Earth system models (ESM) are the most comprehensive tools we have to study climate change and develop climate projections. However, the computational infrastructure required and the cost incurred in running such ESMs precludes direct use of such models in conjunction with a wide variety of tools that can further our understanding of climate. Here we are referring to tools that range from dynamical systems tools that give insight into underlying flow structure and topology to tools that come from various applied mathematical and statistical techniques and are central to quantifying stability, sensitivity, uncertainty and predictability to machine learning tools that are now being rapidly developed or improved. Our approach to facilitate the use of such models is to analyze output of ESM experiments (cf. CMIP) using a range of simpler models that consider integral balances of important quantities such as mass and/or energy in a Bayesian framework.
We highlight the use of this approach in the context of the uptake of heat by the world oceans in the ongoing global warming. Indeed, since in excess of 90% of the anomalous radiative forcing due greenhouse gas emissions is sequestered in the world oceans, the nature of ocean heat uptake crucially determines the surface warming that is realized (cf. climate sensitivity). Nevertheless, ESMs themselves are never run long enough to directly assess climate sensitivity. So, we consider a range of models based on integral balances---balances that have to be realized in all first-principles based models of the climate system including the most detailed state-of-the art climate simulations. The mod
els range from simple models of energy balance to those that consider dynamically important ocean processes such as the conveyor-belt circulation (Meridional Overturning Circulation, MOC), North Atlantic Deep Water (NADW) formation, Antarctic Circumpolar Current (ACC) and eddy mixing. Results from Bayesian analysis of such models using both ESM experiments and actual observations are presented. One such result points to the importance of direct sequestration of heat below 700 m, a process that is not allowed for in the simple models that have been traditionally used to deduce climate sensitivity.