Influence of heterogeneous thermal conductivity on the long-term evolution of the lower-mantle thermochemical structure: implications for primordial reservoirs

Guerrero, Joshua Martin; Deschamps, Frédéric; Li, Yang; Hsieh, Wen-Pin; Tackley, Paul James

doi:https://doi.org/10.5194/se-14-119-2023

Articles | Volume 14, issue 2

https://doi.org/10.5194/se-14-119-2023

© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/se-14-119-2023

© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 14, issue 2

Research article

|

07 Feb 2023

Research article |

| 07 Feb 2023

Influence of heterogeneous thermal conductivity on the long-term evolution of the lower-mantle thermochemical structure: implications for primordial reservoirs

Joshua Martin Guerrero, Frédéric Deschamps, Yang Li, Wen-Pin Hsieh, and Paul James Tackley

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Final revised paper (published on 07 Feb 2023)
Supplement to the final revised paper
Preprint (discussion started on 08 Jun 2022)
Supplement to the preprint

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2022-418', Anonymous Referee #1, 30 Jul 2022

This study uses mantle convection simulations to address the influence of pressure-, temperature- and composition-dependence of thermal conductivity on the fate of a dense primitive layer sitting at the bottom of the mantle, mimicking the LL(S)VPs on the Earth. While previous studies have investigated the effect of those various dependencies of thermal conductivity have been investigated individually, the novelty of this work is to consider consider the interplay between them in the context of the Earth’s lower mantle structure. While I think that the results are worth being published, their presentation in the current manuscript is hard to follow and lacks a clear narrative thread, and more importantly, lacks in interpretation. Therefore, I think the paper would benefit from a thorough re-organization of the results section.

General

The study adopts a rather complex baseline set up (mixed basal + internal heating, phase transition, yield stress) to study the effect of pressure, temperature and composition on thermal conductivity. While my preference goes to simpler models when trying to unravel such systematic trends, one can argue that the current set-up is relevant for an Earth-like case, and I think it is fair.

I find the introduction a bit too light. I would expect some more background on the physics of the various dependencies of thermal conductivity, and in particular that the trends be clearly announced: increase of pressure results in increase of thermal conductivity, increase in temperature results in decrease in thermal conductivity, increase in iron content results in decrease in thermal conductivity (it seems). Also, it seems that considering a variable thermal conductivity is particularly relevant for compressible convection. If this is indeed the case, I would expect more time to be spent discussing why.

In my opinion, the main weakness of the paper in its current state is the lack of apparent organization in its exploration of the parameter space, which makes it pretty confused and fails at highlighting general tendencies in the effect of the different dependences of the thermal conductivity. This is probably due in part to the simultaneous changes in investigated parameters and diagnostic quantities from one section to the other (first time-evolution of the heat flux varying K_C and n, then instantaneous mantle structures varying everything, and finally time-evolution of entrainment again varying K_C and n). While I seem to get the idea in the progression, I had a really hard time getting a clear picture out of this section. Maybe starting by isolating the effect of each dependencies, and then considering their correlations could make things simpler. Maybe also distinguishing more systematically between the effect on mantle flow (pile structure) and on the time-evolution (e.g. of the CMB and surface heat fluxes) could help. Another possibility would be to add dependencies successively to a fiducial model, for which a preferred value of K_D would be selected before considering the effect of n, and in turn a preferred value of n would be selected before adding a third layer with K_C. That could spare some cases of the parameter space if there are reason to think they are less relevant. Thse are suggestion, hopefully that can help. Anyway, one important thing which is lacking in my opinion is also some theoretical speculation on the expected effect of the parameters that should come before presenting the results, and would help their interpretation (e.g. we expect the effect of increaing K_D to increase the thermal conductivity in the lower mantle and thus to make it more stable to convection (it decreses Ra) by homogenizing its temperature, potentially building heat… etc.). I think it is better for the reader to be incited to think in advance of seeing the results.

Specific

This article will probably mainly be read by people familiar with the equations of mantle convections. Nevertheless, I think it would be beneficial to write down the conservation equations (they are not even in the supplementary materials!), at least the heat conservation where the thermal conductivity appears, as it would make clear where the supplementary mechanism induced by varying thermal conductivity operate.

A plot of the thermal conductivity profile corresponding to the reference state for the various K_D, K_C and n (not all of them but the few most relevant combinations, e.g. the cases presented in Figure 2) would be insightful. It could be a supplementary panel in Figure 1, or a stand-alone figure.

