Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to the sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty in the parameter values, functional forms with diverse parameterizations, and level of complexity needed, and thus in the state variable fields. We develop a Bayesian model learning methodology that allows interpolation in the space of candidate dynamical models and discovery of new models from noisy, sparse, and indirect observations, all while estimating state variable fields and parameter values, as well as the joint probability distributions of all learned quantities. We address the challenges of high-dimensional and multidisciplinary dynamics governed by partial differential equations (PDEs) by using state augmentation and the computationally efficient Gaussian Mixture Model – Dynamically Orthogonal filter. Our innovations include stochastic formulation parameters and stochastic complexity parameters to unify candidate models into a single general model as well as stochastic expansion parameters within piecewise function approximations to generate dense candidate model spaces. These innovations allow handling many compatible and embedded candidate models, possibly none of which are accurate, and learning elusive unknown functional forms that augment these models. Our new Bayesian methodology is generalizable and interpretable. It seamlessly and rigorously discriminates among existing models, but also extrapolates out of the space of models to discover new ones. We perform a series of twin experiments based on flows past a ridge coupled with three-to-five component ecosystem models, including flows with chaotic advection. We quantify the learning skill, and evaluate convergence and the sensitivity to hyper-parameters. Our PDE framework successfully discriminates among functional forms and model complexities, and learns in the absence of prior knowledge by searching in dense function spaces. The probabilities of known, uncertain, and unknown model formulations, and of biogeochemical-physical fields and parameters, are updated jointly using Bayes’ law. Non-Gaussian statistics, ambiguity, and biases are captured. The parameter values and the model formulations that best explain the noisy, sparse, and indirect data are identified. When observations are sufficiently informative, model complexity and model functions are discovered.

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.

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.

An ensemble data assimilation scheme, Error Subspace Statistical Estimation (ESSE), is utilized to investigate the seasonal ecosystem dynamics of the Lagoon of Venice and provide guidance on the monitoring and management of the Lagoon, combining a rich data set with a physical-biogeochemical numerical estuary-coastal model. Novel stochastic ecosystem modeling components are developed to represent prior uncertainties in the Lagoon dynamics model, measurement model, and boundary forcing by rivers, open-sea inlets, and industrial discharges. The formulation and parameters of these additive and multiplicative stochastic error models are optimized based on data-model forecast misfits. The sensitivity to initial and boundary conditions is quantified and analyzed. Half-decay characteristic times are estimated for key ecosystem variables, and their spatial and temporal variability are studied. General results of our uncertainty analyses are that boundary forcing and internal mixing have a significant control on the Lagoon dynamics and that data assimilation is needed to reduce prior uncertainties. The error models are used in the ESSE scheme for ensemble uncertainty predictions and data assimilation, and an optimal ensemble dimension is estimated. Overall, higher prior uncertainties are predicted in the central and northern regions of the Lagoon. On the basis of the dominant singular vectors of the ESSE ensemble, the two major northern rivers are the biggest sources of dissolved inorganic nitrogen (DIN) uncertainty in the Lagoon. Other boundary sources such as the southern rivers and industrial discharges can dominate uncertainty modes on certain months. For dissolved inorganic phosphorus (DIP) and phytoplankton, dominant modes are also linked to external boundaries, but internal dynamics effects are more significant than those for DIN. Our posterior estimates of the seasonal biogeochemical fields and of their uncertainties in 2001 cover the whole Lagoon. They provide the means to describe the ecosystem and guide local environmental policies. Specifically, our findings and results based on these fields include the temporal and spatial variability of nutrient and plankton gradients in the Lagoon; dynamical connections among ecosystem fields and their variability; strengths, gradients and mechanisms of the plankton blooms in late spring, summer, and fall; reductions of uncertainties by data assimilation and thus a quantification of data impacts and data needs; and, finally, an assessment of the water quality in the Lagoon in light of the local environmental legislation.

