Tidal Oscillations in the Baltic Sea

Transcription

1 ISSN , Oceanology, 013, Vol. 53, No. 5, pp Pleiades Publishing, Inc., 013. Original Russian Text I.P. Medvedev, A.B. Rabinovich, E.A. Kulikov, 013, published in Okeanologiya, 013, Vol. 53, No. 5, pp MARINE PHYSICS Tidal Oscillations in the Baltic Sea I. P. Medvedev, A. B. Rabinovich, and E. A. Kulikov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russia Received October 15, 01; in final form, February 7, 013 Abstract Long-term hourly data from 35 tide gauge stations, including 15 stations in the Gulf of Finland, were used to examine tidal sea level oscillations of the Baltic Sea. High-resolution spectral analysis revealed the well-defined fine structure of tidal peaks with diurnal peaks at most stations being higher than semidiurnal. At some stations (e.g., Narva, Daugava, and Wladyslawowo), high frequency radiational tidal peaks with periods multiple of the solar day (3, 4, 5, 6, and 8 cpd) were detected; the respective oscillations are supposed to be caused by seabreeze winds. Harmonic analysis of tides for individual yearly sea level series followed by vector averaging over the entire observational period was used to estimate the amplitudes and phases of 16 tidal constituents. The maximum tidal oscillations of cm were found to be observed in the Gulf of Finland and, first of all, in Neva Bay (in the head of the gulf). Diurnal or mixed diurnal tides are predominant in almost the entire Baltic Sea. The comparison of the observed tides with those theoretically computed showed that the existing numerical models of the main tidal harmonics generally quite accurately reproduce the structure of the tides in the Baltic Sea except for some regions of the Gulf of Bothnia. DOI: /S INTRODUCTION Sea level oscillations in the Baltic Sea are influenced by various processes. Long-period oscillations are determined by changes in salinity and water temperature, water exchange with the North Sea through the Danish straits, and river flow. The mesoscale sea level oscillations in the Baltic Sea, reaching a height of several meters in some regions, are associated with storm surges caused by cyclone motions over the sea. The tidal oscillations in the Baltic Sea level are formed by free tidal waves penetrating from the North Sea and forced tidal waves excited directly in its water area [15]. Despite the relatively small amplitudes of tides in the Baltic Sea, their accurate assessment is crucial for the understanding of the overall dynamics of the sea. Tides produce regular periodic oscillations of the sea level and currents, which are permanently present in the Baltic Sea; all the other processes superimpose tidal background. The mechanism responsible for the formation of tides in the Baltic Sea and in the Gulf of Finland in particular, is in many ways similar to the mechanism of the formation of storm surges in this region; so tidal study enables us to get important information about the formation of the St. Petersburg floods [1]. Tidal oscillations in the Baltic Sea have been studied for over 140 years, but the nature of their anomalous features in this body of water still remains unclear [13, 14, 3]. Defant [9] and Magaard, and Krauss [16] summarized the data obtained by various researchers and constructed tidal maps for the main diurnal and semidiurnal harmonics across the entire Baltic Sea. These studies describe the tidal oscillations in the Gulf of Bothnia off the coasts of Sweden and Finland in sufficient detail, but relatively little attention is paid to tides off the coast of the Russian Federation and Baltic states. In most studies conducted earlier, except [13, 14], relatively short series of observational data not exceeding one year were used. The accuracy of these calculations is relatively poor because of low tide levels in the Baltic Sea compared to the noise level. Therefore, calculated amplitudes and phases of tidal constituents based on various series of observations were strongly different. In this work, the analysis is based on long-term series of hourly values of the sea level from 35 stations with 5 of them providing series of observations for more than 15 years. The study was conducted by means of spectral and harmonic analyses of tides [0]. The use of long-term observational series made it possible to significantly increase the accuracy of the calculated tidal constituents, while their spectral analysis revealed a number of interesting effects, in particular, showing the significant role of radiational tides in some areas of the Baltic Sea. In the past decade, papers on numerical simulation of tidal oscillations in the Baltic Sea began to appear (see, e.g., [18, ]). The tidal harmonic constants obtained in this study made it possible to verify the numerical results and to evaluate the accuracy of tidal maps in the Baltic Sea.. OBSERVATIONS In this paper, we used the data from 35 Russian, Latvian, Estonian, Lithuanian, Swedish, Finnish, and 56

