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High levels of genetic diversity and connectivity are crucial for the persistence of local populations, especially at the edge of species’ distribution ranges. Here, we assessed the potential and realized connectivity of populations of the Mediterranean seagrass Posidonia oceanica at its easternmost distribution using physical modelling and genetic analyses. Genetic assessments of diversity and gene flow among populations were carried out with 18 microsatellite loci, while oceanographic connectivity was assessed via Lagrangian dispersal simulations. Levels of genetic and clonal diversities were prevalent among shallow and deep sites without signs of reproductive isolation. Both approaches identified two main clusters corresponding to “Aegean” populations along the western Turkey coast and “Levantine” populations along the southern Turkey coast. Aegean populations were genetically homogeneous, connected by high levels of gene flow, whereas Levantine populations were genetically heterogeneous. Within-sea patterns of genetic connectivity did not fully overlap with those derived from physical modelling; the realized connectivity was greater than that predicted by ocean-current simulations, especially in the Aegean Sea. Lagrangian dispersion dynamics cannot necessarily explain genetic connectivity patterns among populations, which are shaped over longer temporal scales and can be affected by human activities and local environmental conditions.

We present an independent validation of the satellite surface velocity fields released by the ESA Data User Element GlobCurrent Project. The validation methodology is based on the analysis of Lagrangian numerical trajectories integrated from satellite-based sea surface currents. Two case studies were considered: Mediterranean Sea and North Atlantic Ocean.The Finite-Scale Lyapunov Exponents provide a rigorous, quantitative tool to evaluate Lagrangian simulations with respect to real drifter trajectories. An accuracy threshold scale can be identified as the scale above which the error size, propagating along a numerical trajectory, grows no faster than the relative separation between real drifters. Below this threshold, the error growth rate tends to diverge linearly as the error decreases. The mean error growth speed, at early stage, is found to be related to the kinetic energy of the missing scales of motion, not resolved by the GlobCurrent products. Established kinematic Lagrangian models are, also, exploited to compensate the energy gap between real and numerical trajectories in the unresolved scale range. Ultimately, GlobCurrent surface velocity fields are shown to have overall good ‘Lagrangian skills' for large-scale transport and dispersion numerical simulations.

Ecological connectivity is one of the most important processes that shape marine populations and ecosystems, determining their distribution, persistence, and productivity. Here we use the synergy of Lagrangian back-trajectories, otolith-derived ages of larvae, and satellite-based chlorophyll-a to identify spawning areas of European anchovy from ichthyoplanktonic data, collected in the Strait of Sicily (Central Mediterranean Sea), i.e., the crucial channel in between the European and African continents. We obtain new evidence of ecosystem connectivity between North Africa and recruitment regions off the southern European coasts. We assess this result by using bio-energetic modeling, which predicts species-specific responses to environmental changes by producing quantitative information on functional traits. Our work gives support to a collaborative and harmonized use of Geographical Sub-Areas, currently identified by the General Fisheries Commission for the Mediterranean. It also confirms the need to incorporate climate and environmental variability effects into future marine resources management plans, strategies, and directives.

The variation of the Coriolis parameter with the latitude (beta effect) strongly affects the turbulent inverse cascade. In fact, when this effect holds, energy is preferentially transferred towards zonal modes. The consequent emergence of flow structures along the zonal direction can strongly impact transport and modify both zonal and meridional scalar diffusion. We performed a detailed analysis of Lagrangian tracers dispersion on rotating flows simulated in laboratory. A relatively wide range of the zonostrophy index, a parameter used to characterize flow regimes in the presence of a beta effect, is investigated. The degree of anisotropy and the characteristic scales of the flow have been estimated by means of the zonal and radial components of the Finite Scale Lyapunov Exponents. Moreover, we introduced the Lagrangian Anisotropy Index is in order to describe the onset of anisotropy and to verify the agreement with the theoretical predictions.

