The Application of Uncertainty Quantification Techniques and Information Theory to Oil Spill and Ocean Forecasting.

Abstract

Quantifying uncertainties in ocean current forecasts is an important component of formulating a response to an oil spill, e.g. to compute the anticipated oil trajectories. Polynomial Chaos (PC) methods have recently been used to quantify uncertainties in the circulation forecast of the Gulf of Mexico caused by uncertain initial conditions and wind forcing data. The input uncertainties consisted of the amplitudes of perturbation modes whose space-time structure was obtained from Empirical Orthogonal Functions (EOF) decompositions. These e orts were the rst to rely on a PC approach to e ciently quantify uncertainties in an ocean model, and as such have raised a number of issues that we wish to address, namely the realism of the perturbations, the e ective choices in choosing the uncertain variables, the information trade-o s of the di erent uncertain input choices, and the ability to reduce these uncertainties if observational data is available. We explore whether these EOF-based perturbations lead to realistic representation of the uncertainties in the circulation forecast of the Gulf of Mexico. We also use information theoretic metrics to quantify the information gain and the computational trade-o s between di erent wind forcing and initial condition EOF modes. Surface and subsurface model data comparisons show that the observational data falls within the envelope of the ensemble simulations and that the EOF decompositions deliver \realistic" perturbations in the Loop Current region. The result of the computational trade-o s indicate that two initial condition EOF modes are enough to represent the uncertainties in the Loop Current region; while wind forcing EOF modes are necessary in order to capture uncertainties in the coastal zone. This result is consistent with the global sensitivity analysis. The ensemble statistics are then explored using the PC approach and the newly developed contour boxplot method. Specifically, the contour boxplot is used to identify the most representative ensemble member and the outliers. The full probability density functions of sea surface height are estimated using the PC method. With 20 years of satellite observations, the predictability in the circulation forecast of the Gulf of Mexico is investigated using information theory. Finally, we update our knowledge about the uncertain inputs using along track satellite observations. The best initial perturbations are found using the Bayesian optimization approach and the full posterior distributions of the uncertain inputs are estimated using the Bayesian inference framework.