2 TIDAL OSCILLATIONS IN THE BALTIC SEA N S Poland Danish straits Sweden B a l t i c S e a 5 Gulf of Bothnia Gulf of Finland Finland N 1 0 Neva Bay S Gulf of Gulf of Latvia Riga Gdansk 35 Estonia Russia 34 Lithuania Fig. 1. Location of the stations used in this study. The numbers in the figure correspond to the station numbers listed in Table 1. The Neva Bay area is shown in the inset. Polish coastal tide gauges. Their locations are shown in Fig. 1 and their characteristics are given in Table 1. All observational series had 1 hour sampling. The data used were referenced to universal time (Greenwich). The sea level for all stations was referenced to zero of the Baltic height system (0 BS). The series of observations were carefully checked; shifts and spikes were eliminated, short gaps (shorter than one day) were interpolated. The series containing long gaps were excluded from the analysis. The sea level oscillations in the Gulf of Finland are of the greatest interest to this study. In order to examine these oscillations, hourly observational series from fifteen stations were used (Fig. 1). On the southern coast of the gulf, there are the Estonian stations Narva, Suurpea, and Tallinn; while, on the northern coast there are the Finnish tide gauge stations Hanko, Helsinki, and Hamina and the Russian stations Vyborg, Primorsk, Gogland, and Moshchniy. The most densely located tide gauge stations are in Neva Bay (see Box 1a), where the sea level variability was recorded by five tide gauges, i.e., Shepelevo, Lomonosov, Kronstadt, Nevskaya Ustievaya, and the Gorniy Institute. The hourly series of sea level observations obtained at Gorniy Institute station is the longest used in this study (31 years). 3. SPECTRAL ANALYSIS The spectral analysis of sea level records makes it possible to evaluate the distribution of wave energy in various frequency bands and to estimate the frequency-selective properties of the examined water bodies. The spectra were calculated using the Fast Fourier Transform. Following the recommendations of [10], the spectral Kaiser Bessel window with a selected window length of N = 8766 h (i.e. one astronomical year) and with a half-window overlap was used to improve the quality of the calculations and to reduce the Gibbs effect. Accordingly, the spectral resolution was Δf cpd = 1 cpy. As an example, Fig. shows the spectra of sea level oscillations from four stations located in different parts of the Baltic Sea, i.e., Landsort (6) located in the open part of the Baltic Sea, Skulte () in the Gulf of Riga, Hanko (19) at the entrance to the Gulf of Finland, and Kronstadt (10) in the head of the Gulf of Finland (the numbers in the parentheses correspond to the station numbers in Fig. 1 and Table 1). The lengths of the observational series for these stations are different. The number of degrees of freedom (ν) (i.e., 56 for Landsort, 16 for Skulte, 6 for Hanko, and 58 for Kronstadt) and therefore, the confidence intervals for the spectra vary respectively. The major properties of all spectra are similar. Most of the energy is concentrated at low frequencies, and

