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The relationship between the salinity mixing, the diffusive salt transport, and the diahaline exchange flow is examined using salinity coordinates. The diahaline inflow and outflow volume transports are defined in this study as the integral of positive and negative values of the diahaline velocity. A numerical model of the Pearl River Estuary (PRE) shows that this diahaline exchange flow is analogous to the classical concept of estuarine exchange flow with inflow in the bottom layers and outflow at the surface. The inflow and outflow magnitudes increase with salinity, while the net transport equals the freshwater discharge Qr after sufficiently long temporal averaging. In summer, intensified salinity mixing mainly occurs in the surface layers and around the islands. The patchy distribution of intensified diahaline velocity suggests that the water exchange through an isohaline surface can be highly variable in space. In winter, the zones of intensification of salinity mixing occur mainly in deep channels. Apart from the impact of freshwater transport from rivers, the transient mixing is also controlled by an unsteadiness term due to estuarine storage of salt and water volume. In the PRE, the salinity mixing and exchange flow show substantial spring–neap variation, while the universal law of estuarine mixing m = 2SQr (with m being the sum of physical and numerical mixing per salinity class S) holds over longer averaging period (spring–neap cycle). The correlation between the patterns of surface mixing, the vorticity, and the salinity gradients indicates a substantial influence of islands on estuarine mixing in the PRE.

Ocean models relying on geopotential (Z) vertical coordinates suffer from spurious diapycnal mixing created by advection due to the misalignment of isopycnal and grid-layer surfaces. Given the delicateness of diapycnal mixing in ocean models, several studies have been performed to determine its impact, mainly by means of global analyses. Here we present a local analysis of spurious diapycnal mixing based on tracer variance decay. We apply the discrete variance decay (DVD) method proposed by Klingbeil et al. (2014) to diagnose numerical mixing created by several third-order advection schemes used in FESOM (Finite volumE Sea ice Ocean Model). The analysis is applied for an idealized channel flow test setup with Z* vertical coordinates and a linear equation of state. This ensures numerical DVD to be entirely diapycnal enabling identification of its spatial distribution. Further modification of the DVD method is proposed which allows for splitting of total diapycnal mixing into individual contributions from advection and diffusion. The new modifications are then used to compare spurious diapycnal mixing due to advection and explicit horizontal diffusion with parameterized physical diapycnal mixing due to vertical diffusion.

I will present an analytical relation that directly shows how mixing locally drives the overturning circulation. The theory is based on the application of the well-known Water Mass Transformation framework to each local water column. The budgets for volume and tracer content mapped to tracer space are supplemented by a budget for the squared tracer. Mixing is defined by the destruction term of squared tracer, which is equivalent to the decay of tracer variance. I will present maps of the simulated diahaline mixing and the associated diahaline exchange velocity in the Baltic Sea. In addition, our numerical model offers to separately diagnose the mixing due to turbulence parameterizations and the spurious mixing due to discrete transport schemes. This enables us to also quantify the amount of spuriously induced overturning circulation. The planned application to diapycnal exchange and the global overturing circulation will be outlined.

Benthic oxygen dynamics and the exchange of oxygen and other solutes across the sedimentwater interface play a key role for the oxygen budget of many limnic and shallow marine systems. The sediment-water fluxes are largely determined by two factors: sediment biogeochemistry and the thickness of the diffusive boundary layer that is determined by near-bottom turbulence. Here, we present a fully coupled benthic-pelagic modeling system that takes these processes and their interaction into account, focusing especially on the modulation of the sediment-water fluxes by the effects of near-bottom turbulence and stratification. We discuss the special numerical methods required to guarantee positivity and mass conservation across the sediment-water interface in the presence of rapid element transformation, and apply this modeling system to a number of idealized scenarios. Our process-oriented simulations show that near-bottom turbulence provides a crucial control on the sediment-water fluxes, the oxygen penetration depth, and the re-oxidation of reduced compounds diffusing upward from the deeper benthic layers especially on time scales of a few days, characterizing oceanic tides,internal seiching motions in lakes, and mesoscale atmospheric variability. Our results also show that the response of benthic-pelagic fluxes to rapid changes in the forcing conditions (e.g., storm events) can only be understood with a fully coupled modeling approach., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

In this study we present new insights into the overturning circulation in non-tidal, fjord-type estuarine systems driven by diahaline mixing. As a realistic example we analyze two years of numerical model results for the Baltic Sea, a brackish semi-enclosed marginal sea, characterized by strong freshwater surplus. An isohaline water mass transformation framework is applied to quantify and decompose the diahaline exchange flow. Time-averaged effective vertical diahaline velocity is directly calculated from the divergence of the transports below the respective isohaline surface. It is furthermore indirectly estimated from the gradient of local mixing per salinity class with respect to salinity. Under the assumption of negligible horizontal salt transports both estimates should be identical. Our analysis shows a high correlation between the spatial patterns of the two estimates for the diahaline exchange flow. Two dominant types of diahaline exchange flow are analyzed. First of all there is a large scale overturning circulation with inflow at places where the isohaline surface is close to the bottom and with outflow at places where the isohaline is surfacing. Secondly, there is the well-known small-scale overturning circulation localized inside the bottom boundary layer over sloping bathymetry, driven by boundary mixing. Both types of circulation are visualized across selected vertical transects in physical and in salinity space. One major result is that about 50% of the diahaline exchange flow patterns are generated by numerical mixing caused by the truncation error of the advection scheme, despite the fact that an anti-diffusive advection scheme and vertically-adaptive coordinates are used.