I don’t really understand why simulations run until 11 Gyr, but some values are avergaed aroung 4.5 Gyr. Anyway, the averaged values reported in Table 1 do not seem to be used.

Dimensional and non-dimensional quantities are often mixed, which lacks a bit of rigor.

Technical

L. 48: “compositional- dependent” ← “composition-dependent”

L. 84: “a quadratic that smoothly” ← “a quadratic curve that smoothly”

Figure 1: the markers for “<200 ppm water” are hard to see, please change for a more contrasting colour.

L. 118: “We first defined a purely depth- dependent reference case characterized by depth- dependence, K_D = 2.5, with lower mantle conductivities comparable to current estimates” in Figure 1, it seems that K_D = 10 is the closest match to lower mantle estimates.

L. 121: “by approximately 75%” it seems less than that in Figure 2.

L. 122: “in agreement with Li et al. (2022) findings” ← “in agreement with Li et al. (2022)’s findings”

L. 150: “We observed that T_prim increased with greater temperature dependence (top-to-bottom rows in Figure 3).” I don’t see it.

For the snapshot figures, when a parameter is held constant, write it in the caption rather than for each snapshot. That will lighten a bit the figures.

Figure 5: Please alternate colormaps between the different quantities plotted. In particular, don’t take a “divergent” colormap for the primordial mantle one which only has two extremal values, which are both very dark and hard to distinguish in the current plot.

L. 172: “and is equivalent to” ← “and which is equivalent to” ?

Figure 6: Same as figure 5: it is very hard to know which colormap corresponds to the snapshot and which corresponds to the time-evolution plots. Also please change colours for the onset of instability (the magenta is pretty hard to see).

L. 189: “may not compensate (or be exceeded) by” ← “may not compensate (or be exceeded by)”

Supplementary Materials

L. 43: “and the depth variation of thermal expansivity imply a depth average” ← “and the depth variation of thermal expansivity implies a depth average”

L. 176: “The density anomalies [...] is calculated” ← “The density anomalies [...] are calculated”

Figure S1: the y-axis is non-dimensional height, not depth.

Figure S4: What do line styles correspond to?

Citation: https://doi.org/10.5194/egusphere-2022-418-RC1
- AC1: 'Reply on RC1', Joshua Guerrero, 22 Aug 2022
  
  The authors appreciate the comments made by R1 and we address each below. We have decided to expand the introduction and
  
  rearrange the results section so that the manuscript is easier to follow.
  General Comments
  
  -Yes, the mantle convection model set-up we consider is intended to be Earth-like. However, we do not intend on reproducing
  
  the Earth mantle's history. Within this framework we have been able to examine the effect of the thermal conductivity model
  
  on the evolution of the primordial layer at the bottom of the mantle.
  -We agree with R1 that the introduction can be expanded. Regarding the thermal conductivity, each of the component (dependency)
  
  of the conductivity model will be discussed. In addition, we will now address why conductivity is relevant for compressible mantle
  
  convection.
  -We consider the suggestions that R1 outlines for reorganizing the results section. As the manuscript stands, introducing the
  
  reference case K_D = 2.5 first is too much too quickly for the reader. We now separate all the effects so that the progression
  
  of the results is easier to digest. The subsections of the results are now:
  1) Effect of a purely depth- dependent conductivity
  
  2) Effect of a temperature- and depth- dependent conductivity
  
  3) Including the effect of composition- dependent conductivity
  
  4) Long-term stability of thermochemical reservoirs featuring mineral physics derived conductivities
  Specific Comments
  
  -The heat conservation equation will now be added to the Methods section to help the reader understand where the conductivity
  
  model influences mantle dynamics.
  -A new figure with a plot of the initial thermal conductivity profiles for cases featuring mineral physics defined
  
  conductivities are now included so that the conductivity reductions from different temperature- and composition- dependencies
  
  is clarified.
  -The simulation time is long (~11 Gyr) to allow the system to reach a statistically steady state and to investigate how the
  
  heterogeneous conductivity will affect the long-term evolution of the primordial layer. The simulation averages are taken
  
  towards the start of simulations' statistically steady state (approximately 4.5 Gyr). Again, we do not intend to model the exact
  
  evolution of the Earth's mantle. The conditions for simulating Earth's history (i.e., initial conditions, decaying heat sources,
  
  and cooling bottom boundary) are not included in our model setup. In the current version of the manuscript, the averaged values
  
  were inset within the annulus snapshots and their trends were discussed within the results subsections. Specific values were not
  
  used often so that the text would not be inundated with numbers. We now incorporate more references to the Table 1 averages into
  
  the manuscript.
  -The values presented in the manuscript will be presented as dimensional.
  Technical Comments:
  
  -L. 48: for clarity, "composition- dependent" will now be used throughout the manuscript.
  
