The impact of rising atmospheric CO<sub>2</sub> levels and resulting ocean acidification on the physical (solubility) ocean pump of CO<sub>2</sub>

Dreybrodt, Wolfgang

doi:https://doi.org/10.5194/egusphere-2023-1004

Preprints

https://doi.org/10.5194/egusphere-2023-1004

Preprints

30 May 2023

| 30 May 2023

The impact of rising atmospheric CO₂ levels and resulting ocean acidification on the physical (solubility) ocean pump of CO₂

Wolfgang Dreybrodt

Abstract. An alternative measure of the ocean’s carbonate buffer system efficiency to absorb CO₂ from the atmosphere is proposed. Instead of the Revelle factor R = (∆CO2/CO2)/(∆DIC/DIC) = (DIC/CO2)/ (∆DIC/∆CO2) the sensitivity S = (∆DIC/∆CO2) is preferable because it gives directly the change ∆DIC of the concentration of DIC in the seawater caused by the change ∆CO2 of carbon dioxide in the atmosphere. To this end the DIC concentration of seawater at temperature T in equilibrium with a defined CO₂ level in the surrounding atmosphere is calculated by use of the geochemical program PHREEQC. From the function DIC(CO2,T) one obtains by differentiation the sensitivity S = dDIC/dCO2 = ∆DIC/∆CO2 and also the Revelle factor R. Using S as the change of the ocean’s buffer capacity reveals a better insight of its future evolution than using the Revelle factor R.

One finds that the buffer capacity S has declined by about 30 % from 1945 to present and that its future decline from 400 to 600 ppm will be a further 30 %. By calculating the uptake of CO₂ of his equilibrium pump an upper value of 1.3 Gigatons/year is obtained, small in comparison to the 10 Gigatons/year absorbed by the ocean at present. The Revelle factor R at present is calculated R = 13 and rises to 18 at a CO₂ level of 800 ppm. This increase of R has been interpreted as indication of the collapse of the solubility pump. S and R, however, are defined from equilibrium chemistry and are a measure of the CO₂ absorbed by the ocean’s upper mixed layer by increase of the CO₂ level in the atmosphere without regarding its sinking into the deep-ocean by the thermohaline circulation. The difference ∆DIC between the actual value and the value at 280 ppm is transported into the deep-ocean by the global meridional conveyor belt. ∆DIC increases with increasing CO₂ level. At 280 ppm the system ocean-atmosphere is in equilibrium and the sink is zero. At 400 ppm a value of about 1.9 Gtons/year is estimated that increases to 3.9 Gtons/year at 600 ppm and to 5 Gtons/year at 800 ppm. At present CO₂ level increase of 2 ppm/year 10 Gtons/year are absorbed by the ocean. The solubility pump contributes 3.2 Gtons/year: 1.3 Gtons/year by equilibrium absorption into the mixed layer and 1.9 Gtons/yeat by thermohaline circulation. At 600 ppm the total sink is 4.6 Gtons/year and at 800 ppm 5.5 Gtons/year. To conclude, the solubility pump is not endangered by ocean acidification. In contrast, it increases with increasing CO₂ level of the atmosphere to yield significant contribution.

Received: 14 May 2023 – Discussion started: 30 May 2023

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Wolfgang Dreybrodt

Status: closed

RC1:
'Comment on egusphere-2023-1004', Anonymous Referee #1, 01 Jun 2023

Please refer to the supplement pdf file

Citation: https://doi.org/10.5194/egusphere-2023-1004-RC1
- AC1: 'Reply on RC1', Wolfgang Dreybrodt, 08 Jun 2023
  
  Thanks for the comment. In my paper. S is defined as S = dDIC/dCO2 (mmol DIC/ppmCO2). This tells, the increase of DIC concentration in the water caused by a defined increase of CO2 in the atmosphere on any defined steady path in chemical equilibrium. In my work TA and temperature are constant. For seawater the relation between R and S is R = 2.27/(CO2∙S). So, anything criticised on S holds also for R. Both, R and S are valid definitions, but S has to be preferred because of its intelligible meaning in contrast to R.
  
  Citation: https://doi.org/10.5194/egusphere-2023-1004-AC1
RC2:
'Comment on egusphere-2023-1004', Anonymous Referee #2, 19 Jun 2023

Review on
THE IMPACT OF RISING ATMOSPHERIC CO2 LEVELS AND RESULTING OCEAN
ACIDIFICATION TO THE PHYSICAL (SOLUBILITY) OCEAN PUMP OF CO2.
by Wolfgang Dreybrodt
In order to measure the change of DIC in seawater as a response to increasing atmospheric CO2 concentration, the author proposes to use the ’sensitivity’

(1) S = ∆DIC/∆COatm

instead of the Revelle (or buffer) factor

(2) R = (DIC/[CO2]) / (∆DIC/∆CO2) = (∆[CO2]/[CO2]) / (∆DIC/DIC)

where [CO2] is the aquatic CO2 concentration; both DIC and [CO2] are measured in gravimetric units (mol kg−1). The sensitivity comes in units of mol kg−1 ppmv−1 (when using the atmospheric mixing
ratio xCOatm) whereas the Revelle factor is a dimensionless quantity.