Recent studies could link the quantities of estuarine exchange flows to the volume-integrated mixing inside an estuary, where mixing is defined as the destruction of salinity variance. The existing mixing relations quantify mixing inside an estuary by the net boundary fluxes of volume, salinity, and salinity variance, which are quantified as Knudsen or total exchange flow bulk values. So far, river runoff is the only freshwater flux included, and the freshwater exchange due to precipitation and evaporation is neglected. Yet, the latter is the driving force of inverse estuaries, which could not be described by the existing relations. To close this gap, this study considers evaporation and precipitation to complete the existing mixing relations by including cross-surface salinity variance transport. This allows decomposing the mixing into a riverine and a surface transport contribution. The improved relations are tested against idealized two-dimensional numerical simulations of different combinations of freshwater forcing. The mixing diagnosed from the model results agrees exactly with the derived mixing relation. An annual hindcast simulation of the Persian Gulf is then used to test the mixing relations, both exact and approximated, e.g., long-term averaged, for a realistic inverse estuary. The results show that the annual mean mixing contributions of river discharge and evaporation are almost equal, although the freshwater transport due to evaporation is about one order of magnitude larger than the river runoff.

The coastal area is one of the most vulnerable areas that is connecting lands and seas under the intensive human activities subjecting to the ocean forces. Nowadays, as the climate conditions are highly concerned, coastal morphodynamics, one of the most important elements for coastal areas, would become more uncertainty under the climate changes due to its non-linear interaction to the water forces. Therefore, an investigation of tide-wave-morphodynamic interactions is required by including sea level rise in order to involve various responses of morphodynamics to changing climate. In the conference, we will present results from our process-based coupled framework of tide-wave-morphodynamics modelling to consider the climate impacts on the morphodynamic changes in application on Wadden Sea of German Bight, which is one of the most vulnerable coastal areas subjects to sea level rise. The well-evaluated third-generation phase-resolved wave model WAVEWATCH III (WW3) is set up, coupled to the well-validated General Estuary Circulation Model (GETM) including the sediment transport and morphology modules. We applied ensemble-based simulations to reduce the uncertainties of climate effects in downscaling procedure. It is proved that this process-based model is capable for application on climate scenarios in a long term aspect as long as involving specific data analysis. It is desired that the process-based numerical investigation could be one of the most promising methods for studying the coastal morphodynamic responses to climate change as the physical processes could be examined straightforward for this non-linear interactions.Based on the preliminary results from the framework, it is indicated that the wave could propagate further more under sea level rise while the currents are observed to be increased at some locations, particularly at the region (i.e. ebb flats) of North Frisian Wadden Sea (NFW). As a result, the NFW becomes more dynamic under the sea level rise conditions especially at the intertidal areas, whereas the Elbe mouth might has less exchange of sediment far field to east and north Frisian Sea but might be highly dynamic in local, which is much similar to the pattern of observed datasets. The damthat connecting Sylt and main land, interested by lots of previous studies, also shows impact on both hydrodynamic and morphodynamic pattern under climate conditions. Based on the sea level rise scenarios, the significance of bed level changes at most areas of German Bight would be more seriousby keeping the identical pattern of morphological changes as that in present scenarios. However, it might also correlate to storminess, where we could looking in detail based on the process-based modelling. When considering the entire German Bight, it is found that the predominant forces from tide and wave might vary between the North Frisian Sea and East Frisian Sea due to the specific geometry. Tide-predominated and wave-dominated coastal system would be able to coexist in the German Bight. The detailed quantitative and qualitative results would be present in the conference.

The relationship between the diahaline mixing, the diffusive salt transport, and the diahaline exchange flow is examined using salinity coordinates. The diahaline inflow and outflow volume transports are defined in this study as the integral of positive and negative values of the diahaline velocity. A numerical model of the Pearl River Estuary (PRE) shows that this diahaline exchange flow is analogous to the classical concept of estuarine exchange flow with inflow in the bottom layers and outflow at the surface. The inflow and outflow magnitudes increase with salinity, while the net transport equals the freshwater discharge Qr after sufficiently long temporal averaging. In summer, intensified diahaline mixing mainly occurs in the surface layers and around the islands. The patchy distribution of intensified diahaline velocity suggests that the water exchange through an isohaline surface can be highly variable in space. In winter, the zones of intensification of diahaline mixing occur mainly in deep channels. Apart from the impact of freshwater transport from rivers, the transient isohaline mixing is also controlled by an unsteadiness term due to estuarine storage of salt and water volume. In the PRE, the diahaline mixing and exchange flow show substantial spring-neap variation, while the universal law of estuarine mixing m=2SQr (with m being the sum of physical and numerical mixing per salinity class S) holds over longer averaging period (spring-neap cycle). The correlation between the patterns of surface mixing, the vorticity, and the salinity gradients indicates a substantial influence of islands on estuarine mixing in the PRE.

In this talk we present new insights into the overturning circulation of the Baltic Sea. Based on a state-of-the-art 3D numerical model for the entire Baltic Sea, we analyse the estuarine circulation and water mass transformation in salinity space. State and diagnostic variables are binned to salinity classes and conservatively averaged already during model runtime such that exact budgets for local isohaline volumes can be evaluated. Derived maps in salinity space for entrainment velocities, diahaline diffusive fluxes as well as physical and spurious numerical mixing contributions will be shown. The latter is based on a unique separation and quantification of mixing due to turbulence parameterisations and discretisation errors from the applied numerical advection schemes. Finally it is demonstrated that integration of the different new local diagnostics confirms existing bulk theories (e.g. Knudsen theorem, universal law of estuarine mixing).

