| 26 Jun 2026
Probabilistic Modelling and Prediction of Sea Level Dynamics in the Southern Baltic Sea
Abstract. This paper presents a probabilistic approach to the analysis of non-stationary sea level measurement series in the southern Baltic Sea based on tide gauge data for Swinoujscie, Kolobrzeg, Ustka, Wladyslawowo and Gdansk stations. Harmonic analysis (HA), Continuous Wavelet Transform (CWT), AR(1) autoregressive model and Monte Carlo uncertainty propagation were applied to identify trends, multiscale variability and the stochastic structure of the measurement data. The results indicate a spatially consistent sea level rise trend of 1.8–2.2 mm/yr, modulated by multiscale periodic variability and short-term stochasticity. The model used allows for a probabilistic forecast of sea level changes. In addition, the analysis of extremes using the Gumbel distribution indicates an increase in the probability of extreme sea levels along the southern Baltic coast. The proposed methodology extends conventional sea level analysis by integrating probabilistic interpretation, classical uncertainty estimation, and multiscale signal analysis, thereby providing a useful tool for coastal hazard and flood risk assessment and climate change adaptation in coastal regions.
Summary: The manuscript presents a statistical analysis of sea-level time series in the Southern Baltic Sea derived from tide-gauge observations and satellite altimetry. The analysis focuses on identifying trends, accentuation, and oscillations in the time series. The authors design a statistical model to extrapolate sea-.level time series far into the future. They also analyse trends and acceleration of the cyclic components
Recommendations: Although I think that the study can eventually be published , my opinion that this version requires a rather deep revision. I have several major concerns regarding the motivation, the writing of some sections and the utility of other sections, which I explain below.
Main points
1) Regarding the writing of the manuscript, its structure can be clearly improved. The text often includes very long paragraphs, without a clear structure, which will make it difficult for the reader to focus on and follow. This is very clear to me in the introduction, which contains two short paragraphs and one very long paragraph that addresses very different issues and lacks a clear structure.
This problem appears in other sections. I would recommend the authors to revise the text, having a reader in mind. Ideally, one paragraph should develop only one idea.
2) The title is not informative. A reader may well interpret the title as a study of a short-term storm.-surge predictions. The abstract does not include any information about the timescales that the study targets
2) The manuscript fails to explain what the research question is. The introduction just includes a sentence, hidden in the last third paragraph, that 'The research hypothesis was that climate
change affects not only the rise in mean sea level, but also the intensity and dynamics of periodic processes and the frequency of extreme events.' Yet, the study just assumes that all trends derived from the observational period are due to climate change. The study does not analyse model output, nor investigate the physical mechanisms as to why greenhouse gas forcing may also affect the amplitude of periodic variations and the frequency of extreme sea levels in the Baltic Sea.
The manuscript gives the impression that the authors have a method, or several methods, that can be applied to any time series, and just happen to apply it here to the series of Baltic Sea level. The reader is left wondering what the research gaps are and why this analysis has to be undertaken in the first place.
This point is related to my following point
3) The manuscript has not considered previous publication o acceleration of the Baltic Sea level. I include three here, but there may be more. Actually, I may have missed it, but the manuscript does not include any reference to previous studies on Baltic Sea level acceleration.
Also, other relevant papers on the Baltic Sea level are not cited. An example is Stramska (2013) Temporal variability of the Baltic Sea level based on satellite observations, Estuarine, Coastal and Shelf Science 133 (2013) 244- 250, which also includes a spectral analysis of Baltic satellite time series.
Spada, G., Olivieri, M., & Galassi, G. (2014). Anomalous secular sea-level acceleration in the Baltic Sea caused by isostatic adjustment. Annals of Geophysics, 57(4), S0432-S0432.
Hünicke, B., & Zorita, E. (2016). Statistical analysis of the acceleration of Baltic mean sea-level rise, 1900–2012. Frontiers in Marine Science, 3, 125.
Jevrejeva, S., Moore, J. C., Grinsted, A., Matthews, A. P., & Spada, G. (2014). Trends and acceleration in global and regional sea levels since 1807. Global and Planetary Change, 113, 11-22.
4) I am very critical of section 5.4 on the statistical sea level rise forecast. This section just extrapolates the identified trends and quasi-oscillations to produce a 'forecast' of sea-level rise. However, future sea-level rise will be affected by many physical factors that may or may not behave as in the past. For instance, the melting of glaciers and polar ice sheets. There is a huge uncertainty in this factor, and it is really quite a stretch to assume that the melting rate will remain unchanged as it has over the past decades. The same can be said about quasi-oscillations. The only oscillatory phenomena that can be used for sea-level prediction are astronomical factors, which can be reliably calculated. All other climate-related oscillations may or may not change in the future. The issue also remains of how large the variance described by these oscillations is at the relevant time scales, which, unless I missed it, is not addressed in the study. If the variance explained by one oscillation is small, its relevance for any prediction is also small.
My recommendation if to delete this section entirely, as it can be misleading. At the very least, it should be accompanied by a clear disclaimer stating that this prediction is merely an extrapolation of current trends into the future, assuming those trends remain unchanged, which is quite unlikely. I honestly do not see a lot of value in this section