The equilibrium climate sensitivity is also the single most important source of uncertainty for projections of global mean sea level rise, although the variation of temperature change with depth in the ocean and the response of glaciers and ice sheets are also important sources of uncertainty. With regard to the build-up of carbon dioxide in the atmosphere, the largest uncertainties involve interactions between the terrestrial biosphere and climate. The uncertainties in the estimated build-up of atmospheric CO2 are thought to be small for projections spanning two to three decades, but are substantially larger for longer projections.

Both simple and complex models have important roles to play in enhancing our understanding of the range of possible future climatic changes, their impacts, and interactive effects. The more complex models are especially suited for studying those fundamental processes which are resolved by complex models but not by simple models. They also have the potential to provide credible projections of regional scale changes in climatic means and variability. Simple models can be formulated to replicate the global scale average behaviour of complex models and can be calibrated to global scale observations. Due to their computational efficiency and conceptual clarity, simple models are useful for global change scenario development and analysis, and for investigating the interactive effect of subsystem properties. The use of AOGCMs for the simulation of regional, time-varying climatic change, and the use of SCMS for more extensive sensitivity and scenario analysis, are both

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dictated by pragmatic considerations involving computer resources and the level of detail appropriate when coupling various components together. A long-term goal of Earth system science is the development of increasingly sophisticated coupled models of the climate system.

All climate system models used in the SAR WGI have been tested for their ability to reproduce key features of the existing climate, as well as historical and palaeo-climatic changes. While the validity of these models cannot be proven for future conditions, their ability to recover a variety of observed features of the atmosphere/ocean/biosphere system and observed changes during the recent past supports their use for projections of future climatic change.

However, many uncertainties remain regarding the modelling of the climate system. There is considerable uncertainty about the changes that might occur in some climate system processes, such as those involving clouds, in an altered climate. The effect of aerosols on the radiation balance of the climate is also not well known. Difficult-to-predict changes in the ocean circulation could have a significant effect on both regional and global climatic changes. Unexpected changes in the flow of carbon between the atmosphere and terrestrial biosphere and/or the oceans could occur. Nevertheless, research continues to improve our basic understanding of important processes and their representation in models.

1.1 Aims

This Technical Paper is intended as a primer on the climate system and SCMs, and has two objectives: (a) to explain how SCMS work, the processes that are included in them, what their strengths and weaknesses are in relation to more complex models, the purposes to which they are applied, and why they have been used extensively in the SAR WGI; and (b) to fully document the procedures and assumptions used to generate the trace gas concentration, global mean temperature change, and global mean sea level rise projections presented in the SAR WGI (Section 6.3) and in IPCC TP STAB (1997).

Ideally, one seeks a balance whereby each component of the climate system is represented at an appropriate level of detail. How to do this is the modeller's "art". There is no methodological crank to turn, although some overall principles are clear, for example, it would be an inefficient use of computer resources to couple a detailed model for some part of the system with little effect on the particular area of concern to one with crudely represented physical processes that dominates the model output. Einstein once quipped that, "everything should be as simple as possible, but no simpler". Generations of modellers have agonized over what "no simpler" means. This has been a

particularly important issue for assessments of anthropogenic climate change conducted by the IPCC.

The most general computer models for climate change employed by the IPCC are the coupled AOGCMs (see Section 3.1), which solve the equations of the atmosphere and oceans approximately by breaking their domains up into volumetric grids, or boxes, each of which is assigned an average value for properties like velocity, temperature, humidity (atmosphere) and salt (oceans). The size of the box is the models'spatial resolution. The smaller the box, the higher the resolution. An assumption of research involving general circulation models (GCMs) is that the realism of climate simulations will improve as the resolution increases.

In practice, computing limitations do not allow models of high enough resolution to resolve important sub-grid processes. Phenomena occurring over length scales smaller than those of the most highly resolved GCMs, and that cannot be ignored, include cloud formation and cloud interactions with atmospheric radiation; sulphate aerosol dynamics and light scattering, ocean plumes and boundary layers; sub-grid turbulent eddies in both the atmosphere and oceans; atmosphere/biosphere exchanges of mass, energy and momentum; terrestrial biosphere growth, decay and species interactions; and marine biosphere ecosystem dynamics -to cite a few examples. Mismatches between the scale of these processes and computationally realizable grid scales in global models is a well-known problem of Earth system science.

To account for sub-grid climate processes, the approach has been to "parametrize" - that is, to use empirical or semi-empirical relations to approximate net (or area-averaged) effects at the resolution scale of the model (see Section 3 for further discussion). It is important to stress that all climate system models contain empirical parametrizations and that no model derives its results entirely from first principles. The main conceptual difference between simple and complex models is the hierarchical level at which the empiricism enters.

