A Theoretical Analysis for Improving Aerosol-Induced CO2 Retrieval Uncertainties Over Land Based on TanSat Nadir Observations Under Clear Sky Conditions
Round 1
Reviewer 1 Report
Only minor comments are listed below:
Page 4, Line 160:
F(i) should be F(x).
Page 4, Line 164:
“Rodger” should be “Rodgers”.
Page 7, Table2:
fiso, k1, and k2 are missing in the first row of the table.
Author Response
Thanks for the reviewer's comments. These minor incorrect points have been revised as the reviewer suggested in the manuscript.
Reviewer 2 Report
The authors present a thorough analysis on the capability of the TanSat instrument ACGS to retrieve XCO2 in the presence of different types of aerosol loadings. They also investigate the possibility of retrieving aerosol parameters along with the carbon dioxide concentration. The authors use state-of-the-art methods to analyze the performance of an optimal estimation-type retrieval setup. To my knowledge, the presented aerosol retrieval parameterization has the largest number of parameters of any of the major XCO2 retrieval schemes (i.e. ACOS, UoL, RemoTeC, FOCAL, WFM-DOAS).
The presented degrees of freedom (DFS) for the aerosol part of the retrieval are essentially my No. 1 concern about this manuscript. The authors present DFS around 4-7 for the aerosol retrieval, which is significantly higher than what is known from literature for these types of instruments. The paper by Butz (2009) is cited, in which it is estabished that there is almost no sensitivity to the aerosol layer width. Similarly, Guerlet, Butz et al. (2013) state that for GOSAT (which is not unlike TanSat) the aerosol DFS is ~2.5. From experience, it is also very counter-intuitive, as such a high value for the degrees of freedom would mean that aerosols could very easily be co-retrieved, which is not the case, as it is still the largest cause of bias in XCO2 retrievals. Especially given how similar the instrument is to GOSAT and OCO-2, the result comes as a fairly big surprise.
I could not figure out how this discrepancy between the results in the manuscript and the known literature arises (I could not spot any obvious issue), and sadly the authors have not commented on this quite surprising result.
If the authors can shed light on this aspect and explain why the DFS is so much higher than from other known studies, it would probably change the punchline of the paper and increase its value for the community. Otherwise, one has to suspect some issue with the algorithm or calculations.
Finally, I have some minor suggestions:
1) Some of the figures are very difficult to read (Figs 2, 3, and 8 mainly), and would strongy benefit from changes in layout / font size etc. Figure 4, on the other hand, seems too large.
2) Figure 3 could be somewhat informative if changed for better legibility, however it would also be interesting to see the correlation matrix that can be constructed from the posterior covariance matrix C(i,j) = Shat(i,j) / sqrt(Shat(i,i) * Shat(j,j)). This would very quickly show the reader which Jacobians are correlated with each other, and might make the results from Figure 6 (DFS) more accessible - there are probably a few correlated one's amongst them, which reduce the DFS.
3) Figure 9 is not too informative, and I could see that being better placed in the appendix or SI. I think it is sufficient to state the results of that figure, which is done anyway in table 5.
Author Response
Thanks for the reviewer's comments. The point-by-point response is in the Word file.
Author Response File: 
Author Response.docx
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
See attached PDF for review.
Comments for author File: 
Comments.pdf
Author Response
The point-by-point response to the reviewer’s comments is uploaded as a Word file as following.
Author Response File: Author Response.docx
Reviewer 2 Report
This paper provides a new result which is potentially useful to reduce the retrieval errors in XCO2 caused by aerosols.
Based on the linear error analysis, the authors proposed a set of parameters for the aerosol model which minimizes the XCO2 error.
The authors argued that the number of aerosol model parameters to be retrieved should not exceed the DFS of aerosols, which is 4-7, depending on the aerosol types.
The authors presented neither the application to the real observation data nor the synthetic retrieval.
There are several points which should be clarified before the authors’ algorithm is applied to the real data analysis.
The authors examined only one surface type, vegetation, in the manuscript, and state in the supplement that the impact of surface reflectance on aerosol induced interference error in XCO2 is similar.
