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Range-Dynamical Low-Rank Split-Step Fourier Method for the Parabolic Wave Equation

Charous, A. and P.F.J. Lermusiaux, 2024. Range-Dynamical Low-Rank Split-Step Fourier Method for the Parabolic Wave Equation. Journal of the Acoustical Society of America, sub-judice.

Numerical solutions to the parabolic wave equation are plagued by the curse of dimensionality coupled with the Nyquist criterion. As a remedy, a new range-dynamical low-rank split-step Fourier methodology is developed. Our integration scheme scales sub-linearly with the number of classical degrees of freedom in the transverse directions. It is orders of magnitude faster than the classic full-rank split-step Fourier algorithm and also saves copious amounts of storage space. This enables numerical solutions of the parabolic wave equation at higher frequencies and on larger domains, and simulations may be performed on laptops rather than high-performance computing clusters. By using a rank-adaptive scheme to further optimize the low-rank equations, we ensure our approximate solution is highly accurate and efficient. The methodology and algorithms are demonstrated on realistic high-resolution data-assimilative ocean fields in Massachusetts Bay for three-dimensional acoustic configurations with different source locations and frequencies. The acoustic pressure, transmission loss, and phase solutions are analyzed in geometries with seamounts and canyons across and along Stellwagen Bank. The convergence with the rank of the subspace and the properties of the rank-adaptive scheme are demonstrated, and all results are successfully compared with those of the full-rank method when feasible.

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Dynamically Orthogonal Narrow-Angle Parabolic Equations for Stochastic Underwater Sound Propagation. Part II: Applications

Ali, W.H., and P.F.J. Lermusiaux, 2024. Dynamically Orthogonal Narrow-Angle Parabolic Equations for Stochastic Underwater Sound Propagation. Part II: Applications. Journal of the Acoustical Society of America 155(1), 656-672. doi:10.1121/10.0024474

The stochastic dynamically orthogonal (DO) narrow-angle parabolic equations (NAPEs) are exemplified and their properties and capabilities are described using three new 2D stochastic range-independent and range-dependent test cases with uncertain sound speed field, bathymetry, and source location. We validate results against ground-truth deterministic analytical solutions and direct Monte Carlo predictions of acoustic pressure and transmission loss fields. We verify the stochastic convergence and computational advantages of the DO-NAPEs and discuss the differences with normal mode approaches. Results show that a single DO-NAPE simulation can accurately predict stochastic range-dependent acoustic fields and their non-Gaussian probability distributions, with computational savings of several orders of magnitude when compared to direct Monte Carlo methods. With their coupling properties and their adaptation in range to the dominant uncertainties, the DO-NAPEs are shown to predict accurate statistics, from mean and variance to multiple modes and full probability distributions, and to provide excellent reconstructed realizations, from amplitudes and phases to other specific properties of complex realization fields.

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Dynamically Orthogonal Narrow-Angle Parabolic Equations for Stochastic Underwater Sound Propagation. Part I: Theory and Schemes

Ali, W.H., and P.F.J. Lermusiaux, 2024. Dynamically Orthogonal Narrow-Angle Parabolic Equations for Stochastic Underwater Sound Propagation. Part I: Theory and Schemes. Journal of the Acoustical Society of America 155(1), 640-655. doi:10.1121/10.0024466

Robust informative acoustic predictions require precise knowledge of ocean physics, bathymetry, seabed, and acoustic parameters. However, in realistic applications, this information is uncertain due to sparse and heterogeneous measurements and complex ocean physics. Efficient techniques are thus needed to quantify these uncertainties and predict the stochastic acoustic wave fields. In this work, we derive and implement new stochastic differential equations that predict the acoustic pressure fields and their probability distributions. We start from the stochastic acoustic parabolic equation (PE) and employ the instantaneously-optimal Dynamically Orthogonal (DO) equations theory. We derive stochastic DO-PEs that dynamically reduce and march the dominant multi-dimensional uncertainties respecting the nonlinear governing equations and non-Gaussian statistics. We develop the dynamical reduced-order DO-PEs theory for the Narrow-Angle PE (NAPE) and implement numerical schemes for discretizing and integrating the stochastic acoustic fields.

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Stable Rank-adaptive Dynamically Orthogonal Runge-Kutta Schemes

Charous, A. and P.F.J. Lermusiaux, 2024. Stable Rank-adaptive Dynamically Orthogonal Runge-Kutta Schemes. SIAM Journal on Scientific Computing 46(1), A529-A560. doi:10.1137/22M1534948

We develop two new sets of stable, rank-adaptive Dynamically Orthogonal Runge-Kutta (DORK) schemes that capture the high-order curvature of the nonlinear low-rank manifold. The DORK schemes asymptotically approximate the truncated singular value decomposition at a greatly reduced cost while preserving mode continuity using newly derived retractions. We show that arbitrarily high-order optimal perturbative retractions can be obtained, and we prove that these new retractions are stable. In addition, we demonstrate that repeatedly applying retractions yields a gradient-descent algorithm on the low-rank manifold that converges geometrically when approximating a low-rank matrix. When approximating a higher-rank matrix, iterations converge linearly to the best low-rank approximation. We then develop a rank-adaptive retraction that is robust to overapproximation. Building off of these retractions, we derive two novel, rank-adaptive integration schemes that dynamically update the subspace upon which the system dynamics is projected within each time-step: the stable, optimal Dynamically Orthogonal Runge-Kutta (so-DORK) and gradient-descent Dynamically Orthogonal Runge-Kutta (gd-DORK) schemes. These integration schemes are numerically evaluated and compared on an ill-conditioned matrix differential equation, an advection-diffusion partial differential equation, and a nonlinear, stochastic reaction-diffusion partial differential equation. Results show a reduced error accumulation rate with the new stable, optimal and gradient-descent integrators. In addition, we find that rank adaptation allows for highly accurate solutions while preserving computational efficiency.

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Persistent Lagrangian Material Coherence in Fluid and Ocean Flows Using Flow Map Composition

Kulkarni, C.S. and P.F.J. Lermusiaux, 2024. Persistent Lagrangian Material Coherence in Fluid and Ocean Flows Using Flow Map Composition. Ocean Modelling, sub-judice.

In this work, we analyze Lagrangian material coherence in dynamic open domains. We derive and apply new theory and efficient schemes to extract material sets in dynamic flow fields that remain the most or the least coherent throughout the time interval of interest, with special attention to realistic ocean domains that have multiple time-dependent inlets and/or outlets. First, the partial differential equation (PDE)-based method of composition is extended to efficiently compute flow maps in open domains, evolving a dynamic mask field without compounding numerical errors. This permits the use of existing grid based PDE solvers to compute flow maps on their dynamic non-regular domain. Inherent parallelization capabilities with accuracy as trajectory-based schemes but importantly with also an optimal grid-based resolution make this method very attractive. Second, we derive a novel approach to compute material sets in dynamic fluid flows that undergo minimal stress throughout the considered time interval. The level sets of the proposed metric, called the ‘extended polar distance’, yield material subdomains that remain rigid (i.e. only undergo translation and rotation) throughout the time interval of interest up to a certain tolerance. This metric and the corresponding persistently coherent sets and incoherent sets are computed using the PDE-based flow map computation. We further relate the extended polar distance and the diffusion barrier strength metric and show that the extended polar distance rigorously cumulates the tendency of a material subdomain to be prone to diffusion and the average strain it undergoes. We utilize the new theory and numerical methods to analyze Lagrangian coherence in analytical and realistic scenarios – an analytical unsteady double gyre flow and a realistic simulation in the Southern Pacific Ocean. The former helps us better understand the proposed theory in practice, and highlights the evolution of coherent, persistently coherent, and incoherent sets. In the latter Southern Pacific Ocean application, we find that the surface regions around Palau island are highly incoherent due to the steep topography and complex interactive dynamics. However, we also find a rigid set advected by the larger-scale currents around the Island, retrieving its shape at the end, as well as a persistently rigid set that approximately maintains its shape throughout the time interval, maximally resisting advective stretching and diffusive transport.

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Rigid Sets and Coherent Sets in Realistic Ocean Flows

Feppon, F. and P.F.J. Lermusiaux, 2024. Rigid Sets and Coherent Sets in Realistic Ocean Flows. Nonlinear Processes in Geophysics, sub-judice. doi:10.5194/npg-2022-1

This paper focuses on the extractions of Lagrangian Coherent Sets from realistic velocity fields obtained from ocean data and simulations, each of which can be highly resolved and non volume-preserving. We introduce two novel methods for computing two formulations of such sets. First, we propose a new “diffeomorphism-based” criterion to extract “rigid sets”, defined as sets over which the flow map acts approximately as a rigid transformation. Second, we develop a matrix-free methodology that provides a simple and efficient framework to compute “coherent sets” with operator methods. Both new methods and their resulting rigid sets and coherent sets are illustrated and compared using three numerically simulated flow examples, including a high-resolution realistic, submesoscale to large-scale dynamic ocean current field in the Palau Island region of the western Pacific Ocean.

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Gaussian Beam Migration for Wide-Area Deep Ocean Floor Mapping

Charous, A., W.H. Ali, P. Ryu, D. Brown, K. Arsenault, B. Cho, K. Rimpau, A. March, and P.F.J. Lermusiaux, 2023. Gaussian Beam Migration for Wide-Area Deep Ocean Floor Mapping. In: OCEANS '23 IEEE/MTS Gulf Coast, 25–28 September 2023. doi:10.23919/OCEANS52994.2023.10337362

Cost-effective seafloor mapping at high resolution is yet to be attained. A possible solution consists of using a mobile, wide-aperture, sparse array with subarrays distributed across multiple autonomous surface vessels. Such wide-area mapping with multiple dynamic sources and receivers require accurate modeling and processing systems for imaging the seabed. In this paper, we focus on computational schemes and challenges for such high-resolution acoustic imaging or migration. Starting from the imaging condition from the adjoint-state method, we derive a closed-form expression for Gaussian beam migration in stratified media. We employ this technique on simulated data and on real data collected with our novel acoustic array over shipwrecks in the Boston Harbor. We compare Gaussian beam migration with diffraction stack and Kirchhoff migration, and we find that Gaussian beam migration produces the clearest images with the fewest artifacts.

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MSEAS-ParEq for Ocean-Acoustic Modeling around the Globe

Ali, W.H., A. Charous, C. Mirabito, P.J. Haley, Jr., and P.F.J. Lermusiaux, 2023. MSEAS-ParEq for Ocean-Acoustic Modeling around the Globe. In: OCEANS '23 IEEE/MTS Gulf Coast, 25–28 September 2023. doi:10.23919/OCEANS52994.2023.10337377

The multi-scale dynamics of oceanic processes and the complex propagation of acoustic waves are fundamental challenges in marine sciences and operations. Recent computing advances enable such multiresolution ocean and acoustic modeling, but a fully integrated system for sustained coupled predictions and Bayesian data assimilation remains needed. In this study, we integrate the MSEAS Primitive Equation (PE) ocean modeling system and the MSEAS acoustic Parabolic Equation (ParEq) solver, enabling real-time coupled ocean and acoustic predictions. Realistic applications in Massachusetts Bay, the Norwegian Sea, the western Mediterranean Sea, and the New York Bight are used to demonstrate capabilities and validate predictions in diverse shallow and deep-water environments. Results provide the foundation for an end-to-end system for coupled ocean-acoustic probabilistic modeling, Bayesian inversion, and learning.

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Toward Dynamic Data-Driven Systems for Rapid Adaptive Interdisciplinary Ocean Forecasting

Patrikalakis, N.M., P.F.J. Lermusiaux, C. Evangelinos, J.J. McCarthy, A.R. Robinson, H. Schmidt, P.J. Haley, S. Lalis, R. Tian, W.G. Leslie, and W. Cho, 2023. Toward Dynamic Data-Driven Systems for Rapid Adaptive Interdisciplinary Ocean Forecasting. Chapter 14, Handbook of Dynamic Data Driven Applications Systems, F. Darema, E.P. Blasch, S. Ravela, and A.J. Aved (Eds.), pp. 377-395. doi:10.1007/978-3-031-27986-7_14

The state of the ocean evolves and its dynamics involves transitions occurring at multiple scales. For efficient and rapid interdisciplinary forecasting, ocean observing and prediction systems must have the same behavior and adapt to the ever-changing dynamics. This chapter sets the basis of a distributed system for real-time interdisciplinary ocean field and uncertainty forecasting with adaptive modeling and adaptive sampling. The scientific goal is to couple physical and biological oceanography with ocean acoustic measurements. The technical goal is to build a dynamic modeling and instrumentation system based on advanced infrastructures, distributed/grid computing, and efficient information retrieval and visualization interfaces, from which all these are incorporated into the Poseidon system. Importantly, the Poseidon system combines a suite of modern legacy physical models, acoustic models, and ocean current monitoring data assimilation schemes with innovative modeling and adaptive sampling methods. The legacy systems are encapsulated at the binary level using software component methodologies. Measurement models are utilized to link the observed data to the dynamical model variables and structures. With adaptive sampling, the data acquisition is dynamic and aims to minimize the predicted uncertainties, maximize the optimized sampling of key dynamics, and maintain overall coverage. With adaptive modeling, model improvements dynamically select the best model structures and parameters among different physical or biogeochemical parameterizations. The dynamic coupling of models and measurements discussed here, and embodied in the Poseidon system, represents a Dynamic Data-Driven Applications Systems (DDDAS). Technical and scientific progress is highlighted based on examples in Massachusetts Bay, Monterey Bay, and the California Current System.

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Deep Reinforcement Learning for Adaptive Mesh Refinement

Foucart, C., A. Charous, and P.F.J. Lermusiaux, 2023. Deep Reinforcement Learning for Adaptive Mesh Refinement. Journal of Computational Physics 491, 112381. doi:10.1016/j.jcp.2023.112381

Finite element discretizations of problems in computational physics often rely on adaptive mesh refinement (AMR) to preferentially resolve regions containing important features during simulation. However, these spatial refinement strategies are often heuristic and rely on domain-specific knowledge or trial-and-error. We treat the process of adaptive mesh refinement as a local, sequential decision-making problem under incomplete information, formulating AMR as a partially observable Markov decision process. Using a deep reinforcement learning approach, we train policy networks for AMR strategy directly from numerical simulation. The training process does not require an exact solution or a high-fidelity ground truth to the partial differential equation at hand, nor does it require a pre-computed training dataset. The local nature of our reinforcement learning formulation allows the policy network to be trained inexpensively on much smaller problems than those on which they are deployed. The methodology is not specific to any particular partial differential equation, problem dimension, or numerical discretization, and can flexibly incorporate diverse problem physics. To that end, we apply the approach to a diverse set of partial differential equations, using a variety of high-order discontinuous Galerkin and hybridizable discontinuous Galerkin finite element discretizations. We show that the resultant deep reinforcement learning policies are competitive with common AMR heuristics, generalize well across problem classes, and strike a favorable balance between accuracy and cost such that they often lead to a higher accuracy per problem degree of freedom.

