the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 10 Mar 2025
Diffusive and Adiabatic Meridional Overturning Circulations in the Cooling Abyss of the Indo-Pacific Ocean
Abstract. Recent field campaigns have consistently documented bottom-intensified mixing near the seafloor, suggesting diabatic downwelling in the abyssal ocean. This phenomenon appears to contradict with the mass balance of the abyssal ocean, where dense bottom water plunges into the region from the Antarctic side. Previous studies have sought to resolve this apparent paradox by proposing mixing-induced diabatic upwelling along bottom slopes. In contrast, this study offers an alternative perspective, highlighting the role of isopycnal displacement in the transient abyss. Motivated by emerging evidence of a cooling phase in the abyssal Indo-Pacific, likely linked to the last Little Ice Age, this study reinterprets the interior-downwelling paradox from the perspective of unsteady thermal states. Idealized numerical experiments were conducted to explore the abyssal overturning dynamics, with a focus on the behavior of advective, adiabatic, and diffusive overturning circulation streamfunctions in both cooling and warming scenarios. The results reveal that while the direction of diabatic overturning (upwelling or downwelling) depends on the transient state of the ocean, advective overturning circulation consistently exhibits an upwelling pattern, underscoring the inherent robustness of upward water parcel movement within abyssal dynamics.
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RC1: 'Comment on egusphere-2025-989', Anonymous Referee #1, 10 Mar 2025
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The author does not seem to accept that upwelling must occur in Bottom Boundary Layers (BBLs) as a necessary consequence of turbulent mixing decaying to zero at a solid boundary. Instead, the manuscript says “While recent theories have sought to resolve this paradox by incorporating diabatic upwelling within the boundary bottom layer along the slope …” (lines 509-510), and “Previous studies have sought to resolve this apparent paradox by proposing mixing-induced diabatic upwelling along bottom slopes” (lines 10-11). Instead of upward BBL transport, the author invokes the unsteadiness of the ocean circulation to explain how the mean diapycnal flow could be downwards while the mean Eulerian flow is upwards. But the author still needs to explain how the ocean would behave in a steady state. By dismissing the upward transport in the BBL, the author has discarded the process that moves abyssal water upwards in the steady state. Physical processes don’t just disappear because we do not understand them. Rather, physical processes can be made to disappear from our arsenal if and when they can be shown to be based on incorrect physics. Can the author disprove the existence of BBL transport? He has not done so, and I’m sure he cannot.
Another other major problem with this manuscript is the use of overturning streamfunctions. In order to use a streamfunction, the 3D velocity needs to be non-divergent. However, some of the velocities for which the author calculates a streamfunction are divergent velocities. For example, the isopycnal velocity is divergent as is the diapycnal velocity. Hence the conclusions from the maps of these streamlines are erroneous.
The manuscript has clangers like the following “This suggests that there is no longer a need to seek large diffusivities in the ocean with a global average of O(10-4) m2/s. In other words, a locally vanished 𝜅 does not prevent the water parcels from upwelling.” (lines 307-308). This is just plain incorrect. Of course there is still a need for the Munk value of the diapycnal diffusivity, averaged over the abyssal isopycnals. This is how upwelling is achieved, to balance the sinking of the Bottom Water that occurs in steady state. And the physics of mixing that occurred in steady state (before man-made climate change) will still be operating right now. Another clanger appears at line 108 (and in the caption of Figure 1), where it says “The observed bottom-intensified fluxes suggest that the bottom ocean is experiencing a cooling phase.” Also, the ocean modelling has been done in an ocean with a flat bottom and vertical side walls, despite Ferrari et al. (2016) showing that the sloping nature of the sea floor is absolutely critical to the ability of the ocean to allow the downwelling fluid in the interior to escape back to the sea surface via the strongly upwelling bottom boundary layers.
The above are the most glaring completely incorrect aspects of the manuscript. Any of these would be grounds for rejection from a scientific journal.
The manuscript should not be published in Ocean Science.
