Monitoring Atlantic overturning circulation variability with GRACE-like ocean bottom pressure observations - a sensitivity study

“General comments: The theory presented in the article is neither novel nor very complicated (which could justify discussing theoretical and real results in seperate papers), the framework to derive the AMOC variations from GRACElike data has been set up and the GRACE data performing best (JPL CRI mascons) are available at the author?s institute. Therefore, including actual results should be feasible (although not trivial, given that the noise in the GRACE data was neglected in the sensitivity study). This would make for a much more exciting paper, with a much higher contribution to the scientific progress. However, as said before, the methods and results look sound, so I will leave it up to the editor to decide if this manuscript should be accepted for publication in its present form.”

The Referee states that the article might lack of scientific results since the article does not show any results from real data. We share the opinion of Referee #2, who states that the article would result in an extremely long article if results from real data were to be included. Indeed, the basic theory behind deriving transport from ocean bottom pressure is not very complicated. However, using ocean bottom pressure from satellite gravimetry to derive ocean transports is not trivial, since the signals are on the edge of the resolution and sensitivity of satellite gravimetry. We believe this simulation study is essential and justified to examine sensitivity of the available ocean bottom pressure observations derived from satellite gravimetry. It is important to know about strength and weaknesses of the method before simply applying it to real data. Furthermore, there are not many appropriate validation data sets for results from real data. In-situ data are sparse, and they are point measurements, while satellite observations cover large areas. Furthermore, in-situ data also have errors and suffer from drift. Assessing transport from other remote sensing methods, like altimetry, have errors that propagate into a transport estimate. Thus, we believe the present study serves as a rigorous assessment of what to expect from the data with regards to recovering the MOC signal. It will serve as a guide for the user to better understand the advantages and limitations as well as provide an error estimate of the impacts of the resolution.
"The authors find that GRACE-like observations can capture AMOC variations with an interannual RMS error of about 1 Sv. However, it's unclear how this compares to the interannual variability of the AMOC itself. Is this 1 Sv error small enough to still detect a useful signal? This deserves to be discussed in more detail." "Also, the error strongly depends on how one corrects for hydrological leakage. The CRI mascons and optimally placed mascons perform best in most case. In this regard, it should be kept in mind (and mentioned in the manuscript) that the spherical harmonic solutions can be corrected for leakage as well using stand-alone hydrology models (albeit only to a certain extent, since these models aren't perfect). Furthermore, I suggest to include an additional column of figures in figure 7, showing RMS errors for the GRACE simulations without any hydrology included. This way the reader gets a better feel for which part of the error is caused by hydrological leakage, and which part by leakage due to steep bathymetry gradients." Indeed, spherical harmonics solutions can be corrected for leakage as well. But, as the Referee mentions, these models have errors, and together with the required smoothing in the spherical harmonics (300-500 km Gaussian filter, in order to reduce the north-south stripes), the leakage correction does not sufficiently reduce the overall errors in the already small ocean bottom pressure signal, since other errors are introduced and smeared out again with the smoothing. We added a short paragraph to section 2.4.1 in order to clarify this. The suggested additional column has been added to Fig. 8 (instead of Fig. 7). It shows now time series with and without hydrology in a direct comparison. We believe that this provides the reader a better feel for the effect of continental hydrology, as mentioned by the Referee.
