The trajectories' prediction of floating objects above the sea surface represents an important task in search and rescue (SAR) operations. In this paper we show how it is possible to estimate the most probable search area by means of a stochastic model, schematizing the shape of the object appropriately and evaluating the forces acting on it. The LEEWAY model, a Monte Carlo-based ensemble trajectory model, has been used; here, both statistical law to calculate the leeway and an almost deterministic law inspired by the boundary layer theory have been considered. The model is nested within the subregional hydrodynamic model TSCRM (Tyrrhenian Sicily Channel Regional Model) developed in the framework of PON-TESSA (Programma Operativo Nazionale; National Operative Program – TEchnology for the Situational Sea Awareness) project. The main objective of the work is to validate a new approach of leeway calculation that relies on a real person in water (PIW) event, which occurred in the Tyrrhenian Sea in July 2013. The results show that by assimilating a human body to a cylinder and estimating both the transition from laminar to turbulent boundary layer and the drag coefficients, it can be possible to solve a force balance equation, which allows the search area to be estimated with good approximation. This new point of view leads to the possibility of also testing the same approach for other different categories of targets, so as to overcome the limitations associated with the calculation of the leeway in the future by means of standard statistical law.

Meteocean and environmental forecasting is increasingly being used in
operational decision-making in the sea for demographic, geographic and
strategic applications. Safety of lives and assets at sea are a shared
objective of many countries. Having an efficient ocean forecast system is
essential to improve the prediction of sea state and to provide useful
environmental ocean information, so as to increase the effectiveness of search
operations

In coastal areas, high-frequency radars are crucial to acquire
surface two-dimensional current data (

The first step in marine search planning is to determine the most probable
area containing the searched object, and that is even more important if the
target is a person in water (PIW). The definition of the probable search area
is essentially linked to the quantification of some unknowns, such as the
last known position (LKP) and typology, shape and dimensions of the objects.
Moreover, a PIW or object without propulsion is also subject to drift from
ocean currents, wave action and direct wind action

In the Mediterranean Sea, operational forecasts starting from the year 2000
are provided by the Mediterranean Forecasting System (MFS)

Geographical domain of the Tyrrhenian Sicily Channel Regional Model (TSCRM). The color scale represents the sea bottom.

The last known position, represented by the blue
particles' distribution at the alert time; it is based on the automatic information system (AIS) that
gives the ferry position every 6 s (green line on the left of the picture).
The coordinates of the start and end point are defined in
Table

Particles' cloud estimated by the
LEEWAY model overlapped on the hydrodynamic field. Here the leeway
is calculated by statistical law as in

In many cases, SAR activities may also require fields of interest on a high
spatial resolution. Subregional forecast systems that can resolve
small-scale processes as well as fronts characteristics of the study area are
necessary. A numerical technique widely used in operational oceanography to
increase the horizontal resolution is the downscaling procedure

TESSA project is supported by Programma Operativo Nazionale (PON) “Ricerca e Competivita 2007–2013”, which is a National Operational Program of the Ministry for Education, University and Research of Italy. The general aim is to improve products and services of operational oceanography in southern Italy and to integrate them with technological platforms. The latter are set up to disseminate information for situational sea awareness (SSA), and also in support of SAR activities at sea. In Italy these activities are performed by the coastguard, within the competence of the Ministry of Infrastructure and Transport of Italy.

In this paper we present some numerical results demonstrating the prediction of PIW
trajectories in the central Tyrrhenian Sea. We use two different approaches
for the leeway calculation: the first approach is standard and it
consists in leeway calculation by means of the statistical
parameters shown in the

The new approach is embedded in the LEEWAY model, a drift model based on a
stochastic approach

In this section we describe our drift forecast operational numerical model
developed to predict the trajectories of floating objects
(Sect.

Distance of the mass center of each
group planted every 30 min from 20:30 UTC (group 1) on 11 July 2013 to
midnight the following day (group 8), corresponding to the solution in
Fig.

Downwind (up) and crosswind
(down) components of leeway vs. 10 m wind velocity. Each line's
beam, distinguishable by color, is generated by perturbing the error standard
from a normal distribution

Here the standard error coefficients are 4
times greater than ones in

The current forecasting model used in this work is the
Tyrrhenian Sicily Channel Regional Model (TSCRM), an operational,
subregional, nested ocean model implemented for the central Mediterranean
Sea during the framework of the project TESSA. The TSCRM subregional ocean
model covers the area from 8.98 to 16.5

The drift of a floating object above the sea surface is the result of the
balance between hydrodynamic and aerodynamic forces. This balance induces
the object to move with a certain angle relative to downwind direction

Distance of the mass center of
each group planted every 30 min from 20:30 UTC (group 1) on 11 July 2013
to midnight the following day (group 8), corresponding to the solution in
Fig.

Here the standard error coefficients
are set separately on the offset or on the slope of the regression line
according to the wind velocity (blue lines in
Fig.

