Abstract

The ocean is a prime example of multiscale nonlinear fluid dynamical system. Ocean fields are usually complex, with intermittent features and nonstationary heterogeneous statistics. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters, and even the model parameterizations and equations themselves. To reduce uncertainties and allow long-duration measurements, the energy consumption of ocean observing platforms need to be optimized. Predicting the distributions of reachable regions, time-optimal paths, and risk-optimal paths in uncertain, strong and dynamic flows is also essential for their optimal and safe operations. Motivated by the above needs, the objectives of this thesis are to develop and apply the theory, schemes, and computational systems for: (i) Dynamically Orthogonal ocean primitive-equations with a nonlinear free-surface, in order to quantify uncertainties and predict probabilities for four-dimensional (time and 3-d in space) coastal ocean states, respecting their nonlinear governing equations and non-Gaussian statistics; (ii) Stochastic Dynamically Orthogonal level-set optimization for energy-optimal path planning of autonomous agents in coastal regions, rigorously incorporating realistic ocean predictions; (iii) Probabilistic predictions of reachability, time-optimal paths and risk-optimal paths in uncertain, strong and dynamic flows.

The theoretical and computational foundation is laid out and several idealized-to-realistic applications are demonstrated. Examples in the Middle Atlantic Bight region, Northwest Atlantic, and northern Indian ocean are showcased. The probabilistic prediction and path planning methodologies developed here are PDE-based and provide stochastic ocean fields, and energy-optimal, stochastic time-optimal and risk-optimal predictions without heuristics. Computationally, the new methods are several orders of magnitude faster than direct Monte Carlo methods.

Such technologies can be utilized for several commercial and societal applications, now and in the future. Specifically, the probabilistic ocean predictions can be input to a technical decision aide for a sustainable fisheries co-management program in India, which has the potential to provide environment friendly livelihoods to millions of marginal fishermen. The risk-optimal path planning equations can be employed in real-time for efficient ship routing to reduce greenhouse gas emissions and save operational costs.

Arkopal Dutt, a third year graduate student, has been selected to receive a AGU Fall Meeting Student Travel Award to attend the 2017 American Geophysical Union Fall Meeting, to be held from December 11 to 15, 2017, in New Orleans, Louisiana, U.S.A.

Ocean scientists have dreamed and recently started to realize an ocean observing revolution with autonomous observing platforms and sensors. Critical questions to be answered by such autonomous systems are where, when, and what to sample for optimal information, and how to optimally reach the sampling locations. Definitions, concepts, and progress towards answering these questions using quantitative predictions and fundamental principles are presented. Results in reachability and path planning, adaptive sampling, machine learning, and teaming machines with scientists are overviewed. The integrated use of differential equations and theory from varied disciplines is emphasized. The results provide an inference engine and knowledge base for expert autonomous observing systems. They are showcased using a set of recent at-sea campaigns and realistic simulations. Real-time experiments with identical AUVs in the Buzzards Bay and Vineyard Sound region first show that our predicted time-optimal paths were faster than shortest distance paths. Deterministic and probabilistic reachability and path forecasts issued and validated for gliders and floats in the northern Arabian Sea are then presented. Novel Bayesian adaptive sampling for hypothesis testing and optimal learning are finally shown to forecast the observations most informative to estimate the accuracy of model formulations, the values of ecosystem parameters and dynamic fields, and the presence of Lagrangian Coherent Structures.

A pressing environmental question facing the ocean is the potential impact of possible deep-sea mining activities. This work presents our initial results in developing an ocean and plume modeling system for the Bismark Sea where deep sea mining operations will probably take place. We employ the MSEAS modeling system to both simulate the ocean and to downscale initial conditions from a global system (HYCOM) and tidal forcing from the global TPXO-8 Atlas. We found that at least 1.5 km resolution was needed to adequately resolve the multiscale flow fields. In St. Georges channel, the interaction between the tides, background currents, and underlying density fields increased the subtidal flows. Comparing to historical transport estimates, we showed that tidal forcing is needed to maintain the correct subtidal transport through that Channel. Comparisons with past simulations and measured currents all showed good agreement between the MSEAS hindcasts. Quantitative comparisons made between our hindcasts and independent synoptic ARGO profiles showed that the hindcasts beat persistence by 33% to 50%. These comparisons demonstrated that the MSEAS current estimates were useful for assessing plume advection. Our Lagrangian transport and coherence analyses indicate that the specific location and time of the releases can have a big impact on their dispersal. Our results suggest that ocean mining plumes can be best mitigated by managing releases in accord with such ocean modeling and Lagrangian transport forecasts. Real-time integrated mining-modeling-sampling is likely to provide the most effective mitigation strategies.