For efficient progress, model properties and measurement needs can adapt to oceanic events and interactions as they occur. The combination of models and data via data assimilation can also be adaptive. These adaptive concepts are discussed and exemplified within the context of comprehensive real-time ocean observing and prediction systems. Novel adaptive modeling approaches based on simplified maximum likelihood principles are developed and applied to physical and physical-biogeochemical dynamics. In the regional examples shown, they allow the joint calibration of parameter values and model structures. Adaptable components of the Error Subspace Statistical Estimation (ESSE) system are reviewed and illustrated. Results indicate that error estimates, ensemble sizes, error subspace ranks, covariance tapering parameters and stochastic error models can be calibrated by such quantitative adaptation. New adaptive sampling approaches and schemes are outlined. Illustrations suggest that these adaptive schemes can be used in real time with the potential for most efficient sampling.

Scientific computations for the quantification, estimation and prediction of uncertainties for ocean dynamics are developed and exemplified. Primary characteristics of ocean data, models and uncertainties are reviewed and quantitative data assimilation concepts defined. Challenges involved in realistic data-driven simulations of uncertainties for four-dimensional interdisciplinary ocean processes are emphasized. Equations governing uncertainties in the Bayesian probabilistic sense are summarized. Stochastic forcing formulations are introduced and a new stochastic-deterministic ocean model is presented. The computational methodology and numerical system, Error Subspace Statistical Estimation, that is used for the efficient estimation and prediction of oceanic uncertainties based on these equations is then outlined. Capabilities of the ESSE system are illustrated in three data-assimilative applications: estimation of uncertainties for physical-biogeochemical fields, transfers of ocean physics uncertainties to acoustics, and real-time stochastic ensemble predictions with assimilation of a wide range of data types. Relationships with other modern uncertainty quantification schemes and promising research directions are discussed.

Physical and biogeochemical ocean dynamics can be intermittent and highly variable, and involve interactions on multiple scales. In general, the oceanic fields, processes and interactions that matter thus vary in time and space. For efficient forecasting, the structures and parameters of models must evolve and respond dynamically to new data injected into the executing prediction system. The conceptual basis of this adaptive modeling and corresponding computational scheme is the subject of this presentation. Specifically, we discuss the process of adaptive modeling for coupled physical and biogeochemical ocean models. The adaptivity is introduced within an interdisciplinary prediction system. Model-data misfits and data assimilation schemes are used to provide feedback from measurements to applications and modify the runtime behavior of the prediction system. Illustrative examples in Massachusetts Bay and Monterey Bay are presented to highlight ongoing progress.

Data-driven forecasts and simulations for Massachusetts Bay based on in situ observations collected during August – September 1998 and on coupled four-dimensional (4-D) physical and biogeochemical models are carried out, evaluated, and studied. The real-time forecasting and adaptive sampling took place from August 17 to October 5, 1998. Simultaneous synoptic physical and biogeochemical data sets were obtained over a range of scales. For the real-time forecasts, the physical model was initialized using hydrographic data from August 1998 and the new biogeochemical model using historical data. The models were forced with real-time meteorological fields and the physical data were assimilated. The resulting interdisciplinary forecasts were robust and the Bay-scale biogeochemical variability was qualitatively well represented. For the postcruise simulations, the August – September 1998 biogeochemical data are utilized. Extensive comparisons of the coupled model fields with data allowed significant improvements of the biogeochemical model. All physical and biogeochemical data are assimilated using an optimal interpolation scheme. Within this scheme, an approximate biogeochemical balance and dynamical adjustments are utilized to derive the non-observed ecosystem variables from the observed ones. Several processes occurring in the lower trophic levels of Massachusetts Bay during the summer – autumn period over different spatial and temporal scales are described. The coupled dynamics is found to be more vigorous and diverse than previously thought to be the case in this period. For the biogeochemical dynamics, multiscale patchiness occurs. The locations of the patches are mainly defined by physical processes, but their strengths are mainly controlled by biogeochemical processes. The fluxes of nutrients into the euphotic zone are episodic and induced in part by atmospheric forcing. The quasi-weekly passage of storms gradually deepened the mixed layer and often altered the Bay-scale circulation and induced internal submesoscale variability. The physical variability increased the transfer of biogeochemical materials between the surface and deeper layers and modulated the biological processes.