Citation: https://doi.org/10.5194/egusphere-2025-989-RC1 -
AC1: 'Reply on RC1', Lei Han, 13 Mar 2025
reply
I sincerely appreciate the reviewer’s time and effort in evaluating my work. However, I would like to address a key aspect of the feedback provided. The reviewer’s critiques primarily focus on the statements and conclusions I have drawn from my results. I want to clarify that all of these statements are firmly rooted in the outcomes of numerical experiments and data analysis, which form a substantial portion (approximately 30-40%) of my manuscript. Unfortunately, the reviewer’s comments do not extensively engage with these detailed results. I believe that without a thorough examination of the arguments presented in the results section, it is difficult to fairly assess the merits of any paper.
Furthermore, some of the concerns raised by the reviewer were already addressed in the original manuscript. While I recognize that such oversights can occur in the review process, I remain grateful for the reviewer’s efforts and their contribution to this discussion.Below are detailed response (in bold) to the reviewer's comments (in regular fonts and in quotes).
- Reviewer: “The author does not seem to accept that upwelling must occur in Bottom Boundary Layers (BBLs) as a necessary consequence of turbulent mixing decaying to zero at a solid boundary. Instead, the manuscript says “While recent theories have sought to resolve this paradox by incorporating diabatic upwelling within the boundary bottom layer along the slope …” (lines 509-510), and “Previous studies have sought to resolve this apparent paradox by proposing mixing-induced diabatic upwelling along bottom slopes” (lines 10-11). Instead of upward BBL transport, the author invokes the unsteadiness of the ocean circulation to explain how the mean diapycnal flow could be downwards while the mean Eulerian flow is upwards. But the author still needs to explain how the ocean would behave in a steady state. By dismissing the upward transport in the BBL, the author has discarded the process that moves abyssal water upwards in the steady state. Physical processes don’t just disappear because we do not understand them. Rather, physical processes can be made to disappear from our arsenal if and when they can be shown to be based on incorrect physics. Can the author disprove the existence of BBL transport? He has not done so, and I’m sure he cannot. “
Reply:
I recognize the reviewer’s concern that my manuscript might appear to challenge the established theory of upwelling in Bottom Boundary Layers (BBLs), a concept that has been carefully developed and refined over the past nine years. I’d like to address this concern by clarifying my intentions and the perspective I aimed to present in this work.
Firstly, my goal was not to disprove or dismiss the occurrence of BBL upwelling as a necessary consequence of turbulent mixing decaying to zero at a solid boundary. Just as the reviewer said, “I have not done so”. Rather, my manuscript poses a question: can we explore Munk’s upwelling paradox through an alternative lens?
Secondly, I believe that exploring diverse perspectives is a strength of scientific inquiry, particularly when supported by experimental results and data analysis. History offers compelling examples—Copernicus, Galileo, and Einstein all advanced their fields by questioning prevailing assumptions during periods of intense debate. Such moments of controversy often pave the way for breakthroughs. A discipline that embraces new ideas and encourages open dialogue is better positioned to sustain its momentum and drive vigorous development. I hope physical oceanography remains such a field, and my work is intended as a contribution to this ongoing exchange, not a rejection of established knowledge.- Reviewer: “But the author still needs to explain how the ocean would behave in a steady state.”
Reply:
First, discussion of steady-state upwelling has already been included in the manuscript, specifically in Figure 12 and the preceding paragraph. As noted there, “The steady-state scenario (Figure 12, case c) can be regarded as a special case of the warming scenario…” This section outlines how steady-state dynamics fit within the broader framework of my analysis, treating it as a limiting case rather than an overlooked aspect. I am happy to expand this discussion in revisions if further clarification is needed.
Second, the primary objective of this work is to reinterpret Munk’s interior-downwelling paradox, which may arise under the assumption of a steady state. My findings suggest this paradox can be resolved by recognizing a cooling trend in the modern abyssal Indo-Pacific, supported by both direct and indirect observational evidence (will be explained more in later replies). I argue that the steady-state assumption, though adopted by Munk’s original formulation, must be reconsidered. Not only does it give rise to the paradox, but it also conflicts with contemporary observations, such as the widely recognized bottom-intensified mixing. This mixing pattern points to a cooling signal near the seafloor, rather than a steady-state equilibrium (will be elaborated in details in later replies).
