Application of the Probability of Extreme Sea Levels at Selected Baltic Sea Tide Gauge Stations

Abstract

The aim of this study was to analyze the application of the probability of extreme water level predictions along the entire Baltic Sea coast. In the initial part of this work, the critical sea levels off the Baltic States were reviewed. These levels are related to the height of the breakwaters and were determined on the basis of probabilistic methods. Then, the heights of the theoretical water levels in the entire quantile range were determined. Calculations were performed using Gumbel and Pearson III type distributions. Visualizations of the theoretical maximum and minimum water levels, as well as calculations related to the sea surface and length of the coastline, were made using ArcGIS 10.2.1 software. A comparison of theoretical water levels from two periods showed that over the last 60 years, there has been a stable trend of an increase in both the theoretical and observed maximum water levels of 2.6 mm/year. At the same time, the return period for the Baltic tide gauge stations was reduced by an average of about 50%. It could thus be concluded that hydrological hazards in the Baltic Sea region appeared twice as often as they did in the first half of the 20th century. Later in this work, we determined what size of the sea surface and the coastline length corresponded to particular sea level ranges for different return periods. For the maximum theoretical water with a 200-year return period, as much as 19.1% of the Baltic Sea surface and 23.8% of its coastline length may be influenced by extremely high sea levels (≥200 cm). These are areas in the inner parts of the great Baltic gulfs. For them, critical water levels are lower than 200 cm, which indicates a potential risk of storm floods. Based on probability calculations, it could be concluded that Pärnu Bay, within which lies the Pärnu tide gauge station, is the most hydrologically dangerous basin in the Baltic Sea.

1. Introduction

Currently, there are about 220 tide gauges on the coasts of the Baltic Sea, and the network they form carefully monitors the processes of sea level fluctuations. Extreme sea levels that occur during storm surges and storm floods contribute to catastrophic changes in the coastal zone (e.g., abrasion, erosion processes, and destruction of infrastructure). The complex nature of the phenomenon of extreme sea levels makes the forecast of this process complicated. In addition to hydrometeorological and anthropogenic factors, local conditions have a large impact on changes in the sea level, particularly with respect to coastline configuration, morphology, and the bathymetry of the shallow-water coastal zone. Therefore, in order to analyze the hydrological risk a coastal area faces, the probabilistic forecasting of maximum and minimum sea levels is commonly used. Probabilistic analysis determines the so-called theoretical sea levels (theoretical water), which are the highest and lowest water levels that can occur every certain number of years, e.g., once every 10, 20, 100, or 200 years. These numbers of years are called the return period. It is extremely important to prepare the longest possible observation series of maximum and minimum annual sea levels for a long-term probabilistic forecast. Only then can the obtained results be considered credible and practical.

Methods of determining the probability of extreme hydrological events occurring are described in many research papers. Suursaar and Sooäär [1] applied the theoretical Gumbel distribution in analyses of wind speed and wave height for the Estonian coast. They found that the empirical return periods of both maximum wind speeds and wave heights can be satisfactorily matched with the theoretical distribution and therefore used to accurately predict extreme values. Gräwe and Burchard [2], using various statistical distributions, forecasted the height of a storm surge wave in the Western Baltic. They found that by the end of the century (2070–2100), the storm surge height in the Western Baltic will increase to 2.2–2.4 m for a 30-year return period, depending on greenhouse gas emission scenarios. According to the authors of [3], sea level probability distributions for Finnish tide gauge stations in the long run resemble a modified Gaussian distribution, although they are not symmetric. By comparing two 20-year periods of sea level measurements from the beginning and the end of the century on a theoretical distribution curve, it was found that the probability of very high sea levels occurring has increased. Meier [4] found that the water level in the Baltic, associated with a 100-year return period, rises faster than the mean sea level. On the other hand, Lowe and Gregory [5] forecasted, based on a 50-year return period for storm surges, that by the end of this century, the sea level off the entire east coast of Denmark will be about 40–60 cm higher than it is today (under the assumption of an average gas emission scenario). In [6], researchers from the Swedish Meteorological and Hydrological Institute determined the theoretical water level with 10-year, 100-year, and 200-year return periods for the Swedish coast using modeling and climate change scenarios.

Theoretical sea levels with a given probability of their occurrence are used not only in identifying the characteristics of extreme sea levels and storm surges and in the ongoing climate changes; probabilistic forecasting also has a wide range of practical applications—hydraulic engineering, floodplain management, and flood protection for various coasts. There have been many research papers on this topic [7,8,9,10,11]. One example of the use of theoretical sea levels is in the creation of flood risk maps for the Lithuanian coasts of the Baltic Sea and the Curonian Lagoon. In accordance with the 2007 European Floods Directive, these maps assume that water with a 1000-year return period (0.1%) poses a low probability of causing flooding, while the probability for water with a 100-year return period (1%) is medium and that for water with a 10-year return period (10%) is high [12]. Kystdirektoratet, the Danish coastal protection service, published a report [10] that provides theoretical water heights for 20-, 50-, and 100-year return periods; frequency statistics; and the geographic range of extreme sea levels off the Danish coast for all 67 Baltic and North Sea tide gauges. In turn, a report produced by the Swedish Meteorological and Hydrological Institute (SMHI) [11] describes various statistical methods for determining the probability of extreme sea levels occurring off the coast of Sweden. According to the authors of [7], the choice of return period depends on the risk taken and the infrastructure in the coastal zone. For coastal protection in the Netherlands, the return period is 1 time in 10,000 years, and for the shores of the British Isles, the minimum return period is 1 time in 1000 years [7]. The probability of sea levels is also used in predicting the conditions of navigation on fairways and approaches to seaports. For example, one can determine the probability of reaching the level of transit depths (Medium Low Navigable Water), below which navigation is impossible or dangerous [13].

The aim of this study was to analyze the application of the probability of extreme water levels along the entire Baltic Sea coast. This analysis included the so-called maximum and minimum theoretical water levels calculated based on the highest and lowest observed annual sea level values, respectively.

The basis for making a correct probabilistic forecast is knowledge of genesis and occurrence of extreme levels, i.e., the maximum and minimum levels. The occurrence of extreme sea levels, which are the result of storm surges on the Baltic coasts, depends on three basic components [14]:

• The filling-up of the Baltic Sea, that is, the initial sea level prior to the occurrence of an extreme event;
• The action of tangential wind stresses within a given area (wind direction, i.e., shore-bound or seaward; wind velocities; and the duration of wind action);
• The deformation of the sea surface by mesoscale deep low-pressure systems rapidly crossing the Baltic Sea, a phenomenon that produces a water cushion (a baric wave) and seiche-like variations in the sea levels of the Baltic Sea. A water cushion is a surge of water caused by sub-pressure associated with a low-pressure system resulting from the inverse barometer effect (where a 1 hPa drop in pressure in the depression center increases the sea level by 1 cm).

As a result of the interactions among these three factors, extremely high sea levels can occur during the positive phase of a storm surge (i.e., sea level rise), while extremely low levels can occur during the negative phase (i.e., sea level fall) [15].

It should be noted that extremely low sea levels in the Baltic Sea also occur as a result of a completely different mechanism, namely, the eastern circulation of the atmosphere during periods with continuous and prolonged easterly and northern winds, with an extended high over Scandinavia or northwestern Russia. In times like these, relatively low water levels may last for several weeks [16].

The Baltic Sea is a marginal, internal sea on which the dynamics of Atlantic Ocean waters have a minor impact. This is mainly due to the narrow and shallow Danish straits connecting the Baltic with the North Sea.

2. Materials and Methods

2.1. Research Material

This research material contains two ranges of sea level data with different resolutions and periods. The first range of data contains hourly observations of sea levels made at 42 tide gauge stations located along all the coasts of the Baltic Sea from the years 1960 to 2020 (Figure 1). The second type of research material involves the maximum and minimum annual sea levels from 1900 to 1960 (or a slightly shorter period) from 21 Baltic tide gauge stations. Both ranges of measurement data were selected as the longest possible sea level observation periods available from the national hydrological and meteorological institutes of the Baltic states (DMI—Denmark, BSH—Germany, IMGW—Poland, LHS—Lithuania, LEGMC—Latvia, EEA—Estonia, FMI—Finland, and SMHI—Sweden). Although there are some differences among countries, most tide gauge stations on the Baltic Sea coast are fully automated in terms of recording and transmitting data. Each station currently has 2 independent measuring sensors—radar and pressure. Data are recorded with an accuracy of 1 cm.

