Natural purification in proportion to the incoming pollution

The natural purification is proportional to the incoming pollution: Ωx (Zx+1) = ∂x Zx+1with∂x <1measuring the abatement coefficient along the stretch[x, x+1), not necessarily the same from one stretch to another, to express the fact that environments can be heterogeneous – something we have stressed at length in the main body of this publication. The problem of this formulation is that it supposes that the environment purifies better the more polluted it is – which hardly makes biological sense.

The equation defining the spatial dynamics of the quality standard value is therefore:

where it turns out that:

And therefore, at present:

Because of natural purification, it is no longer possible to talk about an opportunity cost being associated with the quality requirement having to be applied to the whole river. Although the maximum pollution standard is uniform along the river and therefore independent of the location, its "value" in the sense of the opportunity cost of the standard varies all the way along the river depending on the natural purification processes by the aquatic environment. In the case in question, we get the highest result when, independently of environmental heterogeneity, the opportunity cost increases the further downstream you go.

This is how we can interpret this result. Let's consider the marginal impact of a pollution increase. If this increase occurs very far upstream, it will benefit the entire natural purification chain all the way downstream. But if this increase occurs downstream, it will only benefit a shorter purification chain. All other things being equal, this means that an increase in pollution very far upstream is less serious than one further downstream – which explains a lower opportunity cost of pollution upstream than downstream and therefore the growth in opportunity cost as we move downstream.

In the case of identical towns looked at above, we can now see that town 1 must make more purification efforts than town 2, i.e. bear higher purification costs such that q₁<q₂. Let's expand on the spatial recurrence of pollution:

The rule of sharing the efforts, at present, means that: q₁= (1-∂) q₂. Town 2 has an advantage in terms of natural purification along the stretch of river joining the two urban areas.

By comparing the opportunity cost in the model without purification to the opportunity costs relating to the stretches, we establish the marginal value of the purification service provided by the natural environments. Let's note some important points. Even if the biophysical characteristics of the environments were the same, there is no reason for the service value thus calculated to be the same over different stretches of the river. This is because it obviously depends on the pollution discharged in the environment, which varies. Secondly, even if the pollution discharged is the same at each release point and that the environments are uniform, there is no reason for the service value to be the same. Indeed, the environments are linked by the river and therefore their spatial position in the pollution purification chain along the river influences the value of the service they provide.

In the simple example we have presented, note that the value of the opportunity cost goes up in a multiplicative manner along the river, while the contaminant mass transfer process is additive in nature. This is a consequence of the proportionality hypothesis. As a result, adding up the costs for each stretch to work out a sort of

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A cknowledgements

The discussion paper which led to this book was produced by the Scientific council working group on "quantitative and qualitative assessment of ecosystem services provided by water and aquatic environments". We extend our warmest thanks to the working group for its very fruitful, collective work.

We are also very grateful to the members of the Scientific council for their constructive comments and lively discussions during the plenary sessions that enabled us to add to and improve the text. Particular thanks goes to Luc Abbadie, Chair of the Scientific council, Bernard Drobenko and Guy Oberlin.

We would also like to thank the Onema R&D department and particularly our co-authors who contributed to this book in a very active and constructive manner and formed a highly effective team with us. Special thanks also to Véronique Barre, our editor for this work, whose gentle persistence ensured the success of this undertaking. We also wish to thank the policy officers of the R&D and the Information and communication departments who provided valuable input.

This book would not be as clear or attractive without the illustrations and we are extremely grateful to Béatrice Saurel, for the art work, and to Amandine Samuel, a trainee at the Information and communication department, for the iconographic research, as well as to the individuals and photo libraries (Onema, Ecology ministry, CNRS, INRA) who provided us with photos free of charge.

The "Comprendre pour agir"

(Knowledge for action) series publishes the results of research and science-advice work, for use by teachers, students, scientists, engineers and water and aquatic-environment managers.

Already published Eléments d’hydromorphologie fluviale(October 2010) Eléments de connaissance pour la gestion du transport solide en rivière (May 2011)

A uthors

Jean-Pierre Amigues & Bernard Chevassus-au-Louis

C o-authors

Véronique Barre, Philippe Dupont, Sarah Hernandez, Véronique Nicolas et Eric Tabacchi

E ditor

Véronique Barre (R&D department, Onema)