Spiciness theory revisited, with new views on neutral density, orthogonality, and passiveness

This paper clarifies the theoretical basis for constructing spiciness variables optimal for characterising ocean water masses. Three essential ingredients are identified: (1) a material density variable γ that is as neutral as feasible, (2) a material state function ξ independent of γ but otherwise arbitrary, and (3) an empirically determined reference function ξr(γ) of γ representing the imagined behaviour of ξ in a notional spiceless ocean. Ingredient (1) is required because contrary to what is often assumed, it is not the properties imposed on ξ (such as orthogonality) that determine its dynamical inertness but the degree of neutrality of γ. The first key result is that it is the anomaly ξ′=ξ-ξr(γ), rather than ξ, that is the variable most suited for characterising ocean water masses, as originally proposed by McDougall and Giles (1987). The second key result is that oceanic sections of normalised ξ′ appear to be relatively insensitive to the choice of ξ, as first suggested by Jackett and McDougall (1985), based on the comparison of very different choices of ξ. It is also argued that the orthogonality of ∇ξ′ to ∇γ in physical space is more germane to spiciness theory than orthogonality in thermohaline space, although how to use it to constrain the choices of ξ and ξr(γ) remains to be fully elucidated. The results are important for they unify the various ways in which spiciness has been defined and used in the literature. They also provide a rigorous theoretical basis justifying the pursuit of a globally defined material density variable maximising neutrality. To illustrate the latter point, this paper proposes a new implementation of the author's recently developed thermodynamic neutral density and explains how to adapt existing definitions of spiciness and spicity to work with it.