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This paper clarifies the theoretical basis for constructing spicinessvariables optimal for characterising ocean water masses. Three essentialingredients are identified: 1) a material density variable $\gamma$ that is asneutral as feasible; 2) a material state function $\xi$ independent of$\gamma$, but otherwise arbitrary; 3) an empirically determined referencefunction $\xi_r(\gamma)$ of $\gamma$ representing the imagined behaviour of$\xi$ in a notional spiceless ocean. Ingredient 1) is required because contraryto what is often assumed, it is not the properties imposed on $\xi$ (such asorthogonality) that determine its dynamical inertness but the degree ofneutrality 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 suitedfor characterising ocean water masses, as originally proposed by McDougall andGiles (1987). The second key result is that oceanic sections of normalised$\xi'$ appear to be relatively insensitive to the choice of $\xi$, as firstsuggested by Jackett and McDougall (1985). It is also argued that orthogonalityof $\nabla \xi'$ to $\nabla \gamma$ in physical space is more germane tospiciness theory than orthogonality in thermohaline space, although how to useit to constrain the choices of $\xi$ and $\xi_r(\gamma)$ remains to be fullyelucidated. The results are important for they unify the various ways in whichspiciness has been defined and used in the literature. They also provide arigorous theoretical basis justifying the pursuit of a globally definedmaterial density variable maximising neutrality. To illustrate the latterpoint, this paper proposes a new implementation of the author's recentlydeveloped thermodynamic neutral density and explains how to adapt existingdefinitions of spiciness/spicity to work with it.

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