The reviewers provided important suggestions to improve the originally submitted manuscript and the authors' replies show that the reviewers' concerns might find satisfactory answers after a major revision.
I recommend the authors to accurately consider all the reviewers' comments, including those from referee #1 about the role of prior distributions and additional independent data.

Following the reviewers' suggestions I think that the paper requires a minor revision to fix several minor flaws, whereas the basic methods and results are good.
I take the freedom of suggesting few further modifications.

- Page 13 "Bayesian parameter-estimation schemes are well posed even in the presence of non-informative or ambiguous data due to the prior information".
Please, provide further information or references to support this statement.

- Page 14 "conductivity is a constant material property".
Please, modify "constant", because, at a fast reading, I considered it as a synonymous of "uniform", i.e., a homogeneous medium.

- Page 16 "As this is a virtual experiment, one could also consider calculating the NRMSE based on the head error in all grid cells, but in a real-world application such data would not exist. In this work, we prefer considering only the head-values at observation points, as it also gives an idea of the usefulness of using available observations as a means to estimate the goodness of the result."
Since you are dealing with a synthetic case study, I think that the NRMSE for the whole head field could be useful to assess how the uncertainties related to sampling the h field might affect the global field estimation.

- Page 20. "With respect to unknown conductivity and unknown recharge, the drawback with head observations, as shown in Sect. 2, is that the observations are non-unique. Including more head observations will, due to the non-uniqueness, not alleviate this drawback. Even a perfectly observed groundwater system could be non-unique, since exactly same head field can be achieved with different combinations of conductivity and recharge. Therefore, the joint estimation is difficult and the goodness of the prior information becomes important."
This sentences should be rewritten, because they are not correct with respect to the classical definitions of inverse problem theory. In particular, the authors confuse and do not properly distinguish uniqueness of the inverse problem and identifiability, which is a property of the forward problem.

I think the authors made a good work to answer the reviewers’ comments. However, a few minor modifications are still necessary before the paper can be published.
See the details in the attached pdf file.

The Authors modified the paper in the right way and I think that the discussion of the results is now thorough and more precise.
As a general remark, I would not normalize the error on the potential with the value of the potential itself, because any potential field could be changed by a constant value, i.e., changing the reference level, without affecting its physical relevance. Moreover, in the test case, the potential varies from 10 m to 50 m and therefore the normalization introduces a bias, since errors in the outflow region are more heavily weighted than those in the inflow and in the high recharge regions. However, these problems are of limited importance for the specific test case, due to the values of the potential, which should not have a very negative impact on these statistics and on the conclusions that can be drawn from their analysis.

Checking the modifications, I found a small typesetting error, which I missed in the previous version of the paper. At page 15, lines 20 and 22, "former" and "latter" should be exchanged with each other. This is the only technical correction to be checked before the publication.