The absolute seawater entropy: Part II. Case studies

TL;DR

This paper tests the absolute seawater entropy $\eta_{\rm abs}$, defined as $\eta_{\rm abs}=\eta_{\rm std/TEOS10}+\Delta \eta_{\rm s}$ with $\Delta \eta_{\rm s}= (\eta_{\rm s0}-\eta_{\rm w0}) \times \frac{(S_{\rm A}-S_{\rm SO})}{1000}$, against concrete ocean data to reveal thermodynamically consistent isentropic structures that TEOS10 misses. Through SCICEX CTD profiles, SCICEX'97 transects, and World Ocean Atlas 2023 (WOA23) surface climatologies across the Arctic, Bay of Bengal, and the Northeast Atlantic–Mediterranean, the study demonstrates how $\eta_{\rm abs}$ yields coherent absolute-entropy alignments along red isentropes and uncovers regional homogenizations (e.g., around $405 \pm 3$ J K$^{-1}$ kg$^{-1}$ tropical regions and a $260$–$270$ J K$^{-1}$ kg$^{-1}$ band in the Mediterranean–Black–C Caspian areas). The work argues that turbulent processes acting on $\eta_{\rm abs}$ (in line with Richardson) plus the nontrivial dependence on $S_{\rm A}$ via $\Delta \eta_{\rm s}$ are essential to explain observed patterns and to maintain a physically meaningful entropy budget. These findings advocate adopting the absolute entropy formulation in TEOS10 outputs to better represent ocean thermodynamics and transport processes.

Abstract

The aim of this second part of the article is to study with several concrete cases the absolute definition of the seawater entropy described in Part I. Observed vertical profiles and polar transects, as well as analysed surface data, show that very different temperature and salinity values can organise to create new isentropic regions that can only be revealed by the absolute formulation of the entropy of seawater (Arctic Ocean; Bay of Bengal; Mediterranean, Black and Caspian Seas). Existing hypotheses to explain these results include the possible impact of turbulent processes that must be applied to the entropies of the atmosphere and oceans.

Figures (7)

• Figure 1: Top (left): an annotated version of the Fig. 1 of Steele_al_JGR_2004 corresponding to a study of the low-resolution SCICEX'96 (cast 43) CTD vertical profiles. Top (middle and right): the corresponding full resolution vertical profiles for the potential temperature ($\theta$, solid blue), Celsius temperature ($T$, dashed purple) conservative temperature ($\Theta$, solid red), and salinity (solid blue), with $S_{\rm SO}=35.165\,04$ g kg${}^{-1}$ the TEOS10 standard salinity (green), for the high-resolution SCICEX'96 CTD (cast 43) vertical profiles. Bottom (left): the corresponding standard (solid blue) and absolute (solid red) versions of the seawater entropy, with the absolute mean value of the salinity increment $\Delta \eta_{\rm s}$ given by (\ref{['Eq_etas_minus_etaw_value']}). Bottom (right): the same $t-S_{\rm A}$ diagram as in the Figs. 1 of the Part I, with the (almost horizontal) TEOS10's standard entropy (thin blue dashed lines), with the (more slantwise) TEOS10's absolute entropy (thick red solid lines), and with the plot of the SCICEX'96 (cast 43) vertical profile coloured from dark-brown to dark-blue for the depth from $14$ m to $300$ m, and then in black up to the last $1004$ m depth.
• Figure 2: On the top: the anotated SCICEX-97 Sample Locations map (green points for the Transect-A and blue points for the Transect-B). Then the four Transect-A figures (from $15$ m to $300$ m depth) for the temperature (${}^{\circ}$C), salinity (g kg${}^{\,-1}$), standard (TEOS10) and absolute (TEOS10+third-law) seawater entropies (J K${}^{\,-1}$ kg${}^{\,-1}$).
• Figure 3: Same as for Figs. \ref{['Fig_SCICEX97_transect_A']}, but for the Transect-B figures.
• Figure 4: The 1991-2020 objectively analyzed annual surface means for the Temperature, Salinity, standard (Std) seawater entropy, absolute (Abs) seawater entropy and difference (Abs$\,-\,$Std) in seawater entropy seawater entropy, computed from the World Ocean Atlas 2023 climatology (WOA23, release February 2024, quarter-degree grid). Documentation and data available at: https://www.ncei.noaa.gov/products/world-ocean-atlas.
• Figure 5: The same as in the Figs. \ref{['Fig_WOA23_global']}, but for the Arctic Ocean.