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
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
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 -
AC3: 'Further response to RC1 on the steady-state abyssal MOC structure', Lei Han, 30 Apr 2025
I would like to provide some additional response to the following comment from the Reviewer #1, supported by results from a recent numerical simulation: “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.”
A similar question concerning the steady-state behavior was also raised by Reviewer #2. To address these concerns, I conducted an additional experiment that extends the model integration to 4000 years, approaching a near steady-state solution.
This simulation is referred to as Exp. 1 in the “Reply to RC2,” and is configured as follows:
Exp. 1: Baseline steady-state configuration with uniform diffusivity of 1×10⁻⁵ m²/s in the interior basin. Forcing: southern sidewall relaxation of 1°C below 2000 m. Surface relaxation of 25°C at the equator. Integrated for 4000 years from rest.
The results are summarized in the figure below. As expected, a robust upwelling overturning cell dominates the abyssal ocean (left panel). The sloshing component, ψₛₗₒ—diagnosed from isopycnal displacements—is negligible due to the stabilized stratification (middle panel), resulting in the residual and diapycnal overturning streamfunctions being nearly identical (right panel). This is consistent with the steady-state configuration illustrated in Figure 12(c) of the manuscript.
[Figure R1. Results of Exp.1. Similar to Figure 11 in the paper, but with the cooling scenario simulation running for 4000 years to quasi-equilibrium. The MOC streamfunctions are residual MOC (left), sloshing MOC (middle), and diapycnal MOC (right), respectively. Negative/positive streamfunction represent anti-clockwise/clockwise) overturning cells. ]
The simulation confirms the persistence of both Eulerian and diabatic upwelling in the abyssal ocean. The residual overturning streamfunction stabilizes at approximately 3.8 Sv within the interior basin after several thousand years of integration (see Figure R2 in the “Reply to RC2”). It seems likely that the bottom water can be upwelled from a flat-bottom basin (I've also run a simulation with randomly generated topography, which includes continental slope, island, and sea mounts. The result shows the abyssal MOC structure and intensity do not alter much compared with the flat-bottom configuration. Please refer to Figure R3 in the "Reply to RC2", also attached below). This finding aligns with an earlier modeling study using a flat-bottom configuration, also implemented with MITgcm at a 2° horizontal resolution (see Figs. 3 and 5 of Ferrari et al., 2016). I would appreciate any further comments or suggestions from the reviewer regarding this result.
[Figure R3 in "Reply on RC2". Exp. 1 with vertical sidewalls (left column) and Exp. 4 with randomly generated topography in the basin (right column). The residual MOC streamfunctions at the end of the simulations (upper row) and the topography (lower row) for the two cases are shown.]
Citation: https://doi.org/10.5194/egusphere-2025-989-AC3 -
AC4: 'Reply on RC1', Lei Han, 10 May 2025
I would like to further address the concern raised in RC1 regarding the use of a novel meridional overturning circulation (MOC) streamfunction, namely the sloshing MOC streamfunction.
The reviewer commented in RC1: “Another 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.”
As already noted in my initial response (AC1), the issue of velocity non-divergence was explicitly acknowledged and discussed in the manuscript (see paragraph around Line 230), but was unfortunately overlooked by the reviewer#1.
I would also like to highlight that the sloshing MOC streamfunction has been utilized to investigate the variability and dynamics of the Atlantic and Indian Ocean MOC in four recent publications: Han (2021, JPO), Han (2023a, JPO), Han (2023b, GRL), and Han (2025, GRL):
- Han, L. (2021). The sloshing and diapycnal meridional overturning circulations in the Indian Ocean. Journal of Physical Oceanography, 51(3), 701-725.
- Han, L. (2023a). Mechanism on the short-term variability of the Atlantic meridional overturning circulation in the subtropical and tropical regions. Journal of Physical Oceanography, 53(9), 2231-2244.
- Han, L. (2023b). Exploring the AMOC connectivity between the rapid and osnap lines with a model-based data set. Geophysical Research Letters, 50(19), e2023GL105225.
- Han, L. (2025). How does a stable AMOC influence the regional climate of the North Atlantic? Geophysical Research Letters, accepted.
Collectively, these works have undergone rigorous reviews four times. While any single publication might benefit from favorable reviews by chance, the consistent acceptance of this framework across four major publications in two highly respected journals—Journal of Physical Oceanography (JPO) and Geophysical Research Letters (GRL)—makes such a coincidence unlikely. What are the chances that the eight reviewers were all mistaken in their assessments? This indicates that the concept has gained a degree of recognition and acceptance within the community.
I’ve explicitly acknowledged the limitations of the new streamfunction in the series of abovementioned publications, including some issues that were not noticed by the reviewer#1. Nonetheless, these limitations do not preclude the method from offering useful insights into overturning dynamics. The usefulness of a diagnostic tool lies not in its perfection, but in whether its inherent errors materially affect the interpretation of the true dynamics. I believe this is the reason why my recent studies utilizing this tool were successfully accepted in all of the peer reviews.
Furthermore, as elaborated in AC1, I approached the diagnostics of isopycnal displacement and Eulerian upwelling from a complementary angle—that is, by considering basin-integrated transports. This method, consistent with that of Monkman and Jansen (2024, JGR), yielded results that align with those obtained using the sloshing MOC streamfunction, thereby reinforcing the robustness of the conclusions.
In light of the above, I respectfully suggest that the criticism of this diagnostic tool may warrant reconsideration.
Citation: https://doi.org/10.5194/egusphere-2025-989-AC4
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AC1: 'Reply on RC1', Lei Han, 13 Mar 2025
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RC2: 'Comment on egusphere-2025-989', Anonymous Referee #2, 10 Apr 2025
In this manuscript the author revisits the balance between advective and diffusive contributions to the overturning in the Pacific ocean from observations, a reanalysis and idealised simulations. They report a general cooling of the abyssal Pacific and interpret this as a potential balance to the formation of dense water at high latitude. Overall the results presented from the analysis of the observations and the models appear to be correct however I have some major concerns about their interpretation and a lack of consideration of the impact of the choices in their idealised model. I believe this manuscript could become publishable however it would need significant revisions to the content and text to provide a more accurate and balanced interpretation of the results presented.
