the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Jul 2025
Quantifying energy barriers associated with density stratification in vertical displacements of water parcels
Abstract. Density stratification affects mixing by limiting the interchange of properties along the water column. This stratification establishes barriers to the vertical displacement of water parcels, which interchange their properties between different layers of the ocean. Quantifying the intensity of these barriers, considering the direction (upward and downward) of the vertical displacement of a water parcel, is the main aim of this study. By employing the buoyancy energy required to displace a water parcel vertically, we propose the buoyancy potential energy (BPE) to analyze energy barriers in detail, describe the stability of a water parcel, and provide an objective integrated measure of stratification intensity in any vertical section of the water column. By illustrating the application of BPE in dynamical and ecological contexts, we demonstrate that it provides a complementary understanding of oceanic stratification. BPE is directly calculated from survey data, eliminating the need to diagnose turbulent processes, and has a straightforward numerical implementation. The routine application of BPE to study diverse ocean-atmosphere interaction processes (e.g., dynamical, thermodynamical, ecological, and biochemical) in which stratification plays a role can extend and enrich our understanding of them.
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- RC1: 'Comment on egusphere-2025-3359', Trevor McDougall, 28 Jul 2025
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CC1: 'Comment on egusphere-2025-3359', Stephen M. Griffies, 29 Aug 2025
I read the fundamentals of this manuscript (i.e., the conceptual
parts). As I found flaws in the fundamentals, I did not read the
details of the analysis.Recommendation: Reject
Detailed comments
I concur with McDougall's concern for the use of potential density as
the foundation for a bulk method to measure vertical stratification in
the ocean. Granted, in many areas of the ocean there are no
worries. But the high latitudes are a place where problems can occur.Instead of starting from first principles, the authors pick an
equation from Vallis (2006) that is not even the final expression he
ends up with to measure stratification. Vallis (2006) concludes on
his page 94 that a local measure of stratification is the vertical
derivative of the locally referenced potential density. I appreciate
that Moreles et al are seeking a bulk measure rather than a local
measure. But when one goes bulk, more theoretical work is needed
to formulate the theory and then to test its relevance in the real
ocean.As coauthor of the Reichl et al (2022) potential energy paper, I was
disappointed that Moreles et al did not provide any specific comment
on the novelty of their proposed method relative to Reichl et
al. Indeed, Reichl et al develop a potential energy approach. They
acknowledge the difficulties with the seawater equation of state and
then test approximations that make use of potential density. The
Reichl approach satisfies the goals of Moreles et al. by providing a
bulk enegetics approach that only requires hydrographic data. So where
does Reichl et al fail where Moreles et al succeed?I was also surprised by the absence of the Rosenthal and Roquet (2025)
paper, DOI: 10.1175/JPO-D-24-0078.1, who propose a center of mass
approach to defining stratification. This approach has some relation
to the Reichl et al potential energy approach.As a further critique, I must admit to being disappointed when authors
write down a mathematical expression that has physical dimensions and
then claim those expressions are physically relevant without showing
their corresponding equations of motion. There have been numerous
attempts at providing a rational theory for ocean energetics, and they
all get quite involved conceptually and mathematically. All of these
details are relevant to the present question. One cannot presume to be
presenting a new diagnostic without placing it within a theoretical
context. Quite simply, stating that one is discussing forces and
energies, without showing how they appear from first principles
arguments, is not physics.Summary:
I consider the Moreles et al manuscript to have the
following flaws that suggest to me that it should not be published.1/ Inaccurate theoretical foundation. In particular, the use of
potential density is problematic when considering bulk measures.
Vallis noted this limitation two pages later than the page 92 quoted
by Moreles as their starting point. McDougall's review provides more
points to this regard.2/ Unclear use of physics. Writing down a math object that has
physical dimensions does not make it physical. This point is relevant
to the claim by Moreles et al that they are writing down forces and
energies when, however, they never write the corresponding equation of
motion and equation of energy.3/ Incomplete literature survey. The recent literature has been
discussing energetic foundations for diagnosing vertical
stratification. Moreles et al need to clearly identify the novelty of
their manuscript. The papers by Reichl et al (2022) and Rosenthal and
Roquet (2025) are central to the proposed Moreles et al approach.
Reichl et al is cited by Moreles, but no theoretical or practical
comparison is provided. Rosenthal and Roquet is not cited.4/ Minor point: I found the use of acronyms to be excessive. In
particular, there are many acronyms in the conclusion that are not
defined within the conclusion. Many readers read the abstract than
conclusions in that order, skipping the intermediate sections. Having
undefined acronyms in the conclusion makes it tough to understand the
main points of the manuscript. I strongly recommend greatly reducing
the use of acronyms, except where they are community standards.Stephen Griffies
Princeton UniversityCitation: https://doi.org/10.5194/egusphere-2025-3359-CC1 -
RC2: 'Comment on egusphere-2025-3359', Stephen M. Griffies, 01 Sep 2025
Please see my signed public comment posted 29 Aug 2025.
Citation: https://doi.org/10.5194/egusphere-2025-3359-RC2
Interactive computing environment
Scripts to calculate the buoyancy potential energy Efraín Moreles and Emmanuel Romero https://doi.org/10.5281/zenodo.14911394
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- 1
The underlying equation, equation (1) of this paper is not correct. The paper cannot be published while this error exists. See the attached pdf.