Quantitative analysis of numerically induced mixing in a coastal model application

In recent years, various attempts have been made to estimate the amount of numerical mixing in numerical ocean models due to discretisation errors of advection schemes. In this study, a high-resolution coastal model using the ocean circulationmodel GETM is applied to the Western Baltic Sea, which is characterised by energetic and episodic inflows of dense bottom waters originating from the Kattegat. The model is equipped with an easy-to-implement diagnostic method for obtaining the numerical mixing which has recently been suggested. In this diagnostic method, the physical mixing is defined as the mean tracer variance decay rate due to turbulent mixing. The numerical mixing due to discretisation errors of tracer advection schemes is defined as the decay rate between the advected square of the tracer variance and the square of the advected tracer, which can be directly compared to the physical variance decay. The source and location of numerical mixing is further investigated by comparing different advection schemes and analysing the amount of numerical mixing in each spatial dimension during the advection time step. The results show that, for the setup used, the numerically and physically induced mixing have the same orders of magnitude but with different vertical and horizontal distributions. As the main mechanism for high numerical mixing, vertical advection of tracers with strong vertical gradients has been identified. The main reason for high numerical mixing is due to bottom-following coordinates when density gradients, especially for regions of steep slopes, are advected normal to isobaths. With the bottom-following coordinates used here, the horizontal gradients are reproduced by a spurious sawtooth-type profile where strong advection through, but not along, the vertical coordinate levels occurs. Additionally, the well known relation between strong tracer gradients and high velocities on the one and high numerical mixing on the other hand is approved quantitatively within this work.     

Reproducibility and variability of submesoscale frontal eddies on a broad,low-energy shelf of freshwater influence

Ocean Dynamics - A multi-decadal simulation of ocean circulation in the northern Gulf of Mexico produces strong submesoscale instabilities in the Mississippi/Atchafalaya plume fronts. The model...     

Regional turbulence patterns driven by meso- and submesoscale processes in the Caribbean Sea

The surface ocean circulation in the Caribbean Sea is characterized by the interaction between anticyclonic eddies and the Caribbean Upwelling System (CUS). These interactions lead to instabilities that modulate the transfer of kinetic energy up- or down-cascade. The interaction of North Brazil Current rings with the islands leads to the formation of submesoscale vorticity filaments leeward of the Lesser Antilles, thus transferring kinetic energy from large to small scales. Within the Caribbean, the upper ocean dynamic ranges from large-scale currents to coastal upwelling filaments and allow the vertical exchange of physical properties and supply KE to larger scales. In this study, we use a regional model with different spatial resolutions (6, 3, and 1 km), focusing on the Guajira Peninsula and the Lesser Antilles in the Caribbean Sea, in order to evaluate the impact of submesoscale processes on the regional KE energy cascade. Ageostrophic velocities emerge as the Rossby number becomes O(1). As model resolution is increased submesoscale motions are more energetic, as seen by the flatter KE spectra when compared to the lower resolution run. KE injection at the large scales is greater in the Guajira region than in the others regions, being more effectively transferred to smaller scales, thus showing that submesoscale dynamics is key in modulating eddy kinetic energy and the energy cascade within the Caribbean Sea.     

Submesoscale features and their interaction with fronts and internal tides in a high-resolution coupled atmosphere-ocean-wave model of the Bay of Bengal

