A Fuzzy-Based Framework for Assessing Uncertainty in Drift Prediction Using Observed Currents and Winds

This paper proposes a fuzzy number—based framework for quantifying and propagating uncertainties through a model for the trajectories of objects drifting at the ocean surface. Various sources of uncertainty that should be considered are discussed. This model is used to explore the effect of parameterizing direct wind drag on the drifting object based on its geometry, and using measured winds to parameterize shear and rotational dynamics in the ocean surface currents along with wave-driven circulation and near-surface wind shear. Parameterizations are formulated in a deterministic manner that avoids the commonly required specification of empirical leeway coefficients. Observations of ocean currents and winds at Ocean Station Papa in the northeast Pacific are used to force the trajectory model in order to focus on uncertainties arising from physical processes, rather than uncertainties introduced by the use of atmospheric and hydrodynamic models. Computed trajectories are compared against observed trajectories from five different types of surface drifters, and optimal combinations of forcing parameterizations are identified for each type of drifter. The model performance is assessed using a novel skill metric that combines traditional assessment of trajectory accuracy with penalties for overestimation of uncertainty. Comparison to the more commonly used leeway method shows similar performance, without requiring the specification of empirical coefficients. When using optimal parameterizations, the model is shown to correctly identify the area in which drifters are expected to be found for the duration of a seven day simulation.

Determining an optimal transport velocity in the marginal ice zone using operational ice-ocean prediction systems

Knowledge of transport in the marginal ice zone (MIZ) is critical for operations in the Arctic and associated emergency response applications, for example, the transport of pollutants, such as oil, as well as predicting drift associated with search and rescue operations. This paper proposes a general transport equation for the MIZ that can be used for operational purposes in the MIZ. This equation is designed to use a mean velocity of the ice and water velocity, which is weighted by the ice concentration. A key component is the introduction of a leeway coefficient for both the ocean and ice components. These leeway coefficients are determined by minimizing the velocity error between the transport model and observed drifter velocity in the MIZ. These leeway values are found to be 3 % of the wind for the water leeway and 2 % and 30° to the right of the wind for the ice leeway, which are consistent with "rule of thumb" values for surface drifters and sea ice respectively. This general transport model is compared with other transport models and the error is reduced by a factor of 2 compared with traditional transport models for 48 hour lead times. The inclusion of a leeway coefficient in the ice is the key component to reduce trajectory errors in the MIZ.

Connectivity Analysis Applied to Mesoscale Eddies in the Western Mediterranean Basin

The Western Mediterranean basin (WMED) is characterized by the presence of energetic and dynamic mesoscale cyclonic and anticyclonic eddies. They mainly originate along the Algerian and the Northern currents and have a large influence on the basin circulation. Eddies can last for months, with longer lifetimes associated with the anticyclones, which can move far from their areas of origin. As they partially isolate and transfer water masses, they also have an impact on water properties (physical, chemical and biological), pollutant’s dispersion and transport of eggs, larvae and planktonic organisms. In this study, a connectivity analysis method is applied to the anticyclonic eddies (AEs) identified by an automated hybrid detection and tracking algorithm south of 42° N in the WMED. The same methodology is also applied to the trajectories of Lagrangian surface drifters available in the study area. The purpose is to highlight the connections between different areas of the basin linked to eddy activities in addition to the connectivity due to the mean surface circulation. Drifter data analysis showed that all the WMED sub-basins are strongly interconnected, with the mean surface circulation allowing a shortcut connection among many areas of the basin. The connectivity analysis of the AEs tracks shows that although AEs are ubiquitous in the WMED, their connectivity is limited to well-defined regions, depending on their origin location. Three main regions: the south-western, the south-eastern and the northern parts of the basin are characterized by AEs recirculation, with sporadic export of eddies to the other WMED zones.