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Lagrangian Surface Signatures Reveal Upper-Ocean Vertical Displacement Conduits Near Oceanic Density Fronts

Aravind, H.M., V. Verma, S. Sarkar, M.A. Freilich, A. Mahadevan, P.J. Haley Jr., P.F.J. Lermusiaux, and M.R. Allshouse, 2023. Lagrangian Surface Signatures Reveal Upper-Ocean Vertical Displacement Conduits Near Oceanic Density Fronts. Ocean Modelling 181, 102136. doi:10.1016/j.ocemod.2022.102136

Vertical transport in the ocean plays a critical role in the exchange of freshwater, heat, nutrients, and other biogeochemical tracers. While there are situations where vertical fluxes are important, studying the vertical transport and displacement of material requires analysis over a finite interval of time. One such example is the subduction of fluid from the mixed layer into the pycnocline, which is known to occur near density fronts. Divergence has been used to estimate vertical velocities indicating that surface measurements, where observational data is most widely available, can be used to locate these vertical transport conduits. We evaluate the correlation between surface signatures derived from Eulerian (horizontal divergence, density gradient, and vertical velocity) and Lagrangian (dilation rate and finite time Lyapunov exponent) metrics and vertical displacement conduits. Two submesoscale resolving models of density fronts and a data-assimilative model of the western Mediterranean were analyzed. The Lagrangian surface signatures locate significantly more of the strongest displacement features and the difference in the expected displacements relative to Eulerian ones increases with the length of the time interval considered. Ensemble analysis of forecasts from the Mediterranean model demonstrates that the Lagrangian surface signatures can be used to identify regions of strongest downward vertical displacement even without knowledge of the true ocean state.

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Stochastic Acoustic Ray Tracing with Dynamically Orthogonal Differential Equations

Humara, M.J., W.H. Ali, A. Charous, M. Bhabra, and P.F.J. Lermusiaux, 2022. Stochastic Acoustic Ray Tracing with Dynamically Orthogonal Differential Equations. In: OCEANS '22 IEEE/MTS Hampton Roads, 17–20 October 2022, pp. 1–10. doi:10.1109/OCEANS47191.2022.9977252

Developing accurate and computationally efficient models for underwater sound propagation in the uncertain, dynamic ocean environment is inherently challenging. In this work, we evaluate the potential of dynamic reduced-order modeling for stochastic ray tracing. We obtain and implement the stochastic dynamically-orthogonal (DO) differential equations for Ray Tracing (DO-Ray). With stochastic DO-Ray, we can start from non-Gaussian environmental uncertainties and compute the stochastic acoustic ray fields in a dynamic reduced order fashion, all while preserving the dominant complex statistics of the ocean environment and the nonlinear relations with ray dynamics. We develop varied algorithms and discuss implementation challenges and solutions, using direct Monte Carlo for comparison. We showcase results in an uncertain deep-sound channel example and observe the ability to represent the stochastic ray trace fields in a dynamic reduced-order fashion.

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High-order Discontinuous Galerkin Methods for Nonhydrostatic Ocean Processes with a Free Surface

Foucart, C., C. Mirabito, P.J. Haley, Jr., and P.F.J. Lermusiaux, 2021. High-order Discontinuous Galerkin Methods for Nonhydrostatic Ocean Processes with a Free Surface. In: OCEANS '21 IEEE/MTS San Diego, 20-23 September 2021, pp. 1-9. doi:10.23919/OCEANS44145.2021.9705767

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.

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Dynamically Orthogonal Differential Equations for Stochastic and Deterministic Reduced-Order Modeling of Ocean Acoustic Wave Propagation

Charous, A. and P.F.J. Lermusiaux, 2021. Dynamically Orthogonal Differential Equations for Stochastic and Deterministic Reduced-Order Modeling of Ocean Acoustic Wave Propagation. In: OCEANS '21 IEEE/MTS San Diego, 20-23 September 2021, pp. 1-7. doi:10.23919/OCEANS44145.2021.9705914

Accurate and computationally efficient acoustic models are needed for varied marine applications. In this paper, we focus our attention on forward models, which are essential to inverse problems such as imaging and mapping. First, we introduce new dynamically orthogonal (DO) equations for the acoustic wave equation in full generality, allowing for stochastic and spatially heterogeneous parameters. These equations may be spatially discretized and integrated in time numerically. Alternatively, the DO equations may be discretized themselves, admitting a non-intrusive reduced-order approach to solve the stochastic wave equation. We demonstrate the latter with a test case of an acoustic pulse traveling through the ocean with an uncertain sound speed. Second, we adapt the spatially discrete DO approach, typically used to reduce the stochastic dimension, to efficient reduced-order modeling of deterministic 3D acoustic propagation. We solve the 3D parabolic wave equation and show that low-rank solutions rapidly converge to the full-rank solution. Together, these approaches offer novel ways to solve stochastic and deterministic problems with strong or weak scattering at a reduced computational cost.

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Coastal Circulation and Water Transport Properties of the Red Sea Project Lagoon

Zhan, P., G. Krokos, S. Langodan, D. Guo, H. Dasari, V.P. Papadopoulos, P.F.J. Lermusiaux, O.M. Knio, and I. Hoteit, 2021. Coastal Circulation and Water Transport Properties of the Red Sea Project Lagoon. Ocean Modelling 161, 101791. doi:10.1016/j.ocemod.2021.101791

The Red Sea Project (RSP) is based on a coastal lagoon with over 90 pristine islands. The project intends to transform the Red Sea coast into a world-class tourist destination. To better understand the regional dynamics and water exchange scenarios in the lagoon, a high-resolution numerical model is implemented. The general and tidal circulation dynamics are then investigated with a particular focus on the response of the lagoon to strong wind jets. Significant variations in winter and summer circulation patterns are identified. The tidal amplitude inside the lagoon is greater than that outside, with strong tidal currents passing over its surrounding coral reef banks. The lagoon rapidly responds to the strong easterly wind jets that occur mainly in winter; it develops a reverse flow at greater depths, and the coastal water elevation is instantly affected. Lagrangian particle simulations are conducted to study the residence time of water in the lagoon. The results suggest that water renewal is slow in winter. Analysis of the Lagrangian coherent structures (LCS) reveals that water renewal is largely linked to the circulation patterns in the lagoon. In winter, the water becomes restricted in the central lagoon with only moderate exchange, whereas in summer, more circulation is observed with a higher degree of interaction between the central lagoon and external water. The results of LCS also highlight the tidal contribution to stirring and mixing while identifying the hotspots of the phenomenon. Our analysis demonstrates an effective approach for studying regional water mixing and connectivity, which could support coastal management in data-limited regions.

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Minimum-Correction Second-Moment Matching: Theory, Algorithms and Applications

Lin, J. and P.F.J. Lermusiaux, 2021. Minimum-Correction Second-Moment Matching: Theory, Algorithms and Applications. Numerische Mathematik 147(3): 611–650. doi:10.1007/s00211-021-01178-8

We address the problem of finding the closest matrix to a given U under the constraint that a prescribed second-moment matrix must be matched, i.e. TŨ=P̃. We obtain a closed-form formula for the unique global optimizer for the full-rank case, that is related to U by an SPD (symmetric positive definite) linear transform. This result is generalized to rank-deficient cases as well as to infinite dimensions. We highlight the geometric intuition behind the theory and study the problem’s rich connections to minimum congruence transform, generalized polar decomposition, optimal transport, and rank-deficient data assimilation. In the special case of =I, minimum-correction second-moment matching reduces to the well-studied optimal orthonormalization problem. We investigate the general strategies for numerically computing the optimizer and analyze existing polar decomposition and matrix square root algorithms. We modify and stabilize two Newton iterations previously deemed unstable for computing the matrix square root, such that they can now be used to efficiently compute both the orthogonal polar factor and the SPD square root. We then verify the higher performance of the various new algorithms using benchmark cases with randomly generated matrices. Lastly, we complete two applications for the stochastic Lorenz-96 dynamical system in a chaotic regime. In reduced subspace tracking using dynamically orthogonal equations, we maintain the numerical orthonormality and continuity of time-varying base vectors. In ensemble square root filtering for data assimilation, the prior samples are transformed into posterior ones by matching the covariance given by the Kalman update while also minimizing the corrections to the prior samples.

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Extent of Impact of Deep-Sea Nodule Mining Midwater Plumes Is Influenced by Sediment Loading, Turbulence and Thresholds

Muñoz-Royo, C., T. Peacock, M.H. Alford, J. Smith, A. Le Boyer, C.S. Kulkarni, P.F.J. Lermusiaux, P.J. Haley, Jr., C. Mirabito, D. Wang, E. Eric Adams, R. Ouillon, A. Breugem, B. Decrop, T. Lanckriet, R.B. Supekar, A.J. Rzeznik, A. Gartman, and S.-J. Ju, 2021. Extent of Impact of Deep-Sea Nodule Mining Midwater Plumes Is Influenced by Sediment Loading, Turbulence and Thresholds. Nature Communications Earth & Environment 2(148), pp. 1-16. doi:10.1038/s43247-021-00213-8

Deep-sea polymetallic nodule mining research activity has substantially increased in recent years, but the expected level of environmental impact is still being established. One environmental concern is the discharge of a sediment plume into the midwater column. We performed a dedicated field study using sediment from the Clarion Clipperton Fracture Zone. The plume was monitored and tracked using both established and novel instrumentation, including acoustic and turbulence measurements. Our field studies reveal that modeling can reliably predict the properties of a midwater plume in the vicinity of the discharge and that sediment aggregation effects are not significant. The plume model is used to drive a numerical simulation of a commercial-scale operation in the Clarion Clipperton Fracture Zone. Key takeaways are that the scale of impact of the plume is notably influenced by the values of environmentally acceptable threshold levels, the quantity of discharged sediment, and the turbulent diffusivity in the Clarion Clipperton Fracture Zone.

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Towards an End-to-End Analysis and Prediction System for Weather, Climate, and Marine Applications in the Red Sea

Hoteit, I., Y. Abualnaja, S. Afzal, B. Ait-El-Fquih, T. Akylas, C. Antony, C. Dawson, K. Asfahani, R.J. Brewin, L. Cavaleri, I. Cerovecki, B. Cornuelle, S. Desamsetti, R. Attada, H. Dasari, J. Sanchez-Garrido, L. Genevier, M. El Gharamti, J.A. Gittings, E. Gokul, G. Gopalakrishnan, D. Guo, B. Hadri, M. Hadwiger, M.A. Hammoud, M. Hendershott, M. Hittawe, A. Karumuri, O. Knio, A. Köhl, S. Kortas, G. Krokos, R. Kunchala, L. Issa, I. Lakkis, S. Langodan, P. Lermusiaux, T. Luong, J. Ma, O. Le Maitre, M. Mazloff, S. El Mohtar, V.P. Papadopoulos, T. Platt, L. Pratt, N. Raboudi, M.-F. Racault, D.E. Raitsos, S. Razak, S. Sanikommu, S. Sathyendranath, S. Sofianos, A. Subramanian, R. Sun, E. Titi, H. Toye, G. Triantafyllou, K. Tsiaras, P. Vasou, Y. Viswanadhapalli, Y. Wang, F. Yao, P. Zhan, and G. Zodiatis, 2021. Towards an End-to-End Analysis and Prediction System for Weather, Climate, and Marine Applications in the Red Sea. Bulletin of the American Meteorological Society 102(1), E99-E122. doi:10.1175/BAMS-D-19-0005.1

The Red Sea, home to the second-longest coral reef system in the world, is a vital resource for the Kingdom of Saudi Arabia. The Red Sea provides 90% of the Kingdom’s potable water by desalinization, supporting tourism, shipping, aquaculture, and fishing industries, which together contribute about 10%–20% of the country’s GDP. All these activities, and those elsewhere in the Red Sea region, critically depend on oceanic and atmospheric conditions. At a time of mega-development projects along the Red Sea coast, and global warming, authorities are working on optimizing the harnessing of environmental resources, including renewable energy and rainwater harvesting. All these require high-resolution weather and climate information. Toward this end, we have undertaken a multipronged research and development activity in which we are developing an integrated data-driven regional coupled modeling system. The telescopically nested components include 5-km- to 600-m-resolution atmospheric models to address weather and climate challenges, 4-km- to 50-m-resolution ocean models with regional and coastal configurations to simulate and predict the general and mesoscale circulation, 4-km- to 100-m-resolution ecosystem models to simulate the biogeochemistry, and 1-km- to 50-m-resolution wave models. In addition, a complementary probabilistic transport modeling system predicts dispersion of contaminant plumes, oil spill, and marine ecosystem connectivity. Advanced ensemble data assimilation capabilities have also been implemented for accurate forecasting. Resulting achievements include significant advancement in our understanding of the regional circulation and its connection to the global climate, development, and validation of long-term Red Sea regional atmospheric–oceanic–wave reanalyses and forecasting capacities. These products are being extensively used by academia, government, and industry in various weather and marine studies and operations, environmental policies, renewable energy applications, impact assessment, flood forecasting, and more.

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Real-time Probabilistic Coupled Ocean Physics-Acoustics Forecasting and Data Assimilation for Underwater GPS

Lermusiaux, P.F.J., C. Mirabito, P.J. Haley, Jr., W.H. Ali, A. Gupta, S. Jana, E. Dorfman, A. Laferriere, A. Kofford, G. Shepard, M. Goldsmith, K. Heaney, E. Coelho, J. Boyle, J. Murray, L. Freitag, and A. Morozov, 2020. Real-time Probabilistic Coupled Ocean Physics-Acoustics Forecasting and Data Assimilation for Underwater GPS. In: OCEANS '20 IEEE/MTS, 5-30 October 2020, pp. 1-9. doi:10.1109/IEEECONF38699.2020.9389003

The widely-used Global Positioning System (GPS) does not work underwater. This presents a severe limitation on the communication capabilities and deployment options for undersea assets such as AUVs and UUVs. To address this challenge, the Positioning System for Deep Ocean Navigation (POSYDON) program aims to develop an undersea system that provides omnipresent, robust positioning across ocean basins. To do so, it is critically important to accurately model sound waves and signals under diverse, and often uncertain, undersea environmental conditions. Probabilistic estimates of the four-dimensional variability of the fields of sound speed, salinity, temperature, and currents are thus needed. In this paper, we employ our MSEAS primitive-equation and error subspace data-assimilative ensemble ocean forecasting system during two real-time POSYDON sea exercises, one in winter 2017 and another in August 2018. We provide real-time high-resolution estimates of sound speed fields and their uncertainty, and describe the ocean conditions from submesoscales eddies and internal tides to warm core rings and larger-scale circulations. We verify our results against independent data of opportunity; in all cases, we show that our probabilistic forecasts demonstrate skill.

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Multi-resolution Probabilistic Ocean Physics-Acoustic Modeling: Validation in the New Jersey Continental Shelf

Lermusiaux, P.F.J., P.J. Haley, Jr., C. Mirabito, W.H. Ali, M. Bhabra, P. Abbot, C.-S. Chiu, and C. Emerson, 2020. Multi-resolution Probabilistic Ocean Physics-Acoustic Modeling: Validation in the New Jersey Continental Shelf. In: OCEANS '20 IEEE/MTS, 5-30 October 2020, pp. 1-9. doi:10.1109/IEEECONF38699.2020.9389193

The reliability of sonar systems in the littoral environment is greatly affected by the variability of the surrounding nonlinear ocean dynamics. This variability occurs on multiple scales in space and time, and involves multiple interacting processes, from internal tides and waves to meandering fronts, eddies, boundary layers, and strong air-sea interactions. We utilize our high-resolution MSEAS-PE ocean modeling system to hindcast the ocean physical environment off the New Jersey continental shelf for the end of June 2009, and then utilize our new MSEAS probabilistic acoustic NAPE and WAPE solvers in a coupled ocean physics-acoustic modeling fashion to predict the transmission and integrated transmission losses, respectively. The coupled models are described, and their predictions verified against independent ocean physics observations and sound propagation measurements from acoustic sources and receivers in the region. Our high-resolution ocean simulations are shown to substantial reduce the RMSE and bias of the coarser simulations. Our acoustic simulations of deterministic and stochastic TL fields also show significant skill.

