A new computational framework for range of scale ocean modelling based on adapting unstructured meshes

Matthew Piggott (m.d.piggott@imperial.ac.uk, http://amcg.ese.ic.ac.uk)

Department of Earth Science and Engineering

Imperial College London

South Kensington Campus

SW7 2AZ

Over the past decade there has been growing interest in the use of unstructured meshes in ocean modelling. Moving from structured to unstructured meshes offers many potential benefits for this application area. In particular the representation of any interaction between a range of spatial and temporal scales, and the formation and evolution of localised features in a priori unknown locations, can benefit hugely from their use. For example, they represent the ideal framework to simulate the coupling between the basin and global scale right down to the coastal, estuarine, and physical process scales. This can be achieved without resorting to the often unsatisfactory approach of grid nesting due to the fact that smooth variations in mesh resolution are possible, and this resolution can be altered in an adaptive manner. When utilising adaptive algorithms models are able to automatically allocate computational resources in an optimal and dynamic manner, as dictated by evolving solution fields or estimates of model error. In addition, an accurate and efficient representation of the extremely complex geometries typical in oceanographic applications is straightforward with an unstructured mesh approach, as are the use of realistic boundary conditions and perhaps the preferential treatment of regions of socio-economic or scientific importance.

In this presentation we shall describe our experiences building a three-dimensional nonhydrostatic ocean model using unstructured adaptive mesh techniques and finite elements. Of particular importance and focus here are mesh anisotropy, load-balanced parallelisation, and techniques for stably and accurately describing model states close to hydrostatic and geostrophic balance on arbitrary irregular meshes. Also, the resulting adaptive mesh model is reliant on having high quality methods for describing the regions of space-time where increased (and decreased) resolution should be used. A variety of error measures based on explicit information (yielding anisotropic information) and implicit information (yielding sensitivity information) will be described. We will also touch upon efforts underway to include arbitrary mesh movement, allowing fronts and eddies to be tracked in a Lagrangian like manner for example, and also an analogue of isopycnic (density level following) or hybrid vertical coordinate behaviour to naturally emerge. Current work on the application and validation of these new techniques to a range of complex oceanographic problems will also be presented.

Numerical developments associated with this application area can and are being reapplied to a variety of other engineering and geophysical problems. In particular the same modelling framework is being used to simulate the turbulent dispersal of pollutants in urban environments. It is also being used to examine the fluid-solid interaction in flood defence structures, and to examine crater formation following meteor impacts.

Numerical studies of tidally forced internal waves and mixing at a sill

Jarle Berntsen1, Jiuxing Xing2 and Alan M. Davies2

1. Department of Mathematics, University of Bergen, Norway

2. Proudman Oceanographic Laboratory, University of Liverpool

A non-hydrostatic terrain following model in cross sectional form is applied to study generation, propagation, and breaking of tidally forced internal waves near a sill in an idealized fjord. On inflow internal waves are generated behind the sill, and they propagate from the sill. When the tide reverses, the waves propagates towards the sill and they break as they meet the sill. In this system there is a transfer of energy from the barotropic tide to internal waves and then to irreversible mixing. The length scales involved ranges from the scale of the forced tide and down to very small processes, probably less than 1m, as the waves break making it very difficult to resolve all relevant length scales with a numerical model. The sensitivity of numerical results to the grid resolution is investigated in two sets of experiments. In one set the eddy viscosities are held constant as the grid is refined. In another set the eddy viscosities are made grid dependent allowing more smaller scale processes to appear as the grid is refined.

High-order well-balanced finite-volume schemes for barotrophic flows. Development and numerical comparisons

Normann Prankratz

Institut für Geometrie und praktische Mathematik, RWTH Aachen

In this talk we compare a classical finite difference and a high order finite volume scheme for barostrophic ocean flows. We study various outflow and inflow boundary conditions as well as their numerical implementation. Main aspects of our analysis are accurracy, stability, and physical relevance.Central test-case is the Ormen Lange oilfield in the Norwegian shelf. Our results strongly confirm the development of mesoscale eddies caused by instability of the the Gulfstream.