  -L. 84: inserted the word 'curve'.
  
  -Figure 1: markers for "< 200 ppm water" are changed to bright green to be more contrasting with the background.
  
  -L. 118: The case with a purely depth- dependent thermal conductivity and K_D = 2.5 is considered as an analogue
  
  for models that already account for the combined depth- and temperature- dependences. In the latter (hypothetical)
  
  model of thermal conductivity, the depth- dependent component would have conductivity values that are much greater
  
  than those defined by K_D = 2.5. To clarify, the sentence has been changed to
  
  "As an analogue for a thermal conductivity model that accounts for depth- and temperature- dependence, we first
  
  consider a purely depth- dependent reference case characterized by depth- dependence, K_D = 2.5. Our reference case
  
  produces lower mantle conductivities that are comparable to current estimates (e.g., Deschamps & Hsieh, 2019; Geballe et al., 2020)."
  
  -L. 121: "by approximately 75%", this refers to a comparison of heat flow values averaged about 4.5 Gyr for cases #4 and #8.
  
  This comparison is between a purely depth- dependent conductivity case (#4) and heterogeneous conductivity case (#8).
  
  The sentence has now been revised to read:
  
  "Comparing the purely depth- dependent conductivity model to the completely heterogeneous conductivity model, the latter greatly
  
  reduced both CMB and surface heat flows (by approximately 76% and 22%, respectively), as less heat can be extracted from the
  
  base."
  
  *The subsection including the timeseries figure has now been moved to the final subsection of the results section. It has now
  
  been updated so that the cases are relevant to the mineral physics derived conductivity profile.
  
  -L. 122: fixed the citation to read "... Li et al., (2022)'s findings".
  
  -L. 150: The mean temperature of primordial material is indicated by T_{prim} (not to be confused with the global mean
  
  temperature of the system <T>). T_{prim} is inset within the annulus and is indicated for each case. T_{prim} can be seen
  
  decreasing for cases with the same K_D value as n is increased. In addition, the temperature field is offset with respect to the
  
  CMB temperature so that the differences in hotter temperatures within the piles is easier to see. The boundary between regular
  
  mantle material and primordial material is indicated by a green contour. When n is increased, the red colour within these
  
  contours becomes more saturated.
  
  -Snapshot figures have been revised so that superfluous conductivity model labels are omitted.
  
  -Figure 5: The colormaps for each different field are now alternated.
  
  -L. 172: inserted the word 'which'.
  
  -Figure 6: The colormap is changed. The onset of instability is now indicated by a dashed cyan line.
  
  -L. 189: The parantheses has been moved.
  
  Supplemental Materials:
  
  -L. 43: "imply" -> "implies".
  
  -L. 176: "is" -> "are".
  
  -Figure S1: "depth" -> "height".
  
  -Figure S4: The case numbers have been added to the legend so that the line styles are now clear.
  
  Citation: https://doi.org/10.5194/egusphere-2022-418-AC1
RC2:
'Comment on egusphere-2022-418', Anonymous Referee #2, 02 Aug 2022

In this paper the authors carried out numerical experiments of thermochemical mantle convection by varying the spatial changes in thermal conductivity to investigate the temporal changes in the distributions of dense "primordial" materials initially imposed above the bottom boundary. My honest impression is, unfortunately, that the manuscript is very hard to follow because of its poor organization and description from the reasons summarized below. I therefore strongly suggest that the authors should thoroughly revise the manuscript before the reconsideration.

1. One of my major criticism is that the main issues in this study were not well described either in the abstract or introduction section. In my understanding the major intention of the authors is to reduce the thermal conductivity in the deep mantle to much lower levels than those simply expected from the dependence on temperature and pressure (or depth), in order to induce an "instability" from the initial layer of dense materials within a sufficiently short period of time. The authors should clearly indicate their ultimate motivation in earlier parts of the manuscript.