Data from all 42 tide gauge stations were used for probability calculations and to visualize the Baltic Sea surface for high and low waters with different return periods. Example probability results for the 10 selected representative tide gauge stations around the Baltic Sea are presented in Section 3.2. At these 10 stations, the recorded sea level fluctuations displayed a similar course to other stations within the particular sub-basins of the Baltic Sea. For this reason, the following stations were deemed representative in their respective Baltic Sea sub-basins: Korsør (the Danish Straits, particularly the Great Belt), Wismar (the Western Baltic), Ustka (the Southern Baltic),Visby (the Central Baltic), Pärnu (Pärnu Bay in the Gulf of Riga), Helsinki and Narva (the Gulf of Finland), Ristna (the Northern Baltic), Vaasa (the middle part of the Gulf of Bothnia), and Kemi (the northern part of the Gulf of Bothnia—Bothnian Bay). This division of the Baltic Sea into sub-basins was based on the results of our earlier work [17] (Figure 1). Sea level values were referenced to the zero of the local tide gauge, the vertical line of which is based on the mean sea level (MSL). The sea level data obtained from national hydrological and meteorological institutes had already been corrected for the elevation or subsidence of land. The Swedish (SMHI) and Finnish (FMI) institutes, due to strong isostatic movements in these countries, perform such corrections annually in relation to the average sea level in a given year for each tide gauge. In the current work, the long-term trend of the mean sea level was not removed from the analyses.

2.2. Determination of the Probability of Theoretical Water Levels—Statistical Distributions

The calculation of the probability of water level occurrence consists of appropriately selecting the theoretical probability distribution and then adopting methods for estimating the parameters of this distribution using statistical material. Confirmation of the correct choice of the distribution can be obtained by using the compatibility tests proposed in the literature. These tests determine the probability of differences between the theoretical and empirical distribution (in this work, the empirical distribution is the sea level observation series). We tested various distributions using MATLAB R2012b software: Gumbel, Generalized Extreme Value (GEV), Weibull, Log-Pearson, and Pearson type III. The Gumbel distribution for the maximum (highest) sea levels and the Pearson type III distribution for the minimum (lowest) values turned out to be the distributions with the greatest consistency with respect to the empirical distribution. This was confirmed by our earlier work in which comparative analyses of probability distributions for the maximum and minimum sea levels were performed [18,19]. The Gumbel distribution was and remains one of the most commonly used statistical distributions in the frequency analysis of extreme events in hydrology like maximum rainfall, flood peaks or maximum river flows, which are critical in hydrological studies [20]. Its preference over other probability distributions can be attributed to several key advantages. The first is specialization of the distribution in extreme value analysis. Coles [21] highlights the utility of the Gumbel distribution in flood frequency analysis, noting its effectiveness in accurately capturing the behavior of extreme hydrological events. This distribution fits well with hydrological data. It is particularly adept at modeling the right tail of the distribution, which corresponds to extreme events in hydrology. This characteristic is crucial for flood risk assessment and management [22]. Hosking and Wallis [23] compared the Gumbel distribution with others, showing its superior performance in predicting rare, high-magnitude flood events, which are pivotal in hydrological planning. In addition, the Gumbel distribution can effectively handle censored data (lost data), which is common in hydrology due to incomplete records or data below the detection limits [24]. The Gumbel distribution is also commonly used in the design of hydrotechnical structures—dams and flood barriers, which the authors write about in this paper.

The Gumbel distribution is based on statistical distributions of extreme values occurring in some larger sets of values. These values are the annual maximum (highest) water levels in the analyzed multi-year periods, namely, 1960–2020 and 1900–1960. The statistical distribution equation is as follows [25]:

$$f(x)={\displaystyle \frac{1}{\widehat{a}}}e\left[-{\displaystyle \frac{x-b}{\widehat{a}}}-e\left(-{\displaystyle \frac{x-b}{\widehat{a}}}\right)\right]$$

(1)

where â is a scale parameter (it determines the dispersion of the distribution along the x-axis); b is a location parameter (it determines the location of the distribution on the x-axis); and e is the base of the natural logarithm.

However, this work takes into account the basic disadvantage of the Gumbel distribution considered in hydrological studies [20,26]. This is the limited flexibility of this distribution when modeling various forms of skewness, which often leads to inaccurate calculations for the upper quantiles of this distribution. The confidence interval for these upper quantiles p = 0.1% and p = 0.2% is wide, over ±15 cm, which affects the uncertainty of the calculation and, as a result, its engineering applications. Therefore, the authors dropped the calculation of the theoretical water height for probabilities p = 0.1% and p = 0.2% (water with 1000- and 500-year return periods) in the current work. Such theoretical water heights are referred to in the hydrological literature as “impossible floods‘’ and will not be relevant for consideration in the current work.

A Pearson type III distribution, typically used in hydrology [27], was used to determine the theoretical minimum water levels. As mentioned earlier, the comparative analysis of probability distributions in the authors’ earlier work showed that the Pearson type III is a more suitable distribution for forecasting minimum sea levels than the other distributions [19]. This is partly due to the much lower values of the standard error for the upper quantiles of this distribution (0.5% and 1%) compared to, for example, the Gumbel distribution. In addition, in some cases of data with significant skewness, the Pearson type III distribution often provides a better fit to the observed data than the Gumbel distribution [28]

The calculations were made using the lowest annual sea levels for the 1960–2020 observational series. The statistical distribution equation is given as follows [27]:

$$f\left(x\right)={\displaystyle \frac{{\alpha }^{\lambda }}{\Gamma \left(\lambda \right)}}{e}^{-\alpha \left(x-\epsilon \right)}{\left(x-\epsilon \right)}^{\lambda -1}$$

(2)

where α, ε, and λ are distribution parameters that should meet the following requirements: x ≥ ε (lower limit of the distribution), α > 0, and λ > 0; and Γ(λ) is the gamma function of the variable λ.

In this paper, the maximum likelihood method (MLE) was applied to estimate the parameters of both the Gumbel distribution and the Pearson type III distribution [19]. In hydrology, parameter estimation is crucial for modeling and predicting hydrological events. Among the many methods used for this purpose, those often used by hydrologists for the Gumbel distribution are the maximum likelihood method (MLE) [29,30,31] and the method of linear moments (L-moments) [23,29,32,33]. Both methods have their advantages and disadvantages, depending on the specific context and requirements of the analysis. However, MLE offers several key merits over L-moments in hydrological and extreme sea level applications. MLEs are asymptotically efficient, meaning they achieve the lowest possible variance among unbiased estimators as the sample size increases. This property ensures that with large datasets, MLE provides highly reliable parameter estimates [23,34]. In most situations, MLE is preferable for a sample size n = 50 [35]. MLE facilitates the derivation of confidence intervals for parameter estimates using the likelihood function, which can be more accurate compared to intervals derived from L-moments. This has been confirmed by comparative studies of both methods [36,37]. In addition, MLE considers the entire probability distribution of the data, making full use of the available information. This comprehensive approach often results in more precise parameter estimates compared to methods that rely on summary statistics [38].

Taking into account the above arguments and the size of the samples analyzed in this study (n = 61 years), the maximum likelihood method (MLE) was chosen to estimate the parameters of the distributions.

In this work, the consistency of the assumed theoretical distribution with respect to the empirical distribution (the observation series of sea levels) was evaluated using Kolmogorov’s normality test. This testing consisted of checking whether the following condition held [27]:

D_max [p/m, N/% − p%] < λ_cr/√N

(3)

where D_max is the difference between the empirical and theoretical probability determined for the point of the sequence that deviates most from the theoretical curve; p/m, N/% is the empirical occurrence probability of the m-th term of the distributive series; p% is the theoretical occurrence probability of sea level values corresponding to the m-th term of the distributive series; λ_cr is the critical value of the Kolmogorov distribution at α = 5%; and N is the size of the distributive series.

As mentioned above, the probability calculations and graphs of the theoretical sea level curves were made using MATLAB R2012b software.

