Abstract/Summary

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 $\gamma$ that is as neutral as feasible; 2) a material state function $\xi$ independent of $\gamma$, but otherwise arbitrary; 3) an empirically determined reference function $\xi_r(\gamma)$ of $\gamma$ representing the imagined behaviour of $\xi$ in a notional spiceless ocean. Ingredient 1) is required because contrary to what is often assumed, it is not the properties imposed on $\xi$ (such as orthogonality) that determine its dynamical inertness but the degree of neutrality of $\gamma$. The first key result is that it is the anomaly $\xi' = \xi - \xi_r(\gamma)$, rather than $\xi$, that is the variable the 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 $\xi'$ appear to be relatively insensitive to the choice of $\xi$, as first suggested by Jackett and McDougall (1985), based on the comparison of very different choices of $\xi$. It is also argued that orthogonality of $\nabla \xi'$ to $\nabla \gamma$ in physical space is more germane to spiciness theory than orthogonality in thermohaline space, although how to use it to constrain the choices of $\xi$ and $\xi_r(\gamma)$ 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/spicity to work with it.