Jan O. Backhaus

A three-dimensional model for the simulation of shelf sea dynamics

A three-dimensional baroclinic primitive equation model based upon a semi-implicit numerical scheme is developed. The scheme is essentially independent of the stringent stability criteria valid for explicit schemes. This favours its application as a baroclinic eddy-resolving model; in this case the only stability limitation will concern internal gravity waves. Implicit algorithms are applied for each space coordinate; they enter in the approximation for the external gravity waves and the vertical shear stress. Further, a stable second order approximation in the time domain is introduced for the Coriolis and pressure gradient terms in the equation of motion. In contrast to the most commonly applied explicit shelf sea models the scheme proposed has two essential advantages: a) it is about factor 5 faster; b) it allows the simulation of ocean/shelf dynamics by including in the model area deep ocean regions without being limited by stability considerations for the free surface. The model thus offers the simulation of a wider range of processes relevant for shelf seas. This is demonstrated by a simulation of low-frequency currents covering a period of half a year.

A climatological data set of temperature and salinity for the Baltic Sea and the North Sea

A climatological monthly mean data set for temperature and salinity in the area of the North Sea and Baltic Sea is presented. More than 3.1 million temperature observations (2.9 million for salinity) collected during the period 1900 to 1996 were compiled and gridded on a 10×10 km grid with 18 vertical levels.

A semi-implicit scheme for the shallow water equations for application to shelf sea modelling

Abstract A semi-implicit scheme for the numerical solution of the shallow water equations is proposed. The scheme is suitable for the simulation of shelf sea dynamics as is demonstrated by some examples of successful application covering a range of grid sizes typical for shelf sea models. The basic outlines of the method are presented. Some practical aspects of computation are discussed which illustrate that an explicit model can be modified easily to the semi-implicit version proposed here. Compared to explicit schemes the semi-implicit approach has two major advantages: (1) its economy (a saving of at least 50% in computing time can be achieved); (2) a closer match is obtained between the time-stepping procedure and the time scales of processes, the spatial scales of which are close to the lower limit of the resolution of the model grid.

Application of a transient reduced gravity plume model to the Denmark Strait Overflow

A hydrostatic, reduced gravity, two-dimensional primitive equation numerical model for the simulation of transient bottom arrested gravity plumes was developed by adopting an algorithm from a wadden sea model (a model that simulates the wetting and drying of mud flats, sand banks, etc.) with a movable lateral boundary. The vertically integrated nonlinear rotational model accounts for the dissipation of momentum due to bottom friction and for the entrainment of water mass properties from a spatially structured but stagnant ambient water body. It predicts the temporal and spatial evolution of the flow field and the water mass modification within a gravity plume that descends on an arbitrary topography. Previous model investigations considered a laterally integrated streamtube, whereas our model resolves the plume horizontally. In the streamtube approach it was assumed that the plume descends in a stationary, almost geostrophic balance modified only by bottom drag and entrainment. The results of this model demonstrate that this balance may be disturbed whenever the plume encounters topographic disturbances, which, for the initial intruding phase in particular, accounts for its highly transient character. The model results are in good agreement with theoretical and laboratory investigations and with observations, as is demonstrated by some basic test experiments. An application to the overflow of dense water through the Denmark Strait is presented.

Study of the generation and propagation of internal waves in the Strait of Gibraltar using a numerical model and synthetic aperture radar images of the European ERS 1 satellite

A weakly nonhydrostatic, two-layer numerical model based on the Boussinesq equations is presented which is capable of describing, among others, the generation and propagation of nonlinear weakly dispersive internal waves in the Strait of Gibraltar. The model depends on one space coordinate only, but it retains several features of a fully three-dimensional model by including a realistic bottom profile, a variable channel width, and a trapezoidal channel cross section. The nonlinear primitive Boussinesq equations include horizontal diffusion, bottom friction, and friction between the two water layers. The model is driven by a height difference of the mean interface depth between the Atlantic and the Mediterranean boundaries and by semidiurnal tidal oscillations of the barotropic transport. The model presented in this paper describes (1) the mean and tidal flow in the Strait of Gibraltar, (2) the variation of the depth of the interface during a tidal cycle, (3) the generation of strong depressions of the interface at the western sides of the Spartel Sill and the Camarinal Sill, (4) the generation of strong eastward propagating internal bores, and (5) their disintegration into trains of internal solitary waves. The surface convergence patterns associated with depressions of the interface at the Camarinal Sill, internal bores, and internal solitary waves are calculated and compared with roughness patterns visible on synthetic aperture radar (SAR) images of the first European Remote Sensing Satellite ERS 1. In total, 155 ERS 1 SAR scenes from 94 satellite overflights over the Strait of Gibraltar, which were acquired in the period from January 1992 to March 1995, have been analyzed. It is shown that the proposed model is capable of explaining the observed temporal and spatial evolution of surface roughness patterns associated with eastward propagating internal waves inside the Strait of Gibraltar as well as the observed east-west asymmetry of the internal wave field.

A finite difference general circulation model for shelf seas and its application to low frequency variability on the North European shelf

Abstract The basic ideas behind the shelf sea circulation model of the Institut fur Meereskunde Hamburg (IFMH) are outlined. The stability and the computational performance of the numerical scheme are essentially based upon implicit algorithms or second order approximations introduced for those terms in the primitive equations which are likely to produce instability. As a result the scheme turns out to be rather stable and much faster than conventional, solely explicit numerical schemes. The application of the IFMH-model on the determination of the low frequency variability of the North European shelf sea provides insight into a frequency domain where information from observational data is rather scarce.

