The analytical solution is derived for rotational frictional flow in a shallow layer of fluid in which the top and bottom Ekman layers join without leaving a frictionless interior.This vertical structure has significant implications for the horizontal flow. In particular, for a layer of water subjected to both a surface wind stress and bottom friction, the vorticity of the horizontal flow is a function not only of the curl of the wind stress (the classical result for deep water known as Ekman pumping) but also of its divergence. The importance of this divergence term peaks for a water depth around 3 times the Ekman layer thickness. This means that a curl-free but non-uniform wind stress on a shallow sea or lake can, through the dual action of rotation and friction, generate vorticity in the wind-driven currents. We also find that the reduction of three-dimensional dynamics to a two-dimensional model is more subtle than one could have anticipated and needs to be approached with utmost care. Taking the bottom stress as dependent solely on the depth-averaged flow, even with some veering, is not appropriate. The bottom stress ought to include a component proportional to the surface stress, which is negligible for large depths but increases with decreasing water depth.

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The Columbia River (CR) estuary is characterized by high river discharge and strong tides that generate high velocity flows and sharp density gradients. Its dynamics strongly affects the coastal ocean circulation. Tidal straining in turn modulates the stratification in the estuary. Simulating the hydrodynamics of the CR estuary and plume therefore requires a multi-scale model as both shelf and estuarine circulations are coupled. Such a model has to keep numerical dissipation as low as possible in order to correctly represent the plume propagation and the salinity intrusion in the estuary. Here, we show that the 3D baroclinic discontinuous Galerkin finite element model SLIM 3D is able to reproduce the main features of the CR estuary-to-ocean continuum. We introduce new vertical discretization and mode splitting that allow us to model a region characterized by complex bathymetry and sharp density and velocity gradients. Our model takes into account the major forcings, i.e. tides, surface wind stress and river discharge, on a single multi-scale grid. The simulation period covers the end of spring-early summer of 2006, a period of high river flow and strong changes in the wind regime. SLIM 3D is validated with in-situ data on the shelf and at multiple locations in the estuary and compared with an operational implementation of SELFE. The model skill in the estuary and on the shelf indicate that SLIM 3D is able to reproduce the key processes driving the river plume dynamics, such as the occurrence of bidirectional plumes or reversals of the inner shelf coastal currents.

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Lagrangian forward and backward models are introduced into a coarse-grid ocean global circulation model to trace the ventilation routes of the deep North Pacific Ocean. The random walk aspect in the Lagrangian model is dictated by a rotated isopycnal diffusivity tensor in the circulation model, and the effect of diffusion is explicitly resolved by means of stochastic terms in the Lagrangian model. The analogy between the probability distribution of a Lagrangian model with Green's function of an Eulerian tracer transport equation is established. The estimated first- and last-passage time density of the deep North Pacific using both the Eulerian and the Lagrangian models ensured that the Lagrangian pathways and their ensemble statistics are consistent with the Eulerian tracer transport and its adjoint model. Moreover, the sample pathways of the ventilated mass fractions of the deep North Pacific particles to and from the ocean surface are studied.

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Interaction of tidal flow with a complex topography and bathymetry including headlands, islands, coral reefs and shoals create a rich submesoscale field of tidal jets, vortices, unsteady wakes, lee eddies and free shear layers, all of which impact marine ecology. A unique and detailed view of the submesoscale variability in a part of the Great Barrier Reef lagoon, Australia, that includes a number of small islands was obtained by using a “stereo” pair of 2-m-resolution visible-band images that were acquired just 54 s apart by the WorldView-3 satellite. Near-surface current and vorticity were extracted at a 50-m-resolution from those data using a cross-correlation technique and an optical-flow method, each yielding a similar result. The satellite-derived data are used to test the ability of the second-generation Louvain-la-Neuve ice-ocean model (SLIM), an unstructured-mesh, finite element model for geophysical and environmental flows, to reproduce the details of the currents in the region. The model succeeds in simulating the large-scale (> 1 km) current patterns, such as the main current and the width and magnitude of the jets developing in the gaps between the islands. Moreover, the order of magnitude of the vorticity and the occurrence of some vortices downstream of the islands are correctly reproduced. The smaller scales (< 500 m) are resolved by the model, although various discrepancies with the data are observed. The smallest scales (< 50 m) are unresolved by both the model- and image-derived velocity fields. This study shows that high-resolution models are able to a significant degree to simulate accurately the currents close to a rugged coast. Very-high-resolution satellite oceanography stereo images offer a new way to obtain snapshots of currents near a complex topography that has reefs, islands and shoals, and is a potential resource that could be more widely used to assess the predictive ability of coastal circulation models.

