General comments

This study updates the ULB-SOM-FFN-coastalv1 pCO2 data product, enhancing its capability to detect the long-term trends spanning from 1982 to 2020 (> 30 years) on a global scale. The authors achieved this objective by using additional environmental predictor (pCO2air) and new pCO2 observations from SOCAT v2022 for training and validation. The average bias between the pCO2 product and SOCAT observations are all close to 0 µatm in different decades (Figure 3), which means that this new version is suitable for investigating decadal trends in coastal pCO2 and CO2 fluxes on a global scale. To the best of my knowledge, this is the first coastal pCO2 product that tries to resolve long-term pCO2 trends. I tried to be picky to find out some potential mistakes, yet it's worth acknowledging that the author's calculations appear to be robust. At least my ability might not be sufficient to identify any big mistakes that might exist.

Nevertheless, as a data user, I would be very grateful if the author could clarify some of my concerns in the article so that I can use this data correctly in the future.

My primary concern revolves around the lack of clarity in defining the term "long-term trend". This study focuses on assessing the "long-term trend" or specifically, the "decadal trend". The term "long-term" is a relative definition, and the term "decadal trend" means the linear or nonlinear tendency of a time series longer than 10 years. Given that Figure 4 and Section 3.2 employ a "30-year" constraint for comparison, It is interesting to ask whether the updated version can be used to identify the linear trends of the 10~30 years time scale.

If the answer is yes, it is suggested to compare the pCO2 product with the buoy data, as mooring data are more continuous than SOCAT observations. Sutton et al. (2019) have comprehensively summarized these time series, with several buoys deployed in coastal areas and with continuous measurements longer than 10 years, including NDBC Buoy 46041 in Cape Elizabeth, NDBC Buoy 41008 in Gray’s Reef, and Coastal Western Gulf of Maine Mooring in the Gulf of Maine. All three of these buoys have records since 2006, rendering them suitable for supplementary comparison, as proposed in Figure 4.

If the answer is no, i.e., the current version doesn’t validate for trends < 30 years, I recommend clearly clarifying the definition of “trend” or “long-term” in the title, abstract, and conclusions, to ensure that the data can be used correctly in future studies.

Ref: Sutton, et al., 2019. Autonomous seawater pCO2 and pH time series from 40 surface buoys and the emergence of anthropogenic trends. Earth Syst. Sci. Data 11, 421–439. https://doi.org/10.5194/essd-11-421-2019

Some other comments:

1. Line 41, “The exchange of carbon dioxide (CO2 ) … depends on … (ΔpCO2)”,
   
   Quantification of fluxes also relies on gas transfer velocity and the solubility of CO2. Suggestion: “… mainly depends on … on the global average”.
2. Line 180, “fCO2to pCO2 using the equation of Takahashi et al. (2012, page 6)”.
   
   I guess you are using this equation ?
   
   pCO2 = fCO2 x [1.00436 – 4.669 x 10-5 x SST (°C)]
   
   It is acceptable to utilize this empirical equation since it will only result in small numerical differences compared to the results computed using CO2SYS. But it is hard to get the 2012 edition now, I recommend referencing a more recent version, such as the 2017 edition, as it will be easier for readers to access the specific equation.
3. Line 183: “In this study, the coastal domain (total surface) … ”.
   
   The 200m isobath has been commonly accepted as the shelf break criterion. An alternative approach is to consider a broader domain characterized by a distance to the coast of less than 200 nautical miles (approximately 370 km or 400 km). A 300 km definition for the wide shelf could also be employed. In the results section, the authors use the term "narrow coastal domain" without providing a distinct definition. I suggest explicitly clarifying this definition in the method section.
4. Line 187: “a total of ~ 14 million and ~ 4 million coastal data”,
   
   discrete samples or grids?
5. Line 193: “global atmospheric reanalysis ERA-interim wind product (Dee et al., 2011)”, ERA-interim is the 3-gen reanalysis data offered by ECMWF, encompassing the period from 1979 to 2019. Given that this work covers the years 1982 to 2020, I'm curious about how you obtained the wind speed data for the final year of your analysis. Furthermore, why not use the latest version ERA5?
6. Line 198, “using the NCEP reanalysis total pressure at sea level (Kalnay et al., 1996).”,
   
   While I believe that the choice of pressure data products has a minimal impact on pCO2air calculations, I'm curious why not use the newer NCEP2 version. Additionally, since this work employed the wind speed from ERA-Interim, why not use pressure data from ERA5 or ERA-Interim, which could offer enhanced spatial resolution to align with the wind speed data. Could you elaborate on the reasons behind these choices?
7. Line 199: “due to the proximity to the continent of the coastal ocean, the latter might be more exposed to anthropogenic sources of CO2”,
   