2. I am not well convinced of the meaningfulness of the onset time of "instability" from the initial layer of dense materials. It seems to me that the authors had assumed that the deformation of the basal layer of dense materials occurs only in an "intrinsic" manner owing to the thermal buoyancy. However, several earlier studies had demonstrated the ultimate importance of "extrinsic" deformation induced by the cold subduction from the top surface. I do not therefore think that the onset time of "instability" can be a good measure to investigate the influence the thermal conductivity at depth on the thermal buoyancy in the basal layer of dense materials.

3. I felt quite odd with the authors' exaggerated claim on the overall profiles of thermal conductivity including "We find that the temperature- and depth- variations combined characterize the mean conductivity ratio from top-to-bottom" in the abstract. It is quite obvious from the assumptions made by the authors themselves.

4. In Section 2.1 the authors should state the reason why the phase change from perovskite (pv) to post-perovskite (ppv) is ignored in their numerical model. If they believe that the pv-ppv phase change is of little importance on the dynamic behaviors of the basal layers of dense materials, the authors should make clear the reason why.

5. I was quite disgusted to see that the profile given by equation (2) is denoted by "KD=9.185". Such a denotation should be used only for the profiles given by equation (1) !!

6. Near equation (3) the authors should indicate the magnitude of the reduction in thermal conductivity due to the increase in temperature within the modeled domain by the choice of n=0.5 and n=0.8.

7. Near equation (4) and later, "compositional correction" should be rephrased with "compositional dependence". The word "CORRECTION" could imply that the numerical experiments without the compositional dependence in thermal conductivity are meaningless.

8. In Section 3.1 "QCMB" is used without explicitly defined.

9. To show the 2-D distributions of thermal conductivity in Figures 4 and 5, the authors should show the ratio of thermal conductivity to its surface value (KS) rather than the values of conductivity itself.

10. The paper by Marzotto et al. (2020) has not been cited anywhere in the main text.

11. Near equation (8) of the Supplement, the spatial coordinates should not be in Cartesian (x,y,z) but in 2-D polar (r,phi) in this study. Similarly in equation (12) of the Supplement, the coordinate is not in 3-D polar (r,theta,phi).

12. In Section 3.1 of the Supplement, I think that the authors can use the potential temperature instead of the "adiabatic correction" a(z).

13. The paper by Xu et al. (2004) has not been cited anywhere in the Supplement.

Citation: https://doi.org/10.5194/egusphere-2022-418-RC2
- CEC1: 'Reply on RC2', Susanne Buiter, 12 Aug 2022
  
  Dear reviewer, dear authors,
  I thank the reviewer for their feedback and suggestions for improvement of the manuscript. As a general note, i would like to use this opportunity to re-iterate that Solid Earth strives for polite and constructive language in all communications, including reviews. Specifically regarding this manuscript, i would ask the authors to ignore the wording that was used in comment 5 and to try to focus on the content of the feedback given. I hope this will work for everyone.
  Susanne Buiter
  
  Citation: https://doi.org/10.5194/egusphere-2022-418-CEC1
- AC2: 'Reply on RC2', Joshua Guerrero, 22 Aug 2022
  
  The authors appreciate the comments made by R2 and we address each below. In addition to the commments made by R1, we have
  
  decided to thoroughly revise the manuscript so that it is easier to follow.
  1. In alignment with the comments of R1, we will expand the introduction section and make the intentions of our study clearer.
  2. We calculate the onset time for instability from the temporal variations in the average height of dense material. It is true
  
  that these variations in average height do not discriminate between 'intrinsic' (i.e., thermal buoyancy) or 'extrinsic'
  
  (i.e., downwellings) deformation. From examining the average height timeseries and animations of the fluid flow we can see the
  
  influence of downwellings. The first downwellings impringe on the initial dense layer but do not result in a rapid uplift of
  
  material (sufficient to eject blobs of dense material). Once the initial dense layer has organized into piles, downwellings tend
  
  to move dense material laterally over the CMB but not rapidly increasing the pile height. Furthermore, we find that it is easier
  
  for downwelling currents to push primordial material that has been made lighter due to their retained heat. We agree that
  
  downwellings are important in deforming the dense primordial layer. This mechanism will now be discussed in addition to the
  
  thermal effect regarding instability.
  3. Right. This statement is a bit of a tautology. The intention for this statement is that for Earth-like models that consider a
  
  variable thermal conductivity, it may be ill advised to isolate for just one dependency. On one hand, to simulate a 2-pile
  
  configuration, a purely depth- dependent conductivity may be employed, but its top-to-bottom ratio should implicitly emulate the
  
