In the context of rapid increase of temperature in the polar regions, inducing a dramatic ice melting, Lagrangian transport in the Arctic Ocean becomes an area of key interest. The aim of this work is to show the phase portrait of the sea currents throughout the Arctic Ocean, which allows us to study aspects of their dynamics. This is done by means of the numerical method known as Lagrangian descriptors, which computes and graphically displays flow structures over a given domain of the ocean, highlighting coherent jet circulation patterns, eddy-like structures and distinguished trajectories. This method was originally based on the computation of the Euclidean arc length of trajectories of a dynamical system. In this work the considered dynamical system is a velocity field given by data sets from COPERNICUS which assimilate observations. The images provide us both a validation of already known and well reported flow structures, and also the discovery of singular features in the ocean which correspond to extreme weather events. ACNOWLEDGEMENTS: We acknowledge L. Bertino and Jiping Xie from NERSC for providing us with the dataset used in this study.
SOCIB, Palma, Spain
Submesoscale blocking of Chl by HF Radar LCSs
The Ibiza channel is one of the major sites in relation to water circulation in the Western Mediterranean basin. While the large scale dynamics is well described by geostrophy, the small scale processes and their relevance in this region are still poorly understood. A preliminary study using the average of FSLE from HF Radar surface currents shows the apparition of Richardson regimen at pair particle separation of 8 km, scales not well resolved by altimetric data. This confirms that relative dispersion, at surface, is controlled locally by submesoscale structures and not only by larger and slower mesoscale structures. To study the influence of local dynamics on the accumulation or dispersion of chlorophyll in the Ibiza Channel we have used high-resolution satellite-derived Chlorophyll-a data from MODIS/Aqua and GLOBCOLOUR products. We have found that Lagrangian Coherent Structures (LCSs) deduced from HF Radar measurements strongly organize the surface distribution of Chl in coastal regions. For instance, in autumn, high values of Chl-a concentration are accumulated at the southwest of Ibiza Island, due to the blocking effect of nutrient rich waters coming from the Atlantic Ocean by a quasi-permanent coherent structure that acts as barrier. Similar relationship between these LCSs and Chl distributions have been found over the year. These barriers prevent Chl-a from traveling towards northern regions of the Western Mediterranean Sea. Thus, such LCSs deduced from HF Radar are a major mechanism for the transport and dispersion of rich coastal waters, impacting physical and biological connectivity over large scales. These results are of great importance as they allow us to infer spatial distribution of relevant ocean variables (Chl-a, SST, salinity) by using hourly HF Radar surface currents. Furthermore these Radar LCSs could be an important tool to localize zones of convergence and divergence for plastic debris accumulation or jellyfish aggregations.
IFISC (CSIC-UIB), Palma de Mallorca, Spain
Pathways of dominant transport in atmospheric and oceanic flows
The last decades have seen very important developments in the Lagrangian description of geophysical fluid transport. Most of the new techniques have focused in the determination of barriers to transport, or of coherent regions with little fluid interchange with the surrounding medium. Less tools are available to identify the actual routes of transport, the dominant pathways along which fluid particles travel and reach different regions. Building on tools from network theory, applied to a discretization of the advection dynamics driven by available velocity fields, we determine optimal paths connecting different regions, quantify the fraction of transport following alternative routes, and highlight regions crossed by a large number of pathways. The approach is illustrated for the surface circulation of the Mediterranean Sea and for an atmospheric blocking event over Eastern Europe.
ICMAT, Madrid, España
Discrete and Continuous Lagrangian Descriptors for Hamiltonian systems.
The goal of this work is to discuss the generalization of the method of Lagrangian descriptors . This method visualizes the phase space structure of Hamiltonian systems, in particular the stable and unstable manifolds of hyperbolic trajectories, in the case of both discrete  and continuous  dynamical systems. Such a method consists of the sum of the p-norm of the velocity field evaluated on the trajectory of points. In this work we discuss formal proofs on why this method highlights invariant manifolds. ACKNOWLEDGEMENTS. The research of C. Lopesino is supported by the MINECO under grant MTM2014-56392-R within the ICMAT Severo Ochoa project SEV-2011-0087. SW is Supported by ONR Grant No. N00014-01-1-0769. REFERENCES  Lopesino, C., Balibrea, F., Wiggins, S., Mancho, A.M. Lagrangian Descriptors for Two Dimensional, Area Preserving Autonomous and Nonautonomous Maps. Communications in Nonlinear Science and Numerical Simulation, 27, pp. 40-51, 2015.  Lopesino, C., Balibrea-Iniesta, F., Garca-Garrido, V. J., Wiggins, S., Mancho, A.M. A theoretical frame- work for Lagrangian descriptors. Submitted.  Mancho, A.M., Wiggins, S., Curbelo, J., and Mendoza, C. Lagrangian descriptors: A method for revealing phase space structures of general time dependent dynamical systems. Communications in Nonlinear Science and Numerical Simulation, 18(12), 3530 - 3557, 2013.
