The authors investigated the potential role of Data Assimilation in improving the accuracy of barotropic processes induced variant scale/mode sea level anomaly in the Mediterranean Sea. The study is based on the state-of-the-art simulation kernel in SHYFEM. The authors comprehensively investigated the improvement of the astronomical tide, surge and seiches implemented by DA, and promoted the adaptability of SHYFEM with inclusion of EnKF. The manuscript is well written and organized with a sensible logic. However, given I still have these several following major concerns, I cannot recommend an acceptance at its present form.

• Although it is still a nowadays great challenge to DA to treat/improve the hindcast and forecast of sea level anomaly in the region where the SLA oscillation is significant, I’m still wondering why the authors conduct this simulation in a two-dimensional or barotropic configuration? Will the inclusion of, e.g. dynamic height associated with the baroclinic processes be really negligible in the region? If it is not, why the heat fluxes, evaporation and precipitation, as well as riverine discharges are excluded? The larger scale circulation, at least those in the synoptic scale, is another issue related to this concern. Could the authors include some discussion related to the unimportance of these processes? Or, the authors may want to state that they are treating those larger-scaled motions as reference levels already, although I don’t think that is a straightforward statement.
• I still have concerns about how did the simulation treat the open boundary condition, although the manuscript did clarify that the authors treated the boundary condition with great effort. If sea level is kind of prescribed at the western boundary, how could the circulation (including their impacts in SLA and currents) be connected with that to the further west of the open boundary, which I think is provided by, for example, the CMEMS reanalyses. I may also suggest the authors include a paragraph to elaborate the way the open boundary condition is implemented or explicitly show the algorithm of the open boundary condition.
• Why the satellite altimetry data is not used as observed data in this research? Are they at least usable for the astronomical tide correction and forecast? If gridded data is problematic, how about the along-track data? There are dataset of harmonic constants extracted from the along-track data by using this operation, and the authors mainly used much higher resolution records at the surrounding tidal gauge. I mean, there are more observations with much higher spatial coverage may help further improved the DA.
• In the perturbation runs, why the drag coefficient Cd in the quadratic formulation is not perturbed? Dissipation of energy with the scales smaller than tides through the bottom friction could also be an important process that determines the characteristics of tidal currents, and in this sense, although the authors stated that the current research is focusing on SLA variations, in the current configuration, accuracy in flows will also be an important aspect. Did the authors analyze whether the current design could also improve flows or not?
• In my opinion, it is still important to rely on DA to improve the parameterization in the simulation, since it is not that feasible for operational users to generate a large number of perturbation runs to have that short-term forecast improved.
• It is really hard to intensify the meshes in Figure 1. Could you zoom in to some critically locations to show the spatial variability of resolution?

Review for the manuscript titled as “Modelling the barotropic sea level in the Mediterranean using data assimilation” by Bajo et al.

The manuscript presents the predictive capability of a 2D barotropic model of the Mediterranean Sea sea level with and without the assimilation of the observations obtained from coastal tide gauges stations. The hydrodynamical model setup and ensemble Kalman filter based data assimilation system is described along with the perturbation schemes applied for ensemble generation. The results are presented for the total sea level as well as different contributions from the astronomical tides, surge and seiche for the hindcast/analysis and forecast periods for the December 2019 seiche occurrence following the November 2019 extreme event in the Adriatic Sea.

The manuscript requires a substantial revision before publication. Below are major comments and minor suggestions.

Major comments

To start with, for the readability of the manuscript, I suggest including a table of experiments to make it easier to follow, especially the results section. A flow chart for the production cycle would also help since it is difficult to understand where the hindcast/analysis ends and where the forecast starts. This may also help for future works since this system is proposed as a candidate for operational forecasting. Moreover, the terminology used can be improved. There are terms used interchangeably such as analysis, reanalysis, hindcast simulation with data assimilation. I suggest homogenising them for an easier read and paying attention throughout the text to use the terminology that is already established, such as using analysis ensemble mean instead of average analysis state.

Secondly, I understand that the manuscript targets seiche in December 2019 however, it would be nice to see the evolution of the error in the sea level over a longer period given that the current version of the model is quite cheap as stated by the authors. I expected at least to see some analysis and the skill of the model in the November 2019 high tide event in the northern Adriatic Sea which resulted in the flooding of the city of Venice.

On the other hand, SHYFEM is shown to be a skillful model in various previous studies. It is hard to understand why a simplified version is used in a development that is a candidate for an operational forecasting system. I think that in the cases where the errors and bias are large there is missing the steric steric part from the thermohaline contribution to sea level variability. This should be clarified and justified.

Finally, it is not easy to completely grasp the improvements brought by the data assimilation of observations from tide gauges since they are limited in space coverage. Satellite observations could be used at least for validation to see the impact, if not assimilated. The results should be supported by maps of, for example, mean dynamic topography, increments. I think there may be other resources for the coastal sea level data for assimilation such as Copernicus Marine, SeaDataNet or EMODNet to better cover the eastern basin.

Minor suggestions

Title:  Mediterranean -> Mediterranean Sea

L27  “easily predictable” -> please refer to the sources of uncertainty in the estimates of tides e.g. bathymetry

L92 Please be more precise about the mesh resolution and give a measure of change from the open ocean to the coastal seas. Danilov (2022) may help. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022MS003177

L101 as done with the atmospheric forcing product, please cite the Copernicus Marine multi-year product explicitly in the references, not only with DOI. It should be clarified why the authors used the multi-year product for the lateral open boundary conditions in the Atlantic Ocean while a NRT analysis/forecast product as in the atmospheric forcing is available in Copernicus Marine catalogs with tides for the experiment period. This is also one of the parameters that defines the type of experiment performed: an analysis, a reanalysis etc…

L102 please explain how you de-tide the sea level.

L124 missing citation in the parentheses. Please add it.

L128 Please add the mean sea level map and compare with the MDT products such as MDT-CMEMS_2020_MED  in Copernicus Marine Catalog

L145 please justify 2 cm of observational error, is it only the instrumental error considered? How do the increments with such a small observational error look like? A map of increments may help to see whether there is an overfitting.

L153 grid -> node

L153 “A_a^* is that of the analysis states not corrected”. What do you mean? The definition of analysis implies a corrected background. Do you mean background? 

L156 “levels” -> of what? 

L162 “average analysis state” -> analysis ensemble mean

L169 Please justify 400 km. For example, Sakov et al. 2012 chose 250 km in a north Atlantic - Arctic Ocean system using the same methodology.

L192 This is the definition of analysis ensemble mean. Please use it.

L 195 Not clear what the discussion here is.

L 201 Why brevity? Why not robustness?

L202-206 a production cycle flow chart may help.

L222 What are the parameters of DA? Inflation and localization? 

L223 Local analysis is only one way of localization. 

L234 Looks like too big error (9.3 cm) even for a free model and with a 2 cm of observation error reduces to only 3.6 cm. Is it because the barotropic model is missing the steric contribution? Please compare with altimeter products.

L347 “is not present in our observations”? Do you mean in the period of observations used? 

L352 There are other sources of error in DA besides model and representativeness error. Please correct.