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The containment of genetically modified (GM) pollen is an issue of significant concern for many countries. For crops that are bee-pollinated, model predictions of outcrossing rates depend on the movement hypothesis used for the pollinators. Previous work studying pollen spread by honeybees, the most important pollinator worldwide, was based on the assumption that honeybee movement can be well approximated by Brownian motion. A number of recent studies, however, suggest that pollinating insects such as bees perform Lévy flights in their search for food. Such flight patterns yield much larger rates of spread, and so the Brownian motion assumption might significantly underestimate the risk associated with GM pollen outcrossing in conventional crops. In this work, we propose a mechanistic model for pollen dispersal in which the bees perform truncated Lévy flights. This assumption leads to a fractional-order diffusion model for pollen that can be tuned to model motion ranging from pure Brownian to pure Lévy. We parametrize our new model by taking the same pollen dispersal dataset used in Brownian motion modelling studies. By numerically solving the model equations, we show that the isolation distances required to keep outcrossing levels below a certain threshold are substantially increased by comparison with the original predictions, suggesting that isolation distances may need to be much larger than originally thought.@en

The 2015/16 ENSO event increased the temperature of waters surrounding northeast Australia to above 30 °C, with large patches of water reaching 32 °C, for over two months, which led to severe bleaching of corals of the Northern Great Barrier Reef (NGBR). This study provides evidence gained from remote-sensing data, oceanographic data and oceanographic modeling, that three factors caused this excessive heating, namely: 1) the shutdown of the North Queensland Coastal Current, which would otherwise have flushed and cooled the Northern Coral Sea and the NGBR through tidal mixing 2) the advection of warm (&#x003E;30 °C) water from the Gulf of Carpentaria eastward through Torres Strait and then southward over the NGBR continental shelf, and 3) presumably local solar heating. The eastward flux of this warm water through Torres Strait was driven by a mean sea level difference on either side of the strait that in turn was controlled by the wind, which also generated the southward advection of this warm water onto the NGBR shelf. On the NGBR shelf, the residence time of this warm water was longer inshore than offshore, and this may explain the observed cross-shelf gradient of coral bleaching intensity. The fate of the Great Barrier Reef is thus controlled by the oceanography of surrounding seas.

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SLIM is an unstructured mesh, finite element model of environmental and geophysical fluid flows, which is being improved to simulate fine-grained sediment transport in riverine and marine water systems. A 2D depth-averaged version of the model is applied to the Mahakam Delta (Borneo, Indonesia), the adjacent ocean, and three lakes in the central part of the Mahakam River catchment. The 2D code is coupled to a 1D section-averaged model for the Mahakam River and four tributaries. The coupled 2D/1D model is mainly aimed at simulating fine-grained sediment transport in the riverine and marine water continuum of the Mahakam River system. Using the observations of suspended sediment concentration (SSC) at five locations in the computational domain, the modelling parameters are first determined in a calibration step, for a given
period of time. A validation step is then performed using data related to another period of time. It is concluded that the coupled 2D/1D model
reproduces very well the observed suspended sediment distribution within the delta. The spatial distribution of sediment concentration in the delta
and its temporal variation are also discussed.@en

Transport timescales (TTS), namely residence time and exposure time, were computed for adjacent shallow meso-tidal tropical estuarines system using the Lagrangian model D-Waq Part coupled with the hydrodynamic model Delft3D-Flow, and the Constituent-oriented Age and Residence time Theory, CART. The main results are threefold: (a) The TTS differs more between releases at high or low tide than between those at spring and neap tides. The exposure time was also calculated and found to be larger than the residence time by a few days. (b) The exposure and residence times were used to evaluate the return coefficient (r) for different scenarios. As with residence and exposure times, the return coefficient was found to differ more between releases at high or low tide than between those at spring and neap tides. (c) For the Caravelas Estuary, where the river inflow was low (~4 m³ s^-1), the residence time was found to be much larger than for the Peruípe Estuary, where the river discharge was greater and nearly constant during the sampling period (~20 m³ s^-1). These results shows the importance of advection in decreasing TTS in the Peruípe Estuary compared to the Caravelas Estuary. The influence of the advection and dispersion agrees with previous simple estimates obtained using the newly modified Land Ocean Interaction Coastal Zone (LOICZ) model by Andutta et al. (2014).