However, this is questionable.
If the surface reflectance is very low, the net effect of aerosol scattering is a decrease of the optical path,
On the other hand, if the surface reflectance is high enough, the net effect is an increase of the optical path though multiple reflection between the surface and aerosols.
Therefore, the authors’ algorithm should be tested under a wide variety of the surface reflectance to demonstrate its validity and generality.
Ocean surface is a related issue.
The authors should examine whether their algorithm is valid for the ocean surface.
The authors proposed to retrieve 4-7 aerosol parameters, depending on the aerosol type, in accordance with the DFS of aerosols.
However, the DFS of aerosols can vary depending on AOT and SNR.
If the DFS of aerosols is less than 4-7, how can we determine an optimized set of aerosol parameters to be retrieved?
The authors employ the aerosol model with two modes, fine and coarse, with different optical properties, but with the same vertical distribution.
The other algorithms such as O’Dell et al. (2012) or Yoshida et al. (2013) employ aerosol models with two or more aerosol components with different vertical profiles.
Is the authors aerosol model sufficient for application to real data analysis?
Detailed comments are listed below:
Page 1, Line 40:
“Carbon dioxide” should be “carbon dioxide”.
Page 2, Lines 53-54:
GOSAT stands for “Greenhouse Gases Observing Satellite”. The manuscript is missing “Gases”.
Page 2, Line 55:
A phrase “less than 1% precision” may mislead the readers. Other phrases, such as “precision better than 1%”, should be used.
Page 2, Line 64:
The word “series” seems to be a typo of “serious”.
Page 4, Lines 149-150:
“averaging the kernel” should be “the averaging kernel”.
Page 5, Equation 8:
The scalar quantity sigma_j is confusing. This should be a vector which has the only non-zero component of sigma_j in its j-th element.
Page 6, Line 227:
To my knowledge, VLIDORT is a multiple-scattering code.
Page 11, Line 345:
Please cite a proper reference for the Carbon Tracker.
Page 11, Lines 346-347:
Please give an explicit expression for the off-diagonal elements of Saco2.
Page 12, Equation 15:
The authors state that they used the SNR curve measured by laboratory experiments. Please give more information so that the reader can know what the SNR was under which the numerical experiments were conducted.
Page 13, Figure 5a:
Were the interference errors calculated from equation 8? Please state explicitly which equation the authors used.
Page 14, Figure 5b:
Were the interference errors calculated from h^T S_i h, or are they the sum of the components presented in Figure 5b? Please explain explicitly how the authors obtained these errors.
Page 17, Line 492:
“from 5 to 8” should be “from 4 to 7”.
Author Response
A point-by-point response to the reviewer’s comments is uploaded as the following Word file.
Author Response File: Author Response.docx
Reviewer 3 Report
A marked up copy of the PDF is also provided with lots of detailed comments.
Title: A new method for correcting aerosol-induced CO2 retrieval uncertainties based on TanSat observation: A theoretical analysis
Author: Xi Chen, et al.
Synopsis: This paper describes a theoretical/simulation study to demonstrate the reduction in XCO2 retrieval error from high spectral resolution SWIR measurements (such as from TanSat) by way of optimizing the aerosol components contained in the state vector. The optimal choice of the retrieval aerosol model is based on the well documented linear error analysis technique as well as analyzing the internally calculated degrees of freedom for signal, which is a common retrieval diagnostic variable.
Overall Review: There is no doubt that the subject matter is of importance to the carbon dioxide remote sensing community, as the best way to treat aerosols as an interferent in the XCO2 retrievals is a well known and contested issue. Many papers on the topic exist in the published literature and additional investigations into this topic are welcome. Overall, the content of the paper is of reasonable quality, although some basic questions arise as to the organization of the discussion and about some of the core assumptions that are made by the authors. My recommendation is that the paper be published, but only after the authors are able to address a few critical questions of concern, detailed below. My review also includes a marked up PDF copy of the manuscript with highlights and comments which should be addressed. Some comments are very minor (typos, phrasing, etc), but a few are substantial in nature. In some cases there may simply be a misunderstanding as to what the authors actually did, and in those cases an attempt should be made to provide a clear explanation in the paper. In other cases some rework of the methodology/data may be required. My comments below are ordered roughly by importance, with #1 being the most important.