Modeling bottom shear stress for transient wave events

Tomas Torsvik

Department of Mathematics, University of Bergen, Norway

The shear stress in the bottom boundary layer induced by waves and currents is important for several physical processes.

Generation of turbulence inside the boundary layer contributes to energy dissipation in the mean flow, which is important from a fluid dynamics point of view. From a morphological point of view, shear stress can be related to the probability of sediment suspension and to bedload sediment transport fluxes. An analytical solution can be found for the bottom boundary layer problem with the no-slip condition for the bottom. The interaction between the mean flow and the bottom shear stress is established by matching the velocities in boundary layer with the bottom boundary condition for the core region. Comparing numerical simulations with data from experiments show that the method provides accurate results for the phase and the magnitude of the shear stress. The direct calculation of the bottom shear stress is computationally demanding because the formulation includes a convolution integral in time. Fortunately, the value of the integral is dominated by the most recent events, which means that a good estimate can be found by considering only the few last time steps at any given time.

Secondary circulation in a 90 degree bend.

Torunn S. Davidsen1, Guttorm Alendal1 and Jarle Berntsen2

1. Bergen Center for Computational Science, University of Bergen, Norway

2. Department of Mathematics, University of Bergen, Norway

Secondary circulation in a curved open channel has been studied by numerical simulations utilizing the MIT general circulation model. As water flows through a bend, a helical motion develops, where the water in the upper part of the water column moves toward the outer bank, while the water deeper down moves toward the inner bank. In addition to being essential to the meandering of rivers, understanding of this curvature-induced secondary circulation is useful for the planning of operations in rivers and near-coast ocean areas and for the design of constructions in such locations. Several papers describe observed curvature effects in rivers and in oceanic flows. In the current work, an idealized process study has been performed, where the effect of channel depth and density stratification has been investigated. Such parameter studies are important to gain insight in the dynamics involved. In more complex and realistic situations, i.e real topography and hydrography, such insight is harder to achieve. One major result is that the dependence on channel depth for the secondary circulation strength changes on each side of a critical value. For channel depths smaller than this critical value, the secondary circulation strength increases with channel depth, in agreement with previous results. However, for channels deeper than this critical value, the secondary circulation decreases with channel depth. This change is connected to a qualitative change in the secondary circulation. Further results will be presented at the meeting.

Potential impacts from CO2 handling on the oceanic environment

Guttorm Alendal

Computational Mathematics Unit

Bergen Center for Computational Science

UNIFOB/University of Bergen

There is an increasing focus on CO2 handling in connection with the new gas power plants that are under construction in Norway. However, CO2 handling is not something the politicians can decide to implement.

Before the concept can be implemented in large scale there are still some technological bottlenecks that will need to be solved. And, there are still uncertainties on what potential environmental consequences industrial scale storage of CO2 might impose. In the ocean there are high uncertainties on both acute and chronic impacts on the marine biota. To be able to address these issues a number of different transport and dissolution studies on CO2 behavior in oceanic waters will have to be performed. Especially processes in the interface between sea water and the benthic sediments will have to addressed. I will try to give an overview of necessary studies, and outline some ongoing and planned activities at the University of Bergen.

Model simulations of tidal currents in Tjeldsundet and Ramsundet, northern Norway.

K. Hjelmervik1, A. Ommundsen2 and B. Gjevik1

1. Department of Mathematics, University of Oslo, Norway

2. Norwegian Defence Research Establishment, Kjeller, Norway

The tidal currents in Tjeldsundet and Ramsundet, two important ship lanes in Ofoten, are simulated by a fully nonlinear ocean model with horizontal grid resolution of 25-50 meters. The depth mean current velocitiy is calculated in every grid for the four most dominant tidal components (M2, S2, N2 and K1). To show the results, the current fields are plotted for the areas with strongest currents; Ballstadstraumen, Sandtorgstraumen and Steinlandsstraumen in Tjeldsunet, and Spannbogstraumen in Ramsundet. The current fields show great variations in current strength, intensivated jets and eddy structures. Some of the eddies are also documented by observations. The results from the simulations have also been compared to fieldmeasurements of water level and currents.

