Marine coastal processes are highly variable over different space scales and
timescales. In this paper we analyse the intermittency properties of particle
size distribution (PSD) recorded every second using a LISST instrument (Laser
In-Situ Scattering and Transmissometry). The particle concentrations have
been recorded over 32 size classes from 2.5 to 500

Ocean data fields show a high variability over many different time and space
scales. Such variability is often associated with turbulence, and
multi-scaling properties of oceanic fields have been reported and studied in
many previous studies: sea state

PSD has a major influence in biological, physical and chemical processes in
the aquatic environment

Most environmental and geophysical data sets are nonlinear and non-stationary
at many different scales of time and space. Intermittency is a property that
occurs in fully developed turbulence ranging between the large-scale
injection and the small-scale dissipation

Empirical mode of decomposition (EMD) together with Hilbert spectral
analysis (HSA) is a well-known time-frequency analysis method for
non-stationary and nonlinear time series

The first part of the paper presents the study area and in situ data, and contains the separation of different size classes and the hyperbolic shape of the PSD. Intermittency analysis using the EMD–AHSA method (presented in the appendices) is then provided in the next section.

The measurements were conducted 50 cm from the bottom of coastal
waters of the eastern English Channel at a fixed station
(50 45.676

We consider here simultaneous measurements of velocity and particle
concentrations. The in situ sampling of Laser In-Situ Scattering and
Transmissometry (LISST 100X type C) has been carried out at 1.0 Hz. The main
part of the instrument is a collimated laser diode and a specially
constructed annular ring detector. The primary information collected by the
LISST is the scattering of the laser at 32 angles, which are converted into
size distribution using an inverting method. The size distribution is
presented as volume concentration with units of micro-litres per litre
(

Location (black triangle) of the sampling station in the eastern English Channel together with the isobaths.

The first 3000 samples of the time series of volume concentrations
of different size classes of PSD.

The volume concentration distributed of a particle size class can also be
expressed as the concentration

The particle size distribution in the ocean, which describes the particle
concentration as a function of particle size/number, typically shows a rapid
decrease in concentration with increasing size from a
sub-micrometre range to hundreds of micrometres. This feature is common to
all the suspended particles and also for plankton micro-organisms

The study carried out by

The first 3000 samples of the time series of PSD
slope (

The study of

We first consider here the scaling and intermittency properties of the
velocity. Figure 4a shows the Fourier and Hilbert (HSA) estimations of the

Turbulent power spectra of

The first 3000 samples of the time series of Shannon entropy
in

Power spectra for different size classes of PSD estimated for
Fourier and Hilbert transforms. Silt/clay

Scaling exponents

The first 3000 samples of the time series of

The LISST system records at each time step a discretised PDF of the particle
size. Hence it is possible to estimate at all time steps the entropy of the
particle size distribution as

The entropy of particle sizes characterises the “disorder” of the size distribution, its information content. We showed here that the dynamics of such a quantity can be considered by using LISST data. A very interesting feature of LISST measurements is hence to be able to characterise nonlinear classical indicators such as the Shannon entropy in a dynamical way.

As explained above, the PSD is decomposed into four different size classes of particles (silt/clay, fine particles, coarse/micro particles and macro particles/flocs). The power spectra of these four size classes have been derived using Fourier as well as Hilbert transforms (Fig. 6) for understanding the turbulent characteristics. Similar spectra are found from Fourier and Hilbert transforms, and there is a good power-law behaviour observed in the high-frequency region (0.09–0.002 Hz).

This scale range has been taken for the extraction of the scaling exponents.
The scaling exponent function

We perform here an analysis of intermittency of concentration dynamics
considering two indicators of this particle concentration:

For comparison purposes, the Haar wavelet structure function method, which
can also be used for negative

An interesting point that can be noticed for these time series is that none
of the scaling moment functions extracted through the AHSA method for various
parameters showed

The Hurst exponent values derived through AHSA and the Haar wavelet method for various parameters.

This work analysed the intermittency and scaling properties of particles
using the AHSA method. The intermittent transport of particles in complex
flows, like in coastal waters, is very important for the study of partition
dynamics, erosion processes, ecosystem modelling, sediment transport and
turbidity dynamics. Suspended particle dynamics in turbulent flows are
complex: some studies showed preferential concentration

This work has analysed the intermittency and scaling properties of the PSD
using different aspects. Time series of normalised volume concentrations of
different size classes of PSD and Shannon entropy have been derived from the
number density of PSD. Here we showed the intermittency of particles for
different size classes. The

Turbulent scaling of these parameters has been derived through both Fourier
power spectra and spectra derived through HSA. The scaling moment function
derived for

We may note also that the Hurst exponents derived for the velocity components and the particle concentrations are negative. This negative sign indicates that small scales show larger fluctuations than large scales. We have here no theoretical interpretation to propose to explain these values, which could be related to the particular statistical characteristics of a bottom boundary-layer flow.

This multiscaling analysis has been tested only in the bottom of the highly dynamic coastal waters of the eastern English channel. Such an analysis is an illustration of the potential provided by LISST data, with many particle size classes recorded at each time step. It may be applied to other time series in the open ocean, coastal waters and also freshwater situations, in order to provide comparison and help to look for universal properties.

Hilbert spectral analysis (HSA) and empirical mode of decomposition (EMD)
were introduced by Norden Huang and collaborators at the end of the 1990s

The decomposition process stops when the residue,

Hilbert spectral analysis (HSA) is the second step of the analysis, which is
applied to each mode

The local frequency is estimated from the phase function:

The HSA represents a time–amplitude frequency analysis. This helps to
estimate a joint PDF

The equation obtained in the previous section giving

The Centre National d'Etudes Spatiales (CNES) and the Centre National de la Recherche Scientifique (CNRS) are acknowledged for the funding of P. R. Renosh's PhD thesis. This study is performed in the framework of the COULCOT-2 project, funded by the CNES/TOSCA programme. Edited by: A. Baas Reviewed by: two anonymous referees