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A discontinuous Galerkin nonhydrostatic atmospheric model is used for two-dimensional and threedimensional simulations. There is a wide range of timescales to be dealt with. To do so, two different implicit/explicit time discretizations are implemented. A stabilization, based upon a reduced-order discretization of the gravity term, is introduced to ensure the balance between pressure and gravity effects. While not affecting significantly the convergence properties of the scheme, this approach allows the simulation of anisotropic flows without generating spurious oscillations, as it happens for a classical discontinuous Galerkin discretization. This approach is shown to be less diffusive than usual spatial filters. A stability analysis demonstrates that the use of this modified scheme discards the instability associated with the usual discretization. Validation against analytical solutions is performed, confirming the good convergence and stability properties of the scheme. Numerical results demonstrate the attractivity of the discontinuous Galerkin method with implicit/explicit time integration for large-scale atmospheric flows.@en

With the second largest outflow in the world and one of the widest hydrological basins, the Congo River is of a major importance both locally and globally. However, relatively few studies have been conducted on its hydrology, as compared to other great rivers such as the Amazon, Nile, Yangtze, or Mississippi. The goal of this study is therefore to help fill this gap and provide the first high-resolution simulation of the Congo river-estuary-coastal sea continuum. To this end, we are using a discontinuous-Galerkin finite element marine model that solves the two-dimensional depth-averaged shallow water equations on an unstructured mesh. To ensure a smooth transition from river to coastal sea, we have considered a model that encompasses both hydrological and coastal ocean processes. An important difficulty in setting up this model was to find data to parameterize and validate it, as it is a rather remote and understudied area. Therefore, an important effort in this study has been to establish a methodology to take advantage of all the data sources available including nautical charts that had to be digitalized. The model surface elevation has then been validated with respect to an altimetric database. Model results suggest the existence of gyres in the vicinity of the river mouth that have never been documented before. The effect of those gyres on the Congo River dynamics has been further investigated by simulating the transport of Lagrangian particles and computing the water age.@en

The concept of age is widely used to quantify the transport rate of tracers - or pollutants - in the environment. The age focuses only on the time taken to reach a given location and disregards other aspects of the path followed by the tracer parcel. To keep track of the subregions visited by the tracer parcel along this path, partial ages are defined as the time spent in the different subregions. Partial ages can be computed in an Eulerian framework in much the same way as the usual age by extending the Constituent oriented Age and Residence Time theory (CART, www.climate.be/CART). In addition to the derivation of theoretical results and properties of partial ages, applications to a 1D model with lateral/transient storage, to the 1D advection-diffusion equation and to the diagnosis of the ventilation of the deep ocean are provided. They demonstrate the versatility of the concept of partial age and the potential new insights that can be gained with it.@en

Large rivers often present a river–lake–delta system, with a wide range of temporal and spatial scales of the flow due to the combined effects of human activities and various natural factors, e.g., river discharge, tides, climatic variability, droughts, floods. Numerical models that allow for simulating the flow in these river–lake–delta systems are essential to study them and predict their evolution under the impact of various forcings. This is because they provide information that cannot be easily measured with sufficient temporal and spatial detail. In this study, we combine one-dimensional sectional-averaged (1D) and two-dimensional depth-averaged (2D) models, in the framework of the finite element model SLIM, to simulate the flow in the Mahakam river–lake–delta system (Indonesia). The 1D model representing the Mahakam River and four tributaries is coupled to the 2D unstructured mesh model implemented on the Mahakam Delta, the adjacent Makassar Strait, and three lakes in the central part of the river catchment. Using observations of water elevation at five stations, the bottom friction for river and tributaries, lakes, delta, and adjacent coastal zone is calibrated. Next, the model is validated using another period of observations of water elevation, flow velocity, and water discharge at various stations. Several criteria are implemented to assess the quality of the simulations, and a good agreement between simulations and observations is achieved in both calibration and validation stages. Different aspects of the flow, i.e., the division of water at two bifurcations in the delta, the effects of the lakes on the flow in the lower part of the system, the area of tidal propagation, are also quantified and discussed.

