A Generalized Transport Theory: Water-Mass Composition and Age

Abstract

A general theory to describe and understand advective and diffusive ocean transport is reported. It allows any passive tracer field with an atmospheric source to be constructed by superposing sea surface contributions with a generalized Green's function called the boundary propagator of the passive tracer equation. The boundary propagator has the interpretation of the joint water-mass and transit-time distribution from the sea surface. The theory thus includes the classical oceanographic idea of water-mass analysis and extends it to allow for a distribution of transit times from the sea surface. The joint water-mass and transit-time distribution contains complete information about the transport processes in the flow. It captures this information in a more accessible way than using velocity and diffusivity fields, however, at least for the case of sequestration and transport of dissolved material by the ocean circulation. The boundary propagator is thus the natural quantity to consider when discussing both steady-state and transient ocean tracers, including the inverse problem of interpreting tracer data in terms of ocean circulation. Two constraints on the shape of the transit-time distributions are derived. First, the asymptotic behavior for a steady, or time-averaged, circulation is exponential decay. Second, integrated over the whole ocean, the transit-time distribution from the sea surface cannot increase. The theory is illustrated using a one-dimensional advection?diffusion model, a box model, and a North Atlantic general circulation model.