Firstly, I think the paper confuses two seemingly similar but distinct problems, namely the long term balances in the ocean associated with a near steady state and a transient response to changes in forcing. Throughout the paper they are reporting an inflation of the coolest layers of the Pacific associated with either changes in surface forcing for the observations and ECCO or relaxation at the southern boundary of the idealised simulation. Whilst I am convinced that this response is a real feature of the current ocean state it can not be maintained for long periods without either the whole ocean becoming cooler over long time periods or an alternative balance being reached (for example by a fundamental change in the structure of stratification). The author interprets this result as an alternative to the upwelling (or warming) of water by mixing processes (such as within the bottom boundary layer) by comparing the rate of inflation of these layers to the diapycnal mixing. Whilst this can be the case for a transient response it is still unclear to me that it can hold over very long time scales or global integrals. In order for this paper to be publishable I would prefer to see a much more nuanced discussion of the transient nature of the response and how it can contributed to the long time average ocean state.
Secondly, I have concerns about the lack of consideration for the impact of the simplifying choices made in their idealised model. It has been shown in previous studies, e.g. Ferrari et al 2016, that the choice of vertical vs sloping side walls can significantly change the impact of mixing in the bottom boundary layer in the upwelling process. This paper makes the simplifying choice of using vertical sidewalls and then interprets the results as implying mixing has a limited role in overturning. Whilst this is a feature of their model it is possible, perhaps likely, that this is simply a result of the choice of sidewalls rather than a feature of the real ocean. Additionally, the choice of the relaxation in the southern part of the domain lacked discussion of the role this choice made in the results presented. The conclusions the author draws would be much more convincing if the sensitivity to these choices was demonstrated, such as through additional simulations.
In addition to these two main concerns I have a series of minor corrections below.
Throughout the paper the author uses both warming / cooling and upwelling / downwelling. It would be much clearer if the separation between these sets of terminology was made clearer at the start in terms of movement in temperature space vs vertical motion without changing temperature. It is common in the literature people to use upwelling to mean across density surfaces so it could cause some confusion if not clearly defined here.
Line 53 – I found the sentence starting here hard to understand.
Line 180 – The statement here that bottom intensified mixing leads to a general cooling through much of the water column is true but a more complete statement would also highlight the warming implied by the zero flux condition at the boundary (as seen in the idealised model).
Line 224 onwards – I found the use of 4 streamfunctions a little confusing here. To me it seems there are 3: Eulerian, Sloshing, Diabatic. Did I miss something?
Paragraph starting 442 – Is this not just a result of having a model with non-zero diffusivity and no mechanism in the model to produce more light surface waters? For example, in a box with some initial stratification and non-zero diffusivity the isopycnals must move towards the upper and lower boundaries until the box is well mixed. It seems to me that this result is just a result of the choices made in the idealisation of the model and is not applicable in a scenario with a source of surface waters.
Line 510 – typo should read “bottom boundary layer”
Citation: https://doi.org/10.5194/egusphere-2025-989-RC2 -
AC2: 'Reply on RC2', Lei Han, 30 Apr 2025
I sincerely appreciate the reviewer’s time and effort in evaluating my work. Thank the reviewer for the constructive feedback and for giving me the opportunity to clarify my study. In response to the reviewer’s concerns, I have conducted a series of additional simulations using MITgcm to better evaluate the robustness of the original interpretations.
Below are detailed response (in bold) to the reviewer's comments (in regular fonts and in quotes).- Reviewer: “In this manuscript the author revisits the balance between advective and diffusive contributions to the overturning in the Pacific ocean from observations, a reanalysis and idealised simulations. They report a general cooling of the abyssal Pacific and interpret this as a potential balance to the formation of dense water at high latitude. Overall the results presented from the analysis of the observations and the models appear to be correct however I have some major concerns about their interpretation and a lack of consideration of the impact of the choices in their idealised model. I believe this manuscript could become publishable however it would need significant revisions to the content and text to provide a more accurate and balanced interpretation of the results presented.”
Reply:
I appreciate the reviewer's encouraging words and constructive comments and questions. In response to the reviewer’s concerns, I have conducted a series of additional simulations using MITgcm to better evaluate the robustness of the original interpretations.
One issue that, although not explicitly raised in the reviewer’s comments, I found important to address is the limited zonal extent (~50° longitude) used in the original idealized simulations. While a wider-basin simulation (double the original width) was included in the original Supplementary Figure S4 to demonstrate that the key conclusions are not sensitive to basin width, I now recognize that employing a more realistic geometry strengthens the credibility of the study. Therefore, I have revised all simulations throughout the manuscript to use a basin width of approximately 100°, which is more consistent with previous studies (e.g., Ferrari et al., 2016 used a 120°-wide basin). All new simulations presented in the revised manuscript are based on this wider-basin configuration. As can be seen in the reply below, these additional simulations help confirm the robustness of the original results.- Reviewer: “Firstly, I think the paper confuses two seemingly similar but distinct problems, namely the long term balances in the ocean associated with a near steady state and a transient response to changes in forcing. Throughout the paper they are reporting an inflation of the coolest layers of the Pacific associated with either changes in surface forcing for the observations and ECCO or relaxation at the southern boundary of the idealised simulation. Whilst I am convinced that this response is a real feature of the current ocean state it can not be maintained for long periods without either the whole ocean becoming cooler over long time periods or an alternative balance being reached (for example by a fundamental change in the structure of stratification). The author interprets this result as an alternative to the upwelling (or warming) of water by mixing processes (such as within the bottom boundary layer) by comparing the rate of inflation of these layers to the diapycnal mixing. Whilst this can be the case for a transient response it is still unclear to me that it can hold over very long time scales or global integrals. In order for this paper to be publishable I would prefer to see a much more nuanced discussion of the transient nature of the response and how it can contributed to the long time average ocean state.”
Reply:
Thank the review for the thoughtful and detailed comments. I fully agree with the reviewer’s distinction between long-term steady-state balances and transient responses to changes in forcing. This is indeed a crucial point, and I appreciate the opportunity to clarify how this distinction is treated in the manuscript.
I acknowledge this separation explicitly in the original manuscript, particularly in Figure 12: panels (a) and (b) depict transient responses of the abyssal MOC to changes in surface or boundary forcing, while panel (c) illustrates the steady-state configuration. The focus of this study has been on the transient cooling/warming responses because they likely represent the current state of the abyssal Indo-Pacific Ocean. These transient dynamics can offer useful insights into observed features—such as bottom-intensified turbulent heat fluxes—that are not consistent with a steady-state configuration. This is the reason why this paper focuses on the transient dynamics rather than the steady state. That said, I fully agree that understanding the steady state remains important, both as a reference and for assessing the long-term sustainability of any transient adjustment.
