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A stochastic operational forecasting system of the Black Sea: Technique and validation Vandenbulcke, Luc ; Barth, Alexander in Ocean Modelling (2015), 93 In this article, we present the latest version of an ensemble forecasting system of the hydrodynamics of the Black Sea, based on the GHER model. The system includes the Weakly Constrained Ensembles ... [more ▼] In this article, we present the latest version of an ensemble forecasting system of the hydrodynamics of the Black Sea, based on the GHER model. The system includes the Weakly Constrained Ensembles algorithm to generate random, but physically balanced perturbations to initialize members of the ensemble. On top of initial conditions, the ensemble accounts also for uncertainty on the atmospheric forcing fields, and on some scalar parameters such as river flows or model diffusion coefficients. The forecasting system also includes the Ocean Assimilation Kit, a sequential data assimilation package implementing the SEEK and Ensemble Kalman filters. A novel aspect of the forecasting system is that not only our best estimate of the future ocean state is provided, but also the associated error estimated from the ensemble of models. The primary goal of this paper is to quantitatively show that the ensemble variability is a good estimation of the model error, regardless of the magnitude of the forecast errors themselves. In order for this estimation to be meaningful, the model itself should also be well validated. Therefore, we describe the model validation against general circulation patterns. Some particular aspects critical for the Black Sea circulation are validated as well: the mixed layer depth and the shelfopen sea exchanges. The model forecasts are also compared with observed sea surface temperature, and errors are compared to those of another operational model as well. [less ▲] Detailed reference viewed: 21 (1 ULg)Assimilation of sea surface temperature, sea ice concentration and sea ice drift in a model of the Southern Ocean Barth, Alexander ; Canter, Martin ; et al in Ocean Modelling (2015), 93 Current ocean models have relatively large errors and biases in the Southern Ocean. The aim of this study is to provide a reanalysis from 1985 to 2006 assimilating sea surface temperature, sea ice ... [more ▼] Current ocean models have relatively large errors and biases in the Southern Ocean. The aim of this study is to provide a reanalysis from 1985 to 2006 assimilating sea surface temperature, sea ice concentration and sea ice drift. In the following it is also shown how surface winds in the Southern Ocean can be improved using sea ice drift estimated from infrared radiometers. Such satellite observations are available since the late seventies and have the potential to improve the wind forcing before more direct measurements of winds over the ocean are available using scatterometry in the late nineties. The model results are compared to the assimilated data and to independent measurements (the World Ocean Database 2009 and the mean dynamic topography based on observations). The overall improvement of the assimilation is quantified, in particular the impact of the assimilation on the representation of the polar front is discussed. Finally a method to identify model errors in the Antarctic sea ice area is proposed based on Model Output Statistics techniques using a series of potential predictors. This approach provides new directions for model improvements. [less ▲] Detailed reference viewed: 23 (1 ULg)Modelling argon dynamics in first-year sea ice ; ; Zhou, Jiayun et al in Ocean Modelling (2014), 73 Abstract: Focusing on physical processes, we aim at constraining the dynamics of argon (Ar), a biogeochemically inert gas, within first year sea ice, using observation data and a one-dimensional halo ... [more ▼] Abstract: Focusing on physical processes, we aim at constraining the dynamics of argon (Ar), a biogeochemically inert gas, within first year sea ice, using observation data and a one-dimensional halo-thermodynamic sea ice model, including parameterization of gas physics. The incorporation and transport of dissolved Ar within sea ice and its rejection via gas-enriched brine drainage to the ocean, are modeled following fluid transport equations through sea ice. Gas bubbles nucleate within sea ice when Ar is above saturation and when the total partial pressure of all three major atmospheric gases (N2, O2 and Ar) is above the brine hydrostatic pressure. The uplift of gas bubbles due to buoyancy is allowed when the brine network is connected with a brine volume above a given threshold. Ice-atmosphere Ar fluxes are formulated as a diffusive process proportional to the differential partial pressure of Ar between brine inclusions and the atmosphere. Two simulations corresponding to two case studies that took place at Point Barrow (Alaska, 2009) and during an ice-tank experiment (INTERICE IV, Hamburg, Germany, 2009) are presented. Basal entrapment and vertical transport due to brine motion enable a qualitatively sound representation of the vertical profile of the total Ar (i.e. the Ar dissolved in brine inclusions and contained