Ocean model

The ICON ocean model „ICOHOM'' is based on the primitive equations of the ocean. Relaxing the underlying assumptions of the primitive equations, namely the hydrostatic and the Boussinesq approximation is a topic of future research. In the primitive equation model the ocean state is represented by the variables horizontal velocity, surface elevation, density, potential temperature and salinity.

Dynamical Kernel

The dynamical kernel for a primitive equation ocean model with a free surface was implemented. The ocean state satisfies the primitive equations:

Momentum Conservation:

Free Surface Elevation:

Volume Conservation:

Tracer Conservation:

The model is completed by an equations-of-state . In the equations above denotes the vertically averaged velocity, is the ocean depth. The remaining notation is standard and self-explanatory. To pose a well-defined problem, the primitive equations have augmented by boundary conditions. For the description of these boundary conditions see chpt. 13 in P. Müller, The Equations of Oceanic Motion, Cambridge University Press, 2006.

Discretization of the Primitive Equations

We have developed the numerical discretization of the primitive equation model on the icosahedral ICON grid. The horizontal discretization follows the discretization of the ICON shallow-water model. In the vertical direction we use a z-coordinate system and a finite-difference approach.

After decomposing the pressure term into a surface pressure and a hydrostatic pressure component , the semi-discretized equations in space are derived by projecting the equations onto the icosahedral ICON grid. The resulting equations are

Normal and Tangential Velocity

Free Surface Elevation:

where

Tracer Conservation – Temperature

Tracer Conservation – Salinity

In the discretized equations the supscripts „e“ and „c“ denote edge- and cell-based variables. The hydrostatic pressure is given by where denotes the depth of the vertical layer „k“.

The ocean state is advanced in time by a semi-implicit two- or three timelevel scheme. The algorithm is independent from the free-surface wave speed. Mass is conserved locally and globally. The tracer transport uses a finite-volume method and has the property of consistency with continuity. The current implementation of the transport algorithm is of low order, the extension to higher-order via flux-limiters is ongoing work.

Not yet developed is the capability of local grid refinement. One application of an increased local grid resolution is the improved representation of coastlines and of lateral boundary process. A second application is to „zoom'' into areas of interests, e.g. sinking regions in the northern latitudes.

Physical Parametrizations

Physical parametrizations will be developed along the lines of the MPI-M's current ocean general circulation model MPI-OM. The atmospheric forcing is derived from the Large-Yeager dataset by interpolation on the ICON grid with the SCRIP software. Regarding the forcing we are following the recommendations of the CORE project (Common ocean-ice reference experiments, see Griffies et.el. Ocean Modelling, (in press).

The external forcing is transfered to the model via „bulk formulae'' which will be developed following the MPI-OM implementation.

Bathymetry data is derived by interpolation of the ETOPO dataset onto the ICON grid using the Climate Data Operators (CDO).

The implementation of the whole package of physical parametrizations including vertical mixing, Gent-McWilliams etc. has started recently and constitutes the next big milestone of the ICON ocean development.

Sea-Ice Model

The sea-ice component of the ICON ocean model will be developed in cooperation with the Max-Planck Junior research group 'Sea-Ice in the Earth System'.

Data Assimilation - Adjoint Modeling

The ICON ocean model will be supplemented with a data assimilation capability (4D-Var). The adjoint ICON ocean model will be generated by an Automatic Differentiation tool. This „adjoint compiler'' will be a component of the ocean model. A new differentiation-enabled Fortran 95 compiler is currently developed in collaboration with the RWTH Aachen. This compiler was sucessfully applied to generate the adjoint ICON shallow-water model. A second application of adjoint modeling apart from Data Assimilation is the analysis of numerical errors. For more details on this see section Error Estimation.

Turbulence Model

We are currently investigating a new non-dissipative turbulence model as an alternative to Reynolds averaging, the so-called Lagrangian-Averaged models. We are collaborating with the Institut for Applied Mathematics of the University Postdam. This work is funded by the DFG-priority programm SPP 1276. See the section Shallow-Water LANS-α.

(pko, 11.10.2008)