Numerical turbulence simulations typically involve parameterizations such as Large Eddy Simulations (LES). Applications to geophysical flows, especially ocean flows, are further complicated by the presence of complex topography and interior landforms such as coastlines, islands, and capes. In this work, we extend pseudo-spectral quasi-geostrophic (QG) numerical schemes and GPU-based solvers to simulate flows with coastal boundaries using the Brinkman volume penalization approach. We incorporate sponging and a splitting scheme to handle inflow and aperiodic boundary conditions. We evaluate four analytical sub-grid-scale (SGS) closures based on the eddy viscosity hypothesis: the standard Smagorinsky and Leith closures, and their dynamic variants. We show applications to QG flows past circular islands and capes with the β-plane approximation. We perform both a priori analysis of the SGS closure terms as well as a posteriori assessment of the SGS terms and simulated vorticity fields. Our results showcase differences between the various closures, especially their approach to phase and feature reconstruction errors in the presence of coastal boundaries.

In this paper, we use our MIT Multidisciplinary Simulation, Estimation, and Assimilation Systems (MSEAS) including Error Subspace Statistical Estimation (ESSE) large-ensemble forecasting to provide real-time probabilistic forecasts for the Gulf of Mexico during the collaborative GRand Adaptive Sampling Experiment (GRASE) from April to September 2025. These forecasts are used for optimal planning and adaptive sampling for multiple platforms deployed during the experiment. We highlight real-time forecasts for probabilistic glider reachability and optimal planning. We showcase mutual information forecasts for optimal adaptive sampling with gliders and floats, maximizing information about the Loop Current (LC) and its eddies (LCEs). We showcase reachability and flow map forecasts for floats, characterizing water mass transports and eddy filamentations. We present probabilistic LCE forecasts using clustering techniques. Finally, we guide two gliders to recovery points using reachability and heading forecasts.

The first steps towards integrating autonomous monitoring, probabilistic forecasting, reachability analysis, and adaptive sampling for the Gulf of Mexico were demonstrated in real-time during the collaborative Mini-Adaptive Sampling Test Run (MASTR) ocean experiment, which took place from February to April 2024. The emphasis of this contribution is on the use of the MIT Multidisciplinary Simulation, Estimation, and Assimilation Systems (MSEAS) including Error Subspace Statistical Estimation (ESSE) large-ensemble forecasting and path planning systems to predict ocean fields and uncertainties, forecast reachable sets and optimal paths for gliders, and guide sampling aircraft and ocean vehicles toward the most informative observations. Deterministic and probabilistic ocean forecasts are exemplified and linked to the variability of the Loop Current (LC) and LC Eddies, demonstrating predictive skill by real-time comparisons to independent data. Risk forecasts in terms of probabilities of currents exceeding 1.5 kt were provided. The most informative sampling patterns for Remote Ocean Current Imaging System (ROCIS) flights were forecast using mutual information between surface currents and density anomaly. Finally, we guided four underwater gliders using probabilistic reachability and path-planning forecasts.

Accurate numerical simulation and modeling of ocean dynamics is playing an increasingly large role in scientific ocean applications. However, resolving these dynamics with traditional computational techniques can often be prohibitively expensive, necessitating the creation of next-generation high-order ocean models. In this work, we apply the local discontinuous Galerkin (LDG) and hybridizable discontinuous Galerkin (HDG) finite element methodology to discretize the ocean equations with a free-surface. We provide comparison of the strengths and weaknesses of the two formulations in terms of accuracy, efficiency, and scalability, and provide detailed discussion of numerical choices and their consequences as they relate to ocean modeling. We verify our methodology with numerical experiments and results from nonhydrostatic gravity wave theory.