For a given change in atmospheric xCO2, ∆xCOatm, and known sensitivity one can immediately
calculate the change in DIC, ∆DIC. This is easy because all the relationships within the marine
carbonate system have to be taken into account already when calculating the sensitivity as
function of DIC, total alkalinity (TA), temperature, and salinity. With decreasing sensitivity -- this is
what currently happens due to increase of DIC -- the change in DIC for a fixed change in
atmospheric xCO2 decreases.

The Revelle factor is also a complicated function of DIC, total alkalinity, temperature, and salinity.
While the sensitivity decreases, the Revelle factor currently increases (for the same reason: mainly
due to increase of DIC). What are the consequences of an increase in R? The Revelle factor is
defined as the relative change of [CO2], (∆[CO2]/[CO2]), divided by the
relative change of DIC, (∆DIC/DIC). At air-sea equilibrium, the aquatic
CO2 concentration, [CO2], is connected by Henry’s law (proportional to) the atmospheric
fugacity of CO2, fCO2. Numerically the fugacity of CO2 is
close to the partial pressure of CO2, pCO2, and to the mixing ratio of CO2, xCO2,
i.e. fCO2 = 280 µatm ≈ pCO2 = 280 µatm ≈ xCO2 = 280 ppmv. Thus the relative change of
aquatic CO2 is proportional to the relative change of atmospheric fCO2. If we are interested in
the relative change of DIC we can rearrange Eq. (2) to obtain

(3) (∆DIC/DIC) = (∆[CO2 ]/[CO2 ])/R is proportional to (∆fCO2 /fCO2 )/R,

i.e. the relative change in DIC for a fixed relative change in fCO2 decreases with increasing R.
Both measures, S and R, although varying in opposite directions have the same consequences
for the direction of ∆DIC changes, and in this sense can be considered as equivalent.
It is a matter of taste which one to use when explaining what is happening to surface ocean DIC
with increasing atmospheric CO2. The sensitivity approach might be easier to convey to the public,
if people are willing to accept that the calculation of S can not be explained in one or two sentences.

A large value of the Revelle factor, say R = 10, means that a relative increase of [CO2] of, for example,
3% would lead to a relative DIC change of only 3%/R = 3%/10 = 0.3%.
How is the sensitivity related to the Revelle factor? Let us consider the sensitivity in the form of
S = ∆DIC/∆fCO2 (units: (mol kg−1) atm−1). In equilibrium, the concentration of CO2 in seawater,
[CO2], is related to the fugacity of CO2 by Henry’s law

[CO2] = K0*fCO2

where the Henry ’constant’, K0 (also denoted KH ), is a function of temperature and salinity.
Inserting Henry’s law into the sensitivity definition leads to

S = ∆DIC/∆fCO2 = K0*∆DIC/∆[CO2]

We now insert R/R on the right hand side and obtain

S = K0*∆DIC/∆[CO2] * (DIC/[CO2]) / (∆DIC/∆CO2) / R
= K0 * DIC /([CO2] * R)

i.e. the sensitivity is proportional to the inverse of the Revelle factor.

Although the sensitivity aspect of the paper might be of interest to the community, many statements lack support (often no references), are mis- leading or even wrong. The author seems to interpret the prediction (cited on p.11) ”The ocean’s capacity to buffer increasing atmospheric CO2 will decline in the future as ocean surface pCO2 increases ...” by Denman et al. (2007) in the sense of a ’collapse of the solubility pump’ (abstract). This is a misunderstanding, because with increasing atmospheric CO2 the uptake of CO2 by the ocean and its transport to deeper layers (solubility pump) will further increase. This is consistent with a decrease of the buffer capacity of the ocean with respect to increasing atmospheric CO2 which can be expressed by an increase of the Revelle factor or a decrease of the sensitivity (inversely related to
each other). Based on this misunderstanding, the author addresses a problem that does not exist.
I can not support publication of this paper.

Detailed remarks:
p.1 The term ’equilibrium pump’ is used several times before an explanation (although not satisfying)
is given on p. 10. The term ’pump’ in biological or solubility pumps means ’transport against a (vertical)
gradient’ (from low to high DIC).

p.1 units: Gt C or Gt CO2? I guess always Gt C

p.2: ’collapse of the solubility pump’ is too strong; ’decline’ does not mean ’collapse’;

p.2 'global meridional conveyor belt': better call it just ’conveyor belt’ (although physical
oceanographers don’t like this term too much) or ’global overturning circulation’ and give
references

p.2 ’At 280 ppm the system ocean-atmosphere is in equilibrium and the sink is zero’:
This refers to the preindustrial period (say from year 1000 to 1750). I would call it steady
state (with large fluxes in and out). Even at that period riverine input of DIC required net
outgassing of CO2 somewhere.

