The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems: Part II - Performance and application to the California Current System

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.     

The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems: Part III - Observation impact and observation sensitivity in the California Current System

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 4D-Var 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 4D-Var systems.     

4DVAR data assimilation in the Intra-Americas Sea with the Regional Ocean Modeling System (ROMS)

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.     

4DVAR data assimilation in the Intra-Americas Sea with the Regional Ocean Modeling System (ROMS)

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.     

基于ROMS和4DVAR的沿轨与网格化SSH数据同化效果评价

Remote sensing products are significant in the data assimilation of an ocean model. Considering the resolution and space coverage of different remote sensing data, two types of sea surface height(SSH) product are employed in the assimilation, including the gridded products from AVISO and the original along-track observations used in the generation. To explore their impact on the assimilation results, an experiment focus on the South China Sea(SCS) is conducted based on the Regional Ocean Modeling System(ROMS) and the four-dimensional variational data assimilation(4 DVAR) technology. The comparison with EN4 data set and Argo profile indicates that, the along-track SSH assimilation result presents to be more accurate than the gridded SSH assimilation, because some noises may have been introduced in the merging process. Moreover, the mesoscale eddy detection capability of the assimilation results is analyzed by a vector geometry–based algorithm. It is verified that, the assimilation of the gridded SSH shows superiority in describing the eddy's characteristics, since the complete structure of the ocean surface has been reconstructed by the original data merging.     

Prediction and assimilation of surf-zone processes using a Bayesian network: Part I: Forward models

Prediction of coastal processes, including waves, currents, and sediment transport, can be obtained from a variety of detailed geophysical-process models with many simulations showing significant skill. This capability supports a wide range of research and applied efforts that can benefit from accurate numerical predictions. However, the predictions are only as accurate as the data used to drive the models and, given the large temporal and spatial variability of the surf zone, inaccuracies in data are unavoidable such that useful predictions require corresponding estimates of uncertainty. We demonstrate how a Bayesian-network model can be used to provide accurate predictions of wave-height evolution in the surf zone given very sparse and/or inaccurate boundary-condition data. The approach is based on a formal treatment of a data-assimilation problem that takes advantage of significant reduction of the dimensionality of the model system. We demonstrate that predictions of a detailed geophysical model of the wave evolution are reproduced accurately using a Bayesian approach. In this surf-zone application, forward prediction skill was 83%, and uncertainties in the model inputs were accurately transferred to uncertainty in output variables. We also demonstrate that if modeling uncertainties were not conveyed to the Bayesian network (i.e., perfect data or model were assumed), then overly optimistic prediction uncertainties were computed. More consistent predictions and uncertainties were obtained by including model-parameter errors as a source of input uncertainty. Improved predictions (skill of 90%) were achieved because the Bayesian network simultaneously estimated optimal parameters while predicting wave heights.     

Prediction and assimilation of surf-zone processes using a Bayesian network: Part II: Inverse models

A Bayesian network model has been developed to simulate a relatively simple problem of wave propagation in the surf zone (detailed in Part I). Here, we demonstrate that this Bayesian model can provide both inverse modeling and data-assimilation solutions for predicting offshore wave heights and depth estimates given limited wave-height and depth information from an onshore location. The inverse method is extended to allow data assimilation using observational inputs that are not compatible with deterministic solutions of the problem. These inputs include sand bar positions (instead of bathymetry) and estimates of the intensity of wave breaking (instead of wave-height observations). Our results indicate that wave breaking information is essential to reduce prediction errors. In many practical situations, this information could be provided from a shore-based observer or from remote-sensing systems. We show that various combinations of the assimilated inputs significantly reduce the uncertainty in the estimates of water depths and wave heights in the model domain. Application of the Bayesian network model to new field data demonstrated significant predictive skill (R² = 0.7) for the inverse estimate of a month-long time series of offshore wave heights. The Bayesian inverse results include uncertainty estimates that were shown to be most accurate when given uncertainty in the inputs (e.g., depth and tuning parameters). Furthermore, the inverse modeling was extended to directly estimate tuning parameters associated with the underlying wave-process model. The inverse estimates of the model parameters not only showed an offshore wave height dependence consistent with results of previous studies but the uncertainty estimates of the tuning parameters also explain previously reported variations in the model parameters.     