2.3. The Use of ArcGis Software to Visualize the Maximum and Minimum Theoretical Water as Well as to Calculate the Sea Surface and the Length of the Coastline

ArcGIS 10.2.1 software was used to visualize the surface of the Baltic Sea based on the calculated theoretical water levels, accounting for their exact geographical locations. The result is a product that can be called a static or statistical model. However, it is not a hydrodynamic model. In the spatial analysis, the kriging method was used, as reported in previous works [15,17]. It is a geostatistical method of interpolating research parameters (in this case, sea levels) that is often used in environmental studies to create maps [39,40]. The main advantage of choosing kriging for the spatial analyses in this work is that it allows the development of isoline maps that reveal clear trends in the differentiation of the examined parameter. This property is not provided by maps prepared, for example, using the inverse distance method, wherein it is more difficult to see regularities. These conclusions have been confirmed by the geostatistical analyses of other researchers [41,42]. In the kriging method, a weighted average of a subset of neighboring points is used to obtain a specific interpolation point using the following expression [42]:

$$Z^{\mathrm{*}}\left(x_0\right)={\sum }_{i=1}^n{w}_{i}Z\left(x_i\right)$$

(4)

where Z* (x₀) is the interpolation value at point x₀; Z(x_i) is the actual value at the measurement point (the sea level of the tide gauge station); w_i is the kriging weight; and n is the number of points included in the kriging procedure (12 for the analyses in this work).

When using the kriging method, it is assumed that the distances between points or their directions with respect to each other reflect a spatial correlation that can be used to explain variations in a surface. Kriging weights are established based on the semivariogram value (semivariance function). In the kriging method, there is a group of admissible, theoretical semivariogram models to which the obtained empirical semivariogram is fitted. The theoretical types of semivariograms in ArcGIS software include spherical, circular, exponential, Gaussian, and linear semivariograms. In this work, interpolation via the kriging method was tested with all of the above semivariogram models. The tests showed that the exponential semivariogram model was the most precise in presenting extreme sea levels in the coastal zone. The remaining models “smoothed” the observed values to a greater extent; they overestimated low sea levels and underestimated high values.

When creating the maps, a land area mask was used, limiting the extent of the polygon to the Baltic Sea area.

To calculate the size of the sea surface and length of the coastline, the contour line of the Baltic Sea coast was obtained; it was created based on data obtained from the EUROSTAT service for Administrative Units from 2016 [43]. The process of determining the area and length of the coastline is presented in the chart below (Figure 2).

Since the resolution of the map base was not high (the pixel size was 4 × 4 km), the percentage data (relative data) were used in the analysis to limit the error value. Data on the area of the entire Baltic Sea (447,896.51 km²) and the total length of the coastline (37,577 km) were taken from the Eurostat database. This line includes the lines of the coasts, gulfs, bays, fjords, islands, and islets. The above numerical values of the area and length of the coast were adopted in the calculations as a reference level, i.e., 100%.

3. Results and Discussion

3.1. Critical Sea Levels off the Baltic States

As mentioned in the introduction, the practical application of probabilistic forecasts of high water levels concerns, to a great extent, the flood risk along coasts. National hydrological services use probability statistics to model storm surges and issue warnings for areas at risk of storm flooding. Each Baltic state conducts its own hydrometeorological monitoring, for which the so-called critical levels or dangerously high sea levels are used. They are warning levels concerning the occurrence of storm floods. These levels are related to the height of the seawalls and are determined based on probabilistic methods. National hydrological services also send warnings about extremely low sea levels on the coast; these levels may pose a threat to the functioning of shipping. They can occur when there are prolonged winds from the land or during the negative phase of a storm surge.

3.1.1. Denmark

The Danish Meteorological Institute (DMI) uses a parameter called heightened water level. It denotes the risk of storm surges and damage in which sea water destroys coastal infrastructure. The warning criterion for heightened water levels is a height exceeding 1.30 m in the Skagerrak and 1.25 m in the Baltic Sea and inland Danish waters. For the western coast of Jutland on the North Sea, this level is higher and amounts to 1.9 m or 2.4 m depending on the location of the water gauge station [44].

In Denmark, for a heightened water level episode to be officially considered a storm surge, it must be a 20-year event (occurring once every 20 years). This event, called the critical level, is calculated separately for each port based on local knowledge about the height of buildings, infrastructure, or the port quay. The critical level concerns the port and the adjacent sections of the coast. The DMI warns of heightened water levels in Danish waters up to 36 h before critical water levels are exceeded [45].

3.1.2. Sweden

The Swedish Meteorological and Hydrological Institute (SMHI) uses the terms high water level and very high water level for various parts of the Swedish coast when issuing sea warnings for areas at risk of storm flooding (

Table 1. Critical sea levels on the Swedish coast [46,47].

Area	High Water Level	Very High Water Level
Bothnian Bay, Western and Southern coasts of Sweden	level ≥ 80 cm	level ≥ 120 cm
Eastern coast except Bothnian Bay	level ≥ 65 cm	level ≥ 100 cm

).

In addition, the SMHI issues low-water-level alerts for Öresund, the Belts, and the Southwest Baltic when the water level is 60 cm below the mean water level and a very-low-water-level alert when it is 100 cm below the mean water level [46]

3.1.3. Germany

The Bundesamt für Seeschifffahrt und Hydrographie, the BSH, has established six categories of hydrological warnings for the coast of the Baltic Sea for both high (flood) and low (runoff) water levels (

Table 2. Critical sea levels on the German coast [48].

Low Tide. Negative Water Level Deviations from Normal Mean Water (NMW)	High Water Positive Water Level Deviations from NMW
from 0.6 m: Information for navigation: Navtex warning from 0.75 m: Information about low water levels from 1.00 m: Negative surge warning from 1.00 m below NMW = light negative surge from 1.25 m below NMW = medium negative surge from 1.50 m below NMW = heavy/pronounced negative surge	from 0.75 m: Information about elevated water levels from 1.00 m: storm surge warning from 1.00 m above NMW = slight storm surge from 1.25 m above NMW = average storm surge from 1.50 m above NMW = heavy storm surge from 2.00 m above NMW = very heavy storm surge

) [48].

In addition, at each tide gauge, the BSH provides the locations, sea level maxima and minima, and recurrence probabilities of extreme events for 2-, 5-, 10-, 20-, 50-, and 100-year return periods [48].

3.1.4. Poland

For the Polish coast, there are three levels of warnings about the occurrence of dangerous hydrological phenomena, and they are given as warning and alarm levels. The first degree (lowest) indicates rapid increases in water levels without exceeding the warning and alarm levels. The second degree (medium) indicates a flood exceeding the warning states, and the third degree (the highest) indicates a flood exceeding the alarm states. The warning and alert levels are set by the Institute of Meteorology and Water Management, and their differentiation depends on the location of the tide gauge station (

Table 3. Critical levels: warning and alarm levels of tide gauge stations of the Polish coast [49].

Tide Gauge	Warning Levels [cm]	Alarm Levels [cm]
Świnoujście	60	80
Kołobrzeg	70	110
Ustka	70	100
Władysławowo	50	70
Gdańsk, Port Północny	50	70
Krynica Morska	60	80

) [49].

3.1.5. Lithuania

For the Lithuanian coast of the Baltic Sea and the Curonian Lagoon, one critical level for flood water and one critical level for low water are set for hydrological warnings (

Table 4. Lithuanian critical levels at water gauge stations [50] (with levels given relative to zero in the LAS 07 system).

Tide Gauges	Very High Water Level [cm]	Very Low Water Level [cm]
Klaipeda, Nida, Vente	≥150	≤100

).

3.1.6. Latvia

The Latvian Environment, Geology, and Meteorology Centre (LEGMC) issues warnings about dangerous hydrological and meteorological conditions. Depending on the intensity of the forecasted hydrological phenomenon, the expected impact, and the probability of occurrence, every phenomenon has four defined levels with respect to flood risk (

Table 5. Flood warning levels for tide gauges of the Latvian coast (levels are given relative to zero in the LAS2000.5 system) [51].

Tide Gauge	Water Level Below Flooding Threat Level [cm]	High Water Level [cm]	Very High Water Level [cm]	Extreme Water Level [cm]
Riga (Daugavgrīva)	114	115–154	155–184	≥185
Liepājā	104	105–134	135–154	≥155
Ventspils	94	95–134	135–154	≥155

).

