Abstract. 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 transformedstationary (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 timevarying 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).

A nonstationary model based on a time-dependent version of the Generalized Pareto Distribution (GPD)-Poisson point process model has been implemented and applied to model extreme wave heights in the Mediterranean basin. Thirty-two years of wave hindcast data have been provided by a forecast/hindcast numerical chain model operational at the University of Genoa (www.dicca.unige.it/meteocean). The nonstationary behavior of wave height maxima prompted the modeling of GEV parameters with harmonic functions. Harmonics have been introduced to model seasonal cycles within a year, also taking into account long-term trend and covariates effects. The model has been applied on eight locations corresponding to buoys belonging to the RON (Rete Ondametrica Nazionale), chosen in order to represent best the main features and variability of waves along the Italian coast. The best performing model is chosen among a large set of possible candidates identified by different combinations of wave heights maxima and model parameters. Direct comparison with stationary results has been performed; furthermore, the model has demonstrated a good performance in gathering different seasonal behaviors related to the main meteorological forcing standing on the Mediterranean Sea. Trends related to extreme significant wave heights have also been evaluated in order to offer some insight into decadal-scale wave climate. Results achieved show how the use of a nonstationary statistical model together with the analysis of the main meteorological forcings characterizing the area could prove useful in understanding wave climate related to atmospheric dynamics.

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Abstract. Statistical approaches to study extreme events require by definition long time series of data. The climate is subject to natural and anthropogenic variations at different temporal scales, leaving their footprint on the frequency and intensity of climatic and hydrological extremes, therefore assumption of stationarity is violated and alternative methods to conventional stationary Extreme Value Analysis (EVA) need to be adopted. In this study we introduce the Transformed-Stationary (TS) methodology for non-stationary EVA. This approach consists in (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 allows a comprehensive formulation of non stationary GEV/GPD models with 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 ones from (a) a stationary EVA on quasi-stationary slices of non stationary series and (b) the previously applied non stationary EVA approach. However, the proposed technique comes with advantages in both cases, as in contrast to (a) it uses the whole time horizon of the series for the estimation of the extremes, allowing for a more accurate estimation of large return levels; and with respect to (b) it decouples the detection of non-stationary patterns from the fitting of the extreme values 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 running mean and standard deviation, and the fitting procedure is a stationary one with a few degrees of freedom and easy to implement and control. An open-source MATLAB toolbox has been developed to cover this methodology, available at https://bitbucket.org/menta78/tseva.

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In this work performances of two different wave spectral models (Wavewatch III and SWAN) are presented. Results are compared with those provided by a validated meteocean modelling chain. Potentialities and deficiencies of either the models are evaluated in relation to their numerical accuracy and ability to represent coastal processes. Both of the models are applied to a coastal area belonging to the Northern Tyrrhenian Sea on a finite-elements computational mesh. As expected the two models provide comparable results. Being conceived for nearshore modelling SWAN provides a more detailed representation of coastal phenomena, including for example a parameterization of diffraction which is neglected by WWIII. On the other hand the Operator Splitting Method employed by WWIII to integrate wave action equation provides a better scalability of time step for different phenomena involved in wave modelling, guaranteeing a better computational efficiency for non-stationary modelling.978-1-4799-8736-8/15/$31.00 ©2015 IEEE