Author’s Response to Referee 1 Commentary

 The authors acknowledge the lack of references in the introduction as well as in the methods section and agree to add in numerous citations throughout the manuscript to address these shortcomings.  We ensure that all our quantitative statements, or observations which carry significant importance which are not our own have been cited throughout our analysis.  We add discussion (with citations) to address all specific comments which point out information gaps. We address all specific comments which have scientific questions that are intended to facilitate discussion and add citations as appropriate.  The authors agree to fix all formatting issues with existing citations, and to add equation numbers throughout the manuscript.  We break down statements throughout the manuscript in cases where a statement is a run on sentence, is unclear, or requires additional explanation.  We also address all other grammatical and technical issues which have been pointed out.  The authors would like to thank Referee 1 for giving feedback that is extremely clear and easy to follow. Referee 1’s comments about our gaps in literature highlight an important weakness in our manuscript and we believe our motivation will be much stronger by addressing them.  We especially thank Referee 1 for asking us questions regarding uncertainties and the assumptions used in our approach as we believe this will address a crucial gap in our data analysis. 

General Changes Throughout Manuscript

1. Equation numbers have been added to all existing equations, and matrices are defined using new equations on separate lines for ease of reference and discussion.

1. Many new citations are being added throughout the introduction, as well as in the methods section.

1. Acronyms for Northern Hemisphere, Southern Hemisphere, and different species are defined at their first occurrence and then referred only by their acronym from then on.

1. Citation formatting errors are being double checked against AMT standard and corrected accordingly.

1. Grammatical and technical fixes are being implemented throughout in accordance with reviewer recommendations. Some sentences have been split or broken into simpler statements where the authors were requested, to aid with the flow and clarity of language.

1. A new Section 2.4.5 in methods is being added to very briefly mention advanced methods of EOF analysis including cyclostationary EOFs so that our usage of them in results has better continuity and is not jarring.

Changes Addressing “Specific Comments” with References to Line/Page Numbers

The following changes are implemented to address the “specific comments” from Referee 1 with line/page references.  Please note that the line numbers refer to the original version of the manuscript

Lines 1-3 Pg 1

We define MOPITT and more clearly describe the objectives of the study.

Line 27 Pg 2

Citations added to describe how the concentration level of NOx affects ozone production.

Line 59 Pg 2-3

Citations added to emphasize retrieval inaccuracies and the lack of monitoring stations across Africa.

Line 63 Pg 3

Citations added to bolster arguments that changes in local trends are difficult to separate from background trends.

Line 83 Pg 3

Citations added to emphasize that the separation of secondary CO from surface emission aids source attribution and inverse modeling studies.

Lines 124-127 Pg 4-5

Citations added for other satellite instruments (TES, AIRS, IASI, TROPOMI, and CrIS)

Line 133 Pg 5

Citations added regarding potential discontinuities of IASI-A retrievals, the smaller number of measurements for TES, and the cloud clearing algorithm used by AIRS.

Line 152 Pg 6

Citations added to emphasize high contribution of anthropogenic emissions from China due to coal reliance and biofuel burning.

Line 171 Pg 7

Discussion added with citations to emphasize the relative contribution to CO due to oxidation from CH₄   as compared to the oxidation from NMHCs. Citations added regarding the temperature dependence of isoprene and terpenes. Discussion added with citations to clarify how the large annual contribution and high reactivity of isoprene makes it the most dominant hydrocarbon emission.  The term “measurable in breath” has been removed and clarified (with citations) by describing the biological processes in animals where we can measure VOC emission.

Line 207 Pg 8

Acronyms for all 4 climate indices are expanded, with references included for each.

Line 213 Pg 8

We clarify the term “EOF” and add a brief description.

Line 228 Pg 9

We redefine the scaled matrix F’ to be the matrix J to avoid confusion with the original F matrix.   

