The representation of ocean circulation and variability in thermodynamic coordinates

The ocean’s circulation is analyzed in Absolute Salinity S_A and Conservative Temperature Θ coordinates. It is separated into 1) an advective component related to geographical displacements in the direction normal to S_A and Θ isosurfaces and 2) into a local component, related to local changes in S_A–Θ values, without a geographical displacement. In this decomposition, the sum of the advective and local components of the circulation is equivalent to the material derivative of S_A and Θ. The sum is directly related to sources and sinks of salt and heat. The advective component is represented by the advective thermohaline streamfunction Ψ^adv _SAΘ. After removing a trend, the local component can be represented by the local thermohaline streamfunction Ψ^loc _SAΘ. Here, Ψ^loc _SAΘ can be diagnosed using a monthly averaged time series of S_A and Θ from an observational dataset. In addition, Ψ^adv S_AΘ and Ψ^loc SAΘ are determined from a coupled climate model. The diathermohaline streamfunction Ψ^dia _SAΘ is the sum of Ψ^adv _SAΘ and Ψ^loc _SAΘ and represents the nondivergent diathermohaline circulation in S_A–Θ coordinates. The diathermohaline trend, resulting from the trend in the local changes of S_A and Θ, quantifies the redistribution of the ocean’s volume in S_A–Θ coordinates over time. It is argued that the diathermohaline streamfunction provides a powerful tool for the analysis of and comparison among ocean models and observation-based gridded climatologies.