  temperature and composition effects. On the other hand, a purely temperature- dependent conductivity will result in the
  
  entrainment of a dense primordial layer. By assuming a parametrized conductivity model, it is predictable what the mean
  
  conductivity ratio from top-to-bottom will be (having specifed the temperature contrast and the dependencies of the conductivity
  
  model).
  4. We will now discuss the reasons why the phase change from perovskite (pv) to post-perovskite (ppv) is ignored in our numerical
  
  model. The effects of the pv-ppv transition properties on the stability and structure of primordial reservoirs has been
  
  investigated previously by Li et al., (2015). There are many controlling parameters for the pv-ppv transition including the
  
  temperature of the CMB, the viscosity contrast between pv and ppv, and the viscosity contrast between ppv and primordial material
  
  that can affect the stability of piles. For instance, weak ppv (i.e., low viscosity contrast between pv and ppv) and a low Tcmb
  
  (i.e., Tcmb ~ 3350 K) can result in entrainment of primordial reservoirs. Because of the model setup we consider in our study,
  
  the inclusion of a pv-ppv transition will result in the entrainment of a dense primordial reservoir. Thus, the pv-ppv phase
  
  transition will mask the effect of thermal conductivity on the stability of primordial reservoirs that we are examining. This
  
  discussion will be added to the new text in the introduction as requested by R1.
  5. All usage of the label "K_D = 9.185" will be replaced with "K_{DH}" to indicate that this depth profile was defined by
  
  parameterizations published in Deschamps and Hsieh, (2019).
  6. The magnitude of the reduction in thermal conductivity depends on temperature (which changes with depth). A simple
  
  calculation can be added to show how much the conductivity is reduced at CMB temperatures for different n values. The
  
  reduction in conductivity will also be shown by the inclusion of a new figure which shows the initial conductivity profiles for cases featuring K_{DH} with different temperature- and composition- dependence.
  7. In alignment with the comments of R1, all usage of "compositional correction" will be rephrased to "composition- dependence".
  8. Q_{CMB} and Q_{SURF} will be clearly defined in Section 3.1.
  9. As suggested by R1, we will keep consistent with dimensional values. We currently present 2D distributions of thermal
  
  conductivity in Figures 4 and 5. By plotting the conductivity fields relative to the surface value k_{S}, it would be converted
  
  to the non-dimensional conductivity field. We will include the non-dimensional conductivity (the ratio of local conductivity to
  
  surface conductivity) field to the Supplement.
  10. Marzotto et al., (2020) will be removed from the references. Conductivity data points included in Figure 1 are from the
  
  references cited within the caption.
  11. Coordinates for 3D geometry (x,y,z) or (r,theta,phi) will be replaced by 2D spherical annulus coordinates (r,phi).
  12. The potential temperature definition will also be stated in addition to the adiabatic correction.
  13. Xu et al., (2004) will be removed from the references. This reference was included in the methods section discussion on the
  
  thermal conductivity model (Section 2.2) and had been moved from the supplement to the main text. The reference to Klemens,(1960)
  
  in the supplement will also be removed for the same reason.
  
  Citation: https://doi.org/10.5194/egusphere-2022-418-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Joshua Guerrero on behalf of the Authors (19 Sep 2022) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (03 Oct 2022) by Juliane Dannberg

RR by Anonymous Referee #1 (31 Oct 2022)

Suggestions for revision or reasons for rejection

The paper now reads much better and gets its message accross much more efficiently I feel.
I have some minor comments. Once addressed, the paper will be ready for publication in my view.

on several occasions: "Thermochemical material" <- primordial material

L. 15: "the depth-dependent ratio should be at leat 9 times ..." <- "the depth-dependent ratio should be at leat 9." (a ratio is dimensionless)

L. 33: add coma between "physical properties" and "most importantly"

L. 36: "An important property that influences mantle dynamics is thermal conductivity." This statement is ou of place here. I would simply remove the sentence.

L. 50: reduce <- reduces

L. 61: Add "is" between "temperature" and "fixed"

L. 63: "reduce" <- "reduces"

L. 62: "should" is repeated twice, you can be a bit more affirmative

L. 69: "The thermal conductivities decrease with an increasing temperature and follow ..." <- "The thermal conductivity decreases with increasing temperature and follows ..."

L. 74-75: "However, these measurements ... 26 GPa for perovskite." I don't understand the point of this sentence.

L. 80: "... even for a moderate temperature dependence." This is not clear

L. 81: "Depending on the interactions between cool subducting, primordial reservoirs..." <- "Depending on their interactions with cool subducting, primordial reservoirs...."

