Lagrangian validation of numerical drifter trajectories using drifting buoys: Application to the Agulhas system

The skill of numerical Lagrangian drifter trajectories in three numerical models is assessed by comparing these numerically obtained paths to the trajectories of drifting buoys in the real ocean. The skill assessment is performed using the two-sample Kolmogorov–Smirnov statistical test. To demonstrate the assessment procedure, it is applied to three different models of the Agulhas region. The test can either be performed using crossing positions of one-dimensional sections in order to test model performance in specific locations, or using the total two-dimensional data set of trajectories. The test yields four quantities: a binary decision of model skill, a confidence level which can be used as a measure of goodness-of-fit of the model, a test statistic which can be used to determine the sensitivity of the confidence level, and cumulative distribution functions that aid in the qualitative analysis. The ordering of models by their confidence levels is the same as the ordering based on the qualitative analysis, which suggests that the method is suited for model validation. Only one of the three models, a 1/10° two-way nested regional ocean model, might have skill in the Agulhas region. The other two models, a 1/2° global model and a 1/8° assimilative model, might have skill only on some sections in the region.     

Bohai Sea oil spill model: a numerical case study

An operational Bohai Sea oil spill serving module (BSOSSM) that can provide users with trajectory and movement information of the released oil is developed for the purpose of informing mitigation of oil spill incidents in the Bohai Sea, China. BSOSSM is one of the serving modules that had been integrated in China digital ocean prototype system, a marine information platform for managing, displaying and disseminating all the data investigated by China 908 Program. The oil spill trajectory is calculated by an oil spill model (OSM), which serves as a component in BSOSSM. The impacts of wind, current, as well as Stokes drift on oil spill trajectory are studied by sensitivity experiments conducted using OSM. Simulation results indicate that wind forcing is the most important factor in controlling the oil trajectory at the sea surface in Bohai Sea, whereas current and Stokes drift play relatively less important roles. However, because the direction of waves generally follows that of the wind, Stokes drift does lead to an increase in oil drift and spreading velocity. Case studies of the Penglai 19-3 oil spill incident (June 2011) and Xingang oil spill (April 2005) demonstrate that OSM can generally reproduce the oil spreading, and is therefore capable of supporting the emergency response of future oil spills in the Bohai Sea through BSOSSM.     

A case study of a modified gravity type cage and mooring system using numerical and physical models

A modified gravity-type cage, developed by SADCO Shelf Ltd., was examined using numerical and physical models to determine if the cage and mooring system is suitable for an exposed site south of the Isles of Shoals, NH. The 3000-m/sup 3/ SADCO Shelf Submersible Fish Cage has angled stays between the upper framework and the ballasted bottom rim (in addition to net) to resist the horizontal shear deformation. The mooring system consists of three legs-each made up of a taut vertical chain and an angled rope, both leading to deadweight anchors. Normalized response amplitudes (response amplitude operators) were found for motion response in heave, surge and pitch, and load response in the anchor and bridle lines, in regular (single frequency) waves. In addition, a stochastic approach was taken to determine the motion and load transfer functions in random waves using a spectrum representative of seas at the selected site. In general, the system motion had a highly damped response, with no resonant peaks within the wave excitation range of 0.05 to 0.45 Hz. The anchor line force response was at all frequencies below 5 kN per meter of wave amplitude. The physical model tests showed consistently more conservative (larger) results compared to those for the numerical model.     

