Abstract
Motivated by the problem of predicting the transport of material in the ocean, the present work went after two general problems. One is to use a probabilistic Lagrangian oil model to forecast the fate of an oil spill. The other is to use a dense array of Lagrangian observations to estimate the near surface submesoscale velocity field. Both problems were tackled with methodologies based on the reconstruction of response surfaces. In the first part, an uncertainty quantification methodology based on a non- intrusive polynomial chaos approach is developed for the forecasting of oceanic oil spills. This allows the model’s output to be presented in a probabilistic framework so that its predictions reflect the uncertainty in its input data. The new capability is illustrated by simulating the far-field dispersal of oil in a Deepwater Horizon blowout scenario. The uncertain input consisted of ocean currents and oil droplet size data, and the main model output analyzed is the ensuing oil concentration in the Gulf of Mexico. A 1331 member ensemble was used to construct a surrogate for the model which was then mined for statistical information. The mean and standard deviations in the oil concentration were calculated for up to 30 days, and the total contribution of each input parameter to the models uncertainty was quantified at different depths. Also, probability density functions of oil concentration were constructed by sampling the surrogate and used to elaborate probabilistic hazard maps of oil impact. The surrogate performance was constantly monitored in order to demarcate the space-time zones where its estimates are reliable. In the second part, a dense array of drifters data is used to reconstruct the near- surface velocity field. The reconstruction is carried out by a procedure known as Gaussian process regression, that statistically interpolates the observations in both space and time. Because the spacing of the drifters evolves with the flow causing the resolution that they provide to vary in space and time, it is important to be able to characterize where and when the estimated velocity field is more or less accurate, which we do by providing fields of interpolation errors. The interpolation procedure uses a covariance function to characterize the flow correlations in space and time. One novelty in this approach is that it allows the data to determine the correlation scales along with the appropriate amplitude of observational noise at these scales. This part is divided in two segments, with two distinct analyses being conducted: in the first one, velocity estimates from 320 drifters are used to reconstruct the surface flow field inside a frontal cyclonic eddy during a 12 hours period. Results show the presence of strong convergence zones inside the cyclone with characteristics of submesoscale fronts, displaying strong relative vorticity and strain rate. In the second segment, a framework to estimate the flow field over a submesoscale front is presented. The framework is based on adjusting the coordinate system to the alignment of the drifters. An extensive testing considering 14 different covariance functions show that this strategy improves considerably the velocity reconstructions over a strong front when compared to a Cartesian coordinate system.