Third, regarding the BBL upwelling theory emphasized by the reviewer, I note that it, too, does not deal with a “steady-state” process but with a cooling framework. For instance, Ferrari et al. (2016) demonstrates this by prescribing a bottom-intensified turbulent density flux in their model. This is similar to the model I employ, though I try not to prescribe a specific density flux profile. Ferrari et al. (2016) states, “The prescribed mixing profile drives an increase in temperature (and hence a decrease in density) over the bottom grid cell and cooling (an increase in density) in the rest of the water column.” I reflect this concept in my Figure 1 and briefly reference it in Section 5, aligning my interpretation with theirs: bottom-intensified mixing supports a cooling trend rather than a steady-state upwelling process alone. This convergence strengthens my case that transient dynamics, rather than a rigid steady-state assumption, offer a viable lens for understanding the paradox.- Reviewer: “Can the author disprove the existence of BBL transport? He has not done so, and I’m sure he cannot.”
Reply:
I appreciate the opportunity to clarify this point. This manuscript does not seek to disprove BBL transport, nor does it deny its potential presence in slope topography. Rather, my aim is to invite consideration of an alternative perspective: how might our understanding of the upwelling problem shift if we view it through the lens of an unsteady background state? This study is intended as a reminder of the value in exploring such differences, not as a rejection of established mechanisms like BBL transport.- Reviewer: “Another other major problem with this manuscript is the use of overturning streamfunctions. In order to use a streamfunction, the 3D velocity needs to be non-divergent. However, some of the velocities for which the author calculates a streamfunction are divergent velocities. For example, the isopycnal velocity is divergent as is the diapycnal velocity. Hence the conclusions from the maps of these streamlines are erroneous. ”
Reply:
First, on the sloshing MOC streamfunction:
I respectfully point out that I have addressed this issue in the last paragraph of Section 3.1 (line 230), which the reviewer may have overlooked. The newly defined meridional overturning circulation (MOC) streamfunction, termed the “sloshing MOC streamfunction”, is not derived from 3D velocity fields, but from the 3D density field. Consequently, the non-divergence criterion does not apply in the traditional sense. This approach leverages the density field to measure adiabaticity, particularly in the ocean interior, where isopycnals act as “almost impermeable barriers” (Young, 2012, JPO). Its effectiveness is evidenced by its successful application in prior studies of MOC variability mechanisms in the Indian and Atlantic Oceans (Han, 2021, JPO; Han, 2023a, JPO; Han, 2023b, GRL).
To illustrate, I attach an example figure from Han (2021, JPO) depicting monthly MOC in the Indian Ocean. The first row shows the Eulerian MOC streamfunction (derived from 3D velocity), the second row presents the sloshing MOC streamfunction (derived from 3D density), and the third row displays their difference. The striking resemblance between the two, despite being generated from entirely distinct variables (velocity versus density), underscores the robustness of this method. Even without adhering to the non-divergence criterion, the sloshing MOC streamfunction proves its strength and validity as an insightful diagnostic tool.
(Sorry if the figure appears too blurry—the 500×500px upload limit is quite restrictive. One can see the original figure in the paper anyway)Second, an alternative perspective without streamfunctions:
OK, let’s forget about the streamfunction for a moment and turn to a concrete, quantitative example instead: the long-term-mean upwelling transport across a plane surface at 4000 m depth, north of 10°N in the Indo-Pacific, calculated using ECCO v4r3 data. The total Eulerian transport of water parcels is obtained by integrating the Eulerian vertical velocity (w_Eul), a direct diagnostic from ECCO, over this region, yielding approximately 6 Sv. In parallel, the isopycnal displacement rate (w_iso) is computed from the ECCO density field, allowing estimation of the upwelling transport of isopycnals (akin to the “isopycnal volume anomaly” of Monkman and Jansen, 2024, JGR), which totals approximately 9 Sv. Comparing these transports reveals a difference of ~3 Sv, indicating that water parcels are crossing isopycnals downard at 4000 m in this region.