The International Lie`ge Colloquium on Ocean Dynamics is organized annually. The topic differs from year to year in an attempt to address, as much as possible, recent problems and incentive new subjects in oceanography. Assembling a group of active and eminent scientists from various countries and often different disciplines, the Colloquia provide a forum for discussion and foster a mutually beneficial exchange of information opening on to a survey of recent discoveries, essential mechanisms, impelling question marks and valuable recommendations for future research. The objective of the 2001 Colloquium was to evaluate the progress of data assimilation methods in marine science and, in particular, in coupled hydrodynamic, ecological and bio-geo-chemical models of the ocean. The past decades have seen important advances in the understanding and modelling of key processes of the ocean circulation and bio-geo-chemical cycles. The increasing capabilities of data and models, and their combination, are allowing the study of multidisciplinary interactions that occur dynamically, in multiple ways, on multiscales and with feedbacks. The capacity of dynamical models to simulate interdisciplinary ocean processes over specific space- time windows and thus forecast their evolution over predictable time scales is also conditioned upon the availability of relevant observations to: initialise and continually update the physical and bio-geo-chemical sectors of the ocean state; provide relevant atmospheric and boundary forcing; calibrate the parameterizations of sub-grid scale processes, growth rates and reaction rates; construct interdisciplinary and multiscale correlation and feature models; identify and estimate the main sources of errors in the models; control or correct for mis-represented or neglected processes. The access to multivariate data sets requires the implementation, exploitation and management of dedicated ocean observing and prediction systems. However, the available data are often limited and, for instance, seldom in a form to be directly compatible or directly inserted into the numerical models. To relate the data to the ocean state on all scales and regions that matter, evolving three-dimensional and multivariate (measurement) models are becoming important. Equally significant is the reduction of observational requirements by design of sampling strategies via Observation System Simulation Experiments and adaptive sampling. Data assimilation is a quantitative approach to extract adequate information content from the data and to improve the consistency between data sets and model estimates. It is also a methodology to dynamically interpolate between data scattered in space and time, allowing comprehensive interpretation of multivariate observations. In general, the goals of data assimilation are to: control the growth of predictability errors; correct dynamical deficiencies; estimate model parameters, including the forcings, initial and boundary conditions; characterise key processes by analysis of four- 0924-7963/03/$ – see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0924-7963(03)00027-7 www.elsevier.com/locate/jmarsys The use of data assimilation in coupled hydrodynamic, ecological and bio-geo-chemical models of the ocean Journal of Marine Systems 40-41 (2003) 1-3 dimensional fields and their statistics (balances of terms, etc.); carry out advanced sensitivity studies and Observation System Simulation Experiments, and conduct efficient operations, management and monitoring. The theoretical framework of data assimilation for marine sciences is now relatively well established, routed in control theory, estimation theory or inverse techniques, from variational to sequential approaches. Ongoing research efforts of special importance for interdisciplinary applications include the: stochastic representation of processes and determination of model and data errors; treatment of (open) boundary conditions and strong nonlinearities; space-time, multivariate extrapolation of limited and noisy data and determination of measurement models; demonstration that bio-geo-chemical models are valid enough and of adequate structures for their deficiencies to be controlled by data assimilation; and finally, ability to provide accurate estimates of fields, parameters, variabilities and errors, with large and complex dynamical models and data sets. Operationally, major engineering and computational challenges for the coming years include the: development of theoretically sound methods into useful, practical and reliable techniques at affordable costs; implementation of scalable, seamless and automated systems linking observing systems, numerical models and assimilation schemes; adequate mix of integrated and distributed (Web-based) networks; construction of user-friendly architectures and establishment of standards for the description of data and software (metadata) for