p.2 ’At 400 ppm a value of about 1.9 Gtons/year is estimated that increases to 3.9 Gtons/year
at 600 ppm and to 5 Gtons/year at 800 ppm.’ Sentence needs more explanation
(... 1.9 Gt C oceanic net uptake ... ; estimated in current paper or from literature?)

p.2 ’At present CO2 level increase of 2 ppm/year 10 Gtons/year are absorbed by the ocean.’
References??? 10 Gt C/yr?

p.2 ’To conclude, the solubility pump is not endangered by ocean acidification. In contrast,
it increases with increasing CO2 level of the atmosphere to yield significant contribution.’
The solubility pump is not properly calculated in the paper (back-of-the-envelop estimation at most).
The DIC increase is a product of sensitivity (decreasing with atmospheric CO2, however,
always positive) and atmospheric CO2 increase.

p.2 ’Thus, the ocean sink has increased proportional to the rise in atmospheric CO2’:
A linear relationship? References?

p.3: ’increase will be permanent.’ I guess you mean ’increase will continue in the future’
p.4 ’This transport pump increases steadily with increasing pCO2.’ The ’transport pump’
is not properly defined/explained. I guess the author assumes no change of circulation
with increasing atmospheric pCO2 and global warming.

p.4 ’The physical pump is the sum of the sink by the equilibrium pump and the overturning
transport pump.’ Both mentioned pumps not properly defined. Sum values of two independent pumps?

p.4 The input and output table of PHREEQC should be replaced by a proper list of relevant
quantities with appropriate units (for example: what is meant by ’CO2(ag) -2.921’)
The sensitivity as a function of DIC, TA, temperature, and salinity is easy to calculate with
freely available software packages (compare, for example, Orr et al., 2015, Orr & Epitalon, 2015,
Humphreys, et al, 2022, especially with CO2SYS available in MATLAB or Python on
GitHub: https://github.com/jamesorr/CO2SYS-MATLAB, https://github.com/mvdh7/PyCO2SYS).

p.5 ’linearly by 0.01°C per 1 ppm increase of CO2 level corresponding to their linear correlation
obtained from NASA data of temperature and CO2 level.’ Reference missing

p.6 ’which 9 units have reacted to carbonates. For low pH < 4 where all DIC is in CO2aq,
S* = 1. At 15°C the value of S = 0.0001 corresponds to value S* = 2.5. ’ S, S*: units missing

p.6: ’(0.051 at 5°C, 0.038 at 15°C. and 0.029 at 5°C)’ two different values (and without units) at 5°C

p.6 ’In other words, the large background of R at 300 ppm prevents a reasonable interpretation.’ ???

p. 7: ’illustrate why the Revelle factor cannot be used easily as quantitative measure because the
reduction of buffer capacity is by its change and not by its absolute value.’ ???

p.8 ’At present public policy seems to be convinced that at least the physical ocean pump will fail
in the near future.’ References???

p.8 ’mixed layers capacity’ capacity for what?

p.9 ’This leads to the conjecture that the physical sink into the mixed layer may not contribute
as significantly to the total ocean sink as thought by using the concept of equilibrium chemistry
(Revelle factor).’ ???

p.9 typos: chage -> change; defition -> definition

p.9 ’From this one may understand why R is used only qualititavely [TYPO] to judge ocean’s
physical pump buffer capacity.’ ???

p.10 ’Therefore, the absorption of CO2 is governed by Henry’s law’ ???

p.10 ’Therefore, dDIC/dCO2 = KH’ is wrong!

p.11 ’This, however, does not mean that the physical pump breaks down as has been
concluded from the increase of the Revelle factor.’ references???

p.11: ’This is governed by the global meridional overturning circulation where surface waters
of the mixed layer flow from the equator to the polar regions and sink there into the deep
ocean by thermohaline circulation.’ oversimplified view

p.11: DICppm not explained

p.12: At present the total Ocean sink is 10 Gt/year. References???

p.14: Kara A. B., Peter A. Rochford, Harley E. Hurlburt. An optimal
definition for ocean mixed layer: incomplete reference

p.15: in reference list, however, not cited:
Köhler P., Hauck J., Völker C., Wolf-Gladrow D. Interactive comment on ”A simple model of 308 the anthropogenically forced CO2 cycle”s by W. Weber et al., Earth Syst. Dynam. Discuss., 6, 309 C813-C813, 2015. www.earth-syst-dynam-discuss.net/6/C813/2015/

and

Zhang X., 2007: Couplings Between Changes in the Climate System and Biogeochemistry. In: 320 Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the 321 Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S., 322 D. Qin, M. Manning, Z. Chen,
M. Marquis, K.B. Averyt, M.Tignor and
H.L. Miller (eds.)]. 323 Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. 2007

References

[1] Humphreys, Matthew P and Lewis, Ernie R and Sharp, Jonathan D and Pierrot, Denis. PyCO2SYS v1.8: marine carbonate system calcula- tions in Python. Geoscientific Model Development, 15(1):15–43, 2022.
[2] Orr, J.C. and J.-M. Epitalon. Improved routines to model the ocean carbonate system: mocsy 2.0. Geoscientific Model Development, 8(3):485– 499, 2015.
[3] Orr, J.C., J.-M. Epitalon, and J.-P. Gattuso. Comparison of ten packages that compute ocean carbonate chemistry. Biogeosciences, 12(5):1483– 1510, 2015.

