The interpretation of temperature and salinity variables in numerical ocean model output and the calculation of heat fluxes and heat content

Trevor J Mcdougall,Paul J Durack,Stephen M Griffies,Rich Pawlowicz,Paul M Barker,Ryan M Holmes

doi:10.5194/gmd-14-6445-2021

Abstract

Abstract. The international Thermodynamic Equation of Seawater 2010 (TEOS-10) defined the enthalpy and entropy of seawater, thus enabling the global ocean heat content to be calculated as the volume integral of the product of in situ density, ρ, and potential enthalpy, h0 (with reference sea pressure of 0 dbar). In terms of Conservative Temperature, Θ, ocean heat content is the volume integral of ρcp0Θ, where cp0 is a constant “isobaric heat capacity”. However, many ocean models in the Coupled Model Intercomparison Project Phase 6 (CMIP6) as well as all models that contributed to earlier phases, such as CMIP5, CMIP3, CMIP2, and CMIP1, used EOS-80 (Equation of State – 1980) rather than the updated TEOS-10, so the question arises of how the salinity and temperature variables in these models should be physically interpreted, with a particular focus on comparison to TEOS-10-compliant observations. In this article we address how heat content, surface heat fluxes, and the meridional heat transport are best calculated using output from these models and how these quantities should be compared with those calculated from corresponding observations. We conclude that even though a model uses the EOS-80, which expects potential temperature as its input temperature, the most appropriate interpretation of the model's temperature variable is actually Conservative Temperature. This perhaps unexpected interpretation is needed to ensure that the air–sea heat flux that leaves and arrives in atmosphere and sea ice models is the same as that which arrives in and leaves the ocean model. We also show that the salinity variable carried by present TEOS-10-based models is Preformed Salinity, while the salinity variable of EOS-80-based models is also proportional to Preformed Salinity. These interpretations of the salinity and temperature variables in ocean models are an update on the comprehensive Griffies et al. (2016) paper that discusses the interpretation of many aspects of coupled Earth system models.

Highlights

Numerical ocean models simulate the ocean by calculating the acceleration of fluid parcels in response to various forces, some of which are related to spatially varying density fields that affect pressure, as well as solving transport equations for the two tracers on which density depends, namely tempera-Published by Copernicus Publications on behalf of the European Geosciences Union.T
That we have argued that Tmodel of EOS-80-based models should be interpreted as being Conservative Temperature, how should the model-based estimates of ocean heat content and ocean heat flux be compared with ocean observations and ocean atlas data? The answer is by evaluating the ocean heat content correctly in the observed data sets using Thermodynamic Equation of Seawater 2010 (TEOS-10), whereby the observed data are used to calculate Conservative Temperature, and this is used together with cp0 to evaluate ocean heat content and meridional heat fluxes
We have made the case that it is advisable to avoid nonconservative sources of heat at the sea surface. It is the prior interpretation of the temperature variable in EOS-80-based models as being potential temperature that implies that the ocean receives a heat flux that is larger by Q than the heat that is lost from the atmosphere

Summary

Introduction

McDougall et al.: The interpretation of temperature and salinity variables in ocean model output ture (the CMIP6 variables identified as thetao or bigthetao) and dissolved matter (“salinity”, CMIP6 variable so) For computational reasons it is useful for the numerical schemes involved to be conservative, meaning that the amount of heat and salt in the ocean changes only due to the area-integrated fluxes of heat and salt that cross the ocean’s boundaries; in the case of salt, this is zero. It is well-known that in situ temperature is not a satisfactory measure of the “heat content” of a water parcel because the in situ temperature of a water parcel changes as the ambient pressure changes (i.e. if a water parcel is transported to a different depth, i.e. pressure, in the ocean). The ocean’s potential temperature is subject to internal sources and sinks – it is not conservative

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