Major Points to Address:
Some clarification is required as to the methodology of the study. I believe what has been done is that an xco2 retrieval algorithm, presumably a variant of the operational TanSat algorithm (?), has been employed for this study. For shorthand I will call it the L2 algorithm, following the common nomenclature. An L2 algorithm contains several major components, one of which is a forward model (FM), used to calculate top of the atmosphere radiances. The basic principle of the Optimal Estimation (OE) framework is to match the FM calculated radiances to the actual measured radiances from the satellite sensor. In a simulation experiment it is generally necessary to begin by calculating “truth” radiances given some predefined set of atmospheric, meteorologic, surface and geometry conditions. In other words, a “scene” is first defined containing all the necessary inputs for a call to the FM, which returns simulated radiances. These simulated radiances then serve as input to the L2 retrieval in an attempt to recover the truth. Typically in a theoretical simulation experiment it is desirable to retain some aspects of reciprocity between the “truth” and retrieval setups, while breaking the reciprocity of other elements. Generally the elements that are not part of the testing suite are held consistent between the truth and retrieval setups. In the current work this might include items such as gas absorption coefficients, instrument parameters (ILS, dispersion, etc), and surface model. On the other hand, elements that are being tested, namely aerosols in the current work, should differ between the truth and retrieval setups. One way to think of this is that the truth setup should be made as realistic as possible, while the retrieval setup necessarily contains many assumptions due to lack of a priori knowledge and/or computational speed requirements. As far as I can tell, the current work has not such break in symmetry between the truth and retrieval setup with regard to the aerosol model. I understand that the complexity of the retrieval setup is made more or less elaborate by way of adding or subtracting aerosol parameters from the state vector, but this is not the same as having a more complicated truth model and a less complicated retrieval model. Perhaps for the current investigation this setup is okay, but I think some clarification and explanation is needed.
As a follow on to item #1, some detailed clarification is needed as to any differences between the truth setup and retrieval setup with respect to the aerosol model. Lines 234-240 give some details about the aerosol model in the FM, but it is not clear if that applies to both the truth and retrieval. One concern is that it seems that the truth setup also uses the Gaussian aerosol configuration with the aerosol peak height at 2 km (Lines 315-317). It would be ideal if the truth calculations contained an aerosol representation that was more complicated compared to the retrieval, such as multilayer and mixed type aerosols. Having the exact same aerosol setup in the true and retrieved setup certainly limits the utility and robustness of the results.
The analysis relies on the linear error analysis and DFS as a quantification of the results. I also wonder about the XCO2 error defined as the difference between the true and retrieved value (call it delta XCO2 for short). In the theoretical simulation experiment this value can always be calculated since the true XCO2 value must be known to calculate simulated radiances. At the end of the day, the minimization of delta XCO2 is very important. If changing the retrieval aerosol model does not reduce delta XCO2 then it could be argued that there is no improvement in the retrieval.
The Aeronet truth data set. Lines 303-306 discuss the limits allowed on the AOD and Angstrom exponent. It seems like disallowing low AOD scenes bias the results toward moderate to heavily contaminated scenes. I wonder if the choice of retrieval aerosol state vector components would change for the very thin aerosol scenes. It is certainly true that many real world scenes will contain AOD < 0.4, but maybe not for UI and BB (?).
Clouds? There is no mention anywhere in the text as to how clouds where considered. The reader is left to assume that all scenes are 100% cloud free. In reality, even with aggressive cloud prefiltering, there will often be some cloud contamination in the scenes, which the XCO2 retrieval will have to handle. The authors should clarify how the simplifying assumption of 0% clouds may affect real world results, i.e., real world results are likely to be less certain.
Only one surface condition was studied. Lines 241-248 describe the use of MODIS BRDF for a vegetated surface. This seems like it could be a limitation of the study since the scattering of light by aerosols is somewhat dependent on the surface brightness. How robust are the final results to other surface type cases, e.g., bright desert surface, agricultural regions, water, etc.