in gas bubbles; TAr). Sensitivity analyses suggest that gas bubble nucleation and rise are of most importance to describe gas dynamics within sea ice. Ice-atmosphere Ar fluxes and the associated parameters do not drastically change the simulated TAr. Ar dynamics are dominated by uptake, transport by brine dynamics and bubble nucleation in winter and early spring; and by an intense and rapid release of gas bubbles to the atmosphere in spring. Important physical processes driving gas dynamics in sea ice are identified, pointing to the need for further field and experimental studies. [less ▲] Detailed reference viewed: 46 (5 ULg)Comparison of different assimilation schemes in a sequential Kalman filter assimilation system Yan, Yajing ; Barth, Alexander ; Beckers, Jean-Marie in Ocean Modelling (2014), 73 Detailed reference viewed: 69 (12 ULg)Generation of analysis and consistent error ﬁelds using the Data Interpolating Variational Analysis (Diva) Troupin, Charles ; Barth, Alexander ; Sirjacobs, Damien et al in Ocean Modelling (2012), 52-53 The Data Interpolating Variational Analysis (Diva) is a method designed to interpolate irregularly-spaced, noisy data onto any desired location, in most cases on regular grids. It is the combination of a ... [more ▼] The Data Interpolating Variational Analysis (Diva) is a method designed to interpolate irregularly-spaced, noisy data onto any desired location, in most cases on regular grids. It is the combination of a particular methodology, based on the minimisation of a cost function, and a numerically efficient method, based on a finite-element solver. The cost function penalises the misfit between the observations and the reconstructed field, as well as the regularity or smoothness of the field. The intrinsic advantages of the method are its natural way to take into account topographic and dynamic constraints (coasts, advection, . . . ) and its capacity to handle large data sets, frequently encountered in oceanography. The method provides gridded fields in two dimensions, usually in horizontal layers. Three-dimension fields are obtained by stacking horizontal layers. In the present work, we summarize the background of the method and describe the possible methods to compute the error field associated to the analysis. In particular, we present new developments leading to a more consistent error estimation, by determining numerically the real covariance function in Diva, which is never formulated explicitly, contrarily to Optimal Interpolation. The real covariance function is obtained by two concurrent executions of Diva, the first providing the covariance for the second. With this improvement, the error field is now perfectly consistent with the inherent background covariance in all cases. A two-dimension application using salinity measurements in the Mediterranean Sea is presented. Applied on these measurements, Optimal Interpolation and Diva provided very similar gridded fields (correlation: 98.6%, RMS of the difference: 0.02). The method using the real covariance produces an error field similar to the one of OI, except in the coastal areas. [less ▲] Detailed reference viewed: 439 (51 ULg)Generation of the Cape Ghir upwelling filament: A numerical study Troupin, Charles ; ; Beckers, Jean-Marie et al in Ocean Modelling (2012), 41 Filaments are narrow, shallow structures of cool water originating from the coast. They are typical features of the four main eastern boundary upwelling systems (EBUS). In spite of their significant ... [more ▼] Filaments are narrow, shallow structures of cool water originating from the coast. They are typical features of the four main eastern boundary upwelling systems (EBUS). In spite of their significant biological and chemical roles, through the offshore exportation of nutrient-rich waters, the physical processes that generate them are still not completely understood. This paper is a process-oriented study of filament generation mechanisms. Our goal is twofold: firstly, to obtain a numerical solution able to well represent the characteristics of the filament off Cape Ghir (30°38'N, northwestern Africa) in the Canary EBUS and secondly, to explain its formation by a simple mechanism based on the balance of potential vorticity. The first goal is achieved by the use of the ROMS model (Regional Ocean Modeling System) in embedded domains around Cape Ghir, with a horizontal resolution going up to 1.5 km for the finest domain. The latter gets its initial and boundary conditions from a parent solution and is forced by climatological, high-resolution atmospheric fields. The modeled filaments display spatial, temporal and physical characteristics in agreement with the available in situ and satellite observations. This model solution is used as a reference to compare the results with a set of process-oriented experiments. These experiments allow us to reach the second objective. Their respective solution serves to highlight the contribution of various processes in the filament generation. Since the study is focused on general processes present under climatological forcing conditions, inter-annual forcing is not necessary. The underlying idea for the filament generation