[Figure 12 of the manuscript]To better address this, I have extended my simulations toward a near steady-state configuration. Specifically, in the idealized model under the cooling scenario, I introduced an additional surface temperature relaxation near the Equator to create a heat source that balances the southern sidewall cooling, thereby enabling the system to reach a steady state. This setup is conceptually similar to the surface relaxation employed by Ferrari et al. (2016). The model was then integrated for 4000 years to reach a near steady state. This simulation is denoted as “Exp. 1”, whose setup is as follows:
Exp. 1: Baseline steady-state configuration with uniform diffusivity of 1×10⁻⁵ m²/s in the interior basin. Forcing: southern sidewall relaxation of 1°C below 2000 m. Surface relaxation of 25°C. Integrated for 4000 years from rest.
The results are shown in Figure R1 (attached below). As expected, a stable upwelling MOC cell dominates the deep ocean (left panel). The sloshing component of the MOC, ψslo—diagnosed from isopycnal displacements—is essentially zero due to the stabilized stratification (middle panel), so the residual and diapycnal MOC streamfunctions become identical (right panel). This outcome is consistent with the steady-state configuration illustrated in Figure 12(c) of the paper (the figure in above). I can add this figure in the revision to support the conclusion on the steady-state dynamics.
[Figure R1. Results of Exp.1. Similar to Figure 11 in the paper, but with the cooling scenario simulation running for 4000 years to quasi-equilibrium. The MOC streamfunctions are residual MOC (left), sloshing MOC (middle), and diapycnal MOC (right), respectively. Negative/positive streamfunction represent anti-clockwise/clockwise) overturning cells.]To further emphasize the transient nature of the response, I have conducted two additional simulations branching from the quasi-equilibrium state (Exp. 1):
Exp. 2: Branching from Exp. 1 at year 4000, but increasing the southern sidewall relaxation temperature to 1.5°C. Integrated for 1000 years.
Exp. 3: Also branching from Exp. 1 at year 4000, but reducing the vertical extent of southern sidewall temperature relaxation from lower 2000 m to lower 1700 m. Integrated for 1000 years.
These two perturbation experiments simulate a weakening of bottom water formation via different mechanisms. To quantify the abyssal overturning strength, we define an index as the maximum absolute value of the MOC streamfunction in the Indo-Pacific basin north of 40°S and below 2000 m. Figure R2 shows the time evolution of this overturning index and the mean KE across the three experiments, capturing the transient adjustment of abyssal overturning strength in response to changes in bottom water formation. These results suggest that the abyssal overturning circulation exhibits a reduction to weakened bottom water formation, and tends to adjust toward a new equilibrium over the long term.
[Figure R2. Time series of abyssal MOC index (left panel) and mean KE (right panel) of the simulations for Exp. 1 (black), Exp. 2 (red), and Exp. 3 (yellow), respectively.]
- Reviewer: “Secondly, I have concerns about the lack of consideration for the impact of the simplifying choices made in their idealised model. It has been shown in previous studies, e.g. Ferrari et al 2016, that the choice of vertical vs sloping side walls can significantly change the impact of mixing in the bottom boundary layer in the upwelling process. This paper makes the simplifying choice of using vertical sidewalls and then interprets the results as implying mixing has a limited role in overturning. Whilst this is a feature of their model it is possible, perhaps likely, that this is simply a result of the choice of sidewalls rather than a feature of the real ocean. Additionally, the choice of the relaxation in the southern part of the domain lacked discussion of the role this choice made in the results presented. The conclusions the author draws would be much more convincing if the sensitivity to these choices was demonstrated, such as through additional simulations.”
Reply:
Thank the reviewer for raising this important point. I fully acknowledge that idealized modeling choices, such as the use of vertical sidewalls and specific relaxation boundary conditions, can influence the results and interpretations. Indeed, as mentioned in the paper, Ferrari et al. (2016) is a foundational reference for this study, and many aspects of the model configuration—including spatial resolution and forcing schemes—were adapted from their setup.
I would like to clarify that this study does not argue against the role of mixing in driving overturning circulations. In fact, all simulations in this study produce notable abyssal overturning cells due to mixing. I’ve also run a case with very low diffusivity, and the abyssal overturning circulation hardly develops. This study attempts to highlight the potential importance of other dynamical processes beyond mixing alone. Moreover, Ferrari et al. (2016) also demonstrated that upwelling overturning circulations can emerge in a domain with vertical sidewalls (see their Figure 3; a snapshot is included below). My results are consistent with theirs in terms of the direction and structure of the residual MOC streamfunction, lending confidence to the validity of my simulation output.
[A combination of Fig. 3 and Fig. 5 of Ferrari et al (2016). Red arrows indicate the directions of the overturning cells.]That said, I appreciate the reviewer’s suggestion to test the sensitivity of our results to topographic effects. To investigate this, I conducted an additional simulation, denoted “Exp. 4,” which has the same configuration as Exp. 1 but with randomly generated bottom topography in the interior basin, including continental slopes, islands, and seamounts (see lower right panel of Figure R3). Interestingly, the upwelling strength and structure in Exp. 4 remain largely similar to those in Exp. 1, albeit with slightly less spatial smoothness. This indicates that the presence of bottom topography does not substantially alter the large-scale abyssal upwelling in our model. These results suggest that the internal dynamics, rather than bottom topography alone, play a more dominant role in driving the upwelling.
[Figure R3. Exp. 1 with vertical sidewalls (left column) and Exp. 4 with randomly generated topography in the basin (right column). The residual MOC streamfunctions at the end of the simulations (upper row) and the topography (lower row) for the two cases are shown.]Regarding the southern boundary temperature relaxation, I agree that the manuscript initially lacked adequate discussion of its role, but it has been addressed here by Exp. 2 and Exp.3. As shown in Exp. 2 and Exp. 3 (in the earlier reply), the strength of abyssal overturning is sensitive to the characteristics of this southern relaxation. Specifically, weaker bottom water formation (either by reducing the relaxation strength or its extent) leads to a weaker abyssal overturning cell.