Large freshwater fluxes into the Bay of Bengal by rainfall and river discharges result in strong salinity fronts in the bay. In this study, a high-resolution coupled atmosphere-ocean-wave model with comprehensive physics is used to model the weather, ocean circulation, and wave field in the Bay of Bengal. Our objective is to explore the submesoscale activity that occurs in a realistic coupled model that resolves mesoscales and allows part of the submesoscale field. Horizontal resolution in the atmosphere varies from 2 to 6 km and is 13 km for surface waves, while the ocean model is submesoscale permitting with resolutions as high as 1.5 km and a vertical resolution of 0.5 m in the upper 10 m. In this paper, three different cases of oceanic submesoscale features are discussed. In the first case, heavy rainfall and intense downdrafts produced by atmospheric convection are found to force submesoscale currents, temperature, and salinity anomalies in the oceanic mixed layer and impact the mesoscale flow. In a second case, strong solitary-like waves are generated by semidiurnal tides in the Andaman Sea and interact with mesoscale flows and fronts and affect submesoscale features generated along fronts. A third source of submesoscale variability is found further north in the Bay of Bengal where river outflows help maintain strong salinity gradients throughout the year. For that case, a comparison with satellite observations of sea surface height anomalies, sea surface temperature, and chlorophyll shows that the model captures the observed mesoscale eddy features of the flow field, but in addition, submesoscale upwelling and downwelling patterns associated with ageostrophic secondary circulations along density fronts are also captured by the model.     

A review of the LATEX project: mesoscale to submesoscale processes in a coastal environment

The main objective of the LAgrangian Transport EXperiment (LATEX) project was to study the influence of coastal mesoscale and submesoscale physical processes on circulation dynamics, cross-shelf exchanges, and biogeochemistry in the western continental shelf of the Gulf of Lion, Northwestern Mediterranean Sea. LATEX was a five-year multidisciplinary project based on the combined analysis of numerical model simulations and multi-platform field experiments. The model component included a ten-year realistic 3D numerical simulation, with a 1 km horizontal resolution over the gulf, nested in a coarser 3 km resolution model. The in situ component involved four cruises, including a large-scale multidisciplinary campaign with two research vessels in 2010. This review concentrates on the physics results of LATEX, addressing three main subjects: (1) the investigation of the mesoscale to submesoscale processes. The eddies are elliptic, baroclinic, and anticyclonic; the strong thermal and saline front is density compensated. Their generation processes are studied; (2) the development of sampling strategies for their direct observations. LATEX has implemented an adaptive strategy Lagrangian tool, with a reference software available on the web, to perform offshore campaigns in a Lagrangian framework; (3) the quantification of horizontal mixing and cross-shelf exchanges. Lateral diffusivity coefficients, calculated in various ways including a novel technique, are in the range classically encountered for their associated scales. Cross-shelf fluxes have been calculated, after retrieving the near-inertial oscillation contribution. Further perspectives are discussed, especially for the ongoing challenge of studying submesoscale features remotely and from in situ data.     

基于卫星测高交叉点的海洋表面地转流速度

在流体静力平衡状态下,海洋Coriolis力和压力梯度平衡就形成地转流,世界上大多数海流都近似为地转流.本文利用卫星测高交叉点方法计算海洋表面地转流速度,分析了利用测高交叉点计算地转流速度的不确定性,上升和下降弧段的海面倾斜在分辨率50 km上可以达到10^-7量级,才可能获得优于10 cm/s的地转流速度.在低纬度或者纬度接近卫星轨道倾角的地区,由交叉点方法计算的地转流速度精度低于中纬度地区.以中国台湾东部黑潮为试验区,利用最新的中国台湾周边海域大地水准面模型参考场计算高精度的大地水准面高,利用TOPEX/Poseidon和Jason-1的GDR数据(2002~2005年)计算海面高,然后计算交叉点的动力高,确定交叉点的地转流速度,结果与中国台湾NCOR(National Center for Ocean Research)的流速基本一致.     

Multi-nest high-resolution model of submesoscale circulation features in the Gulf of Taranto

Recent oceanographic field measurements and high-resolution numerical modelling studies have revealed intense, transient, submesoscale motions characterised by a horizontal length scale of 100–10,000 m. This submesoscale activity increases in the fall and winter when the mixed layer (ML) depth is at its maximum. In this study, the submesoscale motions associated with a large-scale anticyclonic gyre in the central Gulf of Taranto were examined using realistic submesoscale-permitting simulations. We used realistic flow field initial conditions and multiple nesting techniques to perform realistic simulations, with very-high horizontal resolutions (> 200 m) in areas with submesoscale variability. Multiple downscaling was used to increase resolution in areas where instability was active enough to develop multi-scale interactions and produce 5-km-diameter eddies. To generate a submesoscale eddy, a 200-m resolution was required. The submesoscale eddy was formed through small-scale baroclinic instability in the rim of a large-scale anticyclonic gyre leading to large vertical velocities and rapid restratification of the ML in a time-scale of days. The submesoscale eddy was confirmed by observational data from the area and we can say that for the first time we have a proof that the model reproduces a realistic submesoscale vortex, similar in shape and location to the observed one.     