L. 97: ""A comparable" <- "Such a"

L.93: "... is not an insignificant factor to neglect" That's 3 negations in 7 words, please rephrase in a less contrived way!

L. 100: Mention that you consider a compressible fluid, you just said in the previous paragraph that it is important!

L. 119: "We assume primordial" <- "We assume a primordial"

L. 119: "Has a rate" <- "Has a heating rate"

L. 124: "... using an Arrhenius formulation": What about the composition dependence?

L. 139: "has length scale" <- "has a length scale"

L. 159: "Temperature-dependence" <- "The temperature-dependence"

L. 161: "results in lower" <- "decreases"

L. 166: "Composition-dependence" <- "The composition-dependence"

L. 169: "0.8 and 0.5": Can you motivate these values by comparing with the measurements mentioned in the intro?

Figure 2: In cpation: "... for cases featuring KDH" not only KDH, but all dependencies

L. 180: "... eventually be much lower" <- "decrease as they heat up"

L. 203: "influence" <- "influences"

L. 209: "3410 K), an increase" <- "3410 K) and an increase"

L. 210: from (2150 K up to 2290)": explain it: "piles are better at conducting core's heat into the mantle, rather than retaining it"

L. 215: The mantle flow is NEVER turbulent. Please change word

L. 217: "The conductivity fields...": it seems to be a result, but is an assumption: "When only pressure-dependence is considered, the thermcal conductivity field..."

Section 3.2: Break the first paragraph in several (one for each alue of K_D)

L. 242: "was increased, could be compensated" <- "was increased is compensated"

L. 243: "larger than 1 was established <- "larger than 1 is established"

L. 246: "Interestingly, ...", L. 250: "We observe that..." L. 252: "Interestingly, ..." try to suggest and explanation for all these

L. 270: "The percentage conductivity difference" <- "The conductivity difference"

Figure 8: the dashed and dashed-dotted lines do not show as such in the legend

L. 312: "(for different ranges of composition concentration)": what is "composition concentration"?

L. 313: "illustrate" <- "illustrates"

L. 315: "departures from reference" <- "departures from the reference"

L. 318: "observed following the transient period": name the time

L. 320 "over the CMB but not rapidly increasing the pile" <- "over the CMB but do not increase rapidly the pile"

L. 325: "their total height." do you mean their maximum heaight?

L. 327: Does your composition advecetion scheme account for diffusion?

L. 328: "Thus, the average height of the veneer": describe how to visualize it in Figure 8

L. 329: "This is a good quantity to analyse for temporal variations," Not clear

L. 330: "For this conductivity model": which one?

L. 332: "we find that thermal instability appears to manifest very late" relate to Figure 9?

L. 345: "similarly with" <- "similarly to"

L. 380: "the depth- conductivity ratio" Not clear

L. 380: "a negative feedback": to me, it seems to a be a positive feedback

L. 389: "but take a longer period of time to manifest": because piles need to form?

L. 392: "may be masked by their first order influences": Not clear

Hide

RR by Anonymous Referee #3 (11 Nov 2022)

Suggestions for revision or reasons for rejection

Review of : « Influence of heterogeneous thermal conductivity on the long-term evolution of the lower mantle thermochemical structure: implications for primordial reservoirs »
by Guerrero et al.

In this manuscript, the authors seek to understand the effect of laterally-variable thermal conductivity controlled by depth, temperature and/or compositional effects on the shape and the dynamics of deep-seated thermochemical heterogeneities.

This manuscript has gone once into review already, and I generally believe that the authors made significant efforts to reply to the previous referees’ comments, especially on the structure of the introduction and the presentation of the results. However, I still believe that they can still improve their manuscript structure, which I still found hard to follow. I think that the reason is that the authors often use complex phrasing and repeat similar statements throughout the text, which makes the text too cumbersome. I therefore believe that the authors should make significant efforts to simplify the text in general and therefore gain in conciseness and clarity. I here-below detail some of the instances where this can be done.

I also detail a few comments and suggestions. I think that if these comments are adressed, this manuscript should be published, given that the results shown are of general interest for the Solid Earth community.