3.1.7. Estonia

To identify the risk of particularly dangerous storm surges and floods, as well as extremely low water levels, the Estonian Environment Agency (EEA) has established three levels of hydrological warnings, taking into account critical water levels for individual tide gauges of the coast (

Table 6. Degrees of hydrological warnings and critical levels for water gauges of the Estonian coast (levels are given relative to zero in the EH2000 system) [52].

Tide Gauges and Critical Level	Dangerous (Level 1)	Very Dangerous (Level 2)	Extremely Dangerous (Level 3)
Pärnu +180 cm Haapsalu +160 cm Narva-Jõesuu +180 cm Tallinie Pirita +100 cm Tallinnn Port +140 cm Kuressaare +170 cm	The water level has risen to a critical level	The water level has risen ≥0.5 m above the critical limit (depending on location)	The water level has risen ≥1 m above the critical limit and caused widespread flooding

).

3.1.8. Finland

For individual sections of the coast, the Finnish Meteorological Institute (FMI) has defined three degrees of risk regarding storm floods based on the probability of occurrence of certain water levels and one degree of risk for low sea levels (

Table 7. Threat levels and critical sea levels for the Finnish coast (with respect to the theoretical mean water level) [53].

Water Area and Tide Gauge	Low Sea Level [cm]	High Level [cm]	Very High Level [cm]	Dangerously High Level [cm]
		Once a Year	Once in 5 Years	Once Every 20 Years
Northern part of Bothnian Bay (Kemi, Oulu)	−80	115	140	170
Southern part of Bothnian Bay (Raahe, Pietarsaari)	−65	85	110	130
Kvarken (Vaasa)	−50	85	110	130
Bothnian Sea (Kaskinen, Pori, Rauma)	−50	75	100	120
Sea of Åland (Föglö)	−50	65	85	100
Archipelago Sea (Turku) and western part of the Gulf of Finland (Hanko)	−50	70	95	110
Western part of the Gulf of Finland (Helsinki)	−60	80	115	130
Eastern part of the Gulf of Finland (Hamina)	−70	110	145	175

).

It is worth noting that critical sea levels include not only positive surges but also negative ones (Table 2 and Table 7). These low sea levels can occur during storms with offshore winds. Then, the water level may be lower than the transit depths in the fairways, posing a major threat to navigation.

3.1.9. The Russian Federation

At present, in St. Petersburg, water level rises greater than 160 cm above the zero point of the Baltic system of elevation are accepted as floods. Floods are classified as dangerous (increase in water level up to 210 cm), very dangerous (211 to 299 cm), or catastrophic (over 300 cm) [54].

In addition to hydrological warnings against storm floods and breaches of critical sea levels, each Baltic state issues warnings against strong winds during storm events. The limit for average wind speed starts at 14–15 m/s, and that for wind gusts starts at 20 m/s [46].

As can be seen, the sea critical levels determined for the risk of storm floods for the Baltic Sea countries are very diverse. This is mainly due to the location of the water gauge station, bathymetric conditions and hydrotechnical development, and the degree of exposure of the coastal zone to the prevailing directions of low-pressure systems. Therefore, in the next part of this work, probability statistics determined on the basis of a common period, namely, 1960–2020, were used to show, in a uniform frame of reference, which of the Baltic coasts are the most and least threatened by the occurrence of extreme sea levels.

3.2. Geographical Distribution of Theoretical Maximum and Minimum Water Levels of the Baltic Sea

In this study, the theoretical water levels were determined based on the maximum annual and minimum annual sea levels for the 1960–2020 period for all 42 tide gauges located along the entire Baltic Sea coast. Example results for 10 selected representative tide gauge stations of the Baltic Sea are presented in

Table 8. The theoretical maximum sea levels [cm], the probability of their occurrence (P), their return periods (T), and the standard error (SE) [cm] at selected representative Baltic Sea tide gauge stations in 1960–2020.

T (Years)	P (%)	Tide Gauge Station
		Korsør		Wismar		Ustka		Visby		Pärnu
		TW	SE	TW	SE	TW	SE	TW	SE	TW	SE
200	0.5%	173.9	9.8	220.5	11.8	181.7	10.5	98.1	5.4	264.9	15.1
100	1%	162.3	8.6	206.4	10.4	169.3	9.3	91.7	4.8	247.0	13.3
50	2%	150.7	7.5	192.3	9.1	156.7	8.1	85.2	4.2	229.0	11.6
20	5%	135.1	6.0	173.5	7.3	140.0	6.5	76.6	3.4	205.1	9.3
10	10%	123.1	4.9	159.0	6.0	127.1	5.1	69.9	2.7	186.5	7.6
5	20%	110.6	3.9	143.9	4.7	113.6	4.1	63.0	2.1	167.2	5.9
4	25%	106.3	3.5	138.7	4.2	109.1	3.8	60.6	1.9	160.7	5.4
3.33	30%	102.7	3.2	134.4	3.9	105.2	3.5	58.6	1.8	155.2	5.0
2	50%	91.7	2.5	121.0	3.0	93.3	2.7	52.5	1.4	138.1	3.9
1.33	75%	80.0	2.4	106.9	2.6	80.7	2.3	46.0	1.2	120.1	3.3
1.25	80%	77.6	2.4	104.0	2.6	78.2	2.3	44.7	1.2	116.4	3.3
1.11	90%	71.6	2.2	96.7	2.7	71.7	2.4	41.3	1.2	107.1	3.5
1.01	99%	60.0	2.1	82.8	2.5	59.3	2.2	34.9	1.1	89.3	3.3
T (Years)	P (%)	Tide Gauge Station
		Ristna		Helsinki		Narva		Vassa		Kemi
		TW	SE	TW	SE	TW	SE	TW	SE	TW	SE
200	0.5%	221.1	14.5	189.0	11.4	256.0	14.9	194.9	13.0	237.3	13.8
100	1%	203.9	12.8	175.4	10.1	238.2	13.2	179.4	11.5	220.8	12.2
50	2%	186.5	11.2	161.8	8.8	220.5	11.5	163.9	10.0	204.3	10.6
20	5%	163.4	9.0	143.6	7.1	196.7	9.2	143.2	8.1	182.3	8.6
10	10%	145.6	7.3	129.6	5.8	178.4	7.5	127.1	6.6	165.3	7.0
5	20%	127.0	5.7	114.9	4.5	159.3	5.9	110.4	5.1	147.6	5.5
4	25%	120.7	5.2	109.9	4.1	152.8	5.4	104.8	4.7	141.5	5.0
3.33	30%	115.4	4.8	105.7	3.8	147.3	4.9	100.0	4.31	136.5	4.6
2	50%	98.9	3.7	92.8	2.9	130.4	3.8	85.2	3.4	120.8	3.6
1.33	75%	81.6	3.2	79.1	2.5	112.6	3.3	69.7	2.9	104.3	3.0
1.25	80%	78.0	3.2	76.3	2.5	108.9	3.3	66.5	2.9	100.9	3.0
1.11	90%	69.0	3.3	69.3	2.6	99.7	3.4	58.4	3.0	92.3	3.2
1.01	99%	52.0	3.1	55.8	2.4	82.1	3.2	43.1	2.9	76.0	3.0

and

Table 9. Theoretical minimum sea levels [cm], the probability of their occurrence (P), their return periods (T), and the standard error (SE) [cm] at selected Baltic Sea tide gauge stations in 1960–2020.

