We thank both referees for the constructive comments on our manuscript. We would be happy to submit a revised manuscript, if the editor so invites, where the issues raised by the referees have been clarified and all the suggested minor corrections are taken into account.

Regarding comments from Anonymous Referee #1, here are our thoughts (comment in italics, followed by our reply).

"It is worth commenting on numerical uncertainty in climate process models, even for the same input data when solving the same equations with the same algorithms! Truncation and round-off errors contribute to numerical noise that could reach the same order as the solution (see e.g. S.J. Liao. On the reliability of computed chaotic solutions of non-linear differential equations. Tellus A, 61(4): 550–564, 2009). I wonder how much this contributes to the spread in process model projections."

In our understanding, this numerical uncertainty is not nearly as significant source of error in climate projections as the comment suggests. It is true that truncation and round-off errors accumulate when simulating chaotic systems, such as weather, and lead to very different solutions depending on numerical accuracy. However, climate models do not aim to simulate single weather events, but statistical properties of weather over decades. These properties are much more stable and predictable than the day-to-day variability.

Climate models do produce different results even under the same forcing. Partly this stems from structural differences between models, partly from natural variability in the climate system. This is why in our study, we have used a large ensemble of climate models (17 AOGCMs) to project the geostrophic wind in the future. We have also drawn from a wide body of research to characterize the probability distribution of sea level rise to account for methodological differences and uncertainties.

"Presumably, local changes in mean sea level in the Baltic have a knock-on effect on resonant seiching within the semi-enclosed basin. Is this likely to be important in the future?"

As the resonant periods of seiche oscillations depend on water depth, the change in mean sea level does indeed have some effect on seiching. We suspect that this is not very important considering seiches in larger basins, as the mean sea level change is relatively small compared to water depth, but modelling studies should be carried out to properly quantify this effect. The dependency between long-term and short-term sea level variations is an interesting question also regarding other phenomena besides seiches – e.g. wind waves. However, this is outside the scope of this paper, where we concentrate on mean sea level changes.

"Section 2.3. Is the mean sea level in the Baltic Sea affected by large-scale pressure variations associated with teleconnections, such as the North Atlantic Oscillation? Please could the authors comment upon this.”

Yes, mean sea level in the Baltic Sea is associated with the North Atlantic Oscillation (NAO). The correlation between NAO and annual mean sea levels on the Finnish coast have been studied in several papers listed below (Johansson et al. 2001, 2003, 2004). The coefficients of determination (R²) between detrended annual mean sea levels on the Finnish coast and the normalized winter NAO index have been found to vary between 0.37–0.46 depending on station (Johansson et al. 2003, 2004). High NAO is associated with a large longitudinal air pressure difference over the North Atlantic, which in turn is associated with westerly winds that tend to keep water level in the Baltic Sea basin high.

The sea level stations in the southern Baltic Sea show a weaker correlation with the NAO index (Johansson et al. 2003) which the authors relate to the mean sea level slope within the Baltic Sea. Westerly winds pile up water against the eastern coast of the Baltic Sea, reinforcing the correlation between mean sea level and NAO on the Finnish coast.

In this paper, we use the zonal geostrophic wind u_g as the metric to represent the variability in the large-scale atmospheric circulation. While it is related to the same physical mechanism as the NAO index, namely the large-scale circulation over the North Atlantic, the zonal geostrophic wind has even higher correlations with sea levels on the Finnish coast than the NAO index (R² = 0.84–0.89, Johansson et al. 2014). Thus, the teleconnection associated with NAO is accounted for in our study, we just use a different variable that captures the effect even more closely than the NAO index. We will add a mention of this in the finalized manuscript.

References:

• Johansson et al. 2001: Trends in sea level variability in the Baltic Sea. Boreal Environment Research 6: 159–179. http://www.borenv.net/BER/archive/pdfs/ber6/ber6-159s.pdf 
• Johansson et al. 2003: An Improved Estimate for the Long-Term Mean Sea Level on the Finnish Coast. Geophysica 39: 51–73. https://www.geophysica.fi/pdf/geophysica_2003_39_1-2_051_johansson.pdf 
• Johansson et al. 2004: Scenarios for sea level on the Finnish coast. Boreal Environment Research 9: 153–166. http://www.borenv.net/BER/archive/pdfs/ber9/ber9-153.pdf
• Johansson et al. 2014: Global sea level rise scenarios adapted to the Finnish coast. Journal of Marine Systems, 129: 35–46.

We thank both referees for the constructive comments on our manuscript. We would be happy to submit a revised manuscript, if the editor so invites, where the issues raised by the referees have been clarified and all the suggested minor corrections are taken into account.

Regarding comments from Anonymous Referee #2, here are our thoughts (comment in italics, followed by our reply).

"I suppose the models for wind climate changes and land uplift are also subject to different kinds of uncertainty. Please comment on the effect of such uncertainties on the final projections."

The uncertainties in the final mean sea level projections are clearly dominated by the uncertainty in global sea level rise projections. As seen from our Fig. 7, the effect of the wind component is small compared to sea level rise and land uplift. The land uplift, on the other hand, is of the same order of magnitude than sea level rise, but with much narrower uncertainty ranges.

The land uplift has been observed for several decades in the region and thus, the observation uncertainties are small and well known. The uncertainty from the GIA modelling part is less well known, but the observations are constraining the GIA model output. As the total land uplift model is a combination of the two parts (observations + GIA model), the uncertainties become small. Typically the computational uncertainty is an order of magnitude smaller than the provided land uplift values (see Fig 14 in Vestol et al, 2019).

"Why are the probability distributions for wind climate change and land uplift rates assumed to be Gaussian? Any evidence to support this assumption? Have you ever tried any other distributions? What are the effect of other distribution on the MSL probability distributions?"

The Gaussian distribution is the simplest choice, and the one to be used if there is no evidence to support some other type of distribution. The uncertainty in land uplift rates is characterized by the standard deviation given by the NKG2016LU model, which we use to fit the Gaussian distribution. Regarding the wind component, the uncertainty is characterized by the output of the 17-model ensemble used to project the zonal geostrophic wind (Table 2). For either process we do not have evidence that would point to a non-symmetrical distribution.

In any case, as we comment above, the effect of uncertainties in the wind component and land uplift is minor compared to the uncertainty in sea level rise projections. Therefore, there would be little value in trying to elaborate the analysis of uncertainty distributions of the wind component and land uplift.

"Figure 7. This is a very useful graph, which supports the finding that “spatial variations in the MSL projections result essentially depends on the local land uplift rates”. However, I cannot find enough clear description in the main text to interpret this graph."

Thank you for the comment, we will explain this graph more fully in the revised manuscript.

"The discussion. Indeed, before the discussion section, the manuscript is highly readable. However, the discussion is not concise and streamlined. Reader like me can easily get lost. I advised the authors to divide the discussion into several subsections regarding future projections, past trends and spatial variability and etc."

Thank you, we will clarify the discussion in the revised manuscript.