Referee comments in italics and our answers in normal text.

Review of manuscript “Response of a semi-enclosed sea to perturbed freshwater and open ocean salinity forcing” by Arneborg et al. 2025

This study uses high-resolution model sensitivity experiments to examine how the Baltic Sea’s steady-state salinity responds to variations in freshwater forcing and salinity at the boundary of North Sea. From these experiments, the authors constructed a second-order polynomial that relates the basin-mean steady-state salinity to changes in freshwater forcing and boundary salinity. Results show that the Baltic Sea’s response to freshwater forcing is large and non-linear, whereas its response to boundary salinity is more linear but less significant. The authors also analyze the impact of freshwater forcing and boundary salinity changes on the freshwater volume fluxes in and out of Baltic Sea driven by circulation changes.

Overall, the manuscript presents some important results, but it needs some revising and reorganizing before it can be considered for publication. The detailed comments are provided below:

Thanks for a detailed and constructive review. We have answered the comments below, and described how we will improve the manuscript according to the comments where relevant.

1. The study examines the sensitivity of Baltic Sea salinity to net freshwater input into both the Baltic and the North Sea, as well as to variations in salinity at the North Sea boundary. However, it is not clear which specific boundary of the North Sea is used for prescribing or evaluating the boundary salinity. Could you clarify this, and indicate the location on Figure 1? Additionally, it is very likely that changes in the net freshwater forcing would influence the boundary salinity in the North Sea itself. If so, how do you separate the individual impacts of the freshwater forcing and boundary salinity within your analysis?

We mean the open boundary salinities and will make this clearer in the text. It will also be made clearer that the boundary salinity change is intended to represent changes in Nort-East Atlantic salinities rather than salinities at the boundary of the Baltic Sea.

The separation between boundary salinity and fresh water forcing is done by construction in the experiments. When we raise the runoff in the North Sea we freshen it a little bit. Whatever, presumably small, effect that has on our experiments counts as a runoff effect, not as an open boundary salinity effect. So they are naturally separated by the experiment

The influence of fresh-water forcing on salinities in the North Sea are seen in Fig. 5 for the RP+ and RP- cases. At the boundaries the influence is almost zero. This may partly be because the boundaries are specified so, and in reality there may be an influence caused by recirculation of outflowing water into the domain, which we do not capture with a one-way coupled model. The focus in this study is on the changes in the Baltic Sea, and we have placed the open boundary further away from the Baltic Sea than most previous studies. The inflows to the Baltic Sea do include influences of outflowing fresh water to the North Sea, so we believe that we do have a good separation between impacts of freshwater forcing and boundary salinities at the boundary of the model.

2. The figure captions are vaguely written. For example, in Fig.2, it is not clear during which period the observed salinity profiles are compared with the hindcast profiles? Are these averaged over a period?

The time period will be included in the captions. The solid line is the temporal mean and the dashed lines are the 5^th and 95^th percentiles as described in the caption.

3. Figure 2: I suggest plotting the observed salinity profiles in thin lines rather than dots. The multiple grey dots at each depth level

We tend to think that is nice to see the observational points as in the present plot.

4. Figure 3: Please report quantitative statistics for these comparisons. How do the mean and standard deviation of salinity differ between the observations and the hindcast experiments? It would be helpful to list metrics such as bias, root-mean-square error (RMSE), and correlation coefficients.

From the figure, it appears that the bias in the hindcast salinity increases with depth. To better illustrate this, you could include a vertical profile of correlation coefficients (with statistical significance indicated) to show how model–observation agreement varies with depth.

We could add these metrics, but we do not see the value of doing so for this paper. If doing an intercomparison study or optimizing a model, such metrics would make sense, but here we do not see how the metrics would help the reader to decide whether the model describes the necessary processes or not. We don’t know about any relation between, e.g., RMSE for salinity and the model sensitivity to boundary salinity changes. To help the reader, we will instead refer to the Baltic Sea Model Intercomparison project, adding a sentence like: “Generally, the model salinities compare as well with observations as those of the better models in the Baltic Sea Model Intercomparison Project (Gröger et al., 2022) and the model is therefore well suited for the sensitivity study which is the focus of this work.”

5. Figure 4 needs more explanation. Note that the salinity trends are different RP- and RP-SB- runs as compared to the CTL and all other runs. Can this be explained? When you say yearly salinities, do you mean the mean salinity values averaged over each year? The caption is not clear.

