Abstract: The Regional Ocean Modelling System (ROMS) is a new generation ocean general circulation model that is rapidly gaining favour in the ocean modelling community. The tangent linear and adjoint versions of ROMS have recently been developed, and a new suite of tools that utilize these models for a variety of applications are now available to the ocean modelling community. In this report we will describe the tangent linear and adjoint components of ROMS, and present examples from the tools that are currently available to ROMS users. In particular we will condsider the finite time eigenmodes and the adjoint finite time eigenmodes of the tangent linear propagator, the singular vectors of the propagator, and its forcing singular vectors and stochastic optimals. The pseudospectra of the tanget linear resolvent matrix are also considered. In addition, the current status of the ROMS 4D variational data assimilation modules are also discussed. Examples of each type of calculation will be presented for a time evolving double gyre ocean circulation in a rectangular ocean basin.
Abstract: An integrated set of laboratory and numerical model experiments has been conducted to understand the development of residual circulation surrounding a coastal canyon and, further, to explore the degree to which laboratory experiments can provide useful benchmark datasets for numerical models of the coastal ocean. The physical system considered here is the interaction of an oscillatory, along-slope background current with an isolated canyon incised in an otherwise uniform continental slope. The flows considered are laminar and are investigated in a cylindrical test cell mounted on a 1.8 m diameter turntable at Arizona State University. The numerical experiments employ the Spectral Element Ocean Model (SEOM) developed at Rutgers University.
Abstract: The Incremental Strong constraint 4D-Variational (IS4DVAR) system of the Regional Ocean Model System (ROMS) for data assimilation is presented. It has been applied to the California Current System (CCS) to assimilate remotely-sensed and in situ oceanic observations. Results from both twin and realistic experiments are presented. The IS4DVAR control vector is comprised of the model initial conditions and surface forcing, and a focus is given on the ability of ROMS-IS4DVAR to correct the latter. ROMS-IS4DVAR always reduces misfits between the model and the observations that are assimilated. However, without corrections to the surface forcing, the assimilation of surface data can degrade the temperature structure at depth. This behavior is prevented by using surface forcing adjustment in ROMS-IS4DVAR which can reduce errors between the model and surface observations through corrections to surface forcing rather than to temperature at depth. Wind stress corrections generate abnormal spatial and temporal variability in its divergence and curl. However, twin experiments indicate that corrections to wind stress and surface heat flux tend to reduce errors in these forcing fields.
Abstract: The results of an intercomparison experiment performed with five numerical ocean models of different architecture are presented. While all models are able to simulate the large-scale characteristics of the North Atlantic circulation with a fair degree of realism, they also exhibit differences that can be attributed to the choices made in vertical coordinates, domain size, and boundary conditions.
Abstract: A spectral finite-volume (SFV) method is proposed for the numerical solution of the shallow water equations. This is the first phase in the development of a layered (isopycnal) ocean model. Its target applications include, in particular, the simulation of the wind-driven oceanic circulation in geometrically complex basins where layer outcropping and/or isopycnal-bathymetry intersection must be handled explicitly. The present formulation is geometrically flexible and can extend accuracy to arbitrary high order with no change to the basic algorithm. A flux-corrected transport (FCT) algorithm ensures the stability of the computations in regions of vanishing layer thickness and in areas where the flow features are underresolved. The spatial discretization is based on a two-level grid: a globally unstructured elemental grid and a locally structured grid consisting of N x N quadrilateral cells within each element. The numerical solution is continuous within each element but discontinuous across elements; the discontinuity is resolved by upwinding along characteristics. The accuracy and convergence rate of the SFV method are verified on two linearized problems amenable to analytical solution; the SFV solution exhibits a convergence order of N + 1 for smooth solutions. The FCT portion of the model is tested by simulating the formation of an oblique hydraulic jump in a supercritical channel flow. The model is then applied to simulate, in reduced-gravity mode, the double-gyre and wind-driven upper-ocean circulations in a square basin. Finally, the previous experiment is repeated in the North Atlantic basin to illustrate the application of the model in a realistic geometry.
Abstract: Decadal fluctuations in salinity, nutrients, chlorophyll, a variety of zooplankton taxa, and fish stocks in the Northeast Pacific are often poorly correlated with the most widely-used index of large-scale climate variability in the region - the Pacific Decadal Oscillation (PDO).We define a new pattern of climate change, the North Pacific Gyre Oscillation (NPGO) and show that its variability is significantly correlated with previously unexplained fluctuations of salinity, nutrients and chlorophyll. Fluctuations in the NPGO are driven by regional and basin-scale variations in wind-driven upwelling and horizontal advection – the fundamental processes controlling salinity and nutrient concentrations. Nutrient fluctuations drive concomitant changes in phytoplankton concentrations, and may force similar variability in higher trophic levels. The NPGO thus provides a strong indicator of fluctuations in the mechanisms driving planktonic ecosystem dynamics. The NPGO pattern extends beyond the North Pacific and is part of a global-scalemode of climate variability that is evident in global sea level trends and sea surface temperature. Therefore the amplification of the NPGO variance found in observations and in global warming simulations implies that the NPGO may play an increasingly
important role in forcing global-scale decadal changes in marine ecosystems. Citation: Di Lorenzo, E., et al. (2008), North Pacific Gyre Oscillation links ocean climate and ecosystem change, and the El Niño Southern Oscillation (ENSO) are often invoked to explain physical and biological fluctuations in the Northeast Pacific Ocean [Lynn et al., 1998; Lavaniegos and Ohman, 2003, 2007; McGowan et al., 1998]. Changes in the magnitude and sign of the indices have been correlated with variations in biological properties such as zooplankton displacement volume [Roemmich and McGowan, 1995] and fish populations [Hare et al., 1999]. Particularly dramatic physical and biological excursions occurred during the 1976–77 change in the PDO [Hare and Mantua, 2000] [McGowan et al., 2003] and during the 1997–99 ENSO cycle [Peterson and Schwing, 2003]. However, the mechanisms coupling fluctuations in the PDO to changes in biological variables remain unclear. Furthermore, both the PDO and ENSO fail to explain decadal variations of key oceanic variables in the North Pacific, particularly the prominent salinity and nutrient variations seen in the California Cooperative Oceanic Fisheries Investigations (CalCOFI; www.calcofi.org) records from 1949 to 2005 [Schneider et al., 2005; Di Lorenzo et al., 2005].
