Approximations to the ocean’s residual circulation in arbitrary tracer coordinates

The residual circulation is the flow which transports tracers. Its utility is tempered by the challenge associated with its computation: velocity must be mapped into tracer coordinates on a timescale which is short compared to eddy timescales. Several approximations have been introduced which allow the residual circulation to be evaluated using a small number of flow statistics, including the transformed Eulerian mean (TEM), the temporal residual mean (TRM), and the recently introduced statistical transformed Eulerian mean (STEM). This paper discusses the relationship between these approximations and illustrates their differences with a series of analytical and numerical examples. The STEM is found to be superior to the TEM and TRM in both its handling of the surface boundary condition and its ease of implementation.