In this contribution we identify storm time clustering in the Mediterranean
Sea through a comprehensive analysis of the Allan factor. This parameter is
evaluated from a long time series of wave height provided by oceanographic buoy
measurements and hindcast reanalysis of the whole basin, spanning the
period 1979–2014 and characterized by a horizontal resolution of about 0.1

In recent years the occurrence of different coastal storms in a short time
has been studied in the context of storm-driven erosion of beaches and dunes.
Indeed it has been shown by different authors

In the events analysed in the aforementioned studies both the surge and the
wave components played an important role. While studies that identify
time clustering of storm surges are available (e.g.

The Mediterranean Sea wave climate has been extensively studied
(e.g.

Value of significant wave height threshold in metres for the 98 % percentile.

The present work addresses the gap in the knowledge of the occurrence of
time clustering of wave storms by carrying out an analysis of wave storms
sequences using the Allan factor

Here we analyse the AF on long time series of wave height in the
Mediterranean Sea provided by hindcast reanalysis spanning the period 1979–2014

The paper is organized as follows: after the Introduction, Sect.

Hindcast control grid points (red circle) and RON buoys as reference points (yellow circles).

Sequences of natural events such as earthquakes, rainfall and wildfires, can be
seen as realizations of stochastic point processes. A process of this kind
describes events that occur randomly in time and is completely defined by
the times at which these events occur. Here time series of sea states are
considered. Each sea state is defined by a set of spectral parameters, such as
the significant wave height

Storm occurrence for the northern Tyrrhenian reference point (A): 2004/2005 in the top panel, zoomed-in graph of winter 2004/2005 in the bottom panel.

These point processes are studied by defining equally spaced time windows of
duration

Number of storms vs. threshold for the northern Tyrrhenian reference point (A).

The exponent

The occurrence of subsequent wave storms can be interpreted as a
realization of stochastic temporal point process that could attain a
clustered character when a number of its underlying features exhibit
some scaling as a function of some scaling power law. The presence of
such characteristics reveals that the process follows some kind of
clustering in time (

This further clarifies the nature of the process described by the AF and the role of the different cyclic components that contribute to generate above-threshold events.

Wave hindcast in the Mediterranean Sea has been implemented on a time window
covering 36 years, from the first of January 1979 to 31 December 2014
(

Generation and propagation of sea waves have been modelled using
WavewatchIII^{®}, version 3.14

The Italian Sea Wave Measurement Network (Rete Ondametrica Nazionale RON)
started operating in July 1989

In order to assess the reliability of the hindcast time series related to
storm cluster analysis, the results of AF for the RON buoys are analysed and
compared to the corresponding grid points of the hindcast model. These
results are shown in Figs.

Comparison of Allan factor between RON and hindcast data series for different threshold percentiles (98 and 99.5 %).

Comparison of Allan factor between RON and hindcast data series for different threshold percentiles (98 and 99.5 %).

Comparison of Allan factor between hindcast data series for 98 % percentile (black line) and 1000 simulated cyclic Poisson processes (grey lines). The AF corresponding to the 95 % percentile of the AF distribution is also plotted (dashed line). Top left shows point A (northern Tyrrhenian). Top right shows point G (southern Tyrrhenian). Bottom shows point O (south-eastern Mediterranean).

Allan factor (AF) as a function of counting window

Allan factor (AF) as a function of counting window

Allan factor (AF) as a function of counting window

The AF patterns of both the model and data show a consistent behaviour
across the Mediterranean basin. The AF is greater than one for

This analysis reveals that, as expected, the dominant
cyclic component for all the considered time series is the one with a 1-year
period. This was also noted for the RON data in

Results from the control points located over the basin (see Fig.

The first group clearly shows the slope corresponding to the departure from
the Poisson regimes. The change in regimes occurs at around

In the second group only the cyclic Poissonian regime is clearly
recognizable, generally for

The spatial distribution of the slope for small timescales is shown in
Fig.

Spatial distribution of the exponent

The results presented highlighted the presence of a departure from the
Poisson distribution for timescales shorter than

For

The values of

The clustering at the timescales found has the potential to exacerbate local
beach erosion generated by individual storms, as shown in

Wave hindcast data are available for research purposes on request. Please contact Prof. Giovanni Besio at giovanni.besio@unige.it.

Giovanni Besio and Lorenzo Mentaschi developed the wave hindcast and the Allan factor analysis for the Mediterranean Sea; Riccardo Briganti coordinated the work and gave the theoretical ideas to develop the analysis; Alessandro Romano and Paolo De Girolamo developed the analysis for the RON buoy data set and carried out the comparison with the simulated non-homogeneous Poisson point process. All the authors participated actively in the preparation and writing of the manuscript.

The authors declare that they have no conflict of interest.

The work described in this publication was supported by the European Community's Horizon 2020 Research and Innovation Programme through the grant to HYDRALAB-PLUS, Contract no. 654110. Riccardo Briganti expresses his gratitude to the Engineering and Physical Sciences Research Council (EPSRC) for providing the funding through the FloodMEMORY project (grant number: EP/K013513/1). The authors would like to thank Thomas Wahl and an anonymous reviewer for having contributed to the improvement of the manuscript. The authors are grateful to Francesco Serinaldi for the proficuous discussion during the revision of the manuscript and for having made the routines for the simulation of cyclic Poisson processes available. Edited by: I. Didenkulova Reviewed by: T. Wahl and one anonymous referee