This study presents a novel method to estimate the carbon uptake period (CUP) from discrete CO2 observation time series. The process of determining CUP from discrete time series includes two critical steps: curve fitting and CUP onset and end determination. Curve-fitting methods are needed to interpolate observation at gaps and to filter out the noise and undesirable modes of variability. When analyzing CO2 mole fraction from background observation sites, this means removing the effects of local fluxes or synoptic-scale transport variations. Previous studies have shown that the conclusions from the analysis of CO2 time series are sensitive to the choice of the curve-fitting method. CUP estimates are also sensitive to the method used. Previous studies have proposed several methods that use the zero-crossing points or crest and trough of the detrended, zero-centered seasonal cycle.  The study presents a new CUP estimation method and provides a detailed uncertainty assessment of the curve-fitting methods and compares them with other methods reported in the literature. The CUP method and the detailed uncertainty analysis of the different curve-fitting methods presented in this study are very relevant. Overall, the paper is well-written and the figures are clear. I recommend the publication of the paper after the following issues have been addressed.

 

Specific comments:

It is unclear which methods described in this paper are novel. The FDT method is new and innovative, however, I have reservations about the newness of the rest of the methods. In the abstract, the authors write “…a novel curve fitting method….”. The essence of both CCG and the loess method presented here is the same, Equation 1. Is the novel part of the loess method using local regression to smoothen the residuals instead of a low pass FFT filter used in CCG? Or is it that the author’s method uses a 2-degree polynomial and 4 harmonic functions while the CCG method uses a 3-degree polynomial and 4 harmonic function? Moreover, the study note that there is no difference in the performance of the loess and the CCG methods (line 254). Could the authors explain what is then the advantage of the proposed loess method? In the rest of the manuscript, the authors only claim the uncertainty generation and FDT methods are new (Line 64, 264 & 323). The ensemble-based method uses bootstrapping to evaluate the uncertainties of a metric. This is again not so new in my opinion. The main novel method presented in this study is the FDT method. I suggest that the authors (1) make clear which methods are novel. (2) restructure the method section so it does not over-emphasize the newness of the loess method. (3) if the ensemble-generation method is the same for the CCG and loess methods, describe the ensemble-generation in a separate subsection. 

 

The authors have made a good attempt to describe the FDT method. However, I found it difficult to understand how CUP is calculated using the X% threshold. This statement is confusing: “The value of X is chosen to minimize the threshold value (as the rate of uptake towards the beginning and end of the CUP approaches zero) while keeping the uncertainty in timing across the ensemble members small". Does the authors mean the uncertainties are calculated as a function of threshold within the range of 0 to 20 percent, and the onset and termination times are the threshold points where CUP uncertainty is smallest? This becomes clearer in the results section but it will be good to move some of the explanation from the results section to the method section. Perhaps, a figure or an additional panel in figure 4 illustrating this would make the method easier to understand. I also have some concerns about the tested threshold values. Why only 4 discrete values of the threshold were tested? One can easily do this analysis over a continuum. Where does the choice of 0 to 20 percent come from? Why the range does not include positive threshold values, for example, something like -20 to 20 percent?

 

Minor comment:

The study focuses on the importance of uncertainties in CUP estimates of the Northern Hemisphere CO2 emissions when estimated using discrete measurements from select background sites. There are intra-annual variations and long-term trends in atmospheric transport which would affect the relationship between the seasonal cycle of the CO2 observations vs the actual emissions (see Krol et al., 2018, Fu et al., 2015). The transport errors will not be an issue when the FDT is applied to a discrete fluxes time series. I suggest the authors add a discussion about the transport-variation-related errors when analyzing fluxes using remote background observation sites to the discussion section.

 

 

 

Technical corrections:

“Curve-fitting” is irregularly hyphenated in the text. It needs to be hyphenated when used as an adjective, for example in Line 6, 16, 19, and so on.

Line 256: “using two different curve-fitting methods ” => “using the two different curve-fitting methods” is better.