Main comments:

One of the parameters used by the authors to assess thermochemical pile dynamics and instability is the spatial average of (d/)prim. I wonder how this spatial average at all times is representative of individual pile behaviour (since in most models, there are 2 piles). Do they destabilize differently (in terms of tinst for example) or rather synchronously (as suggested by some of the composition field snapshots)? If the latter, this would add to the argument that the instabilities detected by the authors are due to intrinsic properties of the piles.

I would also check whether two separate models with the same input parameters but a different convective history (generated from an initial Tre field with different initial random perturbations) lead to significantly different (d/)prim, hc, ACMB and tins. If so, I would tend to think that the « extrinsic » factors (such as the effect of slabs) are predominant in the dynamics of the thermochemical piles, and that the description of Fig. 8 (From line 311) is not that meaningful to explain the role of conductivity on LLSVP dynamics. Can the authors argue on this point ?

I also wonder whether the authors can go further in the comparison of the dynamics of the thermochemical piles and their properties (such as (d/)prim, hc, ACMB, tinst) in their different models and the observed characteristics of LLSVPs. Can the authors discuss a bit more whether their models can help to refine the conductivity parameters for LLSVP material from the comparison of the dynamics of their modeled LLSVPs with observations ? Can they hint at a conductivity ratio range necessary to match current observations (maybe they could also exploit the QCMB/Qsurface ratios?) ? To what extent can they use their calculated (d/)prim, hc, ACMB, tinst for comparisons with the Earth ? To me, although this is shown as a goal on line 309-310 (in the results section), such a paragraph is currently missing in the discussion section.

I don’t understand why the authors analysed their models at 4.5 Gyr. Indeed, they state in the main text (Line 192-193) and in the supplementary material Lines 118-119 that « the longer simulation time (11Gyr) is necessary to allow the simulations’ heat flows to achieve a quasi steady state ». However, they analyse a their so-called « derived quantities » (supplementary paragraph 3.3) « averaged over a 2 Gyr window centred about t = 4.5 Gyr ». Therefore, it gives the feeling that they analysed their models before reaching a quasi-steady state. Even if it’s not the case, I still wonder why the authors did not analyse the derived quantities at the end of each simulation, to be sure that their quantities shown in Table 1 are derived from a system in quasi-steady state.

To gain in clarity and conciseness, as I previously stated, I would advise the authors to rephrase some of their sentences (use short sentences, mostly with active form, use present tense for conjugated verbs (cf line 208-212), and remove all necessary expressions, such as « In light of this fact », line 30). I would advise to especially focus on the rephrasing of :
- Line 3-9.
- Paragraph line 23-32
- Line 36-41 : «an important property that influences mantle dynamics is thermal conductivity ». Say why directly after and simplify the rest of the paragraph.
- Line 59-68
- Line 69-83
 In fact, so far, the introduction follows this structure (per paragraph) :
1. LLSVPs observations and thermal/thermochemical interpretations,
2. LLSVPs characteristics and influence on stabillity,
3. Measured and estimated conductivity with depth/Tre and composition+ numerical models
4. Estimates and measured conductivity at HP/HT.
5. How does evolve the conductivity with P in measures/estimates.+ effect of composition on heat transfer through LLSVPs.
6. How does evolve the conductivity with increasing Tre (measures/estimates).
7. Effect of P and T dependence of conductivity in numerical models. + importance of considering compressibility.
8. Problem and structure of the article
 Instead, I would change the structure of the introduction and synthesize it into the following paragraphs (this is just a suggestion):
1. Show that LLSVP dynamics, structure, origin and composition are uncertain.
2. Highlight the main characteristics of thermal conductivity as shown by experiments/molecular dynamics…, and the fact that its variations with depth/Tre/composition are uncertain, although significant.
3. Such variations could alter LLSVP dynamics and stability, as shown by already published numerical models.
4. Hightlight the limitations of these existing models (no fully heterogeneous thermal conductivity/ neglection of compressibility, … although these parameters can significantly alter LLSVP structure and dynamics).
5. Goal of the manuscript and structure of the article
- Line 127-135 : Maybe, it's possible to streamline a bit this last paragraph and come more quickly to the point that : "modeling the effect of pv-ppv transition would mask ..."
- Line 374-389 : to me, these paragraphs rather belong to the conclusion, which repeats this. Consider at least reducing the size of that paragraph ?