In this study, we present evidence that interannual and decadal variations of salinity, nutrient upwelling, and surface chlorophyll-a (Chl-a) in the Northeast Pacific are associated with fluctuations in a climate pattern that we term the North Pacific Gyre Oscillation (NPGO). We use the term NPGO because its fluctuations reflect changes in the intensity of the North Pacific gyre circulations.
Abstract: We describe the development and preliminary application of the inverse Regional Ocean Modeling System (ROMS), a four dimensional variational (4DVAR) data assimilation system for high-resolution basin-wide and coastal oceanic flows. Inverse ROMS makes use of the recently developed perturbation tangent linear (TL), representer tangent linear (RP) and adjoint (AD) models to implement an indirect representer-based generalized inverse modeling system. This modeling framework is modular. The TL, RP and AD models are used as stand-alone sub-models within the Inverse Ocean Modeling (IOM) system described in [Chua, B.S., Bennett, A.F., 2001. An inverse ocean modeling system. Ocean Modell. 3, 137–165.]. The system allows the assimilation of a wide range of observation types and uses an iterative algorithm to solve nonlinear assimilation problems. The assimilation is performed either under the perfect model assumption (strong constraint) or by also allowing for errors in the model dynamics (weak constraints). For the weak constraint case the TL and RP models are modified to include additional forcing terms on the right hand side of the model equations. These terms are needed to account for errors in the model Dynamics. Inverse ROMS is tested in a realistic 3D baroclinic upwelling system with complex bottom topography, characterized by strong mesoscale eddy variability. We assimilate synthetic data for upper ocean (0–450 m) temperatures and currents over a period of 10 days using both a high resolution and a spatially and temporally aliased sampling array. During the assimilation period the flow field undergoes substantial changes from the initial state. This allows the inverse solution to extract the dynamically active information from the synthetic observations and improve the trajectory of the model state beyond the assimilation window. Both the strong and weak constraint assimilation experiments show forecast skill greater than persistence and climatology during the 10–20 days after the last observation is assimilated.
Abstract: A coastal ocean forecasting system was developed for the Long-term Ecosystem Observatory (LEO) on New Jersey’s inner shelf. The forecast system comprised an ocean model, the Regional Ocean Modeling System (ROMS), forced by a high-resolution atmospheric forecast, with assimilation of ocean data from ships and coastal radar systems. The forecasts were used to aid the deployment of real-time adaptive sampling observing systems during the July 2001 Coastal Predictive Skill Experiment. Temperature and salinity assimilation data were prepared by optimal interpolation of shipboard towed-body data. Surface current observations from coastal radar (CODAR) were projected vertically for assimilation using a statistically based extrapolation. The assimilation methods tested with the operational forecast system in July 2001 were continuous nudging and intermittent melding of the model forecast and gridded data. Observations from a validation array of current-meter and thermistor moorings deployed on a cross-shore line through the center of the LEO intensive observing area were used to formulate a set of quantitative model skill metrics that focused on aspects of the 2-layer wind-driven upwelling and downwelling circulation that characterizes ocean dynamics during the stratified summer season along this coast. An ensemble of model and data assimilation configurations were tested, showing that the k-profile parameterization for vertical turbulence closure, and assimilation by intermittent melding, comprised the forecast system with the more significant skill as measured by the mean squared error of the validation metric time series.
Abstract: During the course of developing new numerical algorithms for a terrain-following ocean modeling system (TOMS), different numerical aspects have been evaluated through a comparison between two widely used community ocean models, the Princeton ocean model (POM) and the regional ocean modeling system(ROMS). While both models aim at modeling coastal to basin-scale problems using similar grids, their numerical algorithms, code structure, and parameterization options are very different. Sensitivity studies with an idealized channel ﬂow and a steep seamount conﬁguration demonstrate how different algorithms in the two models may affect numerical errors, the stability of the code and the computational efficiency. For example, new pressure gradient schemes using polynomial ﬁts and new time stepping algorithms may reduce numerical errors and allow using longer time steps than standard schemes do. However, the new schemes may require more careful choices of time steps and the use of higher order advection schemes to maintain numerical stability.
Abstract: The biogeochemistry of continental shelf systems plays an important role in the global elemental cycling of nitrogen and carbon, but remains poorly quantified. We have developed a high-resolution physical-biological model for the U.S. east coast continental shelf and adjacent deep ocean that is nested within a basin-wide North Atlantic circulation model in order to estimate nitrogen fluxes in the shelf area of the Middle Atlantic Bight (MAB). Our biological model is a relatively simple representation of nitrogen cycling processes in the water column and organic matter remineralization at the water-sediment interface that explicitly accounts for sediment denitrification. Climatological and regionally integrated means of nitrate, ammonium, and surface chlorophyll are compared with its model equivalents and were found to agree within 1 standard deviation. We also present regional means of primary production and denitrification, and statistical measures of chlorophyll pattern variability. A nitrogen budget for the MAB shows that the sediment denitrification flux is quantitatively important in determining the availability of fixed nitrogen and shelf primary production (it was found to remove 90% of all the nitrogen entering the MAB). Extrapolation of nitrogen fluxes estimated for the MAB to the North Atlantic basin suggests that shelf denitrification removes 2.3 x 10^12 mol N annually; this estimate exceeds estimates of N2 fixation by up to an order of magnitude. Our results emphasize the importance of representing shelf processes in biogeochemical models.
Abstract: The contribution of coastal oceans to the global air-sea CO2 flux is poorly quantified due to insufficient availability of observations and inherent variability of physical, biological and chemical processes. We present simulated air-sea CO2 fluxes from a high-resolution biogeochemical model for the North American east coast continental shelves, a region characterized by significant sediment denitrification. Decreased availability of fixed nitrogen due to denitrification reduces primary production and incorporation of inorganic carbon into organic matter, which leads to an increase in seawater pCO2, but also increases alkalinity, which leads to an opposing decrease in seawater pCO2. Comparison of simulations with different numerical treatments of denitrification and alkalinity allow us to separate and quantify the contributions of sediment denitrification to air-sea CO2 flux. The effective alkalinity flux resulting from denitrification is large compared to estimates of anthropogenically driven coastal acidification.
