We provide a new framework for the study of fl‡uid ‡flows presenting complex uncertain behavior. Our approach is based on the stochastic reduction and analysis of the governing equations using the dynamically orthogonal field equations. By numerically solving these equations we evolve in a fully coupled way the mean fl‡ow and the statistical and spatial characteristics of the stochastic fl‡uctuations. This set of equations is formulated for the general case of stochastic boundary conditions and allows for the application of projection methods that reduce considerably the computational cost. We analyze the transformation of energy from stochastic modes to mean dynamics, and vice-versa, by deriving exact expressions that quantify the interaction among different components of the fl‡ow. The developed framework is illustrated through specifi…c fl‡ows in unstable regimes. In particular we consider the ‡flow behind a disk and the Rayleigh–-Bénard convection for which we construct bifurcation diagrams that describe the variation of the response as well as the energy transfers for different parameters associated with the considered ‡flows and we reveal the low-dimensionality of the underlying stochastic attractor.

An important element of present oceanographic research is the assessment and quantification of uncertainty. These studies are challenging in the coastal ocean due to the wide variety of physical processes occurring on a broad range of spatial and temporal scales. In order to assess new methods for quantifying and predicting uncertainty, a joint Taiwan-US field program was undertaken in August/ September 2009 to compare model forecasts of uncertainties in ocean circulation and acoustic propagation, with high-resolution in situ observations. The geographical setting was the continental shelf and slope northeast of Taiwan, where a feature called the “cold dome” frequently forms. Even though it is hypothesized that Kuroshio subsurface intrusions are the water sources for the cold dome, the dome’s dynamics are highly uncertain, involving multiple scales and many interacting ocean features. During the experiment, a combination of near-surface and profiling drifters, broadscale and high-resolution hydrography, mooring arrays, remote sensing, and regional ocean model forecasts of fields and uncertainties were used to assess mean fields and uncertainties in the region. River runoff from Typhoon Morakot, which hit Taiwan August 7-8, 2009, strongly affected shelf stratification. In addition to the river runoff, a cold cyclonic eddy advected into the region north of the Kuroshio, resulting in a cold dome formation event. Uncertainty forecasts were successfully employed to guide the hydrographic sampling plans. Measurements and forecasts also shed light on the evolution of cold dome waters, including the frequency of eddy shedding to the north-northeast, and interactions with the Kuroshio and tides. For the first time in such a complex region, comparisons between uncertainty forecasts and the model skill at measurement locations validated uncertainty forecasts. To complement the real-time model simulations, historical simulations with another model show that large Kuroshio intrusions were associated with low sea surface height anomalies east of Taiwan, suggesting that there may be some degree of predictability for Kuroshio intrusions.

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.

A comprehensive data set from the ocean and atmosphere was obtained just north of the Monterey Bay as part of the Monterey Bay 2006 (MB06) field experiment. The wind stress, heat fluxes, and sea surface temperature were sampled by the Naval Postgraduate School’s Twin Otter research aircraft. In situ data were collected using ships, moorings, gliders and AUVs. Four data-assimilating numerical models were additionally run, including the Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS) model for the atmosphere and the Harvard Ocean Prediction System (HOPS), the Regional Ocean Modeling System (ROMS), and the Navy Coastal Ocean Model (NCOM) for the ocean. The scientific focus of the Adaptive Sampling and Prediction Experiment (ASAP) was on the upwelling/relaxation cycle and the resulting three-dimensional coastal circulation near a coastal promontory, in this case Point Ano Nuevo, CA. The emphasis of this study is on the circulation over the continental shelf as estimated from the wind forcing, two ADCP moorings, and model outputs. The wind stress during August 2006 consisted of 3-10 day upwelling favorable events separated by brief 1-3 day relaxations. During the first two weeks there was some correlation between local winds and currents and the three models’ capability to reproduce the events. During the last two weeks, largely equatorward surface wind stress forced the sea surface and barotropic poleward flow occurred over the shelf, reducing model skill at predicting the circulation. The poleward flow was apparently remotely forced by mesoscale eddies and alongshore pressure gradients, which were not well simulated by the models. The small, high-resolution model domains were highly reliant on correct open boundary conditions to drive these larger-scale poleward flows. Multiply-nested models were no more effective than well-initialized local models in this respect.

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.

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.

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 13^oC 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.

During the August-September 2003 Autonomous Ocean Sampling Network-II experiment, the Harvard Ocean Prediction System (HOPS) and Error Subspace Statistical Estimation (ESSE) system were utilized in real-time to forecast physical fields and uncertainties, assimilate various ocean measurements (CTD, AUVs, gliders and SST data), provide suggestions for adaptive sampling, and guide dynamical investigations. The qualitative evaluations of the forecasts showed that many of the surface ocean features were predicted, but that their detailed positions and shapes were less accurate. The root-mean-square errors of the real-time forecasts showed that the forecasts had skill out to two days. Mean one-day forecast temperature RMS error was 0.26^oC less than persistence RMS error. Mean two-day forecast temperature RMS error was 0.13^oC less than persistence RMS error. Mean one- or two-day salinity RMS error was 0.036 PSU less than persistence RMS error. The real-time skill in the surface was found to be greater than the skill at depth. Pattern correlation coefficient comparisons showed, on average, greater skill than the RMS errors. For simulations lasting 10 or more days, uncertainties in the boundaries could lead to errors in the Monterey Bay region.

