1995/6 Research Journal
Concurrent Computation Group
I. C. Wolton
OCCAM is a NERC Community Research Project whose primary aim is to develop improved global ocean computer models suitable for research into climate change. This is being achieved by:
The resolution required for realistic calculation of heat transport in the ocean is suprisingly high. Whereas the ocean basins are 5000 km or more across, major currents such as the Gulf Stream may be less than 50 km in width. Similarly meso-scale eddies (which correspond to atmospheric weather systems and are important for mixing heat within the ocean) are only 100-200 km across. As a consequence a horizontal resolution of 30km or less is required for models such as OCCAM, resulting in around a million gridpoints in the horizontal. The basic model has two major components:
Figure 1: Sea surface temperature distribution after 6 months simulation
The presence of sea ice affects the behaviour of the oceans and its interaction with the atmosphere in several ways. Ice is an effective insulator and so heat exchanges are substantially reduced by thick ice. Ice drift velocities are small but the transports of heat and fresh water associated with them are significant because of the high latent heat and the marked contrast between the salinity of sea water and the salt content of sea ice. The salt ejected from freezing sea water leads to the formation of very saline, cold and hence dense water masses which drive major convection systems throughout the world's oceans.
The modelling of these effects is complicated by the fact that sea ice is substantially non-uniform in both thickness and distribution and does not behave as a passive tracer drifting with the wind or ocean current. Much of this variability is due to the strongly non-linear behaviour of sea ice with respect to internal stress in the ice field. Local compression leads to a thickening of the ice through ridge formation which increases its strength with respect to further compression and to shear but offers little resistance to subsequent divergence caused by changing external stresses. As a consequence, leads of open water are formed which allow much greater heat exchange than the surrounding ice pack. This heat exchange causes rapid local formation or melting of ice according to conditions. Leads constantly open and close so that thin ice formed in leads is added to the main ice pack during subsequent compressions and forms a primary source of ice mass.
Until recently, large scale ocean climate models have used highly simplified ice models, usually neglecting ice drift, so that the seasonal ice cycle does not transport heat from one area to another. In reality, ice usually forms in one area, drifts, and melts elsewhere, forming an effective heat engine between ocean basins. To calculate this drift correctly the internal ice dynamics must be represented.
The essential elements required to characterize sea ice dynamics are[1]:
The mass balance must take into account the formation and melting of ice which are governed by thermodynamic processes. These include: conductive and radiative heat transfers from ocean and atmosphere; the presence of overlaying snow; heat conduction through snow and ice layers; mixing with the top layer of the ocean and the formation of reservoirs of latent heat by brine pools within the ice due to absorption of penetrating radiation.
The starting point was a code based on the thermodynamic model of Semtner[3], which additionally assumes that ice drifts passively under the influence of the wind and to a lesser extent the ocean current. This has been updated to be consistent with the data structures used by the parallel OCCAM code.
The next step is to replace the assumption of free ice drift with a rheology and a numerical scheme that models the strongly non-linear internal stress-strain relationship within sea ice. The visco-plastic rheology proposed by Hibler[2] will be used and the numerical scheme adopted by Oberhuber[4] for use with a rather different ocean model will be adapted to OCCAM. In contrast to the explicit schemes used elsewhere in OCCAM, a semi-implicit scheme is essential to enable sensible time steps. A predictor-corrector sequence solves first for ice-thickness, area-coverage and other scalars. This involves iterative line relaxation in the North-South direction. with a direct solution along lines of latitude using a tridiagonal solver, A similar technique is then used to determine the ice velocity, but in this case a block tridiagonal solution is needed to solve the coupled equations for the velocity components. The use of line relaxation on lines of latitude enables a simpler approach to load balancing as ice distributions correlate strongly with latitude.
The parallelisation strategy is partially determined by the existing domain decomposition technique used by OCCAM. However, some further sophistication of the load balancing strategy will be necessary to take account of the extra workload on processors which have to call sea ice routines. The remaining design decision is the implemention of efficient parallel tridiagonal and block tridiagonal solvers. An obvious approach is to use parallel cyclic reduction, but alternative candidates such as the parallel diagonal dominant algorithm[5] and parallel QR factorisation[6] are being investigated.
One of the current problems with modeling the growth and decay of sea ice is the calculation of fluxes of heat and freshwater between the atmosphere and the oceans. At present the atmospheric parameters which partially determine these fluxes are specified as input to the model. This prescriptive approach does not allow for interaction between the atmosphere and ocean and so a long term goal for climate studies is a coupled atmosphere-ocean model. Coupled models already exist but in general either the ocean or the atmospheric model are simplified low resolution models. A comprehensive high resolution coupled model would require much greater computational resources than those currently available, but advances in high performance computing make such models feasible in the foreseeable future. An analysis of the computational issues involved is thus a natural follow on to the present work.
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Copyright (c) 1996 University of Southampton, June 1996.