BAKTRAK: backtracking drifting objects using an iterative algorithm with a forward trajectory model

The task of determining the origin of a drifting object after it has been located is highly complex due to the uncertainties in drift properties and environmental forcing (wind, waves, and surface currents). Usually, the origin is inferred by running a trajectory model (stochastic or deterministic) in reverse. However, this approach has some severe drawbacks, most notably the fact that many drifting objects go through nonlinear state changes underway (e.g., evaporating oil or a capsizing lifeboat). This makes it difficult to naively construct a reverse-time trajectory model which realistically predicts the earliest possible time the object may have started drifting. We propose instead a different approach where the original (forward) trajectory model is kept unaltered while an iterative seeding and selection process allows us to retain only those particles that end up within a certain time–space radius of the observation. An iterative refinement process named BAKTRAK is employed where those trajectories that do not make it to the goal are rejected, and new trajectories are spawned from successful trajectories. This allows the model to be run in the forward direction to determine the point of origin of a drifting object. The method is demonstrated using the leeway stochastic trajectory model for drifting objects due to its relative simplicity and the practical importance of being able to identify the origin of drifting objects. However, the methodology is general and even more applicable to oil drift trajectories, drifting ships, and hazardous material that exhibit nonlinear state changes such as evaporation, chemical weathering, capsizing, or swamping. The backtracking method is tested against the drift trajectory of a life raft and is shown to predict closely the initial release position of the raft and its subsequent trajectory.     

Assessing the fidelity of surface currents from a coastal ocean model and HF radar using drifting buoys in the Middle Atlantic Bight

The rapid expansion of urbanization along the world’s coastal areas requires a more comprehensive and accurate understanding of the coastal ocean. Over the past several decades, numerical ocean circulation models have tried to provide such insight, based on our developing understanding of physical ocean processes. The systematic establishment of coastal ocean observation systems adopting cutting-edge technology, such as high frequency (HF) radar, satellite sensing, and gliders, has put such ocean model predictions to the test, by providing comprehensive observational datasets for the validation of numerical model forecasts. The New York Harbor Observing and Prediction System (NYHOPS) is a comprehensive system for understanding coastal ocean processes on the continental shelf waters of New York and New Jersey. To increase confidence in the system’s ocean circulation predictions in that area, a detailed validation exercise was carried out using HF radar and Lagrangian drifter-derived surface currents from three drifters obtained between March and October 2010. During that period, the root mean square (RMS) differences of both the east–west and north–south currents between NYHOPS and HF radar were approximately 15 cm s^?1. Harmonic analysis of NYHOPS and HF radar surface currents shows similar tidal ellipse parameters for the dominant M₂ tide, with a mean difference of 2.4 cm s^?1 in the semi-major axis and 1.4 cm s^?1 in the semi-minor axis and 3° in orientation and 10° in phase. Surface currents derived independently from drifters along their trajectories showed that NYHOPS and HF radar yielded similarly accurate results. RMS errors when compared to currents derived along the trajectory of the three drifters were approximately 10 cm s^?1. Overall, the analysis suggests that NYHOPS and HF radar had similar skill in estimating the currents over the continental shelf waters of the Middle Atlantic Bight during this time period. An ensemble-based set of particle tracking simulations using one drifter which was tracked for 11 days showed that the ensemble mean separation generally increases with time in a linear fashion. The separation distance is not dominated by high frequency or short spatial scale wavelengths suggesting that both the NYHOPS and HF radar currents are representing tidal and inertial time scales correctly and resolving some of the smaller scale eddies. The growing ensemble mean separation distance is dominated by errors in the mean flow causing the drifters to slowly diverge from their observed positions. The separation distance for both HF radar and NYHOPS stays below 30 km after 5 days, and the two technologies have similar tracking skill at the 95 % level. For comparison, the ensemble mean distance of a drifter from its initial release location (persistence assumption) is estimated to be greater than 70 km in 5 days.     