IFISC (CSIC-UIB), Palma de Mallorca, Spain
Boundaries of the Peruvian Oxygen Minimum Zone shaped by coherent mesoscale dynamics
Dissolved oxygen in sea water is a major factor affecting marine habitats and biogeochemical cycles. Oceanic zones with oxygen deficits represent significant portions of the area and volume of the oceans and are thought to be expanding. The Peruvian oxygen minimum zone is one of the most pronounced and lies in a region of strong mesoscale activity in the form of vortices and frontal regions, whose effect in the dynamics of the oxygen minimum zone is largely unknown. Here, we study this issue from a modeling approach and a Lagrangian point of view, using a coupled physical-biogeochemical simulation of the Peruvian oxygen minimum zone and finite-size Lyapunov exponent fields to understand the link between mesoscale dynamics and oxygen variations. Our results show that, at depths between 380 and 600 meters, mesoscale structures have a relevant dual role. First, their mean positions and paths delimit and maintain the oxygen minimum zone boundaries. Second, their high frequency fluctuations entrain oxygen across these boundaries as eddy fluxes that point towards the interior of the oxygen minimum zone and are one order of magnitude larger than mean fluxes. We conclude that these eddy fluxes contribute to the ventilation of the oxygen minimum zone.
López, María Pilar
Applied Mathematics Dpt. (Biomathematics). UCM, Madrid, Spain
Probability density of the Thorpe displacements at the Spanish planetary boundary layer
The results presented in this paper are based on three ABL field campaings made at Spain and called Almaraz94-95, Sables98 and Sables2006. ABL data from 98 zeppelin-shaped tethered balloon soundings ranking from 150 m to 1000 m under different stratification conditions. In previous works, we have analyzed the behaviour of the maximum Thorpe displacement (dT)max and the Thorpe scale LT. The maximum Thorpe displacements varyes between -900 m and 950 m and the scale LT ranges between 0.2 m and 680 m for the different data sets which cover different stratified mixing conditions. We also deduced that the relation between (dT)max and the Thorpe scale LT is a power law. There is a difference in exponents of the power laws for convective conditions and shear-driven conditions. Now we analyze the probability distribution of Thorpe displacemente P(dT) over a profile. We want to verify if the probability of a small Thorpe displacement is much greater than that of a large dT. We also analyze if the probability density function of Thorpe displacements follow a universal form at ABL and if there is differences between the daytime and nighttime data sets. References Cuxart, J., Yagüe, C., Morales, G., Terradellas, E., Orbe, J., Calvo, J., Fernández, A., Soler, M., Infante, C., Buenestado, P., Espinalt, Joergensen, H., Rees, J., Vilà, J., Redondo, J. Cantalapiedra, I. and Conangla, L.: Stable atmospheric boundary-layer experiment in Spain (Sables 98). A report, Boundary-Layer Meteorology, 96, 337-370, 2000. Dillon, T. M.: Vertical Overturns: A Comparison of Thorpe and Ozmidov Length Scales, J. Geophys. Res., 87(C12), 9601-9613, 1982. Itsweire, E. C.: Measurements of vertical overturns in stably stratified turbulent flow, Phys. Fluids, 27(4), 764-766, 1984. Kitade, Y., Matsuyama, M. and Yoshida, J.: Distribution of overturn induced by internal tides and Thorpe scale in Uchiura Bay, Journal of Oceanography, 59, 845-850, 2003. López P., Cano J. L., Cano D. and Tijera M.: Thorpe method applied to planetary boundary layer data, Il Nuovo Cimento, 31C(5-6), 881-892, 2008. DOI: 10.1393/ncc/i2009-10338-3. López, P. and Cano, J. L.: Study of the overturning length scales at the Spanish planetary boundary layer, Nonlin. Processes Geophys., 23, 75–82, 2016. Lorke A. and Wüest A.: Probability density of displacement and overturning length scales under diverse stratification, J. Geophys. Res., 107 (C12), 3214-3225, 2002. Piera, J., Roget, E. and Catalan, J.: Turbulent patch identification in microstructure profiles: a method based on wavelet denoising and Thorpe displacement analysis, J. Atmospheric and Oceanic Technology, 19, 1390-1402, 2002.