To cleanup marine plastics, accurate modeling is needed. We outline and illustrate a new partial-differential-equation methodology for characterizing and modeling plastic transports in time and space (4D), showcasing results for Massachusetts Bay. We couple our primitive equation model for ocean dynamics with our composition based advection for Lagrangian transport. We show that the ocean physics predictions have skill by comparison with synoptic data. We predict the fate of plastics originating from four sources: rivers, beach and nearshore, local Bay, and remote offshore. We analyze the transport patterns and the regions where plastics accumulate, comparing results with and without plastic settling. Simulations agree with existing debris and plastics data. They also show new results: (i) Currents set-up by wind events strongly affect floating plastics. Winds can for example prevent Merrimack outflows reaching the Bay; (ii) There is significant chaotic stirring between nearshore and offshore floating plastics as explained by ridges of Lagrangian Coherent Structures (LCSs); (iii) With 4D plastic motions and settling, plastics from the Merrimack and nearshore regions can settle to the seabed before offshore advection; (iv) Internal waves and tides can bring plastics downward and out of main currents, leading to settling to the deep bottom. (v) Attractive LCSs ridges are frequent in the northern Cape Cod Bay, west of the South Shore, and southern Stellwagen Bank. They lead to plastic accumulation and sinking along thin subduction zones.

To understand the dynamics and health of marine ecosystems such as lagoons and coral reefs as well as to understand the impact of human activities on these systems, it is imperative to predict the residence times of water masses and connectivity between ocean domains. In the present work, we consider the pristine lagoons and coral reefs of the Red Sea as an example of such sensitive ecosystems, with a large number of marine species, many of which are unique to the region. To study the residence times and connectivity patterns, we make use of recent advances in dynamic three-dimensional Lagrangian analyses using partial differential equations. Specifically, we extend and apply our novel efficient flow map composition scheme to predict the time needed for any particular water parcel to leave the domain of interest (i.e., a lagoon) as well as the time for any particular water parcel to enter that domain. These spatiotemporal residence time fields along with four-dimensional Lagrangian metrics such as finite time Lyapunov exponent (FTLE) fields provide a quantitative description of the Lagrangian pathways and connectivity patterns of lagoons in the Red Sea.

Nonhydrostatic, multiscale processes are an important part of our understanding of ocean dynamics. However, resolving these dynamics with traditional computational techniques can often be prohibitively expensive. We apply the hybridizable discontinuous Galerkin (HDG) finite element methodology to perform computationally efficient, high-order, nonhydrostatic ocean modeling by solving the Navier-Stokes equations with the Boussinesq approximation. In this work, we introduce a distributed implementation of our HDG projection method algorithm. We provide numerical experiments to verify our methodology using the method of manufactured solutions and provide preliminary benchmarking for our distributed implementation that highlight the advantages of the HDG methodology in the context of distributed computing. Lastly, we present simulations in which we capture nonhydrostatic internal waves that form as a result of tidal interactions with ocean topography. First, we consider the case of tidally-driven oscillatory flow over an abrupt, shallow seamount, and next, the case of strongly-stratified, oscillatory flow over a tall seamount. We analyze and compare our simulations to other results in literature.

The interest in hydrokinetic conversion systems has significantly grown over the last decade with a special focus on cross-flow systems, generally known as Vertical Axis Water Turbines (VAWTs). However, analyzing of regions of interest for tidal energy extraction and outlining optimal rotor geometry is currently very computationally expensive via conventional 3D Computational Fluid Dynamics (CFD) methods. In this work, a VAWT load prediction routine developed at University of Pisa based upon the Blade Element-Momentum (BEM) theory is presented and validated against high-resolution 2D CFD simulations. Our model is able to work in two configurations, i.e. Double-Multiple Streamtube (DMST) mode, using 1D flow simplifications for quick analyses, and Hybrid mode, coupled to a CFD software for more accurate results. As a practical application, our routine is employed for a site assessment analysis of the Cape Cod area to quickly highlight oceanic regions with high hydrokinetic potential, where further higher-order and more computationally expensive CFD analyses can be performed. Ocean data are obtained from data-assimilative ocean simulations predicted by the 4D regional ocean modeling system of the Multidisciplinary Simulation, Estimation, and Assimilation Systems (MSEAS) group of the Massachusetts Institute of Technology.