   I can’t understand what “the latter” means, “coastal ocean”?
8. Line 212-214: “by computing (1) … (2) …”,
   
   The final interpolated values use those options in the order of rank (i.e., using an "if... elseif" while programming), or take the average of all options?
9. Line 231: “Ho et al., (2011)”,
   
   I'm interested to know if there is a specific reason for not utilizing the Wanninkhof 2014 method.
10. Line 241, Equation 2. I have this question as well while reading Robaert et al., 2019. Notably, the uncertainty of CO2 solubility appears to be absent from the equation. While it may be plausible to argue that this uncertainty is minimal (0.2%, as suggested by Weiss, 1974), it remains essential to keep this term in the equation.
11. Line 249-252, “𝜎_wind is calculated …”,
    
    The wind speed data products cover different time periods, and please specify the time period for which the standard deviation is calculated.
12. Line 275: “θmap is calculated as the RMSE …”
    
    RMSE of the training set (SOCAT_a vs. predicted) or independent validation set (SOCAT_b vs. predicted)?
13. Line 297: “and a r² of 0.7 are calculated”,
    
    We all know that R2 is the coefficient of determination, but please use the full name the first time it is mentioned in the manuscript.
14. Line 338: “This dataset consists of a pool of 404,206 gridded cells that are uniformly distributed between both hemispheres (SOCAT_b, Fig. S1) and presents a good correspondence with SOCAT_a (93 % of the residuals between SOCAT_b and SOCAT_a are < 5 µatm and with a global RMSE value of 6 µatm, Fig. S2).”
    
    
    
    I tried to comprehend this sentence, but I failed. In my understanding, SOCAT_a and SOCAT_b are independent, they are non-repetitive random samples of the original data set; thus, I can’t understand why they would "correspond." And what are the residuals between SOCAT_b and SOCAT_a mean?
15. Line 381: The title of subsection “Spatial and seasonal dynamics”,
    
    I think it is more appropriate to use "variations" than "dynamics" in the subtitle, as the discussion in this section pertains specifically to variations rather than dynamics.
16. Line 388-389: “Using the shelf break as the outer limit of the coastal domain (‘narrow coastal ocean’, 28 million km²)”,
    
    This marks the initial instance of employing the term "narrow coastal ocean" in the manuscript. Please clarify how you define the “shelf break”, 200m?
17. Line 387-393: The digits numbers are not consistent in the flux section. For example, “0.4 Pg C per year (with an uncertainty of ± 0.03 Pg C yr-1)”, or “-0.2 ± 0.01 Pg C yr -1”.
    
    I suggested using two digits number to keep consistent.
18. Line 440: “(0.1 Pg Cyr -1decade -1and 0.03 Pg C yr -1decade -1”,
    
    What are the uncertainties and p-values? (i.e., Δa in y = (a ± Δa)x + b)
19. Line 455: “increase of the global coastal CO2 sink is to be found in the high latitudes of the northern hemisphere,”,
    
    According to the product, yes. But there are still uncertainties for this conclusion, as the largest errors are observed in the high latitudes of the northern hemisphere (Figure 2c), notably within the Arctic Ocean.
20. Line 507: “latest release of the SOCAT”,
    
    Please include the version information, such as "the latest release of SOCAT (v2022)," to provide further context.

Figures and Tables:

1. Figure 1. The color scale is hard for me to recognize, especially the P9 and P10. The font size of the latitude and width of the color bar can be smaller (like in Figure 2).
2. Table 2.
   
   Row 4, column 1: Sea-ice coverage (ice, no unit)  Sea-ice coverage (dimensionless)
   
   Row 5, column 5: MBL is using the zonal average or meridional average xCO2air? MBL doesn’t provide 3-d gridded data; the resolution is 0.05 sin latitude.
   
   Also, because the SOM and FNN steps use different input variables, I suggest adding one more column or other ways to mention which variables are used in which step.
3. Figure 5. Please adjust the colorbars and latitude font size in (a) and (b) like Figure 2 or Figure 4(a) to provide more information.

