This paper presents a new version of the Dual Ensemble Kalman Filter, namely the Dual-EnKF_OSA, and compares it against the more traditional Joint-EnKF and the Dual-EnKF.
The material is novel and the manuscript is within the scope of HESS.
Apart from some editorial remarks that I have reported below, I have some concerns about how the initialization of the ensemble members is implemented and how it is described in the manuscript (see detailed comments below).
Based on these considerations and on my comments below, I suggest accepting the manuscript after minor revisions.
Lines 51-55: I suggest relaxing this sentence and limiting the ability to handle model structure errors to the cases presented in the cited reference (Hendricks Franssen and Kinzelbach, 1998). In fact the EnKF has been proven to be ineffective when other model structure errors such as, e.g., uncertain variogram model parameters, need to be taken into account (see, e.g., Jafarpour and Tarrahi, 2011: http://dx.doi.org/10.1029/2010WR009090 - "Assessing the performance of the ensemble Kalman filter for subsurface flow data integration under variogram uncertainty").
Lines 124-125: is it necessary to assume that parameters and state variables are independent? This doesn't seem to be realistic to me. You also state that there must be consistency between model parameters and initial hydraulic head fields (lines 439-442).
Figure 1: I suggest adding the x and y axes labels with the corresponding units.
Table 2 (caption): please correct "variorum" in "variogram".
Lines 430-442: the procedure through which you initialize your ensemble members and the motivations for doing so are not clear to me.
In more details:
lines 430-431: what is the "mean hydraulic head of the reference run solution"? Spatial mean? Temporal mean?
line 432: "randomly select" from which set?
Regardless of the fact that the same procedure has already been used by Gharamti et al. (2014), I suggest that all this initialization methodology should be explained more clearly in the manuscript.
Equations 38-39: defined in this way, and consistently with the definition of vector x in equation (1), the two metrics AAE and AESP should refer to system states only. Subsequently, you employ AAE with reference to log-conductivies (e.g., in Figure 4, 5). Please consider revising this inconsistency.
Line 476 and 478, caption of Table 3: I don't understand the reason for using the word "mean" before AESP. Shouldn't the AESP be an averaged quantity? Please consider dropping the word "mean" in "mean AESP". Otherwise state more clearly what you intend with the word "mean" in this context.
Table 3: the results presented in Table 3 in my opinion are not adequately commented: the AESP indices related to log-conductivity do not increase with ensemble size as stated at lines 477. On the same line, it is not clear why the authors say "as expected".
Lines 504-506: Does this mean that updating the model variables is more expensive than running the forward model? Commonly, the updating step consists of a few algebraic equations that can be solved in a very short time, while the forward model run usually requires more time. Could you provide further details for this behavior?
Section 5.4 (and also in many other further instances): you probably mean that the standard deviation of the measurement error is, e.g., 0.10 m, not the measurement error itself.