is the balance of potential vorticity in the Canary EBUS: the upwelling jet is characterized by negative relative vorticity and flows southward along a narrow band of uniform potential vorticity. In the vicinity of the cape, an injection of relative vorticity induced by the wind breaks the existing vorticity balance. The upwelling jet is prevented from continuing its way southward and has to turn offshore to follow lines of equal potential vorticity. The model results highlight the essential role of wind, associated with the particular topography (coastline and bottom) around the cape. The mechanism presented here is general and thus can be applied to other EBUS. [less ▲] Detailed reference viewed: 102 (10 ULg)The effect of topography-enhanced diapycnal mixing on ocean and atmospheric circulation and marine biogeochemistry ; ; et al in Ocean Modelling (2011), 3-4 Detailed reference viewed: 21 (3 ULg)Realistic modelling of the exceptional inflows into the central Baltic Sea in 2003 using terrain-following coordinates ; Beckers, Jean-Marie ; in Ocean Modelling (2011), 39 Dense inflows into the permanently stratified Baltic Sea are renewing the deep waters in the central basins. The present study evaluates the performance of terrain-following coordinates, which are ... [more ▼] Dense inflows into the permanently stratified Baltic Sea are renewing the deep waters in the central basins. The present study evaluates the performance of terrain-following coordinates, which are resolving the along-bottom flow, in an annual simulation covering several inflows reaching the deeper basins of the Baltic Sea in 2003. Therefor the simulations are carried out using sigma-coordinates and vertically adaptive coordinates for two different horizontal resolutions (2 NM and 1 NM). The simulations with the sigma coordinates could not reproduce the hydrography of the major Baltic inflows realistically due to discretisation errors such as numerical mixing and pressure gradient errors. It is shown that the adaptive coordinates improve the simulation, because numerical mixing is reduced and the model’s discretisation supports a more physically-justified representation of the physical processes. For the higher-resolution simulations, adding a parameterisation of internal mixing enhances the effective mixing in the simulation and induces a reduction of the numerical mixing. Additionally to the analysis of the model performance, the inflows’ hydrography as projected by the higher-resolution model using adaptive coordinates is presented. The characteristic cross-channel circulation of gravity currents in channelised bathymetry is found to be an essential feature of the inflow dynamics in the Baltic Sea. The usage of adaptive coordinates reduces the numerical mixing in the simulation as effective as the doubling of the horizontal resolution for sigma-coordinates. However, the numerical mixing accounts for at least 50 % of the salinity mixing in the simulations. [less ▲] Detailed reference viewed: 19 (5 ULg)Non-uniform adaptive vertical grids for 3D numerical ocean models ; ; Beckers, Jean-Marie in Ocean Modelling (2010), 33 A new strategy for the vertical gridding in terrain-following 3D ocean models is presented here. The vertical grid adaptivity is partially given by a vertical diffusion equation for the vertical layer ... [more ▼] A new strategy for the vertical gridding in terrain-following 3D ocean models is presented here. The vertical grid adaptivity is partially given by a vertical diffusion equation for the vertical layer positions, with diffusivities being proportional to shear, stratification and distance from the boundaries. In the horizontal, the grid can be smoothed with respect to z-levels, grid layer slope and density. Lagrangian tendency of the grid movement is supported. The adaptive terrain-following grid can be set to be an Eulerian–Lagrangian grid, a hybrid r–q or r–z grid and combinations of these with great flexibility. With this, internal flow structures such as thermoclines can be well resolved and followed by the grid. A set of idealised examples is presented in the paper, which show that the introduced adaptive grid strategy reduces pressure gradient errors and numerical mixing significantly. The grid adaption strategy is easy to implement in various types of terrain-following ocean models. The idealised examples give evidence that the adaptive grids can improve realistic, long-term simulations of stratified seas while keeping the advantages of terrain-following coordinates. [less ▲] Detailed reference viewed: 78 (30 ULg)Really TVD advection schemes for the depth-integrated transport equation Mercier, Christophe ; Delhez, Eric in Ocean Modelling (2010), 33 Detailed reference viewed: 94 (54 ULg)Consistent computation of the age of water parcels using CART Mercier, Christophe ; Delhez, Eric in Ocean Modelling (2010), 35 The Constituent-oriented Age and Residence time Theory (CART) provides a flexible and efficient framework to diagnose the dynamics of marine systems. Beside the equation for the concentration of ... [more ▼] The Constituent-oriented Age and Residence time Theory (CART) provides a flexible and efficient framework