Multidisciplinary studies are recently aiming to define diagnostic tools for fishery sustainability by coupling ichthyoplanktonic datasets, physical and bio-geochemical oceanographic measurements, and ocean modelling. The main goal of these efforts is to understand those processes that control the dispersion and fate of fish larvae and eggs, and thus tuning the inter-annual variability of the biomass of small pelagic fish species. In this paper we analyse the distribution of eggs and larvae as well as the biological features of the two species of pelagic fish, Engraulis encrasicolus and Sardinella aurita in the north-eastern sector of the Sicily Channel (Mediterranean Sea) from ichthyoplanktonic data collected during the 2010 and 2011 summer cruises. We use Lagrangian simulations and satellite data (i.e., sea surface temperature, wind, and chlorophyll-a concentration) to recognize the main oceanographic patterns that mark eggs and larvae transport processes. We provide a mechanistic explanation of a cross-shore transport process by using a potential vorticity (PV) model that takes into account the role of wind stress in generating cold filaments. Our results show that the strong offshore transport towards Malta occurred in 2010 was likely due to a persistent Mistral wind forcing that generated high-PV cold filaments. This phenomenon was not found in the 2011 analysis, which indeed showed an along-shore transport towards the retention area of Capo Passero. Since, for the first time, we describe the spatial distribution of the early life stage of Sardinella aurita in the northern part of the Sicily Channel and we clarify the link between the ocean dynamics and the fate of small pelagic fish larvae, this work provides a useful, diagnostic tool for the sustainable management of fishery resources.

A deterministic multi-scale dynamical system is introduced and discussed as prototype model for relative dispersion in stationary, homogeneous and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian Chaos. The anomalous "sweeping effect", a known drawback common to kinematic simulations, is removed thanks to the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analysed by computing the Finite-Scale Lyapunov Exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous and isotropic conditions. The mathematics of the model is relatively simple and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer and/or boundary layer turbulence models as well as Lagrangian predictability studies., Comment: 22 pages, 5 figures

Distribution shifts are a common adaptive response of marine ectotherms to climate change but the pace of redistribution depends on species-specific traits that may promote or hamper expansion to northern habitats. Here we show that recently, the loggerhead turtle (Caretta caretta) has begun to nest steadily beyond the northern edge of the species’ range in the Mediterranean basin. This range expansion is associated with a significant warming of spring and summer sea surface temperature (SST) that offers a wider thermal window suitable for nesting. However, we found that post-hatchlings departing from this location experience low winter SST that may affect their survival and thus hamper the stabilization of the site by self-recruitment. The inspection of the Intergovernmental Panel on Climate Change model projections and observational data on SST trends shows that, despite the annual warming for this century, winter SST show little or no trends. Therefore, thermal constraints during the early developmental phase may limit the chance of population growth at this location also in the near future, despite increasingly favourable conditions at the nesting sites. Quantifying and understanding the interplay between dispersal and environmental changes at all life stages is critical for predicting ectotherm range expansion with climate warming.

Multidisciplinary studies are recently seeking to define diagnostic tools for fishery sustainability by coupling ichthyoplanktonic datasets, physical and bio-geochemical oceanographic measurements, and ocean modelling. The main goal of these efforts is the understanding of those processes that control fate and dispersion of fish larvae and eggs and thus tune the inter-annual variability of biomass of fish species. We here analyzed eggs and larvae distribution and biological features of Sardinella aurita in the northeast sector of the Sicily Channel (Mediterranean Sea) collected during the 2010 and 2011 summer cruises. We make use of satellite sea surface temperature, wind, and chlorophyll data to recognize the main oceanographic patterns that mark eggs and larvae transport processes and we pair these data with Lagrangian runs. To provide a physical explanation of the transport processes that we observe, we hire a potential vorticity (PV) model that takes into account the role of wind stress in generating those cold filaments responsible for the offshore delivery of eggs and larvae. Our results show that the strong offshore transport towards Malta occurring in 2010 is related to a persistent wind forcing along the southern Sicilian coast that generated an observable cold filament. Such a pattern is not found in the 2011 analysis, which indeed shows a more favorable condition for sardinella larvae recruiting with a weak offshore transport. Our results want to add some insights regarding operational oceanography for sustainable fishery.

The effect of vertical shear on the horizontal dispersion properties of passive tracer particles on the continental shelf of South Mediterranean is investigated by means of observative and model data. In-situ current measurements reveal that vertical velocity gradients in the upper mixed layer decorrelate quite fast (∼ 1 day), whereas basin-scale ocean circulation models tend to overestimate such decorrelation time because of finite resolution effects. Horizontal dispersion simulated by an eddy-permitting ocean model, like, e.g., the Mediterranean Forecasting System, is mosty affected by: (1) unresolved scale motions, and mesoscale motions that are largely smoothed out; (2) poorly resolved time variability of vertical velocity profiles in the upper layer. For the case study we have analysed, we show that a suitable use of kinematic parameterisations is helpful to implement realistic statistical features of tracer dispersion in two and three dimensions. The approach here suggested provides a functional tool to control the horizontal spreading of small organisms or substance concentrations, and is thus relevant for marine biology, pollutant dispersion as well as oil spill applications.

