A Bayesian framework to objectively combine metrics when developing stressor specific multimetric indicator

[Departement_IRSTEA]Eaux [TR1_IRSTEA]QUASARE

English. In the context of the European Water Framework Directive (WFD), monitoring programs and related indicators have been developed to assess anthropogenic impacts on various components of aquatic ecosystems. While great precautions are usually taken when selecting and calculating relevant core metrics, little attention is generally paid to the generation of the multimetric indicator, i.e. the combination of the different core metrics. Indeed, most multimetric indicators are generated by simply averaging or summing metrics, without taking into account their sensitivity and their variability. Moreover, few indicators provide a rigorous estimate of the uncertainty of the assessments, while this estimation is essential for managers. In this context, we developed a Bayesian framework to build multimetric indicators aiming at improving those two weaknesses. This framework is based on two phases. First, pressure-impact statistical models are developed to quantify the impact of pressure on various fish metrics. Then the Bayesian theorem is applied to estimate probabilities of being at a certain anthropogenic pressure level from fish observation and pressure-impact models outputs. The Bayesian theorem allows to combine objectively the different core metrics, taking into account their sensitivity and their variability, and to provide rigorous uncertainty quantification, which is especially valuable in the WFD context. The method is applied as illustrative example on transitional French water bodies to demonstrate its relevance, especially in the Water Framework Directive context though the method is generic enough to be applied in various contexts.