Developing a Lagrangian sediment transport model for open channel flows

A three-dimensional stochastic Lagrangian particle tracking sediment transport model is developed to solve the discrete advection-dispersion equation using a combination of empirical dispersion equations.The performance of three widely-used longitudinal dispersion coefficient equations was examined to select one of them as the primary dispersion equation term in the developed model. Also, a conditional empirical equation was used to consider the effect of vertical dispersion term in top layers n...     

Radium-barium-silica correlations and a two-dimensional radium model for the world ocean

Radium-barium-silica relationships are examined in various regions of the Pacific. Ra, Ba and Si are not linearly correlated except in the Circumpolar region. From surface water to the intermediate water, Ra usually increases linearly with Ba and Si. In the North Pacific where there is a Ra excess in the deep water, both the Ra-Ba and Ra-Si diagrams show curves concave upward with an increasing slope. The relationships are further complicated by a deep gentle Ba maximum and a broad mid-depth Si maximum.In the western boundary where the Antarctic Bottom Water and Pacific Deep Water are separated by the benthic front, the Ra-Ba and Ra-Si plots show “hooks” of various size and shape caused by a discordance in the depths of the Ra, Ba and Si maxima. The hook becomes smaller toward the south and flips from counterclockwise to clockwise in the southern basin.A two-dimensional horizontal model with a geostrophic circulation pattern is employed to calculate Ra distribution in the deep water with a constant upwelling rate but a variable mean input rate for Ra. The mean input rate or fluxF is the sum of the in-situ production rateJ by particulate dissolution in the water column and the bottom fluxQ_b. The global mean fluxF needed to balance the radiodecay in a steady-state distribution is used as a reference for discussion. It is found that anF value set at1.5 ×F fits the observed data in the deep Atlantic. TheF value needs to be about2.7 ×F in order to produce a comparable distribution in the deep Pacific. These model calculations indicate that a Ra source is required in the northeast Pacific. It appears that no uniqueF can produce a global Ra distribution in deep water comparable to both the Atlantic and Pacific observations. This is also true within the Pacific Ocean itself because of the large Ra excess observed in the northeast Pacific. Thus the Ra input rate is quite variable and increases by a factor of two from the Atlantic to the Pacific. This probably reflects the non-uniformity of the bottom fluxQ_b rather than that of the in-situ productionJ in the world oceans.     

Stochastic earthquake source model for ground motion simulation

In the analysis and design of important structures with relatively long life spans, there is a need to generate strong motion data for possible large events. The source of an earthquake is characterized by the spatial distribution of slip on the fault plane. For future events, this is unknown. In this paper, a stochastic earthquake source model is developed to address this issue. Here, 1D and 2D stochastic models for slip distribution developed by Lavallée et al.(2006) are used. The random field associated with the slip distribution is heavy-tailed stable distribution which can be used for large events. Using 236 past rupture models, the spectral scaling parameter and the four stable or Levy's parameters against empirical relationship for known quantities like magnitude or fault length are developed. The model is validated with data from 411 stations of 1999 Chi-Chi earthquake. The simulated response spectrum showed good agreement to actual data. Further the proposed model is used to generate ground motion for the 1993 Killari Earthquake where strong motion data is not available. The simulated mean peak ground velocity was in turn related to the intensity(MSK) and compared against values in the literature.     

A source-Sink laboratory model of the ocean circulation

Abstract

A two gyre circulation and inertial western boundary currents have been observed in a sloping bottom laboratory model of a barotropic ocean circulation. Water of viscosity v is contained in a rotating (angular velocity ω), square basin of side L (30 cm) with a flat top and a bottom slope (tan θ) such that the depth (H) varies from 12 to 15 cm. The flow is driven by a distributed source and sink at the upper surface, a plate drilled with 342 holes. The hole distribution and size is arranged so that the average imposed vertical velocity, w = w ₀ sin (2πy′/30), models the Ekman divergence from a two gyre zonal wind stress. Fluid flow is observed with the thymol blue technique over the ranges of Rossby numbers (w ₀/2ωL tan θ) from 1.44 × 10^?3 to 1.41 × 10^?2 and Ekman numbers (v/2ωH ²) from 2.13 × 10^?5 to 2.10 × 10^?3. At the largest Rossby numbers the flow pattern changes markedly, but the non-uniformity of the imposed vertical velocity also penetrates deep into the fluid in this regime.     