Melting of the Greenland ice sheet has a big influence on the climate system. Therefore, it is important to understand how the ice melts. Since direct measurements at the underside of floating ice tongues are sparse, high-resolution models for the interaction of ocean and glacial ice are needed to determine sub-glacial melt rates and to understand melt processes. A common problem is that model resolution is often too low, so that the meltwater plume is only represented by one or two layers, and thus the entrainment of warmer water into the plume is not well captured. However, this heat transport towards the ice is crucial for the sub-glacial melt rate.In this talk, we show how we solve this problem with the General Estuarine Transport Model (GETM). GETM features adaptive vertical coordinates that zoom automatically to areas of interest, in particular strong density gradients. A high density contrast exists in the entrainment layer between the relatively fresh and cold meltwater of the plume, and the ambient ocean water. By zooming towards this interface, our adaptive vertical coordinates resolve the meltwater plume with several layers, while keeping the total number of model layers at a modest level to ensure a feasible computation time. In addition, the coordinate levels align to the moving isopycnals – they “follow” the plume –, which strongly reduces numerical mixing and pressure gradient errors.We present this for the fjord of the 79°N-Glacier (79NG), which has the largest floating ice tongue in Greenland. In our idealized 2D-setup, we obtain layers as thin as 0.2 m to 1 m in the meltwater plume, for only 100 levels over a water column of several 100 m depth. Thanks to this high resolution of plume and entrainment layer, our model reproduces the overturning circulation in the glacier cavity correctly; in particular, it shows that the salinity stratification of the adjacent ocean determines the level at which the meltwater plume detaches from the ice tongue. Almost all sub-glacial melting occurs before this detachment, i.e., where the plume is directly at the ice–ocean interface. Furthermore, we can confirm that the highest melt rates exist near the grounding line of the glacier. Finally, our simulated melt rates are consistent with observations at 79NG.Our model, developed in the GROCE (Greenland ice sheet–ocean interaction) project, will form the basis of a realistic 3D-model of the 79NG-fjord in the future.

In this study, results from a realistic 3D hydrodynamic and sediment transport model, applied to a channel in the Dutch Wadden Sea, are analyzed in order to assess the effect of short-term wind forcing, the impact of fresh water effects, and the variability induced by the spring-neap cycle on the transport of suspended sediment. In the investigated region, a pilot study for sediment nourishment, the so-called Mud Motor, is executed. This project aims for the beneficial re-use of dredged harbor sediments through the disposal of these sediments at a location where natural currents are expected to transport them toward a nearby salt marsh area. The model results presented in this study advance the understanding of the driving forces that determine sediment transport in shallow, near-coastal zones, and can help to improve the design of the Mud Motor. In the investigated channel, which is oriented parallel to the coastline, tidal asymmetries generally drive a transport of sediment in flood direction. It was found that already moderate winds along the channel axis reverse (wind in ebb direction), or greatly enhance this transport, up to an export of sediment over the adjacent water shed (wind in flood direction). The most beneficial wind conditions (moderate westerly winds) can cause an accumulation of more than 90% of the initial 200 tons sediment pool on the intertidal area; during less favorable conditions (northeasterly winds), less than a third of the dumped sediment is transported onto the mudflat. On-shore winds induce a transport toward the coast. Surprisingly, sediment pathways are only sensitive to the exact disposal location in the channel during wind conditions that counteract the tidally driven transport, and freshwater effects play no significant role for the dispersal of sediment.

Seismology is the main tool for inferring the deep interior structures of Earth and potentially also of other planetary bodies in the solar system. Terrestrial seismology is influenced by the presence of the ocean-generated microseismic signal, which sets a lower limit on the earthquake detection capabilities but also provides a strong energy source to infer the interior structure on scales from local to continental. Titan is the only other place in the solar system with permanent surface liquids and future lander missions there might carry a seismic package. Therefore, the presence of microseisms would be of great benefit for interior studies, but also for detecting storm-generated waves on the lakes remotely. We estimated the strength of microseismic signals on Titan, based on wind speeds predicted from modeled global circulation models interior structure. We find that storms of more than 2 m/s wind speed, would create a signal that is globally observable with a high-quality broadband sensor and observable to a thousand kilometer distance with a space-ready seismometer, such as the InSight instruments currently operating on the surface of Mars., 24 pages, 6 figures

The well-known Knudsen relations and the total exchange flow (TEF) analysis framework provide quantifications of exchange flow across an open boundary to the adjacent ocean in terms of bulk values (Knudsen theory: inflow and outflow volume or salinity) or with resolution in salinity space (TEF: profiles of volume and salt flux in salinity coordinates). In the present study, these theories are extended toward mixing of salinity, defined as the decay of salinity variance due to turbulent mixing. In addition to the advective fluxes, diffusive fluxes across the boundary are also considered now. These new Knudsen and TEF relations for mixing are derived by applying Gauss’s theorem to the salinity square and salinity variance equations. As a result of the analysis, four different Knudsen relations for the mixing in estuaries are derived. The first one is exact and considers nonperiodicity as well as nonconstancy of the inflow and outflow salinities. The other three formulations are approximate only, in the sense that either nonperiodicity or nonconstancy or both are relaxed. The simplest of those formulations has recently been derived by MacCready et al. and estimates the estuarine mixing as the product of inflow salinity, outflow salinity, and time-averaged river runoff. These four mixing estimates are systematically assessed by means of a number of idealized estuarine test cases. For periodic tidal flow, the simplest estimate still predicts the effective (physical plus numerical) mixing within an error of about 10%.