A numerical model study of the Alboran Sea Gyre

Reduced gravity and two-layer numerical models have been used to study the circulation in the westernmost basin of the Mediterranean Sea, the Alboran Sea. Circulation is forced by flow through a 20 km wide port in the western boundary representing the Strait of Gibraltar.The reduced gravity model domain is a rectangle measuring 600 km × 160 km with 10 km × 5 km grid resolution. When forced by an eastward on northeastward inflow, the model solutions evolve to a steady state which exhibits a meandering current. The first meander of the current forms the northern boundary of an anticyclonic gyre. Horizontal dimensions of the gyre are strongly dependent upon the inflow angle, vorticity associated with the incoming current, magnitude of the incoming transport and the north-south extent of the basin. The meandering current is considered a standing Rossby wave with a highly distorted vorticity trajectory due to the interaction of the current with the northern and southern boundaries. When velocity (transport) is increased, the wavelength increases approximately as √v. As a result the anticyclonic gyre shifts east as velocity increases and west as velocity decreases. These solutions show that bottom topography, winds and coastline features are not necessary mechanisms for the formation of the gyre.Two-layer model solutions were obtained using realistic topography, geometry and a westward moving lower layer. The addition of the lower layer flow and topography distorted the circulation in the upper layer, particulary in the southern half of the basin. This is caused by the large topographically steered currents along the southern shelf.The high variability of the horizontal dimensions and location of the gyre has been observed both experimentally and through satellite imagery. Model results show that the high variability is caused by variations in the inflow velocity.Drifter tracks, both observational and model derived, help determine the circulation in both layers of the Alboran Sea. The close comparison between model and experimental drifters lends credibility to the model circulation and dynamics.     

Numerical study of sand scour with a modified Eulerian model based on incipient motion theory

Application of the standard Eulerian model to simulations of sand scour results in unrealistic phenomena. Therefore, the present work develops a modified Eulerian model based on sand incipient motion theory. The modified model is applied for simulating a two-dimensional single vertical jet and a moving planar jet. The simulation results generally demonstrate fairly good agreement with published results of scour profiles and the velocity contours of the water and sand phases. In addition, equations to describe self-similar scour profiles for the moving planar jet cases are given. The results demonstrate that the modified model efficiently and accurately simulates the two-dimensional sand scour produced by jets, particularly for the moving jet cases.     

A numerical study of sea level and current responses to Hurricane Frederic using a coastal ocean model for the Gulf of Mexico

A three-dimensional, nonlinear, primitive equation ocean general circulation model is used to study the response of the Gulf of Mexico to Hurricane Frederic. The model has free surface dynamics and a second order turbulence closure scheme for the mixed layer. Realistic coastlines, bottom topography and open boundary conditions are used in the study. The model has a vertical sigma coordinate with 18 levels, and a horizontal resolution of 0.2°×0.2° for the entire Gulf. The study focuses on hurricane generated sea level, current, and coastally trapped wave (CTW) responses of the Gulf. Time series of sea levels from U.S. coastal tide gauge stations and the numerical model simulation of sea levels and currents on the shelf are used to study sea level, current and CTW responses. Both model sea levels and observations from tide gauge stations show a westward progression of the surge as a CTW response. The results of the study of sea levels and currents indicate that CTW propagate to the west with phase speeds of 7–10 m s^–1. There is also a strong nonlinear interaction between the Loop Current and hurricane induced currents. The surface current attains a maximum of 200 cm s^–1 in the eastern Gulf. The model surface elevation at several locations is compared with tide gauge data. The current meter data at three moorings are also compared with the model currents. The model simulations show good agreement with observed data for the hurricane induced coastally trapped wave, storm surge, and current distribution in the Gulf.     

Experimental and numerical analysis of container stack dynamics using a scaled model test

This paper describes an approach to simulate a seven-tier stack consisting of scaled model of a 20 ft ISO freight container and its linking connectors, denominated twist locks, subjected to dynamical load induced by its base. The physical (dimensions, mass, and moments of inertia) and structural (longitudinal, transversal and torsional stiffness) characteristics of the scaled models were decided based on two dimensionless numbers: ratios between gravity force and inertia force, and elastic force divided by inertia force, through experimental and numerical analysis. A series of experiments with controlled parameters were performed using a shaking table test to understand the effects of each variable in the container stack dynamics and present enough data to validate the numerical model. The results of this study indicate that the numerical model built is a promising tool for further study. Moreover, the model is able to predict conditions close to real situations faced by container stacks while storage on a ship's deck.     