South Atlantic circulation in a world ocean model

The circulation in the South Atlantic Ocean has been simulated within a global ocean general circulation model. Preliminary analysis of the modelled ocean circulation in the region indicates a rather close agreement of the simulated upper ocean flows with conventional notions of the large-scale geostrophic currents in the region. The modelled South Atlantic Ocean witnesses the return flow and export of North Atlantic Deep Water (NADW) at its northern boundary, the inflow of a rather barotropic Antarctic Circumpolar Current (ACC) through the Drake Passage, and the inflow of warm saline Agulhas water around the Cape of Good Hope. The Agulhas leakage amounts to 8.7 Sv, within recent estimates of the mass transport shed westward at the Agulhas retroflection. Topographic steering of the ACC dominates the structure of flow in the circumpolar ocean. The Benguela Current is seen to be fed by a mixture of saline Indian Ocean water (originating from the Agulhas Current) and fresher Subantarctic surface water (originating in the ACC). The Benguela Current is seen to modify its flow and fate with depth; near the surface it flows north-westwards bifurcating most of its transport northward into the North Atlantic Ocean (for ultimate replacement of North Atlantic surface waters lost to the NADW conveyor). Deeper in the water column, more of the Benguela Current is destined to return with the Brazil Current, though northward flows are still generated where the Benguela Current extension encounters the coast of South America. At intermediate levels, these northward currents trace the flow of Antarctic Intermediate Water (AAIW) equatorward, though even more AAIW is seen to recirculate poleward in the subtropical gyre. In spite of the model’s rather coarse resolution, some subtle features of the Brazil-Malvinas Confluence are simulated rather well, including the latitude at which the two currents meet. Conceptual diagrams of the recirculation and interocean exchange of thermocline, intermediate and deep waters are constructed from an analysis of flows bound between isothermal and isobaric surfaces. This analysis shows how the return path of NADW is partitioned between a cold water route through the Drake Passage (6.5 Sv), a warm water route involving the Agulhas Current sheeding thermocline water westward (2.5 Sv), and a recirculation of intermediate water originating in the Indian Ocean (1.6 Sv).     

A 3D unstructured non-hydrostatic ocean model for internal waves

A 3D non-hydrostatic model is developed to compute internal waves. A novel grid arrangement is incorporated in the model. This not only ensures the homogenous Dirichlet boundary condition for the non-hydrostatic pressure can be precisely and easily imposed but also renders the model relatively simple in its discretized form. The Perot scheme is employed to discretize horizontal advection terms in the horizontal momentum equations, which is based on staggered grids and has the conservative property. Based on previous water wave models, the main works of the present paper are to (1) utilize a semi-implicit, fractional step algorithm to solve the Navier-Stokes equations (NSE); (2) develop a second-order flux-limiter method satisfying the max–min property; (3) incorporate a density equation, which is solved by a high-resolution finite volume method ensuring mass conservation and max–min property based on a vertical boundary-fitted coordinate system; and (4) validate the developed model by using four tests including two internal seiche waves, lock-exchange flow, and internal solitary wave breaking. Comparisons of numerical results with analytical solutions or experimental data or other model results show reasonably good agreement, demonstrating the model’s capability to resolve internal waves relating to complex non-hydrostatic phenomena.     

准地转大洋风生环流的格子Boltzmann数值模拟

建立了求解准地转相当正压涡度方程的格子Boltzmann (LB)模型. 该模型将准地转相当正压涡度方程作为一个平流-扩散-反应方程来加以处理,在整体二阶精度下,通过Chapman_Enskog多尺度分析法,可将格子Boltzmann方程还原到相当正压涡度方程. 在不同Reynolds数、不同边界条件以及不同风应力驱动下的数值解表明,该模型正确反映了风生环流的基本结构和不同边界的耗散特征,并得到风生环流的多平衡态解等非线性特征. 此外,不同Rossby变形半径下的实验证明,小Rossby变形半径更容易激发环流的非线性模态. 通过与同等类型有限差方案的比较,表明本文的LB模型具有稳定性好、精度高等优点.     