The floating ice tongue of the 79° North Glacier (Nioghalvfjerdsfjorden Glacier) in Northeast Greenland has been found to thin over the past two decades. Recent studies suggest the warming of the ocean as one of the main drivers of destabilizing outlet glaciers of the Greenland ice sheet by enhanced subglacial melting. Using a horizontal two-dimensional numerical plume model, we study the hydrodynamic processes determining basal melt rates beneath the glacial tongue of the 79° North Glacier. We specifically investigate the spatial distribution of submarine melting and assess the importance of ice base morphology in controlling basal melting. For our study, we design a suite of simulations by implementing a synthetic network of basal channels. Additionally, we determine the role of subglacial discharge in driving melting along the glacier base. Our model results lead us to the conclusion that channelised basal topographies at the glacier base are the dominant control on the basal melt rates and its spatial distribution.

The present study aims to estimate effective diahaline turbulent salinity fluxes and diffusivities in numerical model simulations of estuarine scenarios. The underlying method is based on a quantification of salinity mixing per salinity class, which is shown to be twice the turbulent salinity transport across the respective isohaline. Using this relation, the recently derived universal law of estuarine mixing, predicting that average mixing per salinity class is twice the respective salinity times the river run‐off, can be directly derived. The turbulent salinity transport is accurately decomposed into physical (due to the turbulence closure) and numerical (due to truncation errors of the salinity advection scheme) contributions. The effective diahaline diffusivity representative for a salinity class and an estuarine region results as the ratio of the diahaline turbulent salinity transport and the respective (negative) salinity gradient, both integrated over the isohaline area in that region and averaged over a specified period. With this approach, the physical (or numerical) diffusivities are calculated as half of the product of physical (or numerical) mixing and the isohaline volume, divided by the square of the isohaline area. The method for accurately calculating physical and numerical diahaline diffusivities is tested and demonstrated for a three‐dimensional idealized exponential estuary. As a major product of this study, maps of the spatial distribution of the effective diahaline diffusivities are shown for the model estuary., Plain Language Summary: Eddy diffusivity determines how intensively concentrations in a fluid are spreading due to turbulent motion. Here, we analyze the diffusivity that spreads salt concentration (i.e., salinity) across a surface of constant salinity (the isohalines), also called effective diahaline diffusivity. A new method is presented that calculates effective diahaline diffusivities based on the specific volume between two specified isohalines, on the salinity mixing within this volume as well as on the surface area of the isohalines. We define mixing as the rate of destruction of salinity variance per unit volume due to turbulent mixing processes. The method applies to computer models of ocean dynamics on scales ranging from coastal to global. In such models, the mixing is determined by statistical mathematical equations of turbulent processes, which is the so‐called physical mixing. In models, additional (numerical) mixing occurs due to numerical inaccuracies of algorithms that move around water masses passively with the currents, a process called advection. Using our method, the total effective diffusivity determined for each isohaline surface can be accurately separated into contributions from physical mixing and numerical mixing. We demonstrate the functioning of the new method for an idealized model simulation of an estuary., Key Points: Mixing and volume per salinity class determine effective diahaline diffusivity. Effective diahaline diffusivity is split into physical and numerical contributions. In an idealized estuary, largest effective diffusivities are found in the brackish waters of the navigational channel.

Coupled atmosphere-ocean models are developed for process understanding at the air-sea interface. Over the last 20 years, there have been studies involving simulations in the range of sub-annual simulations to climate scenarios. The development of coupled models highly depends on the kind and quality of the required data exchange between the model interfaces. This work achieved the development of a two-way coupled atmosphere-ocean model ICONGETM with flexible data exchange via exchange grids provided by the widely used ESMF regridding package. The regridding of flux data between the unstructured atmosphere model ICON and the structured regional ocean model GETM is conducted via these exchange grids. The newly developed model ICONGETM has been demonstrated for a coastal upwelling scenario in the Central Baltic Sea.

The hydrodynamics in estuaries is mainly governed by the competition between a horizontal density gradient, friction, and wind stress. The sensitivity of the estuarine exchange flow to the wind stress increases in the absence of tides, which is investigated here using the example of the weakly tidal Warnow river estuary in the southwestern Baltic Sea—the mouth of which is characterized by strongly varying salinities of 8 to 20 g kg−1. The interaction between a volatile salinity gradient and along-estuary wind forcing is found to cause temporary inversions of the estuarine circulation. Despite the highly dynamic conditions, the applicability of recent theories for isohaline mixing, using the framework of Total Exchange Flow, and the strength of the exchange flow, using a non-dimensional parameter space, could be confirmed. By analyzing salinity fluxes at the mouth of the estuary, a mixing completeness of 84% was calculated for the estuary. Furthermore, inversion of estuarine circulation was typically found for a local Wedderburn number (ratio of non-dimensional wind stress to non-dimensional horizontal density gradient) exceeding 0.33, indicating a high sensitivity to along-estuary wind.