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Search and Rescue at Sea Aided by Hidden Flow Structures

Serra, M., P. Sathe, I. Rypina, A. Kirincich, S.D. Ross, P.F.J. Lermusiaux, A. Allen, T. Peacock, and G. Haller, 2020. Search and Rescue at Sea Aided by Hidden Flow Structures. Nature Communications 11, 1-7. doi:10.1038/s41467-020-16281-x

Every year, hundreds of people die at sea because of vessel and airplane accidents. A key challenge in reducing the number of these fatalities is to make Search and Rescue (SAR) algorithms more efficient. Here, we address this challenge by uncovering hidden TRansient Attracting Profiles (TRAPs) in ocean-surface velocity data. Computable from a single velocity-field snapshot, TRAPs act as short-term attractors for all floating objects. In three different ocean field experiments, we show that TRAPs computed from measured as well as modeled velocities attract deployed drifters and manikins emulating people fallen in the water. TRAPs, which remain hidden to prior flow diagnostics, thus provide critical information for hazard responses, such as SAR and oil spill containment, and hence have the potential to save lives and limit environmental disasters.

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Plastic Pollution in the Coastal Oceans: Characterization and Modeling

Lermusiaux, P.F.J., M. Doshi, C.S. Kulkarni, A. Gupta, P.J. Haley, Jr., C. Mirabito, F. Trotta, S.J. Levang, G.R. Flierl, J. Marshall, T. Peacock, and C. Noble, 2019. Plastic Pollution in the Coastal Oceans: Characterization and Modeling. In: OCEANS '19 MTS/IEEE Seattle, 27-31 October 2019, doi: 10.23919/OCEANS40490.2019.8962786

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.

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Flowmaps and Coherent Sets for Characterizing Residence Times and Connectivity in Lagoons and Coral Reefs: The Case of the Red Sea

Doshi, M.M., C.S. Kulkarni, W.H. Ali, A. Gupta, P.F.J. Lermusiaux, P. Zhan, I. Hoteit, and O.M. Knio, 2019. Flowmaps and Coherent Sets for Characterizing Residence Times and Connectivity in Lagoons and Coral Reefs: The Case of the Red Sea. In: OCEANS '19 MTS/IEEE Seattle, 27-31 October 2019, doi:10.23919/OCEANS40490.2019.8962643

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.

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Stochastic Oceanographic-Acoustic Prediction and Bayesian Inversion for Wide Area Ocean Floor Mapping

Ali, W.H., M.S. Bhabra, P.F.J. Lermusiaux, A. March, J.R. Edwards, K. Rimpau, and P. Ryu, 2019. Stochastic Oceanographic-Acoustic Prediction and Bayesian Inversion for Wide Area Ocean Floor Mapping. In: OCEANS '19 MTS/IEEE Seattle, 27-31 October 2019, doi:10.23919/OCEANS40490.2019.8962870

Covering the vast majority of our planet, the ocean is still largely unmapped and unexplored. Various imaging techniques researched and developed over the past decades, ranging from echo-sounders on ships to LIDAR systems in the air, have only systematically mapped a small fraction of the seafloor at medium resolution. This, in turn, has spurred recent ambitious efforts to map the remaining ocean at high resolution. New approaches are needed since existing systems are neither cost nor time effective. One such approach consists of a sparse aperture mapping technique using autonomous surface vehicles to allow for efficient imaging of wide areas of the ocean floor. Central to the operation of this approach is the need for robust, accurate, and efficient inference methods that effectively provide reliable estimates of the seafloor profile from the measured data. In this work, we utilize such a stochastic prediction and Bayesian inversion and demonstrate results on benchmark problems. We first outline efficient schemes for deterministic and stochastic acoustic modeling using the parabolic wave equation and the optimally-reduced Dynamically Orthogonal equations and showcase results on stochastic test cases. We then present our Bayesian inversion schemes and its results for rigorous nonlinear assimilation and joint bathymetry-ocean physics-acoustics inversion.

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Energy and Momentum Lost to Wake Eddies and Lee Waves Generated by the North Equatorial Current and Tidal Flows at Peleliu, Palau

Johnston, T.M.S., J.A. MacKinnon, P.L. Colin, P.J. Haley, Jr., P.F.J. Lermusiaux, A.J. Lucas, M.A. Merrifield, S.T. Merrifield, C. Mirabito, J.D. Nash, C.Y. Ou, M. Siegelman, E.J. Terrill, A.F. Waterhouse, 2019. Energy and Momentum Lost to Wake Eddies and Lee Waves Generated by the North Equatorial Current and Tidal Flows at Peleliu, Palau, Oceanography 32(4), 110–125. doi:10.5670/oceanog.2019.417

The North Equatorial Current (NEC) transports water westward around numerous islands and over submarine ridges in the western Pacific. As the currents flow over and around this topography, the central question is: how are momentum and energy in the incident flow transferred to finer scales? At the south point of Peleliu Island, Palau, a combination of strong NEC currents and tides flow over a steep, submarine ridge. Energy cascades suddenly from the NEC via the 1 km scale lee waves and wake eddies to turbulence. These submesoscale wake eddies are observed every tidal cycle, and also in model simulations. As the flow in each eddy recirculates and encounters the incident flow again, the associated front contains interleaving temperature (T) structures with 1–10 m horizontal extent. Turbulent dissipation (ε) exceeds 10-5 W kg-1 along this tilted and strongly sheared front. A train of such submesoscale eddies can be seen at least 50 km downstream. Internal lee waves with 1 km wavelengths are also observed over the submarine ridge. The mean form drag exerted by the waves (i.e., upward transport of eastward momentum) of about 1 Pa is sufficient to substantially reduce the westward NEC, if not for other forcing, and is greater than the turbulent bottom drag of about 0.1 Pa. The effect on the incident flow of the form drag from only one submarine ridge may be similar to the bottom drag along the entire coastline of Palau. The observed ε is also consistent with local dissipation of lee wave energy. The circulation, including lee waves and wake eddies, was simulated by a data-driven primitive equation ocean model. The model estimates of the form drags exerted by pressure drops across the submarine ridge and due to wake eddies were found to be about 10 times higher than the lee wave and turbulent bottom drags. The ridge form drag was correlated to both the tidal flow and winds while the submesoscale wake eddy drag was mainly tidal.

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Advection without Compounding Errors through Flow Map Composition

Kulkarni, C.S. and P.F.J. Lermusiaux, 2019. Advection without Compounding Errors through Flow Map Composition. Journal of Computational Physics, 398, 108859. doi:10.1016/j.jcp.2019.108859

We propose a novel numerical methodology to compute the advective transport and diffusion-reaction of tracer quantities. The tracer advection occurs through flow map composition and is super-accurate, yielding numerical solutions almost devoid of compounding numerical errors, while allowing for direct parallelization in the temporal direction. It is computed by implicitly solving the characteristic evolution through a modified transport partial differential equation and domain decomposition in the temporal direction, followed by composition with the known initial condition. This advection scheme allows a rigorous computation of the spatial and temporal error bounds, yields an accuracy comparable to that of Lagrangian methods, and maintains the advantages of Eulerian schemes. We further show that there exists an optimal value of the composition timestep that yields the minimum total numerical error in the computations, and derive the expression for this value. We develop schemes for the addition of tracer diffusion, reaction, and source terms, and for the implementation of boundary conditions. Finally, the methodology is applied in three flow examples, namely an analytical reversible swirl flow, an idealized flow exiting a strait undergoing sudden expansion, and a realistic ocean flow in the Bismarck sea. New benchmark problems for advection-diffusion-reaction schemes are developed and used to compare and contrast results with those of classic schemes. The results highlight the theoretical properties of the methodology as well as its efficiency, super-accuracy with minimal numerical errors, and applicability in realistic simulations.
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Multiscale multiphysics data-informed modeling for three-dimensional ocean acoustic simulation and prediction

Duda, T.F., Y.-T. Lin, A.E. Newhall, K.R. Helfrich, J.F. Lynch, W.G. Zhang, P.F.J. Lermusiaux, and J. Wilkin, 2019. Multiscale Multiphysics Data-Informed Modeling for Three-Dimensional Ocean Acoustic Simulation and Prediction. Journal of the Acoustical Society of America, 146(3), 1996–2015. doi:10.1121/1.5126012

Three-dimensional (3D) underwater sound field computations have been used for a few decades to understand sound propagation effects above sloped seabeds and in areas with strong 3D temperature and salinity variations. For an approximate simulation of effects in nature, the necessary 3D sound-speed field can be made from snapshots of temperature and salinity from an operational data-driven regional ocean model. However, these models invariably have resolution constraints and physics approximations that exclude features that can have strong effects on acoustics, example features being strong submesoscale fronts and nonhydrostatic nonlinear internal waves (NNIWs). Here, work to predict NNIW fields to improve 3D acoustic forecasts using an NNIW model nested in a tide-inclusive data-assimilating regional model is reported. The work was initiated under the Integrated Ocean Dynamics and Acoustics project. The project investigated ocean dynamical processes that affect important details of sound-propagation, with a focus on those with strong intermittency (high kurtosis) that are challenging to predict deterministically. Strong internal tides and NNIW are two such phenomena, with the former being precursors to NNIW, often feeding energy to them. Successful aspects of the modeling are reported along with weaknesses and unresolved issues identified in the course of the work.
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Distributed Implementation and Verification of Hybridizable Discontinuous Galerkin Methods for Nonhydrostatic Ocean Processes

Foucart, C., C. Mirabito, P.J. Haley, Jr., and P.F.J. Lermusiaux, 2018. Distributed Implementation and Verification of Hybridizable Discontinuous Galerkin Methods for Nonhydrostatic Ocean Processes. In: Oceans '18 MTS/IEEE Charleston, 22-25 October 2018. doi:10.1109/oceans.2018.8604679

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.

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Scalable Coupled Ocean and Water Turbine Modeling for Assessing Ocean Energy Extraction

Deluca, S., B. Rocchio, C. Foucart, C. Mirabito, S. Zanforlin, P.J. Haley, and P.F.J. Lermusiaux, 2018. Scalable Coupled Ocean and Water Turbine Modeling for Assessing Ocean Energy Extraction. In: Oceans '18 MTS/IEEE Charleston, 22-25 October 2018. doi:10.1109/oceans.2018.8604646

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.

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Clustering of Massive Ensemble of Vehicle Trajectories in Strong, Dynamic and Uncertain Ocean Flows

Dutt, A., D.N. Subramani, C.S. Kulkarni, and P.F.J. Lermusiaux, 2018. Clustering of Massive Ensemble of Vehicle Trajectories in Strong, Dynamic and Uncertain Ocean Flows. In: Oceans '18 MTS/IEEE Charleston, 22-25 October 2018. doi:10.1109/oceans.2018.8604634

Recent advances in probabilistic forecasting of regional ocean dynamics, and stochastic optimal path planning with massive ensembles motivate principled analysis of their large datasets. Specifically, stochastic time-optimal path planning in strong, dynamic and uncertain ocean flows produces a massive dataset of the stochastic distribution of exact timeoptimal trajectories. To synthesize such big data and draw insights, we apply machine learning and data mining algorithms. Particularly, clustering of the time-optimal trajectories is important to describe their PDFs, identify representative paths, and compute and optimize risk of following these paths. In the present paper, we explore the use of hierarchical clustering algorithms along with a dissimilarity matrix computed from the pairwise discrete Frechet distance between all the optimal trajectories. We apply the algorithms to two datasets of massive ensembles of vehicle trajectories in a stochastic flow past a circular island and stochastic wind driven double gyre flow. These paths are computed by solving our dynamically orthogonal level set equations. Hierarchical clustering is applied to the two datasets, and results are qualitatively and quantitatively analyzed.

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Real-Time Sediment Plume Modeling in the Southern California Bight

Kulkarni, C.S., P.J. Haley, Jr., P.F.J. Lermusiaux, A. Dutt, A. Gupta, C. Mirabito, D.N. Subramani, S. Jana, W.H. Ali, T. Peacock, C.M. Royo, A. Rzeznik, and R. Supekar, 2018. Real-Time Sediment Plume Modeling in the Southern California Bight. In: Oceans '18 MTS/IEEE Charleston, 22-25 October 2018. doi:10.1109/oceans.2018.8653642

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.
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Sensitivity of the Bay of Bengal upper ocean to different winds and river input conditions

Jana, S., A. Gangopadhyay, P.F.J. Lermusiaux, A. Chakraborty, S. Sil, and P.J. Haley Jr., 2018. Sensitivity of the Bay of Bengal Upper Ocean to Different Winds and River Input Conditions. Journal of Marine Systems, 187, 206–222. doi:10.1016/j.jmarsys.2018.08.001

The sensitivity of the Bay of Bengal (BoB) upper ocean circulation and thermohaline structure to varying wind strengths and river salinity conditions is investigated using a set of long-term mesoscale simulations. The Regional Ocean Modeling System (ROMS) simulations differ in their forcing fields for winds (strong vs. weak) and in their representations of river input salinity conditions (seasonally varying estuarine salinity vs. zero salinity). The sensitivities are analyzed in terms of the responses of the surface circulation, thermohaline structure, freshwater plume dispersion, and the coastal upwelling along the western boundary. All the simulations reproduce the main broad-scale features of the Bay, while their magnitudes and variabilities depend on the forcing conditions. The impact of stronger wind is felt at greater depths for temperature than for salinity throughout the domain; however, the impact is realized with vertical distributions that are different in the northern than in the southern Bay.

As expected, the stronger wind-induced enhanced mixing lowers (enhances) the upper ocean temperature (salinity) by 0.2C (0.3 psu), and weakens the near-surface stratification. Moreover, stronger wind enhances eddy activity, strengthens the springtime Western Boundary Current (WBC) and enhances coastal upwelling during spring and summer along the east coast of India. The fresher river input reduces the surface salinity and hence enhances the spreading and intensity of the freshwater plume, stratification, and barrier layer thickness. The lower salinity simulation leads to an eddy-dominant springtime WBC, and enhances the freshness, strength, and southward extent of the autumn East India Coastal Current (EICC). The stronger wind simulations appear to prevent the spreading of the freshwater plume during the summer monsoon due to enhanced mixing. Fresher river input reduces the overall surface salinity by ~0.4 psu; however, it significantly underestimates the salinity near the river mouths, whereas the estuarine salinity river input simulations are closer to reality. These results highlight the importance of river input salinity and realistic strong winds in reducing model biases of high-resolution simulations for the Bay of Bengal.

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Dynamically Orthogonal Numerical Schemes for Efficient Stochastic Advection and Lagrangian Transport

Feppon, F. and P.F.J. Lermusiaux, 2018. Dynamically Orthogonal Numerical Schemes for Efficient Stochastic Advection and Lagrangian Transport. SIAM Review, 60(3), 595–625. doi:10.1137/16m1109394

Quantifying the uncertainty of Lagrangian motion can be performed by solving a large number of ordinary differential equations with random velocities, or equivalently a stochastic transport partial differential equation (PDE) for the ensemble of flow-maps. The Dynamically Orthogonal (DO) decomposition is applied as an efficient dynamical model order reduction to solve for such stochastic advection and Lagrangian transport. Its interpretation as the method that applies instantaneously the truncated SVD on the matrix discretization of the original stochastic PDE is used to obtain new numerical schemes. Fully linear, explicit central advection schemes stabilized with numerical filters are selected to ensure efficiency, accuracy, stability, and direct consistency between the original deterministic and stochastic DO advections and flow-maps. Various strategies are presented for selecting a time-stepping that accounts for the curvature of the fixed rank manifold and the error related to closely singular coefficient matrices. Efficient schemes are developed to dynamically evolve the rank of the reduced solution and to ensure the orthogonality of the basis matrix while preserving its smooth evolution over time. Finally, the new schemes are applied to quantify the uncertain Lagrangian motions of a 2D double gyre flow with random frequency and of a stochastic flow past a cylinder.