Estimating the internal pressure gradient errors in a σ-coordinate ocean model for the Nordic Seas

Internal pressure gradient estimation is problematic in σ-coordinate ocean models and models based on more generalised topography following coordinate systems. Artificial pressure gradients in these models may create artificial flow. In recent literature, several methods for reducing the errors in the estimated internal pressure gradients are suggested. A basin with a bell-shaped seamount in the middle has often been applied as a test case. To supplement the findings from these more idealised experiments, the internal pressure gradient errors in a σ-coordinate ocean model for the Nordic Seas are discussed in the present paper. Three methods for estimating internal pressure gradients are applied in these experiments. The sensitivity of the results to the subtraction of background stratification and to the horizontal viscosity are also investigated. For the extended Nordic Seas case, basin scale modes dominate after a few days of simulation. The errors in the transports across some sections may be larger than 1 Sv (1 Sv = 10⁶ m³ s^− 1) in these studies with 16-km grid resolution. The order of magnitude of the errors in the transports of Atlantic water into the Nordic Seas is approximately 0.5 Sv or between 5 and 10 % of recent transport estimates based on measurements. The results do not indicate that the errors are generally reduced if the background stratification is subtracted when estimating internal pressure gradients in terrain following models. However, the results from the experiments initialised with the background stratification show that the erroneous flows may be reduced considerably by using more recent techniques for estimating internal pressure gradients, especially for higher values of horizontal viscosity.     

Numerical computation of the tidally induced Lagrangian residual current in a model bay

With a depth-averaged numerical model, the tidally induced Lagrangian residual current in a model bay was studied. To correctly reflect the long-term mass transport, it is appropriate to use the Lagrangian residual velocity (LRV) rather than the Eulerian residual velocity (ERV) or the Eulerian residual transport velocity (ETV) to describe the residual current. The parameter κ, which is defined as the ratio of the typical tidal amplitude at the open boundary to the mean water depth, is considered to be the indicator of the nonlinear effect in the system. It is found that the feasibility of making the mass transport velocity (MTV) approximate the LRV is strongly dependent on κ. The error between the MTV and the LRV tends to increase with a growing κ. An additional error will come from the various initial tidal phases due to the Lagrangian drift velocity (LDV) when κ is no longer small. According to the residual vorticity equation based on the MTV, the Coriolis effect is found to influence the residual vorticity mainly through the curl of the tidal stress. A significant difference in the flow pattern indicates that the LRV is sensitive to the bottom friction in different forms.     

Use of the ACDEP trajectory model in the Danish nation-wide Background Monitoring Programme

The frequently observed eutrophication problems in Danish marine waters are associated with high nutrient loads. This paper outlines how the atmospheric part of the load is determined within the framework of the Danish Background Monitoring Programme. The analyses within the programme are carried out by use of both measurements and model calculations, where the modelling part receives the main focus in this paper. The performed calculations indicate that the atmospheric nitrogen deposition to the Danish marine waters is of comparable size to the river run-off, and in some periods even the dominating contribution to the overall nitrogen input. The model results are shown to be sensitive to the resolution of the meteorological input data for the calculations. Strong improvement of the model performance is the result when meteorological data with much higher temporal and spatial resolution are applied.     

An analogue model study of electromagnetic induction for island-continent ocean channels for the H polarization

Using an electromagnetic analogue model, the behavior of time-varying electromagnetic fields for an island near a continental coastline is examined for the H-polarization case, in which the electric field of the inducing source is perpendicular to the continental coastline. A study of the effect of the shape of the island, using square- and circular-island models, indicates that over the island, anomalies in the field components are confined to a smaller area for the circular island than for the square island. A study of the effect of ocean-channel width between the island and continent shows that, as the channel width decreases, anomalies in the magnetic field components over the island decrease. The anomaly in the electric field at the continental coastline first increases and then decreases with decreasing channel width.     

Fast lagrangian particle tracking in unstructured ocean model grids

Ocean Dynamics - Lagrangian particle tracking, based on currents derived from hydrodynamic models, is an important tool in quantifying bio-physical transports in the ocean. Particle tracking in the...     