Processes of stratification and destratification in the German Bight region of fresh water influence (ROFI) are investigated following an extreme river discharge event in June 2013. For this purpose, a high‐resolution baroclinic ocean model is set up and validated against field data. The model results are used to study the temporal and spatial variability of stratification and the duration of persistent stratification in 2013. The relevant processes affecting stratification are investigated by analyzing the potential energy anomaly budget, with a focus on mixing and tidal straining. It is shown that the stratification in the German Bight is highly affected by the spring‐neap tidal cycle, with generally less stratification at spring tides due to dominant tidal mixing. It is also shown that the location of the river plume can modify this pattern. During spring tides, if the river plume is confined to the eastern region, stratification decreases significantly, as expected, due to the dominance of mixing over tidal straining. On the other hand, if the river plume moves toward deeper regions at spring tides, strong tidal straining becomes present. In this condition, mixing is weak, and the dominant tidal straining results in persistent stratification., Key Points: Processes impacting the German Bight stratification are investigated using a high‐resolution baroclinic model. The position of the river plume highly affects the contribution of tidal straining and mixing to changes in stratification. Strong tidal straining can result in persistent stratification even during spring tides., Bundesministerium für Bildung und Forschung (BMBF) http://dx.doi.org/10.13039/501100002347, German Research Foundation http://dx.doi.org/10.13039/501100001659, German Environment Agency http://dx.doi.org/10.13039/501100010809

Microplastics (MP) are omnipresent in the aquatic environment where they pose a risk to ecosystem health and functioning. Little is, however, known about the concentration and transport patterns of this particulate contaminant. Measurement campaigns remain expensive and assessments of regional MP distributions need to rely on a limited number of samples. The prediction of potential MP sink regions in the sea would thus be beneficial for a better estimation of MP concentration levels and a better sampling design. Based on a sediment transport model, this study investigates the transport of different MP model particles, PET and PVC particles with sizes of 10 and 330 μm, under storm conditions. A storm event was chosen because extreme wave heights cause intense sediment erosion down to depths unaffected otherwise, and are therefore critical for determining accumulation regions. The calculation of metocean parameters for such extreme weather events is subject to uncertainties. This sensitivity study targets the propagation of uncertainty from the atmospheric conditions to MP erosion and deposition, on the basis of freely available models and data. We find that atmospheric conditions have a strong impact on the quantity of eroded and deposited material. Thus, even if the settling and resuspension properties of MP were known, a quantitative transport estimation by ocean models would still show considerable uncertainty due to the imperfect knowledge of atmospheric conditions. The uncertainty in the transport depends on the particle size and density, transport of the larger and denser plastic particles only takes place under storm conditions. Less uncertainty exists in the location of erosional and depositional areas, which seems to be mainly influenced by the bathymetry. We conclude, while quantitative model predictions of sedimentary MP concentrations in marine sediments are hampered by the uncertainty in the wind fields during storms, models can be a valuable tool to select sampling locations for sedimentary MP concentrations to support their empirical quantification.

The Total Exchange Flow analysis framework computes consistent bulk values quantifying the estuarine exchange flow using salinity coordinates since salinity is the main contributor to density in estuaries and the salinity budget is entirely controlled by the exchange flow. For deeper and larger estuaries temperature may contribute equally or even more to the density. That is why we included potential temperature as a second coordinate to the Total Exchange Flow analysis framework, which allows gaining insights in the potential temperature-salinity structure of the exchange flow as well as to compute consistent bulk potential temperature and therefore heat exchange values with the ocean. We applied this theory to the exchange flow of the Persian Gulf, a shallow, semienclosed marginal sea, where dominant evaporation leads to the formation of hypersaline and dense Gulf water. This drives an inverse estuarine circulation which is analyzed with special interest on the seasonal cycle of the exchange flow. The exchange flow of the Persian Gulf is numerically simulated with the General Estuarine Transport Model from 1993 to 2016 and validated against observations. Results show that a clear seasonal cycle exists with stronger exchange flow rates in the first half of the year. Furthermore, the composition of the outflowing water is investigated using passive tracers, which mark different surface waters. The results show that in the first half of the year, most outflowing water comes from the southern coast, while in the second half most water originates from the northwestern region.

The activity of macrofauna on the sea floor is since long known to mediate deposition and erosion of sediment, but so far most studies addressed this effect at a local scale. In the present paper, the contribution of the observed macrofauna distribution (exemplified by a bivalve, the bean-like tellin Fabulina fabula, formerly known as Tellina fabula) on large-scale sediment transport in the southern North Sea is investigated by means of a model study. Macrofauna effects are considered with respect to the critical bed shear stress and erodibility, which are two important factors that control the resuspension rate. Simulation results for a typical winter month revealed for the first time that the suspended sediment concentration (SSC) is increased not only locally but beyond the inhabited zones. This alteration is not confined to near-bed zones but can be observed throughout the entire water column, especially during storm events. These effects are most prominent in the fine silt fraction, coarser and finer fractions are less affected. For a selected storm event in February 2010, we explain the counter-intuitive decrease in near-bed SSC in some areas with a high macrofauna abundance compared to a simulation excluding such macrofauna: A high macrofauna-induced entrainment rate leads to rapid exhaustion of available sediments at the bed in the model and consequently limits the near-bed SSC.

The Knudsen theorem for estuarine exchange flow, based on mass conservation of water and salt, and its generalization with resolution in salinity coordinates, the Total Exchange Flow (TEF) analysis framework, are reviewed here. The former had been developed, and applied to quantify exchange flow between the North Sea and the Baltic Sea, more than a century ago. In this paper, the underlying short research paper published in 1900 by Martin Knudsen, originally written in German, is translated into English. Reaching far beyond the Knudsen relation in particular, the extensive scientific achievements of Martin Knudsen on the salinity of seawater are reviewed. Using the Knudsen theorem and the TEF analysis framework, validated multi-decadal (years 1949–2013) model simulations are analyzed in terms of exchange flow through straits of the Western Baltic Sea. When comparing the model results to the original findings of Martin Knudsen, it is impressive to see how relevant his analysis of ratios of averaged inflowing and outflowing water masses still is today, given that they were based on just a few salinity observations. The model-based long-term Knudsen and TEF analyses of exchange flow in the Western Baltic Sea reproduces the Major Baltic Inflows (MBIs) that have occurred since the 1950s. For the complex inflow years 2002/2003, with two baroclinic summer inflows and one barotropic winter inflow in between, the strong underestimation of the exchange flow by Eulerian analysis as compared to TEF analysis is demonstrated.