Observation-based evaluation of surface wave effects on currents and trajectory forecasts

Knowledge of upper ocean currents is needed for trajectory forecasts and is essential for search and rescue operations and oil spill mitigation. This paper addresses effects of surface waves on ocean currents and drifter trajectories using in situ observations. The data set includes colocated measurements of directional wave spectra from a wave rider buoy, ocean currents measured by acoustic Doppler current profilers (ADCPs), as well as data from two types of tracking buoys that sample the currents at two different depths. The ADCP measures the Eulerian current at one point, as modelled by an ocean general circulation model, while the tracking buoys are advected by the Lagrangian current that includes the wave-induced Stokes drift. Based on our observations, we assess the importance of two different wave effects: (a) forcing of the ocean current by wave-induced surface fluxes and the Coriolis–Stokes force, and (b) advection of surface drifters by wave motion, that is the Stokes drift. Recent theoretical developments provide a framework for including these wave effects in ocean model systems. The order of magnitude of the Stokes drift is the same as the Eulerian current judging from the available data. The wave-induced momentum and turbulent kinetic energy fluxes are estimated and shown to be significant. Similarly, the wave-induced Coriolis–Stokes force is significant over time scales related to the inertial period. Surface drifter trajectories were analysed and could be reproduced using the observations of currents, waves and wind. Waves were found to have a significant contribution to the trajectories, and we conclude that adding wave effects in ocean model systems is likely to increase predictability of surface drifter trajectories. The relative importance of the Stokes drift was twice as large as the direct wind drag for the used surface drifter.     

Observation-based evaluation of surface wave effects on currents and trajectory forecasts

Knowledge of upper ocean currents is needed for trajectory forecasts and is essential for search and rescue operations and oil spill mitigation. This paper addresses effects of surface waves on ocean currents and drifter trajectories using in situ observations. The data set includes colocated measurements of directional wave spectra from a wave rider buoy, ocean currents measured by acoustic Doppler current profilers (ADCPs), as well as data from two types of tracking buoys that sample the currents at two different depths. The ADCP measures the Eulerian current at one point, as modelled by an ocean general circulation model, while the tracking buoys are advected by the Lagrangian current that includes the wave-induced Stokes drift. Based on our observations, we assess the importance of two different wave effects: (a) forcing of the ocean current by wave-induced surface fluxes and the Coriolis–Stokes force, and (b) advection of surface drifters by wave motion, that is the Stokes drift. Recent theoretical developments provide a framework for including these wave effects in ocean model systems. The order of magnitude of the Stokes drift is the same as the Eulerian current judging from the available data. The wave-induced momentum and turbulent kinetic energy fluxes are estimated and shown to be significant. Similarly, the wave-induced Coriolis–Stokes force is significant over time scales related to the inertial period. Surface drifter trajectories were analysed and could be reproduced using the observations of currents, waves and wind. Waves were found to have a significant contribution to the trajectories, and we conclude that adding wave effects in ocean model systems is likely to increase predictability of surface drifter trajectories. The relative importance of the Stokes drift was twice as large as the direct wind drag for the used surface drifter.