Citation: https://doi.org/10.5194/egusphere-2023-1004-RC2
- AC2: 'Reply on RC2', Wolfgang Dreybrodt, 07 Aug 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1004/egusphere-2023-1004-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-1004-AC2
RC3:
'Comment on egusphere-2023-1004', Anonymous Referee #3, 04 Jul 2023

Prof Wolfgang Dreybrodt's presents a couple of different thoughts and back-of-the-envolope calculations on the ocean carbon sink. The main point of the manuscript is about simply rearranging the equation of the Revelle factor:
R = (ΔDIC/DIC)/(ΔpCO2/pCO2) ⇔ ΔDIC/ΔpCO2 = R * DIC/pCO2 = S
While ΔDIC/ΔpCO2 is certainly easier to grasp for many people than the Revelle factor, rearranging the equation does, in my opinion, not represent a scientific advancement but rather a comment. Similar rearrangements were already presented in Sarmiento and Gruber (2006) (see for example chapter 10: http://assets.press.princeton.edu/chapters/s10_8223.pdf). While this rearrangement has been used often, it was explicitely documented as chemical surface ocean uptake capacity in a manuscript in review that is part of the RECCAP2 project that estimates the ocean carbon sink (https://www.authorea.com/users/617533/articles/642925-assessment-of-global-ocean-biogeochemistry-models-for-ocean-carbon-sink-estimates-in-reccap2-and-recommendations-for-future-studies).
As such, I do not believe that the scientific novelty or significance of this manuscript is worthy for publication.
In addition to the scientific novelty and significance, I have several major concerns regarding the manuscript:
- The author states that the usage of the Revelle factor lead to the assumption that the solubility pump will break down and uses this statement as a justification for the manuscript. Unfortunately, there is no proof provided in the manuscript. To my knowledge, no such statement exists in the scientific community. While it is recognised that the sink decreases with increasing Revelle factor (Revelle and Suess, 1957), even the high-emission scenario RCP8.5 is not estimated to lead to a collapse of the solubility pump (Rodgers et al., 2020).
- The Introduction is not sufficient with resepect to the existing literature about the subject (see for example the introductions in Friedlingstein et al. (2022)).
- The steps in pCO2 and T are far too large to calculate meaningful derivatives. It remains unclear to me why the author does not just use incremental steps or even better, directly the above-shown equation. This leads to several major errors throughout the manuscript: In Fig. 2, for example, the sensitivity for 'path' and '15°C' at 300 ppm is different although it should be identical as T is still at 15°C for path.
- In Fig. 3, the Revelle factor should be identical for 'path' and '15°C'. Why is there such a large difference?
- Units are not used in a careful manner. As an example: It is often not clear if it is Gt C or Gt CO2.
- The statement that the physical/solubility pump is only responsible for ~32% of the entire anthropogenic carbon sink (lines 227-231) is a result of many wrong assumptions: the ocean is not just a sponge and all water is not 'drained' to the deep ocean, the flux does not only depend on the atm pCO2 but also on the increase of atm pCO2. There are many publications on the importance of the biological and solubility pump but there is no doubt that the solubility pump is the major contribution to the anthropogenic carbon sink (Friedlingstein et al., 2022). This example demonstrates why these 'back-of-the-envelope' equations cannot be used when treating such a complex system as the global ocean.
- Methods are woven into the results section, for example the description of 'path'. This makes it difficult and at points impossible to understand which assumptions have been made for each figure and estimate. A better seperation and a more detailed Methods section is necessary to evaluate this manuscript. For example, the author speaks about a linear fit between temperature and atm pCO2 from NASA data (lines 97 and 98). There is no reference to the exact data that was used.
- Some assumptions are unreasonable. The author speaks about a time when pH decreases below 4. Even under the high-emission scenarios, such a low pH is not possible on average at the ocean surface.
- It is curious that the polar ocean water temperature is given as 5°C
- It is not clear which equilibrium constants were used.
Overall, I believe that this manuscript presents no new findings or results and the simplification of complex mechanisms, which are already presented in detail by Sarmiento and Gruber (2006), by simple equations with strong assumptions, leads to erroneous conclusions. Relatively simple 3-D biogeochemical models in the 1990s were already able to estimate the different parts of the ocean carbon sink in a much better and accurate way (Joos et al., 1999).

