Better quantitative understanding and accurate data-assimilative predictions of the three-dimensional and time-dependent ocean acidification (OA) processes in coastal regions is urgently needed for the protection and sustainable utilization of ocean resources. In this paper, we extend and showcase the use of our MIT-MSEAS systems for high-resolution coupled physical-biogeochemical-acidification simulations and Bayesian learning of OA models in Massachusetts Bay, starting with simple empirical and equilibrium OA models. Simulations are shown to have reasonable skill when compared to available in situ and remote data. The impacts of wind forcing, internal tides, and solitary waves on water transports and mixing, and OA fields, are explored. Strong wind events are shown to reset circulations and the OA state in the Bay. Internal tides increase vertical mixing of waters in the shallow regions. Solitary waves propagating off Stellwagen Bank coupled with lateral turbulent mixing provide a pathway for exchange of surface and deep waters. Both of these effects are shown to impact biological activity and OA. A mechanism for the creation of multiple subsurface chlorophyll maxima is presented, involving wind-induced upwelling, internal tides, and advection of near surface fields. Due to the measurement sparsity and limited understanding of complex OA processes, the state variables and parameterizations of OA models are very uncertain. We thus present a proof-of-concept study to simultaneously learn and estimate the OA state variables and model parameterizations from sparse observations using our novel dynamics-based Bayesian learning framework for high-dimensional and multi-disciplinary estimation. Results are found to be encouraging for more realistic OA model learning.

The rising popularity of aquaculture has led to increased research in offshore algae farming. Central to the efficient operation of such farms is the need for (i) accurate models of the dynamic ocean environment including macroalgae ecosystem dynamics and (ii) intelligent path planning algorithms for autonomous vessels that optimally manage and harvest the algae fields. In this work, we address both these challenges. We first integrate our modeling system of the ocean environment with a model for forecasting the growth and decay of algae fields. These fields are then input into our exact optimal path planning, augmented with the optimal harvesting goals and solved using level set methods. The resulting path is a provable time-optimal route for the vehicle to follow under the constraint of having to monitor or harvest a specified amount of the field to collect. To demonstrate the theory, we simulate algal growth in both idealized and realistic data-assimilative dynamic ocean environments and compute the optimal paths for an autonomous collection vehicle. We demonstrate that our theory and schemes can be used to compute the optimal path in a variety of scenarios – harvesting in the case of discrete farms, a large kelp farm field, or large scale dynamic algal bloom fields.

We describe and investigate several Dynamic Mode Decomposition (DMD) and reduced order projection methods for regional stochastic ocean predictions. We then showcase some of their results as applied to a 300-member set of ensemble forecasts from the POSYDON-POINT sea experiment in the Middle Atlantic–New York Bight region for the period 23–27 August 2018 as well as to a 42-day data-driven reanalysis from the AWACS–SW06 sea experiment in the Middle Atlantic Bight region for the period 14 August to 24 September 2006. We discuss these results for use by autonomous platforms in uncertain scenarios as well the combination of DMD with ideas from large-ensemble forecasting and Dynamically-Orthogonal (DO) differential equations.

Congratulations to Jing Lin on his graduation! Jing succesfully defended and received his PhD from Mechanical Engineering for his research on “Bayesian Learning for High-Dimensional Nonlinear Dynamical Systems: Methodologies, Numerics and Applications to Fluid Flows” with our MSEAS group at MIT. We wish all the best to Jing for his next steps!

We study the performance of sparse regression methods and propose new techniques to distill the governing equations of nonlinear dynamical systems from data. We start from the recently proposed generic methodology of learning interpretable equation forms from data, followed by performance of least absolute shrinkage and selection operator (LASSO) for this purpose. We first develop an algorithm that uses the dual of LASSO optimization for higher accuracy and stability. We then derive a second algorithm that learns the candidate function library in a dynamic data driven applications systems (DDDAS) manner to distill the governing equations of the dynamical system. This is achieved via sequentially thresholded ridge regression (STRidge) over a orthogonal polynomial space. The performance of the methods is illustrated using the Lorenz 63 system and a marine ecosystem model.