3 58 MEDVEDEV et al. Table 1. Characteristics of the stations used for the analysis of sea level oscillations in the Baltic Sea No. Station Name Latitude (N) Longitude (E) Country Beginning End 1 Daugava Latvia Skulte Latvia Pärnu Estonia Ristna Estonia Tallinn Estonia Suurpea Estonia Narva Estonia Shepelevo Russia Lomonosov Russia Kronstadt Russia Nevskaya Ustievaya Russia Gorniy Institute Russia Vyborg Russia Primorsk Russia Moshchniy Russia Gogland Russia Hamina Finland Helsinki Finland Hanko Finland Föglö Finland Rauma Finland Mantyluoto Finland Kaskinen Finland Spikarna Sweden Forsmark Sweden Landsort Sweden Landsort Norra Sweden Visby Sweden Simrisamn Sweden Eland Sweden Wladyslawowo Poland Baltiysk Russia Otrkrytoe Russia Pionerskiy Russia Klaipeda Lithuania quite fast decay is observed at higher frequencies. The general power law of the spectra decay is f, where f is the spectral frequency. This law, indicated in Fig. by a straight line, is typical for the long-wave spectra in the open ocean [6]. However, in the Baltic Sea for specific frequency bands this law is distorted. This is apparently because the basin is almost completely enclosed. In particular, at frequencies from 0.8 to 1.6 cpd, there is a wide bump, which is probably related to the fundamental natural period of 7 h dominant in the Baltic Sea [15]. The individual features of the spectra at specific stations are also determined by the eigen mode structures of the respective water bodies (the gulfs of Riga, Finland, Bothnia, etc.). For example, in the Gulf of Finland, at frequencies from 0.05 to cpd, there is a marked increase of the sea level energy

4 TIDAL OSCILLATIONS IN THE BALTIC SEA 59 (а) 10 Landsort Period, h (b) 10 Skulte O K K 1 O M 1 S 10 M S Spectral density, cm /cpd 10 ν = 56 (c) Hanko f 10 ν = 16 f (d) Kronstadt K 1 M 10 M K 1 S 10 f S f ν = 6 ν = Frequency, cpd Fig.. Spectra of sea level oscillations at (a) Landsort, (b) Skulte, (c) Hanko, and (d) Kronstadt. The peaks corresponding to the main tidal harmonics are indicated. The number of degrees of freedom in calculated spectra ( ν) is specified, and the corresponding confidence intervals are shown. The spectral window length is N = 8766 h (one astronomical year). toward the head of the gulf. At these frequencies, the spectral energy at the entrance of the Gulf of Finland (at Hanko, Fig. c) is approximately an order of magnitude smaller than at the head of the gulf (e.g., at Kronstadt, Fig. d). This increase of the spectrum eastward is probably due to the structure of eigen oscillations in the Gulf of Finland with the nodal line near the entrance and the antinodal point at the head of the gulf (see, e.g., [1, 1]). At frequencies higher than cpd, the difference in the spectral energy for the stations located at the entrance to the gulf and at its head is insignificant. One of the most important features of the sea level spectra in the Baltic Sea are narrow and sharp peaks corresponding to the frequencies of the main tidal harmonics: diurnal K 1 (period of 3.93 h) and (5.8 h) and the semidiurnal M (1.4 h) and S (1.00 h). Although the amplitudes of tidal oscillations in the Baltic Sea are relatively small, because these oscillations are very regular and deterministic, the spectra of the sea level oscillations at all stations have well-

5 530 MEDVEDEV et al. defined tidal peaks. The presence of these tidal peaks in sea level spectra in the Baltic Sea was also indicated by other researchers (see, e.g., [1,17]). The specific feature of tidal oscillations of the Baltic Sea level, which is clearly seen in the spectra, is the marked predominance of the amplitudes of diurnal tidal harmonics over semidiurnal. This feature seems surprising taking into account that in the Atlantic Ocean and the associated marginal seas semidiurnal tides significantly prevail [0]. The strongest dominance of diurnal tides is observed in the eastern part of the Baltic Sea and, above all, in the Gulf of Finland (see the spectrum of sea level oscillations at Kronstadt, Fig. d). At the same time, at Hanko located at the entrance to the gulf (see Fig. 1), the sea level spectral peaks at semidiurnal frequencies (M and S ) are higher than at diurnal frequencies (Fig. c). This appears to be associated with the presence of the eigen mode nodal line for near-diurnal frequency [1,1]. 