The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: A comparison study using a nonlinear reduced gravity ocean model

This paper compares contending advanced data assimilation algorithms using the same dynamical model and measurements. Assimilation experiments use the ensemble Kalman filter (EnKF), the ensemble Kalman smoother (EnKS) and the representer method involving a nonlinear model and synthetic measurements of a mesoscale eddy. Twin model experiments provide the “truth” and assimilated state. The difference between truth and assimilation state is a mispositioning of an eddy in the initial state affected by a temporal shift. The systems are constructed to represent the dynamics, error covariances and data density as similarly as possible, though because of the differing assumptions in the system derivations subtle differences do occur. The results reflect some of these differences in the tangent linear assumption made in the representer adjoint and the temporal covariance of the EnKF, which does not correct initial condition errors. These differences are assessed through the accuracy of each method as a function of measurement density. Results indicate that these methods are comparably accurate for sufficiently dense measurement networks; and each is able to correct the position of a purposefully misplaced mesoscale eddy. As measurement density is decreased, the EnKS and the representer method retain accuracy longer than the EnKF. While the representer method is more accurate than the sequential methods within the time period covered by the observations (particularly during the first part of the assimilation time), the representer method is less accurate during later times and during the forecast time period for sparse networks as the tangent linear assumption becomes less accurate. Furthermore, the representer method proves to be significantly more costly (2–4 times) than the EnKS and EnKF even with only a few outer iterations of the iterated indirect representer method.     

A study of numerical model equations of circulations in East China Sea

Recently many authors have attepmted to model circulations in East China Sea by numerical means, for example, Xi et al^1),2). (henceforth Ref.[1] is referred to as A and[2] as B respectively), Yuan et al. and Chio. We had raised questions in regard to the correctness of the governing equations used in A, as well as their choice of boundary conditions. Comparing numerical solution of A with that of B which employed a correct form of governing equations (but with an incorrect value for the bottom friction coefficient), B asserted that the governing equations used in A were correct. It is, therefore, appropriate to have a discussion on the formulation of proper equations.     

A model for numerical simulation of nonstationary sonar reverberation using linear spectral prediction

An innovative approach to the numerical generation of nonstationery reverberation time series is presented and demonstrated. The computer simulated reverberation time series are of high quality, in that they are accurate representations of those which would result from an actual sonar system (transmit/receive and horizontal/ vertical beampatterns; pulse type, shape, length, and power; frequency and sampling rate), platform (speed and depth), and environment (wind speed and direction, backscattering strengths, and propagation loss). Volume, surface, and/or bottom reverberation as seen by a multiple beam sonar on a moving platform is generated. The approach utilizes recent developments in linear spectral prediction research in which the spectra of stochastic processes are modeled as rational functions and algorithms are used to efficiently compute optimal estimates of coefficients which specify the spectra. A two-fold sequence is formulated; first, the expected reverberation spectra for all beams are predicted and, second, the stochastic time series are generated from the expected spectra. The expected spectra are predicted using a numerical implementation, referred to as the REVSPEC (reverberation spectrum) model, of a general formulation of Faure, Ol'shevskii, and Middleton. Given the spectra, the Levinson-Durbin method is used to solve the Yule-Walker equations of the autoregressive formulation of linear spectral prediction. The numerical implementation of the approach, referred to as the REVSIM (reverberation simulation) model, produces nonstationary coherent multiple-beam reverberation time series. The formulation of the REVSIM model is presented and typical results given. A comparison is made between the simulation outputs of the REVSIM model and those of the REVGEN (reverberation generator) model, a standard well-accepted time series simulation model, to demonstrate the validity of the new approach.     