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Iterated Pressure-Correction Projection Methods for the Unsteady Incompressible Navier-Stokes Equations

Aoussou, J., J. Lin, and P.F.J. Lermusiaux, 2018. Iterated Pressure-Correction Projection Methods for the Unsteady Incompressible Navier-Stokes Equations. Journal of Computational Physics, 373, 940–974. doi:10.1016/j.jcp.2018.06.062

Iterated pressure-correction projection schemes for the unsteady incompressible Navier-Stokes equations are developed, analyzed and exemplified, in relation to preconditioned iterative methods and the pressure-Schur complement equation. Typical pressure-correction schemes perform only one iteration per stage or time step, and suffer from splitting errors that result in spurious numerical boundary layers and a limited order of convergence in time. We show that performing iterations not only reduces the effects of the splitting errors, but can also be more efficient computationally than merely reducing the time step. We devise stopping criteria to recover the desired order of temporal convergence, and to drive the splitting error below the time-integration error. We also develop and implement the iterated pressure corrections with both multi-step and multi-stage time integration schemes. Finally, to reduce further the computational cost of the iterated approach, we combine it with an Aitken acceleration scheme. Our theoretical results are validated and illustrated by numerical test cases for the Stokes and Navier-Stokes equations, using implicit-explicit (IMEX) backwards differences and Runge-Kutta time-integration solvers. The test cases comprise a now classical manufactured solution in the projection method community and a modified version of a more recently proposed manufactured solution. The different error types, stopping criterion, recovered orders of convergence, and acceleration rates are illustrated, as well as the effects of the rotational corrections and time-integration schemes. It is found that iterated pressure-correction schemes can retrieve the accuracy and temporal convergence order of fully-coupled schemes and are computationally more efficient than classic pressure-correction schemes.
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Environmental Ocean and Plume Modeling for Deep Sea Mining in the Bismarck Sea.

Coulin, J., P. J. Haley, Jr., S. Jana, C.S. Kulkarni, P. F. J. Lermusiaux, T. Peacock, 2017. Environmental Ocean and Plume Modeling for Deep Sea Mining in the Bismarck Sea. In: Oceans '17 MTS/IEEE Anchorage, 1-10, 18-21 September 2017.

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.
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The Sea: The Science of Ocean Prediction

Pinardi, N., P.F.J. Lermusiaux, K.H. Brink, and R.H. Preller, 2017. The Sea: The Science of Ocean Prediction. Preface to The Sea. Volume 17, The Science of Ocean Prediction, Part 1. Special Issue, J. Marine Res. 75(3). pp. 101-102

At the beginning of the 20th century Vilhelm Bjerknes defined the “ultimate problem of meteorology and hydrography” as the discovery of “the laws according to which an atmospheric or hydrospheric state develops out of the preceding one” and the “precalculation of future states” from gridded analyzed observations—that is, forecasting. The development of the electronic computer and the vision of several meteorologists allowed the transformation of meteorology into a sophisticated scientific discipline based on physics and mathematics. The first successful meteorological forecast was carried out in the 1950s. Meteorological forecasting became an operational activity at the end of the 1960s. The contributions to society of such operations have been tremendous.

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From weather to ocean predictions: an historical viewpoint

Pinardi, N., L. Cavaleri, P. De Mey, C. Fratianni, I. Huthnance, P.F.J. Lermusiaux, A. Navarra, R. Preller, and S. Tibalidi, 2017. From Weather to Ocean Predictions: an Historical Viewpoint. The Sea. Volume 17, The Science of Ocean Prediction, Part 1, Special Issue, J. Marine Res. 75(3). pp. 103-159. https://doi.org/10.1357/002224017821836789

This paper reviews the historical development of concepts and practices in the science of ocean predictions. It begins with meteorology which conducted the first forecasting experiment in 1950, followed by the wind waves and continuing with tidal and storm surge predictions to arrive at the first successful ocean mesoscale forecast in 1983. The work of Professor A.R.Robinson of Harvard University who produced the first mesoscale ocean predictions for the deep ocean regions is documented for the first time. The scientific and technological developments that made accurate ocean predictions possible are connected with the gradual understanding of the importance of the oceanic mesoscales and their inclusion in the numerical models. Ocean forecasting developed first at the regional level, due to the relatively low computational requirements, but by the end of the nineties it was possible to produce global ocean uncoupled forecasts and coupled ocean-atmosphere seasonal forecasts.

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A Coupled-mode Shallow Water model for tidal analysis: Internal-tide reflection and refraction by the Gulf Stream

Kelly, S.M., P.F.J. Lermusiaux, T. F. Duda, and P.J. Haley Jr., 2016. A Coupled-mode Shallow Water model for tidal analysis: Internal-tide reflection and refraction by the Gulf Stream. J. Phys. Oceanogr., 46, 3661–3679, doi: 10.1175/JPO-D-16-0018.1.

A novel hydrostatic coupled-mode shallow water model (CSW) is developed and used to simulate tides in the greater Middle Atlantic Bight region. The model incorporates realistic stratification and topography, an internal tide generating function (ITGF) that provides internal tide forcing from existing surface tide parameters, and dynamical terms that describe linearized wave- mean-flow and mean-density interactions. Several idealized and realistic simulations are used to verify the model. These verification simulations include internal-tide interactions involving topographic coupling and mean-flow coupling, and comparisons with other simpler and more complex nonlinear primitive-equation models. Then, twenty-four simulations of internal tide generation and propagation in the greater Middle Atlantic Bight region are used to identify significant internal-tide interactions with the Gulf Stream. The simulations indicate that locally generated mode-1 internal tides can refract and/or reflect at the Gulf Stream. The redirected internal tides often re-appear at the shelfbreak, where they produce onshore energy fluxes that are intermittent (i.e., noncoherent) because meanders in the Gulf Stream alter their precise location, phase, and amplitude. These results provide an explanation for the anomalous onshore energy fluxes previously observed at the New Jersey Shelfbreak and linked with the generation of nonlinear internal waves.
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Hybridizable Discontinuous Galerkin Projection Methods for Navier-Stokes and Boussinesq Equations

Ueckermann, M.P. and P.F.J. Lermusiaux, 2016. Hybridizable Discontinuous Galerkin Projection Methods for Navier-Stokes and Boussinesq Equations. Journal of Computational Physics, 306, 390–421. http://dx.doi.org/10.1016/j.jcp.2015.11.028

Schemes for the incompressible Navier-Stokes and Boussinesq equations are formulated and derived combining the novel Hybridizable Discontinuous Galerkin (HDG) method, a projection method, and Implicit-Explicit Runge-Kutta (IMEX-RK) time-integration schemes. We employ an incremental pressure correction and develop the corresponding HDG finite element discretization including consistent edge-space fluxes for the velocity predictor and pressure correction. We then derive the proper forms of the element-local and HDG edge-space final corrections for both velocity and pressure, including the HDG rotational correction. We also find and explain a consistency relation between the HDG stability parameters of the pressure correction and velocity predictor. We discuss and illustrate the effects of the time-splitting error. We then detail how to incorporate the HDG projection method time-split within standard IMEX-RK time-stepping schemes. Our high-order HDG projection schemes are implemented for arbitrary, mixed–element unstructured grids, with both straight-sided and curved meshes. In particular, we provide a quadrature-free integration method for a nodal basis that is consistent with the HDG method. To prevent numerical oscillations, we develop a selective nodal limiting approach. Its applications show that it can stabilize high-order schemes while retaining high-order accuracy in regions where the solution is sufficiently smooth. We perform spatial and temporal convergence studies to evaluate the properties of our integration and selective limiting schemes and to verify that our solvers are properly formulated and implemented. To complete these studies and to illustrate a range of properties for our new schemes, we employ an unsteady tracer advection benchmark, a manufactured solution for the steady diffusion and Stokes equations, and a standard lock-exchange Boussinesq problem.
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Optimizing Velocities and Transports for Complex Coastal Regions and Archipelagos

Haley, P.J., Jr., A. Agarwal, P.F.J. Lermusiaux, 2015. Optimizing Velocities and Transports for Complex Coastal Regions and Archipelagos. Ocean Modeling, 89, 1-28. doi:10.1016/j.ocemod.2015.02.005

We derive and apply a methodology for the initialization of velocity and transport fields in complex multiply-connected regions with multiscale dynamics. The result is initial fields that are consistent with observations, complex geometry and dynamics, and that can simulate the evolution of ocean processes without large spurious initial transients. A class of constrained weighted least squares optimizations is defined to best fit first-guess velocities while satisfying the complex bathymetry, coastline and divergence strong constraints. A weak constraint towards the minimum inter-island transports that are in accord with the first-guess velocities provides important velocity corrections in complex archipelagos. In the optimization weights, the minimum distance and vertical area between pairs of coasts are computed using a Fast Marching Method. Additional information on velocity and transports are included as strong or weak constraints. We apply our methodology around the Hawaiian islands of Kauai/Niihau, in the Taiwan/Kuroshio region and in the Philippines Archipelago. Comparisons with other common initialization strategies, among hindcasts from these initial conditions (ICs), and with independent in situ observations show that our optimization corrects transports, satisfies boundary conditions and redirects currents. Differences between the hindcasts from these different ICs are found to grow for at least 2-3 weeks. When compared to independent in situ observations, simulations from our optimized ICs are shown to have the smallest errors.

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Issues and Progress in the Prediction of Ocean Submesoscale Features and Internal Waves

Duda T.F., W.G. Zhang, K.R. Helfrich, A.E. Newhall, Y.-T. Lin, J.F. Lynch, P.F.J. Lermusiaux, P.J. Haley Jr., J. Wilkin, 2014. Issues and Progress in the Prediction of Ocean Submesoscale Features and Internal Waves. OCEANS'14 MTS/IEEE.

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.

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A Relocatable Ocean Model in support of environmental emergencies – The Costa Concordia emergency case

De Dominicis M., S. Falchetti, F. Trotta, N. Pinardi, L. Giacomelli, E. Napolitano, L. Fazioli, R. Sorgente, P.J. Haley Jr., P.F.J. Lermusiaux, F. Martins and M. Cocco, 2014. A Relocatable Ocean Model in support of environmental emergencies - The Costa Concordia emergency case. Ocean Dynamics, 64, 5:667–688. DOI 10.1007/s10236-014-0705-x

During the Costa Concordia emergency case, regional, subregional, and relocatable ocean models have been used together with the oil spill model, MEDSLIKII, to provide ocean currents forecasts, possible oil spill scenarios, and drifters trajectories simulations. The models results together with the evaluation of their performances are presented in this paper. In particular, we focused this work on the implementation of the Interactive RElocatable Nested Ocean Model (IRENOM), based on the Harvard Ocean Prediction System (HOPS), for the Costa Concordia emergency and on its validation using drifters released in the area of the accident. It is shown that thanks to the capability of improving easily and quickly its configuration, the IRENOM results are of greater accuracy than the results achieved using regional or subregional model products. The model topography, the initialization procedures, and the horizontal resolution are the key model settings to be configured. Furthermore, the IRENOM currents and the MEDSLIK-II simulated trajectories showed to be sensitive to the spatial resolution of the meteorological fields used, providing higher prediction skills with higher resolution wind forcing.
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Multiscale Modeling of Coastal, Shelf and Global Ocean Dynamics

Lermusiaux, P.F.J., J. Schröter, S. Danilov, M. Iskandarani, N. Pinardi and J.J. Westerink, 2013. Multiscale Modeling of Coastal, Shelf and Global Ocean Dynamics, Ocean Dynamics. 63:1341–1344. DOI: 10.1007/s10236-013-0655-8

In contemporary ocean science, modeling systems that integrate understanding of complex multiscale phenomena and utilize efficient numerics are paramount. Many of today’s fundamental ocean science questions involve multiple scales and multiple dynamics. A new generation of modeling systems would allow to study such questions quantitatively, by being less restrictive dynamically and more efficient numerically than more traditional systems. Such multiscale ocean modeling is the theme of this topical issue. Two large international workshops were organized on this theme, one in Cambridge, USA (IMUM2010), and one in Bremerhaven, Germany (IMUM2011). Contributions from the scientific community were encouraged on all aspects of multiscale ocean modeling, from ocean science and dynamics to the development of new computational methods and systems. Building on previous meetings (e.g. Deleersnijder and Lermusiaux, 2008; Deleersnijder et al., 2010), the workshop discussions and the final contributions to the topical issue are summarized next. The scientific application domains discussed and presented ranged from estuaries to the global ocean, including coastal regions and shelf seas. Multi-resolution modeling of physical, biological, chemical, and sea ice processes as well as air-sea interactions were described. The multiscale dynamics considered involved hydrostatic, non-hydrostatic, turbulent and sea surface processes. Computational results and discussions emphasized multi-resolution simulations using unstructured and structured meshes, aiming to widen the range of resolved scales in space and time. They included finite volume and finite element spatial-discretizations, high-order schemes, preconditioners, solver issues, grid generation, adaptive modeling, data assimilation, coupling with atmospheric or biogeochemical models, and distributed computing. The advantages of using unstructured meshes and related approaches, in particular multi-grid embedding, nesting systems, wavelets and other multi-scale decompositions were discussed. Techniques for the study of multi-resolution results, visualization, optimization, model evaluations, and uncertainty quantification were also examined.
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Time-Evolving Acoustic Propagation Modeling in a Complex Ocean Environment

Colin, M.E.G.D., T.F. Duda, L.A. te Raa, T. van Zon, P.J. Haley, Jr., P.F.J. Lermusiaux, W.G. Leslie, C. Mirabito, F.P.A. Lam, A.E. Newhall, Y.-T. Lin, J.F. Lynch, 2013. Time-Evolving Acoustic Propagation Modeling in a Complex Ocean Environment, Proceedings of OCEANS - Bergen, 2013 MTS/IEEE , vol., no., pp.1,9, 10-14 June 2013, doi: 10.1109/OCEANS-Bergen.2013.6608051.

During naval operations, sonar performance estimates often need to be computed in-situ with limited environmental information. This calls for the use of fast acoustic propagation models. Many naval operations are carried out in challenging and dynamic environments. This makes acoustic propagation and sonar performance behavior particularly complex and variable, and complicates prediction. Using data from a field experiment, we have investigated the accuracy with which acoustic propagation loss (PL) can be predicted, using only limited modeling capabilities. Environmental input parameters came from various sources that may be available in a typical naval operation.

The outer continental shelf shallow-water experimental area featured internal tides, packets of nonlinear internal waves, and a meandering water mass front. For a moored source/receiver pair separated by 19.6 km, the acoustic propagation loss for 800 Hz pulses was computed using the peak amplitude. The variations in sound speed translated into considerable PL variability of order 15 dB. Acoustic loss modeling was carried out using a data-driven regional ocean model as well as measured sound speed profile data for comparison. The acoustic model used a two-dimensional parabolic approximation (vertical and radial outward wavenumbers only). The variance of modeled propagation loss was less than that measured. The effect of the internal tides and sub-tidal features was reasonably well modeled; these made use of measured sound speed data. The effects of nonlinear waves were not well modeled, consistent with their known three-dimensional effects but also with the lack of measurements to initialize and constrain them.