Abstract: A lower trophic level NPZD ecosystem model with explicit iron limitation on nutrient uptake is coupled to a three-dimensional coastal ocean circulation model to investigate the regional ecosystem dynamics of the northwestern coastal Gulf of Alaska (CGOA). Iron limitation is included in the NPZD model by adding governing equations for two micro-nutrient compartments: dissolved iron and phytoplankton-associated iron. The model has separate budgets for nitrate (the limiting macro-nutrient in the standard NPZD model) and for iron, with iron limitation on nitrate uptake being imposed as a function of the local phytoplankton realized Fe:C ratio. While the ecosystem model represents a simple approximation of the complex lower trophic level ecosystem of the northwestern CGOA, simulated chlorophyll concentrations reproduce the main characteristics of the spring bloom, high shelf primary production, and “high-nutrient, low-chlorophyll” (HNLC) environment offshore. Over the 1998–2004 period, model-data correlations based on spatially averaged, monthly mean chlorophyll concentrations are on average 0.7, with values as high as 0.9 and as low as 0.5 for individual years. The model also provides insight on the importance of micro- and macro-nutrient limitation on the shelf and offshore, with the shelfbreak region acting as a transition zone where both nitrate and iron availability significantly impact phytoplankton growth. Overall, the relative simplicity of the ecosystem model provides a useful platform to perform long-term simulations to investigate the seasonal and interannual CGOA ecosystem variability, as well as to conduct sensitivity studies to evaluate the robustness of simulated fields to ecosystem model parameterization and forcing. The ability of the model to differentiate between nitrate-limited, and iron-limited growth conditions, and to identify their spatial and temporal occurrences, is also a first step towards understanding the role of environmental gradients in shaping the complex CGOA phytoplankton community structure.
Abstract: Numerical simulations are used to study on-shelf transport of dense water by oscillatory barotropic currents incident upon an isolated coastal canyon. The physical system is a laboratory-scale rotating annulus in which forcing is provided by an oscillatory modulation in the rotation rate, and for which the external non-dimensional parameters match (as closely as possible) those from an appropriate ocean analogue. The numerical simulations were originally conducted for comparison with a companion set of the two (Perenne et al., 2000; Iskandarani et al. 2003; Boyer et al., 2003, this issue). The numerical simulations are here interrogated to determine the three-dimensional structure of the time-mean currents and density field on the shelf, to qualify the resulting on-shore transport of dense water, to characterize the dynamic mechanisms at work, and to expose the underlying (non-dimensional) parameter dependencies.
Abstract: This book offers a comprehensive overview of the models and methods employed in the rapidly advancing field of numerical ocean circulation modeling. For those new to the field, concise reviews of the equations of oceanic motion, sub-grid-scale parameterization, and numerical approximation techniques are presented and four specific numerical models, chosen to span the range of current practice, are described in detail. For more advanced users, a suite of model test problems is developed to illustrate the differences among models, and to serve as a first stage in the quantitative evaluation of future algorithms. The extensive list of references makes this book a valuable text for both graduate students and postdoctoral researchers in the marine sciences and in related fields such as meteorology, and climate and coupled biogeochemical modeling.
Abstract: Systematic improvements in algorithmic design of regional ocean circulation models have led to significant enhancement in simulation ability across a wide range of space/time scales and marine system types. As an example, we briefly review the Regional Ocean Modeling System, a member of a general class of three-dimensional, free-surface, terrain-following numerical models. Noteworthy characteristics of the ROMS computational kernel include: consistent temporal averaging of the barotropic mode to guarantee both exact conservation and constancy preservation properties for tracers; redefined barotropic pressure-gradient terms to account for local variations in the density field; vertical interpolation performed using conservative parabolic splines; and higher-order, quasi-monotone advection algorithms. Examples of quantitative skill assessment are shown for a tidally driven estuary, an ice-covered high-latitude sea, a wind- and buoyancy-forced continental shelf, and a mid-latitude ocean basin. The combination of moderate-order spatial approximations, enhanced conservation properties, and quasi-monotone advection produces both more robust and accurate, and less diffusive, solutions than those produced in earlier terrain-following ocean models. Together with advanced methods of data assimilation and novel observing system technologies, these capabilities constitute the necessary ingredients for multi-purpose regional ocean prediction systems.
Abstract: A primitive equation ocean circulation model in nonlinear terrain-following coordinates is applied to a decadal-length simulation of the circulation in the North Atlantic Ocean. In addition to the stretched sigma coordinate, novel features of the model include the utilization of a weakly dissipative, third-order scheme for tracer advection, and a conservative and constancy-preserving time-stepping algorithm. The objectives of the study are to assess the quality of the new terrain-following model in the limit of realistic basin-scale simulations, and to compare the results obtained with it against those of other North Atlantic models used in recent multi-model comparison studies.
The new model is able to reproduce many features of both the wind-driven and thermohaline circulation, and to do so within error bounds comparable with prior model simulations (e.g., CME and DYNAMO). Quantitative comparison with comparable results obtained with the Miami Isopycnic Coordinate Model (MICOM) show our terrain-following solutions are of similar overall quality when viewed against known measures of merit including meridional overturning and heat flux, Florida Straits and Gulf Stream transport, seasonal cycling of temperature and salinity, andupper ocean currents and tracer fields in the eastern North Atlantic Basin. Sensitivity studies confirm that the nonlinear vertical coordinate contributes significantly to model fidelity, and that the global inventories and spatial structure of the tracer fields are affected in important ways by the choice of lateral advection scheme.