Distance of the mass center of
each group planted every 30 min from 20:30 UTC (group 1) on 11 July 2013
to midnight the following day (group 8), corresponding to the solution in
Fig.

The term leeway refers to an object's motion induced by the atmospheric
wind (10 m reference height) and waves relative to ambient current (between
0.3 and 1.0 m depth). This definition standardizes the reference levels for
the measurements of leeway for SAR objects and provides a practical
way to utilize current and wind vectors from numerical models

Data describing the incident.

It is necessary to assume that the empirical coefficients of linear
regression of Eqs. (

By estimating the linear regression coefficients of

An exhaustive description of the stochastic approach used in the LEEWAY
suite is given by

In this work we present a variation of the calculation of the
leeway, replacing the linear regression equation described by
Eqs. (

Equation (

On the horizontal plane, we solve the equation that distinguishes between the laminar
and the turbulent boundary layer. The resistance to motion for a laminar
boundary layer is only given by the viscosity friction and so we solve
Stokes' law as follows:

If the boundary layer is turbulent, the resistance to motion is given by
the balance of the kinetic energy exchange between the moving body and the
fluids:

Finally we estimate the probability of containment (POC) by overlapping a
spatial grid on the geographical one; we arbitrarily set each grid box to
0.06

Here the slope standard error
coefficient is

Distance of the mass
center of each group planted every 30 min from 20:30 UTC (group 1) on 11 July 2013 to midnight the following day (group 8), corresponding to the solution in
Fig.

Particles' cloud simulated by the model
overlapped to the hydrodynamic structures. Here the leeway is
calculated by means of the force balance equation. The cloud includes the
target at the rescue time, and the dispersion does not seem to swamp the
advection; in particular the particles' cloud seems to separate during a longer
period of time according to hydrodynamic structures (

In this work, the LEEWAY model is used to reproduce a real event that occurred in
the western Tyrrhenian Sea, along the coast of Sardinia. On 11 July 2013 a
man was seen for the last time at approximately 20:30 UTC (start point) on
board a ferry that was on duty from Cagliari (Sardinia) to
Civitavecchia (Italy), and only shortly before midnight (end
point) was the alert given. His body was retrieved at 10:30 UTC on 12 July
2013 at a point of known coordinates (Table

Distance of the mass center of each group
planted every 30 min from 20:30 UTC (group 1) on 11 July 2013 to midnight the following day (group 8), corresponding to the solution in
Fig.

Particles' dispersion in the Bonaria experiment, overlapped on the hydrodynamic field. Three principal surface structures are visible in the experiment: two cyclonic gyres, A and C, separated by the anticyclonic gyre, B. Cyclones A and C are persistent during the period of the simulation. Most particles are planted along the western external part of the gyre A while the smallest amount is planted between the cyclonic gyre C and the anticyclonic gyre B. After 18 h, the particles' set is separated into two subsets: gyre A drives the larger subset westwards near the Sardinia coast, whereas the variability of the current between gyres C and B drives the remaining particles to the open sea.

Distance of the mass center of the particles set planted at a known time/point to simulate the trajectory of a dummy in the Sicilian Channel. Again the leeway is calculated by means of the force balance equation. On the upper right side of the picture the trajectory of the mass center throughout the simulation (21 h) is visible.

The LKP is a critical step, as the accuracy of this information is critical
for the outcome of the search. In this work, we represent it as a line
between start and end points (Table

Numerical simulations of PIW trajectories are run using two different
methodologies. The first one consists in the leeway calculation by
means of the equations described in Eqs. (

In both the methodologies we rely on the conclusions of

We perform three different sets of experiments planting a total of 1000 particles in eight time steps from start to end points of last known position, and subsequently estimating the smallest distance between the mass center of each subset of particles and the retrieval point.

Parameters used to solve the force balance equation about the person in water.

The first set of experiments relates to a check of the target configurations
(sitting, vertical, horizontal/survival, horizontal/deceased and
unknown status) shown in the

We set a jibing frequency from 1 to 8 % for each listed position.

The second set of experiments is performed after choosing the best solution
from the previous study; on the regression line used to calculate the
downwind and crosswind leeway components, we check different
coefficients of the time-invariant Gaussian perturbation (

Finally we carry out the third set of experiments: here the solutions are
calculated using the almost deterministic approach. The human body
geometry is assimilated to a cylinder with a height / width ratio between

To check the reliability of the almost deterministic approach, we run
the model in a different geographical area, using a target similar
to a person and referring to the critical Reynolds number vs. drag coefficient
found in the last experiment. The data, provided by the Italian coastguard,
were collected during SAR training; on 13 November 2013 at 08:30 UTC a
dummy was planted in the Sicilian Channel and it was retrieved 13 h later.The geometrically scaled target and the statistics of the new forcings are
included in the model; we estimate a standard deviation of
0.09 m s

The data from the latter experiment are shown in Table

Particles' cloud overlapped on the
hydrodynamic field in the experiment executed in the Sicilian Channel. In

Particles' dispersion in the Sicilian Channel experiment, overlapped on the hydrodynamic field. The particles' cloud is planted on the external part of an anticyclonic vortex, where the current flowing along the southern Calabria coast interacts with the strong current coming from the north, where the Messina Strait is located. The particles are driven according to the surface circulation pattern.