Weak and strong constraint data assimilation in the inverse Regional Ocean Modeling System (ROMS): Development and application for a baroclinic coastal upwelling system

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.Further investigation in the functional form of the model error covariance and in the use of the representer tangent linear model may lead to improvement in the forecast skill.     

Empirical design of scour protections around monopile foundations: Part 1: Static approach

Together with new opportunities, offshore wind farms raise new engineering challenges. An important aspect relates to the erosion of bottom material around the foundation of the wind turbines, caused by the local increase of the wave and current induced flow velocities by the pile's presence. Typically, the expected scour has a considerable impact on the stability and dynamic behavior of the wind turbine and a scour protection is placed to avoid erosion of the soil close to the foundation. Although much experience exists on the design of scour protections around bridge piers (which are placed in a current alone situation), at present, little design guidelines exist for the specific case of a scour protection around a monopile foundation subjected to a combined wave and current loading.     

The form of the asymptotic depth-limited wind-wave spectrum: Part III — Directional spreading

The directional spreading of both the wavenumber and frequency spectra of finite-depth wind generated waves at the asymptotic depth limit are examined. The analysis uses the Wavelet Directional Method, removing the need to assume a form for the dispersion relationship. The paper shows that both the wavenumber and frequency forms are narrowest at the spectral peak and broaden at wavenumbers (frequencies) both above and below the peak. The directional spreading of the wavenumber spectrum is bi-modal above the spectral peak. In contrast, the frequency spectrum is uni-modal. This difference is shown to be the result of energy in the wind direction being displaced from the linear dispersion shell. A full parametric relationship for the directional spreading of the wavenumber spectrum is developed. The analysis clearly shows that typical dispersion relationships are questionable at high frequencies and that such effects can be significant. This result supports greater attention being focussed on the routine recording of wavenumber spectra, rather than frequency spectra.     

4DVAR Data Assimilation with the Regional Ocean Modeling System (ROMS): Impact on the Water Mass Distributions in the Yellow Sea

In this study, we evaluate the performance of the recently developed incremental strong constraint 4-dimensional variational (4DVAR) data assimilation applied to the Yellow Sea (YS) using the Regional Ocean Modeling System (ROMS). Two assimilation experiments are compared: assimilating remote-sensed sea surface temperature (SST) and both the SST and in-situ profiles measured by shipboard CTD casts into a regional ocean modeling from January to December of 2011. By comparing the two assimilation experiments against a free-run without data assimilation, we investigate how the assimilation affects the hydrographic structures in the YS. Results indicate that the SST assimilation notably improves the model behavior at the surface when compared to the non-assimilative free-run. The SST assimilation also has an impact on the subsurface water structure in the eastern YS; however, the improvement is seasonally dependent, that is, the correction becomes more effective in winter than in summer. This is due to a strong stratification in summer that prevents the assimilation of SST from affecting the subsurface temperature. A significant improvement to the subsurface temperature is made when the in-situ profiles of temperature and salinity are assimilated, forming a tongue-shaped YS bottom cold water from the YS toward the southwestern seas of Jeju Island.     

Large-scale turbulence under a solitary wave: Part 2: Forms and evolution of coherent structures

The instantaneous turbulent velocity field produced by a broken solitary wave propagating on a 1 in 50 plane slope was measured in the longitudinal transverse plane in the middle part of the water column and near the bottom using a stereoscopic particle image velocimetry system. These measurements showed that large-scale turbulence first arrived in the form of a downburst of turbulent fluid. In the middle of the water column, the downbursts arrived shortly after the wave crest had passed. Each downburst was accompanied by two counter-rotating vortices. The latter grew rapidly in size to become a prominent feature of the flow field. Each vortex had a typical length scale of 1/2 to 1 water depth, and carried most of the turbulent kinetic energy in the region between the vortices. Near the bottom, the counter-rotating vortices were not as well defined and covered only a small plane area compared to the entire flow structure. The turbulent fluid descending from above diverged at the bed and the resulting flow structure developed an elongated shape as the source of down-flow travelled onshore with the broken wave. It was found that the transverse spacing between adjacent downbursts ranged from 2 to 5 times the local still water depth. Since vortices cannot end in the interior of the fluid, the counter-rotating vortices must extend to the free surface in the form of a vortex loop. It was suggested that these vortex loops were produced by bending and stretching of primary vorticity generated in the wave breaking process, possibly as a result of three-dimensional water surface deformation. The vortex loops were then carried downward by the falling water from the broken wave.     