Abstract: The dynamics of the seasonal surface circulation in the Philippine Archipelago (117°E–128°E, 0°N–14°N) are investigated using a high-resolution configuration of the Regional Ocean Modeling System (ROMS) for the period of January 2004–March 2008. Three experiments were performed to estimate the relative importance of local, remote and tidal forcing. On the annual mean, the circulation in the Sulu Sea shows inflow from the South China Sea at the Mindoro and Balabac Straits, outflowinto the Sulawesi Sea at the Sibutu Passage, and cyclonic circulation in the southern basin. A strong jet with a maximum speed exceeding 100 cms−1 forms in the northeast Sulu Sea where currents from the Mindoro and Tablas Straits converge. Within the Archipelago, strong westward currents in the Bohol Sea carry the surface water of the western Pacific (WP) from the Surigao Strait into the Sulu Sea via the Dipolog Strait. In the Sibuyan Sea, currents flow westward, which carry the surface water from the WP near the San Bernardino Strait into the Sulu Sea via the Tablas Strait. These surface currents exhibit strong variations or reversals from winter to summer. The cyclonic (anticyclonic) circulation during winter (summer) in the Sulu Sea and seasonally reversing currents within the Archipelago region during the peak of the winter (summer) monsoon result mainly from local wind forcing, while remote forcing dominates the current variations at the Mindoro Strait, western Sulu Sea and Sibutu passage before the monsoons reach their peaks. The temporal variations (with the mean removed), also referred to as anomalies, of volume transports in the upper 40m at eight major Straits are caused predominantly by remote forcing, although local forcing can be large during sometime of a year. For example, at the Mindoro Strait, the correlation between the time series of transport anomalies due to total forcing (local, remote and tides) and that due only to the remote forcing is 0.81 above 95% significance, comparing to the correlation of 0.64 between the total and local forcing. Similarly, at the Sibutu Passage, the correlation is 0.96 for total versus remote effects, comparing to 0.53 for total versus local forcing. The standard deviations of transports from the total, remote and local effects are 0.59 Sv, 0.50 Sv, and 0.36 Sv, respectively, at the Mindoro Strait; and 1.21 Sv, 1.13 Sv, and 0.59 Sv at the Sibutu Passage. Nonlinear rectification of tides reduces the mean westward transports at the Surigao, San Bernardino and Dipolog Straits, and it also has non-negligible influence on the seasonal circulation in the Sulu Sea.
Abstract: A set of spatially nested circulation models is used to explore interannual change in the northeast Pacific (NEP) during 1997–2002, and remote vs. local influence of the 1997–1998 El Niño on this region. Our nested set is based on the primitive equations of motion, and includes a basin-scale model of the north Pacific at not, vert, similar ~40-km resolution (NPac), and a regional model of the Northeast Pacific at not, vert, similar ~10-km resolution. The NEP model spans an area from Baja California through the Bering Sea, from the coast to not, vert, similar2000-km offshore. In this context, “remote influence” refers to effects driven by changes in ocean velocity and temperature outside of the NEP domain; “local influence” refers to direct forcing by winds and runoff within the NEP domain. A base run of this model using hindcast winds and runoff for 1996–2002 replicates the dominant spatial modes of sea-surface height anomalies from satellite data, and coastal sea level from tide gauges. We have performed a series of sensitivity runs with the NEP model for 1997–1998, which analyze the response of coastal sea level to: (1) hindcast winds and coastal runoff, as compared to their monthly climatologies and (2) hindcast boundary conditions (from the NPac model), as compared to their monthly climatologies. Results indicate penetration of sea-surface height (SSH) from the basin-scale model into the NEP domain (e.g., remote influence), with propagation as coastal trapped waves from Baja up through Alaska. Most of the coastal sea-level anomaly off Alaska in El Niño years appears due to direct forcing by local winds and runoff (local influence), and such anomalies are much stronger than those produced off California. We quantify these effects as a function of distance along the coastline, and consider how they might impact the coastal ecosystems of the NEP.
Abstract: The Coastal Gulf of Alaska (CGOA) is productive, with large populations of fish, seabirds, and marine mammals; yet it is subject to downwelling-favorable coastal winds. Downwelling regions in other parts of the world are typically much less productive than their upwelling counterparts. Alternate sources of nutrients to feed primary production in the topographically complex CGOA are poorly known and difficult to quantify. Here we diagnose the output from a spatially nested, coupled hydrodynamic and lower trophic level model of the CGOA, to quantify both horizontal and vertical nutrient fluxes into the euphotic zone. Our nested model includes both nitrogen and iron limitation of phytoplankton production, and is driven by a fine-scale atmospheric model that resolves the effects of local orography on the coastal winds. Results indicate significant “rivers” of cross-shelf nitrogen flux due to horizontal advection, as well as “fountains” of vertical transport over shallow banks due to tidal mixing. Using these results, we constructed a provisional budget of nutrient transport among subregions of the CGOA. Contrary to expectations, this budget reveals substantial upwelling of nutrients over major portions of the shelf, driven by local wind-stress curl. These effects are large enough to overwhelm the smaller downwelling flux at the coast throughout the growing season. Vertical mixing by winds and tides, and horizontal flux from the deep basin, are other substantial contributors to nutrients above the 15-m horizon. These findings help to explain the productivity of this coastal ecosystem.
Abstract: We present a spectral element model to solve the hydrostatic primitive equations governing large-scale geophysical ﬂows. The highlights of this new model include unstructured grids, dual h–p paths to convergence, and good scalability characteristics on present day parallel computers including Beowulf-class systems. The behavior of the model is assessed on three process-oriented test problems involving wave propagation, gravitational adjustment, and nonlinear ﬂow rectiﬁcation, respectively. The ﬁrst of these test problems is a study of the convergence properties of the model when simulating the linear propagation of baroclinic Kelvin waves. The second is an intercomparison of spectral element and ﬁnite-difference model solutions to the adjustment of a density front in a straight channel. Finally, the third problem considers the comparison of model results to measurements obtained from a laboratory simulation of ﬂow around a submarine canyon. The aforementioned tests demonstrate the good performance of the model in the idealized/processoriented limits.
Abstract: We review and compare advection schemes designed for high-order finite element/finite volume methods. The emphasis is on studying, by numerical examples, the properties of these schemes in terms of accuracy, and monotonicity, and their viability for oceanic applications. The schemes reviewed are classical spectral element, Taylor Galerkin Least Square method, the Discontinuous Galerkin method and high-order finite volume method. The latter two schemes exhibit a de?nite robustness due to their small, but finite, inherent numerical dissipation. They also prove the most flexible since their discontinuous representation of the solution allows easy implementations of flux limiting or adaptive procedure. Finally, an ad-hoc but simple adaptive procedure is presented to illustrate DGM's potential; this procedure proved to be extremely effective at controlling Gibbs oscillations in 1D but was too dissipative on the Hecht problem.
Abstract: Direct representation of the free surface in ocean circulation models leads to a number of computational difficulties that are due to the fast time scales associated with free-surface waves. These fast time scales generally result in severe time-step restrictions when the free surface is advanced using an explicit scheme and may result in large phase errors when the free surface is treated implicitly with a large time step. A multiple-scale analysis of the shallow-water equations is used to analyze this stiffness and to guide the construction of a computational methodology that overcomes the associated difficulties. Specifically, we explore a class of fractional step methods that utilize coarsened grids in the propagation of long-wave data. The behavior of the corresponding schemes is examined in detail in light of one-dimensional model problems, based on finite-difference or spectral-element discretizations.
