Ocean surface drift modelling with uncertainty assessment using fuzzy number theory

Date

2023-07-20

Authors

Blanken, Hauke

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Abstract

Predicting the drift of objects floating at the ocean surface is a challenging task, with significant implications on marine emergency operations such as oil spill response and search and rescue efforts. Object drift is governed by a combination of currents, winds, and waves at the ocean surface, and depends strongly on object geometry. This introduces considerable uncertainty into drift prediction, as the model uncertainty from hydrodynamic models for these governing forces is aggregated and combined with systemic uncertainty about their respective influence on the drift of objects with various geometries. The first portion of this thesis examines the observed drift and dispersion of 206 GPS-tracked drifting buoys deployed in a fjord system on the west coast of Canada, which is subject to proposed expansion of shipping for oil and gas resource extraction. The observed mean drift patterns are found to be best explained by considering a combination of observed near-surface currents and winds, but the trajectories of individual buoys are characterized by significant dispersion around the mean. This dispersion results in buoys grounding against the shoreline on timescales of 12 15 hours, and corresponds with observed changes in the dispersion regime from near-field to far-field. Drift tracks exhibit fractal characteristics, and dispersion is found to be well modelled using fractional Brownian motion, rather than a traditional random- walk. Based on this, a statistical model for surface drift in the region is proposed, and shown to skillfully reproduce historical observations of sheening from an oil spill in the region. In the second portion of the thesis, uncertainty assessment in drift prediction us- ing fuzzy numbers is introduced and the relationship between forcing from currents, wind, and waves is examined in detail. Forcing data is taken from an observing platform in the northeast Pacific (Ocean Station Papa). Uncertainty in the forcing data is characterized from reported instrument uncertainty and spectral estimates of energy at unresolved time scales. This uncertainty is expressed and aggregated as fuzzy numbers, and propagated through seven day simulations of the trajectories of a set of surface drifting buoys with five different geometries using the transformation method. For generality, the effect of buoy geometry is accounted for deterministically, thereby avoiding traditionally used empirical coefficients. All possible linear combi- nations of forcing terms are explored, and the optimal combination of forcing terms for each drifter type is identified through the use of a novel skill metric. With the optimal forcing combination, the model is found to correctly identify the area where a buoy is expected to be found for the duration of the simulation. Comparison with the commonly used nine parameter leeway method shows similar performance, but without the need for object-specific empirical coefficients. Finally, the fuzzy-based method for propagating uncertainty in drift trajectory models is extended to spatiotemporally variable velocity fields. For this, a 4th-order Runge-Kutta solver for the integration of velocities, with inverse-distance weighting interpolation, is expanded to include possibility as an additional dimension. Perfor- mance of the method is demonstrated by tracking particles through one revolution of a monopole vortex, the strength of which varies sinusoidally with distance from the center. Both steady and unsteady maximum amplitudes are considered, and a steady uncertainty is prescribed as a fuzzy number. The model is shown to produce adequate results with reasonable computational effort, and the free parameters of the simulation are optimized through a sensitivity analysis.

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Keywords

oceanography, drift prediction, fuzzy number, uncertainty, numerical modelling, dynamics, ocean physics

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