While Ferrari et al. (2016) implemented surface relaxation to simulate bottom water formation, I also tested this configuration. However, I ultimately adopted sidewall relaxation because it is capable of producing bottom-intensified turbulent heat fluxes under cooling scenarios—a feature widely observed in the real ocean. In comparison, surface relaxation does not reproduce this key characteristic. Thus, the sidewall relaxation was chosen to better represent the observed vertical structure of turbulent mixing and abyssal dynamics.- Reviewer: “In addition to these two main concerns I have a series of minor corrections below.
Throughout the paper the author uses both warming / cooling and upwelling / downwelling. It would be much clearer if the separation between these sets of terminology was made clearer at the start in terms of movement in temperature space vs vertical motion without changing temperature. It is common in the literature people to use upwelling to mean across density surfaces so it could cause some confusion if not clearly defined here.”
Reply:
Thank the reviewer for pointing this out. I fully agree that the terminology regarding vertical motion should be clearly defined to avoid confusion. In this study, we distinguish two types of vertical motion. The “movement in temperature space” that the reviewer mentioned is defined as the diapycnal upwelling/downwelling, i.e., the vertical velocity, wdia. While the “vertical motion without changing temperature” is measured by tracking the displacement of the isopycnal, i.e., the vertical velocity, wiso. These definitions have been summarized in Table 1 of the manuscript. If any of these remain unclear, I would greatly appreciate it if the reviewer could specify which part in the text needs clarification so I can address it accordingly.
“people to use upwelling to mean across density surfaces”: In my view, upwelling does not always imply cross-isopycnal process. For example, isopycnal heaving induced by Ekman pumping involves vertical motion without water mass transformation. One of the key objectives of this study is to distinguish between different upwelling concepts, such as adiabatic versus diabatic upwelling. These correspond to the so-called “adiabatic MOC” and “diffusive MOC”, as schematically illustrated in Figure 12 of the manuscript.
In light of this discussion, I have also revisited the term “sloshing MOC”. I do acknowledge that there are some flaws in the definition of the sloshing MOC. Since it is defined by tracking the movement of isopycnals, it includes both adiabatic and diabatic contributions. Therefore, referring to it as purely “adiabatic MOC” is inaccurate. I will revise the terminology used for this component throughout the manuscript to avoid this misinterpretation.- Reviewer: “Line 53 – I found the sentence starting here hard to understand.”
Reply:
Thank the reviewer for pointing this out. I assume the reviewer is referring to the sentence: “Volume budget below deep, cold isotherm within the Pacific basin ‘are not in steady state’ (Purkey and Johnson 2012).” This is a direct quotation from the abstract of Purkey and Johnson (2012), which I cited to support the point that the volume below a given deep isotherm in the Pacific is changing over time. I retain it to preserve the authors’ intent.- Reviewer: “Line 180 – The statement here that bottom intensified mixing leads to a general cooling through much of the water column is true but a more complete statement would also highlight the warming implied by the zero flux condition at the boundary (as seen in the idealised model).”
Reply:
True. This is a good point. Yes, it is always warming in the bottom boundary layer (BBL) as indicated in Figure 1 of the paper. I’ll add a label “warming” for the BBL in the figure to indicate that. That said, I would also like to emphasize that the BBL typically spans only a few tens of meters (Ferrari et al., 2016), whereas the abyssal ocean extends over several thousand meters. Therefore, while the BBL does experience warming due to constrained vertical heat fluxes, its contribution is insufficient to offset the general cooling observed throughout the much thicker overlying water column. I will clarify this point in the revised manuscript to provide a more balanced and complete interpretation.- Reviewer: “Line 224 onwards – I found the use of 4 streamfunctions a little confusing here. To me it seems there are 3: Eulerian, Sloshing, Diabatic. Did I miss something?”
Reply:
The reviewer is correct that the main conceptual categories are three, but they are Advective, Sloshing, and Diabatic. There are 4 streamfunctions in total because I have presented two types of Advective streamfunctions: one defined in the depth coordinate (the traditional Eulerian MOC, ψEul), and one defined in the density coordinate (ψσ). These two are both included in Table 1 and showed in Figure 4 of the manuscript. In a near adiabatic process, their maximum values are comparable even though they are defined in different coordinates unless the isopycnals are significantly titled in zonal direction.
Johnson et al (2019) showed both streamfunctions of AMOC in their Figure 2, which the maximum overturning circulations at each latitude are similar except in the subpolar region. Monkman and Jansen (2024) showed a similar strength ψσ for the Indo-Pacific region (their Figure 3b). I presented both streamfunctions to provide a more comprehensive view of the abyssal Indo-Pacific MOC structure from complementary perspectives. In any case, I will revise the text to eliminate the confusion about 3 or 4 streamfunctions.- Reviewer: “Paragraph starting 442 – Is this not just a result of having a model with non-zero diffusivity and no mechanism in the model to produce more light surface waters? For example, in a box with some initial stratification and non-zero diffusivity the isopycnals must move towards the upper and lower boundaries until the box is well mixed. It seems to me that this result is just a result of the choices made in the idealisation of the model and is not applicable in a scenario with a source of surface waters.”
Reply: Yes, this is precisely the point I intended to convey. The emergence of the diapycnal upper cell is purely a consequence of isopycnals migrating upward due to environmental cooling or non-zero diffusivity, while the water parcels themselves exhibit minimal motion. This result reinforces our main finding regarding the abyssal ocean: in an unsteady state, a non-zero "diapycnal overturning circulation" can arise solely from changes in stratification, without implying actual movement of water parcels.
- Reviewer: “Line 510 – typo should read “bottom boundary layer””
Reply: Exactly. Thank the reviewer for catching this. I’ll make the correction.
References:
- Ferrari, R., A. Mashayek, T. J. McDougall, M. Nikurashin, and J. Campin, 2016: Turning ocean mixing upside down. J. Phys. Oceanogr., 46, 2239-2261.
- Johnson, H. L., P. Cessi, D. P. Marshall, F. Schloesser, & M. A. Spall, 2019: Recent contributions of theory to our understanding of the Atlantic Meridional Overturning Circulation. Journal of Geophysical Research: Oceans, 124, 5376-5399.
- 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.
- Purkey, S. G. and G. C. Johnson, 2012: Global contraction of Antarctic Bottom Water between the 1980s and 2000s. J. Clim., 25, 5830-5844.
