The top-end, climate general circulation models include what are believed to be the most important (physical) processes in the coupled ocean-atmosphere-sea ice system. These models allow us to make a 'best estimate' of what future climate will be like for a given choice of future anthropogenic changes in greenhouse gas and aerosol concentrations. It is natural to assume that models improve if more sophisticated schemes are used, or if their resolution is increased. To what extent that translates into more reliable projections of climate change is another matter, but there is no doubt that improved model formulation has led to the ability of global climate models to simulate some of the large changes observed in the oceans during the 20th century (e.g. Barnett et al. 2001; Gregory et al. 2004; Wu et al. 2004).
Clearly models need sufficient resolution to resolve geometry (such as the overflow sills from the Nordic Seas (e.g. Boning et al. 1996; Roberts and Wood 1997), important ocean bathymetry (e.g. Banks 2000) and boundary currents and other narrow currents (Oka and Hasumi 2006). The need in climate studies for eddy-resolving ocean resolution has not been established, but little work has been done in this field. Regional eddy-resolving ocean models are becoming more widely used (e.g. Smith et al. 2000), often to be employed in short-range ocean forecasting (Johannessen et al. 2006), rather than lengthy climate runs. Comparing the behaviour of a global eddy-permitting (1/3° x 1/3°) and a non-eddying (5/4° x 5/4°) version of the same coupled model to rising CO2 concentrations, Roberts et al. (2004) show that the response of the AMOC and its heat transport to global warming depend on this particular increase in model resolution. Only one study with a global, eddy-resolving ocean model has been reported to date, integrated for 13 years in stand-alone mode (Maltrud and McClean 2005), with promising results in terms of eddy statistics in the model compared to altimeter observations. Variable or perhaps adaptive grids (i.e. finer resolution where and when it is needed, Pain et al. 2005) might provide computationally manageable solutions for high-resolution climate modelling, but are still under development.
Since, as already mentioned, the future development of climate models is liable to involve a large choice of plausible numerical schemes and an equally wide range of observational constraints, the concept of working towards a single best model is not particularly meaningful. It is more helpful to think of a range of models, that spans the possible and likely behaviour of the real climate system (Allen and Ingram 2002). Several groups have already started, through 'perturbed-physics' experiments, to quantify how the uncertainty in model formulation creates uncertainty in climate projections (e.g. Murphy et al. 2004, Schneider von Daimling et al. 2006). But two questions remain.
First, how can we be sure that we have adequately employed 'the full range of models that spans the possible and likely behaviour of the real climate system'? Figure 12.6, just described, provides a clear example. Although, from a large ensemble of model experiments, Fig. 12.6a offered an encouragingly close fit between the density of northern seas and rate of the Atlantic overturning circulation at 45° N, in fact (Fig. 12.6b) the factors controlling density were found to be quite distinct in the three constituent types of experiment ('hosing runs', 'initial perturbation' experiments and greenhouse gas experiments). As a first step, it would be very useful to verify if the distinct trajectories in the ApS - ApT plane are found in other models for similar experiments. If so, then the next step would be for the modelling community to validate the processes that control how a model state evolves along the respective trajectories, by seeking observational analogues for these trajectories (e.g. over a seasonal cycle, or during the Great Salinity Anomaly).This will clearly not be easy in the case of the full spatial domain used to calculate the data in Fig. 12.6, but it may be possible to use spatially degraded coverage, taking data from key regions only.
Second, how can we weigh the contributions of individual models in a multimodel ensemble, such as those contributing to reports by the IPCC? Perturbed-physics multi-model ensembles are likely to become increasingly important in quantifying the impact of model uncertainty on climate projections. Such ensembles are only meaningful if a suitable, observationally based model weighting is applied. Schmittner et al. (2005) provide an example for this, but the absence of repeated, observed realisations of the predictand in the real world prevents us from determining model skill, in the same way as is done for numerical weather prediction. It is a non-trivial task to ascertain what the relevant observations are that constrain prediction of quantities at climate time scales, such as Arctic summer sea ice cover by the 2050s, or AMOC heat transport at 30° N by 2100. One answer may be observational 'weighting by proxy': by identifying model skill in simulating fields for which there are observations, and that are proven to also provide skill measures for the unobserved quantities that we wish to predict.
Acknowledgements Michael Vellinga was supported by the Joint Defra and MoD Programme, (Defra) GA01101 (MoD) CBC/2B/0417_Annex C5. Bob Dickson was supported by the Department for Environment, Food and Rural Affairs under the Defra Science and Research Project OFSOD-iAOOS, contract SD0440. Thanks to Jonathan Gregory for providing model data and to Jochem Marotzke for useful comments on this Chapter.
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