Following the real-time experiment, a reanalysis was performed in which improvements were made in the selection of model parameters and in the open-boundary conditions. The result of the reanalysis was improved long-term stability of the simulations and improved quantitative skill, especially the skill in the main thermocline (RMS simulation error 1^oC less than persistence RMS error out to five days). This allowed for an improved description of the ocean features. During the experiment there were two-week to 10-day long upwelling events. Two types of upwelling events were observed: one with plumes extending westward at point Ano Nuevo (AN) and Point Sur (PS); the other with a thinner band of upwelled water parallel to the coast and across Monterey Bay. During strong upwelling events the flows in the upper 10-20 m had scales similar to atmospheric scales. During relaxation, kinetic energy becomes available and leads to the development of mesoscale features. At 100-300 m depths, broad northward flows were observed, sometimes with a coastal branch following topographic features. An anticyclone was often observed in the subsurface fields in the mouth of Monterey Bay.

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.

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.

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.

Combining an intensive hydrographic data survey with a numerical primitive equation model by data assimilation, the main features of dominant mesoscale to subbasin-scale variability in the Strait of Sicily (Mediterranean Sea) during the summer of 1996 are estimated, revealed and described, and several hydrographic and dynamical properties of the #ow and variabilities discussed. The feature identi”cation is based on two independent real-time analyses of the variability. One analysis `subjectivelya evaluates and studies physical “eld forecasts and their variations. The other more `objectivelya estimates and forecasts the principal components of the variability. The two independent analyses are found to be in agreement and complementary. The dominant dynamical variations are revealed to be associated with “ve features: the Adventure Bank Vortex, Maltese Channel Crest, Ionian Shelfbreak Vortex, Messina Rise Vortex, and temperature and salinity fronts of the Ionian slope. These features and their variations are found to have links with the meanders of the Atlantic Ionian Stream. For each feature, the characteristic physical scales, and their deviations, are quanti”ed. The predominant circulation patterns, pathways and transformations of the modi”ed Atlantic water, Ionian water and modi”ed Levantine intermediate water, are then identi”ed and discussed. For each of these water masses, the ranges of temperature, salinity, depth, velocity and residence times, and the regional variations of these ranges, are computed. Based on the estimated “elds and variability principal components, several properties of the dynamics in the Strait are discussed. These include: general characteristics of the mesoscale anomalies; bifurcations of the Atlantic Ionian Stream; respective roles of topography, atmospheric forcings and internal dynamics; factors controlling (strengthening or weakening) the vortices identi”ed; interactions of the Messina Rise and Ionian Shelfbreak vortices; and, mesoscale dynamics and relatively complex features along the Ionian slope. For evaluation and validation of the results obtained, in situ data, satellite sea surface temperature images and trajectories of surface drifters are employed, as well as comparisons with previous studies.

Considering mesoscale variability in the Strait of Sicily during September 1996, the four-dimensional physical fields and their dominant variability and error covariances are estimated and studied. The methodology applied in real-time combines an intensive data survey and primitive equation dynamics based on the error subspace statistical estimation approach. A sequence of filtering and prediction problems are solved for a period of 10 days, with adaptive learning of the dominant errors. Intercomparisons with optimal interpolation fields, clear sea surface temperature images and available in situ data are utilized for qualitative and quantitative evaluations. The present estimation system is shown to be a comprehensive nonlinear and adaptive assimilation scheme, capable of providing real-time forecasts of ocean fields and associated dominant variability and error covariances. The initialization and evolution of the error subspace is explained. The dominant error eigenvectors, variance and covariance fields are illustrated and their multivariate, multiscale properties described. Five coupled features associated with the dominant variability in the Strait during August-September 1996 emerge from the dominant decomposition of the initial PE variability covariance matrix: the Adventure Bank Vortex, Maltese Channel Crest, Ionian Shelf Break Vortex, Strait of Messina Vortex, and subbasin-scale temperature and salinity fronts of the Ionian slope. From the evolution of the estimated fields and dominant predictability error covariance decompositions, several of the primitive equation processes associated with the variations of these features are revealed, decomposed and studied. In general, the estimation of the evolving dominant decompositions of the multivariate predictability error and variability covariances appears promising for ocean sciences and technology. The practical feedbacks of the present approach which include the determination of data optimals and the refinements of dynamical and measurement models are considered.

This paper describes some preliminary results of the cooperative effort between SACLANT Undersea Research Centre and Harvard University in the development of a regional descriptive and predictive capability for the Strait of Sicily. The aims of the work have been to: 1. determine and describe the underlying dynamics of the region; and, 2. rapidly assess synoptic oceanographic conditions through measurements and modeling. Based on the 1994-1996 surveys, a picture of some semi-permanent features which occur in the Strait of Sicily is beginning to emerge. Dynamical circulation studies, with assimilated data from the surveys, indicate the presence of an Adventure Bank Vortex – ABV., Maltese Channel Crest – MCC., and Ionian Shelf Break Vortex – IBV. A schematic water mass model has been developed for the region. Results from the Rapid Response 96 real-time numerical modeling experiments are presented and evaluated. A newly developed data assimilation methodology, Error Subspace Statistical Estimation – ESSE. is introduced. The ideal Error Subspace spans and tracks the scales and processes where the dominant, most energetic, errors occur, making this methodology especially useful in real-time adaptive sampling. q1999 Elsevier Science B.V. All rights reserved.