T (Years)	P (%)	Tide Gauge Station
		Korsør		Wismar		Ustka		Visby		Pärnu
		TW	SE	TW	SE	TW	SE	TW	SE	TW	SE
1.01	99%	−45.1	1.5	−81.3	3.3	−31.0	1.9	−19.9	1.5	−42.9	2.3
1.11	90%	−55.3	1.8	−90.2	3.4	−42.2	2.1	−29.2	1.6	−54.6	2.4
1.25	80%	−59.9	1.6	−95.9	3.5	−47.4	1.9	−33.3	1.5	−60.5	2.3
1.33	75%	−61.6	1.6	−98.4	3.6	−49.5	2.0	−35.0	1.4	−62.9	2.5
2	50%	−69.2	1.6	−110.8	4.2	−58.4	2.1	−41.7	1.5	−73.4	2.7
3.33	30%	−75.2	1.7	−123.1	4.6	−65.8	2.2	−47.1	1.6	−82.5	2.8
4	25%	−77.2	1.8	−127.2	5.1	−68.2	2.3	−48.9	1.7	−85.5	3.0
5	20%	−79.2	1.9	−131.7	6.9	−70.7	2.9	−50.6	2.0	−88.6	3.9
10	10%	−84.8	2.3	−145.5	8.9	−77.7	3.3	−55.6	2.5	−97.7	5.0
20	5%	−89.4	2.9	−159.2	11.2	−83.6	4.76	−59.6	3.3	−105.7	6.4
50	2%	−94.0	3.7	−172.8	12.2	−89.6	5.3	−63.7	3.6	−113.7	7.1
100	1%	−98.6	4.4	−186.5	12.9	−95.5	5.6	−67.8	3.9	−121.7	7.6
200	0.5%	−102.3	5.1	−199.3	14.3	−100.3	6.5	−71.0	4.5	−128.4	8.7
T (Years)	P (%)	Tide Gauge Station
		Ristna		Helsinki		Narva		Vassa		Kemi
		TW	SE	TW	SE	TW	SE	TW	SE	TW	SE
1.01	99%	−16.4	1.6	−33.2	1.8	−38.5	2.1	−31.2	2.1	−31.1	3.2
1.11	90%	−36.8	1.8	−42.8	1.9	−53.7	2.6	−43.0	2.2	−50.1	3.5
1.25	80%	−44.2	1.6	−47.5	1.8	−60.2	2.2	−48.5	2.1	−58.8	3.2
1.33	75%	−46.8	1.9	−49.4	1.9	−62.7	2.1	−50.8	2.1	−62.3	3.2
2	50%	−56.4	2.1	−57.6	2.1	−72.9	2.2	−60.3	2.3	−76.9	3.4
3.33	30%	−62.5	2.2	−64.6	2.2	−80.8	2.3	−68.1	2.4	−88.8	3.5
4	25%	−64.5	2.4	−67.0	2.3	−83.4	2.4	−70.8	2.5	−92.8	3.7
5	20%	−66.2	3.2	−69.4	2.9	−86.0	2.8	−73.4	3.2	−96.7	4.6
10	10%	−70.5	4.3	−76.3	3.7	−93.0	3.5	−81.0	4.0	−107.9	5.8
20	5%	−73.2	6.0	−82.3	4.8	−98.6	4.5	−87.4	5.2	−117.3	7.5
50	2%	−75.8	6.9	−88.3	5.3	−104.2	5.0	−93.8	5.7	−126.8	8.4
100	1%	−78.5	7.5	−94.3	5.7	−109.8	5.4	−100.3	6.1	−136.2	8.9
200	0.5%	−79.9	9.1	−99.3	6.6	−114.0	6.3	−105.5	7.1	−143.7	10.4

. In addition, Figure 3 shows theoretical and observed sea levels for the Central Baltic (corresponding to the Visby tide gauge) and the Gulf of Finland (corresponding to the Narva tide gauge).

To allow a proper interpretation of sea levels obtained from the probabilistic forecasts, one figure shows the distribution of actual maximum and minimum sea levels in the years 1960–2020 (Figure 4a,b) and the height of the theoretical water level with a 200-year return period (Figure 4c,d).

The results in Table 8 and Table 9 and Figure 3 and Figure 4 indicate that the theoretical water levels at individual tide gauges are related to the distance of these tide gauges from the open waters of the Baltic Sea. In Visby, the 200-year maximum sea level was 98.1 cm, and its annual minimum was –71 cm, the smallest range in the whole Baltic Sea for the 200-year period. This range is so small because this station is located on the coast of the open waters of the Baltic Sea (the Central Baltic, Gotland), where the water level fluctuations are the smallest. For the remaining tide gauges, away from the open waters of the Baltic Sea and located in Baltic gulfs and bays, the ranges of extreme water levels are much higher: for Narva (in the Gulf of Finland), the range was from 256 cm to −114 cm; for Wismar (Western Baltic, Meklemburg Bay), it was from 220.5 cm to –199.3 cm; and for Kemi (Bothnian Bay), it was from 237.3 cm to –143.7 cm.

The theoretical sea levels analyzed in this paper and their distribution and heights (Table 8 and Table 9, Figure 3 and Figure 4c,d) are similar in nature to the actual, observed water levels of the Baltic Sea (Figure 4a,b). This is natural because theoretical water levels are calculated based on observed sea levels. The occurrence of these extreme sea levels is consistent with the so-called geographical pattern written about in a previous research paper [17]. Tide gauges located on the eastern and northeastern coasts of the Baltic Sea, which are exposed to the inflow of western air masses, including the dominant tracks of low-pressure systems, are especially at risk of experiencing extreme hydrological events. This applies above all to the great Baltic gulfs: the Gulf of Riga along with the Pärnu Bay, the Gulf of Finland, and the Bothnian Bay. These water areas have the most storm surges, the longest durations of high sea levels, and the highest water levels [17].

Tide gauges located on the Swedish coasts bordering the Central Baltic and the Northern Baltic, which are the least threatened by extreme levels in the entire Baltic Sea area, have a different character. Several factors influence the course of sea level changes in this area. The first factor is the relatively large average depth and volume of the waters of the Central Baltic Sea (77 m and 5412 km³, respectively) in comparison with other areas of the Baltic Sea. The above hydrographic parameters influence reductions in oscillation dynamics and the smallest range of extreme sea level fluctuations. The next factor is the influence of the Baltic seiche. The central location of this water region in relation to the entire Baltic Sea coast makes tide gauges located in the Central Baltic nodal points for Baltic seiche fluctuations [17,55]. The third factor influencing the lowered maximum and minimum sea levels for the Swedish coasts of the Central and Northern Baltic is the eastern exposure of this coast, facing the opposite direction to the inflow of western air masses and the propagation of low-pressure systems. These conclusions are in line with the results of other studies [3,56,57].

Figure 3 and Figure 4 show the next regularity. The theoretical levels and the observed sea levels increase when moving from the tide gauges located in the open waters of the Baltic Sea (Central Baltic, Gotland, Visby) to the innermost parts of the gulfs (the ends of the gulfs) (Bothnian Bay—Kemi, Gulf of Finland—Hamina, Gulf of Riga—Pärnu, Western Baltic, and Meclenburg Bay—Wismar). This phenomenon, called the gulf effect, is related to the bathygraphic and geomorphological characteristics of the individual gulfs and bays, factors that directly affect the dynamics of water bodies. Authors have described this process in an earlier work [17]. The occurrence of these extreme sea levels is consistent with the so-called geographic pattern.

3.3. Comparison of Theoretical Water Heights for the 1900–1960 and 1960–2020 Periods

The next stage of analysis compares (via calculations of differences) the height of the maximum (positive) theoretical water levels between two 61-year periods, 1900–1960 and 1960–2020, for selected tide gauge stations. Differences were calculated for 21 tide gauges with archival data available since 1900 (or a little later) along the Danish, Swedish, Finnish, and Polish coasts.

As indicated by the positive values in

Table 10. Differences in the heights of positive theoretical sea levels (in cm) between 1960–2020 and 1900–1960 for the 21 available tide gauge stations.