For making the results available for operational use the simulated current fields are implemented in the military chart system MARIA and also distributed by a Web Map Server (METOC WMS).

Model simulations of storm surge currents in Tjeldsundet and Ramsundet, northern Norway.

Birgit Kjoss Lynge1, K. Hjelmervik2 and B. Gjevik2

1. Statens Kartverk Sjø

2. Department of Mathematics, University of Oslo, Norway

During storm surge events sea level differences up to 90 cm are observed between Ofotfjorden and Vågsfjorden respectively at the southern and northern entrances to Tjeldsundet. The difference in sea level will drive strong currents through both Tjeldsundet and Ramsundet.

In order to examine the variability and spatial structure of these current fields simulations have been performed with a depth integrated numerical model with spatial grid resolution 50-100 m. The interaction between the storm surge current and the tide is also examined.

On the use of time scale methods for diagnosing transport of passive tracers in ocean models

Steinar Orre

Nansen Environmental and Remote Sensing Center

A recently developed tracer-based method for calculating the age of tracers in numerical ocean models is advocated. A more ÒpragmaticÓ method is presented as well, where the age is defined as Òthe time lag maximizing the correlation between the discharge from a tracer source and the concentration at a given location downstream of the sourceÓ. While this is without doubt a useful measure for environmental assessments, it is only representative for the age if diffusion is negligible, i.e. pure bulk advection. This feature is demonstrated by simulating idealized tracers released to the North-East Atlantic. In addition, the evolution of the anthropogenic radionuclide Technetium-99 has been simulated. The main source of this soluble radionuclide is the reprocessing plants at Sellafield in the Irish Sea and La Hague on the French coast in the English Channel. The radioactive contaminants follow the general ocean circulation in the area, and are eventually transported northwards along the Norwegian coast heading towards the Arctic Ocean. Comparison with observational time series from two stations along the coast of Norway shows that the model fairly realistically captures both the amplitude and the temporal trend of Technetium-99 from Sellafield and La Hague. The age of tracers from Sellafield and La Hague at the island Hilles¿y on the northern coast of Norway is found to be in the range 5-8 years and 4-6 years, respectively.

The influence of non-hydrostatic pressure and grid resolution on wind forced propagating internal fronts.

Jon Bergh

BCCS/CMU, University of Bergen, Norway

Most numerical ocean models today assume a hydrostatic pressure. This may be a valid approximation in many large scale studies with coarse grid resolution.

However, with higher spatial resolution

non-hydrostatic pressure effects will become important.

In this work results from a two-dimensional cross section version of a

non-hydrostatic $\sigma$-coordinate ocean model is compared to an analytical solution and to results from a hydrostatic ocean model.

A two layer ocean with constant depth, closed boundaries and without rotational effects are forced at the surface with a 12 hours sudden wind-impulse.

The one-way directed wind drag creates downwelling at the downwind end of the basin and upwelling at the opposite side. When the wind-forcing decrease the disturbance of the interface creates two internal fronts propagating away from the opposite boundaries. There is a strengthening of the density gradients at the fronts in connection with enhanced vertical velocities. In this situation we can expect non-hydrostatic effects and the horizontal and the vertical resolution to be crucial for the shape and behavior of the front.

The analytical linear two layer solution for this theoretical case shows first mode surface and internal seiches characterized by the densities and heights of the two layers.

The non-linear ocean model resolve the large scale physics. The shape and the speed of the fronts are compared to the analytical solution. At the stratified interface non-linear and non-hydrostatic effects create instabilities resulting in erosion and mixing of the interface.

