Reviewer 1

This technical note addresses an important methodological issue in high-precision DIC measurements by coulometry, focusing on how to handle the background signal. The authors analyze a long-term dataset of 263 internal-standard DIC measurements across 89 analysis sessions (~7 years) and compare three blank-correction approaches: a traditional constant blank, a per-measurement blank, and a fitted blank. They show that using per-measurement or fitted blanks improves precision, and the fitted-blank approach also reduces extreme outliers.

Overall, the manuscript is clear and well written. The problem is motivated by the need for climate-quality DIC uncertainty. The methods are described in sufficient detail, and the statistical analysis is appropriate. This is a useful and practical contribution to the oceanographic inorganic carbon community, especially since small improvements in precision matter when looking at decadal trends. Making the tool open also helps with reproducibility. I have a few comments and minor suggestions below. I recommend publication with minor revisions.

We thank the reviewer for their positive assessment and constructive suggestions.

Comments and suggestions:

1. Although the Introduction provides a detailed explanation of the principle of DIC measurements by coulometry, it would be helpful if the Methods section also described the actual operational procedure and relevant parameters. This would provide a practical reference for others.

We understand the reviewer’s point but we prefer not to include this. The operational procedure is already very well explained by the references cited (especially the Dickson et al., 2007 SOP). We think it is better to keep the established SOP as the practical reference that people look at for the full operational procedure; writing our own version of it may lead to conflicts and confusion.

1. The method for identifying the blank period seems reasonable. Figure 1 notes that not all titrations ran for 12 minutes, with some stopping at 8 or 10 minutes. It would be helpful if the authors could clarify how the end of a titration is determined in practice.

We added to the first paragraph of Sect. 2.1:

“Depending on the instrument, the integration time may be fixed, or it may vary per sample, for example finishing after the counts per minute stay below some threshold for a certain duration.”

1. Figure 2 shows Equation 2 fitted to per-measurement blanks for four different analysis sessions. I am curious about how this approach performs when the analysis period is much longer (for example, over a month at sea), where blank values might show periodic variations. Would Equation 2 still provide a good fit in such cases, or would a segmented approach be required? It would be better to mention this in the manuscript.

An analysis session is linked to the chemicals in the coulometer cell so would rarely exceed ~24 hours. In a month at sea, presumably the coulometer cell would be refreshed on a daily basis, so indeed Eq. (2) would be applied separately to each day.

From this comment, we realised we had not clearly defined what we meant by an “analysis session”. So we added to the start of Sect. 2.2:

“The fitting procedure should be carried out separately for each analysis session. An analysis session consists of a set of measurements all conducted with the same coulometer cell and chemicals, so a separate analysis session begins each time the chemicals in the coulometer cell are replaced.”

1. Figure 3 mentions “normalized DIC” and ΔDIC, but ΔDIC is not explicitly defined. From the methods, it seems that ΔDIC represents the deviation of each measurement from the mean DIC of its session. I suggest defining this clearly in either the figure caption or the methods section.

We added “(∆DIC)” at the appropriate point in the caption.

1. The manuscript includes a lot of variables and parameters across equations. To make it easier to follow, a table or appendix summarizing all symbols and their definitions could be helpful.

Both reviewers made this suggestion so we added an Appendix with a summary table (Table A1). We point out the existence of this table in a note next to the first appearance of a symbol (b_m, second paragraph of Sect. 2.1).

Minor points:

Line 75: “mean average increments” could be simplified to “mean increments.”

Figure 3 caption: change “with measurements are sorted” to “with measurements sorted.”

Both fixed.

Reviewer 2

The manuscript describes a methodological improvement of coulometer-based DIC measurements by using a different method do determine the system’s blank. Including the traditional method of determining the blank at the beginning of each measurement sequence the authors present two alternative methods that take into account a potential (and likely) drift of the system’s blank which improves the uncertainty for each measured DIC sample.

The manuscript is well written and the motivation is clearly laid out. The statistical section is very detailed and readers that are less skilled in these techniques need to read this carefully.

We thank the reviewer for their positive assessment and constructive suggestions.

There are many variables and I suggest to add a table summarizing all these variable names. This would make the reading easier.

Both reviewers made this suggestion so we added an Appendix with a summary table (Table A1). We point out the existence of this table in a note next to the first appearance of a symbol (b_m, second paragraph of Sect. 2.1).

I have only some minor comments (see below) and suggest publication after considering the comments:

Line 44ff: Does it make sense to mention that OH- ions are formed at a platinum electrode to neutralize the formed acid?

Yes, this is better than what we had written because we had stated that the electric current “reverses the reaction” of hydroxyethylcarbamic acid formation, which is not strictly true. The sentence now reads (changed part underlined):

“An electrical current is then applied across the cell, which neutralises the acid by forming hydroxide ions at the platinum cathode.”

Line 61: the reference to the Python package should be already here.

Reference added.

Line 72: Fig. 1 shows a plot of coulometer increments vs. titration time, so it’s the other way around?

Fixed.

Line 88: It would have helped me to write “bf(ts) = ...” to make it clear that this function depends on time. It is clear when looking at it but it would make the reading easier.

Updated as suggested.

Line 95: Either change to "we selected" or "the selected outliers needs...".

We’re not sure which part the reviewer is suggesting we change here. We re-read the text around this line carefully and could not spot any problems.

Line 107: Is it C(t_s) ? It is actually a time depending (or better measurement dependent) function.

The b_f part is time-varying, but C is mainly a function of C_raw, so it doesn’t seem appropriate to write C(t_s) in this case. But we have changed b_f to b_f(t_s) in Eq. (5) to make it clearer that that part does vary with t_s.

Line 109: “c_r” is not introduced, yet.

This was the counts for each minute within a measurement. It appeared only in Eq. (6). We decided on reflection that explicitly including this equation was overcomplicating things, as the statement “C_raw [is] the total counts integrated across the titration” is already clear. So we have removed Eq. (6) and therefore no longer need to define c_r.

Line 120: the part “carbon in Dutch” is not necessary. But if you want to keep it it should be mentioned above in line 61

We removed this part.

Fig 1: Since violine plots are not that common, I’m wondering if it makes sense to explain with one or two sentences what the form actually illustrates.

We added to the caption: “The widths of the shaded areas show the proportion of data points at each number of increments.”

Fig 2: Just a nice to have: it would be interesting to see the constant blank that was determined at the beginning of the day to visualize the difference. I guess it would be the first blank measurement.

We don’t use the 10-minute approach to determine a constant blank, so we don’t have the data to be able to add this to the plots.

Fig 3a: a) Is it "frequency" or abundance?

It is number of measurements. We updated the y-axis label to this both here and on Fig. 4 to avoid confusion. Therefore we also released a new version of the code used for the analysis and figures and updated the Zenodo citation to match. A complete overview of the changes in the code can be found here: https://github.com/mvdh7/coulometer-blank/compare/preprint...revisions

There are more colors in the plot, than explained in the legend.

This is because the histogram bars are semi-transparent. We added a note to this effect in the caption. It is like this so that the shapes of all three histograms can be seen even when they overlap each other.