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).

Hydrothermal-vent alvinellid polychaete dispersal in the eastern Pacific .1. Influence of vent site distribution, bottom currents, and biological patterns

Deep-sea hydrothermal-vent habitats are typically linear, discontinuous, and short-lived. Some of the vent fauna such as the endemic polychaete family Alvinellidae are thought to lack a planktotrophic larval stage and therefore not to broadcast-release their offspring. The genetic evidence points to exchanges on a scale that seems to contradict this type of reproductive pattern. However, the rift valley may topographically rectify the bottom currents, thereby facilitating the dispersal of propagules between active vent sites separated in some cases by 10s of kilometers or more along the ridge axis. A propagule flux model based on a matrix of intersite distances, long-term current-meter data, and information on the biology and ecology of Alvinellidae was developed to test this hypothesis. Calculations of the number of migrants exchanged between two populations per generation (N-m) allowed comparisons with estimates obtained from genetic studies. N, displays a logarithmic decrease with increasing dispersal duration and reaches the critical value of 1 after 8 d when the propagule Aux model was run in standard conditions. At most, propagule traveling time cannot reasonably exceed 15-30 d, according to the model, whereas reported distances between sites would require longer lasting dispersal abilities. Two nonexclusive explanations are proposed. First, some aspects of the biology of Alvinellidae have been overlooked and long-distance dispersal does occur. Second, such dispersal never occurs in Alvinellidae, but the spatial-temporal dynamics of vent sites over geological timescales allows short-range dispersal processes to maintain gene flow.