This project is engaged in developing coupled atmosphere-ocean models of varying degrees of complexity and applying them to improve our understanding of the feedbacks between the atmosphere and ocean, to quantify the uncertainties that limit our ability to predict climate change, and to make projections of climate change. A key focus of the project is to use estimates from 20th century observations of climate sensitivity to investigate the rate at which warming penetrates into the deep ocean, and to study the associated uncertainties due to observational errors and natural variability. The uncertainties are expressed as probability density functions (pdfs) and are updated as new observations become available. The pdfs are used to evaluate the performance of state-of-the-art coupled GCMs and to make probabilistic projections of global warming. Recent results indicate that coupled GCMs overestimate how rapidly heat penetrates into the deep ocean, and that as a result the IPCC's projections of 21st century warming underestimate the warming. To address that shortcoming, we are also working to advance the development of ocean models by implementing improved representations of the ocean-mixing processes in that affect heat uptake.