Two years (2021–2022) of high-frequency-radar (HFR) sea surface current data in the Gulf of Trieste (northern Adriatic Sea) are analysed. Two different timescales are extracted using a superstatistical formalism: a relaxation time and a larger timescale over which the system is Gaussian. We propose obtaining an ocean current probability density function (PDF) combining (i) a Gaussian PDF for the fast fluctuations and (ii) a convolution of exponential PDFs for the slowly evolving variance of the Gaussian function rather than for the thermodynamic

In the Gulf of Trieste there are three distinct main wind forcing regimes: bora, sirocco, and low wind, leading to a succession of different sea current dynamics on different timescales. The universality class PDF successfully fits the observed data over the 2 observation years and also for each wind regime separately with a different variance of the variance PDF, which is the only free parameter in all the fits.

Earth-observing systems provide us with an ever-increasing amount of data. This allows us today to move from considering low-order moments of fluctuating observations, averages and variances, to their probability density functions (PDFs), which give a complete characterization of the statistics and help expose the underlying dynamics. These PDFs are mostly non-Gaussian with fat tails, showing that extreme events are more frequent as compared to Gaussian statistics. Furthermore, when the system is subject to slow external forcing, the PDF of the fast fluctuations, characterized by the signal decorrelation time, evolves on a slower timescale. Examples of such dynamics are fast weather statistics (days) under slowly evolving climate conditions (tens of years) or fast sea surface current fluctuations (hourly) during slowly varying synoptic weather conditions (a few days), which is the problem considered here. Superstatistics, introduced by

Superstatistics is a method widely used today in various scientific fields: environmental science (

The main wind regimes consist of bora and sirocco wind events. The bora is a east-north-easterly katabatic wind with gusts reaching up to 50

High-frequency radar (HFR) is a powerful technology to measure horizontal surface currents and sea waves over a grid in a wide area of the sea. The HFR technology is founded on the principle of Bragg scattering of the electromagnetic radiation over the rough conductive sea surface

This study aims to investigate the ocean currents in the Gulf of Trieste, focusing on the fluctuations of the recorded signals. This is done by adopting a superstatistical approach

The paper is organized as follows: in Sect.

Two classes of data sets are analysed: the sea surface horizontal HFR current data and the modelled wind data within the area of the Gulf of Trieste (northern Adriatic Sea, Fig.

Sea surface currents consist of HFR-combined current data coming from two beam-forming WEllen RAdar stations operating in the Gulf of Trieste (Fig.

The quality-control standards from the EU high-frequency node

The grid points close to the HFR baseline have a major data coverage but show a more anisotropic behaviour than those far away (Fig.

The atmosphere data consist of the forecasted wind velocity field at 10

Only the data from the closest WRF grid point to the P point are used for the following analysis. This point will be called “

The analysis follows closely the framework introduced by

Consider a non-equilibrium system, characterized by a variable

Classification of the wind regimes.

Superstatistics considers dynamics where the temperature or the variance is slowly varying in time. When the decorrelation time is much faster than the time over which the variance evolves (

Several studies (

Starting from the longitudinal component

First, consider the timescale

Secondly, consider the timescale

A large time separation

As the reader can see from Eq. (

Superstatistics allows us to uncover the physics of a non-equilibrium system by finding the PDF of a variable by separating the timescales and bringing out the evolution of the local equilibrium PDF.

First we have identified and clustered the wind regimes blowing over the Gulf of Trieste in the analysed period. Since bora and sirocco are synoptic winds, the daily wind time series have been used (Fig.

It is interesting to see that the bora shows the highest speed peaks (Fig.

Next, we have considered the current data. Before following the

Velocity increment kurtosis value

The velocity increments correlation functions were calculated together with the relaxation time

Velocity increments

The resultant

From our estimations of the observations (not shown), the thermodynamic betas

Our environmental system has 2 spatial degrees of freedom, so we can describe

This fact would give the following

Velocity increment PDFs (

Using Eqs. (

The

Best-fit standard deviations from Eq. (

PDFs of

Using the best-fit coefficients

We have observed that the sea surface current velocity increments show fat tails in their distributions. Superstatistics is a powerful tool for determining the PDF. In practice, it relies on the timescale separation between the fast fluctuations (for which the Maxwell–Boltzmann statistics applies) and their slow driver (the temperature in statistical thermodynamics), which makes the local PDF evolve with time. From the velocity increment time series, we have extracted the two different timescales: the relaxation time

From the PDF of the variance we obtained the analytical distribution of the velocity increments. Fitting the distribution to our data we observe a good agreement, even if superstatistics works in the limit of infinite timescale separations

The velocity increments second-order moments differ between the forcing regimes (bora, sirocco, and low wind), with the strongest wind forcing (bora) leading to the lowest fluctuations of the velocity increments. This might be a consequence of the sea surface current tendency to settle on a mean outflow (from the gulf) during the bora or might indicate that an increased wave activity and turbulent exchange in the vertical of the horizontal momentum, operating at even shorter timescales than

Parameterizations of turbulent motions generally rely on a velocity scale and a length scale, averaged over a large timescale. The availability of a considerable amount of data allows us here to go further by determining the PDF of the velocity fluctuations at different timescales. More precisely, the PDF of the fast velocity fluctuations is Gaussian and the PDF of the velocity variance at timescales larger than

The HFR sea surface current data of the Gulf of Trieste are freely available from the European HFR node at the following DOI:

The supplement related to this article is available online at:

SF performed the major part of the research and the writing of the manuscript. LU and AW contributed to the research and the writing.

The contact author has declared that none of the authors has any competing interests.

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The forecasts, analyses, and related services are based on data and products of the Regional Center for Environmental Modelling (CRMA), which is a sector of the Friuli Venezia Giulia Environmental Agency (ARPA FVG) ITALY (

This work was funded by the Initiatives de recherche À Grenoble Alpes (IRGA) 2022 through the FASIOM project.

This paper was edited by Norbert Marwan and reviewed by three anonymous referees.