Solar zenith angle vs satellite viewing angle effects. Lines 257-258 mention that a range of SZA where tested and the results are discussed in terms of varying SZA. But it seems that all simulations were run with TanSat viewing in nadir mode. One can presume that the effects will become more pronounced when both TanSat and the sun are at high angles. But perhaps for the simulation experiment varying one of these angle is sufficient with the assumption that the results would be symmetric, i.e. the photons are agnostic to the individual solar/satellite geometries and only care about the combined scattering angle. Some comment needed.
Shouldn’t Section 3 include some information about where the true CO2 values come from. Unless I’m completely confused there must be a truth value from models (or some other source) in order to simulate radiances. I found this value later on Line 345.
Similarly, for each scene there must be meteorology to define the atmospheric state, including pressure, temperature and water vapor profiles. The former two are important for the calculation of trace gas absorptions. Lines 278-281 mention these elements in the state vector but gives no indication of where the values come from for the truth simulations. Perhaps they come from the Aeronet? Please clarify.
Instrument model. Was the exact same instrument model (ILS, dispersion, etc) used in the truth and retrieval setup? Lines 259 mentions use of a Gaussian slit function. Is that a generic model or was the real TanSat model used in either the truth or retrieval?
It seems like a more logical way to organize the paper is for Section 3 to focus on the Truth aspects of the methodology, while Section 4 would include the description of the retrieval setup. In that vein it seems to me that parts of subsections 3.2 and 3.3 belong in Section 4. Please clarify if I am mistaken.
Comments for author File: Comments.docx
Author Response
A point-by-point response to the reviewer’s comments is uploaded as the following Word file.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
In general, I find this version improved over the original. The additional material and explanations are very helpful. However, the fundamental limitations of this paper still remain:
1) That this is a purely linear analysis for DOFs and errors resulting from nonlinearity of the forward model are not included
2) That, while realistic TYPES of aerosols are included in the simulations, realistic vertical profiles of clouds and aerosols are not included.
3) That it is still not clear what actual range of surface reflectivities are included in the simulations.
These limitations call into question the generality and usefulness of the results. #3 above could be addressed by provided histograms or maps of the actual surface reflectvities of the soil & vegetation types in the 3 wavebands for the four solar zenith angles used. It would be very interesting to see what range of surface reflectivities was actually spanned in the simulations. To be clear, I mean the reflectivity implied by the BRDF evaluated in the direct beam, sun-surface-satellite geometry.
Author Response
Thanks for the reviewer's comments. The authors' response is in the Word file.
Author Response File: Author Response.docx
Reviewer 2 Report
Only minor comments are listed below:
Page 4, Line 158;
“Rodger” should be “Rodgers”.
Page 6, Lines 242-243:
The description of the nadir mode of the TanSat observation is somewhat confusing.
In my understanding, TanSat looks nadir in the nadir mode, and the description “tracking of the principle (typo of principal?) plane containing the surface target” should be discarded.
Page 6, Lines 245:246:
I could not understand the sentence “we only focus on CO2 retrieval over land due to different algorithms for different modes”. This might be, for example, “we focus on CO2 retrieval in the nadir mode over land”.
Author Response
Thanks for the reviewer's comments. The authors' response is in the Word file.
Author Response File: Author Response.docx
Reviewer 3 Report
Thank you for taking into account my review comments and providing explanations as needed. The updated title is a nice informative improvement. The text now makes it clear that no full L2 retrievals were conducted, a point on which I was confused from the initial draft. I still think it would be prudent for a "full synthetic" analysis to be conducted in which the new aerosol model formulation is tested on simulated L1b radiances. But I suppose that is for a future analysis, along with trying the new aerosol implementation on real TANSAT (or other satellite) measurement.
Overall I am satisfied that the paper is suitable for publication in it's current form.
Author Response
We thank the reviewer for reading our responses and raising some comments and recommendations. The idea provided by the reviewer about testing our optimal aerosol model by simulated TanSat measurements is actually our next step, as well as applying in real TanSat data. Maybe they could be found in our future paper.