The disappearance of Malaysia Airlines flight MH370 on the morning of the 8th of March 2014 is one of the great mysteries of our time. One relevant aspect of this mystery is that not a single piece of debris from the aircraft was found during the intensive surface search carried out in the months following the crash. Difficulties in the search efforts were due to the uncertainty in the plane’s final impact point and the time passed since the accident and rise the question on how the debris was scattered in an always moving ocean, for which there exist multiple datasets that do not uniquely determine its state. Our approach to this problem is based on dynamical systems tools that identify dynamic barriers and coherent structures governing transport. By combining publicly available information supplied by different ocean data sources with these mathematical techniques, we are able to assess the spatio-temporal state of the ocean in the priority search area at the time of impact and the following weeks. Using this information we propose a revised search strategy by showing why one might not have expected to find debris in some large search areas targeted by the search services and determining regions where one might have expected impact debris to be located and that were not subjected to any exploration. This research has been supported by MINECO under grants MTM2014-56392-R and ICMAT Severo Ochoa project SEV-2011-0087 and ONR grant No. N00014- 01-1-0769. Computational support from CESGA is acknowledged.  V. J. García-Garrido, A. M. Mancho, S. Wiggins, and C. Mendoza. A dynamical systems approach to the surface search for debris associated with the disappearance of flight MH370. Nonlin. Processes Geophys 22 (6) (2015) 701-712.
Redondo, Jose Manuel
UPC, Barcelona Tech., Barcelona, Spain
Vortices, Streaks and Fronts in Ocean/Atmosphere interfaces
Remote sensing by electromagnetic wave ( IR, visible, UV, radar ) technology, both in active and passive methods (Synthetic Aperture Radar (SAR), Spectra/ Wavelet, etc…) provide better discrimination and higher resolution in complex geophysical flows. In the ocean surface, and even more so, in the coastal zone, where turbulent flow is generated in the ocean surface either by waves, wind or/and local currents. The conditions are non-homogeneous, and in the presence of a pollutant the SAR detects many interesting topological features [1, 2]. New techniques are used for the analysis, of Images provided by the ESA ERS1/2, ASAR, ENVISAT, RADARSAT and other Canadian and Russian Satellites. We shall concentrate and provide statistics, as well as describing some events detected by several satellites and with additional cruise observations and measurements  in the North-west Mediterranean Sea area between 1996 and 2012 as well as in other European Coastal regions. The structure of the flows are presented and used to parametrize mixing at their relevant scales. The PDF of the basic instabilities are different if they are analysed at scales smaler, or greater than the Rossby Deformation Radius scale. RL. The Results show the ability to identify different SAR signatures and provide calibrations for the different configurations of vortices, (round or eliptical), fronts, spirals, Langmuir cells, oil spills and tensioactive slicks are all relevant and eventually allow some predictions of the self-similar structure of the environmental rotating/stratified turbulence. Such complex coastal field-dependent behavior is strongly influenced by stratification and rotation of the turbulence ; non homogeneous, and non local spectra are observed only in the range smaller than the local RL. The measures of diffusivity from buoy or tracer experiments are used to calibrate the behavior of different tracers and pollutants. Using different polarization and intensity levels from satellite imagery, we may distinguish between natural and man-made sea surface features due to their distinct self-similar and fractal appearece as a function of spill parameters , environmental conditions and history of both oil release and coupled Atmosphere-Ocean interface weather conditions.  Redondo, J.; Matulka, A.M.; Carrillo, J. (2010) Vortex decay in stratified flows. Topic Problems of Fluid Mech. 2010. Praga,AS.127-130.  Castilla R., Redondo J.M., Gamez P.J. and Babiano A. (2007), Non Linear Processes in Geophysics, 14, (2007) 139-151.  Sekula E., Redondo J. M. (2008)The structure of turbulent Jets, Vortices and Boundary layer:, Il Nuovo Cimento, 31, 893-907.  Redondo J.M. and Platonov A. (2009) Environmental Research Letters.