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Numerical Schemes for Dynamically Orthogonal Equations of Stochastic Fluid and Ocean Flows

Ueckermann, M.P., P.F.J. Lermusiaux and T.P. Sapsis, 2013. Numerical Schemes for Dynamically Orthogonal Equations of Stochastic Fluid and Ocean Flows. J. Comp. Phys., 233, 272-294, doi: 10.1016/j.jcp.2012.08.041.

The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non- homogeneous fluid and ocean flows. The Dynamically Orthogonal (DO) field equations provide an efficient time-dependent adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier-Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the orthonormal modes that define a basis for the evolving DO subspace, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with Total Variation Diminishing schemes for the advection terms. Other results specific to the DO equations include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size in- stead of quadratic; (ii) symmetric Total Variation Diminishing-based advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify the correctness of our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.
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Special issue of Dynamics of Atmospheres and Oceans in honor of Prof. A.R. Robinson

Lermusiaux, P.F.J, A.J. Miller and N. Pinardi, 2011. Special issue of Dynamics of Atmospheres and Oceans in honor of Prof. A.R. Robinson, Editorial, Dynamics of Atmospheres and Oceans, 52, 1-3, doi:10.1016/j.dynatmoce.2011.08.001.

Professor Allan R. Robinson was one of the founding fathers of geophysical fluid dynamics. His research interests and seminal contributions have encompassed the dynamics of rotating and stratified fluids, boundary-layer flows, thermocline dynamics, the dynamics and modeling of mesoscale ocean currents, and the influence of physical processes on ocean biology. He is recognized as one of the pioneers and leading experts in modern ocean prediction, and contributed significantly to the techniques for the assimilation of data into ocean forecasting models. In the late 1950s and 1960s, Prof. Robinson’s research focused on fundamental geophysical fluid dynamics, including major contributions to thermocline theory, the wind-driven ocean circulation, coastally trapped waves, inertial currents and boundary layers. In the early 1970s, Prof. Robinson initiated investigations on realistic flow fields focusing in particular on mesoscale dynamics and forecasting, with contributions to western boundary currents, mesoscale eddies and baroclinic instabilities. He pioneered “ocean weather forecasting science” at the beginning of the 1980s, especially the development of conceptual models for the assimilation of both in situ and satellite data, specializing in the 1990s in the coupling between the deep sea and the coastal ocean. Focusing on mesoscale dynamics and coastal interactions, he also contributed to the development of new coupled physical-biological-acoustical and optical models, and he developed theories on the effects of oceanic motions on biological dynamics. Professor Robinson was also the Founding Editor of Dynamics of Atmospheres and Oceans.
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The California Current System: A Multiscale Overview and the Development of a Feature-Oriented Regional Modeling System (FORMS)

Gangopadhyay, A., P.F.J. Lermusiaux, L. Rosenfeld, A.R. Robinson, L. Calado, H.S. Kim, W.G. Leslie and P.J. Haley, Jr., 2011. The California Current System: A Multiscale Overview and the Development of a Feature-Oriented Regional Modeling System (FORMS). Dynamics of Atmospheres and Oceans, 52, 131-169, doi:10.1016/j.dynatmoce.2011.04.003.

Over the past decade, the feature-oriented regional modeling methodology has been developed and applied in several ocean domains, including the western North Atlantic and tropical North Atlantic. This methodology is model-independent and can be utilized with or without satellite and/or in situ observations. Here we develop new feature-oriented models for the eastern North Pacific from 36 to 48? – essentially, most of the regional eastern boundary current. This is the first time feature-modeling has been applied to a complex eastern boundary current system. As a prerequisite to feature modeling, prevalent features that comprise the multiscale and complex circulation in the California Current system (CCS) are first overviewed. This description is based on contemporary understanding of the features and their dominant space and time scales of variability. A synergistic configuration of circulation features interacting with one another on multiple and sometimes overlapping space and time scales as a meander-eddy-upwelling system is presented. The second step is to define the feature-oriented regional modeling system (FORMS). The major multiscale circulation features include the mean flow and southeastward meandering jet(s) of the California Current (CC), the poleward flowing California Undercurrent (CUC), and six upwelling regions along the coastline. Next, the typical synoptic width, location, vertical extent, and core characteristics of these features and their dominant scales of variability are identified from past observational, theoretical and modeling studies. The parameterized features are then melded with the climatology, in situ and remotely sensed data, as available. The methodology is exemplified here for initialization of primitiveequation models. Dynamical simulations are run as nowcasts and short-term (4-6 weeks) forecasts using these feature models (FM) as initial fields and the Princeton Ocean Model (POM) for dynamics. The set of simulations over a 40-day period illustrate the applicability of FORMS to a transient eastern boundary current region such as the CCS. Comparisons are made with simulations initialized from climatology only. The FORMS approach increases skill in several factors, including the: (i) maintenance of the low-salinity pool in the core of the CC; (ii) representation of eddy activity inshore of the coastal transition zone; (iii) realistic eddy kinetic energy evolution; (iv) subsurface (intermediate depth) mesoscale feature evolution; and (v) deep poleward flow evolution.
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Multiscale Physical and Biological Dynamics in the Philippines Archipelago: Predictions and Processes

Lermusiaux, P.F.J., P.J. Haley, Jr., W.G. Leslie, A. Agarwal, O. Logutov and L.J. Burton, 2011. Multiscale Physical and Biological Dynamics in the Philippines Archipelago: Predictions and Processes. Oceanography. PhilEx Issue, 24(1), 70-89, doi:10.5670/oceanog.2011.05.

The Philippine Archipelago is remarkable because of its complex geometry, with multiple islands and passages, and its multiscale dynamics, from the large-scale open-ocean and atmospheric forcing, to the strong tides and internal waves in narrow straits and at steep shelfbreaks. We employ our multiresolution modeling system to predict and study multiscale dynamics in the region, without the use of any synoptic in situ data, so as to evaluate modeling capabilities when only sparse remotely sensed sea surface height is available for assimilation. We focus on the February to March 2009 period, compare our simulation results to ocean observations, and utilize our simulations to quantify and discover oceanic features in the region. The findings include: the physical drivers for the biogeochemical features; the diverse circulation features in each sub-sea and their variations on multiple scales; the flow fields within the major straits and their variability; the transports to and from the Sulu Sea and the corresponding balances; and finally, the multiscale mechanisms involved in the formation of the deep Sulu Sea water.
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Computational Studies of 3D Ocean sound fields in areas of complex seafloor topography and active ocean dynamics

Duda, T.F., Y.-T. Lin, W.G. Zhang, B.D. Cornuelle, P.F.J. Lermusiaux, 2011. Computational Studies of 3D Ocean sound fields in areas of complex seafloor topography and active ocean dynamics. Proceedings of the 10th International Conference on Theoretical and Computational Acoustics, NTU, Taiwan, 12pp.

Over the last four decades the use of numerical flow models in oceanography has vastly increased. Models are run operationally for regional locations, ocean basins, and the entire earth. In addition, specialized research models targeting specific processes and areas are routinely produced. These models are often coupled with biological and chemical models for research into biological-physical and biogeochemical-physical interactions. The role of some models is to create conditions close to reality, in a deterministic sense, whereas others have the role of imitating mean behavior or fluctuation behavior. The role of yet another family of models is to alter conditions from reality to study the ramifications, examples being interdisciplinary climate models [1-3]. All of these models provide full access to time- evolving three-dimensional fields (4-D fields) for process studies, or for predictive purposes. There is strong motivation for using these models for ocean acoustic studies. Suitably formulated models can include the important flow and water-mass features of the ocean, with the important features covering a wide dynamic range. Each feature has its own acoustic propagation or scattering signature, with some signatures having an interfering effect on underwater acoustic activities. The signature can be in the temporal domain, the spatial domain, or both. An important part of ocean acoustics research at this time is identifying which processes are dominant at specific times and places, and models are well suited to this. Significant acoustic effects of water-column and seafloor features occur in concert. However, they have traditionally been studied individually, sometimes in idealized or very simple form. Despite the isolation of the processes, many of these studies have been very successful. Examples are the analysis of the Pekeris waveguide [4], adiabatic mode propagation in a smoothly varying waveguide [5], and propagation through idealized internal waves [6-8]. The state of our knowledge now demands that the full complexity be analyzed, as can be done using the ocean models. Initial efforts that have coupled four-dimensional ocean fields with 2D acoustics modeling include data assimilation and uncertainty studies [9, 10], end-to-end computations [11], real-time at-sea predictions [12] and coupled adaptive sampling [13]. In the present work, a specific focus is on 3D acoustic effects coupled to 4D ocean predictions. We have thus motivated the use of oceanographic flow models as a straightforward approach for objective and comprehensive study of sound propagation in realistic environments, which we refer to as coupled ocean/acoustics modeling. The alternative of investigating the overall effects of simultaneously occurring feature types by constructing idealized process models with multiple features (straight line internal waves in two-layer fluid over a uniformly sloped bottom and one eddy, for example) is likely to lack objectivity or completeness. In fact, such feature models are mainly utilized to initialize ocean models or describe/assimilate specific features [14]. Coupled ocean/acoustics modeling can have high value, under the condition that the synthesized environments are sufficiently inclusive, representative, and accurate. This is a nontrivial condition; many challenges remain for flow models in terms of boundary conditions and data assimilation, resolution of near-boundary effects and mixing effects, and three-dimensional nonlinear gravity waves with hydrostatic pressure. Note that making acoustic propagation predictions, without analysis of the behavior or the mechanisms at work, is a byproduct of coupled ocean-acoustic modeling. Coupled ocean/acoustics modeling is becoming more common. Nevertheless, the approach is relatively recent and the best research path to take at this time deserves discussion. In this paper we discuss the potential of this method, and inform the discussion with some example computations from recent work in the Mid Atlantic Bight.
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Many Task Computing for Real-Time Uncertainty Prediction and Data Assimilation in the Ocean

Evangelinos, C., P.F.J. Lermusiaux, J. Xu, P.J. Haley, and C.N. Hill, 2011. Many Task Computing for Real-Time Uncertainty Prediction and Data Assimilation in the Ocean. IEEE Transactions on Parallel and Distributed Systems, Special Issue on Many-Task Computing, I. Foster, I. Raicu and Y. Zhao (Guest Eds.), 22, doi: 10.1109/TPDS.2011.64.

Uncertainty prediction for ocean and climate predictions is essential for multiple applications today. Many-Task Computing can play a significant role in making such predictions feasible. In this manuscript, we focus on ocean uncertainty prediction using the Error Subspace Statistical Estimation (ESSE) approach. In ESSE, uncertainties are represented by an error subspace of variable size. To predict these uncertainties, we perturb an initial state based on the initial error subspace and integrate the corresponding ensemble of initial conditions forward in time, including stochastic forcing during each simulation. The dominant error covariance (generated via SVD of the ensemble) is used for data assimilation. The resulting ocean fields are used as inputs for predictions of underwater sound propagation. ESSE is a classic case of Many Task Computing: It uses dynamic heterogeneous workflows and ESSE ensembles are data intensive applications. We first study the execution characteristics of a distributed ESSE workflow on a medium size dedicated cluster, examine in more detail the I/O patterns exhibited and throughputs achieved by its components as well as the overall ensemble performance seen in practice. We then study the performance/usability challenges of employing Amazon EC2 and the Teragrid to augment our ESSE ensembles and provide better solutions faster.
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Statistical Field Estimation for Complex Coastal Regions and Archipelagos

Agarwal, A. and P.F.J. Lermusiaux, 2011. Statistical Field Estimation for Complex Coastal Regions and Archipelagos. Ocean Modeling, 40(2), 164-189, doi: 10.1016/j.ocemod.2011.08.001.

A fundamental requirement in realistic ocean simulations and dynamical studies is the optimal estimation of gridded fields from the spatially irregular and multivariate data sets that are collected by varied platforms. In this work, we derive and utilize new schemes for the mapping and dynamical inference of ocean fields in complex multiply-connected domains and study the computational properties of these schemes. Specifically, we extend a Bayesian-based multiscale Objective Analysis (OA) approach to complex coastal regions and archipelagos. Such OAs commonly require an estimate of the distances between data and model points, without going across complex landforms. New OA schemes that estimate the length of shortest sea paths using the Level Set Method (LSM) and Fast Marching Method (FMM) are thus derived, implemented and utilized in idealized and realistic ocean cases. An FMM-based methodology for the estimation of total velocity under geostrophic balance in complex domains is also presented. Comparisons with other OA approaches are provided, including those using stochastically forced partial differential equations (SPDEs). We find that the FMM-based OA scheme is the most efficient and accurate. The FMM-based field maps do not require postprocessing (smoothing). Mathematical and computational properties of our new OA schemes are studied in detail, using fundamental theorems and illustrations. We find that higher-order FMM’s schemes improve accuracy and that a multi-order scheme is efficient. We also provide solutions that ensure the use of positive-definite covariances, even in complex multiply-connected domains.
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Merging Multiple Partial-Depth Data Time Series Using Objective Empirical Orthogonal Function Fitting

Lin, Y.-T., A.E. Newhall, T.F. Duda, P.F. J. Lermusiaux and P.J. Haley, Jr., 2010. Merging Multiple Partial-Depth Data Time Series Using Objective Empirical Orthogonal Function Fitting. IEEE Transactions, Journal of Oceanic Engineering. 35(4) 710-721. doi:10.1109/JOE.2010.2052875.

In this paper, a method for merging partial overlap- ping time series of ocean profiles into a single time series of profiles using empirical orthogonal function (EOF) decomposition with the objective analysis is presented. The method is used to handle internal waves passing two or more mooring locations from multiple directions, a situation where patterns of variability cannot be accounted for with a simple time lag. Data from one mooring are decomposed into linear combination of EOFs. Objective analysis using data from another mooring and these patterns is then used to build the necessary profile for merging the data, which is a linear combination of the EOFs. This method is applied to temperature data collected at a two vertical moorings in the 2006 New Jersey Shelf Shallow Water Experiment (SW06). Resulting profiles specify conditions for 35 days from sea surface to seafloor at a primary site and allow for reliable acoustic propagation modeling, mode decomposition, and beamforming.
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Automated Sensor Networks to Advance Ocean Science

Schofield, O., S. Glenn, J. Orcutt, M. Arrott, M. Meisinger, A. Gangopadhyay, W. Brown, R. Signell, M. Moline, Y. Chao, S. Chien, D. Thompson, A. Balasuriya, P.F.J. Lermusiaux and M. Oliver, 2010. Automated Sensor Networks to Advance Ocean Science. EOS, Vol. 91, No. 39, 28 September 2010.

