Waiting times for sea level variations in the Port of Trieste: a computational data-driven study

We report here a series of detailed statistical analyses on the sea level variations in the Port of Trieste using one of the largest existing catalogues that covers more than a century of measurements. We show that the distribution of waiting times, which are defined here akin to econophysics, namely the series of shortest time spans between a given sea level L and the next sea level of at least L + {\delta} in the catalogue, exhibits a distinct scale-free character for small values of {\delta}, while for larger values of {\delta} the distribution is very similar to the exponential distribution. The distribution of waiting times for small values of {\delta} is typical for complex systems exhibiting criticality and is reported abundantly in the literature, while the exponential-like distribution observed for large values of {\delta} has been observed in contexts as diverse as magnetic systems and light sleep duration.