"The simulations and results are based on the assumption that the GRACE data are free of error (BTW, this should be mentioned clearly in the abstract). This is justified, but a short discussion should be included on how these errors will affect the results when working with real data. Chambers and Bonin (OS, 2012) found an error of 1.5-2.5 cm water equivalent in the North-Atlanic. How would this translate into AMOC transport error?" We included this in the abstract and in section 2.3. The most prominent errors in the GRACE solution are the correlated errors, resulting in North-South stripes in the spherical harmonic solutions. A lot of smoothing is required to reduce these errors. We applied a Gaussian filter with a 300 km radius to smooth the data, corresponding to the minimum amount of smoothing which would be required for real data. Additionally, we chose a spherical harmonic expansion up to d/o 60, which approximately corresponds to the d/o up to which signal content would prevail over the noise content in real data. The mascon solutions have intrinsically removed much of the correlated striping errors through the application of geophysical constraints, and no additional smoothing is required (the mascon-smoothing is effectively mimicked by the 3-degree binning). That means we can assume that no additional smoothing is required for the mason solutions. In this application here, the limitation is not predominantly the actual error on the GRACE gravity data, but first and foremost the spatial resolution, which is closely related to assigning the appropriate depth to each OBP observation. The error caused by assigning the OBP value to the incorrect depth is still by far the dominant error source here and the limitation to using GRACE data to derive ocean transport. Therefore, focus is more on the leakage effects (i.e. assigning the correct depth to the OBP observations) than actual GRACE errors. Chambers and Bonin (OS, 2012) found a mean error of 2 cm in the spherical harmonic GRACE solutions in the North Atlantic. A 2 cm error in ocean bottom pressure would result in an error of about 0.002 Sv/m in the derived transport. Assuming the northward transport layer spans roughly 1000 m, this leads to an error of about 2 Sv from spherical harmonics. However, we note that mascon data errors are estimated to be about 30% smaller than this in the current study region (see Watkins et al. 2015).
"Finally, an important scientific question is whether the AMOC is declining in strength or not. The summary and outlook sections should briefly mention this and discuss how feasible this is with GRACE data (will GIA be a problem? How many years of observations would be required to detect a significant trend, given the 1 Sv error in this study?)." Indeed, AMOC trends are of great interest. Trends in the ocean bottom pressure can be recovered by GRACE, however, the uncertainty in GRACE trend corrections for GIA (from models) and leakage correction can significantly corrupt a transport-related OBP trend. In addition, the ECCO2 model is not free from model drift, which must be corrected for. An unrealistic drift could contaminate the statistics here. Therefore, we decided to remove the trend and only focus on interannual signals. A detailed trend correction study for GRACE is beyond the scope of this paper, however, we intent to pursue a detailed evaluation in future studies (same answer as to Referee #2's question).
"-minor comments: * p 1771, line 6: Why are you using a 15-month running mean and not, for example, 13 (1 yr) months or 19 months (1 1/2 yr). Add motivation." A 15 months running mean is chosen in order to obtain interannual signals only. The exact filter length does not affect the results in any significant way, any fiter length from 13 to 19 months could have been used.
"* p 1771, line 8-21: Many of the readers of Ocean Science are not familiar with the GRACE data and the different products available. I think it would be good to give a short description of the standard products (spherical harmonics) and the mascon products, and how they differ in use and spatial/temporal resolution." A short discussion about the available GRACE products is added to section 2.3. "* p. 1772, line 3: 'Aliasing' might not be the best choice here, suggest to change to "contamination" (in the GRACE jargon, 'aliasing' usually refers to high-frequency signals causing spurious long-term signals due to the temporal sampling by the satellites)." Changed.
"* section 2.4: The SH60 data is listed as having a spatial resolution of 3 degrees in table 1, but looking at the detail in figure 3c this appears incorrect. How did you define your grid for the spherical harmonics solutions: a regular lat/lon grid, or did you shift the grid in longitudinal direction (for each latitude) so that the grid points are optimally placed along the coast line? Just as for the mascons solutions, such a variable grid will most likely reduce leakage from hydrology and improve the results." All the grids, on which ocean bottom pressure data is sampled, are regular 0.25 deg lat-lon grids. However, this grid sampling does not define the resolution of the data. It accommodates the highest resolution, which is the original 0.25 deg ECCO2 data. However, the smoothed data is still sampled on the same grid. Therefore, grid sampling or location of the grid cells does not affect the coastal resolution of the spherical harmonic data. The resolution is restricted by the maximum spherical harmonic degree and order (which is 60, and corresponds to about 3 deg). In contrast to the spherical harmonic truncation, the mascon data is binned to 3 degree mascon cells, and the location of the cells actually makes a difference. "* Section 3.1: The RMS errors of the mascon solutions show a peculiar feature at 29-30 N, extending to about 3000 m depth, which is absent in the spherical harmonics solutions. Any idea what's causing this? Please discuss briefly in the manuscript. Also, would it be possible ot apply the CRI approach to the position optimized mascons to further reduce the RMS error?" At about 25-30 N the topography on the Western boundary is extremely steep, in particular between 1000 and 3000 m depth (In Fig. 2 the 1000 and 3000 m depth contour lines are extremely close together). This steep gradient causes a lot of leakage in one interpolated mascon cell, which covers depth layers from above 1000 m to below 3000 m, but gets assigned a single averaged OBP value. The SH solution does appear to perform somewhat better here, but the actual measurement errors likely would cancel this apparent advantage. We discuss this briefly in section 3.1 now. Regarding the combination of CRI and position optimized mascons please refer to our response to the first comment of Referee #2.