Citation: https://doi.org/10.5194/egusphere-2025-989-AC2
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AC2: 'Reply on RC2', Lei Han, 30 Apr 2025
Status: closed
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RC1: 'Comment on egusphere-2025-989', Anonymous Referee #1, 10 Mar 2025
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
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 -
AC3: 'Further response to RC1 on the steady-state abyssal MOC structure', Lei Han, 30 Apr 2025
I would like to provide some additional response to the following comment from the Reviewer #1, supported by results from a recent numerical simulation: “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.”
A similar question concerning the steady-state behavior was also raised by Reviewer #2. To address these concerns, I conducted an additional experiment that extends the model integration to 4000 years, approaching a near steady-state solution.
This simulation is referred to as Exp. 1 in the “Reply to RC2,” and is configured as follows:
Exp. 1: Baseline steady-state configuration with uniform diffusivity of 1×10⁻⁵ m²/s in the interior basin. Forcing: southern sidewall relaxation of 1°C below 2000 m. Surface relaxation of 25°C at the equator. Integrated for 4000 years from rest.
The results are summarized in the figure below. As expected, a robust upwelling overturning cell dominates the abyssal ocean (left panel). The sloshing component, ψₛₗₒ—diagnosed from isopycnal displacements—is negligible due to the stabilized stratification (middle panel), resulting in the residual and diapycnal overturning streamfunctions being nearly identical (right panel). This is consistent with the steady-state configuration illustrated in Figure 12(c) of the manuscript.[Figure R1. Results of Exp.1. Similar to Figure 11 in the paper, but with the cooling scenario simulation running for 4000 years to quasi-equilibrium. The MOC streamfunctions are residual MOC (left), sloshing MOC (middle), and diapycnal MOC (right), respectively. Negative/positive streamfunction represent anti-clockwise/clockwise) overturning cells. ]
The simulation confirms the persistence of both Eulerian and diabatic upwelling in the abyssal ocean. The residual overturning streamfunction stabilizes at approximately 3.8 Sv within the interior basin after several thousand years of integration (see Figure R2 in the “Reply to RC2”). It seems likely that the bottom water can be upwelled from a flat-bottom basin (I've also run a simulation with randomly generated topography, which includes continental slope, island, and sea mounts. The result shows the abyssal MOC structure and intensity do not alter much compared with the flat-bottom configuration. Please refer to Figure R3 in the "Reply to RC2", also attached below). This finding aligns with an earlier modeling study using a flat-bottom configuration, also implemented with MITgcm at a 2° horizontal resolution (see Figs. 3 and 5 of Ferrari et al., 2016). I would appreciate any further comments or suggestions from the reviewer regarding this result.
[Figure R3 in "Reply on RC2". Exp. 1 with vertical sidewalls (left column) and Exp. 4 with randomly generated topography in the basin (right column). The residual MOC streamfunctions at the end of the simulations (upper row) and the topography (lower row) for the two cases are shown.]
Citation: https://doi.org/10.5194/egusphere-2025-989-AC3 -
AC4: 'Reply on RC1', Lei Han, 10 May 2025
I would like to further address the concern raised in RC1 regarding the use of a novel meridional overturning circulation (MOC) streamfunction, namely the sloshing MOC streamfunction.
The reviewer commented in RC1: “Another 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.”
As already noted in my initial response (AC1), the issue of velocity non-divergence was explicitly acknowledged and discussed in the manuscript (see paragraph around Line 230), but was unfortunately overlooked by the reviewer#1.
I would also like to highlight that the sloshing MOC streamfunction has been utilized to investigate the variability and dynamics of the Atlantic and Indian Ocean MOC in four recent publications: Han (2021, JPO), Han (2023a, JPO), Han (2023b, GRL), and Han (2025, GRL):
- Han, L. (2021). The sloshing and diapycnal meridional overturning circulations in the Indian Ocean. Journal of Physical Oceanography, 51(3), 701-725.
- Han, L. (2023a). Mechanism on the short-term variability of the Atlantic meridional overturning circulation in the subtropical and tropical regions. Journal of Physical Oceanography, 53(9), 2231-2244.
- Han, L. (2023b). Exploring the AMOC connectivity between the rapid and osnap lines with a model-based data set. Geophysical Research Letters, 50(19), e2023GL105225.
- Han, L. (2025). How does a stable AMOC influence the regional climate of the North Atlantic? Geophysical Research Letters, accepted.
Collectively, these works have undergone rigorous reviews four times. While any single publication might benefit from favorable reviews by chance, the consistent acceptance of this framework across four major publications in two highly respected journals—Journal of Physical Oceanography (JPO) and Geophysical Research Letters (GRL)—makes such a coincidence unlikely. What are the chances that the eight reviewers were all mistaken in their assessments? This indicates that the concept has gained a degree of recognition and acceptance within the community.
I’ve explicitly acknowledged the limitations of the new streamfunction in the series of abovementioned publications, including some issues that were not noticed by the reviewer#1. Nonetheless, these limitations do not preclude the method from offering useful insights into overturning dynamics. The usefulness of a diagnostic tool lies not in its perfection, but in whether its inherent errors materially affect the interpretation of the true dynamics. I believe this is the reason why my recent studies utilizing this tool were successfully accepted in all of the peer reviews.
Furthermore, as elaborated in AC1, I approached the diagnostics of isopycnal displacement and Eulerian upwelling from a complementary angle—that is, by considering basin-integrated transports. This method, consistent with that of Monkman and Jansen (2024, JGR), yielded results that align with those obtained using the sloshing MOC streamfunction, thereby reinforcing the robustness of the conclusions.
In light of the above, I respectfully suggest that the criticism of this diagnostic tool may warrant reconsideration.
Citation: https://doi.org/10.5194/egusphere-2025-989-AC4
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AC1: 'Reply on RC1', Lei Han, 13 Mar 2025
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RC2: 'Comment on egusphere-2025-989', Anonymous Referee #2, 10 Apr 2025
In this manuscript the author revisits the balance between advective and diffusive contributions to the overturning in the Pacific ocean from observations, a reanalysis and idealised simulations. They report a general cooling of the abyssal Pacific and interpret this as a potential balance to the formation of dense water at high latitude. Overall the results presented from the analysis of the observations and the models appear to be correct however I have some major concerns about their interpretation and a lack of consideration of the impact of the choices in their idealised model. I believe this manuscript could become publishable however it would need significant revisions to the content and text to provide a more accurate and balanced interpretation of the results presented.