4. RADIATIONAL TIDES In addition to spectral peaks associated with major diurnal and semidiurnal tidal constituents, spectral peaks at frequencies of 3, 4, 5, 6, 7, and 8 cpd, multiples of the solar day, are well defined in the sea level spectra at some stations, in particular at Narva, Wladyslawowo, and Daugava (Fig. 3) (for clarity, not a logarithmic, as in Fig., but a linear scale is used in Fig. 3 for the frequency axis). Typically, the long-wave spectra at frequencies higher than tidal are rather monotonic, which is distorted at frequencies of approximately of 3, 4, 5, and 6 cycles per lunar day [6, 0]. These spectral peaks are associated with higher tidal harmonics, which are formed in shallow water areas as a result of the nonlinear interaction of major gravitational tidal constituents associated mainly with movements of the Moon [0]. In the Baltic Sea, the tides are weak and there are no conditions to generate nonlinear shallow water harmonics. In the considered case, the precise diurnal cyclicity suggests that these oscillations are associated not with the Moon but with the Sun and are caused not by gravitational effects but by the solar radiational effects on the sea level. Munk and Cartwright called the movements directly or indirectly related to the radiation of the Sun as radiational tides [19]. Thus, the radiational harmonics are annual (Sa), semiannual (Ssa), and diurnal (S 1 ) species. The corresponding sea level oscillations are formed not under the influence of gravitational forcing but due to the solar radiation [0]. Radiation exposure also affects the semidiurnal frequency. As shown by Zetler [6] and Wunsch [4], the radiational harmonic S is typically about 16% of the gravitational S. Radiation tides are formed by the combined effect of various periodic factors associated with Sun radiation. The most important of them are (1) oscillations of the air temperature and associated sea surface temperature, () atmospheric tides, and (3) seabreeze winds. The prevalence of one of these factors depends on the specific physical and geographical conditions in the area of the observations [4]. The effect of highfrequency radiational species S 3, S 4, S 5, S 6, S 7, etc., was found by Kulikov and Rabinovich [, 3 ] based on the data of the second Soviet American expedition to measure tsunamis in the open ocean and was explained by the asymmetry (day/night) of the solar radiation on the atmosphere and ocean surface. Figure 3a shows the sea level spectrum at Daugava. The peaks at frequencies of 3, 4, 5, and 6 cpd are quite pronounced and comparable with those of the major tidal constituents. The radiational tides at Narva (Fig. 3b) are relatively weaker and have their main peaks at frequencies of 3, 4, and 5 cpd. At Wladyslawowo, broad radiational peaks are observed at frequencies of 3, 4, 5, 6, 7, and 8 cpd (Fig. 3c). Apparently, the main factor forcing radiational harmonics at some stations of the Baltic coast are the seabreeze winds. This specific factor strongly depends on the particular observational area, while the variability of the air/water temperature and the atmospheric tides do not have such a selective nature. Note that because of the closeness of the frequencies of the diurnal radiational (S 1 ) and the gravitatinal (K 1 and P 1 ) tidal harmonics, their separation is quite a challenge, but it is possible to resolve them based on long series of observations (see the next section). It should be emphasized that although the amplitudes of the radiational tidal sea level oscillations are relatively small (except of seasonal oscillations), tidal currents caused by radiational effects, in particular by seabreeze winds, can be quite significant in the surface layer and reach 1 knots and more (see, e.g., [5]). 5. HIGH RESOLUTION SPECTRA Long series of tide gauge observations make it possible to provide the detailed tidal spectroscopy and even to split individual tidal harmonics [19]. Such an analysis is especially useful in areas with strong tidal oscillations (see, e.g., [7, 11]). However, even in areas with relatively weak tides, in particular in the Baltic Sea, the high-resolution spectra can reveal certain properties of the tidal formation imperceptible in the ordinary spectra. For this analysis, we selected two stations with long-term and high-quality observational series, i.e., Gorniy Institute (31) and Tallinn (18). The length of the spectral window for both data sets was N = h = days, the spectral resolution was Δf cpd, and the number of degrees of freedom was ν = 10 for the first station and ν = 4 for the second. Most attention was paid to the diurnal and semidiurnal frequency bands (Fig. 4). The most interesting features of sea level oscillations in the Baltic Sea found as a result of this analysis are as follows: (1) The background long wave noise level in the diurnal frequency range was significantly higher (by