     

Exploring an ‘ideal hill': how lithology and transport mechanisms affect the possibility of a steady state during weathering and erosion

We present a model of chemical reaction within hills to explore how evolving porosity (and by inference, permeability) affects flow pathways and weathering. The model consists of hydrologic and reactive-transport equations that describe alteration of ferrous minerals and feldspar. These reactions were chosen because previous work emphasized that oxygen- and acid-driven weathering affects porosity differently in felsic and mafic rocks. A parameter controlling the order of the fronts is presented. In the absence of erosion, the two reaction fronts move at different velocities and the relative depths depend on geochemical conditions and starting composition. In turn, the fronts and associated changes in porosity drastically affect both the vertical and lateral velocities of water flow. For these cases, estimates of weathering advance rates based on simple models that posit unidirectional constant-velocity advection do not apply. In the model hills, weathering advance rates diminish with time as the Darcy velocities decrease with depth. The system can thus attain a dynamical steady state at any erosion rate where the regolith thickness is constant in time and velocities of both fronts become equal to one another and to the erosion rate. The slower the advection velocities in a system, the faster it attains a steady state. For example, a massive rock with relatively fast-dissolving minerals such as diabase – where solute transport across the reaction front mainly occurs by diffusion – can reach a steady state more quickly than granitoid rocks in which advection contributes to solute transport. The attainment of a steady state is controlled by coupling between weathering and hydrologic processes that force water to flow horizontally above reaction fronts where permeability changes rapidly with depth and acts as a partial barrier to fluid flow. Published 2020. This article is a U.S. Government work and is in the public domain in the USA.     

Wind-induced subduction at the South Atlantic subtropical front

The South Atlantic Subtropical Front, associated with the eastward-flowing South Atlantic Current, separates the colder, nutrient-rich waters of the subpolar gyre from the warmer, nutrient-poor waters of the subtropical gyre. Perturbations to the quasi-geostrophic, eastward flow generate meanders and filaments which induce cross-frontal exchange of water properties. Down-front winds transport denser waters from the South over warm waters from the North, inducing convective instability and subduction. Such processes occur over spatial scales of the order of 1 km and thus require high horizontal spatial resolution. In this modeling study, a high-resolution (4 km) regional grid is embedded in a basin-wide configuration (12 km) of the South Atlantic Ocean in order to test the importance of submesoscale processes in water mass subduction along the subtropical front. Stronger and more numerous eddies obtained in the high-resolution run yield more intense zonal jets along the frontal zone. Such stronger jets are more susceptible to instabilities, frontogenesis, and the generation of submesoscale meanders and filaments with \(\mathcal {O}(1)\) Rossby number. As a consequence, vertical velocities larger than 100 md ¹ are obtained in the high-resolution run, one order of magnitude larger than in the low-resolution run. Wind-driven subduction occurs along the frontal region, associated with negative Ertel potential vorticity in the surface layer. Such processes are not observed in the low-resolution run. A passive tracer experiment shows that waters with density characteristics similar to subtropical mode waters are preferentially subducted along the frontal region. The wind-driven buoyancy flux is shown to be much larger than thermal or haline fluxes during the wintertime, which highlights the importance of the frictional component in extracting PV from the surface ocean and inducing subduction, a process that has been overlooked in subtropical mode water formation in the region.     

Estimating ventilation time scales using overturning stream functions

A simple method for estimating ventilation time scales from overturning stream functions is proposed. The stream function may be computed using either geometric coordinates or a generalized vertical coordinate, such as potential density (salinity in our study). The method is tested with a three-dimensional circulation model describing an idealized semi-enclosed ocean basin ventilated through a narrow strait over a sill, and the result is compared to age estimates obtained from a passive numerical age tracer. The best result is obtained when using the stream function in salinity coordinates. In this case, the reservoir-averaged advection time obtained from the overturning stream function in salinity coordinates agrees rather well with the mean age of the age tracer, and the corresponding maximum ages agree very well.     

Floating marine debris surface drift: Convergence and accumulation toward the South Pacific subtropical gyre

Whatever its origin is, a floating particle at the sea surface is advected by ocean currents. Surface currents could be derived from in situ observations or combined with satellite data. For a better resolution in time and space, we use satellite-derived sea-surface height and wind stress fields with a 1/3° grid from 1993 to 2001 to determine the surface circulation of the South Pacific Ocean. Surface currents are then used to compute the Lagrangian trajectories of floating debris. Results show an accumulation of the debris in the eastern-centre region of the South Pacific subtropical gyre ([120°W; 80°W]–[20°S; 40°S]), resulting from a three-step process: in the first two years, mostly forced by Ekman drift, the debris drift towards the tropical convergence zone (30°S). Then they are advected eastward mostly forced by geostrophic currents. They finally reach the eastern-centre region of the South Pacific subtropical gyre from where they could not escape.     