An analogue model for studying magnetic variations induced by ocean waves

The scale factors to permit a laboratory analogue model study of the problem of magnetic fields induced by ocean waves in the earth's field are derived. An analogue model employing surface fluid waves in mercury to simulate ocean waves is described. In the analogue model, magnetic field measurements were made 1 cm above a 2 cm deep model mercury ocean for a wave period of 0.21 s. This model simulates measurements 38 m above the surface of a shallow ocean 78 m deep for a wave period of 13 s. The validity of the analogue modelling technique is established by the good agreement obtained in comparing the analogue model measurements of the induced magnetic fields with fields using Podney's expression for an ocean of finite depth.     

A relocatable ocean model in support of environmental emergencies

During the Costa Concordia emergency case, regional, subregional, and relocatable ocean models have been used together with the oil spill model, MEDSLIK-II, to provide ocean currents forecasts, possible oil spill scenarios, and drifters trajectories simulations. The models results together with the evaluation of their performances are presented in this paper. In particular, we focused this work on the implementation of the Interactive Relocatable Nested Ocean Model (IRENOM), based on the Harvard Ocean Prediction System (HOPS), for the Costa Concordia emergency and on its validation using drifters released in the area of the accident. It is shown that thanks to the capability of improving easily and quickly its configuration, the IRENOM results are of greater accuracy than the results achieved using regional or subregional model products. The model topography, and to the initialization procedures, and the horizontal resolution are the key model settings to be configured. Furthermore, the IRENOM currents and the MEDSLIK-II simulated trajectories showed to be sensitive to the spatial resolution of the meteorological fields used, providing higher prediction skills with higher resolution wind forcing.     

An analogue model study of electromagnetic induction for island-continent ocean channels

The behaviour of time-varying electromagnetic fields near an island situated in a shallow ocean with a nearby continent is investigated using a scaled analogue model. To study the effect of the proximity of the continent, various island-continent distances are treated. The presence of the continent tends to augment enhancements of the field components at the island coastlines for all channel widths studied, while the island affects the enhancements of the fields over the continental coastline only for very narrow channel widths (half the island width or less), and does not affect the horizontal to vertical magnetic field ratio at the coastline at all. To examine the effect of the shape of the island, square and circular island models are used. For the frequencies studied, the island shape has little effect on the fields over the continental coastline, but over the island, the spatial variation of the fields is considerably less for the circular island than for the square island.     

Equilibration mechanisms in an adjoint ocean general circulation model

We examine the equilibrated and time-evolving adjoint solutions of an ocean general circulation model. Adjoint models calculate the sensitivity of a diagnostic, (here, the strength of the meridional overturning) to all forcing fields in a single integration. The time evolution of the sensitivity patterns demonstrates the validity of the adjoint modeling approach over climatological time scales in coarse-resolution ocean models. Our objective is to identify the principle adjustment mechanisms through which the meridional overturning strength adapts to perturbations in wind and buoyancy forcing. The adjoint approach is shown to be a valuable alternative to traditional perturbation methods in highlighting the processes and time scales important to ocean and climate modeling.     

成层地基自由场地面运动的随机模型

地表土层通常具有成层的特点,在地震工程中将覆盖土层简化为力学性质沿竖向成层变化,水平向为各向同性的层状半空间体才会得到更符合实际情况的解答.采用频域分析方法,对多层横观各向同性土层对垂直向上的入射剪切波的反应进行了分析.在此基础上,分析了自由场地面运动的频率响应函数,计算了响应位移的功率谱密度函数,并给出了算例.算例表明,多层土的功率谱密度函数具有多个峰值.采用频域分析方法计算层状土地基在地震作用下的位移和应力响应,避免了时域分析时对波在界面处多次反射和透射的反复追踪,思路清晰,步骤简明.     

A non-breaking-wave-generated turbulence mixing scheme for a global ocean general circulation model

Ocean Dynamics - A novel vertical mixing scheme to describe the influence of the non-breaking surface waves in ocean general circulation models is proposed based on the second-order turbulence...