6 TIDAL OSCILLATIONS IN THE BALTIC SEA O K 1 1 M (а) Daugava S S 3 S 4 S5 S 6 S 7 Spectral density, cm /cpd ν = 16 ν = 56 K 1 M S (b) Narva S 3 S 4 S 5 S 6 S 7 (c) Wladyslawowo 10 M K 1 S S 3 S 4 S 5 S 6 S 7 10 ν = Frequency, cpd Fig. 3. Spectra of sea level oscillations at (a) Daugava, (b) Narva, and (c) Wladyslawowo. The main tidal peaks, including the peaks caused by the high frequency radiational harmonics, are indicated. more than an order of magnitude) than in the semidiurnal frequency range. () The spectral peaks corresponding to the major tidal harmonics were clearly above the noise level and significantly exceeded the confidence spectral level. This is not only for the semidiurnal frequency band, where the noise level is low, but also for the diurnal band, where it is high. (3) The spectral peaks corresponding to the diurnal tidal harmonics dominate. The amplitude of the О 1 harmonic (the main lunar diurnal harmonic with a period of 5.8 h) is even higher than of К 1 (the lunisolar declinational harmonic with a period of 3.93 h), although the theoretical ratio of these harmonics is: HO H K 1 (4) In contrast, the ratios of four major semidiurnal harmonics (М, S, N, and K ) is in good agreement with the theoretical ratio. One of the interesting effects revealed as a result of the high-resolution spectral analysis was the manifes-

7 53 MEDVEDEV et al. tation of the radiation harmonic S 1. Its frequency is located between the frequencies of gravitational harmonics К 1 and Р 1 and was indistinguishable in the conventional spectra. At Gorniy Institute, the magnitude of S 1 is only slightly inferior to the P 1 harmonic, and, at Tallinn, it even exceeds it. In general, the results of the spectral analysis show the clear prevalence of tidal harmonics in comparison with the background noise level in the Baltic Sea. Because of this, it is possible to calculate tides directly by means of the harmonic analysis (see, e.g., [0]). 6. HARMONIC ANALYSIS OF THE TIDES In this paper, the least squares method of harmonic analysis [5, 0] was used to estimate mean tidal amplitudes and phases. Using this method, the tidal constituents for 35 stations in the Baltic Sea were computed. Yearly series of observations without significant gaps were used in this analysis. Short gaps were interpolated. The results of the calculations for individual years were followed by vector averaging over the entire observational period [8]. In total, 16 tidal constituents were calculated, i.e., two seasonal (Sa and Ssa), six diurnal (Q 1,, P 1, S 1, K 1, J 1 ), four semidiurnal (N, M, S, and K ), and four high frequency shallow water harmonics (MK 3, MO 3, M 4, and MS 4 ). The following expressions (see [0]) were used to estimate errors in the calculated tidal amplitudes ( ε H ) and phases ( ): ε G σ ε H = Δω, 1 σδω ε H ε G = = (in radians), (1) T Δω H TΔω H where σ Δω is the variance of the noise (background oscillations) in the frequency range of Δω (diurnal or semidiurnal), T is the length of the series used for the calculations (in this case, Т = 1 year), and H is the amplitude of the corresponding tidal harmonic. From (1), it is clear that the amplitude error is absolute and uniform for all harmonics in the particular frequency range, while the phase error is relative; i.e., the smaller the amplitude of the corresponding harmonic, the greater the phase error. According to the spectral analysis (Section 5), for Gorniy Institute, σ ˆ Δω(1) = ΔωS = 3.1 cm x (1) for the diurnal range and σ ˆ Δω() = ΔωS =. cm x () for the semidiurnal range, where Sˆ x(1, ) is the mean spectrum value for the respective frequency range (Fig. 4a), and Δω = 0. cpd is the width of the range. For Tallinn, the similar variances are significantly smaller, i.e., σ Δω (1) = 5.1 cm and σ = 0.31 cm Δω () (Fig. 4b). The calculated error values for diurnal amplitudes at these stations are ε H (1) = ±6 cm (Gorniy Institute) and ±0.6 cm (Tallinn), and for semidiurnal amplitudes these values are ε H () = ±0.17 cm and ±0.06 cm, respectively. The values of the phase error (ε G ) are inversely proportional to the amplitudes of the corresponding harmonics. For Gorniy Institute, these errors (based on the data from Table ) are ±65 (K 1 ), ±71 ( ), ±30 (M ), and ±67 (S ), and, for Tallinn, these values are ±63 (K 1 ), ±57 ( ), ±31 (M ) and ±70 (S ). For the other stations, the