This 3 Sv of diapycnal downwelling raises an intriguing question: could it reflect the long-standing “interior-downwelling” puzzle posed by Munk’s abyssal recipes, particularly under conditions of bottom-intensified mixing? I have schematized this basic concept as a cooling scenario in Figure 12 of the manuscript (attached below).
The underlying mechanism, wherein isopycnals ascend more rapidly than material surfaces (water parcels) due to cooling and thus lead to a downward diapycnal velocity, is further elucidated in Figure 7(a) (see below).
- Reviewer: “The manuscript has clangers like the following “This suggests that there is no longer a need to seek large diffusivities in the ocean with a global average of O(10-4) m2/s. In other words, a locally vanished 𝜅 does not prevent the water parcels from upwelling.” (lines 307-308). This is just plain incorrect. Of course there is still a need for the Munk value of the diapycnal diffusivity, averaged over the abyssal isopycnals. This is how upwelling is achieved, to balance the sinking of the Bottom Water that occurs in steady state. And the physics of mixing that occurred in steady state (before man-made climate change) will still be operating right now. ”
Reply:
I appreciate this perspective and would like to respond by drawing on a laboratory demonstration of overturning circulation.
In this experiment (YouTube link: https://www.youtube.com/watch?v=eZzpvLz4yAk), cold (blue-colored) water at the right end of a tank exhibits significant upward motion as it creeps along the bottom and encounters the vertical wall boundary on the right side. Notably, mixing in this setup is expected to be minimal, as no mechanical energy sources—such as internal tides present in the real ocean—are introduced. Yet, the bottom cold water rises at a rate that appears to exceed typical upwelling speeds in the actual ocean. If upwelling were solely balanced by mixing, as the reviewer suggests, would this imply that mixing in the tank is stronger than in the real ocean?
Additionally, this experiment uses a flat-bottom tank. The reviewer later argues that “the sloping nature of the sea floor is absolutely critical to the ability of the ocean to allow the downwelling fluid in the interior to escape back to the sea surface.” Yet, in this flat-bottom setup, bottom water still rises without a sloping topography. Could this suggest the presence of physical processes beyond the BBL upwelling mechanism that also facilitate the ascent of bottom water? To be clear, I am not asserting that the BBL upwelling mechanism is invalid or inoperative. Rather, inspired by this lab demonstration, I am exploring the possibility that an additional process might contribute to upwelling alongside BBL dynamics.
That said, I recognize that this discussion, as presented in the manuscript, is peripheral to its primary scope and lacks robust evidence to fully substantiate it. While an MITgcm experiment could potentially provide such support, I propose deferring that investigation for now. To address the reviewer’s concern and maintain focus on the manuscript’s core objectives, I am willing to remove this paragraph in the revision. I value the reviewer’s insight and welcome further guidance on refining the manuscript accordingly.
YouTube link: https://www.youtube.com/watch?v=eZzpvLz4yAk
- Reviewer: “Another clanger appears at line 108 (and in the caption of Figure 1), where it says “The observed bottom-intensified fluxes suggest that the bottom ocean is experiencing a cooling phase.” ”
Reply:
Well, I respectfully suggest that if this constitutes an error, it is one shared by the BBL upwelling theory itself. As I noted earlier, Ferrari et al. (2016) assert, “The prescribed mixing profile drives an increase in temperature (and hence a decrease in density) over the bottom grid cell and cooling (an increase in density) in the rest of the water column.”
To further bolster this point, I have reviewed presentations on BBL upwelling theory by Ferrari himself. In one such video, at timestamp 29:28 (available at: https://www.youtube.com/watch?v=z0JirrUVkVE), Ferrari explicitly indicates “cooling” in the bottom water above the BBL. I’ve included a snapshot from this presentation for reference (see below). This aligns with the concept of cooling within the domain of bottom-intensified mixing, precisely as depicted in my Figure 1. Thus, my statement reflects a perspective consistent with established work in the field, including Ferrari’s own contributions.
