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).

Mean structure of the North Atlantic subtropical permanent pycnocline from in-situ observations

In the north Atlantic subtropical gyre, the oceanic vertical structure of density is characterized by a region of rapid increase with depth. This layer is called the permanent pycnocline. The permanent pycnocline is found below a surface mode water ,which are ventilated every winter when penetrated locally by the mixed layer. Assessing the structure and variability of the permanent pycnocline is of a major interest in the understanding of the climate system because the pycnocline layer delimits important heat and anthropogenic reservoir. Moreover, the heat content structure translate into changes in the large scale stratification feature, such as the permanent pycnocline. We developed a new objective algorithm for the characterization of the large scale structure of the permanent pycnocline (OAC-P). Argo data have been used with OAC-P to provide a detailed description of the mean structure of the North-Atlantic subtropical pycnocline (e.g.: depth, thickness, temperature, salinity, density, potential vorticity). Results reveal a surprisingly complex structure with inhomogeneous properties. While the classical bowl shape of the pycnocline depth is captured, much more complex pycnocline structure emerges at the regional scale. In the southern recirculation gyre of the Gulf Stream Extension, the pycnocline is deep, thick, the maximum of stratification is found in the middle on the layer and follow an isopycnal surface. But local processes influence and modify this textbook description and the pycnocline is characterized by a vertically asymmetric structure and gradients in thermohaline properties. T/S distribution along the permanent pycnocline depth is complex and reveals a diversity of water masses resulting from mixing of different source waters. We will present the observed mean structure of the North-Atlantic subtropical permanent pycnocline and relate it to physical processes that constraint it.