It is essential, for example, to account for the heat and carbon that enter the oceans as the climate warms from the greenhouse effect of CO2 emitted by fossil fuel burning. The internal mixing and transport in the oceans of this energy and mass invading at the air-sea interface are key processes that must be represented in any model used to project future CO2, climate and sea level variations. The rate at which heat and dissolved carbon penetrate the thermocline (roughly the first kilometre of ocean depth) controls how much global warming is realized for a given radiative forcing, and how much CO2 remains in the atmosphere. In principle, these processes could be computed by AOGCMs, but AOGCMs are presently too time-consuming to run on computers for a wide range of emission scenarios. For this reason, the global mean CO2, temperature, and sea level projections for the IS92 emission scenarios and the CO2

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stabilization calculations presented in the SAR WGI, and similar calculations in IPCC TPSTAB (1997), were carried out with simple models.

The choice of the most appropriate level of parametrization for climate system modelling is a qualitative judgement based on the best scientific knowledge and computer limitations. Consider the one-dimensional upwelling-diffusion ocean introduced by Hoffert, et al. (1980, 1981) and subsequently developed by many other researchers (Section 3.1), used to parametrize the world's oceans in several IPCC carbon cycle, climate and sea level calculations. In this paradigm, the three-dimensional world oceans are replaced by a single horizontally-averaged column in which carbon concentration and temperature vary with depth. The column exchanges mass and energy at its top with a well-mixed ocean surface layer; at its bottom, the column is fed by cold water from a downwelling polar sea. This one-dimensional paradigm works well at simulating historical climate and carbon cycle variations. To simplify further by replacing the column with a single well-mixed box or a purely diffusive ocean would make it too simple. A well-mixed box cannot account for the fact that the mixing time of the oceans is long compared to the rates at which carbon emissions and radiative forcing at the surface are changing. The result would be incorrect rates of heat and mass uptake over time. Things are already "as simple as possible" with a one-dimensional upwelling-diffusion ocean, so we stop there.

Another frequently asked question is: "how do we know if model predictions are credible"? Science today recognizes that there is no way to prove the absolute truth of any hypothesis or model, since it is always possible that a different explanation might account for the same observations. In this sense, even the most well-established physical laws are "conditional". Rather, the test should be whether a theory or model is false. The more independent challenges that a theory or model passes successfully, the more confidence one can have in it. Indeed, the testability of a conjecture has become a necessary condition for it to be considered in the domain of science. As Sir Karl Raimund Popper, philosopher of science and developer of the doctrine of falsifiability, put it, “Our belief in any particular natural law cannot have a safer basis than our unsuccessful critical attempts to refute it" (Popper, 1969).

The application of the falsifiability rule can be seen in the values of the climate sensitivity (Section 2.3), equivalent to the

equilibrium temperature change for a CO2 doubling, estimated by the SAR WGI to lie, most probably, in the range of 1.5 to 4.5°C (SAR WGI: Technical Summary, Section D.2). Climate sensitivity is computed in AGCMs based on a combination of physical laws and sub-grid scale model parametrizations, but is directly specified as an input in simple ocean/climate models. At least four independent methods have been used to estimate the climate sensitivity: (a) from simulations with three-dimensional AGCMs (Cess, et al., 1989); (b) from direct observations, at the relevant temporal and spatial scales, of the key processes that determine radiative damping to space and hence climate sensitivity (e.g., Soden and Fu, 1995); (c) from reconstructions of radiative forcing and climate response of ancient (palaeo-) climates (Hoffert and Covey, 1992); and (d) from comparisons of ocean/climate model runs with historical global temperature records (see Section 4.2 and Figure 10). Each method has unique disadvantages and uncertainties. However, all of these independent methods give results that are consistent with the SAR WGI range 1.5 to 4.5°C, and are inconsistent with values substantially lower or higher.

Finally, simple climate system models appear to have the drawback of dealing only with global or zonal averages, whereas regional variations of temperature and precipitation change are needed to complete the link in integrated assessments from emissions to impacts. Again, in practice, many present-day integrated assessments are conducted with models whose core transient climate calculations are done with simple ocean/climate models using regional distributions of temperature and precipitation (typically produced by AOGCMs) that have been scaled to the global mean temperature change (Santer, et al., 1990; Hulme, et al., 1995).

The foregoing considerations are meant to explain the rationale underlying the use of simplified models of the climate system in the SAR, and do not suggest that a particular modelling methodology or level of complexity is inherently superior for climate system analysis for all time. Indeed, the consensus of the climate modelling community is that detailed threedimensionally resolved models of atmosphere and ocean dynamics, and correspondingly highly resolved models of the Earth's terrestrial and marine biota, are the long-term goals of Earth system science. These modelling efforts need to proceed in parallel with, and mutually reinforce, the more idealized models of the climate system used in work relating to scenario analysis and climate policy, as the IPCC process evolves.