Flow under standing waves: Part 1. Shear stress distribution,energy flux and steady streaming

The conditions for energy flux, momentum flux and the resulting streaming velocity are analysed for standing waves formed in front of a fully reflecting wall. The exchange of energy between the outer wave motion and the near bed oscillatory boundary layer is considered, determining the horizontal energy flux inside and outside the boundary layer. The momentum balance, the mean shear stress and the resulting time averaged streaming velocities are determined. For a laminar bed boundary layer the analysis of the wave drift gives results similar to the original work of Longuet–Higgins from 1953. The work is extended to turbulent bed boundary layers by application of a numerical model. The similarities and differences between laminar and turbulent flow conditions are discussed, and quantitative results for the magnitude of the mean shear stress and drift velocity are presented. Full two-dimensional simulations of standing waves have also been made by application of a general purpose Navier–Stokes solver. The results agree well with those obtained by the boundary layer analysis. Wave reflection from a plane sloping wall is also investigated by using the same numerical model and by physical laboratory experiments. The phase shift of the reflected wave train is compared with theoretical and empirical models.     

Developing a building policy for the erosion zone: Solutions to some key (Dutch) questions

In those coastal communities where the most seaward strip of mainland consists of dunes, these dunes often serve as a flexible sea defence. In addition, this strip offers large potential for housing and commercial enterprises. Unfortunately, due to severe storm surges part of this strip (the erosion zone) is subject to erosion, and as a result of which any buildings or infrastructure located here, are destroyed. Therefore, as we will illustrate in this paper, a building policy for this zone should reflect a compromise between two opposite interests: exploitation of the existing potential and, prevention of an unacceptable high risk due to erosion. Accordingly, the authors have developed a framework for such a building policy on the basis of which the desirability of various different types of investments and the location within the erosion zone of such investments can be determined. The examples that are used to illustrate this framework in this paper are limited to experiences in The Netherlands as relevant data and experiences are available and relatively easy accessible here. Nevertheless, the approach as is described is generic and applicable worldwide suggesting that the discovered unused potential for exploitation is not just limited to The Netherlands.     

Review of three-dimensional ecological modelling related to the North Sea shelf system: Part 1: models and their results

The state-of-the-art in modelling the marine ecosystem of the greater North Sea is reviewed, providing an overview especially about three-dimensional models that describe and predict how the marine ecosystem of the greater North Sea area functions and how concentrations and fluxes of biologically important elements vary in space and time, throughout the shelf and over years, in response to physical forcing. Articles with a strong concentration on modelling were selected from the available literature, and all articles around the existing “ecological modelling groups” dealing with the area of the North Sea were sorted in chronological order of their appearance in the literature. We found eleven of such groups and described their different modelling efforts. Selecting the seven three-dimensional models (NORWECOM, GHER, ECOHAM, ERSEM, ELISE, COHERENS and POL3dERSEM), we characterized the complexity of the models, by comparing the resolution in time and space, and the resolution of the trophic structure by discussing the number and kind of state variables and of the processes relating these state variables to each other.The review of biogeochemical/ecological modelling for the greater North Sea shows that important findings by model simulations have either confirmed existing knowledge derived from field work or have given new insight into the mechanisms of the functioning of the North Sea system: the temporal and spatial development and magnitude of primary production, its spreading from the coasts to the north-west over the open North Sea, its mechanisms of limitation, the functioning of the pelagic small food web and of the benthic web, the mechanisms of nutrient regeneration, the effects of riverine and atmospheric nutrient inputs causing eutrophication of coastal waters, the extent of eutrophication in the North Sea, and the budgets for nitrogen, phosphorus, and silicon. The three-dimensional ecological models of the greater North Sea have provided consistent distributions and dynamics of the lower trophic levels on their regional, annual and decadal scales which cannot be derived to this degree of coverage by observations.The state-of-the-art in validation for these models is presented in part 2