The methods are those of the theory of dynamical systems, deterministic and stochastic, including those of parameter estimation and model optimization. We draw on results about the lack of structural stability of deterministic dynamical systems in general, and apply preliminary results on the stabilizing effects of random perturbations on the robustness of certain statistical properties of the perturbed systems. These methods will be applied systematically across a hierarchy of models.
Simple models, to which the theoretical results can be applied directly, will be used to test a number of ideas that extend the known theoretical results and point to practical methods for more realistic models. In selecting these simple models, we will concentrate on specific features of climate variability on inter-annual and inter-decadal time scales. Intermediate models with considerable climatic realism will be optimized in a systematic way and used to check the sensitivity of the range of
predictions to changes in parameters. These intermediate models will be chosen among those that are widely tested and accepted as computationally efficient but recognizably related to general circulation models (GCMs). Finally, existing single-model and multi-model ensembles of climate simulations and projections will be examined to verify to which extent the results from the intermediate models can be used to systematically optimize and test the sensitivity of IPCC-class coupled GCMs.
Potential impacts include the development of a strategy for replacing the ad hoc ÒtuningÓ of GCMs, used so far by the climate modeling community, by a systematic approach for their optimization, including an a priori estimate of their sensitivity. Such a strategy could modify the approach to future IPCC assessment reports, greatly enhance the robustness of their climate projections, and improve the confidence of decision makers and the public in these projections.
Similar issues of robustness arise in many other areas of the physical and life sciences. The results obtained for climate models could help resolve similar difficulties in population dynamics, epidemiology, macroeconomics and other areas. Given the close interaction between mathematics, physical sciences, statistics and numerical methods that the project involves, a major benefit will accrue to its junior participants in terms of their effectiveness across disciplinary boundaries.
Last but not least, the methods for systematic optimization and sensitivity study involved in the project are intrinsically parallelizable and scalable. These methods can thus directly take advantage of future architectures and increases in computer power contemplated by SciDAC.