This paper assesses the capabilities of the ensemble Kalman filter (EnKF) to inversely estimate spatially variable hydraulic conductivity and recharge fields by assimilating hydraulic head data into a groundwater flow model. The main take-home message of this study is that good prior knowledge of the spatial structure of the variable of interest is fundamental to obtain accurate predictions. Overall, the paper is interesting for a wide audience, scientifically sound, well written and within the scopes of the journal. I recommend publication after minor revisions, mostly related to the lack of some relevant references in the Introduction and Discussion. See specific comments below.
Page 5569, line 9: another example of successful EnKF application to fully 3D problem can be found in Camporese et al. (WRR 2011), who assimilated electrical conductivity from ERT imaging.
Page 5569, line 23, to page 5570, line 3: again, other studies where EnKF was used starting from initially biased prior geostatistical parameters are reported in Camporese et al. (WRR 2011, WRR 2015). The former, in particular, concluded that EnKF is able to correct the mean and, to some extent, the variance, but not the correlation length.
Page 5574, equation (6): please provide appropriate citations for this statement.
Page 5576, lines 21-26: for a detailed discussion of the linearization operated by the ensemble Kalman filter applied to groundwater models, see Crestani et al., 2013, already cited in the paper.
Page 5576, line 27 to page 5577, line 8: this paragraph sounds like an anticipation of the results. You could either give appropriate references to justify why you expect such results (e.g., Camporese et al, WRR 2011, Bailey and Baù, HESS, 2012), and/or, even better, move this discussion to the results section and comment about similarities and differences with the abovementioned references. Bailey and Baù (HESS, 2012), for instance, showed that it is possible to correct mean and variance of the geostatistical model by iteratively applying an ensemble smoothing scheme, whereas no evidence is available yet on whether this is also possible for the correlation length.
Page 5578, line 16: please define sigma_h more precisely; is it the standard deviation of the observed heads?
Page 5579, lines 7-11: this is irrelevant, unless you decide to show and discuss the results of these simulations. If these simulations were successful, why don’t you show them? Otherwise, the sentence can be removed.
Page 5583, lines 12-27: I am not sure this could actually help to improve the results, but it may be worth mentioning the existence and possible usefulness of dual state/parameter update techniques such as those reported, for instance, by El Gharamti et al. (AWR, 2013). The idea behind such assimilation techniques is to update the parameter first and then, after re-running the last time-step with the updated parameters, the state (in your case, this could be replaced by the recharge), instead of putting all the states and parameters together in the same augmented vector. This strategy has been reported to improve the stability and physical consistency of the updated variables.
Minor English edits are required throughout (e.g., change all occurrences of “standpoint of view” simply to “standpoint” or “point of view”; several typos such as “then” instead of “than”, etc).
Page 5570, lines 6-10: choose either “Section” or “Sect.” and be consistent throughout.
Page 5573: I would rename Section 3.1 as “Ensemble Kalman filter”.
Page 5573, line 18: symbol h has already been used to denote hydraulic head. Please change to avoid confusion.
Page 5575, line 1: please double-check expression for P’ x_t y_t; what is Tyt_x_t?
Equations 11, 12, and 13: not a big difference here with 2000 ensemble members, but in theory the unbiased estimator of covariance matrices is obtained dividing by n-1.
Page 5579, line 16: please make it clear (here and in the caption) that top row in Figure 3 represents final estimated fields of recharge after all the assimilation steps, obtained as the ensemble mean. As it is described now, it is not very clear what the Figure actually represents.