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This paper examines the vulnerability to flooding and erosion of four open beach study sites in Europe. A framework for the quantitative estimation of present and future coastal flood and erosion risks is established using methods, data and tools from across a range of disciplines, including topographic and bathymetric data, climate data from observation, hindcast and model projections, statistical modelling of current and future climates and integrated risk analysis tools. Uncertainties in the estimation of future coastal system dynamics are considered, as are the consequences for the inland systems. Different implementations of the framework are applied to the study sites which have different wave, tidal and surge climate conditions. These sites are: Santander, Spain—the Atlantic Ocean; Bellocchio, Italy—the Adriatic Sea; Varna, Bulgaria—the Black Sea; and the Teign Estuary, UK—the northern Atlantic Ocean. The complexity of each system is first simplified by sub-division into coastal “impact units” defined by homogeneity in the local key forcing parameters: wave, wind, tide, river discharge, run-off, etc. This reduces the simulation to that of a number of simpler linear problems which are treated by applying the first two components of the Source–Pathway–Receptor–Consequence (S–P–R–C) approach. The case studies reveal the flexibility of this approach, which is found useful for the rapid assessment of the risks of flooding and erosion for a range of scenarios and the likely effectiveness of flood defences

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In the present study, a recently developed novel approach (Bender et al. in J Hydrol 514:123-130, 2014) has been further extended to investigate the changes in the joint probabilities of extreme offshore and nearshore marine variables with time and to assess design the total water level (TWL) at the shoreline under the effects of climate change. The nonstationary generalised extreme value (GEV) distribution has been utilised to model the marginal distribution functions of marine variables (wave characteristics and sea levels), within a 40-year moving window. All parameters of the GEV were tested for statistically significant linear and polynomial trends over time, and best-fitted trends have been detected. Different copula functions were fitted at the 40-year moving windows, to model the dependence structure of extreme offshore significant wave heights and peak spectral periods, and of wave-induced sea levels on the shoreline and nearshore sea levels due to storm surges. The most appropriate bivariate models were then selected. Statistically significant polynomial trends were detected in the dependence parameters of the selected copulas, and time-dependent most likely bivariate events were extracted to be used in the estimation of the TWL at the shoreline. The methods of the present work were implemented in three selected Greek coastal areas in the Aegean Sea. The analysis revealed different variations in the most likely estimates of the offshore wave characteristics and nearshore storm surges in the three study areas, as well as in the time-dependent estimates of TWL at the shoreline. The approach combines nonstationarity and bivariate analysis, blends coastal and offshore marine features and finally provides non-trivial alterations in the response of coastal sea level dynamics to climate change signals, compared to former work on the subject. The methodology produces reasonable estimates of design quantities for coastal structures and boundary conditions for the assessment of flood hazard and risk in coastal areas.

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Joint probability analysis is most often conducted within a stationary framework. In the present study a nonstationary bivariate approach is used to investigate the changes in the joint probabilities of extreme wave heights and corresponding storm surges with time. The dependence structure of the studied variables is modelled using copulas. The nonstationary Generalized Extreme Value (GEV) distribution is utilized to model the marginal distribution functions of the variables, within a 40-year moving time window. All parameters of the GEV are tested for statistically significant linear and polynomial trends over time. Then different copula functions are fitted to model the dependence structure of the data. The nonstationarity of the dependence structure of the studied variables is also investigated. The methods and techniques of the present work are implemented to wave height annual maxima and corresponding storm surges at two selected areas of the Aegean Sea. The analysis reveals the existence of trends in the joint exceedance probabilities of the variables, in the most likely events selected for each time interval, as well as in a defined hazard series, such as the water level at the coastline.

In the present paper a statistical model for extreme value analysis is developed, considering seasonality. The model is applied to significant wave height data from the N. Aegean Sea. To build this model, a non-stationary point process is used, which incorporates apart from a time varying threshold and harmonic functions with a period of one year, a component l w (t) estimated through the wavelet transform. The wavelet transform has a dual role in the present study. It detects the significant ''periodicities'' of the signal by means of the wavelet global and scale-averaged power spectra and then is used to reconstruct the part of the time series, l w (t), represented by these significant features. A number of candidate models, which incorporate l w (t) in their location and scale parameters are tried. To avoid overparameterisation, an automatic model selection procedure based on the Akaike information criterion is carried out. The best obtained model is graphically evaluated by means of diagnostic plots. Finally, ''aggregated'' return levels with return periods of 20, 50 and 100 years, as well as time-dependent quantiles are estimated, combining the results of the wavelet analysis and the Poisson process model, identifying a significant reduction in return level estimation uncertainty, compared to more simple non-stationary models.