The two reports are generally favourable, but both raise the question about the novelty of this paper with repsect to previous papers by the same research group. Therefore, it is necessary to carefully revise the paper and, in particular, to reinforce it along this direction.

Both reviewers expressed a positive evaluation of the present version, but one of them provides a detailed list of corrections.
I think that if the authors submit a carefully revised version of the manuscript, it could be finally acceptable.
In particular, I expect that the authors properly take into account the comments and answer the questions by Referee #3.
Moreover, I think that it is neecessary to improve the description of the novelty of this approach in the introductory section and to improve the discussion of the results for the test case and how much they can be generalized and applicable to real case studies.
I also suggest some technical modifications, listed in the non-public comments to the Authors, as they are of minor interest for the large audience.

I appreciated the Authors' effort in the last revision of the manuscript, which was even more effective to improve the paper quality than the first revision.
The paper is now ready for publication, provided minor techncial corrections are introduced, as listed below.
Line 55. Modify "some forms of model errors", as this expression is not informative.
Line 384. The saturated thickness is given by b=h-z_{bot}, where z_{bot} is the height of the impermeable aquifer bottom. Details about z_{bot} must be given: is it constant (horizontal aquifer bottom) or variable? If variable, please, specify how.
Lines 393 & 394. The correction can be further improved. My (TeX) suggestion is: "with a geometric mean of $10^{-13}\,\mathrm{m/s}$, a variance of $Y = \log K$ equal to 1.5". The same holds for the caption of Figure 1.
Line 476. Substitute "frequency" with "period".
Line 495. I think it is preferable the expression "time-averaged AESP".
Line 541. Check the expression "as the frequency of observations in time decreases".
Line 622. Substitute "observations sampling frequency" with "sampling period".
Table 2. Erase parentheses around the measurement units.
Figure 1. Substitute the heading of the colour scale with "$Y = \log K$, for $K$ in m/s". The same correction in Figure 8.
Figure 2. Modify the heading of the colour scale in analogy to what has been described here above for Figure 1. Also, check the values and maps, because recharge q should be given in m/s, since the dimension of q are [L/T] (see line 391).
Figure 3. The change to the labels are not sufficient to make them clearly visible and readable. Please, improve the label formats.
Figure 4. Erase "-water" from the y-axis title of the upper plot. Use "log K (K in m/s)" for the y-axis titles of the lower plot.
Figure 5. Substitute x-axis title with "Observation sampling period (days)".
Figure 7. Substitute the x-axes titles with "Time (months)".