A rigorous derivation of the Water Mass Transformation framework, the relation between mixing and dia-surface exchange flow, and links to recent theories in estuarine research

Abstract In this paper we present the analytical derivation of a local Water Mass Transformation (WMT) framework for an individual water column. We exactly formulate the mapping of the governing equations from geopotential coordinates to an arbitrary tracer space. Unique definitions for the local effective vertical dia-surface fluxes are given. In tracer space we derive new relations between the local dia-tracer fluxes and the mixing per tracer class. The key relation between the effective vertical dia-tracer velocity and the mixing per tracer class directly formulates how the overturning circulation is linked to local tracer variance dissipation. Horizontal integration of the governing equations in tracer space and the relations between the dia-tracer quantities finally recovers the well-known integral WMT formulations.