Knowledge of the link between ocean hydrodynamics and distribution of small pelagic fish species is fundamental for the sustainable management of fishery resources. Both commercial and scientific communities are indeed seeking to provide services that could "connect the dots" among in situ and remote observations, numerical ocean modelling, and fisheries. In the Mediterranean Sea and, in particular, in the Sicily Channel the reproductive strategy of the European Anchovy (Engraulis encrasicolus) is strongly influenced by the oceanographic patterns, which are often visible in sea surface temperature satellite data. Based on these experimental evidences, we propose here a more general approach where the role of ocean currents, wind effects, and mesoscale activity are tied together. To investigate how these features affect anchovy larvae distribution, we pair ichthyoplankton observations to a wide remote sensing data set, and to Lagrangian numerical simulations for larval transport. Our analysis shows that while the wind-induced coastal current is able to transport anchovy larvae from spawning areas to the recruiting area off the Sicilian south-eastern tip, significant cross-shore transport due to the combination of strong northwesterly mistral winds and topographic effects delivers larvae away from the coastal conveyor belt. We then use a potential vorticity approach to describe the occurrence of larvae cross-shore transport. We conclude that monitoring and quantifying the upwelling on the southern Sicilian coast during the spawning season allows to estimate the cross-shore transport of larvae and the consequent decrease of individuals within the recruiting area.

This chapter presents basic elements of chaotic dynamical system theory. The concept of Lyapunov exponent, predictability time and Lagrangian chaos are introduced together with examples. The second part is devoted to the discussion of Lagrangian chaos, in particular in two dimensions, and its relation with Eulerian properties of the flow. The last part of the chapter contains an introduction to diffusion and transport processes, with particular emphasis on the treatment of non-ideal cases.

Relative dispersion in a neutrally stratified planetary boundary layer (PBL) is investigated by means of Large-Eddy Simulations (LES). Despite the small extension of the inertial range of scales in the simulated PBL, our Lagrangian statistics turns out to be compatible with the Richardson $t^3$ law for the average of square particle separation. This emerges from the application of nonstandard methods of analysis through which a precise measure of the Richardson constant was also possible. Its values is estimated as $C_2\sim 0.5$ in close agreement with recent experiments and three-dimensional direct numerical simulations., Comment: 15 LaTex pages, 4 PS figures

A detailed analysis of Lagrangian tracer dispersion is performed on datasets obtained from laboratory experiments that simulate rotating turbulence in the presence of a β effect. Compatible with the limitations of the experimental apparatus, a relatively wide range of the zonostrophy index Rβ, a parameter used to characterize flow regimes in β-plane turbulence, is explored. The considered range spans from values ~O(10−1), for which the flow is nearly isotropic, to values ~O(1), corresponding to the so-called transitional range in which the flow gradually leaves the friction-dominated regime to enter the full zonostrophic regime. The degree of anistropy and the characteristic scales of the flow have been estimated by means of a Lagrangian approach based on the reconstruction of tracer trajectories and on the measure of the finite-scale Lyapunov exponents (FSLE). The FSLE analysis allows one to identify the regimes of two-particle dispersion and to relate them to the physical parameters of the system. Moreover, a Lagrangian anisotropy index (LAI) is introduced and defined in terms of the FSLE zonal and radial components, in order to describe the onset of anisotropy and to check if it is consistent with the theoretical predictions. It is remarkable that the finite-scale dispersion rates are very sensitive to the degree of anistropy of turbulence, more so than other indicators defined in terms of Eulerian quantities. Furthermore, they offer an effective diagnostic tool of the degree of anisotropy that can be used even prior to attaining a fully developed regime of zonostrophic turbulence.

A set of numerical experiments is presented, in which we study the dynamics of passive particles advected by given two-dimensional velocity fields and perturbed by a non-white noise with a characteristic time τ. Data and model results have shown that this kind of random perturbation is able to represent subgridscale processes for upper ocean mesoscale turbulence for regions of the world ocean where turbulence can be assumed to be homogeneous. Extensive computations in different fields characterized by cell-like structure, both stationary and time-dependent, representing very idealized geophysical flow situations, show that the presence of a finite correlation time scale does lead to enhanced or arrested dispersion, depending on the considered flow; however, it does not seem to affect the gross qualitative behaviour of the dispersion processes, which is primarily affected by the large-scale velocity field.

