Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics

We study the flow obtained from a three-layer, eddy-resolving quasigeostrophic ocean circulation model subject to an applied wind stress curl. For this model we will consider transport between the northern and southern gyres separated by an eastward jet. We will focus on the use of techniques from dynamical systems theory, particularly lobe dynamics, in the forming of geometric structures that govern transport. By “govern”, we mean they can be used to compute Lagrangian transport quantities, such as the flux across the jet. We will consider periodic, quasiperiodic, and chaotic velocity fields, and thus assess the effectiveness of dynamical systems techniques in flows with progressively more spatio-temporal complexity. The numerical methods necessary to implement the dynamical systems techniques and the significance of lobe dynamics as a signature of specific “events”, such as rings pinching off from a meandering jet, are also discussed

Lagrangian Structures in Very High-Frequency Radar Data and Optimal Pollution Timing

Very High-frequency (VHF) radar technology produces detailed surface velocity maps near the surface of coastal waters. The use of measured velocity data in environmental prediction, however, has remained unexplored. In this paper, we uncover a striking flow structure in coastal radar observations along the coast of Florida. This structure governs the spread of organic contaminants or passive drifters released in the area. We compute the Lyapunov exponents of the VHF radar data to determine optimal release windows in which contaminants are advected efficiently away from the coast and we show that a VHF radar-based pollution release scheme using the hidden flow structure reduces the effect of industrial pollution in the coastal environment

Impacts of rainfall on the water quality of the Newport River Estuary (Eastern North Carolina, USA)

The Newport River Estuary (NPRE), an important North Carolina (NC) shellfish harvesting area, has been experiencing alterations to the land-water interface due to increasing population and coastal development. Water quality degradation in the estuary over the last decade has led to an increase of shellfish harvesting area closures, and has been postulated to be due to non-point source contamination in the form of stormwater. Water samples were taken in the NPRE (n = 179) over a range of weather conditions and all seasons from August 2004 to September 2006. Fecal coliform (FC), as estimated by E. coli (EC), and Enterococcus (ENT) concentrations (MPN per 100 ml) were examined in relation to rainfall levels and distance from land. The relationships among the fecal indicator bacteria (FIB) and environmental parameters were also examined. The data revealed a significant increase in FC concentrations after measured rainfall amounts of 2.54cm (general threshold) and 3.81cm (management action threshold). However, higher than expected FIB concentrations existed during conditions of negligible rainfall (<0.25 cm), indicating a possible reservoir population in the sediment. Overall, stormwater runoff appears to be adversely impacting water quality in the NPRE

Optimal Pollution Mitigation in Monterey Bay Based on Coastal Radar Data and Nonlinear Dynamics

The article of record as published may be found at http://dx.doi.org/10.1021/es0630691High-frequency (HF) radar technology produces detailed velocity maps near the surface of estuaries and bays. The use of velocity data in environmental prediction, nonetheless, remains unexplored. In this paper, we uncover a striking flow structure in coastal radar observations of Monterey Bay, along the California coastline. This complex structure governs the spread of organic contaminants, such as agricultural runoff which is a typical source of pollution in the bay. We show that a HF radar-based pollution release scheme using this flow structure reduces the impact of pollution on the coastal environment in the bay. We predict the motion of the Lagrangian flow structures from finite-time Lyapunov exponents of the coastal HF velocity data. From this prediction, we obtain optimal release times, at which pollution leaves the bay most efficiently.Office of Naval Research grant N00014-01-1-0208ASAP MURI N00014-02-1-0826Office of Naval Research grant N00014-01-1-0208ASAP MURI N00014-02-1-082

Leaking method approach to surface transport in the Mediterranean Sea from a numerical ocean model

We use Lagrangian diagnostics (the leaking and the exchange methods) to characterize surface transport out of and between selected regions in the Western Mediterranean. Velocity fields are obtained from a numerical model. Residence times of water of Atlantic origin in the Algerian basin, with a strong seasonal dependence, are calculated. Exchange rates between these waters and the ones occupying the northern basin are also evaluated. At surface, northward transport is dominant, and involves filamental features and eddy structures that can be identified with the Algerian eddies. The impact on these results of the presence of small scale turbulent motions is evaluated by adding Lagrangian diffusion.Comment: 21 pages using the elsart style. Higher resolution figures available from http://www.imedea.uib.es/physdept/publications/showpaper_en.php?indice=119