to diagnose the dynamics of marine systems. Beside the equation for the concentration of appropriate (real or artificial) tracers, the method requires the resolution of differential problems for the so-called age concentration of each of these tracers. Thanks to its Eulerian formulation as an advection/diffusion problem with source terms, the method is easily implemented in existing models. However, some numerical artifacts should be avoided in order to produce physically meaningful results leading to a better understanding of the system under study. In this paper, we address two such issues that are related to the degree of implicitness of the different terms and to the advection scheme. To enforce the consistency between the discrete equations for the concentration of a tracer and for its age concentration, the degree of implicitness must be identical in the source/sink terms of the two equations. However, the ageing term should be computed in a completely explicit (respectively implicit) way if the discretization of the source/sink terms is implicit in time (respectively explicit). A specific attention should also be paid to the advection schemes for the concentration and the age concentration. The raw application of Total Variation Diminishing (TVD) scheme for both equations can lead to the occurrence of artificial local extreme values and spatial oscillations of the age field. While the TVD behavior of the discrete age field cannot be guaranteed, appropriate modifications of the flux/slope limiters used in the TVD schemes can be implemented to enforce a maximum principle that prevents the occurrence of age values outside the physically acceptable range. [less ▲] Detailed reference viewed: 47 (23 ULg)An analysis of the error space of a high-resolution implementation of the GHER hydrodynamic model in the Mediterranean Sea Vandenbulcke, Luc ; ; Alvera Azcarate, Aïda et al in Ocean Modelling (2008), 24(1-2), 46-64 An ensemble of 250 model setups covering the Mediterranean Sea is built by perturbing various parameters: the bathymetry, the initial conditions, atmospheric forcing fields (air temperature, cloud ... [more ▼] An ensemble of 250 model setups covering the Mediterranean Sea is built by perturbing various parameters: the bathymetry, the initial conditions, atmospheric forcing fields (air temperature, cloud coverage, wind), and internal model parameters (diffusion coefficients). The ensemble is then forwarded in time using the GHER hydrodynamic model, allowing to obtain information about the expected error associated with the forecast in a natural way. The evolution of this error is analyzed. In particular, we examine the time evolution and stationarity of its spatial average, and the spatial distribution of the error at different instants, by means of its first to fourth order moments, and of empirical orthogonal functions. We verify whether the a posteriori error distribution is Gaussian using the Anderson-Darling test. From these results, we are able to assess what parameters and forcing fields are most critical for the forecast. Qualitative conclusions are obtained throughout the text, in accordance with our expectations. Moreover, quantitative estimations of the expected error are also given. (C) 2008 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 150 (34 ULg)Overshootings and spurious oscillations caused by biharmonic mixing Delhez, Eric ; in Ocean Modelling (2007), 17(3), 183-198 Biharmonic mixing is often used in large scale numerical models of the ocean because of its scale selectivity; it effectively damps small scale noise and leaves the large scale dynamics nearly unaffected ... [more ▼] Biharmonic mixing is often used in large scale numerical models of the ocean because of its scale selectivity; it effectively damps small scale noise and leaves the large scale dynamics nearly unaffected. The biharmonic operator lacks however positiveness and monotonicity and can therefore produce unphysical results exhibiting spurious overshootings and oscillations. This problematic behaviour cannot be avoided by the addition of an ordinary Laplacian diffusion term. It appears in both continuous and discrete approaches/solutions in both unbounded and bounded domains. The overshootings and oscillations are induced by the strong damping of the smaller scale modes and are therefore comparable to the Gibbs' phenomenon. With appropriate boundary conditions, the variance of the field decreases monotonically and the oscillations are expected to remain small. The lack of positiveness is however a severe drawback for (dynamic) tracer studies. (C) 2007 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 73 (7 ULg)Filtering inertia-gravity waves from the initial conditions of the linear shallow water equations Barth, Alexander ; Beckers, Jean-Marie ; Alvera Azcarate, Aïda et al in Ocean Modelling (2007), 19(3-4), 204-218 A method for filtering inertia-gravity waves from elevation and depth-averaged velocity is described. This filtering scheme is derived from the linear shallow water equations for constant depth and ... [more ▼] A method for filtering inertia-gravity waves from elevation and depth-averaged velocity is