We will add more explanation to describe what the figure shows, including “when the freshwater forcing decreases (blue lines), the salinities increase”. We write “yearly mean salinities averaged over the whole Baltic Sea volume inside the sill transect (Fig. 1)” in the text and “Yearly mean salinities for the Baltic Sea averaged over the volume inside the sill transect” in the captions.

6. Figure 5: How do these salinity anomaly maps for different runs compare with the CTL run?

The hindcast run (CTL) would only show zeros. We have added “(CTL)” to make it clearer that CTL is the hincast run.

7. Figure 6 caption is too vague. Specify the units.

Caption will be improved.

8. Figures 8 and 9: Over what period have these volume and salt fluxes been integrated? Is there no inflow of salt into the Baltic sea, given all positive values of F in Fig. 9?

The period is 1990 – 2017 which will now be mentioned also in the caption. There are inflows of about 250000 kg/s (maximum value of F) on average for the CTL case. Have we written somewhere that there are no inflows?

9. Figure 11: In the caption, you need to mention that these are the differences in fluxes between the RP+ and RP- experiments.

We will add the following to the caption: “The fluxes are based on the differences between runs RP+ and RP- but normalized to represent an increase in Qf of 100 m3/s.”

10. I recommend moving the equations and the calculations estimating percentage changes in salinity due to variations in inflows, outflows, and related terms from the Summary section to the Results section. The final section should focus primarily on synthesizing and highlighting the main findings.

We prefer not to move these calculations and discussion. The main results of the study are the polynomial and the total exchange flow analysis results based on the 3D model calculations. The calculations in the discussion part of Section 4 are more speculative with a number of underlying assumptions, and are meant more as a suggested simplified interpretation of the Baltic Sea sensitivity to the investigated forcing factors than a firm result of the simulations.

11. The manuscript would be strengthened if the authors placed their results in better context with previous studies. In the Introduction, the authors state that their work differs from earlier studies because the model includes the North Sea domain. Could the authors elaborate on what difference this inclusion makes for the analysis and interpretation of salinity variability in the Baltic Sea? How do the results compare with those from previous studies that did not include the North Sea

We will extend the text comparing our results with earlier studies in Section 4. We will not focus too much on the importance of including the North Sea domain, but we will write in the introduction that this is important in order to study the influence of North Atlantic salinities on the Baltic Sea, which has been investigated to a very limited degree in the past.

Please find the correct response to referee #1 in the attached file.

Referee comments in italics and our answers in normal text.

Review of manuscript “Response of a semi-enclosed sea to perturbed freshwater and open ocean salinity forcing” by Arneborg et al. 2025

This study uses high-resolution model sensitivity experiments to examine how the Baltic Sea’s steady-state salinity responds to variations in freshwater forcing and salinity at the boundary of North Sea. From these experiments, the authors constructed a second-order polynomial that relates the basin-mean steady-state salinity to changes in freshwater forcing and boundary salinity. Results show that the Baltic Sea’s response to freshwater forcing is large and non-linear, whereas its response to boundary salinity is more linear but less significant. The authors also analyze the impact of freshwater forcing and boundary salinity changes on the freshwater volume fluxes in and out of Baltic Sea driven by circulation changes.

Overall, the manuscript presents some important results, but it needs some revising and reorganizing before it can be considered for publication. The detailed comments are provided below:

Thanks for a detailed and constructive review. We have answered the comments below, and described how we will improve the manuscript according to the comments where relevant.

1. The study examines the sensitivity of Baltic Sea salinity to net freshwater input into both the Baltic and the North Sea, as well as to variations in salinity at the North Sea boundary. However, it is not clear which specific boundary of the North Sea is used for prescribing or evaluating the boundary salinity. Could you clarify this, and indicate the location on Figure 1? Additionally, it is very likely that changes in the net freshwater forcing would influence the boundary salinity in the North Sea itself. If so, how do you separate the individual impacts of the freshwater forcing and boundary salinity within your analysis?

We mean the open boundary salinities and will make this clearer in the text. It will also be made clearer that the boundary salinity change is intended to represent changes in Nort-East Atlantic salinities rather than salinities at the boundary of the Baltic Sea.

The separation between boundary salinity and fresh water forcing is done by construction in the experiments. When we raise the runoff in the North Sea we freshen it a little bit. Whatever, presumably small, effect that has on our experiments counts as a runoff effect, not as an open boundary salinity effect. So they are naturally separated by the experiment

The influence of fresh-water forcing on salinities in the North Sea are seen in Fig. 5 for the RP+ and RP- cases. At the boundaries the influence is almost zero. This may partly be because the boundaries are specified so, and in reality there may be an influence caused by recirculation of outflowing water into the domain, which we do not capture with a one-way coupled model. The focus in this study is on the changes in the Baltic Sea, and we have placed the open boundary further away from the Baltic Sea than most previous studies. The inflows to the Baltic Sea do include influences of outflowing fresh water to the North Sea, so we believe that we do have a good separation between impacts of freshwater forcing and boundary salinities at the boundary of the model.

