M. J. Olascoaga

Forecasting sudden changes in environmental pollution patterns

The lack of reliable forecasts for the spread of oceanic and atmospheric contamination hinders the effective protection of the ecosystem, society, and the economy from the fallouts of environmental disasters. The consequences can be dire, as evidenced by the Deepwater Horizon oil spill in the Gulf of Mexico in 2010. We present a methodology to predict major short-term changes in environmental contamination patterns, such as oil spills in the ocean and ash clouds in the atmosphere. Our approach is based on new mathematical results on the objective (frame-independent) identification of key material surfaces that drive tracer mixing in unsteady, finite-time flow data. Some of these material surfaces, known as Lagrangian coherent structures (LCSs), turn out to admit highly attracting cores that lead to inevitable material instabilities even under future uncertainties or unexpected perturbations to the observed flow. These LCS cores have the potential to forecast imminent shape changes in the contamination pattern, even before the instability builds up and brings large masses of water or air into motion. Exploiting this potential, the LCS-core analysis developed here provides a model-independent forecasting scheme that relies only on already observed or validated flow velocities at the time the prediction is made. We use this methodology to obtain high-precision forecasts of two major instabilities that occurred in the shape of the Deepwater Horizon oil spill. This is achieved using simulated surface currents preceding the prediction times and assuming that the oil behaves as a passive tracer.

Objective Detection of Oceanic Eddies and the Agulhas Leakage

Mesoscale oceanic eddies are routinely detected from instantaneous velocities derived from satellite altimetry data. While simple to implement, this approach often gives spurious results and hides true material transport. Here it is shown how geodesic transport theory, a recently developed technique from nonlinear dynamical systems, uncovers eddies objectively. Applying this theory to altimetry-derived velocities in the South Atlantic reveals, for the first time, Agulhas rings that preserve their material coherence for several months, while ring candidates yielded by other approaches tend to disperse or leak within weeks. These findings suggest that available velocity-based estimates for the Agulhas leakage, as well as for its impact on ocean circulation and climate, need revision.

On the Lagrangian Dynamics of Atmospheric Zonal Jets and the Permeability of the Stratospheric Polar Vortex

The Lagrangian dynamics of zonal jets in the atmosphere are considered, with particular attention paid to explaining why, under commonly encountered conditions, zonal jets serve as barriers to meridional transport. The velocity field is assumed to be two-dimensional and incompressible, and composed of a steady zonal flow with an isolated maximum (a zonal jet) on which two or more traveling Rossby waves are superimposed. The associated Lagrangian motion is studied with the aid of the Kolmogorov–Arnold–Moser (KAM) theory, including nontrivial extensions of well-known results. These extensions include applicability of the theory when the usual statements of nondegeneracy are violated, and applicability of the theory to multiply periodic systems, including the absence of Arnold diffusion in such systems. These results, together with numerical simulations based on a model system, provide an explanation of the mechanism by which zonal jets serve as barriers to the meridional transport of passive tracers under commonly encountered conditions. Causes for the breakdown of such a barrier are discussed. It is argued that a barrier of this type accounts for the sharp boundary of the Antarctic ozone hole at the perimeter of the stratospheric polar vortex in the austral spring.

Tracing the Early Development of Harmful Algal Blooms on the West Florida Shelf with the Aid of Lagrangian Coherent Structures.

Several theories have been proposed to explain the development of harmful algal blooms (HABs) produced by the toxic dinoflagellate Karenia brevis on the West Florida Shelf. However, because the early stages of HAB development are usually not detected, these theories have been so far very difficult to verify. In this paper we employ simulated Lagrangian coherent structures (LCSs) to trace potential early locations of the development of a HAB in late 2004 before it was transported to a region where it could be detected by satellite imagery. The LCSs, which are extracted from surface ocean currents produced by a data-assimilative HYCOM (HYbrid-Coordinate Ocean Model) simulation, constitute material fluid barriers that demarcate potential pathways for HAB evolution. Using a simplified population dynamics model we infer the factors that could possibly lead to the development of the HAB in question. The population dynamics model determines nitrogen in two components, nutrients and phytoplankton, which are assumed to be passively advected by surface ocean currents produced by the above HYCOM simulation. Two nutrient sources are inferred for the HAB whose evolution is found to be strongly tied to the simulated LCSs. These nutrient sources are found to be located nearshore and possibly due to land runoff.