described. This filtering scheme is derived from the linear shallow water equations for constant depth and constant Coriolis frequency. The filtered solution is obtained by retaining only the eigenvectors corresponding to the geostrophic equilibrium and by discarding explicitly the eigenvectors corresponding to the fast moving inertia-gravity waves. An alternative formulation is derived using a variational approach. Both filtering methods are tested numerically for a periodic domain with constant depth and the variational approach is implemented for a closed domain with large topographic variations. The filtering methods significantly reduce the amplitudes of the inertia-gravity waves while preserving the mean flow. The variational method is compared to the Incremental Analysis Update technique and the benefits of the variational filter are presented. (C) 2007 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 70 (13 ULg)Coupling a two-way nested primitive equation model and a statistical SST predictor of the Ligurian Sea via data assimilation Barth, Alexander ; Alvera Azcarate, Aïda ; Beckers, Jean-Marie et al in Ocean Modelling (2006), 13(3-4), 255-270 A primitive equation model and a statistical predictor are coupled by data assimilation in order to combine the strength of both approaches. In this work, the system of two-way nested models centred in ... [more ▼] A primitive equation model and a statistical predictor are coupled by data assimilation in order to combine the strength of both approaches. In this work, the system of two-way nested models centred in the Ligurian Sea and the satellite-based ocean forecasting (SOFT) system predicting the sea surface temperature (SST) are used. The data assimilation scheme is a simplified reduced order Kalman filter based on a constant error space. The assimilation of predicted SST improves the forecast of the hydrodynamic model compared to the forecast obtained by assimilating past SST observations used by the statistical predictor. This study shows that the SST of the SOFT predictor can be used to correct atmospheric heat fluxes. Traditionally this is done by relaxing the model SST towards the climatological SST. Therefore, the assimilation of SOFT SST and climatological SST are also compared. (c) 2006 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 74 (12 ULg)Reconstruction of incomplete oceanographic data sets using empirical orthogonal functions: application to the Adriatic Sea surface temperature Alvera Azcarate, Aïda ; Barth, Alexander ; et al in Ocean Modelling (2005), 9(4), 325-346 A method for the reconstruction of missing data based on an EOF decomposition has been applied to a large data set, a test case of Sea Surface Temperature satellite images of the Adriatic Sea. The EOF ... [more ▼] A method for the reconstruction of missing data based on an EOF decomposition has been applied to a large data set, a test case of Sea Surface Temperature satellite images of the Adriatic Sea. The EOF decomposition is realised with a Lanczos method, which allows optimising computational time for large matrices. The results show that the reconstruction method leads to accurate reconstructions as well as a low cpu time when dealing with realistic cases. The method has been tested with different amounts of missing data, artificially adding clouds ranging from 40% to 80% of data loss, and then compared to the same data set with no missing data. A comparison with in situ data has also been made. These validation studies show that results are robust, even when the amount of missing data is very high. The reconstruction of the data from the Adriatic Sea shows realistic features and a reliable temperature distribution. In addition, the method is compared to an Optimal Interpolation reconstruction. The results obtained with both methods are very similar. The main difference is the computational time, which is reduced nearly 30 times with the method presented here. Once the reconstruction has been performed, the EOF decomposition is analysed to show the method's reliability, and a cold event on the Albanian coast is studied. The reconstructed data reflect the effect of wind on the Albanian coast, that led to a cold-water episode in this zone for a 6-day period. (c) 2004 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 190 (36 ULg)Non-uniform adaptive vertical grids in one-dimensional numerical ocean models ; Beckers, Jean-Marie in Ocean Modelling (2004), 6(1), 51-81 It is demonstrated in this paper how the concept of general vertical coordinates can be exploited for constructing adaptive grids in primitive equation ocean models. The term adaptive is used here in the ... [more ▼] It is demonstrated in this paper how the concept of general vertical coordinates can be exploited for constructing adaptive grids in primitive equation ocean models. The term adaptive is used here in the sense of coordinate iso-surfaces which follow certain internal structures of the flow in such a way that higher vertical resolution is obtained in locations where vertical gradients are large. The internal structures considered here are shear and stratification. In this paper, one-dimensional models