Oceanography is evolving from a ship-based expeditionary science to a distributed, observatory- based approach in which scientists continuously interact with instruments in the field. These new capabilities will facilitate the collection of long- term time series while also providing an interactive capability to conduct experiments using data streaming in real time. The U.S. National Science Foundation has funded the Ocean Observatories Initiative (OOI), which over the next 5 years will deploy infrastructure to expand scientists’ ability to remotely study the ocean. The OOI is deploying infrastructure that spans global, regional, and coastal scales. A global component will address planetary- scale problems using a new network of moored buoys linked to shore via satellite telecommunications. A regional cabled observatory will “wire” a single region in the northeastern Pacific Ocean with a high-speed optical and power grid. The coastal component will expand existing coastal observing assets to study the importance of high-frequency forcing on the coastal environment. These components will be linked by a robust cyberinfrastructure (CI) that will integrate marine observatories into a coherent system of systems. This CI infrastructure will also provide a Web- based social network enabled by real- time visualization and access to numerical model information, to provide the foundation for adaptive sampling science. Thus, oceanographers will have access to automated machine-to-machine sensor networks that can be scalable to increase in size and incorporate new technology for decades to come. A case study of this CI in action shows how a community of ocean scientists and engineers located throughout the United States at 12 different institutions used the automated ocean observatory to address daily adaptive science priorities in real time.
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High Order Schemes for 2D Unsteady Biogeochemical Ocean Models

Ueckermann, M.P. and P.F.J. Lermusiaux, 2010. High Order Schemes for 2D Unsteady Biogeochemical Ocean Models. Ocean Dynamics, 60, 1415-1445, doi:10.1007/s10236-010-0351-x

Accurate numerical modeling of biogeochemical ocean dynamics is essential for numerous applications, including coastal ecosystem science, environmental management and energy, and climate dynamics. Evaluating computational requirements for such often highly nonlinear and multiscale dynamics is critical. To do so, we complete comprehensive numerical analyses, comparing low- to high-order discretization schemes, both in time and space, employing standard and hybrid discontinuous Galerkin finite element methods, on both straight and new curved elements. Our analyses and syntheses focus on nutrient-phytoplankton-zooplankton dynamics under advection and diffusion within an ocean strait or sill, in an idealized 2D geometry. For the dynamics, we investigate three biological regimes, one with single stable points at all depths and two with stable limit cycles. We also examine interactions that are dominated by the biology, by the advection, or that are balanced. For these regimes and interactions, we study the sensitivity to multiple numerical parameters including quadrature-free and quadrature-based discretizations of the source terms, order of the spatial discretizations of advection and diffusion operators, order of the temporal discretization in explicit schemes, and resolution of the spatial mesh, with and without curved elements. A first finding is that both quadrature-based and quadrature-free discretizations give accurate results in well-resolved regions, but the quadrature-based scheme has smaller errors in underresolved regions. We show that low-order temporal discretizations allow rapidly growing numerical errors in biological fields. We find that if a spatial discretization (mesh resolution and polynomial degree) does not resolve the solution, oscillations due to discontinuities in tracer fields can be locally significant for both lowand high-order discretizations. When the solution is sufficiently resolved, higher-order schemes on coarser grids perform better (higher accuracy, less dissipative) for the same cost than lower-order scheme on finer grids. This result applies to both passive and reactive tracers and is confirmed by quantitative analyses of truncation errors and smoothness of solution fields. To reduce oscillations in un-resolved regions, we develop a numerical filter that is active only when and where the solution is not smooth locally. Finally, we consider idealized simulations of biological patchiness. Results reveal that higher-order numerical schemes can maintain patches for long-term integrations while lowerorder schemes are much too dissipative and cannot, even at very high resolutions. Implications for the use of simulations to better understand biological blooms, patchiness, and other nonlinear reactive dynamics in coastal regions with complex bathymetric features are considerable.
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Multiscale two-way embedding schemes for free-surface primitive-equations in the Multidisciplinary Simulation, Estimation and Assimilation System

Haley, P.J., Jr. and P.F.J. Lermusiaux, 2010. Multiscale two-way embedding schemes for free-surface primitive-equations in the Multidisciplinary Simulation, Estimation and Assimilation System. Ocean Dynamics, 60, 1497-1537. doi:10.1007/s10236-010-0349-4.

We derive conservative time-dependent structured discretizations and two-way embedded (nested) schemes for multiscale ocean dynamics governed by primitive equations (PEs) with a nonlinear free surface. Our multiscale goal is to resolve tidalto- mesoscale processes and interactions over large multiresolution telescoping domains with complex geometries including shallow seas with strong tides, steep shelfbreaks, and deep ocean interactions. We first provide an implicit time-stepping algorithm for the nonlinear free-surface PEs and then derive a consistent time-dependent spatial discretization with a generalized vertical grid. This leads to a novel timedependent finite volume formulation for structured grids on spherical or Cartesian coordinates, second order in time and space, which preserves mass and tracers in the presence of a time-varying free surface. We then introduce the concept of two-way nesting, implicit in space and time, which exchanges all of the updated fields values across grids, as soon as they become available. A class of such powerful nesting schemes applicable to telescoping grids of PE models with a nonlinear free surface is derived. The schemes mainly differ in the fine-to-coarse scale transfers and in the interpolations and numerical filtering, specifically for the barotropic velocity and surface pressure components of the two-way exchanges. Our scheme comparisons show that for nesting with free surfaces, the most accurate scheme has the strongest implicit couplings among grids. We complete a theoretical truncation error analysis to confirm and mathematically explain findings. Results of our discretizations and two-way nesting are presented in realistic multiscale simulations with data assimilation for the middle Atlantic Bight shelfbreak region off the east coast of the USA, the Philippine archipelago, and the Taiwan-Kuroshio region. Multiscale modeling with two-way nesting enables an easy use of different sub-gridscale parameterizations in each nested domain. The new developments drastically enhance the predictive capability and robustness of our predictions, both qualitatively and quantitatively. Without them, our multiscale multiprocess simulations either were not possible or did not match ocean data.
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Multi-scale modelling of coastal, shelf and global ocean dynamics

Deleersnijder, E., V. Legat and P.F.J. Lermusiaux, 2010. Multi-scale modelling of coastal, shelf and global ocean dynamics. Ocean Dynamics. 60, 1357-1359. doi:10.1007/s10236-010-0363-6.

Methods for widening the range of resolved scales (i.e. performing multi-scale simulations) in ocean sciences and engineering are developing rapidly, now allowing multiscale ocean dynamics studies. Having recourse to grid nesting has been and still is a popular method for increasing marine models’ resolution when and where needed and for easily allowing the use of different dynamics at different resolution. However, this is not the only way to achieve this goal. Various techniques for modifying locally the grid resolution or dealing with complex-geometry domains are available. For instance, composite, structured grids and unstructured meshes offer an almost infinite geometrical flexibility. This special issue focuses on multi-scale modelling of coastal, shelf and global ocean dynamics, including the development of new methodologies and schemes and their applications to ocean process studies. Several articles focus on numerical aspects of unstructured mesh space discretisation. Danilov (2010) shows that the noise developing on triangular meshes on which the location of the variables is inspired by Arakawa’s C-grid is the largest for regimes close to geostrophic balance. The noise can be reduced by specific operators but cannot be entirely suppressed, “making the triangular C-grid a suboptimal choice for large-scale ocean modelling”. Then, the companion articles of Blaise et al. (2010) and Comblen et al. (2010) describe the space and time discretisation of a three-dimensional, baroclinic, finite element model based on the discontinuous Galerkin (DG) technique. This is a significant step forward in the field of finite element ocean modelling, though this model cannot yet be regarded as suitable for tackling realistic applications. Ueckermann and Lermusiaux (2010) also consider DG finite element techniques, focusing on biological-physical dynamics in regions with complex bathymetric features. They compare low- to high-order discretisations, both in time and space, for regimes in which biology dominates, advection dominates or terms are balanced. They find that higher-order schemes on relatively coarse grids generally perform better than low-order schemes on fine grids. Kleptsova et al. (2010) assess various advection schemes for z-coordinate, threedimensional models in which flooding and drying is taken into account. In this study, the ability to conserve momentum is regarded as the main criterion for selecting a suitable method. On the other hand, Massmann (2010) assesses automatic differentiation for obtaining the adjoint of an unstructured mesh, tidal model of the European continental shelf. Two articles deal with grid nesting. Nash and Hartnett (2010) introduce a flooding and drying method that can be used in structured, nested grid systems. This can be regarded as an alternative to flooding and drying techniques that are being developed for unstructured mesh models (e.g. Karna et al. 2010). Then, Haley and Lermusiaux (2010) derive conservative time-dependent structured finite volume discretisations and implicit two-way embedded schemes for primitive equations with the intent to resolve tidal-to-mesoscale processes over large multi-resolution telescoping domains with complex geometries including shallow seas with strong tides, steep shelf breaks and deep ocean interactions. The authors present realistic simulations with data assimilation in three regions with diverse dynamics and show that their developments enhance the predictive capability, leading to better match with ocean data. Various multi-scale, realistic simulations are presented. Using a finite element ice model and a slab ocean as in Lietaer et al. (2008), Terwisscha van Scheltinga et al. (2010) model the Canadian Arctic Archipelago, focusing on the pathways for freshwater and sea-ice transport from the Arctic Ocean to the Labrador Sea and the Atlantic Ocean. The unstructured mesh can represent the complex geometry and narrow straits at high resolution and allows improving transports of water masses and sea ice. Walters et al. (2010) have recourse to an unstructured mesh model to study tides and current in Greater Cook Strait (New Zealand). They identify the mechanisms causing residual currents. By means of the unstructured mesh Finite Volume Coastal Ocean Model (FVCOM), Wang et al. (2010) study the hydrodynamics of the Bohai Sea. Xu et al. (2010) simulate coastal and urban inundation due to storm surges along US East and Gulf Coasts. A sensitivity analysis reveals the importance of precise topographic data and the need for a bottom drag coefficient accounting for the presence of mangroves. Finally, Yang and Khangaonkar (2010) resort to FVCOM to simulate the three-dimensional circulation of Puget Sound, a large complex estuary system in the Pacific Northwest coastal ocean, including variable forcing from tides, the atmosphere and river inflows. Comparisons of model estimates with measurements for tidal elevation, velocity, temperature and salinity are deemed to be promising, from larger-scale circulation features to nearshore tide flats. This special issue suggests that numerical techniques for multi-scale space discretisation are progressively becoming mature. One direction for future progress lies in the improvement of time discretisation methods for the new generation models, so that they can successfully compete with finite difference, structured mesh models based on (almost) constant resolution grids that have been developed and used over the past 40 years (e.g. Griffies et al. 2009).
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Preparing to Predict: The Second Autonomous Ocean Sampling Network (AOSN-II) Experiment in the Monterey Bay

Ramp, S.R., R. E. Davis, N. E. Leonard, I. Shulman, Y. Chao, A. R. Robinson, J. Marsden, P.F.J. Lermusiaux, D. Fratantoni, J. D. Paduan, F. Chavez, F. L. Bahr, S. Liang, W. Leslie, and Z. Li, 2009. Preparing to Predict: The Second Autonomous Ocean Sampling Network (AOSN-II) Experiment in the Monterey Bay. Special issue on AOSN-II, Deep Sea Research, Part II, 56, 68-86, doi: 10.1016/j.dsr2.2008.08.013.

The Autonomous Ocean Sampling Network Phase Two (AOSN-II) experiment was conducted in and offshore from the Monterey Bay on the central California coast during July 23-September 6, 2003. The objective of the experiment was to learn how to apply new tools, technologies, and analysis techniques to adaptively sample the coastal ocean in a manner demonstrably superior to traditional methodologies, and to use the information gathered to improve predictive skill for quantities of interest to end-users. The scientific goal was to study the upwelling/relaxation cycle near an open coastal bay in an eastern boundary current region, particularly as it developed and spread from a coastal headland. The suite of observational tools used included a low-flying aircraft, a fleet of underwater gliders, including several under adaptive autonomous control, and propeller-driven AUVs in addition to moorings, ships, and other more traditional hardware. The data were delivered in real time and assimilated into the Harvard Ocean Prediction System (HOPS), the Navy Coastal Ocean Model (NCOM), and the Jet Propulsion Laboratory implementation of the Regional Ocean Modeling System (JPL/ROMS).

Two upwelling events and one relaxation event were sampled during the experiment. The upwelling in both cases began when a pool of cold water less than 13oC appeared near Cape Ano Nuevo and subsequently spread offshore and southward across the bay as the equatorward wind stress continued. The primary difference between the events was that the first event spread offshore and southward, while the second event spread only southward and not offshore. The difference is attributed to the position and strength of meanders and eddies of the California Current System offshore, which blocked or steered the cold upwelled water. The space and time scales of the mesoscale variability were much shorter than have been previously observed in deep-water eddies offshore. Additional process studies are needed to elucidate the dynamics of the flow.
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Underwater acoustic sparse aperture system performance: Using transmitter channel state information for multipath & interference rejection

Puryear, A., L.J. Burton, P.F.J. Lermusiaux, and V.W.S. Chan, 2009. Underwater acoustic sparse aperture system performance: Using transmitter channel state information for multipath & interference rejection. OCEANS 2009-EUROPE, pp. 1-9, 11-14 May 2009, doi:10.1109/OCEANSE.2009.5278156.

Today’s situational awareness requirements in the undersea environment present severe challenges for acoustic communication systems. Acoustic propagation through the ocean environment severely limits the capacity of existing underwater communication systems. Specifically, the presence of internal waves coupled with the ocean sound channel creates a stochastic field that introduces deep fades and significant intersymbol interference (ISI) thereby limiting reliable communication to low data rates. In this paper we present a communication architecture that optimally predistorts the acoustic wave via spatial modulation and detects the acoustic wave with optimal spatial recombination to maximize reliable information throughput. This effectively allows the system to allocate its power to the most efficient propagation modes while mitigating ISI. Channel state information is available to the transmitter through low rate feedback. New results include the asymptotic distribution of singular values for a large number of apertures. Further, we present spatial modulation at the transmitter and spatial recombination at the receiver that asymptotically minimize bit error rate (BER). We show that, in many applications, the number of apertures can be made large enough so that asymptotic results approximate finite results well. Additionally, we show that the interference noise power is reduced proportional to the inverse of the number of receive apertures. Finally, we calculate the asymptotic BER for the sparse aperture acoustic system.
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Acoustically Focused Adaptive Sampling and On-board Routing for Marine Rapid Environmental Assessment

Wang, D., P.F.J. Lermusiaux, P.J. Haley, D. Eickstedt, W.G. Leslie and H. Schmidt, 2009. Acoustically Focused Adaptive Sampling and On-board Routing for Marine Rapid Environmental Assessment. Special issue of Journal of Marine Systems on "Coastal processes: challenges for monitoring and prediction", Drs. J.W. Book, Prof. M. Orlic and Michel Rixen (Guest Eds), 78, S393-S407, doi: 10.1016/j.jmarsys.2009.01.037.

Variabilities in the coastal ocean environment span a wide range of spatial and temporal scales. From an acoustic viewpoint, the limited oceanographic measurements and today’s ocean computational capabilities are not always able to provide oceanic-acoustic predictions in high-resolution and with enough accuracy. Adaptive Rapid Environmental Assessment (AREA) is an adaptive sampling concept being developed in connection with the emergence of Autonomous Ocean Sampling Networks and interdisciplinary ensemble predictions and adaptive sampling via Error Subspace Statistical Estimation (ESSE). By adaptively and optimally deploying in situ sampling resources and assimilating these data into coupled nested ocean and acoustic models, AREA can dramatically improve the estimation of ocean fields that matter for acoustic predictions. These concepts are outlined and a methodology is developed and illustrated based on the Focused Acoustic Forecasting-05 (FAF05) exercise in the northern Tyrrhenian sea. The methodology first couples the data-assimilative environmental and acoustic propagation ensemble modeling. An adaptive sampling plan is then predicted, using the uncertainty of the acoustic predictions as input to an optimization scheme which finds the parameter values of autonomous sampling behaviors that optimally reduce this forecast of the acoustic uncertainty. To compute this reduction, the expected statistics of unknown data to be sampled by different candidate sampling behaviors are assimilated. The predicted-optimal parameter values are then fed to the sampling vehicles. A second adaptation of these parameters is ultimately carried out in the water by the sampling vehicles using onboard routing, in response to the real ocean data that they acquire. The autonomy architecture and algorithms used to implement this methodology are also described. Results from a number of real-time AREA simulations using data collected during the Focused Acoustic Forecasting (FAF05) exercise are presented and discussed for the case of a single Autonomous Underwater Vehicle (AUV). For FAF05, the main AREA-ESSE application was the optimal tracking of the ocean thermocline based on ocean-acoustic ensemble prediction, adaptive sampling plans for vertical Yo-Yo behaviors and subsequent onboard Yo-Yo routing.
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Many Task Computing for Multidisciplinary Ocean Sciences: Real-Time Uncertainty Prediction and Data Assimilation

Evangelinos, C., P.F.J. Lermusiaux, J. Xu, P.J. Haley, and C.N. Hill, 2009. Many Task Computing for Multidisciplinary Ocean Sciences: Real-Time Uncertainty Prediction and Data Assimilation. Conference on High Performance Networking and Computing, Proceedings of the 2nd Workshop on Many-Task Computing on Grids and Supercomputers (Portland, OR, 16 November 2009), 10pp. doi.acm.org/10.1145/1646468.1646482.