Abstract: A nonconforming spectral element ocean model, which allows a combination of higher- and lower-order elements in a single formulation, is presented. The choice between the order of interpolating polynomials and the number of elements can be adjusted locally in a subregion of a domain, based on the geometric and dynamic properties of a solution. High-order elements are applied in regions with smooth properties and achieve high-order convergence rates. In the regions where smoothness of the solution is limited and/or geometric requirements are complex, low-order elements are used. This paper presents a nonconforming spectral element method based on mortar elements. Convergence of the method is analyzed using several elliptic and hyperbolic test problems in two and three dimensions. To test the method, a study of wave propagation through a nonconforming interface for two problems in a realistic geometry is also presented.
Abstract: The numerical simulation of turbulent oceanic flows is susceptible to the appearance of instabilities associated with the misrepresentation of nonlinear interactions among small-scale motions. Specialized filters and differencing schemes have been successfully used in the past to suppress the growth of these instabilities in finite-difference ocean models. Here, we introduce a new filtering procedure designed to control the growth of nonlinear instabilities in the spectral element solution of nonlinear oceanic flows. The new procedure involves two separate steps. First, a spectral filter is applied to the vorticity and divergence fields to damp oscillations in high-gradient regions and to restore spectral accuracy away from them. Second, the associated velocity field is computed from a set of Poisson equations, and its boundary conditions and interelement continuity are restored. This two-step strategy avoids the loss of C0 continuity and the weakening of Dirichlet boundary conditions that can result when the filter is directly applied to the velocity field. The behavior of the filter is investigated numerically on the canonical problem of the double-gyre wind-driven circulation in a rectangular basin using a spectral element shallow water model. The parameters of the simulation are chosen to produce mesoscale eddies. The filter is able to stabilize the simulation even at coarse resolution and to recover the ‘‘correct’’ statistical behavior with as few as two grid points per Rossby deformation radius. Finally, a simulation of the wind-driven circulation in the North Atlantic Ocean is performed to illustrate the effectiveness of the filter in realistic settings.
Abstract: A primitive equation, hydrostatic, terrain-following coordinate ocean general circulation model (OGCM) is used to investigate the mean water mass pathways from the subtropics to the tropics in the Atlantic Ocean. The OGCM is used in a fully realistic configuration of the Atlantic, from 30S to 65N, with realistic bathymetry. Surface forcings are provided by the COADS climatology. A non-eddy-resolving numerical simulation is analyzed with 3/4 degrees horizontal resolution and 20 terrain-following vertical levels.
The primary objective of this study is to assess the theoretical framework extending the ventilated thermocline theory to the equator in the context of the numerical calculation, and to establish whether the predictions of a steady-state theory can be verified in a time-dependent simulation, in which rectified seasonal effects on the time mean yearly circulation may be important. The Bernoulli function is evaluated on isopycnal surfaces outcropping in the subtropics in both hemispheres and floats are injected at different northern and southern latitudes. In both hemispheres, the interior flow velocities are parallel to the Bernoulli streamlines that are significantly modified by inertia only very near the equator and on the Equatorial UnderCurrent (EUC).
In the Northern Atlantic, pathways from the subtropics to the tropics exist for the isopycnal surfaces outcropping at 20–22N. The injected floats reach the EUC following a zigzag pattern determined by the tropical current system. It is impossible to distinguish between the western boundary and the interior exchange windows as they are merged together forming a broad exchange pathway east of the northwestward flowing North Brazil Current NBC . This exchange window disappears for the floats injected north of ~30N, and corresponding outcropping isopycnals 25.5 kgrm3, where only the recirculating window of the subtropical gyre remains.
In the Southern Atlantic, all the floats injected between 6 and 15S migrate to the western boundary where they are entrained in the NBC. There is no interior exchange window. At the equator, some are directly entrained into the EUC, some overshoot and retroflect at ~8N, then join the EUC.
As the numerical simulation is carried out under surface forcings that include the seasonal cycle, we can assess the impact of the seasonal cycle on the steady-state analysis. The most important effect is due to the Atlantic Intertropical Convergence Zone ITCZ , which in summer is strong, and produces an island of Ekman upwelling between 10 and 20N, which is reflected in the yearly mean properties. The ICTZ-induced upwelling and interior stratification support a corresponding island of high potential vorticity that penetrates in depth to all the isopycnals outcropping between 20 and 25N. This high potential vorticity island creates a barrier that constrains the floats injected at and north of 20N to flow around it to reach the Equator and the EUC.
Abstract: The barotropic Rossby wave field in the North Atlantic Ocean is studied in an eddy-resolving ocean model simulation. The meandering model Gulf Stream radiates barotropic Rossby waves southward through preferred corridors defined by topographic features. The smoother region between the Bermuda Rise and the mid-Atlantic Ridge is a particularly striking corridor of barotropic wave radiation in the 20–50 day period band. Barotropic Rossby waves are also preferentially excited at higher frequencies over the Bermuda Rise, suggesting resonant excitation of topographic Rossby normal modes. The prevalence of these radiated waves suggests that they may be an important energy sink for the equilibrium state of the Gulf Stream.
Abstract: The Regional Ocean Modelling System (ROMS) is a new generation ocean general circulation model that is rapidly gaining favour in the ocean modelling community. The tangent linear and adjoint versions of ROMS have recently been developed, and a new suite of tools that utilize these models for a variety of applications are now available to the ocean modelling community. In this paper we will describe the tangent linear and adjoint components of ROMS, and present examples from the tools that are currently available to ROMS users In particular we will consider the nite time eigenmodes and the adjoint nite time eigenmodes of the tangent linear propagator, the singular vectors of the propagator, and its forcing singular vectors and stochastic optimals. The pseudospectra of the tangent linear resolvent matrix are also considered. Examples of each type of calculation will be presented for a time evolving double gyre ocean circulation in a rectangular ocean basin.