Line 253 Pg 10

We clarify the term “SVD” and add a brief description

Line 267 Pg 10

We clarify the term “PCA” and add a brief description

Line 268 Pg 10

We discuss, with supporting citations, how our motivation for using asymptotic          approximation is due to simplicity, unlike similar methods that rely on statistical analysis and resampling the dataset. 

Line 272 Pg 10-11

We discuss, with supporting citations, the strengths and weaknesses of using an asymptotic expansion as compared with other methods.

Line 277 Pg 11

Significant discussion has been added, together with supporting citations, to explain why our estimation for the effective sample size is only valid for the case of red noise Gaussian processes where the true sample size N is very large.

Line 280-282 Pg 11

Discussion is added, with references, regarding tests that can be used to determine if eigenvalues are degenerate or potentially represent white noise.

Line 285 Pg 11

Discussion is added, with references, to better describe specifically how the list of drawbacks for EOF analysis affect results, and how best to mitigate them.

Line 409 Pg 16

Citations added to emphasize that one potential benefit of varimax rotation is to make spatial patterns simpler and easier to interpret.

Line 462 Pg 19

Discussion is added, with references, to bolster our argument for why we do not see a connection between Residual mode 1 and oceanic variability from oceanic cycles.  We mention potential issues including dependance of modes, thermal gradients near the surface, and variability from other small scale oceanic processes.

Changes to Figures

Fig 1 (Referee #1)

       We change the y axis magnitude to “molecules/cm²”.

Fig 2 (Referee #1)

Please label our colorbar with the proper units molecules/cm²).

Fig 3 (Referee #1)

We add subplot names to our figures, and grid bin our data using a consistent colorbar.  We label our colorbar with proper units.

Fig 4 (Referee #1)

We add subplot names to our figures.

Fig 5 (Referee #1)

We alter our color scheme so that the lines do not blend in as much.

Fig 6 (Referee #1)

We add subplot names to our figures, and grid-bin them using a consistent colorbar.  We label our colorbar with proper units.

Fig 7 (Referee #1)

We add subplot names to our figures.

Fig 8 (Referee #1)

We add subplot names to our figures.

Fig 9 (Referee #1)

We grid-bin the data and we label our colorbar with proper units.

Fig 10 (Referee #1)

We add subplot names to our figures.

Author’s Response to Referee 2 Commentary

The authors acknowledge that many EOF tutorials already exist in the literature and as such agree to reduce the amount of technical detail in the methods portion of our manuscript, moving these aspects to the appendix instead. The authors add in a table to our introduction section on source variability with an accompanying discussion to help us summarize our current understanding of the variability from specific sources of CO.  We add additional discussion in our introduction to make a better case up front for why we had expected EOF analysis to have better success in being able to separate sources into independent signals. We also add in our Results section 3.2 a clearer recommendation for why in our specific case, it was better to use our unrotated modes rather than to use our varimax modes.  We agree to incorporate all changes which have been requested in the specific and technical comments.  The authors would like to thank Referee 2 for asking many general questions regarding our manuscript including its structure, motivation, and our approach to data analysis. We especially appreciate Referee 2’s questions about area weighting in our data and our time scales, as we believe answering these questions will address a vital gap in our methods.  We also appreciate that Referee 2 was kind enough to give us 2 specific citations to help us address gaps in our literature.

General Changes Throughout Manuscript

1. We add a table with discussion to Section 2.2 of our introduction to aid in summarizing current understanding CO variability from specific sources and to understand what scales of time are most relevant.

1. We add additional discussion in our introduction to make a better case up front for why we had expected EOF analysis to have success in being able to separate sources into independent signals.

1. We reorganize our Methods section, putting the more technical details in our appendix to reduce the emphasis of our paper being a tutorial on EOF analysis.

Changes Addressing “Specific Comments” with References to Line/Page Numbers

The following changes are implemented to address the “specific comments” from Referee 2, with line/page references.  For each change we indicate in parenthesis which referee is being addressed in our proposed changes.  Please note that the line numbers refer to the original version of the manuscript.

