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

As is well known, three independent variables are needed to fully characterise the thermodynamic state of a fluid parcel in the standard approximation of seawater as a binary fluid. The standard description usually relies on the use of a temperature variable (such as potential temperature

Although behaving predominantly as passive tracers, density-compensated anomalies may occasionally “activate” and couple with density and ocean dynamics. This may happen, for instance, when isopycnal mixing of

From a dynamical viewpoint, in situ density

Once a choice for

If one accepts that it is the spiciness anomaly

Are there any special benefits associated with one particular choice of spiciness as a state function (

How should

While any

Orthogonality in

Comparison of different spiciness as state functions along 30

From a purely empirical viewpoint, neither spiciness (however defined) nor

Since salinity satisfies neither form of orthogonality, it is natural to ask which properties make it superior to spiciness and spicity as a water mass indicator. Because two signals are visually most easily contrasted when their respective isocontours are orthogonal to each other, it is natural to ask whether salinity could owe its superiority to being on average more orthogonal to density than other variables in physical space. To test this, the median angle between

Median angle between

The main aim of this paper is to explore the above ideas further and to clarify their inter-linkages. One of its key points is to emphasise that spiciness is a property, not a substance, and hence that it is spiciness as an anomaly rather than spiciness as a state function that is the relevant concept to quantify water mass contrasts. This important point was recognised early on by

As mentioned above, density-compensated thermohaline variations are truly passive only if defined along surfaces of constant in situ

Until recently, isopycnal analysis in oceanography has relied on two main approaches: the use of vertically stacked potential densities referenced to a discrete set of reference pressures “patched” at the points of discontinuity following

Recently,

The software used to compute

Thermodynamic neutral density

Atlantic sections along 30

A full account of the performances and properties of

Since spiciness is a water mass property that can a priori be measured in terms of the isopycnal variations of any arbitrary function

To examine the benefits that might be attached to a particular choice of spiciness as a state function

The

The

The re-scaled salinity and temperature

Both

The

Same as Fig.

As stated previously, it is important to recognise that spiciness is not a substance but a property that cannot be described without taking into account empirical information about the particular water masses to be analysed. Whether this point is well known is unclear because the distinction between a property and a substance is rarely evoked if ever in the spiciness literature. As a result, it follows that the usefulness of spiciness-as-a-state-function variables such as those of

Because any function

Are there any benefits in constructing a dedicated spiciness as a state function

Since neither the

In physics, the scale to measure some quantities is commonly accepted to be arbitrary, which is why several scales (e.g. Kelvin, Celsius, and Fahrenheit) have been developed over time to measure temperature, for instance. To what extent is the problem of quantifying spiciness as a property similar to or different from that of constructing a temperature scale?

To what extent is the problem of deciding in favour of a particular choice of

Are there any additional constraints that

Non-linear regression between

The MATLAB documentation page reviewing the various least-squares methods can be consulted at

Isocontours of

To make them more comparable, the various

Atlantic Ocean sections along 30

Scatter plots of various normalised

In the Introduction, I showed that the superior ability of salinity to pick up the different water mass signals of the Atlantic Ocean

Based on an arguably subjective visual comparison of the different panels in Fig.

Schematics of the effect of subtracting a suitably defined function of density

In this paper, I have revisited the theory of spiciness and established that its main ingredients are (1) a quasi-material density-like variable

Ingredient (1) is required because, contrary to what has been assumed by some authors, it is not the properties of

One of the main key points repeatedly emphasised in this paper is that spiciness is not a substance but a property that cannot be meaningfully defined independently of the particular ocean water masses to be analysed. This is why spiciness as a property is really best measured by the anomaly

One key advantage of

The values entering the definition of the reference density profile

Coefficients for the analytical reference density profile

Coefficients for the polynomial function

The re-scaled salinity and temperature coordinates given by Eq. (

Comparison between potential density (referenced at

The accuracy of the quasi-linear approximation

MATLAB and Python subroutines for computing the variable reference pressure

The author declares that there is no conflict of interest.

The comments of Jan Zika and two anonymous reviewers, as well as the technical editing of Ilker Fer, greatly helped improving clarity of the paper and are gratefully acknowledged.

This research has been supported by the NERC-funded OUTCROP project (grant no. NE/R010536/1).

This paper was edited by Ilker Fer and reviewed by Jan Zika and two anonymous referees.