I have reviewed the manuscript by Hernandez et al. entitled "Evaluating high-frequency radar data assimilation impact in coastal ocean operational modelling." As the title implies, this study is focused on high frequency (HF) radar impacts as a data source for ocean circulation models. HF radar networks have been proliferating in coastal areas worldwide for the primary purpose of mapping ocean surface currents out to ranges of 150 km with resolution of a few kilometers. The wide-area and real-time coverage derived from these networks makes them an important new tool for managing resources, responding to emergencies, and researching ecosystem responses in coastal areas. The goal of the present study and others before it is to develop and assess techniques for also using the HF radar-derived surface current mapping data as an assimilation source for 3-D circulation models. In this way, the impact of the HF radar observations can be expanded in both space and into the future through the use of models. The topic, therefore, should be of interest to a wide range of managers and scientists.

This manuscript is well written and the illustrations are clear. In addition, the authors provide a comprehensive and helpful review of past results involving the assimilation of HF radar-derived surface velocity. For these reasons, I recommend the manuscript for publication with only minor corrections.

The one substantive concern I have is to insure that the basis for the conclusion that HF radar assimilation improves the model outside the range of the HF radar observations is accurate and consistent. It is mentioned in the abstract, in the final sentence of the conclusions, and in lines 344-346 that the data assimilation improves the results even outside the data coverage area. This conclusion may be true and it is strictly supported by the data, but I don't believe that the independent test data in this particular study is adequate to make the conclusion. In particular, Figure 9 shows that the results in the model domain outside the HF radar coverage area are actually better than they are within the HF radar coverage area. That result is dubious in terms of justifying the conclusion. It is more likely that the currents in the test region outside the HF radar coverage area happen to be very steady leading to a particularly good model-data match in that location, a possibility that is referred to in the text. Hence, I believe that the conclusion of improved data assimilation results outside the HF radar coverage area should be tempered or removed in this particular case.

I find Figure 10 to be particularly interesting and useful in terms of guiding operational systems. It illustrates (and quantifies) the clear benefits of data assimilation for traditional data sets and it shows the added benefit of assimilating HF radar data in addition to those traditional data sets.

MINOR COMMENTS:

Line 38: This sentence is awkward. Please review and revise it.

Line 111: "It operates since" should be "It has operated since"

Line 308 and Figure 8: The text refers to a set of 1000 Lagrangian particles but the figure refers to only 100 particles. Please reconcile this.

Line 406: "this constrain" should be "this constraint"

Line 427: "contrarily to" should be "contrary to the case for"

The paper describes the impact of assimilation of HF radar data at the Ibiza Channel (Western Mediterranean Sea). The authors assimilate commonly used data sets (Sea surface temperature, sea level anomaly and Argo profiles) in combination with HF radar data. For the HF radar data two options are considered: either assimilating the total currents (derived from the radial currents) or directly assimilating radial currents. Both assimilation experiments are validated against drifter observations. The authors conclude that the assimilation using total currents fits the Lagrangian observations the best.

Comments:

1.  There are some general properties about the Kalman-based assimilation systems with transformed observations that should be mentioned to set the context of the study. If the hypotheses of the Kalman filter are verified (in particular the model is linear, error covariances are perfectly known), then the analysis would provide exactly the results under any invertible linear transformation of the observations (provided the observation operator and the obs. error covariance matrix are transformed accordingly).

The assimilation of any additional observation has the impact to reduce the error of the analysis on average. The consequence of these two properties is that the assimilation of transformed observations (possibly using a non-invertible linear transformation) should not be better than the error using the non-transformed observations. In practice this can be  shown by considering the observations associated to a zero singular value of the transformation and the observation with a non-zero singular value separately; the observations with a zero singular value are ignored by the transformation (these correspond to radial HF radar observations for which no matching second HF radar observation exist to derive total currents).

Under these, admittedly restrictive, assumptions, the assimilation of radial currents should work better than the assimilation of total currents. Intuitively, this makes sense because all the information of the total currents is already included in the radial currents and the radial currents have additional information not included in the total currents.

However, for real-world experiments there are some assumptions not verified which can lead to the opposite conclusion. In particular, we know that the model is non-linear, observation error covariances are not perfectly known and arbitrary observation operators cannot be specified by most current assimilation systems. Also it is not completely clear if the mapping from total currents to radial currents is a linear process (can you clarify this point?). I suggest that the authors include this additional information to clarify to the reader the motivation of this study.

2. The observational error covariance is a crucial parameter in the assimilation system which is often not very well known because of the contribution of the representativity error.

Maybe I missed it but I did not see the particular values that were used. It is a bit surprising that the same error covariance values were used for radial currents and total currents. Can you expand this discussion by including the different values of the observational error covariance that were tested in your sensitivity test (line 432)? See also below.

I recommend the publication of this manuscript  after revision.

Minor comments:

Line 130: This is a bit confusing. Maybe you can expand this part: "It sometimes happens that there are enough radial observations to compute the total observation for most of the periods but with none of those radial observations satisfying the temporal threshold by itself."

Equation 3: The notation is a bit odd as you have a vector on the left hand side and a scalar on the right hand side.

Line 202: Notice that the nudging is not applied to the velocity fields: quite surprising. Did you also test nudging the velocity field?

Equation 5: ss: should it be upper-case SS?

Table 2, Table 4: can you also include the RMS (without normalization)? Can you also include in this table a validation metric which is sensitive to the direction of the current, not only the speed of the current? (e.g. the RMS error of u and v components individually?)

Line 305: diffusion term: how large is the diffusion coefficient? And how was it determined?

Line 432: "The observation error is considered equal for total and radial currents in this study. ..." This is quite surprising as one would expect the radials a bit noisier and the total currents error variance should depend on the location (among others due to GDOP). Can the paragraph be expanded? Can you also include the value of the observational error covariance?