Firstly, I think the paper confuses two seemingly similar but distinct problems, namely the long term balances in the ocean associated with a near steady state and a transient response to changes in forcing. Throughout the paper they are reporting an inflation of the coolest layers of the Pacific associated with either changes in surface forcing for the observations and ECCO or relaxation at the southern boundary of the idealised simulation. Whilst I am convinced that this response is a real feature of the current ocean state it can not be maintained for long periods without either the whole ocean becoming cooler over long time periods or an alternative balance being reached (for example by a fundamental change in the structure of stratification). The author interprets this result as an alternative to the upwelling (or warming) of water by mixing processes (such as within the bottom boundary layer) by comparing the rate of inflation of these layers to the diapycnal mixing. Whilst this can be the case for a transient response it is still unclear to me that it can hold over very long time scales or global integrals. In order for this paper to be publishable I would prefer to see a much more nuanced discussion of the transient nature of the response and how it can contributed to the long time average ocean state.
Secondly, I have concerns about the lack of consideration for the impact of the simplifying choices made in their idealised model. It has been shown in previous studies, e.g. Ferrari et al 2016, that the choice of vertical vs sloping side walls can significantly change the impact of mixing in the bottom boundary layer in the upwelling process. This paper makes the simplifying choice of using vertical sidewalls and then interprets the results as implying mixing has a limited role in overturning. Whilst this is a feature of their model it is possible, perhaps likely, that this is simply a result of the choice of sidewalls rather than a feature of the real ocean. Additionally, the choice of the relaxation in the southern part of the domain lacked discussion of the role this choice made in the results presented. The conclusions the author draws would be much more convincing if the sensitivity to these choices was demonstrated, such as through additional simulations.
In addition to these two main concerns I have a series of minor corrections below.
Throughout the paper the author uses both warming / cooling and upwelling / downwelling. It would be much clearer if the separation between these sets of terminology was made clearer at the start in terms of movement in temperature space vs vertical motion without changing temperature. It is common in the literature people to use upwelling to mean across density surfaces so it could cause some confusion if not clearly defined here.
Line 53 – I found the sentence starting here hard to understand.
Line 180 – The statement here that bottom intensified mixing leads to a general cooling through much of the water column is true but a more complete statement would also highlight the warming implied by the zero flux condition at the boundary (as seen in the idealised model).
Line 224 onwards – I found the use of 4 streamfunctions a little confusing here. To me it seems there are 3: Eulerian, Sloshing, Diabatic. Did I miss something?
Paragraph starting 442 – Is this not just a result of having a model with non-zero diffusivity and no mechanism in the model to produce more light surface waters? For example, in a box with some initial stratification and non-zero diffusivity the isopycnals must move towards the upper and lower boundaries until the box is well mixed. It seems to me that this result is just a result of the choices made in the idealisation of the model and is not applicable in a scenario with a source of surface waters.
Line 510 – typo should read “bottom boundary layer”
Citation: https://doi.org/10.5194/egusphere-2025-989-RC2 -
AC2: 'Reply on RC2', Lei Han, 30 Apr 2025
I sincerely appreciate the reviewer’s time and effort in evaluating my work. Thank the reviewer for the constructive feedback and for giving me the opportunity to clarify my study. In response to the reviewer’s concerns, I have conducted a series of additional simulations using MITgcm to better evaluate the robustness of the original interpretations.
Below are detailed response (in bold) to the reviewer's comments (in regular fonts and in quotes).- Reviewer: “In this manuscript the author revisits the balance between advective and diffusive contributions to the overturning in the Pacific ocean from observations, a reanalysis and idealised simulations. They report a general cooling of the abyssal Pacific and interpret this as a potential balance to the formation of dense water at high latitude. Overall the results presented from the analysis of the observations and the models appear to be correct however I have some major concerns about their interpretation and a lack of consideration of the impact of the choices in their idealised model. I believe this manuscript could become publishable however it would need significant revisions to the content and text to provide a more accurate and balanced interpretation of the results presented.”
Reply:
I appreciate the reviewer's encouraging words and constructive comments and questions. In response to the reviewer’s concerns, I have conducted a series of additional simulations using MITgcm to better evaluate the robustness of the original interpretations.
One issue that, although not explicitly raised in the reviewer’s comments, I found important to address is the limited zonal extent (~50° longitude) used in the original idealized simulations. While a wider-basin simulation (double the original width) was included in the original Supplementary Figure S4 to demonstrate that the key conclusions are not sensitive to basin width, I now recognize that employing a more realistic geometry strengthens the credibility of the study. Therefore, I have revised all simulations throughout the manuscript to use a basin width of approximately 100°, which is more consistent with previous studies (e.g., Ferrari et al., 2016 used a 120°-wide basin). All new simulations presented in the revised manuscript are based on this wider-basin configuration. As can be seen in the reply below, these additional simulations help confirm the robustness of the original results.- Reviewer: “Firstly, I think the paper confuses two seemingly similar but distinct problems, namely the long term balances in the ocean associated with a near steady state and a transient response to changes in forcing. Throughout the paper they are reporting an inflation of the coolest layers of the Pacific associated with either changes in surface forcing for the observations and ECCO or relaxation at the southern boundary of the idealised simulation. Whilst I am convinced that this response is a real feature of the current ocean state it can not be maintained for long periods without either the whole ocean becoming cooler over long time periods or an alternative balance being reached (for example by a fundamental change in the structure of stratification). The author interprets this result as an alternative to the upwelling (or warming) of water by mixing processes (such as within the bottom boundary layer) by comparing the rate of inflation of these layers to the diapycnal mixing. Whilst this can be the case for a transient response it is still unclear to me that it can hold over very long time scales or global integrals. In order for this paper to be publishable I would prefer to see a much more nuanced discussion of the transient nature of the response and how it can contributed to the long time average ocean state.”
Reply:
Thank the review for the thoughtful and detailed comments. I fully agree with the reviewer’s distinction between long-term steady-state balances and transient responses to changes in forcing. This is indeed a crucial point, and I appreciate the opportunity to clarify how this distinction is treated in the manuscript.
I acknowledge this separation explicitly in the original manuscript, particularly in Figure 12: panels (a) and (b) depict transient responses of the abyssal MOC to changes in surface or boundary forcing, while panel (c) illustrates the steady-state configuration. The focus of this study has been on the transient cooling/warming responses because they likely represent the current state of the abyssal Indo-Pacific Ocean. These transient dynamics can offer useful insights into observed features—such as bottom-intensified turbulent heat fluxes—that are not consistent with a steady-state configuration. This is the reason why this paper focuses on the transient dynamics rather than the steady state. That said, I fully agree that understanding the steady state remains important, both as a reference and for assessing the long-term sustainability of any transient adjustment.