[1] Geophysical turbulence is strongly influenced by the variation of the Coriolis force with latitude (β-effect): when this effect is significant an anisotropic inverse cascade is developed since energy is preferentially transferred towards zonal modes. The consequent emergence of flow structures along the zonal direction can strongly impact turbulent transport and modify meridional scalar diffusion. In this letter we investigate zonal and meridional diffusion in laboratory experiments of turbulence affected by aβ-effect. The degree of anisotropy and the flow characteristic scales have been quantified according to a Lagrangian approach based on the reconstruction of tracer trajectories, i.e., in analogy with oceanic drifters data, and on the Finite-Scale Lyapunov Exponent (FSLE) analysis. An experimental confirmation of a recently introduced scaling law for the meridional diffusion in the marginally zonostrophic regime is also presented.

An unusually intense subsynoptic-scale cyclone has been documented in southeastern Italy on 26 September 2006. Numerical simulations are performed with the Weather Research and Forecasting model (WRF). Model results show that the model is able to realistically capture the timing and intensity of the cyclone, identifying in this small-scale cyclone the typical characteristics of a Mediterranean tropical-like cyclone. Sensitivity experiments to sea surface temperature ( SST ) of the simulated cyclone are discussed in the present paper. In these experiments the SST was changed by a constant few degrees uniformly throughout the Mediterranean Sea. The simulated-cyclone sensitivity to SST is studied in the framework of an air–sea interaction theory, in particular during the two phases that are fundamental for the development of an environment favorable to severe convection and thus for the cyclone to be self-sustained. The modifications of the properties of the simulated cyclones are then analyzed using an objective evaluation, based on a phase diagram used to study the tropical–extratropical transition of cyclones. The present simulations show that the features typical of a tropical cyclone are progressively lost as the SST is reduced. In the colder SST experiments, the lower intensity of the sea-surface fluxes has the effect of delaying and reducing the development of convection and the intensification of the cyclone, so that the cyclone loses the characteristics of a tropical cyclone when SST is reduced by more than 4 °C. On the other hand, the cyclone shows a pressure minimum deeper than the control run, with a persistent symmetric warm core, for SST increased by more than 2 °C. Finally, when SST is changed by less than 2 °C, the cyclone depth and trajectory are not significantly affected by the change in SST and, like the control run, show tropical-like features only for a limited period.

In the framework of Monitoring by Ocean Drifters (MONDO) Project, a set of Lagrangian drifters were released in proximity of the Brazil Current, the western branch of the Subtropical Gyre in the South Atlantic Ocean. The experimental strategy of deploying part of the buoys in clusters offers the opportunity to examine relative dispersion on a wide range of scales. Adopting a dynamical systems approach, we focus our attention on scale-dependent indicators, like the finite-scale Lyapunov exponent (FSLE) and the finite-scale (mean square) relative velocity (FSRV) between two drifters as function of their separation, and compare them with classic time-dependent statistical quantities like the mean square relative displacement between two drifters and the effective diffusivity as functions of the time lag from the release. We find that, dependently on the given observable, the quasigeostrophic turbulence scenario is overall compatible with our data analysis, with discrepancies from the expected behavior of 2D turbulent trajectories likely to be ascribed to the non stationary and non homogeneous characteristics of the flow, as well as to possible ageostrophic effects. Submesoscale features of O(1) km are considered to play a role, to some extent, in determining the properties of relative dispersion as well as the shape of the energy spectrum. We present, also, numerical simulations of an OGCM of the South Atlantic, and discuss the comparison between experimental and model data about mesoscale dispersion., 26 pages, 16 figures

The authors compute the maximum Lyapunov exponent lambda of an earthquake model which exhibits deterministic chaos and they discuss its relation with the predictability time of the system. A method is proposed to estimate lambda by the calculation of the entropy of Markov processes which mimic (i) a Poincare map of the model and (ii) a random map related to the seismic signal. The latter map can be obtained using experimental records generated by low-dimensional chaotic system where Poincare maps are not feasible.

A 3D multiscale kinematic velocity field is introduced as a model to simulate Lagrangian turbulent dispersion. The incompressible velocity field is a nonlinear deterministic function, periodic in space and time, that generates chaotic mixing of Lagrangian trajectories. Relative dispersion properties, for example Richardson’s law, are correctly reproduced under two basic conditions: 1) the velocity amplitudes of the spatial modes must be related to the corresponding wavelengths through the Kolmogorov scaling and 2) the problem of the lack of a “sweeping effect” of the small eddies by the large eddies, common to kinematic simulations, has to be taken into account. It is shown that, as far as Lagrangian dispersion is concerned, the model presented herein can be successfully applied as an additional subgrid contribution for large eddy simulations of the planetary boundary layer flow.