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In the context of the emergence of extraterrestrial oceanography, we adapted an existing oceanographic model, SLIM (www.climate.be/slim), to the conditions of Titan, a moon of Saturn. The tidal response of the largest southern lake at Titan’s surface, namely Ontario Lacus, is simulated. SLIM solves the 2D, depth-averaged shallow water equations on an unstructured mesh using the discontinuous Galerkin finite element method, which allows for high spatial resolution wherever needed. The impact of the wind forcing, the bathymetry, and the bottom friction is also discussed. The predicted maximum tidal range is about 0.56 m in the southern part of the lake, which is more than twice as large as the previous estimates (see Tokano, Ocean Dyn 60:(4) 803–817
doi:10.1007/s10236-010-0285-3 2010). The patterns and magnitude of the current are also markedly different from those of previous studies: the tidal motion is not aligned with the major axis of the lake and the speed is larger
nearshore. Indeed, the main tidal component rotates clockwise in an exact period of one Titan day and the tidal currents can reach 0.046 ms−1 close to the shores depending on the geometry and the bathymetry. Except for these
specific nearshore regions, the current speed is less than 0.02 ms−1. Circular patterns can be observed offshore, their rotational direction and size varying along the day.@en

Aim Connectivity is a key determinant of coral reef resilience. However, connectivity models rarely account for deep or submerged reefs, despite their widespread occurrence in many coral reef provinces. Here, we model coral larval connectivity among submerged and near-sea-surface (NSS) reefs, investigate differences in dispersal potential for coral larvae from these differing reef morphologies and estimate the potential for deeper reef habitats (> 10 m) to provide a source of larvae to shallower reef habitats (< 10 m). Location Great Barrier Reef, Australia. Methods We used two newly developed, high-resolution models to identify the location and spatial extent of submerged and NSS reefs and to simulate oceanographic currents (‘SLIM’) affecting larval dispersal. Dispersal patterns for five depth-generalist coral species with differing life histories and dispersal potential were modelled using an individual-based model (IBM). Results Near-sea-surface reefs were the largest source of larvae successfully settling, but submerged reefs exported a greater proportion of larvae per unit area to other reefs. Larvae originating from submerged reefs also dispersed greater distances. Recruits on shallow-water reef habitats primarily originated from other shallow areas, but two-way connectivity did occur between deep and shallow habitats. Empirical data indicate that long-term coral cover has declined most steeply on the shallow habitats predicted by our model to be highly dependent on other shallow habitats for recruits. Main conclusions Submerged reefs may contribute significantly to larval production and should therefore be considered in connectivity analyses. The hydrodynamic environment on submerged reefs results in larvae dispersing greater distances, potentially increasing their importance as source reefs following disturbances. Deep reef habitats are generally less exposed to disturbances and could therefore constitute an important larval source to some shallow habitats following disturbances. Given the importance of connectivity to coral reef resilience, greater attention should be afforded to identifying and protecting submerged reefs and other deeper habitats.@en

Understanding the transport and fate of suspended sediment exported by rivers is crucial for the management of sensitive marine ecosystems. Sediment transport and fate can vary considerably depending on the geophysical characteristics of the coastal environment. Fine sediment transport was studied in a setting in between “open” (uninterrupted coasts) and “semi-enclosed” (bays) coastal systems, namely a “semi-open” system of shallow coastal water with long (∼20 km) stretches of open coasts separated by capes and headlands. The case study was the large, seasonal, Burdekin River that discharges to a wide continental shelf containing headlands and shallow embayments adjacent to the Great Barrier Reef, Australia. A new three-dimensional fine sediment module for the unstructured-mesh SLIM 3D hydrodynamic model was developed. The model was successfully validated against available field data. The results were compared to previous studies on the Burdekin River sediment transport and differences were analysed. Wind direction and speed during river floods largely control the dynamics and the fate of the fine sediment. Most (67% for 2007) of the riverine fine sediment load is deposited near the river mouth; the remaining sediment is transported further afield in a riverine freshwater plume; that sediment can reach sensitive marine ecosystems and should be a priority for management. During the rest of the year, when the river flow has ceased, wind-driven resuspension events redistribute the deposited sediment within embayments but generate negligible longshore transport. This study suggests that semi-open systems trap most of the riverine fine sediment, somewhat like semi-enclosed systems.@en