The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis

Statistical approaches to study extreme events require, by definition, long time series of data. In many scientific disciplines, these series are often subject to variations at different temporal scales that affect the frequency and intensity of their extremes. Therefore, the assumption of stationarity is violated and alternative methods to conventional stationary extreme value analysis (EVA) must be adopted. Using the example of environmental variables subject to climate change, in this study we introduce the transformed-stationary (TS) methodology for non-stationary EVA. This approach consists of (i) transforming a non-stationary time series into a stationary one, to which the stationary EVA theory can be applied, and (ii) reverse transforming the result into a non-stationary extreme value distribution. As a transformation, we propose and discuss a simple time-varying normalization of the signal and show that it enables a comprehensive formulation of non-stationary generalized extreme value (GEV) and generalized Pareto distribution (GPD) models with a constant shape parameter. A validation of the methodology is carried out on time series of significant wave height, residual water level, and river discharge, which show varying degrees of long-term and seasonal variability. The results from the proposed approach are comparable with the results from (a) a stationary EVA on quasi-stationary slices of non-stationary series and (b) the established method for non-stationary EVA. However, the proposed technique comes with advantages in both cases. For example, in contrast to (a), the proposed technique uses the whole time horizon of the series for the estimation of the extremes, allowing for a more accurate estimation of large return levels. Furthermore, with respect to (b), it decouples the detection of non-stationary patterns from the fitting of the extreme value distribution. As a result, the steps of the analysis are simplified and intermediate diagnostics are possible. In particular, the transformation can be carried out by means of simple statistical techniques such as low-pass filters based on the running mean and the standard deviation, and the fitting procedure is a stationary one with a few degrees of freedom and is easy to implement and control. An open-source MAT-LAB toolbox has been developed to cover this methodology, which is available at https://github.com/menta78/tsEva/(Mentaschi et al., 2016).

Determination of thresholds in marine molluscs as an alternative to the Environmental Quality Standards in marine water defined in the Water Framework Directive

The Water Framework Directive (WFD) establishes Environmental Quality Standards (EQS) in marine water for 34 priority substances. Among these substances, 25 are hydrophobic and bioaccumulable (2 metals and 23 organic compounds). For these 25 substances, monitoring in water matrix is not appropriate and an alternative matrix should be developed. Bivalve mollusks, particularly mussels (Mytilus edulis, Mytilus galloprovincialis), are used by Ifremer as a quantitative biological indicator since 1979 in France, to assess the marine water quality. This study has been carried out in order to determine thresholds in mussels at least as protective as EQS in marine water laid down by the WFD. Three steps are defined: - Provide an overview of knowledges about the relations between the concentrations of contaminants in the marine water and mussels through bioaccumulation factor (BAF) and bioconcentration factor (BCF). This allows to examine how a BCF or a BAF can be determined: BCF can be determined experimentally (according to US EPA or ASTM standards), or by Quantitative Activity-Structure Relationship models (QSAR): four equations can be used for mussels. BAF can be determined by field experiment; but none standards exists. It could be determined by using QSAR but this method is considered as invalid for mussels, or by using existing model: Dynamic Budget Model, but this is complex to use. - Collect concentrations data in marine water (Cwater) in bibliography for those 25 substances; and compare them with concentration in mussels (Cmussels) obtained through French monitoring network of chemicals contaminants (ROCCH) and biological integrator network RINBIO. According to available data, this leads to determine the BAF or the BCF (Cmussels /Cwater) with field data. - Compare BAF and BCF values (when available) obtained with various methods for these substances: BCF (stemming from the bibliography, using experimental process), BCF calculated by QSAR and BAF determined using field data. This study points out that experimental BCF data are available for 3 substances (Chlorpyrifos, HCH, Pentachlorobenzene). BCF by QSAR can be calculated for 20 substances. The use of field data allows to evaluate 4 BAF for organic compounds and 2 BAF for metals. Using these BAF or BCF value, thresholds in shellfish can be determined as an alternative to EQS in marine water.