variations. You also should indicate where the maximum (interannual) variabilty occurs in the model domain. In figure 7, you should also include a line showing the RMS of the AMOC transport at the three layers so the reader can get a feel of the signal-to-noise ratio. How the RMS errors of the GRACE simulations compare to the RMS of the model AMOC should also be discussed in the main text, conclusions and abstract." A new panel is added to Fig. 6 to show the variability of the transport signal (derived from ECCO2). Adding another line makes the plots crowded and less readable. We found it more helpful to indicate the significance level in the caption.

"-Technical comments:
* Define the GRACE acronym on first occurrence * p. 1767, line 12: to monitor *the* AMOC. * p. 1772, line 7: CRI, define abbreviation on first occurrence. * p. 1773, line 4: change "60 • " to "degree and order 60" * formula 1: define 'eta' symbol * p. 1770, lines 6-13: this paragraph is a partial repeat of lines 19-25 on page 1767. Restructure these two paragraphs to avoid overlap." All changed 5 Comments by Anonymous Referee # 2 "-Is there a reason that you cannot combine the mascons pos opt with CRI? It seems like this could provide even better results." Technically, it is possible to apply the CRI filter to the position optimized mascons. However, optimizing the position in the Atlantic Ocean would shift the whole mascon configuration globally. The main point of the simulation here was to show that mascon placement with respect to the topography actually makes a difference. Instead of computing a new global mascon solution with the position optimized mascons, which includes coastline correction, the goal is working towards a new 1 deg mascon solution, which would have even more benefits than a new coastline resolution improvement.
"-L225-228. In the methods, the authors use a fixed depth to separate their layers (909 m). However, the depth of maximum overturning may vary with time and with latitude. At a minimum, you should mention this in the paper, as it is a significant and known issue with estimating the overturning with alternative observational strategies (mentioned, I believe, in Send et al (2011) for the MOVE array at 16N)." Indeed, the depth of maximum overturning can vary with latitude and time, this is now added to the text. It may introduce (small) errors when the total overturning transport is computed (added to the text in section 3.2). However, when comparing layer transport to the ECCO2 model reference, the choice of the depth of the layers is not crucial. Therefore, we think it is feasible to choose the maximum overturning to be constant to evaluate the method of deriving transport from OBP observations at a GRACE-like resolution. But we do note now that there is a spatial & temporal variation of the AMOC structure.
"-Related to the above comment, more a question for thought than something that needs changing. Suppose that the top 100 m was entirely wind-driven Ekman transport. Would you be able to reconstruct the overturning and perhaps constrain some variability by applying a mass conservation constraint? Or in other words, if you add up your 3 layers, how close to zero do you get? It should differ from zero by the Ekman transport and perhaps by the AABW circulation. If you can reconstruct the overturning, perhaps you can make a GRACE-derived version of Fig. 6." When the three layers considered here are added up, the remainder (Ekman+ABW) is in the same order of magnitude as the signals which we obtain for the three individual layers. Furthermore, the remaining signal agrees reasonably well with the Ekman + ABW signals from ECCO2 (i.e. in our case transports above 100 m and below 5000 m depth). Summing up the two layers that contain the southward transport should give a reasonable estimate of the AMOC transport anomalies (assuming mass conservation). Therefore, we added new plots showing the sum of the two deeper layers from a mascon resolution with CRI in comparison to the model truth transport. GRACE can only be used to observe temporal AMOC anomalies, but not the full signal. Therefore, a temporal mean of the full signal cannot be derived form GRACE.