- Reviewer: “Also, the ocean modelling has been done in an ocean with a flat bottom and vertical side walls, despite Ferrari et al. (2016) showing that the sloping nature of the sea floor is absolutely critical to the ability of the ocean to allow the downwelling fluid in the interior to escape back to the sea surface via the strongly upwelling bottom boundary layers. ”
Reply:
I appreciate the reviewer’s observation regarding the setup of my ocean modeling, which employs a flat bottom and vertical sidewalls. I welcome this opportunity to clarify the consistency and implications of my approach.
My numerical experiments with a flat-bottom and vertical-sidewall configuration successfully simulate Eulerian (or residual) upwelling—tracking the movement of water parcels—in all cases, as evident in Figure 11 and Figure S3 of my manuscript. Intriguingly, Ferrari et al. (2016), as cited by the reviewer, also demonstrate Eulerian upwelling in a flat-bottom ocean. While they indeed utilize a bowl-shaped topography in parts of their study, they additionally employ a box (flat-bottom) configuration (see their Figure 3). Their residual MOC streamfunction, presented in Figure 5 (snapshot provided below), clearly reveals upwelling in the bottom ocean. For clarity, I have overlaid red arrows on this figure to highlight the direction of the overturning streamfunction, which unambiguously indicates upward motion.
My results align closely with Ferrari et al.’s flat-bottom and vertical-sidewall experiment, both in terms of topographic setup and the observed outcomes. This raises a question: if both studies demonstrate upwelling in a flat-bottom context, why might the reviewer question the validity of my findings while endorsing theirs? Our collective results suggest that upwelling is not exclusively dependent on a sloping seafloor but can also occur over a flat bottom. This consistency underscores the robustness of my simulations and their compatibility with established work.
I am grateful for the reviewer’s insight, which has prompted this detailed comparison. I am open to further discussion or adjustments to ensure my presentation fully addresses any lingering concerns about the role of topography in these dynamics.
(Ferrari et al 2016)- Reviewer: “The above are the most glaring completely incorrect aspects of the manuscript. Any of these would be grounds for rejection from a scientific journal.
The manuscript should not be published in Ocean Science.”
Reply:
To be frank, I find great satisfaction in addressing each point in above, even when the critiques are sharply worded or express strong objections. I see immense value in such feedback, as it likely mirrors questions or reservations that others in the community might also hold. This dialogue with the reviewer offers me a meaningful opportunity to refine and clarify my ideas for a wider audience.
I am grateful that EGU’s Ocean Science provides a platform for open discourse. This environment allows new ideas to be presented, scrutinized, and refined, ultimately driving advancements in our collective understanding. I hope the broader community continues to embrace fresh perspectives and diverse voices, as such openness is fundamental to the robust growth of our discipline.
Thank the reviewer once again for his/her critical insights, which have enriched this process. I look forward to further refining my work in light of this exchange, with the aim of contributing constructively to the field.References:
- Ferrari, R., A. Mashayek, T. J. McDougall, M. Nikurashin, and J. Campin, 2016: Turning ocean mixing upside down. 585 J. Phys. Oceanogr., 46, 2239-2261.
- Han, L., 2021: The sloshing and diapycnal meridional overturning circulations in the Indian Ocean. J. Phys. Oceanogr., 51, 701-725.
- Han, L., 2023a: Mechanism on the short-term variability of the Atlantic meridional overturning circulation in the subtropical and tropical regions. J. Phys. Oceanogr., 53, 2231-2244.
- Han, L., 2023b: Exploring the AMOC Connectivity Between the RAPID and OSNAP Lines with a Model‐Based Data Set. Geophys. Res. Lett., 50, e2023GL105225.
- Monkman, T. and M. F. Jansen, 2024: The Global Overturning Circulation and the Role of Non‐Equilibrium Effects in ECCOv4r4. J. Geophys. Res., 129, e2023JC019690.
- Young, W. R., 2012: An exact thickness-weighted average formulation of the Boussinesq equations. J. Phys. Oceanogr., 42, 692–707
Citation: https://doi.org/10.5194/egusphere-2025-989-AC1
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AC1: 'Reply on RC1', Lei Han, 13 Mar 2025
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