The Materiality and Neutrality of Neutral Density and Orthobaric Density

The materiality and neutrality of neutral density and several forms of orthobaric density are calculated and compared using a simple idealization of the warm-sphere water mass properties of the Atlantic Ocean. Materiality is the value of the material derivative, expressed as a quasi-vertical velocity, following the motion of each of the variables: zero materiality denotes perfect conservation. Neutrality is the difference between the dip in the isopleth surfaces of the respective variables and the dip in the neutral planes. The materiality and neutrality of the neutral density of a water sample are composed of contributions from the following: ( I) how closely the sample's temperature and salinity lie in relation to the local reference theta-S relation, (II) the spatial variation of the reference theta-S relation, (III) the neutrality of the underlying reference neutral density surfaces, and (IV) irreversible exchanges of heat and salinity. Type II contributions dominate but have been neglected in previous assessments of neutral density properties. The materiality and neutrality of surfaces of simple orthobaric density, defined using a spatially uniform theta-S relation, have contributions analogous to types I and IV, but lack any of types II or III. Extending the concept of orthobaric density to permit spatial variation of the theta-S relation diminishes the type I contributions, but the effect is counterbalanced by the emergence of type II contributions. Discrete analogs of extended orthobaric density, based on regionally averaged theta-S relations matched at interregional boundaries, reveal a close analogy between the extended orthobaric density and the practical neutral density. Neutral density is not superior, even to simple orthobaric density, in terms of materiality or neutrality.