amplitude and phase errors are generally similar. Thus, the errors of the calculated amplitude values are relatively low, while for phases they can be significant. The results of the calculations of tidal amplitudes and phases for various years confirm this tendency, i.e. relatively consistent amplitude values for major diurnal and semidiurnal constituents (within ±0.3 cm) and rather large discrepancy in phases (±8 30 ). Nevertheless, the averaging of the calculation results over a large number of years can significantly improve the accuracy because the error decreases as 1 n, where n is the number of independent yearly series of observations used for the calculations. The harmonic deviation and the errors were determined for all series of observations and for all specific harmonics at individual stations. For stations in the Gulf of Finland, the amplitude error for major diurnal harmonics and K 1 is about 14% of the estimated value. For Baltiysk, the error value for the harmonic is 5% of the amplitude. The phase error for major diurnal harmonics is 8. The amplitude and phase of constituent M changes insignificantly from year to year. The amplitude error is less than 5% of its value, the phase error is ~ 4. As an example, the averaged values of tidal amplitudes and phases calculated for six stations located in various parts of the Baltic Sea are given in Table. The annual (Sa) and semiannual (Ssa) seasonal harmonics clearly dominate. Thus, the amplitude of the Sa harmonic at Daugava reaches 19.4 cm (together with Ssa, the overall variation is almost meters!). At Tallinn, the annual harmonic amplitude reaches 15 cm and at Gorniy Institute it is 1.3 cm. Significant seasonal sea level changes are also observed at other stations. The semiannual harmonic Ssa at almost all stations is weaker than the annual, although there are exceptions (Baltiysk and Landsort). The dominating contribution of seasonal oscillations to the overall energy budget of sea level oscillations in the Baltic Sea was noted by Lisitzin [15]. The interannual variability of annual and semiannual harmonics is high: the Sa and Ssa amplitudes vary from year to year with a standard deviation for most of the stations of 3 and 5 cm, respectively. The phases of seasonal harmonics are also strongly variable, i.e., the difference in the Sa phases for two consecutive years can be up to 80. In general, the analysis of seasonal oscillations in the Baltic Sea is an independent issue which requires a special study.

8 TIDAL OSCILLATIONS IN THE BALTIC SEA (а) Gorniy Institute S 1 P 1 K 1 M Q 1 S N 10 K Spectral density, cm /cpd K 1 S 1 Q 1 P 1 (b) Tallinn M 10 S K N Frequency, cpd Fig. 4. High-resolution spectra of sea level oscillations in the Baltic Sea level for diurnal and semidiurnal frequency bands at (a) Gorniy Institute and (b) Tallinn. The thin dashed line shows the confidence levels for diurnal and semidiurnal harmonics calculated in accordance with the χ distribution for each band. For better visualization, the spectra for Gorniy Institute were raised by one order of magnitude in comparison with Tallinn. Most attention was paid to the analysis of the major diurnal and semidiurnal tidal harmonics. The amplitudes of the diurnal harmonics and K 1 are approximately equal and reach their maximum values at the head of the Gulf of Finland (about 3 cm at Kronstadt and Gorniy Institute), as well as in the Gulf of Riga (up to 1.8 cm). The amplitudes of constituents Р 1 and S 1 have similar values ( cm) and are approximately equal to 0.33 of the amplitude of К 1. The maximum amplitudes of the main semidiurnal М harmonic (about cm) are observed at the head of the Gulf of Finland (Kronstadt, Gorniy Institute and other stations in the area). The ratio of the major diurnal harmonics to the major semidiurnal harmonics ( Form Factor ) determines the type of tides (see, e.g., [0]): HK + H 1 O1 F =. () HM + H S For the six stations shown in Table, the largest value of this ratio was observed at Daugava (F = 4.6), where there is a regular diurnal tide, while the lowest value