The increasing demand for renewable energy is projected to result in a 40-fold increase in offshore wind electricity in the European Union by 2030. Despite a great number of local impact studies for selected marine populations, the regional ecosystem impacts of offshore wind farm (OWF) structures are not yet well assessed nor understood. Our study investigates whether the accumulation of epifauna, dominated by the filter feeder Mytilus edulis (blue mussel), on turbine structures affects pelagic primary productivity and ecosystem functioning in the southern North Sea. We estimate the anthropogenically increased potential distribution based on the current projections of turbine locations and reported patterns of M. edulis settlement. This distribution is integrated through the Modular Coupling System for Shelves and Coasts to state-of-the-art hydrodynamic and ecosystem models. Our simulations reveal non-negligible potential changes in regional annual primary productivity of up to 8% within the OWF area, and induced maximal increases of the same magnitude in daily productivity also far from the wind farms. Our setup and modular coupling are effective tools for system scale studies of other environmental changes arising from large-scale offshore wind farming such as ocean physics and distributions of pelagic top predators.

A correction to this paper has been published: https://doi.org/10.1007/s12237-021-00964-9

For more than a century, estuarine exchange flow has been quantified by means of the Knudsen relations which connect bulk quantities such as inflow and outflow volume fluxes and salinities. These relations are closely linked to estuarine mixing. The recently developed Total Exchange Flow (TEF) analysis framework, which uses salinity coordinates to calculate these bulk quantities, allows an exact formulation of the Knudsen relations in realistic cases. There are however numerical issues, since the original method does not converge to the TEF bulk values for an increasing number of salinity classes. In the present study, this problem is investigated and the method of dividing salinities, described by MacCready et al. (2018), is mathematically introduced. A challenging yet compact analytical scenario for a well-mixed estuarine exchange flow is investigated for both methods, showing the proper convergence of the dividing salinity method. Furthermore, the dividing salinity method is applied to model results of the Baltic Sea to demonstrate the analysis of realistic exchange flows and exchange flows with more than two layers.

Transport algorithms of numerical ocean circulation models are frequently exhibiting truncation errors leading to spurious diapycnal mixing of water masses. This chapter discusses methods that might be useful in diagnosing spurious diapycnal mixing and describes some approaches that might be helpful for its reduction. The first one is related to the use of the Arbitrary Lagrangian Eulerian (ALE) vertical coordinate which allows the implementation of vertically moving meshes that may partly follow the isopycnals even if the basic vertical coordinate differs from isopycnal. The second approach relies on modified advection schemes with the dissipative part of the transport operators directed isopycnally. Finally the third approach deals with new efficient and stable advection algorithms of arbitrary high order based on the WENO-ADER method, which can be applied to both structured and unstructured meshes. While practical benefits of using the reviewed approaches depend on applications, there are indications that equipping present state-of-the-art ocean circulation models with them would lead to reduced spurious transformations.

Detailed knowledge of species distributions at a fine spatial scale is an essential prerequisite for the understanding of ecosystems. However, relating species distributions to environmental variables is difficult, and distribution patterns of mobile benthic top predators can only be estimated at a rough spatial scale using visual cues. This is particularly problematic in systems with strong environmental gradients, such as intertidal habitats. Monitoring predators using GPS tags allows collecting precise spatial data over wide areas and during night time. We collected fine-scale data on prey abundance and quality, sediment composition, inundation time of tidal flats, and foraging distances from nest sites to develop a predictive distribution model for oystercatchers (Haematopus ostralegus) in the Wadden Sea, Germany. This shorebird species was able to identify the patches with high biomass and abundance of its endobenthic prey at a very fine spatial scale. Modelling suggested that prey abundance and biomass were essential for predicting oystercatcher occurrence: the probability of encountering a foraging oystercatcher was higher than expected in areas with >100 cockles per m(2) and areas with 80 g ash-free dry weight per m(2). Our modelling approach also showed that habitat use by oystercatchers was very strongly dependent on abiotic factors, i.e., oystercatchers preferred muddy and low-lying tidal flats with short exposure times close to their breeding sites. Oystercatchers only used patches >4 km away from their breeding territories if such patches were particularly prey-rich. This study demonstrates the importance of fine-scale models of predators and environmental predictors in patchy environments. These results have two conclusions with important management implications: (1) fine-scale models of distribution data for predators can provide a valuable indicator of the location of important sites worthy of protection; and (2) abiotic predictors alone are suitable to identify potential valuable feeding sites for oystercatchers without the need for time-consuming collection of prey-base data, even in a coastal zone with strong gradients. (C) 2015 Elsevier B.V. All rights reserved.