Abstract: Adjoint methods of sensitivity analysis were applied to the California Current using the Regional Ocean Modeling Systems (ROMS) with medium resolution, aimed at diagnosing the circulation sensitivity to variations in surface forcing. The sensitivities of coastal variations in SST, eddy kinetic energy, and baroclinic instability of complex time-evolving flows were quantified. Each aspect of the circulation exhibits significant interannual and seasonal variations in sensitivity controlled by mesoscale circulation features. Central California SST is equally sensitive to wind stress and surface heat flux, but less so to wind stress curl, displaying the greatest sensitivity when upwelling-favorable winds are relaxing and the least sensitivity during the peak of upwelling. SST sensitivity is typically 2–4 times larger during summer than during spring, although larger variations occur during some years. The sensitivity of central coast eddy kinetic energy to surface forcing is constant on average throughout the year. Perturbations in the wind that align with mesoscale eddies to enhance the strength of the circulation by local Ekman pumping yield the greatest sensitivities. The sensitivity of the potential for baroclinic instability is greatest when nearshore horizontal temperature gradients are largest, and it is associated with variations in wind stress concentrated along the core of the California Current. The sensitivity varies by a factor of ;1.5 throughout the year. A new and important aspect of this work is identification of the complex flow dependence and seasonal dependence of the sensitivity of the ROMS California Current System (CCS) circulation to variations in surface forcing that was hitherto not previously appreciated.
Abstract: The Regional Ocean Modeling System (ROMS) is one of the few community ocean general circulation models for which a 4-dimensional variational data assimilation (4D-Var) capability has been developed. The ROMS 4D-Var capability is unique in that three variants of 4D-Var are supported: a primal formulation of incremental strong constraint 4D-Var (I4D-Var), a dual formulation based on a physical-space statistical analysis system (4D-PSAS), and a dual formulation representer-based variant of 4D-Var (R4DVar). In each case, ROMS is used in conjunction with available observations to identify a best estimateof the ocean circulation based on a set of a priori hypotheses about errors in the initial conditions, boundary conditions, surface forcing, and errors in the model in the case of 4D-PSAS and R4D-Var. In the primal formulation of I4D-Var the search for the best circulation estimate is performed in the full space of the model control vector, while for the dual formulations of 4D-PSAS and R4D-Var only the sub-space of linear functions of the model state vector spanned by the observations (i.e. the dual space) is searched. In oceanographic applications, the number of observations is typically much less than the dimension of the model control vector, so there are clear advantages to limiting the search to the space spanned by the observations. In the case of 4D-PSAS and R4D-Var, the strong constraint assumption (i.e. that the model is error free) can be relaxed leading to the so-called weak constraint formulation. This paper describes the three aforementioned variants of 4D-Var as they are implemented in ROMS. Critical components that are common to each approach are conjugate gradient descent, preconditioning, and error covariance models, which are also described. Finally, several powerful 4D-Var diagnostic tools are discussed, namely computation of posterior errors, eigenvector analysis of the posterior error covariance, observation impact, and observation sensitivity.
Abstract: The Regional Ocean Modeling System (ROMS) 4-dimensional variational (4D-Var) data assimilation systems have been systematically applied to the mesoscale circulation environment of the California Current to demonstrate the performance and practical utility of the various components of ROMS 4D-Var. In particular, we present a comparison of three approaches to 4D-Var, namely: the primal formulation of the incremental strong constraint approach; the dual formulation ‘‘physical-space statistical analysis system’’; and the dual formulation indirect representer approach. In agreement with theoretical considerations all three approaches converge to the same ocean circulation estimate when using the same observations and prior information. However, the rate of convergence of the dual formulation was found to be inferior to that of the primal formulation. Other aspects of the 4D-Var performance that relate to the use of multiple outer-loops, preconditioning, and the weak constraint are also explored. A systematic evaluation of the impact of the various components of the 4D-Var control vector (i.e. the initial conditions, surface forcing and open boundary conditions) is also presented. It is shown that correcting for uncertainties in the model initial conditions exerts the largest influence on the ability of the model to fit the available observations. Various important diagnostics of 4D-Var are also examined, including estimates of the posterior error, the information content of the observation array, and innovation-based consistency checks on the prior error assumptions. Using these diagnostic tools, we find that more than 90% of the observations assimilated into the model provide redundant information. This is a symptom of the large percentage of satellite data that are used and to some extent the nature of the data processing employed. This is the second in a series of three papers describing the ROMS 4D-Var systems.
Abstract: The critical role played by observations during ocean data assimilation was explored when the Regional Ocean Modeling System (ROMS) 4-dimensional variational (4D-Var) data assimilation system was applied sequentially to the California Current circulation. The adjoint of the 4D-Var gain matrix was used to quantify the impact of individual observations and observation platforms on different aspects of the 4D-Var circulation estimates during both analysis and subsequent forecast cycles. In this study we focus on the alongshore and cross-shore transport of the California Current System associated with wind induced coastal upwelling along the central California coast. The majority of the observations available during any given analysis cycle are from satellite platforms in the form of SST and SSH, and on average these data exert the largest controlling influence on the analysis increments and forecast skill of coastal transport. However, subsurface in situ observations from Argo floats, CTDs, XBTs and tagged marine mammals often have a considerable impact on analyses and forecasts of coastal transport, even though these observations represent a relatively small fraction of the available data at any particular time.
During 4D-Var the observations are used to correct for uncertainties in the model control variables, namely the initial conditions, surface forcing, and open boundary conditions. It is found that correcting for uncertainties in both the initial conditions and surface forcing has the largest impact on the analysis increments in alongshore transport, while the cross-shore transport is controlled mainly by the surface forcing. The memory of the circulation associated with the control variable increments was also explored in relation to 7 day forecasts of the coastal circulation. Despite the importance of correcting for surface forcing uncertainties during analysis cycles, the coastal transport during forecast cycles initialized from the analyses has less memory of the surface forcing corrections, and is controlled primarily by the analysis initial conditions.
Using the adjoint of the entire 4D-Var system we have also explored the sensitivity of the coastal transport to changes in the observations and the observation array. A single integration of the adjoint of 4DVar can be used to predict the change that occurs when observations from different platforms are omitted from the 4D-Var analysis. Thus observing system experiments can be performed for each data assimilation cycle at a fraction of the computational cost that would be required to repeat the 4D-Var analyses when observations are withheld. This is the third part of a three part series describing the ROMS 4DVar systems.