T (Years)	P (%)	Tide Gauge Station
		Smögen	Kungs-Holmsfort	Landsort	Stockholm	Ratan	Furuö-Grund	Frederikshavn	Aarhus	Hornbaek	Korsør
200	0.5%	13.1	7.96	24.9	20.2	28.2	34.4	16.2	12.8	16.8	10.0
100	1%	12.0	8.08	22.3	18.2	26.1	32.7	14.4	12.4	15.6	9.4
75	1.33%	11.6	8.14	21.2	17.5	25.3	32.0	13.7	12.3	15.2	9.2
50	2%	11.0	8.21	19.7	16.3	24.1	31.0	12.7	12.1	14.5	8.9
20	5%	9.6	8.39	16.2	13.8	21.3	28.7	10.4	11.7	12.9	8.1
10	10%	8.5	8.52	13.5	11.8	19.2	27.0	8.6	11.3	11.7	7.6
5	20%	7.3	8.66	10.7	9.7	17.0	25.1	6.7	11.0	10.4	7.0
4	25%	7.0	8.7	9.8	9.0	16.3	24.5	6.1	10.8	10.0	6.8
3.33	30%	6.6	8.75	9.0	8.4	15.6	24.0	5.6	10.7	9.7	6.6
2	50%	5.6	8.86	6.5	6.6	13.7	22.3	3.9	10.4	8.5	6.1
1.33	75%	4.6	9	3.9	4.7	11.6	20.6	2.2	10.1	7.4	5.6
1.25	80%	4.3	9.02	3.3	4.3	11.2	20.3	1.8	10.0	7.1	5.4
1.11	90%	3.8	9.09	2.0	3.3	10.1	19.4	0.9	9.8	6.5	5.2
1.01	99%	2.8	9.22	−0.6	1.4	8.1	17.7	−0.8	9.5	5.4	4.6
T (Years)	P (%)		Tide Gauge Station
		Gedser	Frederica	Slipshavn	Copen-hagen	Hirt-hals	Świn-ujście	Kołobrzeg	Gdańsk	Helsinki	Hanko	Vaasa
200	0.5%	−5.2	2.6	22.4	34.0	5.5	5.3	−2.6	29.4	45.9	34.4	36.5
100	1%	−3.7	3.5	20.9	30.1	5.3	6.3	−0.4	27.5	41.3	31.4	33.3
75	1.33%	−3.0	3.8	20.3	28.5	5.2	6.8	0.4	26.6	39.4	30.1	32.0
50	2%	−2.1	4.3	19.4	26.3	5.0	7.4	1.7	25.5	36.7	28.3	30.2
20	5%	−0.1	5.5	17.4	21.1	4.7	8.8	4.6	22.8	30.6	24.2	25.9
10	10%	1.4	6.4	15.9	17.1	4.5	9.9	6.8	20.8	25.8	21.0	22.6
5	20%	3.1	7.3	14.3	12.9	4.3	11.0	9.2	18.6	20.9	17.8	19.2
4	25%	3.6	7.6	13.8	11.5	4.2	11.4	9.9	17.9	19.2	16.6	18.0
3.33	30%	4.1	7.9	13.3	10.3	4.1	11.7	10.6	17.3	17.8	15.7	17.1
2	50%	5.5	8.7	11.9	6.6	3.9	12.7	12.7	15.4	13.4	12.8	14.0
1.33	75%	7.1	9.6	10.4	2.8	3.7	13.8	14.8	13.4	8.8	9.7	10.9
1.25	80%	7.4	9.8	10.1	2.0	3.6	14.0	15.3	13.0	7.9	9.1	10.2
1.11	90%	8.2	10.2	9.3	0.0	3.5	14.6	16.4	11.9	5.5	7.5	8.5
1.01	99%	9.7	11.1	7.9	−3.9	3.3	15.6	18.6	10.0	1.0	4.5	5.4

, the theoretical water levels were higher for the period 1960–2010 for the vast majority of the tide gauges analyzed in the full range of quantiles (from 0.1 to 99%). This is a result of the steady sea level rise in the Baltic Sea during this period. Only for the Gedser and Kołobrzeg tide gauges is a part of the upper range of quantiles negative. This may be due to storm surges at the beginning of the 20th century and the specific location of the tide gauge station (depth and position relative to the cyclone track) [56].

A comparison of the two periods in terms of the height of the theoretical water levels also reveals a shortening of the return period in the Baltic Sea. For example, for Świnoujście (in the Southern Baltic), after 61 years, the 100-year water level shifted to the 73-year water level (Figure 5a), and in Hanko (Northern Baltic), it shifted to approximately the 15-year water level (Figure 5b). This indicates a steady increase in both the theoretical and observed maximum annual sea levels in the last half-century.

The results of calculations of changes in the return period and the theoretical water level for all 21 tide gauge stations between the 1960–2020 and 1900–1960 periods are presented in

Table 11. Change in the return period and the maximum theoretical water level between the 1960–2020 and 1900–1960 periods in the Baltic Sea (SE1 and SE2—standard errors for these periods).

Tide Gauge	Return Periods Change [Years]	Theoretical Water Change [cm]	SE1	SE2	Tide Gauge	Return Periods Change [Years]	Theoretical Water Change [cm]	SE1	SE2
	100 → 45	149 → 161	7.8	7.6		100 → 79	149 → 153	7.2	7.7
Smögen (SE)	50 → 25	139 → 150	6.7	6.6	Fredericia (DK)	50 → 37	139 → 143	6.3	6.7
(since 1910)	10 → 6	117 → 125	4.4	4.4		10 → 6	114 → 121	4.1	4.4
	100 → 56	129 → 137	7.3	7.4		100 → 25	140 → 161	7.8	6.5
Kungsholmsfort (SE)	50 → 27	119 → 127	6.4	6.4	Slipshavn (DK)	50 → 14	131 → 151	6.7	5.6
	10 → 6	95 → 104	4.2	4.2		10 → 4	111 → 126	4.4	3.7
	100 → 16	85 → 107	6.0	4.1		100 → 27	169 → 199	12.0	8.9
Landsort (SE)	50 → 10	79 → 99	5.3	3.6	Copenhagen (DK)	50 → 17	157 → 183	10.1	7.7
	10 → 4	66 → 80	3.5	2.4		10 → 5	128 → 145	6.9	5.1
	100 → 25	98 → 117	6.5	5.1		100 → 70	148 → 153	7.4	7.0
Stockholm (SE)	50 → 14	92 → 108	5.7	4.5	Hirthals (DK)	50 → 35	138 → 143	6.5	6.1
	10 → 4	75 → 87	3.7	2.9		10 → 7	116 → 120	4.2	4.0
	100 → 27	142 → 167	10.2	8.7		100 → 73	171 → 177	9.5	10.4
Ratan (SE)	50 → 15	130 → 154	8.9	7.6	Świnoujście (PL)	50 → 32	157 → 164	8.3	9.1
	10 → 4	102 → 121	5.8	5.0		10 → 6	124 → 134	5.5	6.0
	100 → 20	139 → 172	9.7	9.9		100 → 104	182 → 181	10.0	11.6
Furuögrund (SE)	50 → 10	128 → 159	8.5	8.6	Kołobrzeg (PL)	50 → 46	167 → 168	8.7	10.1
(since 1916)	10 → 3	101 → 128	5.6	5.6		10 → 7	130 → 137	5.7	6.6
	100 → 47	156 → 170	8.7	7.5		100 → 26	152 → 179	10.4	8.9
Frederikshavn (DK)	50 → 24	146 → 158	7.6	6.5	Gdańsk (PL)	50 → 15	140 → 165	9.1	7.8
	10 → 6	122 → 131	5.0	4.3		10 → 4	111 → 132	6.0	5.1
	100 → 47	163 → 176	8.1	7.9		100 → 12	134 → 175	10.1	6.9
Aarhus (DK)	50 → 24	152 → 164	7.1	6.9	Helsinki (FI)	50 → 8	125 → 162	8.8	6.0
	10 → 5	127 → 139	4.7	4.5	(since 1904)	10 → 3	104 → 130	5.8	4.0
	100 → 46	186 → 201	10.4	9.5		100 → 15	116 → 148	8.5	6.3
Hornbaek (DK)	50 → 25	173 → 187	9.0	8.3	Hanko (FI)	50 → 9	108 → 136	7.4	5.5
	10 → 6	143 → 154	5.9	5.4		10 → 3	88 → 109	4.9	3.6
	100 → 57	153 → 162	8.6	8.2		100 → 23	146 → 179	11.5	11.3
Korsør (DK)	50 → 29	142 → 151	7.5	7.2	Vaasa (FI)	50 → 13	134 → 164	10.0	10.0
	10 → 7	116 → 123	4.9	4.7	(since 1922)	10 → 4	104 → 127	6.6	6.5
	100 → 125	191 → 188	9.5	10.6		100 → 46	148 → 165	8.9	8.2
Gedser (DK)	50 → 55	177 → 175	8.3	9.2	BALTIC SEA	50 → 23	137 → 153	7.8	7.1
	10 → 9.8	143 → 144	5.4	6.1		10 → 5	111 → 125	5.1	4.7

.