Wave-ice dynamical interaction: a numerical model and its application

In this paper, an ice floe inner stress caused by the wave-induced bending moment is derived to estimate the stress failure of ice floe. The strain and stress failures are combined to establish a wave-induced ice yield scheme. We added ice stress and strain failure module in the Finite-Volume Community Ocean Model (FVCOM), which already includes module of ice-induced wave attenuation. Thus a fully coupled wave-ice dynamical interaction model is established based on the ice and wave modules of FVCOM. This model is applied to reproduce the ice and wave fields of the breakup events observed during the second Sea Ice Physics and Ecosystem Experiment (SIPEX-2) voyage. The simulation results show that by adopting the combined wave-induced ice yield scheme, the model can successfully predict the ice breakup events, which the strain failure model is unable to predict. By comparing the critical significant wave height deduced from strain and stress failure schemes, it is concluded that the ice breakup is caused by the strain failure when wave periods are shorter than a threshold value, while the stress failure is the main reason for the ice breakup when wave periods are longer than the threshold value. Neglecting either of these two ice-break inducement mechanisms could overestimate the ice floe size, and thus underestimate the velocity of the ice lateral melt and increase the error of simulation of polar ice extent.     

Characteristics and mechanisms of the upwelling in the southern Taiwan Strait: a three-dimensional numerical model study

Using a nested circulation model based on the Princeton Ocean Model, we investigate the characteristics and mechanisms of two main upwellings in the southern Taiwan Strait: the Southwest upwelling and the Taiwan Bank upwelling. The Southwest upwelling exists in summer when the southwesterly monsoon dominates, and the Taiwan Bank upwelling occurs over a longer period from May to September. The upslope current over a distinctly widened shelf transports the cold water on-shoreward at the lower layer and the southwesterly monsoon wind drives the cold water to the surface layer, forming the Southwest upwelling, while tidal residual current weakens the upslope advection. For the Taiwan Bank upwelling, the upward transport of the South China Sea water due to the Bank topography carries the cold water from the subsurface layer to the depth of approximately 25 m near the Taiwan Bank, then the strong tidal mixing forces this upwelled water further upward to the surface layer.     

Estuary/ocean exchange and tidal mixing in a Gulf of Maine Estuary: A Lagrangian modeling study

A Lagrangian particle method embedded within a 2-D finite element code, is used to study the transport and ocean–estuary exchange processes in the well-mixed Great Bay Estuarine System in New Hampshire, USA. The 2-D finite element model, driven by residual, semi-diurnal and diurnal tidal constituents, includes the effects of wetting and drying of estuarine mud flats through the use of a porous medium transport module. The particle method includes tidal advection, plus a random walk model in the horizontal that simulates sub-grid scale turbulent transport processes. Our approach involves instantaneous, massive [O(500,000)] particle releases that enable the quantification of ocean–estuary and inter-bay exchanges in a Markovian framework. The effects of the release time, spring–neap cycle, riverine discharge and diffusion strength on the intra-estuary and estuary–ocean exchange are also investigated.The results show a rather dynamic interaction between the ocean and the estuary with a fraction of the exiting particles being caught up in the Gulf of Maine Coastal Current and swept away. Three somewhat different estimates of estuarine residence time are calculated to provide complementary views of estuary flushing. Maps of residence time versus release location uncover a strong spatial dependency of residence time within the estuary that has very important ramifications for local water quality. Simulations with and without the turbulent random walk show that the combined effect of advective shear and turbulent diffusion is very effective at spreading particles throughout the estuary relatively quickly, even at low (1 m²/s) diffusivity. The results presented here show that a first-order Markov Chain approach has applicability and a high potential for improving our understanding of the mixing processes in estuaries.     

径流和风对涌潮影响的数值模拟

由于实际江道中地形和江道轮廓等复杂性,难以分析涌潮演变规律。以钱塘江河口为基础,建立了概化河口的水动力数学模型,将复杂问题简单化,通过数学模型计算分析了径流和风况对潮差、涨潮历时、涌潮高度和涌潮传播速度的影响。结果表明,不同河段存在涌潮高度最大值的相应临界流量,越往下游,临界径流量越大;涌潮高度随风向变化规律是"逆风"<"无风"<"顺风";顺风条件下,风速越大,涌潮高度越大。