Dynamics along the Norwegian continental slope. Description of special events and modelling approach

Jan-Petter Mathisen1, Jarle Berntsen2, Gunnar Furnes2, Gunnar Mørk1

1. Fugro OCEANOR

2. Department of Mathematics, University of Bergen, Norway

3. Norsk Hydro

Since 1998 extensive measurements campaigns have been carried out along the shelf slope and the deep water in the Norwegian Sea and the in the Ormen Lange area as a part of the Norwegian Deepwater Programme and the Ormen Lange project. These measurements have revealed that the dynamic in this area is rather complex caused by several processes such as slope jet, eddies, internal waves etc. These processes generate large currents with rapid variations both in the water column and near the bottom, which influence both the design and operations.

In this presentation we will give a general presentation of the dynamics on the slope, with emphasis on events at Ormen Lange with periods of 45 minutes. These events were recorded during a one year fine scale measurement campaign in 2005-2006.

An overview over some modelling activities focusing on the Ormen Lange area will be given. Some insight in the processes involved has been gained through these numerical exercises. However, it is still very difficult to capture with a numerical model all the relevant length and time scales involved. This will be further discussed in the presentation. Results from a model exercise focusing on the oscillating events with periods of 45 min will be presented.

Studying the pathways and modifications of Subantarctic Mode Water in the South Atlantic Ocean, using the HYbrid Coordinate Ocean Model and in situ measurements from NEMO subsurface drifting floats.

Gisle Nondal1, 2, Richard G. J. Bellerby3, 1, Peter M. Haugan1, 3, Karen M. Assmann3, Laurent Bertino2, Annette Samuelsen2 and Ola M. Johannessen1, 2.

1Geophysical Institute at the University of Bergen, Allégaten 70, 5007 Bergen, Norway.

2Mohn-Sverdrup Center/Nansen Center, Thormøhlensgate 47, N-5006, Bergen, Norway.

3Bjerknes Centre for Climate Research, University of Bergen, Allégaten 50, 5007 Bergen, Norway.

Subantarctic Mode Water (SAMW) is one of the most abundant water masses in the world oceans, supplying large amounts of nutrients to the southern hemisphere as well as the North Atlantic Ocean. SAMW plays an important role in ventilating the thermocline, and it has been shown that this water mass is important in detecting anthropogenic climate change. Mode water simulation is a good target for numerical models, particularly those including a mixed layer. In order to model mode waters and their variations accurately, various processes must be correctly simulated, including: plausible separation of western boundary currents and their extensions, frontal systems, mixed-layer processes given proper surface forcing, eddy activity in the formation area, advection/ventilation/subduction processes and isopycnal/diapycnal mixing.

The model tool used is the HYbrid Coordinate Ocean Model (HYCOM), and this model has been set up for various regions at the Nansen Center. Preliminary results from a version of HYCOM set up for the Indian Ocean including Antarctica (INDIA) as well as results from the HYCOM model TOPAZ2 will be shown. The INDIA model has been used, in concert with field data, to determine the optimum site for a recent deployment of NEMO drifters which in turn will be used to further optimize the model.

Decadal changes in ocean chlorophyll – Caused by variations in penetration depths of oceanic convection in winter ?

Henning Wehde

Norwegian Institute for Water Research (NIVA)

During the last decades a decrease of ocean chlorophyll was observed in the northern high latitudes by comparing data from the Coastal Zone Color Scanner (CZCS, 1979-86) with Sea-viewing Wide Field-of-view Sensor (SeaWiFS, 1997-2000) records (Gregg and Conkrght, 2002).

Simultaneously a decrease of penetration depths of oceanic convection in Winter was observed. Based on our hypothesis on the strong relationship between oceanic convection and primary production (Wehde 1996, Backhaus et al., 1999, 2003, Wehde 2001), i.e. the support of production by oceanic convection in winter, it is postulated, that it is the decrease of the strength of oceanic convection which causes the decrease in ocean chlorophyll.

In support of this a coupled phytoplankton convection model and a phytoplankton mixed layer model were developed and applied for the northern North Atlantic. The model and a statistical analysis of model results will be presented and the model results will be compared with the records from the CZCS and the SeaWiFS Sensors.