efficient communication, dissemination and management. In addition to addressing the above items, the 33rd Lie`ge Colloquium has offered the opportunity to: – review the status and current progress of data assimilation methodologies utilised in the physical, acoustical, optical and bio-geo-chemical scientific communities; – demonstrate the potentials of data assimilation systems developed for coupled physical/ecosystem models, from scientific to management inquiries; – examine the impact of data assimilation and inverse modelling in improving model parameterisations; – discuss the observability and controllability properties of, and identify the missing gaps in current observing and prediction systems; and exchange the results of and the learnings from preoperational marine exercises. The presentations given during the Colloquium lead to discussions on a series of topics organized within the following sections: (1) Interdisciplinary research progress and issues: data, models, data assimilation criteria. (2) Observations for interdisciplinary data assimilation. (3) Advanced fields estimation for interdisciplinary systems. (4) Estimation of interdisciplinary parameters and model structures. (5) Assimilation methodologies for physical and interdisciplinary systems. (6) Toward operational interdisciplinary oceanography and data assimilation. A subset of these presentations is reported in the present Special Issue. As was pointed out during the Colloquium, coupled biological-physical data assimilation is in its infancy and much can be accomplished now by the immediate application of existing methods. Data assimilation intimately links dynamical models and observations, and it can play a critical role in the important area of fundamental biological oceanographic dynamical model development and validation over a hierarchy of complexities. Since coupled assimilation for coupled processes is challenging and can be complicated, care must be exercised in understanding, modeling and controlling errors and in performing sensitivity analyses to establish the robustness of results. Compatible interdisciplinary data sets are essential and data assimilation should iteratively define data impact and data requirements. Based on the results presented during the Colloquium, data assimilation is expected to enable future marine technologies and naval operations otherwise impossible or not feasible. Interdisciplinary predictability research, multiscale in both space and time, is required. State and parameter estimation via data assimilation is central to the successful establishment of advanced interdisciplinary ocean observing and prediction systems which, functioning in real time, will contribute to novel and efficient capabilities to manage, and to operate in our oceans. The Scientific Committee and the participants to the 33rd Lie`ge Colloquium wish to express their 2 Preface gratitude to the Ministe`re de l’Enseignement Supe’rieur et de la Recherche Scientifique de la Communaute – Francaise de Belgique, the Fonds National de la Recherche Scientifique de Belgique (F.N.R.S., Belgium), the Ministe`re de l’Emploi et de la Formation du Gouvernement Wallon, the University of Lie`ge, the Commission of European Union, the Scientific Committee on Oceanographic Research (SCOR), the International Oceanographic Commission of the UNESCO, the US Office of Naval Research, the National Science Foundation (NSF, USA) and the International Association for the Physical Sciences of the Ocean (IAPSO) for their most valuable support.

Data assimilation is a modern methodology of relating natural data and dynamical models. The general dynamics of a model is combined or melded with a set of observations. All dynamical models are to some extent approximate, and all data sets are finite and to some extent limited by error bounds. The purpose of data assimilation is to provide estimates of nature which are better estimates than can be obtained by using only the observational data or the dynamical model. There are a number of specific approaches to data assimilation which are suitable for estimation of the state of nature, including natural parameters, and for evaluation of the dynamical approximations. Progress is accelerating in understanding the dynamics of real ocean biological- physical interactive processes. Although most biophysical processes in the sea await discovery, new techniques and novel interdisciplinary studies are evolving ocean science to a new level of realism. Generally, understanding proceeds from a quantitative description of four-dimensional structures and events, through the identification of specific dynamics, to the formulation of simple generalizations. The emergence of realistic interdisciplinary four-dimensional data assimilative ocean models and systems is contributing significantly and increasingly to this progress.

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.