A generic aggregation approach to account for statistical uncertainty when combining multiple assessment results

Abstract The one-out-all-out approach (OOAO) for aggregating the assessments of single elements (e.g. species or ecosystem components) has found application in environmental polices such as the European Water Framework Directive or the Marine Strategy Framework Directive (MSFD). However, the OOAO has been challenged as being too pessimistic by making positive assessment results virtually impossible along the increasing number of aggregated elements. This study presents a generic approach, the probabilistic One-out-all-out approach, (pOOAO), to account for this issue and thereby reconciling the OOAO with probabilistic aggregation methods The pOOAO allows to determine the minimum number of elements (K GES ), which should meet their assessment benchmarks and thus should achieve a good status. By pre-setting a generic confidence level for each single assessment (e.g. 0.95) the binomial distribution can be used to obtain K GES for any number of assessed elements. The pOOAO can also accommodate for the integration of assessments from multiple indicators within an element by adjusting the confidence level in relation to the number of integrated indicators. Depending on the generic confidence level as well as on the number of and integrated indicators and aggregated elements, the pOOAO is either consistent with the OOAO or allows for a certain number of negative assessment results, which are attributed to statistical uncertainty and error propagation. The pOOAO is consistent with the OOAO if the desired confidence level in the single assessment results is very high (>0.99) and/or the number of aggregated elements and integrated indicators is low. Through this flexibility the pOOAO could find wide application within integrated ecosystem assessments frameworks such as the MSFD, but would require to estimate the confidence level for each single assessment.