We show how a general formulation of the Fluctuation-Response Relation is able to describe in detail the connection between response properties to external perturbations and spontaneous fluctuations in systems with fast and slow variables. The method is tested by using the 360-variable Lorenz-96 model, where slow and fast variables are coupled to one another with reciprocal feedback, and a simplified low dimensional system. In the Fluctuation-Response context, the influence of the fast dynamics on the slow dynamics relies in a non trivial behavior of a suitable quadratic response function. This has important consequences for the modeling of the slow dynamics in terms of a Langevin equation: beyond a certain intrinsic time interval even the optimal model can give just statistical prediction., 40 pages

The EOLE Experiment is revisited to study turbulent processes in the lower stratosphere circulation from a Lagrangian viewpoint and resolve a discrepancy on the slope of the atmospheric energy spectrum between the work of Morel and Larcheveque (1974) and recent studies using aircraft data. Relative dispersion of balloon pairs is studied by calculating the Finite Scale Lyapunov Exponent, an exit time-based technique which is particularly efficient in cases where processes with different spatial scales are interfering. Our main result is to reconciliate the EOLE dataset with recent studies supporting a k^{-5/3} energy spectrum in the range 100-1000 km. Our results also show exponential separation at smaller scale, with characteristic time of order 1 day, and agree with the standard diffusion of about 10^7 m^2/s at large scales. A still open question is the origin of a k^{-5/3} spectrum in the mesoscale range, between 100 and 1000 km., 19 pages, 1 table + 5 (pdf) figures

We study relative dispersion of passive scalar in non-ideal cases, i.e. in situations in which asymptotic techniques cannot be applied; typically when the characteristic length scale of the Eulerian velocity field is not much smaller than the domain size. Of course, in such a situation usual asymptotic quantities (the diffusion coefficients) do not give any relevant information about the transport mechanisms. On the other hand, we shall show that the Finite Size Lyapunov Exponent, originally introduced for the predictability problem, appears to be rather powerful in approaching the non-asymptotic transport properties. This technique is applied in a series of numerical experiments in simple flows with chaotic behaviors, in experimental data analysis of drifter and to study relative dispersion in fully developed turbulence., Comment: 19 RevTeX pages + 8 figures included, submitted on Chaos special issue on Transport and Mixing

The authors show that long-term memory effects, present in the chaotic dispersion process generated by a meandering jet model, can be nonetheless taken into account by a first-order Markov process, provided that the states of the phase-space "partition,'' conceived in a wider sense, are appropriately defined.

We study the response of dynamical systems to finite amplitude perturbation. A generalized Fluctuation-Response relation is derived, which links the average relaxation toward equilibrium to the invariant measure of the system and points out the relevance of the amplitude of the initial perturbation. Numerical computations on systems with many characteristic times show the relevance of the above relation in realistic cases., 7 pages, 5 figures

We address the problem of measuring time-properties of Response Functions (Green functions) in Gaussian models (Orszag-McLaughin) and strongly non-Gaussian models (shell models for turbulence). We introduce the concept of {\it halving time statistics} to have a statistically stable tool to quantify the time decay of Response Functions and Generalized Response Functions of high order. We show numerically that in shell models for three dimensional turbulence Response Functions are inertial range quantities. This is a strong indication that the invariant measure describing the shell-velocity fluctuations is characterized by short range interactions between neighboring shells.

Three different data sets of numerical drifters are obtained with degrading the time sampling (1 day, 1 month and 1 year) of the Eulerian velocity field computed from a Mediterranean general circulation model. The Finite-Scale Lyapunov Exponent (FSLE) technique is used to characterize, for each of the three data sets, Lagrangian dispersion properties in relation to the time resolution of the field. In particular, we are interested in measuring th eunpredictability of trajectories due to the uncertainly in the knowledge of the velocity field. Our data analysis indicates that surface relative dispersion of the Mediterranean Sea has two regimes; exponential spreading due to chaotic advection at small scales (~mesoscale) and super-diffusion at larger scales (up to ~sub-basin scales). In this scenario, it is shown that trajectory evolution is most sensitive to the time sampling of the field at small spatial scales, while, at scales larger than (~100 km, it is essentially independent from the details of the models. Also, FSLE is employed to visualize the geographical regions characterized by high Lagrangian unpredictability. The relation of FSLE with common oceangraphic observables (e.g., local shear, velocity variance) is duscussed. © 2002 Published by Elsevier Science Ltd.