9 534 MEDVEDEV et al. Table. Amplitudes and phases of the tidal constituents for six selected stations in the Baltic Sea Harmonic Baltiysk Daugava Kronstadt Tallinn Gorniy Institute Landsort H, cm G, H, cm G, H, cm G, H, cm G, H, cm G, H, cm G, Sa Ssa Q P S K J N M S K MO MK M MS F I was observed at Baltiysk (F = 0.9), where there are mixed semidiurnal tides. A rough estimate of the maximum possible theoretical tidal height can be evaluated as [3]: I = ( HK + H (3) 1 O + H 1 M + H S ). According to the data presented in Table, the maximum tides (I ~ 18 cm) are at the head of the Gulf of Finland (Kronstadt and Gorniy Institute) and the minimum tides (I = 3.5 cm) are at the eastern part of the Gulf of Gdansk (Baltiysk). The nonlinear tidal effects in the Baltic Sea are weak. According to the results of the harmonic analysis, the amplitudes of high frequency shallow water constituents proved to be negligible, which is consistent with the results of the spectral analysis (Fig. ). The averaged values of the amplitudes and phases of the major tidal harmonics (О 1, К 1, M, and S ) and also of the characteristics F and I for all 35 stations are shown in Table 3. In general, the results of the analysis of all 35 stations confirm the previous findings based on analyses of six stations presented in Table : (1) The eastern part of the Baltic Sea is dominated by diurnal tides. This prevalence is particularly noticeable in the central part of the Gulf of Finland (Hels- inki, F = 8.1; Suurpea, F = 6.3) and in the eastern part of the Gulf of Riga (Pärnu, F = 6.5). () The maximum relative impact of semidiurnal tides (F ~ 0.9) is in the Gulf of Gdansk (Wladyslawowo and Baltiysk) and at the entrance to the Gulf of Bothnia (Föglö, Rauma, and Hanko). In these areas, mixed semidiurnal tides are observed. (3) The main diurnal harmonics K 1 and change within the Baltic Sea basin in a similar way, and their amplitudes are approximately equal. (4) The maximum total tide (I ~ cm) is observed at the head of the Gulf of Finland and, above all, in Neva Bay (Nevskaya Ustievaya, Lomonosov Kronstadt, and Gorniy Institute). 7. DISCUSSION The results of analysis of the long-term sea level observations in the Baltic Sea demonstrate that in most parts of the sea (in particular, in the gulfs of Bothnia, Riga and Finland), the type of tides is either diurnal (F > 3) or mixed diurnal (1.5 < F < 3.0). Only at the entrance to the Gulf of Bothnia, in the Gulf of Gdansk, and in some western parts of the Baltic Sea do mixed semidiurnal tides prevail ( < F < 1.5). It is

10 TIDAL OSCILLATIONS IN THE BALTIC SEA 535 Table 3. Calculated amplitudes and phases of major tidal constituents (, K 1, M, and S ) for all the stations. Parameters F (tidal Form Factor) and I (the characteristic tidal height) are also specified No. Station K 1 M S F I H, cm G, H, cm G, H, cm G, H, cm G, 1 Daugava Skulte Pärnu Ristna Tallinn Suurpea Narva Shepelevo Lomonosov Kronstadt Nevskaya Ustievaya Gorniy Institute Vyborg Primorsk Moshchniy Gogland Hamina Helsinki Hanko Föglö Rauma Mantyluoto Kaskinen Spikarna Forsmark Landsort Landsort Norra Visby Simrisamn Åland Wladyslawowo Baltiysk Otrkrytoe Pionerskiy Klaipeda known that diurnal tides in the Atlantic Ocean and the marginal seas of the ocean are small compared to semidiurnal tides. For example, in the North Sea, which is connected to the Baltic Sea by the Danish straits, the amplitudes of the semidiurnal harmonics are approximately 0 30 times greater than those of the diurnal tides [0]. Consequently, either the diurnal tide is formed directly in the Baltic Sea (i.e., it is indigenous (locally generated) by the definition of Nekrasov [4]) or resonant amplification of small diurnal tidal waves entering the sea occurs in the sea as a whole and in its individual gulfs(similar to the resonance amplification of the incoming tsunami and meteotsunami waves in some water bodies of the World Ocean [1]). The possible resonant nature of diurnal tides in the Baltic Sea is indicated by the fact that the amplitude of

11 536 MEDVEDEV et al. N S Gulf of Riga Gulf of Bothnia Neva Bay Gulf of Finland M Gulf of Riga Gulf of Bothnia Neva Bay Gulf of Finland Fig. 5. Tidal maps of diurnal ( ) and semidiurnal (M ) harmonics in the Baltic Sea according to the calculations and observations. The solid lines are isoamplitudes, the dashed lines are cotidal lines (isophases) according to the numerical calculations [18, ]. The observed values are placed near the respective sites, the amplitude is in the numerator (in regular font) and the phase is in the denominator (in italics).