Cyclonic circulation and climatology of SST, CHL and wind stress curl in a semi-enclosed bay (Bahía de La Paz, Gulf of California)

The first direct current observations (with LADCP and surface drifters) in Bahía de La Paz, a bay in the southwestern Gulf of California (GC), concur with previous reports that the main dynamical feature during summer is a closed cyclonic circulation. However, we found that geostrophic calculations overestimate the speed of the orbital velocity: actual speeds (0.20-0.25 m s-1) were ~25-40% lower than those estimated from geostrophic balance (0.25-0.35 m s-1). The reason is that the centrifugal force cannot be neglected in this case. The mean rotation period during ship-borne observations in August 2004 was ~1.4 days, but it varied during the time that surface drifters were inside the bay, from ~1-2 days in June-July to ~2.5-3 days in September-October. The analysis of satellite data (wind velocity, sea surface temperature and chlorophyll) show that from May to September the wind stress curl is strong and cyclonic, and the surface of the bay is cooler and richer than the adjacent Gulf of California waters, which could be attributed to the positive wind stress curl. This positive wind stress curl on the bay is part of a larger-scale positive wind stress curl distribution that surrounds the southern part of the Baja California Peninsula during summer, probably enhanced in the bay by local topography features. Although there is an exchange of water between the bay and the GC, its effect on the dynamics is poorly known.

Properties and evolution of a submesoscale cyclonic spiral

The evolution of a submesoscale cyclonic spiral of 1 km in diameter is simulated with ROMS (Regional Ocean Modeling System) using 33.3 m horizontal resolution in a triple-nested configuration. The generation of the spiral starts from a dense filament that is rolled into a vortex and detaches from the filament. During spin-up, extreme values are attained by various quantities, that are organized in single-arm and multi-arm spirals. The spin-down starts when the cyclone separates from the filament. At the same time, the horizontal speed develops a dipole-like pattern and isotachs form closed contours around the vortex center. The amplitudes of most quantities decrease significantly, but the instantaneous vertical velocity w exhibits high-frequency oscillations and more pronounced extremes than during spin-up. The oscillations are due to vortex Rossby waves (VRWs), that circle the eddy counterclockwise and generate multi-arm spirals with alternating signs by means of azimuthal vorticity advection. Experiments with virtual surface drifters and isopycnal floats indicate downwelling everywhere near the surface. The downwelling is most intense in the center of the spiral at all depth levels, leading to a radial outflow in the thermocline and weak upwelling at the periphery. This overturning circulation is driven by convergent near-surface flow and associated subduction of isopycnals. While the downwelling in the center may support the export of particulate organic carbon from the mixed layer into the main thermocline, the upwelling at the periphery effectuates an upward isopycnal transport of nutrients, enhancing the growth of phytoplankton in the euphotic zone.

Observing and quantifying kinematic properties and lagrangian coherent structures of ocean flows using drifter experiments

This thesis analyzes data from two types of unique drifter experiments in order to characterize two aspects of ocean flows that are often difficult to study. First, vertical velocities and their associated transport processes are often challenging to observe in the real ocean since vertical velocities are typically orders of magnitude smaller than horizontal velocities in mesoscale and submesoscale flows. Second, Lagrangian coherent structures (LCS) are features which categorize ocean flows into regimes of distinct behavior. These structures are also difficult to quantify in the real ocean, since sets of gridded trajectories from real ocean data (rather than model fields) are rarely available. The first experiment uses drifters drogued at multiple depths in the Alboran Sea to observe and characterize the ocean’s vertical structure, particularly near a strong front where vertical velocities are expected to be much stronger than other regions of the Ocean. The second experiment uses a roughly gridded pattern of surface drifters in the Gulf of Mexico to study LCSs as quantified by methods from dynamical systems such as finitetime Lyapunov exponents (FTLEs), trajectory arc-length, correlation dimension, dilation, Lagrangian-averaged vorticity deviation (LAVD), and spectral clustering. This thesis includes the first attempt to apply these dynamical systems techniques to real drifters for LCS detection. Overall, these experiments and the methods used in this paper are shown to be promising new techniques for quantifying both the vertical structure of ocean flows and Lagrangian Coherent Structures of flows using real drifter data. Future work may involve modified versions of the experiments, with denser sets of ocean drifters in the horizontal and/or vertical directions.