References:

Gregg, W. W., and M. E. Conkright, (2002): Decadal changes in global ocean chlorophyll. Geophysical Research Letters, Vol. 29, No. 15, 10.1029/2002GL014689.

Wehde, H., (1996): Einfluss der Konvekton auf die Phytoplanktonentwicklung. Diploma thesis. University of Hamburg.

Wehde, H., (2001): Phytokonvektion im offenen Ozean; Feldexperimente und numerische Prozessstudien. ZMK Hamburg, Reihe B: 38

Backhaus, J. O., H. Wehde, E. N. Hegseth, and J. Kämpf, (1999): ‘Phyto-convection’- on the role of oceanic convection in primary production. Mar Ecol Prog Ser, 189: 77-92

Backhaus, J. O., E. N. Hegseth, , H. Wehde, X. Irigoien, K. Hatten and K. Logemann, (2003): Convection and primary production in winter. Mar Ecol Prog Ser, 251: 1-14

The Skagerrak circulation's sensitivity to freshwater discharges.

Lars Petter Røed1,2 and Jon Albretsen2

1. Norwegian Meteorological Institute (met.no)

2. Department of Geosciences Meteorology and Oceanography (MetOs), University of Oslo

We assess the performance of a marginally eddy-resolving numerical ocean model in simulating the pattern and variability of the hydrography in the Skagerrak/northern North Sea area. The model is a version of the widely used Princeton Ocean Model. Results from a series of five multi-year simulations of the mesoscale response are described and analyzed both qualitatively and quantitatively. The simulations differ in their representation of the lateral freshwater supply, i.e., the Baltic outflow and the major rivers. We find that in general the model faithfully reproduces many of the observed large scale hydrographic features including their patterns and their variance. Not surprisingly we find that the Baltic outflow is by far the most significant freshwater source. We also find that the large scale cyclonic circulation and the location of fronts are robust features of the circulation. We furthermore demonstrate that a realistic representation of the freshwater supply is not a necessary requirement in modeling the mesoscale structures using a recently developed energy diagnostic scheme to analyze the results. This is somewhat surprising since a change in the representation of the freshwater input significantly impacts the actual values of the hydrography. Finally, we find that a correct representation of the hydrography in the Norwegian Coastal Current correlates with a worsening of the hydrography in the inflowing water along the Danish Coast. A further exploration of the impact of the lateral open boundary forcing, e.g., the input of Atlantic water, is therefore needed.

Nedskalering av klimascenario for Nordsjøen

Bjørn Ådlandsvik

Havforskningsinstitituttet

En regional havsirkulasjonsmodell (ROMS) er brukt til å nedskalere resultater fra den globalt koblete atmosfære-hav modellen BCM til Nordsjøen. Dette er gjort både for 1900-tallet (IPCC 20C3M) og for framtidig klima (IPCC A1B). Resultatene fra BCM og nedskaleringen for 1900-tallet er sammenlignet med observasjoner. Nedskaleringen øker verdien av resultatene ved å få fram regionale detaljer, riktigere Atlantisk innstrømning og vintertemperatur. Det nedskalerte framtidige klimascenariet for perioden 2070-2099 viser en oppvarming, sterkest om vinteren, og en økning i den Atlantiske innstrømningen.

SOR versus Multigrid for time dependent non hydrostatic model problems.

Helge Avlesen

Bergen Center for Computational Science, University of Bergen, Norway

Nonhydrostatic ocean models include one or more elliptic equations that are much more expensive computationally to solve than the traditional explicit methods ocean modellers are used to. In time dependent problems this easily becomes an issue. We have studied the performance of various iterative methods for a 2d vertical shelf model and will present some preliminary results.