12 TIDAL OSCILLATIONS IN THE BALTIC SEA 537 lunar diurnal harmonic (having a period of 5.8 h, which is closer to the fundamental Baltic Sea period of 7 h denoted in Fig. ) exceeds the mean amplitude of the luni-solar declinational harmonic K 1 (period of 3.93 h), despite that in the tidal potential, the amplitude of is approximately 30% smaller than that of K 1 [0]. This question requires more detailed research. The calculations of mean tidal amplitudes and phases at 35 stations made it possible to compare these observations with the results of numerical modeling of tidal oscillations in the Baltic Sea. Figure 5 shows the theoretical tidal maps of M and according to the data from [18, ] and the observed amplitudes and phases for these two harmonics based on results of the present study. Some differences in the phases are observed on the east coast of the Gulf of Bothnia, while the amplitudes are reproduced accurately. There are certain differences in this area, as well as at the entrance to the Gulf of Bothnia, for M. However, in general, the agreement of the calculations and observations is good. The constructed tidal maps [18, ] correctly reproduce the main features of the tidal dynamics in the Baltic Sea. The complicated distribution of tidal amplitudes and phases with amphidromic systems in certain large gulfs appears to be formed under the influence of eigen sea level oscillations in the Baltic Sea and its gulfs. The presence of the amphidromic points leads to rapid phase changes in specific parts of the sea and abrupt amplitude changes. The complex geometry of the Baltic Sea contributes to the formation of numerous local oscillation systems. In order to study them, it is necessary to conduct detailed numerical simulations using a fine-resolution grid and additional sea level measurements. 8. CONCLUSIONS In studies conducted in this paper, the long-term hourly observations of sea level changes in the Baltic Sea were thoroughly examined. The results of this analysis demonstrate that the sea level spectrum at frequencies higher than 5 cpd (i.e., at periods shorter than 1.5 days) is formed under the significant influence of the tidal forces of the Moon and the Sun; the structure of the tidal oscillations and the sea level response to the external forcing are determined by the structure of eigen oscillations in the Baltic Sea and its individual water bodies. The general character of sea level spectra in the Baltic Sea, and the frequency decay according to the power law f, is associated with natural long-wave background oscillations formed under the influence of atmospheric processes. However, the distortion of this law and formation of a broad uplift ( bump ) at frequency range from 0.8 to 1.6 cpd with the center frequency at about 0.9 cpd (7-hour period) at stations in the Gulf of Finland is probably associated with the fundamental mode of the Gulf of Finland, which, according to calculations [1, 1, 15], has approximately this particular period. It may be assumed that specifically the structure of this mode, which is similar to the Helmholtz mode (see [1]), leads to the increase in spectral density and amplification of diurnal oscillations toward the gulf head. Despite their relatively small amplitude, tidal oscillations in the Baltic Sea clearly manifest themselves in the form of sharp and distinct spectral peaks (Figs., 4). The peaks of major diurnal tidal harmonics О 1 and К 1 at most of the stations exceed the peaks associated with main semidiurnal harmonics М and S. 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