Error Subspace Statistical Estimation (ESSE), an uncertainty prediction and data assimilation methodology employed for real-time ocean forecasts, is based on a characterization and prediction of the largest uncertainties. This is carried out by evolving an error subspace of variable size. We use an ensemble of stochastic model simulations, initialized based on an estimate of the dominant initial uncertainties, to predict the error subspace of the model fields. The dominant error covariance (generated via an SVD of the ensemble-generated error covariance matrix) is used for data assimilation. The resulting ocean fields are provided as the input to acoustic modeling, allowing for the prediction and study of the spatiotemporal variations in acoustic propagation and their uncertainties. The ESSE procedure is a classic case of Many Task Computing: These codes are managed based on dynamic workflows for the: (i) perturbation of the initial mean state, (ii) subsequent ensemble of stochastic PE model runs, (iii) continuous generation of the covariance matrix, (iv) successive computations of the SVD of the ensemble spread until a convergence criterion is satisfied, and (v) data assimilation. Its ensemble nature makes it a many task data intensive application and its dynamic workflow gives it heterogeneity. Subsequent acoustics propagation modeling involves a very large ensemble of short-in-duration acoustics runs.
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A multigrid methodology for assimilation of measurements into regional tidal models

Logutov, O.G., 2008. A multigrid methodology for assimilation of measurements into regional tidal models. Ocean Dynamics, 58, 441-460, doi:10.1007/s10236-008-0163-4.

This paper presents a rigorous, yet practical, method of multigrid data assimilation into regional structured-grid tidal models. The new inverse tidal nesting scheme, with nesting across multiple grids, is designed to provide a fit of the tidal dynamics to data in areas with highly complex bathymetry and coastline geometry. In these areas, computational constraints make it impractical to fully resolve local topographic and coastal features around all of the observation sites in a stand-alone computation. The proposed strategy consists of increasing the model resolution in multiple limited area domains around the observation locations where a representativeness error is detected in order to improve the representation of the measurements with respect to the dynamics. Multiple high-resolution nested domains are set up and data assimilation is carried out using these embedded nested computations. Every nested domain is coupled to the outer domain through the open boundary conditions (OBCs). Data inversion is carried out in a control space of the outer domain model. A level of generality is retained throughout the presentation with respect to the choice of the control space; however, a specific example of using the outer domain OBCs as the control space is provided, with other sensible choices discussed. In the forward scheme, the computations in the nested domains do not affect the solution in the outer domain. The subsequent inverse computations utilize the observation-minus-model residuals of the forward computations across these multiple nested domains in order to obtain the optimal values of parameters in the control space of the outer domain model. The inversion is carried out by propagating the uncertainty from the control space to model tidal fields at observation locations in the outer and in the nested domains using efficient low-rank error covariance representations. Subsequently, an analysis increment in the control space of the outer domain model is computed and the multigrid system is steered optimally towards observations while preserving a perfect dynamical balance. The method is illustrated using a real-world application in the context of the Philippines Strait Dynamics experiment.
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Multi-Scale Modelling: Nested Grid and Unstructured Mesh Approaches, Editorial

Deleersnijder, E. and P.F.J. Lermusiaux, (Guest Eds.), 2008. Multi-Scale Modelling: Nested Grid and Unstructured Mesh Approaches, Editorial. Ocean Dynamics, 58, 335-336, Springer. doi: 10.1007/s10236-008-0170-5.

In 1969, the Journal of Computational Physics published a seminal article by K. Bryan presenting the first ocean general circulation model. Since then, many numerical studies of the World Ocean, as well as regional or coastal flows, used models directly or indirectly inspired by the work of Bryan and his colleagues. A number of these models have evolved into highly modular and versatile computational systems, including multiple physical modules and options as well as varied biogeochemical, ecosystem and acoustics modeling capabilities. Several modeling systems are now well-documented tools, which are widely used in research institutions and various organizations around the world. The list of such modeling systems is large and too long to be summarized in this editorial. Over the last three decades, significant progress has been made in the parameterization of subgrid-scale processes, in data assimilation methodologies and in boundary condition schemes, as well as in the efficient implementation of algorithms on fast vector and subsequently parallel computers, allowing higher and higher resolution in space and time. However, many of today’s popular modeling systems can still be regarded as members of the first generation of ocean models: at their core, rather similar geophysical fluid dynamics equations are solved numerically using a conservative finite-difference method on a structured grid. Today, several aspects of structured-grid models could benefit from significant upgrades, learning from major advances in computational fluid dynamics. In particular, the use of a structured grid limits the flexibility in the spatial resolution and does not allow one to take full advantage of numerical algorithms such as finite volumes and finite elements, which can achieve their best performance when implemented on unstructured meshes. Even though many of today’s complex marine modeling and data assimilation systems have evolved significantly since Bryan’s prototype, it would be challenging to modify them step-by-step from a structured-grid approach to an unstructured-grid one. Therefore, novel marine model design research is underway, paving the way for the second generation of ocean modeling systems. It is difficult to predict today if this new generation of ocean models will achieve its chief objective: widening the range of resolved scales of motion with increased efficiencies and accuracies, possibly allowing multi-resolution, multi-scale, and multidynamics numerical simulations of marine flows, all occurring seamlessly within distributed computing environments. In fact, hybrid approaches merging the advantages of structured and unstructured-grid modeling may be the way forward. Whether or not unstructured mesh approaches will prevail is all the more difficult to predict now that structured mesh modelers have developed powerful solutions for increasing the resolution when and where needed. For instance, grid embedding is still a popular and useful method for enhancing model resolution. It can involve multiply nested domains and allows the relatively straightforward use of different dynamics or models in each domain. Research is also underway for developing multigrid, wavelet, and other multi-scale decompositions for the numerical solution of dynamical equations but also for the study of results, model evaluation or data assimilation. This special issue presents a number of examples of the abovementioned developments. Ringler et al. examine the potential of spherical centroidal Voronoi tessellations for performing multi-resolution simulations; they apply this method to the Greenland ice sheet and the North Atlantic Ocean. Lambrechts et al. present a triangular mesh generation system and its applications to the World Ocean and various shelf seas, including the Great Barrier Reef, Australia. Finite element models on unstructured grids are described and utilized in several manuscripts. Bellafiore et al. study the Adriatic Sea and the Lagoon of Venice, while Jones and Davies simulate tides and storm surges along the western coast of Britain. Danilov et al. assess two finite element discretizations, i.e., a continuous element and a non-conforming one, and compare the results of these discretizations with those of a finite-difference model. In Harig et al., the tsunami generated by the great Sumatra-Andaman earthquake of 26 December 2004 is simulated by means of a finite element model. Comparisons are carried out with various types of data as well as with the results of a structured mesh model using a nested structured-grid system. A nested-grid ocean circulation model is also employed by Yang and Sheng to carry out a process study on the Inner Scotian Shelf, Canada, focusing on the circulation induced by a tropical storm. Debreu and Blayo present a detailed review of two-way embedding algorithms for structured-grid models. Finally, Logutov develops a multi-scale assimilation scheme for tidal data within the framework of a multiply nested structured-grid barotropic tidal modeling approach. As illustrated by these manuscripts, the next generation of ocean modelers is motivated by a wide range of research opportunities over a rich spectrum of needs. Future progress will involve fundamental and applied numerical and computational research as well as new multi-scale geophysical fluid modeling. Domains of ongoing interest range from estuaries to the global ocean, including coastal regions and shelf seas. New multi-scale modeling of physical as well as biological, chemical or interdisciplinary processes will flourish in the coming decades. We are grateful to the authors for their contributions and to the chief-editor for his support in this endeavor. We are thankful to the reviewers for their time and help in assessing the manuscripts submitted to this special issue. Eric Deleersnijder is a Research associate with the Belgian National Fund for Scientific Research (FNRS); he is indebted to the Communaut Francaise de Belgique for its support through contract ARC 04/09-316. Pierre Lermusiaux is grateful to the Office of Naval Research for support under grant N00014-08-1-1097 to the Massachusetts Institute of Technology.
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Inverse Barotropic Tidal Estimation for Regional Ocean Applications

Logutov, O.G. and Lermusiaux, P.F.J., 2008. Inverse Barotropic Tidal Estimation for Regional Ocean Applications. Ocean Modeling, 25, 17-34. doi: 10.1016/j.ocemod.2008.06.004.

Correct representation of tidal processes in regional ocean models is contingent on the accurate specification of open boundary conditions. This paper describes a new inverse scheme for the assimilation of observational data into a depth-integrated spectral shallow water tidal model and the numerical implementation of this scheme into a stand-alone computational system for regional tidal prediction. A novel aspect is a specific implementation of the inverse which does not require an adjoint model. An optimization is carried out in the open boundary condition space rather than in the observational space or model state space. Our approach reflects the specifics of regional tidal modeling applications in which open boundary conditions (OBCs) typically constitute a significant source of uncertainty. Regional tidal models rely predominantly on global tidal estimates for open boundary conditions. As the resolution of global tidal models is insufficient to fully resolve regional topographic and coastal features, the a priori OBC estimates potentially contain an error. It is, therefore, desirable to correct these OBCs by finding an inverse OBC estimate that is fitted to the regional observations, in accord with the regional dynamics and respective error estimates. The data assimilation strategy presented in this paper provides a consistent and practical estimation scheme for littoral ocean science and applications where tidal effects are significant. Illustrations of our methodological and computational results are presented in the area of Dabob Bay and Hood Canal, WA, which is a region connected to the open Pacific ocean through a series of inland waterways and complex shorelines and bathymetry.
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Verification and Training of Real-Time Forecasting of Multi-Scale Ocean Dynamics for MREA

Leslie, W.G., A.R. Robinson, P.J. Haley, O. Logoutov, P. Moreno, P.F.J. Lermusiaux, E. Coehlo, 2008. Verification and Training of Real-Time Forecasting of Multi-Scale Ocean Dynamics for MREA. Journal of Marine Systems, 69, 3-16, doi: 10.1016/j.jmarsys.2007.02.001.

The Harvard Ocean Prediction System (HOPS) provides real-time and hindcast, multi-scale oceanic field estimates for Maritime Rapid Environmental Assessment (MREA). Results of aspects of the validation, calibration and verification of HOPS for MREA03 and MREA04 are presented, with implications for future MREA exercises. A new method of model training, via bias correction through the use of limited data, was applied to MREA03 and shown to produce significant forecast improvement while reducing computational requirements. Advances in, and the demand for, adaptive modeling, require that aspects of validation, calibration and verification be carried out in real-time in order to expand the usage and relevance of dynamical forecast-based MREA tactical decision aids
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Web-Enabled Configuration and Control of Legacy Codes: An Application to Ocean Modeling

Evangelinos, C., P.F.J. Lermusiaux, S. Geiger, R.C. Chang, and N.M. Patrikalakis, 2006. Web-Enabled Configuration and Control of Legacy Codes: An Application to Ocean Modeling. Ocean Modeling, 13, 197-220.

For modern interdisciplinary ocean prediction and assimilation systems, a significant part of the complexity facing users is the very large number of possible setups and parameters, both at build-time and at run-time, especially for the core physical, biological and acoustical ocean predictive models. The configuration of these modeling systems for both local as well as remote execution can be a daunting and error-prone task in the absence of a graphical user interface (GUI) and of software that automatically controls the adequacy and compatibility of options and parameters. We propose to encapsulate the configurability and requirements of ocean prediction codes using an eXtensible Markup Language (XML) based description, thereby creating new computer-readable manuals for the executable binaries. These manuals allow us to generate a GUI, check for correctness of compilation and input parameters, and finally drive execution of the prediction system components, all in an automated and transparent manner. This web-enabled configuration and automated control software has been developed (it is currently in “beta” form) and exemplified for components of the interdisciplinary Harvard ocean prediction system (HOPS) and for the uncertainty prediction components of the error subspace statistical estimation (ESSE) system. Importantly, the approach is general and applies to other existing ocean modeling applications and to other “legacy” codes.
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Dynamics and Lagrangian Coherent Structures in the Ocean and their Uncertainty

Lermusiaux, P.F.J. and F. Lekien, 2005. Dynamics and Lagrangian Coherent Structures in the Ocean and their Uncertainty. Extended Abstract in report of the "Dynamical System Methods in Fluid Dynamics" Oberwolfach Workshop. Jerrold E. Marsden and Jurgen Scheurle (Eds.), Mathematisches Forschungsinstitut Oberwolfach, July 31st - August 6th, 2005, Germany. 2pp.

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
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Prediction Systems with Data Assimilation for Coupled Ocean Science and Ocean Acoustics

Robinson, A.R. and P.F.J. Lermusiaux, 2004. Prediction Systems with Data Assimilation for Coupled Ocean Science and Ocean Acoustics, Proceedings of the Sixth International Conference on Theoretical and Computational Acoustics (A. Tolstoy, et al., editors), World Scientific Publishing, 325-342. Refereed invited Keynote Manuscript.

Ocean science and ocean acoustics today are engaged in coupled interdisciplinary research on both fundamental dynamics and applications. In this context interdisciplinary data assimilation, which melds observations and fundamental dynamical models for field and parameter estimation is emerging as a novel and powerful methodology, but computational demands present challenging constraints which need to be overcome. These ideas are developed within the concept of an interdisciplinary system for assessing sonar system performance. An end-to-end system, which couples meteorology-physical oceanography-geoacoustics-ocean acoustics-bottom-noise-target-sonar data and models, is used to estimate uncertainties and their transfers and feedbacks. The approach to interdisciplinary data assimilation for this system importantly involves a full, interdisciplinary state vector and error covariance matrix. An idealized end-to-end system example is presented based upon the Shelfbreak PRIMER experiment in the Middle Atlantic Bight. Uncertainties in the physics are transferred to the acoustics and to a passive sonar using fully coupled physical and acoustical data assimilation.
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Forecasting synoptic transients in the Eastern Ligurian Sea

Robinson, A.R., J. Sellschopp, W.G. Leslie, A. Alvarez, G. Baldasserini, P.J. Haley, P.F.J. Lermusiaux, C.J. Lozano, E. Nacini, R. Onken, R. Stoner, P. Zanasca, 2003. Forecasting synoptic transients in the Eastern Ligurian Sea. In "Rapid Environmental Assessment", Bovio, E., R. Tyce and H. Schmidt (Editors), SACLANTCEN Conference Proceedings Series CP-46, Saclantcen, La Spezia, Italy.

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.

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Data driven simulations of synoptic circulation and transports in the Tunisia-Sardinia-Sicily region

Onken, R., A.R. Robinson, P.F.J. Lermusiaux, P.J. Haley Jr. and L.A. Anderson, 2003. Data driven simulations of synoptic circulation and transports in the Tunisia-Sardinia-Sicily region. Journal of Geophysical Research, 108, (C9), 8123-8136.