Eddy diffusivity derived from drifter data for dispersion model applications

Ocean transport and dispersion processes are at the present time simulated using Lagrangian stochastic models coupled with Eulerian circulation models that are supplying analyses and forecasts of the ocean currents at unprecedented time and space resolution. Using the Lagrangian approach, each particle displacement is described by an average motion and a fluctuating part. The first one represents the advection associated with the Eulerian current field of the circulation models while the second one describes the sub-grid scale diffusion. The focus of this study is to quantify the sub-grid scale diffusion of the Lagrangian models written in terms of a horizontal eddy diffusivity. Using a large database of drifters released in different regions of the Mediterranean Sea, the Lagrangian sub-grid scale diffusion has been computed, by considering different regimes when averaging statistical quantities. In addition, the real drifters have been simulated using a trajectory model forced by OGCM currents, focusing on how the Lagrangian properties are reproduced by the simulated trajectories.     

Dispersion of passive tracers in model flows: effects of the parametrization of small-scale processes

A set of numerical experiments is presented, in which we study the dynamics of passive particles advected by given two-dimensional velocity fields and perturbed by a non-white noise with a characteristic time . Data and model results have shown that this kind of random perturbation is able to represent subgridscale processes for upper ocean mesoscale turbulence for regions of the world ocean where turbulence can be assumed to be homogeneous. Extensive computations in different fields characterized by cell-like structure, both stationary and time-dependent, representing very idealized geophysical flow situations, show that the presence of a finite correlation time scale does lead to enhanced or arrested dispersion, depending on the considered flow; however, it does not seem to affect the gross qualitative behaviour of the dispersion processes, which is primarily affected by the large-scale velocity field.     

Performance of GOCE and GRACE-derived mean dynamic topographies in resolving Antarctic Circumpolar Current fronts

Presently, two satellite missions, Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE), are making detailed measurements of the Earth’s gravity field, from which the geoid can be obtained. The mean dynamic topography (MDT) is the difference between the time-averaged sea surface height and the geoid. The GOCE mission is aimed at determining the geoid with superior accuracy and spatial resolution, so that a more accurate MDT can be estimated. In this study, we determine the mean positions of the Antarctic Circumpolar Current fronts using the purely geodetic estimates of the MDT constructed from an altimetric mean sea surface and GOCE and GRACE geoids. Overall, the frontal positions obtained from the GOCE and GRACE MDTs are close to each other. This means that these independent estimates are robust and can potentially be used to validate frontal positions obtained from sparse and irregular in situ measurements. The geodetic frontal positions are compared to earlier estimates as well as to those derived from MDTs based on satellite and in situ measurements and those obtained from an ocean data synthesis product. The position of the Sub-Antarctic Front identified in the GOCE MDT is found to be in better agreement with the previous estimates than that identified in the GRACE MDT. The geostrophic velocities derived from the GOCE MDT are also closer to observations than those derived from the GRACE MDT. Our results thus show that the GOCE mission represents an improvement upon GRACE in terms of the time-averaged geoid.     