are applied in order to demonstrate the ability of such grid adaptation methods to follow internal structures even in flow situations dominated by vertical mixing processes. Here, a variational approach is considered for the generation of grids which results in a diffusion equation for the vertical coordinate. The method is tested for five different idealised and realistic scenarios with the result that the discretisation error can be significantly reduced in comparison to equidistant Cartesian grids. Some recommendations for extending these methods for three-dimensional models are given at the end of this paper. (C) 2003 Elsevier Science Ltd. All rights reserved. [less ▲] Detailed reference viewed: 32 (8 ULg)Evaluation of ocean model ventilation with CFC-11: comparison of 13 global ocean models ; ; et al in Ocean Modelling (2002), 4(2), 89-120 We compared the 13 models participating in the Ocean Carbon Model Intercomparison Project (OCMIP) with regards to their skill in matching observed distributions of CFC-11. This analysis characterizes the ... [more ▼] We compared the 13 models participating in the Ocean Carbon Model Intercomparison Project (OCMIP) with regards to their skill in matching observed distributions of CFC-11. This analysis characterizes the abilities of these models to ventilate the ocean on timescales relevant for anthropogenic CO2 uptake. We found a large range in the modeled global inventory (+/- 30\%), mainly due to differences in ventilation from the high latitudes. In the Southern Ocean, models differ particularly in the longitudinal distribution of the CFC uptake in the intermediate water, whereas the latitudinal distribution is mainly controlled by the subgrid-scale parameterization. Models with isopycnal diffusion and eddy-induced velocity parameterization produce more realistic intermediate water ventilation. Deep and bottom water ventilation also varies substantially between the models. Models coupled to a sea-ice model systematically provide more realistic AABW formation source region; however these same models also largely overestimate AABW ventilation if no specific parameterization of brine rejection during sea-ice formation is included. In the North Pacific Ocean, all models exhibit a systematic large underestimation of the CFC uptake in the thermocline of the subtropical gyre, while no systematic difference toward the observations is found in the subpolar gyre. In the North Atlantic Ocean, the CFC uptake is globally underestimated in subsurface. In the deep ocean, all but the adjoint model, failed to produce the two recently ventilated branches observed in the North Atlantic Deep Water (NADW). Furthermore, simulated transport in the Deep Western Boundary Current (DWBC) is too sluggish in all but the isopycnal model, where it is too rapid. (C) 2002 Elsevier Science Ltd. All rights reserved. [less ▲] Detailed reference viewed: 31 (1 ULg)A numerically efficient data analysis method with error map generation ; Beckers, Jean-Marie ; et al in Ocean Modelling (2000), 2 The variational inverse model (VIM) for data analysis was already shown to be statistically equivalent to objective analysis (OA) provided the covariance function for the OA and the VIM reproducing kernel ... [more ▼] The variational inverse model (VIM) for data analysis was already shown to be statistically equivalent to objective analysis (OA) provided the covariance function for the OA and the VIM reproducing kernel are identical. The VIM, however does not allow a direct derivation of the error field associated with the analysis. The purpose of the paper is to extend the one to one correspondance between the two analysis shemes by proposing a heuristic statistical error expression for the VIM. The numerical efficiency on analysis and error map generation of both methods is compared on quasi-synoptic and climatological data sets. It is shown that the VIM analysis and error map generation offers interesting numerical skills in both case studies. [less ▲] Detailed reference viewed: 28 (6 ULg)On some stability properties of the discretization of damped propagation of shallow-water inertia–gravity waves on the Arakawa B-grid Beckers, Jean-Marie in Ocean Modelling (1999), 1(2-4), 53-69 We investigate a problem mentioned by Deleersnijder and Campin (Deleersnijder, E., & Campin, J. -M. (1993). Ocean Modelling 97, 2), who looked at the problem of the discretization of inertia–gravity waves ... [more ▼] We investigate a problem mentioned by Deleersnijder and Campin (Deleersnijder, E., & Campin, J. -M. (1993). Ocean Modelling 97, 2), who looked at the problem of the discretization of inertia–gravity waves in the staggered B-grid. We generalize this study by adding diffusion. General stability conditions are found with the help of Miller's theorem, and the paradox found in Deleersnijder and Campin (Deleersnijder, E., & Campin, J. -M. (1993). Ocean Modelling 97, 2) is discussed. It is argued that it stems from inappropriate application of boundary conditions in conjunction with a Coriolis force treatment which could produce mechanical work. [less ▲] Detailed reference viewed: 14 (4 ULg) |
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