Lakes are important ecosystems that provide a number of ecosystem services including provision of drinking water, flood control, fisheries and in general a high natural, cultural and aesthetic value. Provisioning services from lakes are particularly relevant in regions where lakes supply drinking water. In these water bodies, a high water quality is of utmost importance in order to produce drinking water at required quantities and at affordable prices. High nutrient loading, eutrophication, and toxicant pollution, however, are growing stressors in many places, driving severe water quality deteriorations that harm domestic water supply, quality of life and social welfare. Fast growing urban areas are particularly vulnerable to these deteriorations in surface water resources, because waste, waste water, and chemical pollutants (heavy metals, pesticides, etc.) are affecting nearby aquatic ecosystems. While in river ecosystems these pollution pressures only affect water users further downstream, i.e. not directly the pollution producer responsible for the water quality deterioration, standing water bodies like lakes or reservoirs directly and often negatively feed back to the adjacent urban communities.

Neobiotic species can have profound impacts on food webs and entire ecosystems. The American razor clam Ensis leei was introduced into the Wadden Sea by vessels in the late 1970s and has since spread widely. It has been suggested that Ensis does not interact strongly with other benthic species. The abundance and biomass of E. leei were recorded in 2393 samples in the north-eastern Wadden Sea and 800 samples in the south-eastern Wadden Sea over a total period of 9 years. Using an interdisciplinary approach, we developed a habitat prediction model using sedimentological and hydrodynamic predictors to help understand the shape of the ecological niche occupied by Ensis in the Wadden Sea. Our model showed that Ensis preferred areas with moderately high bed shear stress and prolonged or constant water coverage. Ensis preferred coarse sediments in the northern sub-area but coarse and muddy sediments in the southern sub-area and was negatively affected by the sand mason worm Lanice conchilega in the northern sub-area. Predictions of the spatial distribution of Ensis using the northern and southern datasets revealed major differences in predicted hot-spots throughout the entire study site. This study thus highlights the need to collect a sufficiently large dataset from different sub-areas of the Wadden Sea to allow valid conclusions to be drawn regarding the spatial distribution of Ensis. The negative effects of L. conchilega on Ensis abundance and biomass as well as the occurrence of Ensis in muddy sediments in the south suggest that the ecological niche of this neobiotic species is likely to overlap partly with the native fauna of the Wadden Sea.

In lakes and reservoirs, physical processes control temperature dynamics and stratification, which are important determinants of water quality. In large lakes, even extensive monitoring programs leave some of the patterns undiscovered and unresolved. Lake models can complement measurements in higher spatial and temporal resolution. These models require a set of driving data, particularly meteorological input data, which are compulsory to the models but at many locations not available at the desired scale or quality. It remains an open question whether these meteorological input data can be acquired in a sufficient quality by employing atmospheric models. In this study, we used the European Centre for Medium-Range Weather Forecasts’ (ECMWF) ERA-Interim atmospheric reanalysis data as meteorological forcing for the three-dimensional hydrodynamic General Estuarine Transport Model (GETM). With this combination, we modelled the spatio-temporal variation in water temperature in the large, shallow Lake Chaohu, China. The model succeeded in reproducing the seasonal patterns of cooling and warming. While the model did predict diurnal patterns, these patterns were not precise enough to correctly estimate the extent of short stratification events. Nevertheless, applying reanalysis data proved useful for simulating general patterns of stratification dynamics and seasonal thermodynamics in a large shallow lake over the year. Utilising reanalysis data together with hydrodynamic models can, therefore, inform about water temperature dynamics in the respective water bodies and, by that, complement local measurements.

International audience; The state of the art of the numerics of hydrodynamic non-hydrostatic structured-grid coastal ocean models is reviewed here. First, some fundamental differences in the hydrodynamics of the coastal ocean, such as the large surface elevation variation compared to the mean water depth, are contrasted against large scale ocean dynamics. Then the hydrodynamic equations as they are used in coastal ocean models as well as in large scale ocean models are presented, including parameterisations for turbulent transports. As steps towards discretisation, coordinate transformations and vertical and horizontal discretisations based on a finite-volume approach are discussed with focus on the specific requirements for coastal ocean models. As in large scale ocean models, splitting of internal and external modes is essential also for coastal ocean models, but specific care is needed when wetting an drying of inter-tidal flats is included. As one obvious characteristics of coastal ocean models, open boundaries occur and need to be treated in a way that correct model forcing from outside is transmitted to the model domain without reflecting waves from the inside. Here, also new developments in two-way nesting are presented. Single processes such as internal inertia-gravity waves, advection and turbulence closure models are discussed with focus on the coastal scales. Some overview on existing hydrostatic structured-grid coastal ocean models is given, including their extensions towards non-hydrostatic models. Finally, an outlook on future perspectives is made.

This paper quantifies spurious dissipation and mixing of various advection schemes in idealised experiments of lateral shear and baroclinic instabilities in numerical simulations of a re-entrant Eady channel for configurations with large and small Rossby numbers. In addition, a two-dimensional barotropic shear instability test case is used to examine numerical dissipation of momentum advection in isolation, without any baroclinic effects. Effects of advection schemes on the evolution of background potential energy and the dynamics of the restratification process are analysed. The advection schemes for momentum and tracers are considered using several different methods including a recently developed local dissipation analysis. As highly accurate but computationally demanding schemes we apply WENO and MP5, and as more efficient lower-order total variation diminishing (TVD) schemes we use among others the SPL-max-View the MathML source13 and a third-order-upwind scheme. The analysis shows that the MP5 and SPL-max-View the MathML source13 schemes provide the most accurate results. Following our comprehensive analysis of computational costs, the MP5 scheme is approximately 2.3 times more expensive in our implementation. In contrast to the configuration with a small Rossby number, in which significant differences between schemes are apparent, the different advection schemes behave similarly for a larger Rossby number. Regions of high numerical dissipation are shown to be associated with low grid Reynolds numbers. The major outcome of the present study is that generally positive global numerical dissipation and positive background potential energy evolution delay the restratification process.