"-Is there a reason that the OBP data were detrended? Can GRACE recover trends in bottom pressure associated with trends in transport?" See answer to Referee #1's question -model drift is also an issue, so we de-trend everything to not be affected by that (the other reasons are still valid, of course). that the AMOC can be estimated w/1 Sv error (L301), but based on the remainder of the conclusion and the absence of a figure showing the AMOC time series (rather than layer transport time series as in Fig. 8) leads me to wonder whether the AMOC time series was constructed or not. It would be worth adding a time series of the AMOC (a new Fig 9), perhaps for the two chosen latitudes? Since Fig. 8 is quite busy with a lot of lines, perhaps the new figure could include only the model reference and the best estimate of the AMOC (either or both of the top 0-909m layer and the sum of the lower two layers)? I think this figure is necessary if you want to use "AMOC" in your title, rather than something more like "transbasin transports"." We have added a new Fig. 9 showing the total southward transport, derived from OBP at a GRACElike mascon resolution and at the original ECCO2 0.25 deg resolution, compared to the ECCO2 model truth. This figure is additionally discussed in the text, error RMS and correlation coefficients are interpreted. Furthermore we updated Fig. 8 and added time series derived from OBP data without hydrology, as suggested by Referee # 1. This should be more clear now. We also decided to skip the negative example for 35 N. The fact that some latitudes are more favorable to the GRACE resolution than other is made clear in Fig. 7 already.

"Textual comments:
On the title, you say "GRACE-type" but in the paper, "GRACE-like". I think "GRACE-like" may be more appropriate. L17-20. Long sentence. L22, 23. Write out acronyms on first usage. Note "RAPID" is not an acronym, though MOCHA and MOVE are. Elsewhere there are other acronyms not spelled out. L29. Consider whether a reference to Frajka-Williams (2015) for AMOC variability manifest in sea level changes is appropriate and helpful. L31 and throughout. Suggest not capitalising Eastern and Western. L35. "zonal cross section" could be replaced by "latitude"? L38. The "i.e." is probably not necessary L40-41. I think the other major difference is the smoothing of OBP fields in a GRACE-like manner. L65. Odd punctuation within the parentheses. L70. Clarification. The quantity T(z) is not really a transport (or at least does not have units of Sv), but rather a transport-per-unit-depth. Eq(3), delta z is not defined. L86. inter-annual -> interannual. Not necessary to specify "periods greater than annual" L92. From a quick skim of Elipot et al. (2013), I don?t see where they used hydrographic data to confirm the dominance of the western boundary. I do see, their section 2a, references to Kanzow metal 2010 and Bingham and Hughes 2008 on the dominance of the western boundary. Possibly you are referring instead to Elipot et al. (2014), their section 3b(1)i? L105-106. This is also a limitation of in situ pressure. S2.2. Any more model details? I don?t think you mention that this is a state estimate with data assimilation. Is GRACE data assimilated, though that doesn"t necessarily matter for this analysis. L116. is -> are. "data" is plural. L117. "longitude" and "latitude" are unnecessary. L134. Gulf stream -> Gulf Stream" All changed. The enlargement of the mascons is to show the effect of the coastline resolution improvement. There is no such process for the spherical harmonics, the data is very smooth. However, we added an enlarged plot of the spherical harmonic solution.
"L153-154. Awkward. Suggest "Besides signal leakage from continental hydrology, leakage of the signal within the ocean between different depths must be considered." L160. optimal -> optimally" Corrected.
" Fig. 5 (see also comment on L70), suggest referring to T as transport-per-unit-depth as. Some x-axes appear to have disappeared. TWS in figure should be "hydrology" to match caption. Is there no mascons optimised plus CRI version?" All changed. We did not compute a mascon position optimized plus CRI version, instead there is an effort towards a one degree mascon solution, which will be even more beneficial (see also response to first comment) "L168. I don't understand what "forward-simulated" means here." Unnecessary, it's removed.