The problem of error growth due to the incomplete knowledge of the evolution law which rules the dynamics of a given physical system is addressed. Major interest is devoted to the analysis of error amplification in systems with many characteristic times and scales. The importance of a proper parameterization of fast scales in systems with many strongly interacting degrees of freedom is highlighted and its consequences for the modelization of geophysical systems are discussed., 20 pages RevTeX, 6 eps figures (included)

In this paper we investigate mixing and transport in correspondence of a meandering jet. The large-scale flow field is a kinematically assigned streamfunction. Two basic mixing mechanisms are considered, first separately and then combined together: deterministic chaotic advection, induced by a time dependence of the flow, and turbulent diffusion, described by means of a stochastic model for particle motion. Rather than looking at the details of particle trajectories, fluid exchange is studied in terms of markovian approximations. The two-dimensional physical space accessible to fluid particles is subdivided into regions characterized by different Lagrangian behaviours. From the observed transitions between regions it is possible to derive a number of relevant quantities characterizing transport and mixing in the studied flow regime, such as residence times, meridional mixing, correlation functions. These estimated quantities are compared with the corresponding ones resulting from the actual simulations. The outcome of the comparison suggests the possibility of describing in a satisfactory way at least some of the mixing properties ot the system through the very simplified approach of a first order markovian approximation, whereas other properties exhibit memory patterns of higher order., Comment: 31 pages laTeX, 19 figures postscript

We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a local--in--time version of these quantities. In systems where the time scale related to the time periodic variation of the parameter is much larger than the ``internal'' time scale, one has that the local quantities strongly depend on the phase of the cycle. In this case, the standard global quantities can give misleading information., 15 pages, Revtex 2.0, 8 figures, included. All files packed with uufiles

We consider passive inertial particles settling under the combined action of gravity and a Stokes drag in two-dimensional velocity fields with increasing complexity. The average settling speed is studied in simple steady and time-dependent cellular and in turbulent flows. Different regimes are identified in relation to the physical properties and complexity of the fields. While for steady and slowly varying weak cellular fields the settling velocity is a decreasing quadratic function of the Eulerian velocity, the same behaviour does not occur for actual turbulent fields. Large fluid velocities, on the other hand, generally speeds up the settling process. The relationships between settling times and the properties of particle trajectories in the different regimes are discussed.

During the last decades, scientific community has been investigating both biological and hydrographic processes that affect fisheries. Such an interdisciplinary and synergic approach is nowadays giving a fundamental contribution, in particular, in connecting the dots between hydrographic phenomena and biomass variability and distribution of small pelagic fish. Here we estimate impacts of hydrographic fluctuations on small pelagic fishery, focusing on the inter-annual variability that characterizes connectivity between spawning and recruiting areas for the European anchovy (Engraulis encrasicolus, Linnaues 1758), in the Northern side of the Sicily Channel (Mediterranean Sea). Results show that coastal transport dynamics of a specific year largely affect the biomass recorded the following year. Our work, moreover, quantifies the specific monetary impacts on landings of European anchovy fishery due to hydrodynamics variability, connecting biomass fluctuations with fishery economics in a highly dynamic and exploited marine environment as the Sicily Channel. In particular, we build a model that attributes a monetary value to the hydrographic phenomena (i.e., cross-shore vs. alongshore eggs and larvae transport), registered in the FAO Geographical Sub-Area (GSA) 16 (Southern Sicily). This allows us to provide a monetary estimation of catches, derived from different transport dynamics. Our results highlight the paramount importance that hydrographic phenomena can have over the socio-economic performance of a fishery.

One of the major issues concerning the study of a dynamical system is the response to perturbations. In climate dynamics, for example, it is of major interest to understand how a given variable, e.g., the temperature, is sensitive to alterations of some other component of the system, e.g., the greenhouse gas concentration. We review the connection between equilibrium and non-equilibrium properties, also known as Fluctuation-Relaxation Relation, and its main aspects in chaotic and turbulent systems. We consider, in particular, the effects of the fast variables on the slow variables in a multiscale system, as far as the sensitivity properties are concerned. Two examples about (widely speaking) climate modelling are discussed: the Lorenz-96 model and the double-potential well model. Both of them, despite their apparent simplicity, hide the same kind of interesting features of much more complex systems.