[Figure 12 of the manuscript]To better address this, I have extended my simulations toward a near steady-state configuration. Specifically, in the idealized model under the cooling scenario, I introduced an additional surface temperature relaxation near the Equator to create a heat source that balances the southern sidewall cooling, thereby enabling the system to reach a steady state. This setup is conceptually similar to the surface relaxation employed by Ferrari et al. (2016). The model was then integrated for 4000 years to reach a near steady state. This simulation is denoted as “Exp. 1”, whose setup is as follows:
Exp. 1: Baseline steady-state configuration with uniform diffusivity of 1×10⁻⁵ m²/s in the interior basin. Forcing: southern sidewall relaxation of 1°C below 2000 m. Surface relaxation of 25°C. Integrated for 4000 years from rest.
The results are shown in Figure R1 (attached below). As expected, a stable upwelling MOC cell dominates the deep ocean (left panel). The sloshing component of the MOC, ψslo—diagnosed from isopycnal displacements—is essentially zero due to the stabilized stratification (middle panel), so the residual and diapycnal MOC streamfunctions become identical (right panel). This outcome is consistent with the steady-state configuration illustrated in Figure 12(c) of the paper (the figure in above). I can add this figure in the revision to support the conclusion on the steady-state dynamics.
[Figure R1. Results of Exp.1. Similar to Figure 11 in the paper, but with the cooling scenario simulation running for 4000 years to quasi-equilibrium. The MOC streamfunctions are residual MOC (left), sloshing MOC (middle), and diapycnal MOC (right), respectively. Negative/positive streamfunction represent anti-clockwise/clockwise) overturning cells.]To further emphasize the transient nature of the response, I have conducted two additional simulations branching from the quasi-equilibrium state (Exp. 1):
Exp. 2: Branching from Exp. 1 at year 4000, but increasing the southern sidewall relaxation temperature to 1.5°C. Integrated for 1000 years.
Exp. 3: Also branching from Exp. 1 at year 4000, but reducing the vertical extent of southern sidewall temperature relaxation from lower 2000 m to lower 1700 m. Integrated for 1000 years.
These two perturbation experiments simulate a weakening of bottom water formation via different mechanisms. To quantify the abyssal overturning strength, we define an index as the maximum absolute value of the MOC streamfunction in the Indo-Pacific basin north of 40°S and below 2000 m. Figure R2 shows the time evolution of this overturning index and the mean KE across the three experiments, capturing the transient adjustment of abyssal overturning strength in response to changes in bottom water formation. These results suggest that the abyssal overturning circulation exhibits a reduction to weakened bottom water formation, and tends to adjust toward a new equilibrium over the long term.[Figure R2. Time series of abyssal MOC index (left panel) and mean KE (right panel) of the simulations for Exp. 1 (black), Exp. 2 (red), and Exp. 3 (yellow), respectively.]
- Reviewer: “Secondly, I have concerns about the lack of consideration for the impact of the simplifying choices made in their idealised model. It has been shown in previous studies, e.g. Ferrari et al 2016, that the choice of vertical vs sloping side walls can significantly change the impact of mixing in the bottom boundary layer in the upwelling process. This paper makes the simplifying choice of using vertical sidewalls and then interprets the results as implying mixing has a limited role in overturning. Whilst this is a feature of their model it is possible, perhaps likely, that this is simply a result of the choice of sidewalls rather than a feature of the real ocean. Additionally, the choice of the relaxation in the southern part of the domain lacked discussion of the role this choice made in the results presented. The conclusions the author draws would be much more convincing if the sensitivity to these choices was demonstrated, such as through additional simulations.”
Reply:
Thank the reviewer for raising this important point. I fully acknowledge that idealized modeling choices, such as the use of vertical sidewalls and specific relaxation boundary conditions, can influence the results and interpretations. Indeed, as mentioned in the paper, Ferrari et al. (2016) is a foundational reference for this study, and many aspects of the model configuration—including spatial resolution and forcing schemes—were adapted from their setup.
I would like to clarify that this study does not argue against the role of mixing in driving overturning circulations. In fact, all simulations in this study produce notable abyssal overturning cells due to mixing. I’ve also run a case with very low diffusivity, and the abyssal overturning circulation hardly develops. This study attempts to highlight the potential importance of other dynamical processes beyond mixing alone. Moreover, Ferrari et al. (2016) also demonstrated that upwelling overturning circulations can emerge in a domain with vertical sidewalls (see their Figure 3; a snapshot is included below). My results are consistent with theirs in terms of the direction and structure of the residual MOC streamfunction, lending confidence to the validity of my simulation output.
[A combination of Fig. 3 and Fig. 5 of Ferrari et al (2016). Red arrows indicate the directions of the overturning cells.]That said, I appreciate the reviewer’s suggestion to test the sensitivity of our results to topographic effects. To investigate this, I conducted an additional simulation, denoted “Exp. 4,” which has the same configuration as Exp. 1 but with randomly generated bottom topography in the interior basin, including continental slopes, islands, and seamounts (see lower right panel of Figure R3). Interestingly, the upwelling strength and structure in Exp. 4 remain largely similar to those in Exp. 1, albeit with slightly less spatial smoothness. This indicates that the presence of bottom topography does not substantially alter the large-scale abyssal upwelling in our model. These results suggest that the internal dynamics, rather than bottom topography alone, play a more dominant role in driving the upwelling.
[Figure R3. Exp. 1 with vertical sidewalls (left column) and Exp. 4 with randomly generated topography in the basin (right column). The residual MOC streamfunctions at the end of the simulations (upper row) and the topography (lower row) for the two cases are shown.]Regarding the southern boundary temperature relaxation, I agree that the manuscript initially lacked adequate discussion of its role, but it has been addressed here by Exp. 2 and Exp.3. As shown in Exp. 2 and Exp. 3 (in the earlier reply), the strength of abyssal overturning is sensitive to the characteristics of this southern relaxation. Specifically, weaker bottom water formation (either by reducing the relaxation strength or its extent) leads to a weaker abyssal overturning cell.
