Statistical properties of coastal long waves analysed through sea-level time-gradient functions: Exemplary analysis of the Siracusa, Italy, tide-gauge data

This study presents a new method to analyse the properties of the sea-level signal recorded by coastal tide gauges in the long wave range that is in a window between wind/storm waves and tides and is typical of several phenomena like local seiches, coastal shelf resonances and tsunamis. The method consists of computing four specific functions based on the time gradient (slope) of the recorded sea level oscillations, namely the instantaneous slope (IS) as well as three more functions based on IS, namely the reconstructed sea level (RSL), the background slope (BS) and the control function (CF). These functions are examined through a traditional spectral fast Fourier transform (FFT) analysis and also through a statistical analysis, showing that they can be characterised by probability distribution functions PDFs such as the Student's distribution (IS and RSL) and the beta distribution (CF). As an example, the method has been applied to data from the tide-gauge station of Siracusa, Italy.