Open-boundary modal analysis: Interpolation, extrapolation, and filtering

Increasingly accurate remote sensing techniques are available today, and methods such as modal analysis are used to transform, interpolate, and regularize the measured velocity fields. Until recently, the modes used did not incorporate flow across an open boundary of the domain. Open boundaries are an important concept when the domain is not completely closed by a shoreline. Previous modal analysis methods, such as those of Lipphardt et al. (2000), project the data onto closed-boundary modes, and then add a zero-order mode to simulate flow across the boundary. Chu et al. (2003) propose an alternative where the modes are constrained by a prescribed boundary condition. These methods require an a priori knowledge of the normal velocity at the open boundary. This flux must be extrapolated from the data or extracted from a numerical model of a larger-scale domain, increasing the complexity of the operation. In addition, such methods make it difficult to add a threshold on the length scale of open-boundary processes. Moreover, the boundary condition changes in time, and the computation of all or some modes must be done at each time step. Hence real-time applications, where robustness and efficiency are key factors, were hardly practical. We present an improved procedure in which we add scalable boundary modes to the set of eigenfunctions. The end result of open-boundary modal analysis (OMA) is a set of time and data independent eigenfunctions that can be used to interpolate, extrapolate and filter flows on an arbitrary domain with or without flow through segments of the boundary. The modes depend only on the geometry and do not change in time

Space/Time Analysis of Fecal Pollution and Rainfall in an Eastern North Carolina Estuary

The Newport River Estuary (NPRE) is a high priority shellfish harvesting area in eastern North Carolina (NC) that is impaired due to fecal contamination, specifically exceeding recommended levels for fecal coliforms. A hydrologic-driven mean trend model was developed, as a function of antecedent rainfall, in the NPRE to predict levels of E. coli (EC, measured as a proxy for fecal coliforms). This mean trend model was integrated in a Bayesian Maximum Entropy (BME) framework to produce informative Space/Time (S/T) maps depicting fecal contamination across the NPRE during winter and summer months. These maps showed that during dry winter months, corresponding to the oyster harvesting season in NC (October 1st to March 30th), predicted EC concentrations were below the shellfish harvesting standard (14 MPN per 100 ml). However, after substantial rainfall 3.81 cm (1.5 inches), the NPRE did not appear to meet this requirement. Warmer months resulted in the predicted EC concentrations exceeding the threshold for the NPRE. Predicted ENT concentrations were generally below the recreational water quality threshold (104 MPN per 100 ml), except for warmer months after substantial rainfall. Once established, this combined approach produces near real-time visual information on which to base water quality management decisions

Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a "heuristic argument" that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper "side-by-side" comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field ("time averages") are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.Comment: 52 pages, 25 figure

Lagrangian transport through an ocean front in the North-Western Mediterranean Sea

We analyze with the tools of lobe dynamics the velocity field from a numerical simulation of the surface circulation in the Northwestern Mediterranean Sea. We identify relevant hyperbolic trajectories and their manifolds, and show that the transport mechanism known as the `turnstile', previously identified in abstract dynamical systems and simplified model flows, is also at work in this complex and rather realistic ocean flow. In addition nonlinear dynamics techniques are shown to be powerful enough to identify the key geometric structures in this part of the Mediterranean. In particular the North Balearic Front, the westernmost part of the transition zone between saltier and fresher waters in the Western Mediterranean is interpreted in terms of the presence of a semipermanent ``Lagrangian barrier'' across which little transport occurs. Our construction also reveals the routes along which this transport happens. Topological changes in that picture, associated with the crossing by eddies and that may be interpreted as the breakdown of the front, are also observed during the simulation.Comment: 34 pages, 6 (multiple) figures. Version with higher quality figures available from http://www.imedea.uib.es/physdept/publications/showpaper_en.php?indice=1764 . Problems with paper size fixe

Transport in an idealized three-gyre system with application to the Adriatic Sea

Author Posting. © American Meteorological Society, 2009. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 39 (2009): 675-690, doi:10.1175/2008JPO3975.1.Motivated by observations of surface drifters in the Adriatic Sea, transport in a three-gyre system is studied with the aid of dynamical systems techniques. Particular attention is paid to the issue of intergyre transport. The velocity field is assumed to be two-dimensional and incompressible and composed of a steady three-gyre background flow on which a time-dependent perturbation is superimposed. Two systems of this type are considered: 1) an observationally motivated, analytically prescribed model consisting of a steady background on which a multiperiodic time-dependent perturbation is superimposed, and 2) an observationally based model of the Adriatic Sea consisting of the mean surface circulation derived from surface drifter trajectories on which a time-dependent altimetry-based perturbation velocity field is superimposed. It is shown that for a small perturbation to the steady three-gyre background, two of the gyres exchange no fluid with the third gyre. When the perturbation strength exceeds a certain threshold, transport between all three gyres occurs. This behavior is described theoretically, illustrated using the analytic model and shown to be consistent with the observationally based model of the Adriatic. The relevance of the work presented to more complicated multiple-gyre problems is discussed.This work was supported by the National Science Foundation Grants CMG0417425 and CMG0825547