The results given in Table 11 show a stable increasing trend for both the theoretical and observed maximum water levels in the second half of the 20th century and at the beginning of the 21st century in the Baltic Sea. The sea level rise averaged for the entire Baltic coast was 15.6 cm (2.6 mm/year). In addition, Table 11 shows that the return period for the Baltic tide gauge stations has reduced by half on average over the last 60 years. It can be concluded that hydrological hazards in the Baltic Sea region appear twice as often as they did in the first half of the 20th century. This mechanism is associated with an increase in the average sea level and an intensification of the western atmospheric circulation. The processes describing the increase in the average and maximum water levels in the Baltic Sea are covered in a number of research papers [15,58]. The 6th IPCC report [59] determined that between 1971 and 2006, the global mean sea level (GMSL) rose at a rate of 1.9 mm per year [0.8 to 2.9], and in subsequent years, 2006–2018, the GMSL increase rate was equal to 3.7 mm per year [3.2 to 4.2]. The rate of long-term changes in maximum and minimum sea levels is often several times higher than the rate of changes in the average sea level [3,60]. The aforementioned process of a strong increase in extreme levels is caused not only by global factors, which dominate average sea level trends, but also by changes in regional and local atmospheric circulation resulting in changes in the wind and pressure fields and in the hydrological regime [1,3,61]. There are noticeable processes of increasing activity of mid-latitude cyclones (low-pressure systems) over Northern Europe as well as over the Baltic Sea region [62,63,64]. In the second half of the 20th century, the number of cyclones from the North Atlantic crossing the Baltic Sea showed an increasing trend, especially in the cold season [63]. During the same period, the mean and minimum pressure of strong cyclones (<981.1 hPa) crossing the Baltic Sea decreased significantly [65]

The comparison of the two long-term periods of theoretical water levels also showed that it is necessary to use the longest possible series of sea level observations for probability calculations, as doing so ensures that the reliability of the corresponding probabilistic forecast will be high.

It should be noted that, in the current work, we also compared the minimum theoretical water levels for 1960–2020 and 1900–1960. Unfortunately, the results obtained showed ambiguous trends in changes in the height of minimum theoretical sea levels. The reason is the rarer occurrence of low sea levels, which appear during the passage of deep lows as a negative phase of a storm surge or during the eastern circulation of the atmosphere, processes conducive to lowering the water levels of the Baltic Sea.

3.4. Changes in the Area and Length of the Coastline Corresponding to Different Theoretical Water Heights and Different Return Periods in the Baltic Sea

In this subsection, we determined what size of the sea surface and lengths of the coastline will correspond to different ranges of sea levels for 1-year, 50-year, 100-year, and 200-year return periods. Information on how the parameters of the size of the sea area and length of the coastline change, corresponding to a stable increase in water level, can be used in the future in the hydrodynamic modeling and forecasting of hydrological threats to the coastal zone under changing climate conditions.

This analysis was performed for both maximum and minimum theoretical water levels. The calculations were made using ArcGis software, and the results are given in percentage values (the details of the method used are described in Section 2.3). A visualization of the surface of the Baltic Sea in four return periods for the maximum and minimum theoretical water levels is presented in Figure 6 and Figure 7, respectively. The results of changes in the area and length of the coastline corresponding to different ranges of theoretical water levels are presented in

Table 12. Changes in the area and length of the coastline of the Baltic Sea corresponding to different ranges of maximum theoretical sea levels (100% of the sea surface = 447,896.51 km², and 100% of the length of the coastline = 37,577.0 km).

Sea Level Ranges [cm]	1-Year Return Period		50-Year Return Period		100-Year Return Period		200-Year Return Period
	Surface [%]	Coastline Length [%]	Surface [%]	Coastline Length [%]	Surface [%]	Coastline Length [%]	Surface [%]	Coastline Length [%]
250–300	-	-	-	-	-	-	2.5	3.0
200–250	-	-	5.9	5.6	10.9	13.0	16.6	20.8
150–200	-	-	44.6	48.0	61.4	53.9	65.1	54.2
100–150	-	-	46.2	43.8	27.0	33.0	15.8	22.0
<100	100	100	3.3	2.6	0.7	0.1	-	-
Summary:	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0

for the maximum water levels and

Table 13. Changes in the area and length of the coastline of the Baltic Sea corresponding to different ranges of minimum theoretical sea levels (100% of the sea surface = 447,896.51 km² and 100% of the length of the coastline = 37,577.0 km).

Sea Level Ranges [cm]	1-Year Return Period		50-Year Return Period		100-Year Return Period		200-Year Return Period
	Surface [%]	Coastline Length [%]	Surface [%]	Coastline Length [%]	Surface [%]	Coastline Length [%]	Surface [%]	Coastline Length [%]
−250 to −200	-	-	-	-	-	-	-	-
−200 to −150	-	-	0.9	1.5	2.0	2.6	2.8	5.1
−150 to −100	-	-	30.9	34.7	36.4	41.4	40.0	46.7
>−100	100	100	68.2	63.8	61.6	55.9	57.2	48.3
Summary:	100	100	100	100	100	100	100	100

for the minimum water levels.

Figure 6 and Table 12 show the regularity in which the extension of the return period was accompanied by an increase in the area of high sea levels (≥200 cm) and, at the same time, a decrease in the area of lower sea levels (≤150 cm). For the maximum theoretical water level with a 200-year return period, as much as 19.1% of the Baltic Sea surface and 23.8% of its coastline length may be influenced by extremely high sea levels (≥200 cm). These are the areas of the inner parts of the great Baltic gulfs: Finland, Riga, Bothnian Bay, Mecklemurg Bay, and Kiel Bay. For these areas, the critical water levels are lower than 200 cm (Section 3.1, Table 1, Table 2, Table 6 and Table 7), indicating a potential risk of storm floods. The hydrological characteristics of these gulfs are related to the geographical pattern of the occurrence of extreme sea levels as well as the so-called gulf effect (Section 3.2), as described in earlier work [17].

Reverse regularities, although they do not have such great dynamics of changes, occur for the minimum theoretical water level (Figure 7, Table 13). As the return period increases, the areas with the highest sea level (>−100 cm) shrink, while the remaining areas with a lower sea level (<−100 cm) expand and the corresponding length of the coastline increases. For the minimum theoretical water level with a 200-year return period, only 2.8% of the Baltic Sea area and 5.1% of its coastline are affected by extremely low water levels (<−150 cm). The coastal zone of the Western Baltic Sea may be the main basin of the Baltic Sea, where, due to low water levels, there may be threats to shipping and navigation (Figure 4b and Figure 7). The Western Baltic Sea, particularly Mecklemurg Bay and Kiel Bay, has the most frequent and deepest decreases as well as the lowest sea levels. The eastern exposure of these shallow bays favors the outflow of water from their basins by fast-moving mesoscale low-pressure systems crossing the Baltic Sea from west to east [17]. It is worth adding that for a significant part of the Bothnian Bay and Gulf of Finland coasts, the occurrence of 50-year theoretical water in the range of −100 cm to −150 cm may cause navigation and transportation problems (Figure 7b). The critical low water level for these sub-basins determined by the FMI hydrological service ranges from −60 cm to −80 cm (Section 3.1, Table 7) [53].

An additional conclusion resulting from the comparison of the theoretical maximum and minimum water levels is the advantage of high water levels over low levels in terms of the area of occurrence and range of fluctuations (Figure 6 and Figure 7). There are two reasons for this asymmetry. The first reason is the predominance of western circulation and western winds, which participate in the filling of the Baltic Sea basin (passing of deep low pressure systems, which generate storm surges). Eastern circulation and eastern winds lowering the water level in the Baltic Sea occur much less frequently. The second reason relates to the physical nature of a storm surge, which most often occurs with earlier filling of the Baltic Sea (an increase above the average levels) and an uplift of the water as a result of negative pressure under moving deep low-pressure systems (the barometric effect). As a result, the above factors will inhibit rapid and significant drops in sea level when there are strong winds from the land [66].

3.5. The Number of Observations of Exceeding the Theoretical Water Height for Different Return Periods

Interesting hydrological issues in the coastal zone are cases where the actually observed sea level reached and exceeded the height of the theoretical water level with a definite return period for a particular water gauge. By knowing the number of such cases, it is possible to determine which sections of the coast are particularly vulnerable to dangerous hydrological phenomena such as storm surges and storm floods. This information is also very important in hydrotechnics for the construction of flood embankments, whose height is determined based on the theoretical water height within a specified return period. Therefore, in this part of this research, the number of observations of exceedances of the theoretical water level height was determined for each of the 42 tide gauges based on the series of observed hourly sea levels from 1960 to 2020. For the calculations, five return periods were selected: 20, 50, 100 and 200 years. The results along with the number of observations are presented in Figure 8 and in

Table A1. The number of observations of exceedances of the theoretical water height for return periods of different lengths from 1960 to 2020.

