The Representation of Ocean Circulation and Variability in Thermodynamic Coordinates

The ocean's circulation is analyzed in Absolute Salinity S-A and Conservative Temperature Theta coordinates. It is separated into 1) an advective component related to geographical displacements in the direction normal to S-A and Theta isosurfaces and 2) into a local component, related to local changes in S-A-Theta 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 Theta. The sum is directly related to sources and sinks of salt and heat. The advective component is represented by the advective thermohaline streamfunction Psi(adv)(SA Theta). After removing a trend, the local component can be represented by the local thermohaline streamfunction Psi(loc)(SA Theta). Here, Psi(loc)(SA Theta) can be diagnosed using a monthly averaged time series of S-A and Theta from an observational dataset. In addition, Psi(adv)(SA Theta) and Psi(loc)(SA Theta) are determined from a coupled climate model. The diathermohaline streamfunction Psi(dia)(SA Theta) is the sum of Psi(adv)(SA Theta) and Psi(loc)(SA Theta) and represents the nondivergent diathermohaline circulation in S-A-Theta coordinates. The diathermohaline trend, resulting from the trend in the local changes of S-A and Theta, quantifies the redistribution of the ocean's volume in S-A-Theta 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.