Data from a hydrographic survey of the Tunisia-Sardinia-Sicily region are assimilated into a primitive equations ocean model. The model simulation is then averaged in time over the short duration of the data survey. The corresponding results, consistent with data and dynamics, are providing new insight into the circulation of Modified Atlantic Water (MAW) and Levantine Intermediate Water (LIW) in this region of the western Mediterranean. For MAW these insights include a southward jet off the east coast of Sardinia, anticyclonic recirculation cells on the Algerian and Tunisian shelves, and a secondary flow splitting in the Strait of Sicily. For the LIW regime a detailed view of the circulation in the Strait of Sicily is given, indicating that LIW proceeds from the strait to the Tyrrhenian Sea. No evidence is found for a direct current path to the Sardinia Channel. Complex circulation patterns are validated by two-way nesting of critical regions. Volume transports are computed for the Strait of Sicily, the Sardinia Channel, and the passage between Sardinia and Sicily.
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Rapid real-time interdisciplinary ocean forecasting using adaptive sampling and adaptive modeling and legacy codes: Component encapsulation using XML

Evangelinos C., R. Chang, P.F.J. Lermusiaux and N.M. Patrikalakis, 2003. Rapid real-time interdisciplinary ocean forecasting using adaptive sampling and adaptive modeling and legacy codes: Component encapsulation using XML. Lecture Notes in Computer Science, 2660, 375-384.

We present the high level architecture of a real-time interdisciplinary ocean forecasting system that employs adaptive elements in both modeling and sampling. We also discuss an important issue that arises in creating an integrated, web-accessible framework for such a system out of existing stand-alone components: transparent support for handling legacy binaries. Such binaries, that are most common in scientific applications, expect a standard input stream, maybe some command line options, a set of input files and generate a set of output files as well as standard output and error streams. Legacy applications of this form are encapsulated using XML. We present a method that uses XML documents to describe the parameters for executing a binary.
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Modeling Uncertainties in the Prediction of the Acoustic Wavefield in a Shelfbreak Environment

Lermusiaux, P.F.J., C.-S. Chiu and A.R. Robinson, 2002. Modeling Uncertainties in the Prediction of the Acoustic Wavefield in a Shelfbreak Environment. Refereed invited Manuscript, Proceedings of the 5th International conference on theoretical and computational acoustics, May 21-25, 2001. (Eds: E.-C. Shang, Q. Li and T.F. Gao), World Scientific Publishing Co., 191-200.

The uncertainties in the predicted acoustic wavefield associated with the transmission of low- frequency sound from the continental slope, through the shelfbreak front, onto the continental shelf are examined. The locale and sensor geometry being investigated is that of the New England continental shelfbreak with a moored low-frequency sound source on the slope. Our method of investigation employs computational fluid mechanics coupled with computational acoustics. The coupled methodology for uncertainty estimation is that of Error Subspace Statistical Estimation. Specifically, based on observed oceanographic data during the 1996 Shelfbreak Primer Experiment, the Harvard University primitive-equation ocean model is initialized with many realizations of physical fields and then integrated to produce many realizations of a five-day regional forecast of the sound speed field. In doing so, the initial physical realizations are obtained by perturbing the physical initial conditions in statistical accord with a realistic error subspace. The different forecast realizations of the sound speed field are then fed into a Naval Postgraduate School coupled-mode sound propagation model to produce realizations of the predicted acoustic wavefield in a vertical plane across the shelfbreak frontal zone. The combined ocean and acoustic results from this Monte Carlo simulation study provide insights into the relations between the uncertainties in the ocean and acoustic estimates. The modeled uncertainties in the transmission loss estimate and their relations to the error statistics in the ocean estimate are discussed.
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Four-dimensional data assimilation for coupled physical-acoustical fields

Lermusiaux, P.F.J. and C.-S. Chiu, 2002. Four-dimensional data assimilation for coupled physical-acoustical fields. In "Acoustic Variability, 2002". N.G. Pace and F.B. Jensen (Eds.), Saclantcen. Kluwer Academic Press, 417-424.

The estimation of oceanic environmental and acoustical fields is considered as a single coupled data assimilation problem. The four-dimensional data assimilation methodology employed is Error Subspace Statistical Estimation. Environmental fields and their dominant uncertainties are predicted by an ocean dynamical model and transferred to acoustical fields and uncertainties by an acoustic propagation model. The resulting coupled dominant uncertainties define the error subspace. The available physical and acoustical data are then assimilated into the predicted fields in accord with the error subspace and all data uncertainties. The criterion for data assimilation is presently to correct the predicted fields such that the total error variance in the error subspace is minimized. The approach is exemplified for the New England continental shelfbreak region, using data collected during the 1996 Shelfbreak Primer Experiment. The methodology is discussed, computational issues are outlined and the assimilation of model-simulated acoustical data is carried out. Results are encouraging and provide some insights into the dominant variability and uncertainty properties of acoustical fields.
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Advanced interdisciplinary data assimilation: Filtering and smoothing via error subspace statistical estimation.

Lermusiaux, P.F.J., A.R. Robinson, P.J. Haley and W.G. Leslie, 2002. Advanced interdisciplinary data assimilation: Filtering and smoothing via error subspace statistical estimation. Proceedings of "The OCEANS 2002 MTS/IEEE" conference, Holland Publications, 795-802.

The efficient interdisciplinary 4D data assimilation with nonlinear models via Error Subspace Statistical Estimation (ESSE) is reviewed and exemplified. ESSE is based on evolving an error subspace, of variable size, that spans and tracks the scales and processes where the dominant errors occur. A specific focus here is the use of ESSE in interdisciplinary smoothing which allows the correction of past estimates based on future data, dynamics and model errors. ESSE is useful for a wide range of purposes which are illustrated by three investigations: (i) smoothing estimation of physical ocean fields in the Eastern Mediterranean, (ii) coupled physical-acoustical data assimilation in the Middle Atlantic Bight shelfbreak, and (iii) coupled physical-biological smoothing and dynamics in Massachusetts Bay.
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On the mapping of multivariate geophysical fields: sensitivity to size, scales and dynamics

Lermusiaux, P.F.J., 2002. On the mapping of multivariate geophysical fields: sensitivity to size, scales and dynamics. Journal of Atmospheric and Oceanic Technology, 19, 1602-1637.

The effects of a priori parameters on the error subspace estimation and mapping methodology introduced by P. F. J. Lermusiaux et al. is investigated. The approach is three-dimensional, multivariate, and multiscale. The sensitivities of the subspace and a posteriori fields to the size of the subspace, scales considered, and nonlinearities in the dynamical adjustments are studied. Applications focus on the mesoscale to subbasin-scale physics in the northwestern Levantine Sea during 10 February-15 March and 19 March-16 April 1995. Forecasts generated from various analyzed fields are compared to in situ and satellite data. The sensitivities to size show that the truncation to a subspace is efficient. The use of criteria to determine adequate sizes is emphasized and a backof- the-envelope rule is outlined. The sensitivities to scales confirm that, for a given region, smaller scales usually require larger subspaces because of spectral redness. However, synoptic conditions are also shown to strongly influence the ordering of scales. The sensitivities to the dynamical adjustment reveal that nonlinearities can modify the variability decomposition, especially the dominant eigenvectors, and that changes are largest for the features and regions with high shears. Based on the estimated variability variance fields, eigenvalue spectra, multivariate eigenvectors and (cross)-covariance functions, dominant dynamical balances and the spatial distribution of hydrographic and velocity characteristic scales are obtained for primary regional features. In particular, the Ierapetra Eddy is found to be close to gradient-wind balance and coastal-trapped waves are anticipated to occur along the northern escarpment of the basin.
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Transfer of uncertainties through physical-acoustical-sonar end-to-end systems: A conceptual basis

Robinson, A.R., P. Abbot, P.F.J. Lermusiaux and L. Dillman, 2002. Transfer of uncertainties through physical-acoustical-sonar end-to-end systems: A conceptual basis. In "Acoustic Variability, 2002:. N.G. Pace and F.B. Jensen (Eds.), SACLANTCEN. Kluwer Academic Press, 603-610.

An interdisciplinary team of scientists is collaborating to enhance the understanding of the uncertainty in the ocean environment, including the sea bottom, and characterize its impact on tactical system performance. To accomplish these goals quantitatively an end-to-end system approach is necessary. The conceptual basis of this approach and the framework of the end-to-end system, including its components, is the subject of this presentation. Specifically, we present a generic approach to characterize variabilities and uncertainties arising from regional scales and processes, construct uncertainty models for a generic sonar system, and transfer uncertainties from the acoustic environment to the sonar and its signal processing. Illustrative examples are presented to highlight recent progress toward the development of the methodology and components of the system.
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Predictive Skill, Predictive Capability and Predictability in Ocean Forecasting

Robinson, A.R., P.J. Haley, P.F.J. Lermusiaux and W.G. Leslie, 2002. Predictive Skill, Predictive Capability and Predictability in Ocean Forecasting. Proceedings of "The OCEANS 2002 MTS/IEEE" conference, Holland Publications, 787-794.

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.
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Evolving the subspace of the three-dimensional multiscale ocean variability: Massachusetts Bay

Lermusiaux, P.F.J., 2001. Evolving the subspace of the three-dimensional multiscale ocean variability: Massachusetts Bay. Journal of Marine Systems, Special issue on "Three-dimensional ocean circulation: Lagrangian measurements and diagnostic analyses", 29/1-4, 385-422, doi: 10.1016/S0924-7963(01)00025-2.

A data and dynamics driven approach to estimate, decompose, organize and analyze the evolving three-dimensional variability of ocean fields is outlined. Variability refers here to the statistics of the differences between ocean states and a reference state. In general, these statistics evolve in time and space. For a first endeavor, the variability subspace defined by the dominant eigendecomposition of a normalized form of the variability covariance is evolved. A multiscale methodology for its initialization and forecast is outlined. It combines data and primitive equation dynamics within a Monte-Carlo approach. The methodology is applied to part of a multidisciplinary experiment that occurred in Massachusetts Bay in late summer and early fall of 1998. For a 4-day time period, the three-dimensional and multivariate properties of the variability standard deviations and dominant eigenvectors are studied. Two variability patterns are discussed in detail. One relates to a displacement of the Gulf of Maine coastal current offshore from Cape Ann, with the creation of adjacent mesoscale recirculation cells. The other relates to a Bay-wide coastal upwelling mode from Barnstable Harbor to Gloucester in response to strong southerly winds. Snapshots and tendencies of physical fields and trajectories of simulated Lagrangian drifters are employed to diagnose and illustrate the use of the dominant variability covariance. The variability subspace is shown to guide the dynamical analysis of the physical fields. For the stratified conditions, it is found that strong wind events can alter the structures of the buoyancy flow and that circulation features are more variable than previously described, on multiple scales. In several locations, the factors estimated to be important include some or all of the atmospheric and surface pressure forcings, and associated Ekman transports and downwelling/upwelling processes, the Coriolis force, the pressure force, inertia and mixing.
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The development and demonstration of an advanced fisheries management information system

Robinson, A.R., B.J. Rothschild, W.G. Leslie, J.J. Bisagni, M.F. Borges, W.S. Brown, D. Cai, P. Fortier, A. Gangopadhyay, P.J. Haley, Jr., H.S. Kim, L. Lanerolle, P.F.J. Lermusiaux, C.J. Lozano, M.G. Miller, G. Strout and M.A. Sundermeyer, 2001. The development and demonstration of an advanced fisheries management information system. Proc. of the 17th Conference on Interactive Information and Processing Systems for Meteorology, Oceanography and Hydrology, Albuquerque, New Mexico. American Meteorological Society, 186-190.

Fishery management regulates size and species-specific fishing mortality to optimize biological production from the fish populations and economic production from the fishery. Fishery management is similar to management in industries and in natural resources where the goals of management are intended to optimize outputs relative to inputs. However, the management of fish populations is among the most difficult. The difficulties arise because (a) the dynamics of the natural production system are extremely complicated; involving an infinitude of variables and interacting natural systems and (b) the size-and species-specific fishing mortality (i.e. system control) is difficult to measure, calibrate, and deploy. Despite the difficulties, it is believed that significant advances can be made by employing a fishery management system that involves knowing the short-term (daily to weekly) variability in the structures of environmental and fish fields. We need new information systems that bring together existing critical technologies and thereby place fishery management in a total-systems feedback-control context. Such a system would monitor the state of the structure of all stocks simultaneously in near real-time, be adaptive to the evolving fishery and consider the effects of the environment and economics. To do this the system would need to (a) employ new in situ and remote sensors in innovative ways, (b) develop new data streams to support the development of new information, (c) employ modern modeling, information and knowledge-base technology to process the diverse information and (d) generate management advice and fishing strategies that would optimize the production of fish.

The Advanced Fisheries Management Information System (AFMIS), built through a collaboration of Harvard University and the Center for Marine Science and Technology at the University of Massachusetts at Dartmouth, is intended to apply state-of-the-art multidisciplinary and computational capabilities to operational fisheries management. The system development concept is aimed toward: 1) utilizing information on the “state” of ocean physics, biology, and chemistry; the assessment of spatially-resolved fish-stock population dynamics and the temporal-spatial deployment of fishing effort to be used in fishing and in the operational management of fish stocks; and, 2) forecasting and understanding physical and biological conditions leading to recruitment variability. Systems components are being developed in the context of using the Harvard Ocean Prediction System to support or otherwise interact with the: 1) synthesis and analysis of very large data sets; 2) building of a multidisciplinary multiscale model (coupled ocean physics/N-P-Z/fish dynamics/management models) appropriate for the northwest Atlantic shelf, particularly Georges Bank and Massachusetts Bay; 3) the application and development of data assimilation techniques; and, 4) with an emphasis on the incorporation of remotely sensed data into the data stream.

AFMIS is designed to model a large region of the northwest Atlantic (NWA) as the deep ocean influences the slope and shelves. Several smaller domains, including the Gulf of Maine (GOM) and Georges Bank (GB) are nested within this larger domain (Figure 1). This provides a capability to zoom into these domains with higher resolution while maintaining the essential physics which are coupled to the larger domain. AFMIS will be maintained by the assimilation of a variety of real time data. Specifically this includes sea surface temperature (SST), color (SSC), and height (SSH) obtained from several space-based remote sensors (AVHRR, SeaWiFS and Topex/Poseidon). The assimilation of the variety of real-time remotely sensed data supported by in situ data will allow nowcasting and forecasting over significant periods of time.

A real-time demonstration of concept (RTDOC) nowcasting and forecasting exercise to demonstrate important aspects of the AFMIS concept by producing real time coupled forecasts of physical fields, biological and chemical fields, and fish abundance fields took place in March-May 2000. The RTDOC was designed to verify the physics, to validate the biology and chemistry but only to demonstrate the concept of forecasting the fish fields, since the fish dynamical models are at a very early stage of development. In addition, it demonstrated the integrated system concept and the implication for future coupling of a management model. This note reports on the RTDOC.

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Real-time Forecasting of the Multidisciplinary Coastal Ocean with the Littoral Ocean Observing and Predicting System (LOOPS)

Robinson, A.R. and the LOOPS Group, 1999. Real-time Forecasting of the Multidisciplinary Coastal Ocean with the Littoral Ocean Observing and Predicting System (LOOPS). Preprint Volume of the Third Conference on Coastal Atmospheric and Oceanic Prediction and Processes, 3-5 November 1999, New Orleans, LA, American Meteorological Society, Boston, MA.

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.
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