Interactive comment on “ Spatio-temporal structure of Baltic free sea level oscillations in barotropic and baroclinic conditions from hydrodynamic modelling ”

Free sea level oscillations in barotropic and baroclinic conditions were examined using numerical 12 experiments based on a 3D hydrodynamic model of the Baltic Sea. In a barotropic environment, the highest 13 amplitudes of free sea level oscillations are observed in the northern Gulf of Bothnia, eastern Gulf of Finland, 14 and south-western Baltic Sea. In these areas, the maximum variance appears within the frequency range 15 corresponding to periods of 13–44 hr. In a stratified environment, after the cessation of meteorological forcing, 16 water masses relax to the equilibrium state in the form of mesoscale oscillations at the same frequencies as well 17 as in the form of rapidly decaying low-frequency (seasonal) oscillations. The total amplitudes of free baroclinic 18 perturbations are significantly larger than those of barotropic perturbations, reaching 15–17 cm. Contrary to 19 barotropic, oscillations in baroclinic conditions are strongly pronounced in the deep-water areas of the Baltic Sea 20 Proper. Specific spatial patterns of amplitudes and phases of free barotropic and baroclinic sea level oscillations 21 identified them as progressive-standing waves representing barotropic or baroclinic modes of gravity waves and 22 topographic Rossby waves. 23 24

The hydrodynamic model INMOM is professional and up-to-date (although not much used as the input for international research publications). The idea is to spin up the system for a certain time interval under the impact of a strong atmospheric forcing, and then let the system run at its own, with the goal to detect the maximum number of self-oscillations over two years. To do so, the authors implement several simplifications that are not fully realistic but eventually help to detect various kinds of self-oscillations. In essence, the system of detected oscillations should be invariant with respect to the initial disturbance; however, this feature should be at least shortly discussed (and at best with some supporting evidence from other parts of the World). Also, in this context it would be important to explain why in both the barotropic and baroclinic implementations, the Baltic Sea was considered a fully enclosed basin, with no water exchange with the North Sea as stated on lines 175-177. It is also important to comment shortly on possible differences with runs that would resolve water exchange between the North and Baltic Sea. Also, it remains unclear whether river water input and ice conditions were also neglected in both the barotropic and baroclinic implementations (line 177).
On lines 182-183 it is said that "Setting the turbulent viscosity to zero for the vertical components and to the minimum values for the horizontal components allows the damping of the simulated sea level fluctuations to be reduced." Please comment whether you did so and, if yes, how the modelled spectra relate to the actual spectra of motions. Again, I guess, the results are qualitatively invariant with respect to the par-ticular set of settings, and stronger damping would simply render some self-oscillation patterns undetectable.
The text is written in good English, with a few minor items to adjust. I recommend the manuscript for publication with minor and fairly straightforward revisions along the recommendations above and below.
Minor aspects to adjust: Line 29: "may resonate" would be more exact.
Lines 30-31: The source "Kulikov and Medvedev, 2013" addresses generic spectrum of water level in the Baltic Sea and seems inappropriate in the context of this particular claim.
Lines 37-39: For the benefit of readers I recommend to include also a reference to (Leppäranta and Myrberg, 2009). The provided references are correct but they are not easily accessible today, and some of them are written in German or Russian.
Line 60 and elsewhere: I recommend using "Baltic proper" as this is not a proper name.
Lines 87-88: it is recommended to say already here that the model uses sigmacoordinates in vertical. Line 104: better say "with a spatial resolution of 2 nautical miles" or similar, and indicate the resolution also in kilometers (cf. line 115).
Lines 133-134: remove repeating information "and includes the station coordinates, sea level measurement frequency, number of sea level measurements used in this study, and percentage of missing data" that is found in the table caption.

C3
Line 138, Table 1: (i) remove the column "Period" and mention this interval in the caption; (ii) use "measurement interval/frequency" or similar instead of "span".
Line 144: define SSH for the reader.
Line 145: the additional criteria of accuracy $P_{m}$ is not defined but still used below (e.g., on line 166). Lines 146-157: please punctuate the text in formulas as part of the sentences.
Lines 152-154: I don't think it makes sense to show the basic formulas (3)-(5) in a research paper of this type.
Line 166: please check the format the expression "Pm < 0.674σtg".
Line 199: the expression "k=0,1,2. . ." should be removed as the role of k becomes evident from the expression for f(t); also, the definition of angular frequency would be better placed in line with the rest or the text. Line 378: include the classic expression for the long wave speed into the text also here. There is no need for a displayed equation.
Line 423, the expression "the maximum dispersion of free oscillations occurs" seems to contain too much cryptic jargon. Consider saying: "the most intense free oscillations