Principle of equilibrium fluctuations

The ocean is forced by the fluxes of momentum, heat, and fresh water at the sea surface. When driving an ocean model using stationary fluxes for a sufficiently long time, we expect the model  to produce an equilibrated ocean characterized by stationary fluctuations. These fluctuations are not all synchronized with the surface fluxes.  For an ensemble obtained by forcing the ocean model with the same fluxes (starting from slightly different initial states),   fluctuations (at a time) that are  synchronized with the surface fluxes can be identified as the mean across the ensemble (at that time), and those not synchronized with the surface fluxes as the deviations from the mean across the ensemble. In case that the model has a sufficiently fine resolution, we expect that the latter — also known as intrinsic ocean variability — is substantial. The intrinsic ocean variability has to get its energy from somewhere. The only possible energy source is the surface fluxes, which originate from atmospheric motions supported (essentially) by the Sun. In this sense, intrinsic ocean variability can be considered as a feature of an ocean that is in equilibrium with a huge reservoir. 

 

The principle that governs equilibrium fluctuations — no matter how the equilibrium is reached — is a form of fluctuation-dissipation relation. The relation ensures that in an equilibrium with a reservoir, anything  that generates fluctuations must also dissipate fluctuations, and anything that dissipates fluctuations must also generate fluctuations. This principle makes a dynamical system in equilibrium with a reservoir be inherently random, even when the forcing resulting from the reservoir, such as the surface fluxes, is purely deterministic.  We evaluate this principle using solutions from the Lorenz's 1963 model and solutions obtained from the ICON ocean model with a horizontal resolution of  5 km.