2. The figure captions are vaguely written. For example, in Fig.2, it is not clear during which period the observed salinity profiles are compared with the hindcast profiles? Are these averaged over a period?

The time period will be included in the captions. The solid line is the temporal mean and the dashed lines are the 5^th and 95^th percentiles as described in the caption.

3. Figure 2: I suggest plotting the observed salinity profiles in thin lines rather than dots. The multiple grey dots at each depth level

We tend to think that it is nice to see the observational points as in the present plot.

4. Figure 3: Please report quantitative statistics for these comparisons. How do the mean and standard deviation of salinity differ between the observations and the hindcast experiments? It would be helpful to list metrics such as bias, root-mean-square error (RMSE), and correlation coefficients.

From the figure, it appears that the bias in the hindcast salinity increases with depth. To better illustrate this, you could include a vertical profile of correlation coefficients (with statistical significance indicated) to show how model–observation agreement varies with depth.

We could add these metrics, but we do not see the value of doing so for this paper. If doing an intercomparison study or optimizing a model, such metrics would make sense, but here we do not see how the metrics would help the reader to decide whether the model describes the necessary processes or not. We don’t know about any relation between, e.g., RMSE for salinity and the model sensitivity to boundary salinity changes. To help the reader, we will instead refer to the Baltic Sea Model Intercomparison project, adding a sentence like: “Generally, the model salinities compare as well with observations as those of the better models in the Baltic Sea Model Intercomparison Project (Gröger et al., 2022) and the model is therefore well suited for the sensitivity study which is the focus of this work.”

5. Figure 4 needs more explanation. Note that the salinity trends are different RP- and RP-SB- runs as compared to the CTL and all other runs. Can this be explained? When you say yearly salinities, do you mean the mean salinity values averaged over each year? The caption is not clear.

We will add more explanation to describe what the figure shows, including “when the freshwater forcing decreases (blue lines), the salinities increase”. We write “yearly mean salinities averaged over the whole Baltic Sea volume inside the sill transect (Fig. 1)” in the text and “Yearly mean salinities for the Baltic Sea averaged over the volume inside the sill transect” in the captions.

6. Figure 5: How do these salinity anomaly maps for different runs compare with the CTL run?

The hindcast run (CTL) would only show zeros. We have added “(CTL)” to make it clearer that CTL is the hincast run.

7. Figure 6 caption is too vague. Specify the units.

Caption will be improved.

8. Figures 8 and 9: Over what period have these volume and salt fluxes been integrated? Is there no inflow of salt into the Baltic sea, given all positive values of F in Fig. 9?

The period is 1990 – 2017 which will now be mentioned also in the caption. There are inflows of about 250000 kg/s (maximum value of F) on average for the CTL case. Have we written somewhere that there are no inflows?

9. Figure 11: In the caption, you need to mention that these are the differences in fluxes between the RP+ and RP- experiments.

We will add the following to the caption: “The fluxes are based on the differences between runs RP+ and RP- but normalized to represent an increase in Qf of 100 m3/s.”

10. I recommend moving the equations and the calculations estimating percentage changes in salinity due to variations in inflows, outflows, and related terms from the Summary section to the Results section. The final section should focus primarily on synthesizing and highlighting the main findings.

We prefer not to move these calculations and discussion. The main results of the study are the polynomial and the total exchange flow analysis results based on the 3D model calculations. The calculations in the discussion part of Section 4 are more speculative with a number of underlying assumptions, and are meant more as a suggested simplified interpretation of the Baltic Sea sensitivity to the investigated forcing factors than a firm result of the simulations.

11. The manuscript would be strengthened if the authors placed their results in better context with previous studies. In the Introduction, the authors state that their work differs from earlier studies because the model includes the North Sea domain. Could the authors elaborate on what difference this inclusion makes for the analysis and interpretation of salinity variability in the Baltic Sea? How do the results compare with those from previous studies that did not include the North Sea

We will extend the text comparing our results with earlier studies in Section 4. We will not focus too much on the importance of including the North Sea domain, but we will write in the introduction that this is important in order to study the influence of North Atlantic salinities on the Baltic Sea, which has been investigated to a very limited degree in the past.