Abstract: A high-resolution primitive equation numerical model is used to generate a poleward flow along a meridionally oriented eastern boundary slope/shelf system by imposing an along-coast density gradient as the forcing mechanism. Wind forcing is applied to the resulting quasi-steady current system, and the subinertial response is analyzed. Parallel experiments with no slope-poleward flow are conducted for comparison. Moderately strong upwelling- and downwelling-favorable, week-to-month-scale wind events modify the poleward flow but do not significantly change the density-driven current structure at the slope. The alongshore transport within the slope region is reduced by 0.2–0.3 Sv (from 1.2 Sv, where Sv = 10^6 m^3 s^-1), under the influence of either downwelling or upwelling winds. Independent of the wind direction, the density-driven poleward flow always remains surface intensified. Wind-driven shelf currents develop with a considerable degree of independence from the slopepoleward circulation. On the shelf, the density field is modified by cross-shelf buoyancy advection within the boundary layers and by strong vertical mixing. The presence of the poleward flow over the slope constitutes an important factor in the behavior of the bottom boundary layer at the shelf break and for the patterns of crossslope circulation.
Abstract: The generation and evolution of a density-driven Eastern Poleward Current is investigated using a high-resolution primitive equation numerical model. The simulations focus on the Iberian Poleward Current (IPC) as a case study. The flow is generated by a meridional upper ocean density gradient balanced by an eastward surface-intensified flow that adjusts at the coastal margin. The resulting current system has a baroclinic character with poleward flow at the surface layer, and equatorward flow underneath. A few weeks after initialization, the sheared along-slope flow generates several vorticity structures downstream of the main topographic features. In the lee of the topography, persistent anticyclones are observed and deep cyclogenesis is induced in relation to the meandering of the upper layer jet. These structures evolve preferentially as cyclone/anticyclone eddy pairs, and after interaction some dipoles are ejected offslope. Within a period of a few months, the initial meridional gradient evolves into a complex system of fronts, eddies and slope flows. The dynamics of flow topography interaction is analyzed. A comparison with satellite imagery of the IPC is conducted and similarity in scales and patterns is noted.
Abstract: We present the feasibility of a prototype, near real-time assimilation and ensemble prediction system for the Intra-Americas Sea run autonomously aboard a ship of opportunity based on the Regional Ocean Modeling System (ROMS). Predicting an ocean state depends upon numerical models that contain uncertainties in their modeled physics, initial conditions, and model state. An advanced model, four-dimensional variational assimilation, and ensemble forecasting techniques are used to account for each of these uncertainties. Every 3 days, data from the previous 7 days period were assimilated to generate an estimate of the circulation and to create an ensemble of 2 weeks forecasts of the ocean state. This paper presents the methods and results for a multi-resolution assimilation system and ensemble forecasts of surface fields and dominant surface circulation features. When compared to post-processed science quality observations, the state estimates suffer from our reliance on real-time, quick-look satellite observations of the ocean surface. Despite a number of issues, the ensemble forecast estimate is often superior to observational persistence. This proof-of-concept prototype performed well enough to reveal deficiencies, provide useful insights, valuable lessons, and guidance for future improvements in realtime ocean forecasting.
Abstract: We present the background, development, and preparation of a state-of-the-art 4D variational (4DVAR) data assimilation system in the Regional Ocean Modeling System (ROMS) with an application in the Intra-Americas Sea (IAS). This initial application with a coarse model shows the efficacy of the 4DVAR methodology for use within complex ocean environments, and serves as preparation for deploying an operational, real-time assimilation system onboard the Royal Caribbean Cruise Lines ship Explorer of the Seas. Assimilating satellite sea surface height and temperature observations with in situ data from the ship in 14 day cycles over 2 years from January 2005 through March 2007, reduces the observation-model misfit by over 75%. Using measures of the Loop Current dynamics, we show that the assimilated solution is consistent with observed statistics.
Abstract: We introduce a new ocean circulation model featuring an improved vertical coordinate representation. This new coordinate is a generalized sigma-coordinate; however, it is capable of simultaneously maintaining high resolution in the surface layer as well as dealing with steep and/or tall topography. The model equations are the three-dimensional, free-sruface, primitive equations with orthogonal curvilinear coordinates in the horizontal an the new general coordinate in the vertical. Vertical mixing is treated implicitly by the generalized Crank-Nicolson method based on a Galerkin finite element formulation. Two alternate parameterizations of surface mixing are incorporated, based respectively on the approaches of Price, Weller and Pinkel and Mellor and Yamada. Finally, a quadrature formula of Lagrange interpolation is employed to produce a more accurate calculation of pressure and vertical velocity. Three test are used to demonstrate the accuracy, stability, and applicability of the model: the diurnal cycling of the surface mixed layer, flow around a tall seamount, and a regional simulation of the California current system.
Abstract: The Glenn and Grant (1987) continental shelf bottom boundary layer model for the flow and suspended sediment concetration in the constant stress layer above a noncohesive movable sediment bed has been updated. The Reynolds fluxes for sediment mass and fluid momentum are closed using a continuous, time-invariant linear eddy viscosity modified by a continuous stability parameter to represent the influence of supended sediment-induced stratification thoroughout the constant stress region. Glenn and Grant (1987) use a less realistic discontinuous eddy viscosity and neglect the stratification correction in the wave boundary layer. For typical model parameters the two models produce currents above the wave boundary layer that are in better agreement than the supended sediment concentrations. Within the wave boundary layer the differences are much greater for both the current and the sediment concentration. This leads to significant differences in the sediment transport throughout the constant stress layer. Sensitivities of the updated model were examined on the basis of observed wave and current data acquired during storms on the inner continental shelf. Comparisons between the stratified and neutral versions of the updated model indicate that the stratified version produces a total depth-integrated sediment transport that can be 2 orders of magnitude less than, and time-averaged shear velocities that can be nearly half of, that predicted by the neutral version. Sensitivities to grain size distributions indicate that even a small amount of finer sediment can stratify the storm-driven flows. Sensitivities to closure constants within the range of reported values also produce up to an order of magnitude variation in sediment transport, illustrating the need for dedicated field experiments to refine further estimates of these parameters.
Abstract: The merged TOPEX/POSEIDON and ERS-1/2 altimeter data from 1993 through 2001 and the Spectral Element Ocean Model (SEOM) have been used to investigate Indian Ocean Kelvin waves (IOKWs), specifically their propagation and energy intrusion into Lombok Strait. The altimeter data show the frequent occurrence of IOKWs in either April/May or November/December for the years of 1993–2001 (except 1994) with intraseasonal wave periods (phase speeds) ranging from 35 (1.5) to 90 days (2.9 ms−1). From the altimeter data, it is estimated that 55.6 ± 13.9% of the incoming IOKW energy enters Lombok Strait. The SEOM results indicate an energy intrusion rate of 65%, showing good agreement with the altimeter data. The majority of the incoming IOKW energy is used to increase Kelvin wave energy entering Lombok Strait. This suggests that Lombok Strait acts as a significant transition point for Kelvin wave energy from the Indian Ocean to the internal Indonesian Seas.