Rip?current pulses tied to Lagrangian coherent structures

The trapping and ejection of surfzone floating material is examined by unveiling Lagrangian Coherent Structures (LCSs) hidden in the pulsating rip?current surface velocity field produced by a three?dimensional numerical model resolving wave?group induced Very Low Frequency motions (VLFs). LCSs explain the typically observed patchiness of flotsam within the surf zone and the streaky distribution outside of the surf zone. The ejection of surfzone material occurs when filament?like LCSs separate form the main rip?current circulation corresponding to a situation where eddies temporarily extend the rip current beyond the surf zone and subsequently detach. The LCSs support the idea that VLFs form the dominant exchange mechanism of surfzone floating material with the inner shelf.

Zonal Jets as Transport Barriers in Planetary Atmospheres

Abstract The connection between transport barriers and potential vorticity (PV) barriers in PV-conserving flows is investigated with a focus on zonal jets in planetary atmospheres. A perturbed PV staircase model is used to illustrate important concepts. This flow consists of a sequence of narrow eastward and broad westward zonal jets with a staircase PV structure; the PV steps are at the latitudes of the cores of the eastward jets. Numerically simulated solutions to the quasigeostrophic PV conservation equation in a perturbed PV staircase flow are presented. These simulations reveal that both eastward and westward zonal jets serve as robust meridional transport barriers. The surprise is that westward jets, across which the background PV gradient vanishes, serve as robust transport barriers. A theoretical explanation of the underlying barrier mechanism is provided. It is argued that transport barriers near the cores of westward zonal jets, across which the background PV gradient is small, are found in Jupi...

Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean

Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.

Surface ocean mixing inferred from different multisatellite altimetry measurements

Abstract Two sea surface height (SSH) anomaly fields distributed by Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) Altimetry are evaluated in terms of the effects that they produce on mixing. One SSH anomaly field, tagged REF, is constructed using measurements made by two satellite altimeters; the other SSH anomaly field, tagged UPD, is constructed using measurements made by up to four satellite altimeters. Advection is supplied by surface geostrophic currents derived from the total SSH fields resulting from the addition of these SSH anomaly fields to a mean SSH field. Emphasis is placed on the extraction from the currents of Lagrangian coherent structures (LCSs), which, acting as skeletons for patterns formed by passively advected tracers, entirely control mixing. The diagnostic tool employed to detect LCSs is provided by the computation of finite-time Lyapunov exponents. It is found that currents inferred using UPD SSH anomalies support mixing with characteristics similar t...

Coherent water transport across the South Atlantic

The role of mesoscale eddies in transporting Agulhas leakage is investigated using a recent technique from nonlinear dynamical systems theory applied on geostrophic currents inferred from the over two decade long satellite altimetry record. Eddies are found to acquire material coherence away from the Agulhas retroflection, near the Walvis Ridge in the South Atlantic. Yearly, one to four coherent material eddies are detected with diameters ranging from 40 to 280 km. A total of 23 eddy cores of about 50 km in diameter and with at least 30% of their contents traceable into the Indian Ocean were found to travel across the subtropical gyre with minor filamentation. Only one eddy core was found to pour its contents on the North Brazil Current. While the ability of eddies to carry Agulhas leakage northwestward across the South Atlantic is supported by our analysis, this is more restricted than suggested by earlier ring transport assessments.

Zonal Jets as Meridional Transport Barriers in the Subtropical and Polar Lower Stratosphere

Abstract Applications of recent results from dynamical systems theory to the study of transport and mixing in incompressible two-dimensional flows lead to the expectation that, independent of the background potential vorticity (PV) distribution, weakly perturbed zonal jets are associated with barriers that inhibit meridional transport. Here the authors provide evidence in support of this expectation based on the analysis of isentropic winds in the lower stratosphere as produced by the Canadian Middle Atmosphere Model (CMAM), a comprehensive general circulation model. Specifically, barriers to meridional transport are found to be associated with the (eastward) austral polar night jet, for which the meridional gradient of background PV is large, and also for the (westward) boreal summer subtropical jet, for which the background PV gradient is quite small. The identification of the meridional transport barriers is based on the computation of finite-time Lyapunov exponents (FTLEs), which characterize the amou...