Tide Gauge	Number of Observations of Exceedances
	20 Years Return Period	50 Years Return Period	100 Years Return Period	200 Years Return Period
Smögen (SE)	-	-	-	-
Klagshamn (SE)	1	-	-	-
Ystad-Skanör (SE)	2	1	-	-
Kungsholmsfort (SE)	-	-	-	-
Oskarshamn (SE)	1	-	-	-
Visby (SE)	8	-	-	-
Marviken (SE)	5	-	-	-
Landsort (SE)	3	-	-	-
Stockholm (SE)	4	2	-	-
Forsmark (SE)	1	1	-	-
Spikarna (SE)	2	-	-	-
Ratan (SE)	1	-	-	-
Furuögrund (SE)	2	-	-	-
Frederikshavn (DK)	7	1	-	-
Aarhus (DK)	5	-	-	-
Hornbaek (DK)	1	1	-	-
Fynshav (DK)	2	-	-	-
Korsor (DK)	2	2	-	-
Gedser (DK)	1	-	-	-
Wismar (DE)	5	1	-	-
Warnemunde (DE)	4	-	-	-
Sassnitz (DE)	-	-	-	-
Greifswald (DE)	4	-	-	-
Świnoujście	2	-	-	-
Kołobrzeg (PL)	-	-	-	-
Ustka (PL)	1	-	-	-
Władysławowo (PL)	1	-	-	-
Gdańsk (PL)	-	-	-	-
Kłajpeda (LT)	2	-	-	-
Pärnu (EE)	3	3	3	1
Ristna (EE)	4	1	1	-
Tallinn (EE)	-	-	-	-
Narva (EE)	-	-	-	-
Hamina (FI)	1	-	-	-
Helsinki (FI)	1	-	-	-
Hanko (FI)	2	-	-	-
Degerby (FI)	-	-	-	-
Mäntyluoto (FI)	1	-	-	-
Vaasa (FI)	-	-	-	-
Kemi (FI)	4	1	-	-
Daugavgrīva (LV)	3	2	1	-
Ventspils (LV)	2	-	-	-

in Appendix A.

The number of observations of exceedances of the theoretical water height for each tide gauge depends on several factors. These are, first, the distance and exposure of the water gauge in relation to the course of the low-pressure system and, second, the bathymetric and geomorphological characteristics of the coastal zone. The next factor follows from the previous factors. The lower the range of water fluctuations at a particular tide gauge, the greater the probability that even a not-very-active low-pressure system will generate an exceedance of the theoretical water level. A good example here is Visby station, which is characterized by the lowest range of sea level fluctuations in the Baltic Sea (Section 3.2). In the 60-year period from 1960 to 2020, there were eight cases of exceedances of the theoretical water level with a 20-year return period (Figure 8). However, based on the probability statistics, the 20-year water level is expected to be exceeded about three times in 60 years.

However, the most important conclusion from Figure 8 is that Pärnu Bay, encompassing the Pärnu tide gauge station, is the most hydrologically dangerous basin of the Baltic Sea. From 1960 to 2020, there were three exceedances of the theoretical water level with 20-, 50-, and 100-year return periods. For this tide gauge, the theoretical water level with a 200-year return period was also exceeded. This distinguishes Pärnu from other tide gauge stations in the Baltic Sea (Figure 8, Appendix A).

Pärnu Bay is located in the north-eastern part of the Gulf of Riga (Figure 1). This small-surface bay (444 km²) with a shallow depth (4.7 m on average) is exposed on the southwest, the direction from which low-pressure systems move in and prevailing winds blow most often [67,68,69]. The Pärnu tide gauge located at the end of this bay registered the highest sea level maximum of 275 cm during catastrophic storm surges generated by cyclone Gudrun on 9 January 2005. This record level is the result of the high (+70 cm), initial level of the Baltic Sea, a fast-traveling cyclone with a favorable trajectory, and strong SW–W winds [70].

The extratropical cyclone Gudrun (central pressure 961 hPa, wind speed up to 30 m/s) on 8–9 January 2005 was the largest storm surge in the multiyear period 1960–2020 and caused significant damage in the coastal zone on the Baltic Sea. The tide gauge stations located on the Gulf of Finland and the Gulf of Riga recorded their highest extremes during the last 60 years: Hanko (132 cm), Helsinki (150 cm), Narva (194 cm), Hamina (197 cm), Ristna 209 cm and Pärnu (275 cm) [71]. During this storm, the 200-year water was exceeded in Pärnu by 10 cm, the 100-year water in Ristna by 5 cm and the 50-year water in Daugavgrīva by 2 cm. In contrast, the 20-year water was exceeded in Hamina, Hanko and Helsinki by 14 cm, 11 cm and 6 cm, respectively.

A slightly smaller storm surge occurred in Pärnu Bay on October 18, 1967, when the maximum sea level reached 264 cm. Then the 100-year water was exceeded by 4 cm. According to previous research by the authors of [17], the Pärnu tide gauge recorded the largest number of storm surges in the Baltic Sea per year (8.4, on average), the highest sea levels, and the largest annual average number of hours with high (≥70 cm) and very high (≥100 cm) sea levels (219 and 47 h per year, respectively). These extreme parameters result from the morphological and bathymetric characteristics of Pärnu Bay. Estonian researchers have comprehensively characterized the water dynamics of this bay. Suursaar et al. [72] used a hydrodynamic model to determine that a wind direction of 220° was the most conducive to a sea level rise in Pärnu Bay. With wind blowing from this direction and at a constant speed of 20 m/s, the sea level in Pärnu Bay may increase to 1.2 m. However, during a seiche in the Gulf of Riga with a 5 h period, the amplitude of the water level fluctuations in Pärnu Bay may rise 1.5 m. Other results indicate that a wind speed increase of 1 m/s (in the wind speed range of 27–30 m/s) raises the sea level in Pärnu Bay by 20 cm [70].

According to the authors of [1,50], using the probability distribution to forecast the highest sea levels during the largest storm surges does not yield a good result for tide gauges located in bays with specific morphometric features (e.g., Pärnu Bay). For such places, the values of extreme sea levels deviate from the distribution curve, and when forecasting in these waters, the return period should be replaced by hydrodynamic modeling.

4. Conclusions

The analyses carried out in this work indicate several main conclusions:

• The critical sea levels determined by the national hydrological services of Baltic Sea countries regarding the risk of storm floods are very diverse. This is mainly due to the locations of the tide gauge stations, bathymetric conditions, and hydrotechnical development.
• Over the last 60 years, a stable trend of an increase in both the theoretical and observed maximum water levels in the Baltic Sea has been visible. The sea level rise averaged for the entire Baltic Sea coast was 15.6 cm (2.6 mm/year). At the same time, the return period for the Baltic tide gauge stations reduced by about 50% (on average). It can be concluded that hydrological hazards in the Baltic Sea region now appear twice as often as they did in the first half of the 20th century.
• For the maximum theoretical water level with a 200-year return period, as much as 19.1% of the Baltic Sea surface and 23.8% of its coastline length may be influenced by extremely high sea levels (≥200 cm). These are the areas in the inner parts of the gulfs: Finland, Riga, Bothnian Bay, Mecklemurg Bay, and Kiel Bay. For these areas, the critical water levels are lower than 200 cm, indicating a potential risk of storm floods.
• Pärnu Bay, within which lies Pärnu station, is the most hydrologically dangerous basin of the Baltic Sea. In 1960 to 2020, there were three cases of exceedances of the theoretical water level with 20-, 50-, and 100-year return periods and one case of an exceedance of the theoretical water level with a 200-year return period. This distinguishes Pärnu from other tide gauge stations in the Baltic Sea.

For both current flood risk and future risk under the conditions of an assumed sea level rise, probabilistic statistics are a good tool for adaptation to climate change. In the future, climate change adaptation will need more focus on extreme events, i.e., storm surges, not just a stable rise in sea levels.