It is well known that in numerical models the advective transport relative to fixed or moving grids needs to be discretised with sufficient accuracy to minimise the spurious decay of tracer variance (spurious mixing). In this paper a general analysis of discrete variance decay (DVD) caused by advective and diffusive fluxes is established. Lacking a general closed derivation for the local DVD rate, two non-invasive methods to estimate local DVD during model runtime are discussed. Whereas the first was presented recently by Burchard and Rennau (2008), the second is a newly proposed alternative. This alternative analysis method is argued to have a more consistent foundation. In particular, it recovers a physically sound definition of discrete variance in a Finite-Volume cell. The diagnosed DVD can be separated into physical and numerical (spurious) contributions, with the latter originating from discretisation errors. Based on the DVD analysis, a 3D dissipation analysis is developed to quantify the physically and numerically induced loss of kinetic energy. This dissipation analysis provides a missing piece of information to assess the discrete energy conservation of an ocean model. Analyses are performed and evaluated for three test cases, with complexities ranging from idealised 1D advection to a realistic ocean modelling application to the Western Baltic Sea. In all test cases the proposed alternative DVD analysis method is demonstrated to provide a reliable diagnostic tool for the local quantification of physically and numerically induced dissipation and mixing.

Recent results from a tracer release experiment have shown that, similar to many lakes and ocean basins, deep-water mixing in the Baltic Sea is largely determined by mixing processes occurring in the energetic near-bottom region. Due to the complexity and small vertical extent of this region, however, previous modeling studies of the Baltic Sea have so far not been able to provide a numerically and physically sound representation of boundary mixing. Here we discuss first results from a nested high-resolution simulation of the central Baltic Sea that aims at a realistic description of the turbulent bottom boundary layer with the help of new numerical techniques (adaptive coordinates) and state-of-the-art turbulence modeling. Using a comprehensive data set from the Baltic Sea Tracer Release Experiment, we show that the model is able to reproduce the key dynamical processes (near-inertial waves, topographic waves, and a rim current) with excellent accuracy. Boundary mixing triggered by these processes was found to result in simulated basin-scale mixing rates in close agreement with observations, including a seasonal variability that has been emphasized in previous studies. These results may be relevant also for the description of mixing in large lakes and other stratified basins.

In this study a model system consisting of the three-dimensional General Estuarine Transport Model (GETM) and the third generation wind wave model SWAN was developed. Both models were coupled in two-way mode. The effects of waves were included into the ocean model by implementing the depth-dependent Radiation stress formulation (RS) of Mellor (2011a) and the Vortex force formulation (VF) presented by Bennis et al. (2011) . Thus, the developed model system offers a direct comparison of these two formulations. The enhancement of the vertical eddy viscosity due to the energy transfer by white capping and breaking waves was taken into account by means of injecting turbulent kinetic energy at the surface. Wave-current interaction inside the bottom boundary layer was considered as well. The implementation of both wave-averaged formulations was validated against three flume experiments. One of these experiments with long period surface waves (swell), had not been evaluated before. The validation showed the capability of the model system to reproduce the three-dimensional interaction of waves and currents. For the flume test cases the wave-induced water level changes (wave set-up and set-down) and the corresponding depth-integrated wave-averaged velocities were similar for RS and VF. Both formulations produced comparable velocity profiles for short period waves. However, for large period waves, VF overestimated the wave set-down near the main breaking points and RS showed artificial offshore-directed transport at the surface where wave shoaling was taking place. Finally the validated model system was applied to a realistic barred beach scenario. For RS and VF the resulting velocity profiles were similar after being significantly improved by a roller evolution method. Both wave-averaged formulations generally provided similar results, but some shortcomings were revealed. Although VF partly showed significant deviations from the measurements, its results were still physically reasonable. In contrast, RS showed unrealistic offshore-directed transport in the wave-shoaling regions and close to steep bathymetry.

The increasing demand for the investigation of nonhydrostatic effects in ocean modelling requires crucial modifications to models applying the hydrostatic pressure assumption. Within many studies the capability of the pressure-correcting projection method for the inclusion of the missing nonhydrostatic pressure contribution into an existing hydrostatic model kernel was verified. It provides accurate results but also requires computational (and implementational) effort for solving a Poisson equation for the pressure correction. In contrast, some studies were based on an alternative approach that does not require the inversion of a Poisson equation. Within this alternative approach the nonhydrostatic pressure contribution is calculated by an explicit vertical integration of the additional nonhydrostatic terms in the balance of vertical momentum. Since ocean models are not intended to replace classical engineering tools and are usually applied to nearly hydrostatic flows, this straight-forward extension of the hydrostatic procedure is an interesting option. However, the feasibility of the alternative approach was not tested within a full 3D explicit mode-splitting model yet. Furthermore, the nonhydrostatic capability of the alternative approach has so far not been validated against well known nonhydrostatic benchmark test cases. In order to assess the potential of the alternative approach for future ocean modelling applications, in the present study these required but still missing investigations are carried out. To demonstrate the necessary modifications to an explicit mode-splitting hydrostatic model kernel, the extension of the General Estuarine Transport Model (GETM) is outlined. The simulation results of laboratory and idealised oceanic test cases are presented and compared to analytical theory, laboratory experiments and other numerical simulations. This validation indicates the nonhydrostatic capability of the extended GETM. However, stability issues limited the efficiency and the applicability of the straight-forward inclusion of nonhydrostatic dynamics.