References

Fortunat Joos et al. Global Warming and Marine Carbon Cycle Feedbacks on Future Atmospheric CO2.Science284,464-467(1999).DOI:10.1126/science.284.5413.464

Revelle, R., & Suess, H. E. (1957). Carbon dioxide exchange between atmosphere and ocean and the question of an increase of atmospheric CO₂ during the past decades. Tellus, 9, 1– 10. https://doi.org/10.3402/tellusa.v9i1.9075

Rodgers, K. B., Schlunegger, S., Slater, R. D., Ishii, M., Frölicher, T. L., Toyama, K., et al. (2020). Reemergence of anthropogenic carbon into the ocean's mixed layer strongly amplifies transient climate sensitivity. Geophysical Research Letters, 47, e2020GL089275. https://doi.org/10.1029/2020GL089275

Sarmiento, Jorge L., and Nicolas Gruber. Ocean Biogeochemical Dynamics. Princeton University Press, 2006. https://doi.org/10.2307/j.ctt3fgxqx.

Citation: https://doi.org/10.5194/egusphere-2023-1004-RC3
- AC3: 'Reply on RC3', Wolfgang Dreybrodt, 07 Aug 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1004/egusphere-2023-1004-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-1004-AC3

Status: closed

RC1:
'Comment on egusphere-2023-1004', Anonymous Referee #1, 01 Jun 2023

Please refer to the supplement pdf file

Citation: https://doi.org/10.5194/egusphere-2023-1004-RC1
- AC1: 'Reply on RC1', Wolfgang Dreybrodt, 08 Jun 2023
  
  Thanks for the comment. In my paper. S is defined as S = dDIC/dCO2 (mmol DIC/ppmCO2). This tells, the increase of DIC concentration in the water caused by a defined increase of CO2 in the atmosphere on any defined steady path in chemical equilibrium. In my work TA and temperature are constant. For seawater the relation between R and S is R = 2.27/(CO2∙S). So, anything criticised on S holds also for R. Both, R and S are valid definitions, but S has to be preferred because of its intelligible meaning in contrast to R.
  
  Citation: https://doi.org/10.5194/egusphere-2023-1004-AC1
RC2:
'Comment on egusphere-2023-1004', Anonymous Referee #2, 19 Jun 2023

Review on
THE IMPACT OF RISING ATMOSPHERIC CO2 LEVELS AND RESULTING OCEAN
ACIDIFICATION TO THE PHYSICAL (SOLUBILITY) OCEAN PUMP OF CO2.
by Wolfgang Dreybrodt
In order to measure the change of DIC in seawater as a response to increasing atmospheric CO2 concentration, the author proposes to use the ’sensitivity’

(1) S = ∆DIC/∆COatm

instead of the Revelle (or buffer) factor

(2) R = (DIC/[CO2]) / (∆DIC/∆CO2) = (∆[CO2]/[CO2]) / (∆DIC/DIC)

where [CO2] is the aquatic CO2 concentration; both DIC and [CO2] are measured in gravimetric units (mol kg−1). The sensitivity comes in units of mol kg−1 ppmv−1 (when using the atmospheric mixing
ratio xCOatm) whereas the Revelle factor is a dimensionless quantity.

For a given change in atmospheric xCO2, ∆xCOatm, and known sensitivity one can immediately
calculate the change in DIC, ∆DIC. This is easy because all the relationships within the marine
carbonate system have to be taken into account already when calculating the sensitivity as
function of DIC, total alkalinity (TA), temperature, and salinity. With decreasing sensitivity -- this is
what currently happens due to increase of DIC -- the change in DIC for a fixed change in
atmospheric xCO2 decreases.

The Revelle factor is also a complicated function of DIC, total alkalinity, temperature, and salinity.
While the sensitivity decreases, the Revelle factor currently increases (for the same reason: mainly
due to increase of DIC). What are the consequences of an increase in R? The Revelle factor is
defined as the relative change of [CO2], (∆[CO2]/[CO2]), divided by the
relative change of DIC, (∆DIC/DIC). At air-sea equilibrium, the aquatic
CO2 concentration, [CO2], is connected by Henry’s law (proportional to) the atmospheric
fugacity of CO2, fCO2. Numerically the fugacity of CO2 is
close to the partial pressure of CO2, pCO2, and to the mixing ratio of CO2, xCO2,
i.e. fCO2 = 280 µatm ≈ pCO2 = 280 µatm ≈ xCO2 = 280 ppmv. Thus the relative change of
aquatic CO2 is proportional to the relative change of atmospheric fCO2. If we are interested in
the relative change of DIC we can rearrange Eq. (2) to obtain

(3) (∆DIC/DIC) = (∆[CO2 ]/[CO2 ])/R is proportional to (∆fCO2 /fCO2 )/R,

i.e. the relative change in DIC for a fixed relative change in fCO2 decreases with increasing R.
Both measures, S and R, although varying in opposite directions have the same consequences
for the direction of ∆DIC changes, and in this sense can be considered as equivalent.
It is a matter of taste which one to use when explaining what is happening to surface ocean DIC
with increasing atmospheric CO2. The sensitivity approach might be easier to convey to the public,
if people are willing to accept that the calculation of S can not be explained in one or two sentences.

