Bayesian networks as a tool of achieving more robust results of cost-proportionality analysis within the WFD
Abstract
With increasing concerns about Europe's water quality, EU implemented Water Framework Directive (Directive 2000/60 EC; WFD). The WFD's primary purpose is to protect European water bodies.
The directive introduces a "good status" and requires all water bodies within EU member states to reach it by 2015. Not achieving the "good status" is justifiable for example in a case of disproportionate costs, which means it is appropriate to apply for an exemption to extend the deadline to 2021/2027.
It can be used only if implementation of measures proves to be too costly compared to generated benefits. The WFD does not provide a clear explanation how to assess cost proportionality, thus several various approaches were created in EU member states.
These approaches are mostly based on (i) cost-benefit analysis, (ii) criteria analysis or (iii) combination of those. However, the methodologies often treat measure's effectiveness as a constant and do not allow it to vary.
In reality, the same measure does not necessarily work the same way in different conditions and this uncertainty should therefore be included in the analysis. Bayesian networks provide an elegant way of including effectivity variance into calculations.
Using a graph structure and conditional probabilities, likelihood of reaching a predetermined target can be assessed. The paper illustrates Bayesian approach on a small Czech catchment of Stanovice water reservoir.
Excessive inflows of dissolved phosphorus cause eutrophication and the "good status" is not reached. Measures capable of reducing phosphorus inflows by 200 kg a year were previously selected.
Based on observations in the literature and real data, probability distribution of each measure type's effectiveness was estimated. Using simulated values from the created distributions and discretizing into several categories, it was concluded the 200-kg target is reached with probability of 70% based on preliminary results Bayesian networks allow us to incorporate uncertainty into cost-proportionality analysis.
One does not need to stop with effectiveness. Bayesian networks can be used to involve uncertainty into assessment of costs and benefits as well.
Results of such analysis are more robust and reliable. On the other hand, Bayesian networks never give a clear answer, results are always probabilistic.
Despite this minor flaw, Bayesian networks improve quality of cost-proportionality analysis and provide a way for possible extension of existing approaches.