With advances in engineering and technology, mining the deep sea for untapped rare metal resources from the bottom of the ocean has recently become economically viable. However, extracting these metal ores from the seabed creates plumes of fine particles that are deposited at various depths within the ocean, and these may be extremely harmful to the marine ecosystems and its components. Thus, for sustainable management, it is of utmost importance to carefully monitor and predict the impact of such harmful activities including plume dispersion on the marine environment. To forecast the plume dispersion in real-time, data-driven ocean modeling has to be coupled with accurate, efficient, and rigorous sediment plume transport computations. The goal of the present paper is to demonstrate the real-time applications of our coupled 3D-and-time data-driven ocean modeling and plume transport forecasting system. Here, the region of focus is the southern California bight, where the PLUMEX 2018 deep sea mining real-time sea experiment was recently conducted (23 Feb – 5 Mar, 2018). Specifically, we demonstrate the improved capabilities of the multiscale MSEAS primitive equation ocean modeling system to capture the complex oceanic phenomenon in the region of interest, the application of the novel method of composition to efficiently and accurately compute the transport of sediment plumes in 3D+1 domains, and the portability of our software and prediction system to different operational regions and its potential in estimating the environmental impacts of deep sea mining activities, ultimately aiding sustainable management and science-based regulations.

Data-constrained dynamical ocean modeling for the purpose of detailed forecasting and prediction continues to evolve and improve in quality. Modeling methods and computational capabilities have each improved. The result is that mesoscale phenomena can be modeled with skill, given sufficient data. However, many submesoscale features are less well modeled and remain largely unpredicted from a deterministic event standpoint, and possibly also from a statistical property standpoint. A multi-institution project is underway with goals of uncovering more of the details of a few submesoscale processes, working toward better predictions of their occurrence and their variability. A further component of our project is application of the new ocean models to ocean acoustic modeling and prediction. This paper focuses on one portion of the ongoing work: Efforts to link nonhydrostatic-physics models of continental-shelf nonlinear internal wave evolution to data-driven regional models. Ocean front-related effects are also touched on.

The observation, computation and study of “Lagrangian Coherent Structures” (LCS) in turbulent geophysical flows have been active areas of research in fluid mechanics for the last 30 years. Growing evidence for the existence of LCSs in geophysical flows (e.g., eddies, oscillating jets, chaotic mixing) and other fluid flows (e.g., separation prole at the surface of an airfoil, entrainment and detrainment by a vortex) generates an increasing interest for the extraction and understanding of these structures as well as their properties. In parallel, realistic ocean modeling with dense data assimilation has developed in the past decades and is now able to provide accurate nowcasts and predictions of ocean flow fields to study coherent structures. Robust numerical methods and sufficiently fast hardware are now available to compute real-time forecasts of oceanographic states and render associated coherent structures. It is therefore natural to expect the direct predictions of LCSs based on these advanced models. The impact of uncertainties on the coherent structures is becoming an increasingly important question for practical applications. The transfer of these uncertainties from the ocean state to the LCSs is an unexplored but intriguing scientific problem. These two questions are the motivation and focus of this presentation. Using the classic formalism of continuous-discrete estimation [1], the spatially discretized dynamics of the ocean state vector x and observations are described by (1a) dx =M(x; t) + d yok (1b) = H(xk; tk) + k where M and H are the model and measurement model operator, respectively. The stochastic forcings d and k are Wiener/Brownian motion processes,   N(0;Q(t)), and white Gaussian sequences, k  N(0;Rk), respectively. In other words, Efd(t)d T (t)g := Q(t) dt. The initial conditions are also uncertain and x(t0) is random with a prior PDF, p(x(t0)), i.e. x(t0) = bx0 + n(0) with n(0) random. Of course, vectors and operators in Eqs. (1a-b) are multivariate which impacts the PDFs: e.g. their moments are also multivariate. The estimation problem at time t consists of combining all available information on x(t), the dynamics and data (Eqs. 1a-b), their prior distributions and the initial conditions p(x(t0)). Defining the set of all observations prior to time t by yt

Oceanographic conditions in the Gulf of Procchio, along the northern Elba coast, are influenced by the circulation in the Corsica channel and the southeastern Ligurian Sea. In order to support ocean prediction by nested models, an initial 4-day CTD survey provided initial ocean conditions. The purposes of the forecasts were threefold: i) in support of AUV exercises; ii) as an experiment in the development of rapid environmental assessment (REA) methodology; and, iii) as a rigorous real time test of a distributed ocean ocean prediction system technology. The Harvard Ocean Prediction System (HOPS) was set up around Elba in a very high resolution domain (225 m horizontally) which was two-way nested in a high resolution domain (675 m) in the channel between Italy and Corsica. The HOPS channel domain was physically interfaced with a one-way nest to the CU-POM model run in a larger Ligurian Sea domain. Eleven nowcasts and 2-3 day forecasts were issued during the period 26 September to 10 October, 2000 for the channel domain and for a Procchio Bay operational sub-domain of the Elba domain.