Internal Waves in the Strait of Messina Studied by a Numerical Model and Synthetic Aperture Radar Images from the ERS 1/2 Satellites

A new numerical two-layer model is presented, which describes the generation of internal tidal bores and their disintegration into internal solitary waves in the Strait of Messina. This model is used to explain observations made by the synthetic aperture radar (SAR) from the European Remote Sensing satellites ERS 1 and ERS 2. The analysis of available ERS 1/2 SAR data of the Strait of Messina and adjacent sea areas show that 1) northward as well as southward propagating internal waves are generated in the Strait of Messina, 2) southward propagating internal waves are observed more frequently than northward propagating internal waves, 3) sea surface manifestations of southward as well as northward propagating internal waves are stronger during periods where a strong seasonal thermocline is known to be present, 4) southward propagating internal bores are released from the sill between 1 and 5 hours after maximum northward tidal flow and northward propagating internal bores are released between 2 and 6 hours after maximum southward tidal flow, and 5) the spatial separation between the first two internal solitary waves of southward propagating wave trains is smaller in the period from July to September than in the period from October to June. The numerical two-layer model is a composite of two models consisting of 1) a hydrostatic “generation model,” which describes the dynamics of the water masses in the region close to the strait’s sill, where internal bores are generated, and 2) a weakly nonhydrostatic “propagation model,” which describes the dynamics of the water masses outside of the sill region where internal bores may disintegrate into internal solitary waves. Due to a technique for movable lateral boundaries, the generation model is capable of simulating the dynamics of a lower layer that may intersect the bottom topography. The proposed generation–propagation model depends on one space variable only, but it retains several features of a fully three-dimensional model by including a realistic channel depth and a realistic channel width. It is driven by semidiurnal tidal oscillations of the sea level at the two open boundaries of the model domain. Numerical simulations elucidate several observed characteristics of the internal wave field in the Strait of Messina, such as north–south asymmetry, times of release of the internal bores from the strait’s sill, propagation speeds, and spatial separations between the first two solitary waves of internal wave trains.

Mixing in the Bosphorus Strait and the Black Sea continental shelf: observations and a model of the dense water outflow

Counterflowing waters of the Black Sea and Mediterranean Sea are mixed by turbulent entrainment processes along their course through the Turkish Straits. In the Bosphorus Strait, the entrainment into the upper layer from below is abruptly increased when the flow is accelerated in the narrower southern reach, where the flow passes through a contraction. In contrast, the lower layer salinity decreases towards the north first by gradual entrainment within the Strait and later at an increased rate in the wide continental shelf region upon exit into the Black Sea. After passing over the sill located north of the Strait, the flow on the continental shelf proceeds in the form of a gravity current following the local slopes. The topography of the shelf region, assembled from various sources of high-resolution surveys and maps, is reminiscent of a river delta. The water properties and thickness of the Mediterranean plume is modified by turbulent entrainment, shelf currents, stratification, bottom friction and slope. The flow first spreads out on the mid-shelf slope, follows the delta features to reach the shelf edge and, finally, cascades down the steep continental slope. Horizontal spreading by convective instabilities and eastward propagation of anomalous properties along the continental slope are characteristic features of the deeper region adjacent to the shelf. The behaviour of the density current is revealed by results obtained from a reduced gravity model, suggesting that the slope and fine-scale features of the bottom topography are crucial elements in determining plume behaviour. The model results are found to be robust to environmental changes and in good correspondence with observed flow features, especially when the topography with realistic fine scales and slope are adequately represented.

Simulations of the north sea circulation, its variability, and its implementation as hydrodynamical forcing in ERSEM

Abstract The rationale is given of how the gross physical features of the circulation and the stratification of the North Sea have been aggregated for inclusion in the ecosystem box model ERSEM. As the ecosystem dynamics are to a large extent determined by small-scale physical events, the ecosystem model is forced with the circulation of a specific year rather than using the long-term mean circulation field. Especially the vertical exchange processes have been explicitly included, because the primary production strongly depends on them. Simulations with a general circulation model (GCM), forced by three-hourly meteorological fields, have been utilized to derive daily horizontal transport values driving ERSEM on boxes of sizes of a few 100 km. The daily vertical transports across a fixed 30-m interface provide the necessary short-term event character of the vertical exchange. For the years 1988 and 1989 the properties of the hydrodynamic flow fields are presented in terms of trajectories of the flow, thermocline depths, of water budgets, flushing times and diffusion rates. The results of the standard simulation with ERSEM show that the daily variability of the circulation, being smoothed by the box integration procedure, is transferred to the chemical and biological state variables to a very limited degree only.

Transport of conservative passive tracers in the North Sea: first results of a circulation and transport model

Abstract A simple Lagrangian transport model was applied to obtain estimates of transport routes of conservative passive tracers in the North Sea. A vertically integrated time-dependent flow field derived from the daily output of a three-dimensional baroclinic circulation model was used in the transport model. The simulation period covers the years from 1969 to 1982. The calculations were carried out in order to get estimates of both, the low-frequency flow in the North Sea and the resulting dispersion of matter within the sea. Point sources are assumed which release tracers continuously and with a constant rate. Hence the variability of the flow field can be visualized by the temporal and spatial fate of the released tracer ensemble. The model results are displayed in three different ways to provide a comprehensive description of the complex spacetime character of the system.