Abstract: A two-equation turbulence model (one equation for turbulence kinetic energy and a second for a generic turbulence length-scale quantity) proposed by Umlauf and Burchard [J. Marine Research 61 (2003) 235] is implemented in a three-dimensional oceanographic model (Regional Oceanographic Modeling System; ROMS v2.0). These two equations, along with several stability functions, can represent many popular turbulence closures, including the k-kl (Mellor-Yamada Level 2.5), k-epsilon, and k-omega schemes. The implementation adds flexibility to the model by providing an unprecedented range of turbulence closure selections in a single 3D oceanographic model and allows comparison and evaluation of turbulence models in an otherwise identical numerical environment. This also allows evaluation of the effect of turbulence models on other processes such as suspended-sediment distribution or ecological processes. Performance of the turbulence models and sediment-transport schemes is investigated with three test cases for (1) steady barotropic flow in a rectangular channel, (2) wind-induced surface mixed-layer deepening in a stratified fluid, and (3) oscillatory strati?ed pressure-gradient driven flow (estuarine circulation) in a rectangular channel. Results from k-epsilon, k-omega, and gen (a new closure proposed by Umlauf and Burchard [J. Marine Research 61 (2003) 235]) are very similar for these cases, but the k-kl closure results depend on a wall-proximity function that must be chosen to suit the flow. Greater variations appear in simulations of suspended-sediment concentrations than in salinity simulations because the transport of suspended-sediment ampli?es minor variations in the methods. The amplification is caused by the added physics of a vertical settling rate, bottom stress dependent resuspension, and diffusive transport of sediment in regions of well mixed salt and temperature. Despite the amplified sensitivity of sediment to turbulence models in the estuary test case, the four closures investigated here all generated estuarine turbidity maxima that were similar in their shape, location, and concentrations.
Abstract: We are developing a three-dimensional numerical model that implements algorithms for sediment transport and evolution of bottom morphology in the coastal-circulation model Regional Ocean Modeling System (ROMS v3.0), and provides a two-way link between ROMS and the wave model Simulating Waves in the Nearshore (SWAN) via the Model-Coupling Toolkit. The coupled model is applicable for fluvial, estuarine, shelf, and nearshore (surfzone) environments. Three-dimensional radiation-stress terms have been included in the momentum equations, along with effects of a surface wave roller model. The sediment-transport algorithms are implemented for an unlimited number of user-defined noncohesive sediment classes. Each class has attributes of grain diameter, density, settling velocity, critical stress threshold for erosion, and erodibility constant. Suspended-sediment transport in the water column is computed with the same advection–diffusion algorithm used for all passive tracers and an additional algorithm for vertical settling that is not limited by the CFL criterion. Erosion and deposition are based on flux formulations. A multi-level bed framework tracks the distribution of every size class in each layer and stores bulk properties including layer thickness, porosity, and mass, allowing computation of bed morphology and stratigraphy. Also tracked are bed-surface properties including active-layer thickness, ripple geometry, and bed roughness. Bedload transport is calculated for mobile sediment classes in the top layer. Bottom-boundary layer submodels parameterize wave–current interactions that enhance bottom stresses and thereby facilitate sediment transport and increase bottom drag, creating a feedback to the circulation. The model is demonstrated in a series of simple test cases and a realistic application in Massachusetts Bay.
Abstract: A coastal ocean forecasting system was developed for the Long-term Ecosystem Observatory (LEO) on New Jersey’s inner shelf. The forecast system comprised an ocean model, the Regional Ocean Modeling System, forced by a high-resolution atmospheric forecast, with assimilation of ocean data from ships and coastal radar systems. The forecasts were used to aid the deployment of real-time adaptive sampling observing systems during the July 2001 Coastal Predictive Skill Experiment. Temperature and salinity assimilation data were prepared by optimal interpolation of shipboard towed-body data. Surface current observations from coastal radar were projected vertically for assimilation using a statistically based extrapolation. The assimilation methods tested with the operational forecast system in July 2001 were continuous nudging and intermittent melding of the model forecast and gridded data. Observations from a validation array of current meter and thermistor moorings deployed on a cross-shore line through the center of the LEO intensive observing area were used to formulate a set of quantitative model skill metrics that focused on aspects of the two-layer wind-driven upwelling and downwelling circulation that characterizes ocean dynamics during the stratified summer season along this coast. An ensemble of model and data assimilation configurations were tested, showing that the k profile parameterization for vertical turbulence closure, and assimilation by intermittent melding, comprised the forecast system with the more significant skill as measured by the mean squared error of the validation metric time series.
Abstract: Adjoint sensitivity analysis is used to study the New York Bight circulation for three idealized situations: an unforced buoyant river plume, and upwelling and downwelling wind forcing. A derivation of adjoint sensitivity is presented that clarifies how the method simultaneously addresses initial, boundary, and forcing sensitivities. Considerations of interpretation and appropriate definitions of sensitivity scalar indices are discussed. The adjoint method identifies the oceanic conditions and forcing that are ‘‘dynamically upstream’’ to a region or feature of interest, as well as the relative roles of the prior ocean state, forcing, and dynamical influences. To illustrate the method, which is quite general, the authors consider coastal sea surface temperature (SST) variability and define the adjoint scalar index as the temporal–spatial mean squared SST anomaly on a segment of the New Jersey coast at the conclusion of a 3-day period. In the absence of wind, surface temperature advection dominates the SST anomaly with two sources of surface water identified. Downwelling winds amplify upstream advective influence. Sensitivity to temperature is separated into direct advection and the dynamic effect on density stratification and mixing. For upwelling conditions, this decomposition shows that coastal SST is controlled by both advection from the south and subsurface, but above the 5-m depth, and temperature-related density stratification between 5 and 15 m to 10 km offshore. By identifying the timing and location of ocean conditions crucial to subsequent prediction of specific circulation features, the adjoint sensitivity method has application to quantitative evaluation of observational sampling strategies.