The 'Ribbon' Model Concept
Numerical modelling of the global ocean currently requires models specifically deigned for the task at hand. These models contain the computational physics and software engineering necessary to resolve the global ocean’s dominant large scale physics without compromising run times. While these models may be eddy resolving in the ocean basins, on coastal margins their accuracy deteriorates due to their inability to resolve the dominant scales of motion. It is in these coastal zones that accurate numerical prediction is often required to address numerous coastal issues. In the past global models have been unsuitable for high resolution limited area modelling of coastal domains, however, recently there has been a convergence of global and regional models to the extent that some global models (e.g. MOM4p1) are capable of accurately representing limited area coastal domains. This is largely due to the inclusion of adequate turbulence closure and open boundary algorithms required to characterise coastal processes.
Although global models contain the computational physics necessary for coastal modelling, often their I/O, choice of grid stencil, curvilinear capability and treatment of land cells makes them cumbersome or inefficient to use in this capacity. It is fair to say that most regional and global models contain comparable computational physics, in terms of higher order advection schemes, sophisticated turbulence closure and horizontal mixing, vertical discretization, time stepping schemes and methods to increase run-times (e.g. implicit schemes, Adams-Bashforth approaches etc). The strengths of global models lie in their ability to efficiently produce solutions for long simulations on grids containing of the order of 1 million cells. This is accomplished via vector or massive distributed processing techniques, and quite often the whole model design is purpose built around the philosophy of speed. Global applications typically take a great deal of time to set up correctly, and require many months of continuous running to generate solutions for many decades to centuries. Being a global domain, which does not change, these models only need to be set up once. There is often not the opportunity to have a large turnover of runs, consequently these models are typically validated by ensuring the general circulation patterns and mass transports are correct, total heat/salt/mass content does not drift over time and mean mixed layers and T/S solutions are comparable to climatology. Ensuring that eta, T or S compares accurately with measured data is generally not a priority, and these models typically perform better in some geographic areas than in others.
Regional models on the other hand are typically required to be calibrated to measured data. This involves many simulations to be performed, which typically take a very short time to complete in comparison to global models due to their smaller grids and shorter simulation lengths. Regional modelling typically involves a large number of simulations to be performed with a rapid turn-over of simulations. Being regional by nature, many grids covering different geographic regions and spatial extents are generated to resolve the desired ocean physics, often with higher resolutions grids nested inside coarser ones. These requirements dictate that regional models must be easy and fast to set up, typically using unformatted input files with grid and time-step independent forcing (i.e. no data pre-processing). Also they must be efficient on single processor, or on small distributed systems, since often users do not have access to large supercomputers, the simulation turnover and model initiation / suspension is frequent (i.e. lots of stopping and starting models to achieve a stable, calibrated run), multiple instances of the model are typically invoked and using massively parallel processing on smaller grids does not result in massive increases in performance. General curvilinear capability is an advantage to resolve coastal domains. This requires more advanced I/O for visualisation and nesting. Model output must contain enough spatial information so that dedicated visualisation packages are able to display variables at the correct geographic location. Model code must contain interpolation routines so that input forcing data, arranged on any geographic projection, can be efficiently interpolated onto the irregular curvilinear grid. The Arakawa C grid is generally more suited to coastal applications, being able to better resolve short-waves and only requiring 1 cell to resolve a channel. The diagnostics supported by the model are generally different for global and coastal applications
These differing requirements between global and regional models mean that, although global models may be capable of producing regional solutions, in practice their applicability may be compromised. However, the regional approach is far from ideal, as unlimited model applications need to be produced to piece together an understanding of the oceanography of one’s continental margins. The limited areas of these models also means that open boundaries are present, and the treatment of these open boundaries are a notorious source of error and instability in regional models. Any cross-shelf open boundaries are particularly troublesome, since the coast acts as a waveguide and barrier to flow so that the model interior must respond to oceanic flow and wave forcing on the upstream boundary, and transmit these phenomena without reflection on the downstream. This must be achieved without over or under-specification. The inclusion of cross-shelf OBC’s often compromises the model’s accuracy, and often a model only behaves adequately some distance away from these boundaries, prompting the use of a much larger domain than is desired. Taking advantage of a global model’s strengths can overcome these issues, to provide long term, high resolution solutions on the entire coastal margins of a continent. High resolution can be achieved by using a similar number of cells as a global application, and run-times can be acceptable using massive parallel processing. Regional models typically do not support the infrastructure for these massively parallel simulations. The model only needs to be set up once, and then can be used to create a simulation of decadal length. It may be possible to use the cyclic capability of these models, as is done on a sphere, to eliminate cross-shelf boundaries altogether. This is easily possible, for example, around the coast of Australia, and the description of such a ‘ribbon’ model and associated output is described here.
The model anticipted to be used was MOM4p1, however, owing to the difficulty in procuring a large number of processors for long periods of time, the model is currenty run using SHOC.
'Ribbon' Model Grid
The basic ribbon model grid comprises a cyclic polar grid with branches to account for Tasmania, the South Australian Gulfs, Gulf of Carpenteria and King Sound (Figure 1). The grid is 2000 x 500 cells, resulting in 1 million surface cells and 50 layers in the vertical. Vertical resolution is 1 m at the surface, and increases exponentially with depth to a constant resolution of 200 m. The minimum depth at the coast is 4 m. The number of 2D wet cells is ~180,000, or ~18% of the grid. This is due to a large amont of 'dead' space created from the 4 braches. The number of 3D wet cells is ~4 million, with a large number of dry cells existing below the sea bed. A picture of the grid domain and bathymetry is presented in Figure 2.
Figure 1. Curvilinear grid representation.
Figure 2. Model grid and bathymetry.
The offshore extent of the grid may be tailored to user's ultimate requirements of the ribbon model; i.e. if the purpose of the model is for characterisation of shelf / slope processes, then the offshore extent would likely be further than displayed in Figure 2. If the purpose is to achive high resolution in the coastal zone to that the model can be used as a nesting vehicle for separate high resolution local models, then an offshore extent to the shelf edge is appropritae. The ribbon model depicted in Figure 2 favours such an approach.