Mechanisms of Lateral Spreading in a Near-Field Buoyant River Plume Entering a Fjord

Observations collected from a fast-flowing buoyant river plume entering the head of Doubtful Sound, New Zealand, were analysed to examine the drivers of plume lateral spreading. The near-field plume is characterised by flow speeds of over 2 ms−1, and strong stratification (N2 > 0.1 s−2), resulting in enhanced shear which supports the elevated turbulence dissipation rates (ϵ > 10−3 W kg−1). Estimates of plume lateral spreading rates were derived from the trajectories of Lagrangian GPS surface drifters and from cross-plume hydrographic transects. Lateral spreading rates derived from the latter compared favourably with estimates derived from a control volume technique in a previous study. The lateral spreading of the plume was driven by a baroclinic pressure gradient toward the base of the plume. However, spreading rates were underestimated by the surface drifters. A convergence of near-surface flow from the barotropic pressure gradient concentrated the drifters within the plume core. The combination of enhanced internal turbulence stress and mixing at the base of the surface layer, and the presence of steep fjord sidewalls likely reduced the rate of lateral spreading relative to the theoretical spreading rate. The estimates of plume width from the observations provided evidence of scale-dependent dispersion which followed a 4/3 power law. Two theoretical models of dispersion, turbulence and shear flow dispersion, were examined to assess which was capable of representing the observed spreading. An analytical horizontal shear-flow dispersion model generated estimates of lateral dispersion that were consistent with the observed 4/3 law of dispersion. Therefore, horizontal shear dispersion appeared to be the dominant mechanism of dispersion, thus spreading, in the surface plume layer.

Observational Evidence and Open Questions on the Role of Internal Tidal Waves on the Concentration and Transport of Floating Plastic Debris

Tidal currents flowing over benthic relief (e.g., banks, shelf break) can produce large internal waves. These waves propagate away from their origin and are capable of crossing the continental shelf and seas. Studies of shoreward transport of larval invertebrates and fish by these internal waves unintentionally tested whether they can capture, concentrate and transport floating plastic. Plastic surface drifters deployed in front of sets of internal wave convergences were often captured (>90% captured) and transported kilometers by the waves. There are, however, few investigations into how internal tidal waves may affect the fate and distribution of floating plastic waste. A number of areas of future research are suggested: (1) How much floating plastic is found in internal wave convergences? (2) How buoyant must floating plastic be to be captured by internal waves? (3) Why did only some sets of internal waves cause concentration and transport of surface material? (4) Do concentration and transport of floating plastic vary over the spring/neap tidal cycle? (5) Do seasonal changes in the depth of the pycnocline alter the transport of floating plastic by internal waves? (6) Plastic debris deposited on shore may not be evenly distributed, but may be more abundant landward of sites on the shelf break that more readily generate large internal waves. (7) Internal waves that travel long distances (10–100 s of km) have the potential to accumulate large amounts of plastic debris. (8) At locations where internal waves cross the continental shelf, how far offshore does transport commence?

Extracting statistically significant eddy signals from large Lagrangian datasets using wavelet ridge analysis, with application to the Gulf of Mexico

A method for objectively extracting the displacement signals associated with coherent eddies from Lagrangian trajectories is presented, refined, and applied to a large dataset of 3770 surface drifters from the Gulf of Mexico. The method, wavelet ridge analysis, is a general method for the analysis of modulated oscillations, here modified to be more suitable to the eddy-detection problem. A means for formally assessing statistical significance is introduced, addressing the issue of false positives arising by chance from an unstructured turbulent background and opening the door to confident application of the method to very large datasets. Significance is measured through a frequency-dependent comparison with a stochastic dataset having statistical and spectral properties that match the original, but lacking organized oscillations due to eddies or waves. The application to the Gulf of Mexico reveals major asymmetries between cyclones and anticyclones, with anticyclones dominating at radii larger than about 50 km, but an unexpectedly rich population of highly nonlinear cyclones dominating at smaller radii. Both the method and the Gulf of Mexico eddy dataset are made freely available to the community for noncommercial use in future research.

On the non-geostrophic appearance of some mean surface velocity observations in the Gulf of Mexico

A previous study of currents in the Gulf of Mexico by the author used long-term means from three independent data sources. Ship-drift results are in good agreement with surface drifters, but these two do not agree with satellite sea-surface heights (SSH). The agreement between the first two suggested the possibility that there could be errors in the SSH or that the mean surface flow is not in geostrophic balance. The present results, using the addition of a fourth long-term mean from hydrographic data, which agrees with the SSH, resolves the issue. The lack of agreement between different long-term means is from inadequate coverage in space and time in data from ship drifts and drifters.