Dear authors,

Thank you for your responses to the two reviewers and for the revised manuscript. One of the reviewers had asked for major revisions. Both the reviewer and myself are happy with your answers and revisions. The additional discussion provided regarding the intra-hour variability and the typical diurnal variation at the HUN tower will be helpful for other sites. We agree that a generalization of the results to other sites is not straightforward and beyond the scope of this short paper.

I would like to congratulate you on this carefully crafted and concise study! It is a welcome contribution to the question, how measurement uncertainties should be stated and how observation/representation errors should be treated in atmospheric inverse models.

I have a number of small corrections, which I would like you to incorporate before the manuscript can be published. You can find these corrections in the attached annotated pdf of the manuscript.

In addition, I have the following comment:

There is actually an ISO standard for how to quantify uncertainties of incomplete temporal averages, see
https://www.iso.org/standard/32066.html

Unfortunately, the document is not freely available. The standard recommends a quantification of the additional uncertainty caused by incomplete coverage of the averaging interval according to the following formula:

# uncertainty due to incomplete coverage
sigma_miss = sqrt( (1-nn/nn.max) * 1/nn ) * sd(x)

x: observation vector
nn: length of x
nn.max: number of potential samples in time interval

Here, nn is the number of samples taken during the (e.g. hourly) averaging time interval and nn.max is the maximum number of samples that would be possible if there were no gaps. Sd(x) is the standard deviation of the measurements during the hourly interval. The equation thus uses the existing measurements during the averaging time interval to learn about the temporal variability of the signal in order to estimate the influence of an incomplete sampling.

This uncertainty is then added to the analytical uncertainty sigma_mean of a true hourly measurement, i.e.

sigma_X = sqrt(sigma_mean^2 + sigma_miss^2), where X is the hourly mean.

I would find it useful to check how well this formula describes the uncertainty of your data. Could you please send me a brief response on this point? We should then be able to quickly proceed with the publication.

Best regards
Dominik Brunner

Dear authors,

Thank you very much for the corrections and the careful answer. I agree that the ISO standard is only valid if there are not trends in the data. It only considers the number of samples taken during the hour, but not how evenly they are distributed over the 1hour interval, which according to your analysis is essential.

I am fully satisfied with your amendments and your response. I accept the manuscript for publication and would like to congratulate you once again for this concise and careful piece of work.

Kind regards
Dominik Brunner