"L170-178. I don't understand the discussion of how removing a mean introduces errors." Removing a mean over all depth would propagate information (and errors!) from very shallow areas to deeper layers. Since continental hydrology is a much larger signal in magnitude than ocean bottom pressure, even after leakage correction the hydrology leakage errors are still significant. By not removing a mean, we avoid the very deep layers being "contaminated" by the hydrology signal (that tends to contaminate the shallower layers more).
"L180-185. How much of the error is due to not capturing the variability vs not capturing the magnitude?" The majority of the error is due to not capturing the correct magnitude due to mascon averaging, see also Fig. 8. "L187. Can you discuss the source of the leakage at 25N in more detail? hydrology? depth? Some influence of the Bahamas? Ok, you say in L196 that it's due to the mascons. Why 25N? Interestingly, the latitudes for which this is a problem appear to correspond to those latitudes where the Willis (2010) method of recovering the AMOC from Argo and altimetry works, presumably due to the steep bathymetry (allowing Argo floats to get close to the boundary)." The steep bathymetry is the reason for leakage in the mascons. At about 25 N the 1000 m and 3000 m depth contour line are almost next to each other (Fig 2). With a three degree mascon, values from above 1000 m to below 3000 m will be averaged out into one OBP value for one mascon. We added this to the text. "S3.1 This is a long paragraph. Suggest breaking somewhere. L192? also L206?
L213. remove comma L225. Kanzow et al. (2007) also showed something like this for timescales of 10-days." Corrected. 8 "*L225-228. This is assuming that you know your depth of maximum overturning. This is probably an unavoidable limitation of your study. It is also a limitation of the MOVE array at 16N. At 26N, the depth of maximum overturning varies (McCarthy et al, 2015). If there were to be a trend in the depth of maximum overturning, for instance, but you chose a fixed depth of 909 m, you would not measure the part of the trend in the AMOC associated with the changing depth." We added a sentence to point out issued with choosing a fixed depth. However, we do not estimate trends from GRACE, since the errors associated with GIA corrections are too large (our answer to third comment). "*L270. So, errors in the middle layer are high, but in the lower layer are low. Where is the signal of variability dominant? Is it enough to resolve the upper and deep layer to recover the MOC?" There is slightly more signal variability in the middle layer (new Fig. 6) but the deep layer can serve as a proxy for AMOC variability (e.g. RAPID time series). The upper layer misses the Ekman transport (which cannot be observed by GRACE) for the complete AMOC signal. However, we constructed the complete AMOC time series, by summing up all southward transport. See new Fig. 9. "* Fig. 8, why is the green line missing from the left column? Ah, ok, I see from L278 that they are covered.
Perhaps make one dashed? Also, can the axes be rescaled to contain all the lines? Is it worth plotting only the best reconstructions in this case, to really see how well they do? Yellow and green lines are very hard to read. For the best reconstructions, can you comment on what part of the variability is well-reconstructed? Does GRACE get the trend if not the interannual variability?" Fig. 8 has been updated according the suggestions. It should be much better to read now. There is still one instance where the scale doe snot fully accommodate the curves, however, we prefer to choose the axes as they are now, because otherwise, other (more important) details would be less readable. The actual value of the points which are not accommodated are not important. Annual signal and trend are removed, see above (trends from GRACE). "L280. form->from" Corrected.
"L301. Is it worth mentioning that this is about as well as RAPID can recover AMOC variability (Mccarthy et al 2015), though that was for full time variability. " This has been added to the conclusions section. " L305. OPB -> OBP *Suggest one additional figure. While the medium layer is certainly ruining some of your signal, can you come up with an estimate of the MOC at your two sample latitudes? perhaps the best estimate, and plot those time series with only the best estimate and the model-reference time series? And perhaps discuss the variance explained. " Corrected and a new Fig. 9 is added and discussed in the text.