Statistical analysis of Lagrangian transport of subtropical waters in the Japan Sea based on AVISO altimetry data

Northward near-surface Lagrangian transport of subtropical waters in the Japan Sea frontal zone is simulated and analysed based on altimeter data for the period from 2 January 1993 to 15 June 2015. Computing different Lagrangian indicators for a large number of synthetic tracers launched weekly for 21 years in the southern part of the Sea, we find preferred transport pathways across the Subpolar Front. This cross-frontal transport is statistically shown to be meridionally inhomogeneous with gates and barriers whose locations are determined by the local advection velocity field. The gates open due to suitable dispositions of mesoscale eddies facilitating propagation of subtropical waters to the north. It is documented for the western, central and eastern gates with the help of different kinds of Lagrangian maps and verified by some tracks of available drifters. The transport through the gates occurs by a portion-like manner, i.e. subtropical tracers pass the gates in specific places and during specific time intervals. There are some forbidden zones in the frontal area where the northward transport has not been observed during all the observation period. They exist due to long-term peculiarities of the advection velocity field.

Statistical analysis of Lagrangian transport of subtropical waters in the Japan Sea based on AVISO altimetry data

Northward near-surface Lagrangian transport of subtropical waters in the Japan Sea frontal zone is simulated and analyzed based on altimeter data for the period from January 2, 1993 to June 15, 2015. Computing different Lagrangian indicators for a large number of synthetic tracers launched weekly for 21 years in the southern part of the Sea, we find preferred transport pathways across the Subpolar Front. This cross-frontal transport is statistically shown to be meridionally inhomogeneous with "gates" and "barriers" whose locations are determined by the local advection velocity field. The gates "open" due to suitable dispositions of mesoscale eddies facilitating propagation of subtropical waters to the north. It is documented for the western, central and eastern gates with the help of different kinds of Lagrangian maps and verified by some tracks of available drifters. The transport through the gates occurs by a portion-like manner, i.e., subtropical tracers pass the gates in specific places and during specific time intervals. There are some "forbidden" zones in the frontal area where the northward transport has not been observed during all the observation period. They exist due to long-term peculiarities of the advection velocity field there.

On planar caustics

We study local invariants of planar caustics, that is, invariants of Lagrangian maps from surfaces to [Formula: see text] whose increments in generic homotopies are determined entirely by diffeomorphism types of local bifurcations of the caustics. Such invariants are dual to trivial codimension 1 cycles supported on the discriminant in the space [Formula: see text] of the Lagrangian maps. We obtain a description of the spaces of the discriminantal cycles (possibly non-trivial) for the Lagrangian maps of an arbitrary surface, both for the integer and mod 2 coefficients. It is shown that all integer local invariants of caustics of Lagrangian maps without corank 2 points are essentially exhausted by the numbers of various singular points of the caustics and the Ohmoto–Aicardi linking invariant of ordinary maps. As an application, we use the discriminantal cycles to establish non-contractibility of certain loops in [Formula: see text].

The biogeochemical structuring role of horizontal stirring: Lagrangian perspectives on iron delivery downstream of the Kerguelen Plateau

Field campaigns are instrumental in providing ground truth for understanding and modeling global ocean biogeochemical budgets. A survey however can only inspect a fraction of the global oceans, typically a region hundreds of kilometers wide for a temporal window of the order of (at most) several weeks. This spatiotemporal domain is also the one in which the mesoscale activity induces through horizontal stirring a strong variability in the biogeochemical tracers, with ephemeral, local contrasts which can easily mask the regional and seasonal gradients. Therefore, whenever local in situ measures are used to infer larger-scale budgets, one faces the challenge of identifying the mesoscale structuring effect, if not simply to filter it out. In the case of the KEOPS2 investigation of biogeochemical responses to natural iron fertilization, this problem was tackled by designing an adaptive sampling strategy based on regionally optimized multisatellite products analyzed in real time by specifically designed Lagrangian diagnostics. This strategy identified the different mesoscale and stirring structures present in the region and tracked the dynamical frontiers among them. It also enabled back trajectories for the ship-sampled stations to be estimated, providing important insights into the timing and pathways of iron supply, which were explored further using a model based on first-order iron removal. This context was essential for the interpretation of the field results. The mesoscale circulation-based strategy was also validated post-cruise by comparing the Lagrangian maps derived from satellites with the patterns of more than one hundred drifters, including some adaptively released during KEOPS2 and a subsequent research voyage. The KEOPS2 strategy was adapted to the specific biogeochemical characteristics of the region, but its principles are general and will be useful for future in situ biogeochemical surveys.

The biogeochemical structuring role of horizontal stirring: Lagrangian perspectives on iron delivery downstream of the Kerguelen plateau

Field campaigns are instrumental in providing ground truth for understanding and modelling global ocean biogeochemical budgets. A survey however can only inspect a fraction of the global oceans, typically a region 100s km wide for a temporal window of the order of (at most) several weeks. This spatiotemporal domain is also the one in which the mesoscale activity induces through horizontal stirring a strong variability in the biogeochemical tracers, with ephemeral, local contrasts which can easily mask the regional and seasonal gradients. Therefore, whenever local in-situ measures are used to infer larger scale budgets one faces the challenge of identifying the mesoscale structuring effect, if not simply to filter it out. In the case of the KEOPS2 investigation of biogeochemical responses to natural iron fertilization, this problem was tackled by designing an adaptive sampling strategy based on regionally-optimized multisatellite products analyzed in real time by specifically designed Lagrangian diagnostics. This strategy identified the different mesoscale and stirring structures present in the region and tracked the dynamical frontiers among them. It also enabled back-trajectories for the ship sampled stations to be estimated, providing important insights into the timing and pathways of iron supply, which were explored further using model based on first order iron removal. This context was essential for the interpretation of the field results. The mesoscale circulation based strategy was also validated post-cruise by comparing the Lagrangian maps derived from satellite with the patterns of more than one hundred drifters adaptively released during KEOPS2 and a subsequent research voyage. The KEOPS2 strategy was adapted to the specific biogeochemical characteristics of the region, but its principles are general and will be useful for future in-situ biogeochemical surveys.

Lagrangian transport in a microtidal coastal area: the Bay of Palma, island of Mallorca, Spain

Coastal transport in the Bay of Palma, a small region in the island of Mallorca, Spain, is characterized in terms of Lagrangian descriptors. The data sets used for this study are the output for two months (one in autumn and one in summer) of a high resolution numerical model, ROMS (Regional Ocean Model System), forced atmospherically and with a spatial resolution of 300 m. The two months were selected because of their different wind regime, which is the main driver of the sea dynamics in this area. Finite-size Lyapunov exponents (FSLEs) were used to locate semi-persistent Lagrangian coherent structures (LCS) and to understand the different flow regimes in the bay. The different wind directions and regularity in the two months have a clear impact on the surface bay dynamics, whereas only topographic features appear clearly in the bottom structures. The fluid interchange between the bay and the open ocean was studied by computing particle trajectories and residence time (RT) maps. The escape rate of particles out of the bay is qualitatively different, with a 32% greater escape rate of particles to the ocean in October than in July, owing to the different geometric characteristics of the flow. We show that LCSs separate regions with different transport properties by displaying spatial distributions of residence times on synoptic Lagrangian maps together with the location of the LCSs. Correlations between the time-dependent behavior of FSLE and RT are also investigated, showing a negative dependence when the stirring characterized by FSLE values moves particles in the direction of escape.