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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, submitted.

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.

Optimizing Velocities and Transports for Complex Coastal Regions and Archipelagos

Haley, P.J., Jr., A. Agarwal, P.F.J. Lermusiaux, 2014. Optimizing Velocities and Transports for Complex Coastal Regions and Archipelagos. Ocean Modeling, sub-judice.

We derive and apply a methodology for the efficient initialization of velocity and transport fields in coastal regions with multiscale dynamics and complex geometries. First-guess velocity fields are constructed from data, reduced dynamics, prior knowledge and/or downscaled velocities from existing simulations. A class of constrained weighted least squares optimizations is defined to best fit the first-guess velocities while satisfying bathymetry, coastline and divergence strong constraints. To obtain the exact solutions for these best fits, we derive Euler-Lagrange equations for the interior, boundary and island streamfunction variables. In the optimization weights, the minimum distance and vertical area between pairs of islands are computed using a Fast Marching Method. Additional information on velocity and transports are included as strong or weak constraints, and the optimized sub-tidal velocity and transports are again solved for directly. Downscaling and nesting considerations are provided. Tidal contributions are finally added at the end. The result is initial fields that are sufficiently consistent with observations, complex geometry and dynamics to simulate the evolution of ocean processes without large spurious initial transients. 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 and with independent in situ observations show that our semi-analytical optimization corrects transports, satisfies boundary conditions and redirects currents. Without it, initial fields in complex regions are too erroneous and damage predictions.

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.

Multiscale Modeling of Coastal, Shelf and Global Ocean Dynamics

Lermusiaux, P.F.J., J. Schröter, S. Danilov, M. Iskandaranu, 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.

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.

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.

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.

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).

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.

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.

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

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 ows have been active areas of research in uid mechanics for the last 30 years. Growing evidence for the existence of LCSs in geophysical ows (e.g., eddies, oscillating jets, chaotic mixing) and other uid ows (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 ow elds to study coherent structures. Robust numerical methods and suciently 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 scienti c 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)). De ning the set of all observations prior to time t by yt

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.