 

References:

Krol, M., de Bruine, M., Killaars, L., Ouwersloot, H., Pozzer, A., Yin, Y., Chevallier, F., Bousquet, P., Patra, P., Belikov, D., Maksyutov, S., Dhomse, S., Feng, W., and Chipperfield, M. P.: Age of air as a diagnostic for transport timescales in global models, Geosci. Model Dev., 11, 3109–3130, https://doi.org/10.5194/gmd-11-3109-2018, 2018.

Fu, Q., Lin, P., Solomon, S., and Hartmann, D. L.: Observational evidence of strengthening of the Brewer-Dobson circulation since 1980, J. Geophys. Res.-Atmos., 120, 10214–10228, 2015

 

This study presents a curve-fitting method and an ensemble-based approach for quantifying the carbon uptake period (CUP; onset, termination and duration) from atmospheric CO₂ measurements. The authors have applied the technique to a handful of sites in the Northern hemisphere and shown that the uncertainty associated with the onset and termination of CUP is less with their proposed approach relative to more traditional techniques prevalent within the community. While the illustrations are high-quality, the scientific relevance and the overall flow of the manuscript needs to be improved. Right now, the manuscript reads like a collection of results based on investigations that were conducted and a figure and text to support the investigation. It does not dig deep into the implication of some of the findings (for e.g., Figure 13 is fascinating from a carbon cycle perspective but not explained in any great detail). In addition, the authors have applied their approach to only one seasonal cycle metric and it is not clear if the proposed alternative can be applied to other metrics. There are also inherent assumptions related to the first derivative method that require additional investigations. Along with my comments below, I have suggested a few basic analyses and additional sensitivity test that will improve this study and make it scientifically robust and appealing to the larger carbon cycle science community. I sincerely hope that the authors consider these suggestions. for improving the manuscript. 

Comments:

1. Line 1 in the Abstract should read – ‘High-quality, long time series measurements of …’
2. Lines 9 – 10: It is a bit misleading to claim that that the approach has been applied to analyze different seasonal cycle metrics as well as claims about the novelty of the approach. The authors have implemented this approach for quantifying one seasonal cycle metric, i.e., the carbon uptake period and associated parameters. What other metrics can be robustly calculated using this approach? It would be extremely relevant to include this in the discussion section. Right now, the Discussion section reads more like a collection of results than a true Discussion that provides scientific implications (see also comment #7) and relevance of this method for the carbon cycle community. In addition, the technique proposed by the authors are not new per se, but its application for quantifying the seasonal cycle metric is novel – the authors need to clearly distinguish this throughout the manuscript.
3. Lines 21 – 22 – the statement is applicable to not just measurements made at Mauna Loa, but almost all atmospheric CO₂ measurements, be it in situ or remotely-sensed. Kindly rephrase to either make it more generic or more specific to Mauna Loa.
4. Line 50 – The authors should be more specific about which metrics they are talking about and specify the ones that are highly sensitive to data gaps or noise in the time-series.
5. Line 69 – 70 - What about checking an alternate approach? In the Introduction, the authors made the argument that multiple approaches should be tested. Why haven't they implemented that rationale here?
6. Lines 146-152, Page 7 – A big assumption in implementing the FDT approach is that “the first derivative of the CO2 dry air mole fraction is a proxy for the flux”, thereby completely ignoring the role of atmospheric transport. This is especially relevant as the majority of sites the authors have selected are the marine boundary layer sites, which are designed to sample the background flux and not necessarily changes in local flux. Can the authors demonstrate the robustness of their assumption by doing pseudo-data / simulated data experiments? For example, the authors can use known fluxes from CarbonTracker or CarbonTracker-Europe, generate pseudo-data at the sites used in the study, and demonstrate that the first derivative is indeed an approximation of the flux signal.
7. Section 5 – Discussion – other than a few segments, this section seems to be a continuation of the previous section. The authors need to rethink the way they present this section, move the results to the previous section and/or focus more on the scientific implications of their findings. It would also be useful to dig deep into a couple of the results and talk about the scientific findings rather than present one result after the another.
8. Figure 13 - What are the conclusions from this figure? Do we show any important trends? Any relevance to carbon cycle science? Similar to the previous comment, this seems another missed opportunity to delve deeper into the results and provide scientific implications and context for the results. I would strongly recommend the authors to select a few key results and figures, and then delve deeper into them rather than presenting all results and figures generated during their investigation.