The greatest a priori uncertainty and, therefore, the greatest value of information is obtained when the damage is high and its probability of occurrence is low, or inversely. The peaks of the graphs in

In

The limits of these maximal information values for damage that tend towards infinity are, taking Equation (7): ?7,991/year, ?5,706/year and ?2,850/year, respectively, for uncertainties of 1%, 5% and 10%.

The European Water Framework Directive is placing increasing demands on the acquisition of information

about the quality of aquatic environments. In France, the cost of water quality monitoring is estimated at 30 million euros per year. Consequently, a reflection on the rationalization of monitoring networks is necessary. To do this, it is important to estimate the economic value of information produced by a network.

The aim of this article is to contribute to this reflection. To do so, we used the Bayesian framework to define the value of additional information in relation to the following parameters: prior probabilities on the states of nature, costs linked to a poor decision (error costs) and accuracy of additional information. We then analyzed the impact of these parameters on this value, particularly the combined role of prior probabilities and error costs that increased or decreased the value of information depending on the initial uncertainty level. We then illustrated the results using a case study of a stream in the Bas-Rhin department in France.

In the Bayesian framework, the value of information is based on the direct use of this information to influence a decision. The limit of this method is that it does not calculate a value prior to the decision and ignores the future potential uses of the information. In our illustration, this would mean that the Steinbach measurement station would not have any more value once the wastewater station is operational. Nevertheless, even if the Bayesian framework only provides a partial estimation of the value of information, it in no way detracts from its explanatory power.

Knowing the economic value of the information produced by water quality monitoring networks can lead to a cost-benefit analysis to rationalize the design of these networks. To do this, it is also necessary to study the costs of monitoring stations whose calculation is not necessarily direct when certain costs are shared and the frequencies and types of measurements are irregular. However, this is not within the scope of this article.

We would like to express our deep gratitude to Alain Kieber, head of the Réseaud’ Intérêt Départemental (RID 67) of the Conseil Départemental du Bas-Rhin, for providing us with all of the information necessary to build our case study.

François Destandau,Amadou Pascal Diop, (2016) An Analysis of the Value of Additional Information Provided by Water Quality Measurement Network. Journal of Water Resource and Protection,08,767-776. doi: 10.4236/jwarp.2016.88062