Scalar advection schemes for ocean modelling on unstructured triangular grids

Several schemes for scalar advection on unstructured triangular grids are assessed for possible use in ocean modelling applications. Finite element, finite volume and finite volume–element approaches are evaluated. A series of tests, including a numerical order of convergence analysis, idealized rotating cone and cylinder experiments, and transport of a tracer through the Stommel Gyre representation of ocean basin-scale circulation, are carried out. Volume element Eulerian–Lagrangian and third-order Runge-Kutta discontinuous Galerkin schemes are recommended for use in tracer studies. Taylor–Galerkin and second-order Runge–Kutta discontinuous Galerkin are found to be robust and accurate second-order schemes. When positivity is required, a fluctuation redistribution scheme was found to be an easily implemented, accurate, and computationally efficient approach. Responsible editor: Phil Dyke     

Seasonality of the submesoscale dynamics in the Gulf Stream region

Frontogenesis and frontal instabilities in the mixed layer are known to be important processes in the formation of submesoscale features. We study the seasonality of such processes in the Gulf Stream (GS) region. To approach this problem, a realistic simulation with the Hybrid Coordinate Ocean Model is integrated for 18 months at two horizontal resolutions: a high-resolution (1/48°) simulation able to resolve part of the submesoscale regime and the full range of mesoscale dynamics, and a coarser resolution (1/12°) case, in which submesoscales are not resolved. Results provide an insight into submesoscale dynamics in the complex GS region. A clear seasonal cycle is observed, with submesoscale features mostly present during winter. The submesoscale field is quantitatively characterized in terms of deviation from geostrophy and 2D dynamics. The limiting and controlling factor in the occurrence of submesoscales appears to be the depth of the mixed layer, which controls the reservoir of available potential energy available at the mesoscale fronts that are present most of the year. Atmospheric forcings are the main energy source behind submesoscale formation, but mostly indirectly through mixed layer deepening. The mixed layer instability scaling suggested in the (Fox-Kemper et al., J Phys Oceanogr 38:1145–1165, 2008) parametrization appears to hold, indicating that the parametrization is appropriate even in this complex and mesoscale dominated area.     

Properties of winter mixed layer variability on the shelf-slope region facing the Kuroshio—study of Tosa Bay, southern Japan

To examine the properties of winter mixed layer (ML) variability in the shelf-slope waters facing the Kuroshio, we analyzed historical temperature records and the simulated results of a triply nested high-resolution numerical model. As a candidate of the shelf-slope waters, we focused on Tosa Bay, off the southern Japan. A time series of observed monthly mean ML temperatures and depths in the bay exhibits a remarkable seasonal variation. The period when the ML develops can be divided into two regimes: from September to November, when the sea surface cooling is gradually enhanced, the ML temperature and depth decreases and increases, respectively; from January to March, the ML temperature and depth are kept nearly constant, while the sea surface cooling in January reaches its annual maximum. In the latter regime, variance for the monthly mean ML depth is the largest of the year. To further study the ML properties in the latter regime corresponding to winter, we examined simulated results. It was found that the largest variance for ML depth is attributed to a dominant intramonthly variation. This is related to a submesoscale variation with typical spatial scales of 10–20 km, induced by the Kuroshio and its frontal disturbances. Simulated monthly mean heat balance within the ML showed that heat advection balances with heat flux at the sea surface and entrainment through the ML bottom. Moreover, the monthly mean heat advection is determined mainly by the intramonthly eddy heat advection, suggesting that the high-frequency intramonthly variation related to submesoscale variations contributes significantly to the low-frequency monthly variations of the ML in winter.     

Combining T/P altimetric data with hydrographic data to estimate the mean dynamic topography of the North Atlantic and improve the geoid

The mean dynamic topography of the surface of the North Atlantic is estimated using an inverse model of the ocean circulation constrained by hydro-graphic and altimetric observations. In the North Atlantic, altimetric observations have no significant impact on the topography estimate because of the limited precision of available geoid height models. They have a significant impact, however, when uncertainties in the density field are increased to simulate interpolation errors in regions where hydrographic data are scarce. This result, which moderates the conclusion drawn by Ganachaud and co-workers of no significant contribution of altimetric observations to the determination of the large-scale steady circulation, reflects the simple idea that altimetric data are most useful near the surface of the ocean and in areas where the hydrography is poorly determined. One application of the present inverse estimate of the mean dynamic topography is to compute a geoid height correction over the North Atlantic which reduces the uncertainty in the geoid height expanded to spherical harmonic 40 down to a level of about 5 cm.