Three dimensional dissolution and spreading of CO2 from a CO2 lake

modelled using an advanced vertical turbulence mixing scheme

Lars Inge Enstad

Bergen Center for Computational Science, University of Bergen, Norway

If liquid CO2 is stored as a dense "lake" on the deep ocean floor, it is expected to dissolve in seawater. A similar situation occurs when CO2 is dissolved from a saturated benthic boundary layer caused by a potential leak from the sea-floor. Ocean currents and turbulence may increase the net rate of release by several orders of magnitude compared to molecular diffusion. However, density stratification in the seawater created by dissolved CO2 will tend to reduce vertical mixing. This scenario has previously been modelled using two dimensional domain (Fer \& Haugan (2003) and Haugan \& Alendal (2005)). There has also been a three dimensional study (Enstad et al. (2006)) using the MIT general circulation model (http://mitgcm.org).

Recently this model has been extended with a new more sophisticated vertical mixing scheme. This is done by coupling the MITgcm model with the General Ocean Turbulence Model (GOTM, http://gotm.net/).The coupling of the two models has been verified using idealised flow cases such as Couette flow, channel flow and the Kato-Phillips experiment.

The study shows that the lateral direction is important since the dense water tends to move in lateral directions. The dissolution rates are found to be, to the order of magnitude, similar to results for comparable cases from previous 2D studies. The volume of water with a specific pH reduction will, after a transient period, become constant in the vicinity of the lake. Thevertical turbulence model take into account density effects on thevertical mixing and hence should give a more realistic representation of the CO2 plume than constant eddy diffusivity models.

Use of hydrodynamics for decision making (Henrik Rye).

Henrik Rye

SINTEF Materials and Chemistry

SINTEF is presently developing a (set of) models to be applied by the oil industry for reducing impacts caused by discharges to the sea. A set of models is developed to include simulation of impacts in the water column and in the sediment. The method used to calculate the actual (potential) impact is outlined (PEC/PNEC approach).

Modelling the physical and biological responses of a stratified fjord to a submerged freshwater discharge

Ingrid Ellingsen, Thomas McClimans, Dag Slagstad

SINTEF Fisheries and Aquaculture, N-7465 Trondheim, Norway

Artificial upwelling is used to improve the environmental conditions for the growth of non-toxic algae in stratified fjords. A diffusor plate was mounted above a submerged discharge of freshwater from a hydropower plant to enhance the upwelling of nutrients. Laboratory tests showed that the entrainment to the buoyant plume could be enhanced by a factor of up to three using the plate. The increased entrainment of seawater to the buoyant plume led to a deeper intrusion of the discharge into the compensation current and a longer residence time in the local fjord arm. The manipulation led to a reduction of the ambient stratification and an increased supply of nutrient-rich seawater to the euphotic zone. An ocean-coastal model based on the primitive equations confirms this. A biological model was coupled to the hydrodynamic model and used to see how the manipulation affected algae growth and composition. The field of influence from the discharge extended several kilometers into the fjord and gave a significant increase in the primary production of non-toxic diatoms.

Incremental remapping for ocean modelling.

Mats Bentsen.

Nansen Environmental and Remote Sensing Center, Bergen, Norway.

Incremental remapping was recently introduced as a transport/advection algorithm. The method solves the transport equations in conservation form and, in the context of layered ocean modelling, it ensures monotonicity of layer thickness for a non-divergent velocity field. Monotonicity is ensured for associated tracers for any velocity field that does not violate the CFL condition of the method. Adding tracers leads to a small incremental computational cost, since the method is geometrical in nature and many computations can be reused. These features make incremental remapping interesting for layered ocean modelling, especially taking into account the increasing interest in earth system modelling where the ocean component must deal with a large number of tracers. The traditional incremental remapping algorithm is naturally suited for B-grid models. Methods for implementing incremental remapping for C-grid models will be discussed. Solving transport equations for temperature and salinity within a layer with some reference density, typically introduces numerical density errors. A method for reducing this error using incremental remapping will be discussed. The Miami Isopycnic Coordinate Ocean Model has been modified so that incremental remapping could be implemented. Results from this effort will be shown.