A large value of the Revelle factor, say R = 10, means that a relative increase of [CO2] of, for example,
3% would lead to a relative DIC change of only 3%/R = 3%/10 = 0.3%.
How is the sensitivity related to the Revelle factor? Let us consider the sensitivity in the form of
S = ∆DIC/∆fCO2 (units: (mol kg−1) atm−1). In equilibrium, the concentration of CO2 in seawater,
[CO2], is related to the fugacity of CO2 by Henry’s law

[CO2] = K0*fCO2

where the Henry ’constant’, K0 (also denoted KH ), is a function of temperature and salinity.
Inserting Henry’s law into the sensitivity definition leads to

S = ∆DIC/∆fCO2 = K0*∆DIC/∆[CO2]

We now insert R/R on the right hand side and obtain

S = K0*∆DIC/∆[CO2] * (DIC/[CO2]) / (∆DIC/∆CO2) / R
= K0 * DIC /([CO2] * R)

i.e. the sensitivity is proportional to the inverse of the Revelle factor.

Although the sensitivity aspect of the paper might be of interest to the community, many statements lack support (often no references), are mis- leading or even wrong. The author seems to interpret the prediction (cited on p.11) ”The ocean’s capacity to buffer increasing atmospheric CO2 will decline in the future as ocean surface pCO2 increases ...” by Denman et al. (2007) in the sense of a ’collapse of the solubility pump’ (abstract). This is a misunderstanding, because with increasing atmospheric CO2 the uptake of CO2 by the ocean and its transport to deeper layers (solubility pump) will further increase. This is consistent with a decrease of the buffer capacity of the ocean with respect to increasing atmospheric CO2 which can be expressed by an increase of the Revelle factor or a decrease of the sensitivity (inversely related to
each other). Based on this misunderstanding, the author addresses a problem that does not exist.
I can not support publication of this paper.

Detailed remarks:
p.1 The term ’equilibrium pump’ is used several times before an explanation (although not satisfying)
is given on p. 10. The term ’pump’ in biological or solubility pumps means ’transport against a (vertical)
gradient’ (from low to high DIC).

p.1 units: Gt C or Gt CO2? I guess always Gt C

p.2: ’collapse of the solubility pump’ is too strong; ’decline’ does not mean ’collapse’;

p.2 'global meridional conveyor belt': better call it just ’conveyor belt’ (although physical
oceanographers don’t like this term too much) or ’global overturning circulation’ and give
references

p.2 ’At 280 ppm the system ocean-atmosphere is in equilibrium and the sink is zero’:
This refers to the preindustrial period (say from year 1000 to 1750). I would call it steady
state (with large fluxes in and out). Even at that period riverine input of DIC required net
outgassing of CO2 somewhere.

p.2 ’At 400 ppm a value of about 1.9 Gtons/year is estimated that increases to 3.9 Gtons/year
at 600 ppm and to 5 Gtons/year at 800 ppm.’ Sentence needs more explanation
(... 1.9 Gt C oceanic net uptake ... ; estimated in current paper or from literature?)

p.2 ’At present CO2 level increase of 2 ppm/year 10 Gtons/year are absorbed by the ocean.’
References??? 10 Gt C/yr?

p.2 ’To conclude, the solubility pump is not endangered by ocean acidification. In contrast,
it increases with increasing CO2 level of the atmosphere to yield significant contribution.’
The solubility pump is not properly calculated in the paper (back-of-the-envelop estimation at most).
The DIC increase is a product of sensitivity (decreasing with atmospheric CO2, however,
always positive) and atmospheric CO2 increase.

p.2 ’Thus, the ocean sink has increased proportional to the rise in atmospheric CO2’:
A linear relationship? References?

p.3: ’increase will be permanent.’ I guess you mean ’increase will continue in the future’
p.4 ’This transport pump increases steadily with increasing pCO2.’ The ’transport pump’
is not properly defined/explained. I guess the author assumes no change of circulation
with increasing atmospheric pCO2 and global warming.

p.4 ’The physical pump is the sum of the sink by the equilibrium pump and the overturning
transport pump.’ Both mentioned pumps not properly defined. Sum values of two independent pumps?

p.4 The input and output table of PHREEQC should be replaced by a proper list of relevant
quantities with appropriate units (for example: what is meant by ’CO2(ag) -2.921’)
The sensitivity as a function of DIC, TA, temperature, and salinity is easy to calculate with
freely available software packages (compare, for example, Orr et al., 2015, Orr & Epitalon, 2015,
Humphreys, et al, 2022, especially with CO2SYS available in MATLAB or Python on
GitHub: https://github.com/jamesorr/CO2SYS-MATLAB, https://github.com/mvdh7/PyCO2SYS).