Some grammatical mistakes:

Line 43: “the number of … have considerably”, should be “has” I think

Line 104: benchmark should be plural

Line 124: “in a first step”, should be “in the first step”

Line 143: “P9 represent”, should be “represents”

Line 367: “Largest RMSE” should be “The largest RMSE”

Line 376: “CO2 exchanges” should be “CO2 exchange”

Line 383: “both hemisphere” should be “hemispheres”, “a CO2 sinks” should be “CO2 sinks”

Line 426: typo, “through”

Line 441: “at global scale” should be “at a/the global scale”

Line 461: “our results … and emphasizes” should be “emphasize”

Line 510: “However, these investigation ..” should be “investigations”

Line 532: “to calculated” should be “to calculate”

Thank you for the opportunity to review "A novel sea surface partial pressure of carbon dioxide (pCO₂) data product for the global coastal ocean resolving trends over the 1982-2020 period"

Summary and overall impression 

The paper is well written. It highlights one of the potential sources of differences in existing global pCO2-products as they do not explicitly include the coastal ocean and the ones that do, cannot yet sufficiently capture the specific and changing conditions occurring along the coastal domain and only provide a climatology covering a relatively short period of time. The authors propose a resolution by addressing these shortcomings of the original global coastal pCO2-product by Laruelle et al. (2017) which was limited to the 1998-2015 period and expanding it to a much longer period (1982-2020) while updating the methodology to resolve long-term trends in global pCO2.

I strongly endorse the utilisation of two-step machine learning approaches for estimating sea surface pCO2 such as SOM-FFN where the authors first created biogeochemical clusters or provinces using SOM, and secondly, within each province identified in the step 1, established FFN-based nonlinear relationships between the observed sea surface pCO2 and independent environmental variables or drivers. The methodology setup is well explained.

However, I have made a few comments about some confusing terms, which I believe should be addressed quickly before publication. Overall, I enthusiastically recommend publication of the manuscript.

General Comments:

I understand that 1998-2015 (Laruelle et al., 2017) is relatively short to evaluate the long-term trends of the coastal air-sea CO2 fluxes, but how can this period not be suitable to evaluate inter-annual variability as you mentioned? Given that it is 19 years of observations, can you elaborate more on this point? For example, how do you define “long-term trend”?

Specific and Minor Comments:

Line 131: “… each 0.25° cell is allocated to one of the 10 provinces (or neurons).” The content of the parenthesis, "or neurons" does not line up with the full sentence. It looks as if biogeochemical provinces/clusters were also neurons. A province is a self-organised map (SOM), a lattice of neurons or a single-layer neural network. I understand you referenced Landschutzer et al. (2013, 2014) which provide more details, but I suggest a revision of this segment to avoid confusion.

Lines 297-298: “... since the algorithm minimizes the Root Mean Square Error (RMSE) between measurements and target observations.” There seems to be some confusion here. Isn’t the algorithm supposed to minimize the RMSE between “reconstructed values” and “target observations”? 

In Fig 3a-b, the similarity of the shape and spread of the four histograms of the residuals between decades raises questions on how you obtained the two sets of data SOCAT_a (80%) and SOCAT_b(20%). Since you randomly divided the original dataset to obtain them (Lines 179-182), how can you explain the “perfect“ representation of data across the four decades?

Given that “the spatial extension of the provinces varies from one month to the other because of the seasonal variations of the environmental drivers”, I suggest an update of the caption of Table 2 to be specific with the “biogeochemical provinces” on which spatial evaluation is performed.

Lines 338-339: “This dataset consists of a pool of 404,206 gridded cells that are uniformly distributed between both hemispheres”. From reading this, it now seems clear that you randomly divided the gridded cells of the original dataset (pCO2 observations). If this is the case, provide a better explanation in Sect. 2.1 because this would clarify my earlier comments on Fig. 3a-b.

Line 333: “can likely also explain”. The term "can explain" already implies a level of likelihood or possibility, so adding "likely" before it is unnecessary and redundant.

Check the units of ∆𝑝𝐶𝑂2 and pCO2 throughout the manuscript. You put “atm“ instead of “µatm“. See Lines 226-227, for example.

Line 140: “South Hemisphere” should be read “Southern Hemisphere”.

Line 147: “a target variable” should be read “the target variable” given that it is known.

Line 157: instead of “calculate”, I suggest you use “estimate“ as it sounds more appropriate.

Line 288: “see section 3.3.3” should be written “Sect. 3.3.3“ for consistency  

Line 396: “southern Hemisphere” should be written “Southern Hemisphere“..

Line 406 and Fig. 6’s caption: “RMS” is used instead of “RMSE“. I suggest you check these also throughout the manuscript.

Line 407: “rms values” should be written “RMSE values”.

Line 487: “and can be display large variations the regional scale …” This sentence needs revision.

Line 495: “depend” instead of “depending”.

Line 496: “use“ instead of “used“.