Other comments:

- Line 15 : I’m not sure that we can say that a profile is underestimated. Does it mean that the value of conductivity is underestimated at some specific depths, or at all depths ? If the latter, maybe replace by « when conductivity is underestimated » ?
- Line 20 : « greater » : by how much ?
- Line 25-26 : replace by « have been defined as purely thermal (Davies et al, 2012) or thermo-chemical (e.g...) in nature. »
- Line 30-31 : add references for both end-member views on the origin of thermochemical piles.
- Line 32 : why/how do he authors choose one of the end-members ?
- Line 33 : something missing between « properties » and « most » ?
- Line 34 : I would remove the term HPE in the abstract, and instead give the full name « heat-producing elements » in the introduction on line 34 : «heat-producing elements (HPE) », and then use just HPE, for example on line 118.
- Line 35 : « underestimating their density and viscosity contrasts… » : This could lead the reader to think that we know the correct range of variation of these parameters… Then, what defines what is the “correct” proportion of entrained material? Develop a bit here.
- Line 39: “,which,”
- Line 50 : « reduces » instead of « reduce »
- Line 59 : instead of « new », shouldn’t it rather be « unprecise/unconstrained » ?
- Merge lines 59-61 into 1 sentence.
- Line 61 : « is fixed » ?
- Line 84 : « using » instead of « utilizing » ?
- Line 100-105 : should the authors precise somewhere that they will use compressible models ?
- Line 124-126 : simplify : « …to avoid the development of a stagnant-lid » and then « nondimensional viscosity varies between 10-3 and 105».
- Line 144 : « First, we consider a linear depth-dependence… »
- Line 145 : Add « where KD = … »
- Line 154 : add a reference to Fig.1
- Line 159 : « Temperature-dependence of conductivity is … »
- Line 161 : Lower compared to what ? Precise it.
- Line 183 : remove « and may be used to briefly outline where heterogeneous conductivity affects the dynamics. »
- Line 212 : « through » or « to » ?
- Line 217-220 : t is evident that using a depth-dependent only conductivity, conductivity will have a radially symetric distribution and that piles will have an identical conductivity to the one of the surronding mantle. I would therefore remove these parts.
- Line 218 : which simplification are we talking about. I get it but it’s not clear. Consider rephrasing.
- Line 217-227 : there are many repetitions in this paragraph (notably on the fact that conductivity increases from surface to CMB – line 217/224-225). Consider shortening it.
- Line 226 : remove « greatly » ?
- Line 252 : replace « in a lower extent» by « to a lower extent» ?
- Line 254 : replace reservoirs » by « piles » ?
- Line 256 : replace « much » by « more » ?
- Line 287-288 : consider reformulating (especially, I don’t understand what the authors mean by « slowly manifested thermal instability » and how it relates to « Thus, a much earlier ejection… »)
- Line 309 : « liberating ». Use a different word ?
- Line 315-322 : consider adding a subduction isotherm on the composition snapshots of Fig. 8 to better illustrate this discussion. And clearly identify the « transient period » on the plots ?
- Line 343 : « sooner compared to the reference case ».

- Table. S1 : « Total internal heating rate » is not a non-dimensional parameter. Add spaces or line-centered dots between units in the units column. Add the non-dim value for the yield-stress gradient. Its unit should be Pa km-1 or Pa m-1.
- Fig 3 and next figures with similar snapshots : is the temperature field the relative total temperature difference compared to the CMB or the total temperature minus the adiabat difference with the CMB ?
- Figure 8 and SI 11, SI 12 and SI 13 : the legend of the bars are the same for hc, hc > 0.9, and hc = 0.02-0.9. They should be different from one another, to reflect the different linestyles of the green lines. I would use a different colour than cyan for the onset of instabiliy because it’s not clearly visible. In the caption fo Fig 8, say explicitly that hc is the height of primordial material. And say explicitly that the height are plotted using green lines.

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ED: Publish subject to minor revisions (review by editor) (20 Nov 2022) by Juliane Dannberg

AR by Joshua Guerrero on behalf of the Authors (02 Dec 2022) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (09 Jan 2023) by Juliane Dannberg

ED: Publish subject to technical corrections (10 Jan 2023) by Susanne Buiter (Executive editor)

AR by Joshua Guerrero on behalf of the Authors (12 Jan 2023) Manuscript

Short summary

The mantle thermal conductivity's dependencies on temperature, pressure, and composition are often suppressed in numerical models. We examine the effect of these dependencies on the long-term evolution of lower-mantle thermochemical structure. We propose that depth-dependent conductivities derived from mantle minerals, along with moderate temperature and compositional correction, emulate the Earth's mean lowermost-mantle conductivity values and produce a stable two-pile configuration.