ABSTRACT
Prediction of the Earth’s climate is a computational grand-challenge problem. Spatial scales range from global atmospheric circulation to cloud microphysics, and time-scales important for climate range from the thousand year overturning of the deep ocean to the nearly instantaneous equilibration of solar radiation balance. Mathematical models of geophysical flows provide the theoretical structure for our understanding of weather patterns and ocean currents. These now-classical developments have been extended through numerical analysis and simulation to encompass model equations that cannot be solved except using supercomputers. That mathematics and physics lie at the
heart of climate modeling is the primary basis for thinking that we can predict complex climate interactions. The degree of confidence in climate models is bounded by their ability to accurately simulate historical climate equilibrium and variation, as well as their ability to encapsulate the scientific understanding of instantaneous interactions at the process level. Observational weather data, as well as measurements of physical, chemical, and biological processes, are a constant check on the validity and fidelity of the models and point to areas that are poorly understood or represented inadequately. In large part because of the ability of ever-more-powerful computers to integrate increasingly rich data and complex models, the understanding of coupled climate feedbacks and responses has advanced rapidly.
