Data assimilation provides a method to optimally merge observations with Earth system models to make better predictions with these models. Increasingly, coupled models for different compartments of the Earth system are used. This allows to assimilate different observation types for different compartments of the Earth system. This session focuses on weakly and strongly coupled data assimilation across compartments of the Earth system that are used to predict states and fluxes of water and energy. Examples are data assimilation for the atmosphere-ocean system, data assimilation for the atmosphere-land system and data assimilation for the land surface-subsurface system. Optimally exploiting observations in a compartment of the terrestrial system to update also states in other compartments of the terrestrial system still has strong methodological challenges, for example related to the fact that weak correlations between states of different compartments need to be exploited and only a small ensemble of coupled model simulations can be made. Another challenge is the very different time scales at which compartments of the Earth system act. Coupled data assimilation allows to determine the value of different measurement types for the predictions of states and fluxes, and the additional value of measurements to update states across compartments. Another aspect of scientific interest for weakly or fully coupled data assimilation is the software engineering related to coupling a data assimilation framework to a physical model, in order to build a computationally efficient and flexible framework.