Simulation has greatly advanced climate science, but not sufficiently to the profit of theory and understanding. How can simulation better advance climate science and what mathematical issues does this raise?
Our hypothesis is that the development of climate science (i.e., theory and understanding) will be best served by focusing computational and intellectual resources on model and data hierarchies. Where “model and data hierarchies” refer to successively more complex models, or data structures, and the relations among them. Classic examples are the equations that emerge at different order in an asymptotic expansion; or microscopic, mesoscopic, macroscopic representations of systems that emerge in statistical physics and material science. In the atmosphere/ocean system such approaches lead to familiar families of equation sets used to explore specific phenomena, and the statistical theories (parameterizations) used to close the systems which emerge at different orders; but such ideas are also relevant to the data used to test such systems.
By bringing together physicists, mathematicians, statisticians, engineers and climate-scientists, and focusing on several themes that reach across scales and scientific methodologies, our program will provide a framework for advancing our use of hierarchical methods in our attempt to understand the climate system. In addition to tutorials and a summary workshop; the program will tie together four week-long workshops addressing specific currents in the broader stream of ideas: Equation Hierarchies; Numerical Hierarchies; Simulation Hierarchies; and Data Hierarchies.