The fluctuation-dissipation theorem for moist atmospheric convection

Much of our current understanding of the interaction of cumulus convection with larger scales of motion is based on an assumption of statistical equilibrium between an ensemble of convective clouds and a large-scale forcing. Using a cloud-resolving numerical model, we show that the statistics of this equilibrium are well-represented by a canonical ensemble of non-interacting clouds. The non-equilibrium response of the system is found to relate to the statistics of the equilibrium fluctuations according to the classical fluctation-dissipation theorem. This result is used to demonstrate that the time-scale of adjustment to equilibrium is given by the time taken for a gravity wave to cross the cloud separation distance. The implications of these results for convective parameterisation and new observational tests will be discussed.