In this section, the main results of each set of experiments are shown. The
first set of experiments is about the configuration of the target and the
effects of the corresponding jibing; the coefficients of the regression line
are set as in

The second set of experiments studies the influence of the leeway
coefficients' perturbations on the results. The leeway estimated by
means of experimental data is heteroscedastic (the variance in fact increases
with wind velocity;

Finally we checked the error standard variations only on the offset or only
on the slope, and we verified that a good final configuration is obtained
when the offset error perturbation coefficient is the same as that proposed in

The previous experiments pointed out the different performances of the model
when the real statistics on forcings and the statistical regression line to
calculate the leeway velocity are used. Not only the
heteroscedasticity of the experimental dataset compiled by

The third set of experiments consists in simulating the PIW drift by means of
the almost deterministic law. After checking the projected frontal
area by means of the allometric parameters for a “standard human body”
according to

The results now show that at retrieval time the cloud includes the target
(Fig.

Data for the second experiment: a dummy planted at a known point and rescued after 12.5 h.

Parameters to solve the force balance equation for the dummy in the Sicilian Channel

In Fig.

We checked our approach in a different area (Sicilian Channel), using
experimental data (Table

In our experiment the dummy was planted in an area where the northern border of
the anticyclonic vortex, located in the area 15.3–16.3

In general, both Fig.

We have presented the results of numerical experiments performed to estimate the probability of containment (POC) of a person in water (PIW). We have referred to a real event that occurred in the western Tyrrhenian Sea. The LEEWAY model, nested within the subregional hydrodynamic model TSCRM, has been used. The real statistic of the forcings on the observation period was accounted for and the last known position has been based on the trajectory of the ferry during 3.5 h, recorded by the automatic information system; to reproduce the event, a set of 1000 particles planted in eight time steps was used.

The objective of the work has been to validate an almost deterministic law to calculate the leeway, based on the boundary layer theory; these results have been compared with those obtained estimating the leeway by means of the standard statistical approach. In this approach, the covariance matrix of the line regression coefficients' estimators would be required to estimate the leeway correctly; it is not known, so we have checked different arbitrary coefficients of the corresponding standard errors. The best results have been obtained when a new value on the slope was set equal to 1.5, while the offset one was set equal to 0.5.

To calculate the leeway in the almost deterministic approach, the PIW was cylinder-shaped with a height / width ratio equal to 4.44; the critical Reynolds number was found in the range between 165 000 and 168 000 and the drag coefficients were estimated equal to 1.12. Now that the results have shown that at the retrieval time, the particles' cloud includes the target, and the third subset of particles is representative of the event, then we can also estimate the time of the accident with good approximation. These results are comparable with the results estimated by means of the standard statistical approach, only when the coefficients of the regression line standard error are correctly set, but we cannot know them in advance. The important result is that in the new approach, the real event is correctly reproduced and the distance of the mass center of the favored subset of particles is more than halved compared to the best solution obtained through the statistical approach, resulting in 1.3 km. The tests in the Sicilian Channel using a similar target have confirmed the reliability of the method.

A second important result is that the particles' distribution in both experiments is coherent with the hydrodynamic structures, highlighting the importance of having an efficient operational ocean prediction system for SAR activity; the hydrodynamic field is required not only because it forces the Lagrangian model, but also because it allows the final results to be read in a more full way. We think, in fact, that the results of the POC can be improved by splitting the set of particles into as many subsets as there are hydrodynamic structures, so that each subset can significatively contribute with its own POC; it corresponds to the consideration of as many time-evolving probability density functions of the location of the search object as there are hydrodynamic structures.

Finally, the Stokes drift will have also to be included.

The results obtained here encourage other different target categories to be explored. We believe that in the long term it will allow the limitations connected with the standard approach based on the statistical parameters to be overcome, providing leeway-drift formulae for practical use based on appropriate Reynolds critical numbers and drag coefficients for specific targets. This idea is supported by the realistic option to execute tests in naval tanks, simulating different meteomarine conditions, scaling opportunely specific targets and then overcoming the costs and difficulties of acquiring field data.

The data used to carry out this research are free and available on request by writing to the author.

We would like to thank to C. te Sirio Faé of Italian coastguard for providing the data for our experiments and for supporting in the interpretation of the IAMSAR manual. Thanks are also expressed to colleagues of the CNR-INSEAN: Massimo Miozzi for his constructive comments during the work and Paola Carratú for her special contribution.

This study was supported by the Italian project PON-TESSA (PON01-02823) and by RITMARE (Ricerca ITaliana per il MARE) Flagship Project of Italy (PNR 2011–2013, approved by CIPE with adjudication 2/2011 on 23/03/2011), funded by the Ministry for Education, University and Research of Italy – MIUR.Edited by: R. Archetti Reviewed by: two anonymous referees