p.5 ’linearly by 0.01°C per 1 ppm increase of CO2 level corresponding to their linear correlation
obtained from NASA data of temperature and CO2 level.’ Reference missing

p.6 ’which 9 units have reacted to carbonates. For low pH < 4 where all DIC is in CO2aq,
S* = 1. At 15°C the value of S = 0.0001 corresponds to value S* = 2.5. ’ S, S*: units missing

p.6: ’(0.051 at 5°C, 0.038 at 15°C. and 0.029 at 5°C)’ two different values (and without units) at 5°C

p.6 ’In other words, the large background of R at 300 ppm prevents a reasonable interpretation.’ ???

p. 7: ’illustrate why the Revelle factor cannot be used easily as quantitative measure because the
reduction of buffer capacity is by its change and not by its absolute value.’ ???

p.8 ’At present public policy seems to be convinced that at least the physical ocean pump will fail
in the near future.’ References???

p.8 ’mixed layers capacity’ capacity for what?

p.9 ’This leads to the conjecture that the physical sink into the mixed layer may not contribute
as significantly to the total ocean sink as thought by using the concept of equilibrium chemistry
(Revelle factor).’ ???

p.9 typos: chage -> change; defition -> definition

p.9 ’From this one may understand why R is used only qualititavely [TYPO] to judge ocean’s
physical pump buffer capacity.’ ???

p.10 ’Therefore, the absorption of CO2 is governed by Henry’s law’ ???

p.10 ’Therefore, dDIC/dCO2 = KH’ is wrong!

p.11 ’This, however, does not mean that the physical pump breaks down as has been
concluded from the increase of the Revelle factor.’ references???

p.11: ’This is governed by the global meridional overturning circulation where surface waters
of the mixed layer flow from the equator to the polar regions and sink there into the deep
ocean by thermohaline circulation.’ oversimplified view

p.11: DICppm not explained

p.12: At present the total Ocean sink is 10 Gt/year. References???

p.14: Kara A. B., Peter A. Rochford, Harley E. Hurlburt. An optimal
definition for ocean mixed layer: incomplete reference

p.15: in reference list, however, not cited:
Köhler P., Hauck J., Völker C., Wolf-Gladrow D. Interactive comment on ”A simple model of 308 the anthropogenically forced CO2 cycle”s by W. Weber et al., Earth Syst. Dynam. Discuss., 6, 309 C813-C813, 2015. www.earth-syst-dynam-discuss.net/6/C813/2015/

and

Zhang X., 2007: Couplings Between Changes in the Climate System and Biogeochemistry. In: 320 Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the 321 Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S., 322 D. Qin, M. Manning, Z. Chen,
M. Marquis, K.B. Averyt, M.Tignor and
H.L. Miller (eds.)]. 323 Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. 2007

References

[1] Humphreys, Matthew P and Lewis, Ernie R and Sharp, Jonathan D and Pierrot, Denis. PyCO2SYS v1.8: marine carbonate system calcula- tions in Python. Geoscientific Model Development, 15(1):15–43, 2022.
[2] Orr, J.C. and J.-M. Epitalon. Improved routines to model the ocean carbonate system: mocsy 2.0. Geoscientific Model Development, 8(3):485– 499, 2015.
[3] Orr, J.C., J.-M. Epitalon, and J.-P. Gattuso. Comparison of ten packages that compute ocean carbonate chemistry. Biogeosciences, 12(5):1483– 1510, 2015.

Citation: https://doi.org/10.5194/egusphere-2023-1004-RC2
- AC2: 'Reply on RC2', Wolfgang Dreybrodt, 07 Aug 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1004/egusphere-2023-1004-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-1004-AC2
RC3:
'Comment on egusphere-2023-1004', Anonymous Referee #3, 04 Jul 2023