Line 87 Pg. 3

We clarify that in our specific context the global background refers to a mathematical, non-physical quantity and simply refers to an average value.

Lines 90-100 Pg 3-4

We add discussion regarding the application of EOFs to air quality monitoring in the US. We use citations including Eder, B. et. al. (1993), who used EOFs to study spatiotemporal variability of non-urban ozone.

Line 136 Pg. 5

We add discussion that daily data would not be better suited because MOPITT does not have daily global coverage. We must ensure global coverage in the analysis because EOF analysis fails to produce patterns if there are gaps in the data.

Line 141 Pg. 5

Discussion is added regarding the fact that our data was detrended by taking the globally averaged time series and then applying a Fourier fit to it.  Because the trends in the total column data are a non-linear combination of the trends from individual sources, it is not immediately clear what sources may have had their long-term trends removed.

Lines 185-188 Pg 7

We edit our discussion with appropriate citations including Fiore et al. (2024) to incorporate up-to-date information on the sinks and sources of OH.

Lines 250-251 Pg 9-10

We add discussion regarding the fact that for our specific application, it makes very little difference in whether we choose to normalize our covariance since we are only using one observation field.  If we were to compare EOFs of different datasets, then we should normalize the covariance.

Results 3.1 Pg 15-16

We respond to a comment that initially refers to Figure 2, however because it refers to multiple patterns, we assume Referee 2 had intended to ask about how the EOF patterns may change over time in Figure 3.  We clarify that the EOF patterns did not show significant changes when we segmented the data into yearly sets to compare them from year to year.  It’s possible this could be because the data had long-term trends removed.

Lines 403-405 Pg 15-16

We clarify that our data is area weighted, and we include a new equation to indicate the weighting in Methods 2.1.  We discuss, using citations, that this choice is to ensure that the EOFs are invariant to the choice of grid and each pixel contributes equally to the total variance.

       Results 3.2 Pg 16-19

We add discussion to clarify that for our study, varimax rotation did not improve the representation of modes and that for further analysis with our seasonal decomposition we used our unrotated EOF modes.  We note that decision should not be done in general for climate data. Our decision is because our unrotated modes were reproducible across multiple domains and had better representation with respect to variance.

Lines 441-442 Pg 17

We add discussion to indicate that we have no reason to believe the patterns fit the behavior of source variability *or* that of weather patterns either large scale or local scale.

Line 459 Pg 18-19

We add discussion in the introduction as well as to results Section 3.2 to describe sources of oceanic CO including photoproduction from colored dissolved organic matter (CDOM), direct production from phytoplankton, and dark production from CDOM in the absence of sunlight.

Line 476 Pg 20-21

We clarify, using citations, that the use of time scales for CO makes sense even when the scales are longer than its lifetime.  Some variability of CO is driven by large scale weather patterns, for example mixing time is about 6 months and hemispheric exchanges can happen across 1-2 years. It also makes sense from a perspective of studying the impact of climate drivers

Line 534 Pg 25

We add discussion as to what physical processes drive the sharp gradients in skewness related to Figure 9.  The annual cycle should be driven by seasonal changes in its sources and sinks and will differ depending on hemisphere and region.  For example, in the northern hemisphere it’s primarily driven by changes in fossil fuel burning usage i.e. it’s largest in winter and smallest in summer because of changes in heating demands.  In the southern hemisphere biomass plumes drive variability in central Africa and over part of Australia while biogenic and VOC emission mostly drives changes in South America.  The large banding effect over latitude in the SH variability is probably because of a combination of regional transport as well as long term variability due to the North/South movement of the ITCZ which affects the strength of hemispheric exchanges through the Hadley circulation.

Appendix A1. Line 589. Pg 27

Here we clarify the reason for our normalization and mention other potential normalizations which could be used.