While Ferrari et al. (2016) implemented surface relaxation to simulate bottom water formation, I also tested this configuration. However, I ultimately adopted sidewall relaxation because it is capable of producing bottom-intensified turbulent heat fluxes under cooling scenarios—a feature widely observed in the real ocean. In comparison, surface relaxation does not reproduce this key characteristic. Thus, the sidewall relaxation was chosen to better represent the observed vertical structure of turbulent mixing and abyssal dynamics.- Reviewer: “In addition to these two main concerns I have a series of minor corrections below.
Throughout the paper the author uses both warming / cooling and upwelling / downwelling. It would be much clearer if the separation between these sets of terminology was made clearer at the start in terms of movement in temperature space vs vertical motion without changing temperature. It is common in the literature people to use upwelling to mean across density surfaces so it could cause some confusion if not clearly defined here.”
Reply:
Thank the reviewer for pointing this out. I fully agree that the terminology regarding vertical motion should be clearly defined to avoid confusion. In this study, we distinguish two types of vertical motion. The “movement in temperature space” that the reviewer mentioned is defined as the diapycnal upwelling/downwelling, i.e., the vertical velocity, wdia. While the “vertical motion without changing temperature” is measured by tracking the displacement of the isopycnal, i.e., the vertical velocity, wiso. These definitions have been summarized in Table 1 of the manuscript. If any of these remain unclear, I would greatly appreciate it if the reviewer could specify which part in the text needs clarification so I can address it accordingly.
“people to use upwelling to mean across density surfaces”: In my view, upwelling does not always imply cross-isopycnal process. For example, isopycnal heaving induced by Ekman pumping involves vertical motion without water mass transformation. One of the key objectives of this study is to distinguish between different upwelling concepts, such as adiabatic versus diabatic upwelling. These correspond to the so-called “adiabatic MOC” and “diffusive MOC”, as schematically illustrated in Figure 12 of the manuscript.
In light of this discussion, I have also revisited the term “sloshing MOC”. I do acknowledge that there are some flaws in the definition of the sloshing MOC. Since it is defined by tracking the movement of isopycnals, it includes both adiabatic and diabatic contributions. Therefore, referring to it as purely “adiabatic MOC” is inaccurate. I will revise the terminology used for this component throughout the manuscript to avoid this misinterpretation.- Reviewer: “Line 53 – I found the sentence starting here hard to understand.”
Reply:
Thank the reviewer for pointing this out. I assume the reviewer is referring to the sentence: “Volume budget below deep, cold isotherm within the Pacific basin ‘are not in steady state’ (Purkey and Johnson 2012).” This is a direct quotation from the abstract of Purkey and Johnson (2012), which I cited to support the point that the volume below a given deep isotherm in the Pacific is changing over time. I retain it to preserve the authors’ intent.- Reviewer: “Line 180 – The statement here that bottom intensified mixing leads to a general cooling through much of the water column is true but a more complete statement would also highlight the warming implied by the zero flux condition at the boundary (as seen in the idealised model).”
Reply:
True. This is a good point. Yes, it is always warming in the bottom boundary layer (BBL) as indicated in Figure 1 of the paper. I’ll add a label “warming” for the BBL in the figure to indicate that. That said, I would also like to emphasize that the BBL typically spans only a few tens of meters (Ferrari et al., 2016), whereas the abyssal ocean extends over several thousand meters. Therefore, while the BBL does experience warming due to constrained vertical heat fluxes, its contribution is insufficient to offset the general cooling observed throughout the much thicker overlying water column. I will clarify this point in the revised manuscript to provide a more balanced and complete interpretation.- Reviewer: “Line 224 onwards – I found the use of 4 streamfunctions a little confusing here. To me it seems there are 3: Eulerian, Sloshing, Diabatic. Did I miss something?”
Reply:
The reviewer is correct that the main conceptual categories are three, but they are Advective, Sloshing, and Diabatic. There are 4 streamfunctions in total because I have presented two types of Advective streamfunctions: one defined in the depth coordinate (the traditional Eulerian MOC, ψEul), and one defined in the density coordinate (ψσ). These two are both included in Table 1 and showed in Figure 4 of the manuscript. In a near adiabatic process, their maximum values are comparable even though they are defined in different coordinates unless the isopycnals are significantly titled in zonal direction.
Johnson et al (2019) showed both streamfunctions of AMOC in their Figure 2, which the maximum overturning circulations at each latitude are similar except in the subpolar region. Monkman and Jansen (2024) showed a similar strength ψσ for the Indo-Pacific region (their Figure 3b). I presented both streamfunctions to provide a more comprehensive view of the abyssal Indo-Pacific MOC structure from complementary perspectives. In any case, I will revise the text to eliminate the confusion about 3 or 4 streamfunctions.- Reviewer: “Paragraph starting 442 – Is this not just a result of having a model with non-zero diffusivity and no mechanism in the model to produce more light surface waters? For example, in a box with some initial stratification and non-zero diffusivity the isopycnals must move towards the upper and lower boundaries until the box is well mixed. It seems to me that this result is just a result of the choices made in the idealisation of the model and is not applicable in a scenario with a source of surface waters.”
Reply: Yes, this is precisely the point I intended to convey. The emergence of the diapycnal upper cell is purely a consequence of isopycnals migrating upward due to environmental cooling or non-zero diffusivity, while the water parcels themselves exhibit minimal motion. This result reinforces our main finding regarding the abyssal ocean: in an unsteady state, a non-zero "diapycnal overturning circulation" can arise solely from changes in stratification, without implying actual movement of water parcels.
- Reviewer: “Line 510 – typo should read “bottom boundary layer””
Reply: Exactly. Thank the reviewer for catching this. I’ll make the correction.
References:
- Ferrari, R., A. Mashayek, T. J. McDougall, M. Nikurashin, and J. Campin, 2016: Turning ocean mixing upside down. J. Phys. Oceanogr., 46, 2239-2261.
- Johnson, H. L., P. Cessi, D. P. Marshall, F. Schloesser, & M. A. Spall, 2019: Recent contributions of theory to our understanding of the Atlantic Meridional Overturning Circulation. Journal of Geophysical Research: Oceans, 124, 5376-5399.
- 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.
- Purkey, S. G. and G. C. Johnson, 2012: Global contraction of Antarctic Bottom Water between the 1980s and 2000s. J. Clim., 25, 5830-5844.
Citation: https://doi.org/10.5194/egusphere-2025-989-AC2
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AC2: 'Reply on RC2', Lei Han, 30 Apr 2025
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