Prof Wolfgang Dreybrodt's presents a couple of different thoughts and back-of-the-envolope calculations on the ocean carbon sink. The main point of the manuscript is about simply rearranging the equation of the Revelle factor:
R = (ΔDIC/DIC)/(ΔpCO2/pCO2) ⇔ ΔDIC/ΔpCO2 = R * DIC/pCO2 = S
While ΔDIC/ΔpCO2 is certainly easier to grasp for many people than the Revelle factor, rearranging the equation does, in my opinion, not represent a scientific advancement but rather a comment. Similar rearrangements were already presented in Sarmiento and Gruber (2006) (see for example chapter 10: http://assets.press.princeton.edu/chapters/s10_8223.pdf). While this rearrangement has been used often, it was explicitely documented as chemical surface ocean uptake capacity in a manuscript in review that is part of the RECCAP2 project that estimates the ocean carbon sink (https://www.authorea.com/users/617533/articles/642925-assessment-of-global-ocean-biogeochemistry-models-for-ocean-carbon-sink-estimates-in-reccap2-and-recommendations-for-future-studies).
As such, I do not believe that the scientific novelty or significance of this manuscript is worthy for publication.
In addition to the scientific novelty and significance, I have several major concerns regarding the manuscript:
- The author states that the usage of the Revelle factor lead to the assumption that the solubility pump will break down and uses this statement as a justification for the manuscript. Unfortunately, there is no proof provided in the manuscript. To my knowledge, no such statement exists in the scientific community. While it is recognised that the sink decreases with increasing Revelle factor (Revelle and Suess, 1957), even the high-emission scenario RCP8.5 is not estimated to lead to a collapse of the solubility pump (Rodgers et al., 2020).
- The Introduction is not sufficient with resepect to the existing literature about the subject (see for example the introductions in Friedlingstein et al. (2022)).
- The steps in pCO2 and T are far too large to calculate meaningful derivatives. It remains unclear to me why the author does not just use incremental steps or even better, directly the above-shown equation. This leads to several major errors throughout the manuscript: In Fig. 2, for example, the sensitivity for 'path' and '15°C' at 300 ppm is different although it should be identical as T is still at 15°C for path.
- In Fig. 3, the Revelle factor should be identical for 'path' and '15°C'. Why is there such a large difference?
- Units are not used in a careful manner. As an example: It is often not clear if it is Gt C or Gt CO2.
- The statement that the physical/solubility pump is only responsible for ~32% of the entire anthropogenic carbon sink (lines 227-231) is a result of many wrong assumptions: the ocean is not just a sponge and all water is not 'drained' to the deep ocean, the flux does not only depend on the atm pCO2 but also on the increase of atm pCO2. There are many publications on the importance of the biological and solubility pump but there is no doubt that the solubility pump is the major contribution to the anthropogenic carbon sink (Friedlingstein et al., 2022). This example demonstrates why these 'back-of-the-envelope' equations cannot be used when treating such a complex system as the global ocean.
- Methods are woven into the results section, for example the description of 'path'. This makes it difficult and at points impossible to understand which assumptions have been made for each figure and estimate. A better seperation and a more detailed Methods section is necessary to evaluate this manuscript. For example, the author speaks about a linear fit between temperature and atm pCO2 from NASA data (lines 97 and 98). There is no reference to the exact data that was used.
- Some assumptions are unreasonable. The author speaks about a time when pH decreases below 4. Even under the high-emission scenarios, such a low pH is not possible on average at the ocean surface.
- It is curious that the polar ocean water temperature is given as 5°C
- It is not clear which equilibrium constants were used.
Overall, I believe that this manuscript presents no new findings or results and the simplification of complex mechanisms, which are already presented in detail by Sarmiento and Gruber (2006), by simple equations with strong assumptions, leads to erroneous conclusions. Relatively simple 3-D biogeochemical models in the 1990s were already able to estimate the different parts of the ocean carbon sink in a much better and accurate way (Joos et al., 1999).

References

Fortunat Joos et al. Global Warming and Marine Carbon Cycle Feedbacks on Future Atmospheric CO2.Science284,464-467(1999).DOI:10.1126/science.284.5413.464

Revelle, R., & Suess, H. E. (1957). Carbon dioxide exchange between atmosphere and ocean and the question of an increase of atmospheric CO₂ during the past decades. Tellus, 9, 1– 10. https://doi.org/10.3402/tellusa.v9i1.9075

Rodgers, K. B., Schlunegger, S., Slater, R. D., Ishii, M., Frölicher, T. L., Toyama, K., et al. (2020). Reemergence of anthropogenic carbon into the ocean's mixed layer strongly amplifies transient climate sensitivity. Geophysical Research Letters, 47, e2020GL089275. https://doi.org/10.1029/2020GL089275

Sarmiento, Jorge L., and Nicolas Gruber. Ocean Biogeochemical Dynamics. Princeton University Press, 2006. https://doi.org/10.2307/j.ctt3fgxqx.

Citation: https://doi.org/10.5194/egusphere-2023-1004-RC3
- AC3: 'Reply on RC3', Wolfgang Dreybrodt, 07 Aug 2023
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1004/egusphere-2023-1004-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2023-1004-AC3

Wolfgang Dreybrodt

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Short summary

The physical pump transporting atmospheric CO₂ to ocean consists of two parts: The first absorbs CO₂ to the upper mixed layer by rise of atmospheric CO₂. This amount of anthropogenic carbon is calculated. From this, its capacity at present is 1.3 Gtons/year declining to 0.4 for CO₂ above 600 ppm. The second sink transports anthropogenic DIC by thermohaline circulation. This pump increases from 1.9 at present to 5 Gtons/year at 800 ppm , The total pump is not switched off by acidification.


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The impact of rising atmospheric CO2 levels and resulting ocean acidification on the physical (solubility) ocean pump of CO2

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The impact of rising atmospheric CO₂ levels and resulting ocean acidification on the physical (solubility) ocean pump of CO₂