After initialization with the NRV Alliance, CTD survey data adaptive sampling patterns for nightly excursions of the Alliance were designed on the basis of forecasts to obtain data for assimilation which would most efficiently maintain the structures and variability of the flow in future dynamical forecasts. Images of satellite sea surface temperature were regularly processed and used for track planning and also for model verification. Rapid environmental assessment (REA) techniques were used for data processing and transmission from ship to shore and vice versa for model results. ADCP data validated well the flow in the channel. Additionally and importantly, the direction and strength of the flow in Procchio Bay were correctly forecast by dynamics supported only by external observations. CU-POM model hydrographic and geostrophic flow data was assimilated successfully on boundary strips of the HOPS domain. Flow fields with/without CU-POM nesting were qualitatively similar and a quantitative analysis of differences is under study. A significant result was the demonstration of a powerful and efficient distributed ocean observing and prediction system with in situ data collected in the Ligurian Sea, satellite data collected at SACLANTCEN, forecast modeling at Harvard University and the University of Colorado, and adaptive sampling tracks designed at Harvard. The distributed system functioned smoothly and effectively and coped with the adverse six-hour time difference between Massachusetts and Italy.

We discuss the concepts involved in the evaluation and quantitative verification of ocean forecasts and present two predictive skill experiments to develop and research these concepts, carried out in the North Atlantic and Mediterranean Sea in 2001 and 2002. Ocean forecasting involves complex ocean observing and prediction systems for ocean regions with multi-scale interdisciplinary dynamical processes and strong, intermittent events. Now that ocean forecasting is becoming more common, it is critically important to interpret and evaluate regional forecasts in order to establish their usefulness to the scientific and applied communities. The Assessment of Skill for Coastal Ocean Transients (ASCOT) project is a series of real-time Coastal Predictive Skill (CPSE) and Rapid Environmental Assessment (REA) experiments and simulations focused on quantitative skill evaluation, carried out by the Harvard Ocean Prediction System group in collaboration with the NATO SACLANT Undersea Research Centre. ASCOT-01 was carried out in Massachusetts Bay and the Gulf of Maine in June 2001. ASCOT-02 took place in May 2002 in the Corsican Channel near the island of Elba in the Mediterranean Sea. Results from the ASCOT exercises highlight the dual use of data for skill evaluation and assimilation, real-time adaptive sampling and skill optimization and present both real-time and a posteriori evaluations of predictive skill and predictive capability.

The Littoral Ocean Observing and Predicting System (LOOPS) concept is that of a generic, versatile and portable system, applicable to multidisciplinary, multiscale generic coastal processes. The LOOPS advanced systems concept consists of: a modular, scalable structure for linking, with feedbacks, models, observational networks and data assimilation and adaptive sampling algorithms; and an efficient and robust, integrated and distributed, system software architecture and infrastructure. LOOPS applications include scientific research, coastal zone management and rapid environmental assessment for naval and civilian emergency operations. The LOOPS design is the scientific and technical conceptual basis of an interdisciplinary national littoral laboratory system. The LOOPS partners include: J.G. Bellingham (MBARI), C. Chryssostomidis (MIT), T.D. Dickey (UCSB), E. Levine (NUWC), N. Patrikalakis (MIT), D.L. Porter (JHU/APL), B.J. Rothschild (Umass-Dartmouth), H. Schmidt (MIT), K. Sherman (NMFS), D.V. Holliday (Marconi Aerospace) and D.K. Atwood (Raytheon). LOOPS objectives and accomplishments are summarized in the final section of this note.