M. Keruss, J. Sennikovs
 

Abstract

The water level fluctuations in the Baltic Sea are caused mainly by the meteorological forcing. High amplitudes of these fluctuations make evaluation of the tidal amplitudes difficult. The main goal of this study is to find optimum filtering of the water level time-series for the correct determination of the tidal characteristics.

An extensive set of the water elevation data from several gauging stations around the Latvian coast of the Baltic Sea and the Gulf of Riga has been analysed. The temporal span of the data (25 years) allowed determination of the amplitudes of the main tidal constituents. The values of them are in the range from 1 to 3 centimeters. Occasional measurements of the amplitudes of the internal tidal waves in the Gulf of Riga are found to be in agreement with the ones calculated from the determined surface tidal amplitudes.
 

1. Introduction

Tidal fluctuations constitute a significant part of the total sea level changes in the coastal zone of the large part of the World Ocean [1,2]. Very high tidal sea level fluctuations have been observed in the semi-enclosed basins bounded with the World Ocean [6]. The Baltic Sea is weakly connected to the North Sea through the Danish straits. The Gulf of Riga is shallow semi-enclosed basin connected to the Baltic Sea. Contrary to the World Ocean, the main part of the sea level changes are due to the meteorological forcing whilst tidal fluctuations are not directly observable here. The present paper deals with the determination of tides in those shallow water bodies. The aims of this study are to

• quantify the tidal amplitudes in the Baltic Sea and the Gulf of Riga,
• explain how tides are formed there,
• estimate the accuracy of the obtained tidal amplitudes.

The key factors influencing the sea level in the Baltic Sea are meteorological forcing, long-term fluctuations and tidal forcing. The main part of sea-level changes arises from the fluctuations of the atmospheric pressure and from the wind setup [3]. Tidal wave constitutes a small part from the total sea level variations in the Baltic Sea. This fact explains why there is so small amount of literature sources about the tides here. Some estimations of the magnitude of the tidal wave in the Baltic Sea according to the tidal equilibrium theory are given in [9]. There are some investigations about the tidal fluctuations in the Baltic Sea penetrating from North Sea [8]. These fluctuations are vanishing in the spectrum of total oscillations as stated in [8]. The estimates of the tidal amplitudes in different regions of the Baltic Sea are at Copenhagen - 1 cm, at Kiel - 14 cm, at Hanko - 8 cm, and at Kronstadt - 1 cm.
 

2. Description of sea level data, methods of sampling and methods of determination of the tidal magnitudes

The present study deals with the water level data measured at the Latvian coastal gauges from 1977 to 1993. All measurements have been performed using standardised methods of the Hydrometeorological Agency of the former USSR [10]. The sampling frequency and quality of data differ between the different gauges. The most continuous data series with the sampling frequency of 1 hour are at the Liepâja, Daugavgrîva and Lielupe gauges. There are some gaps in the observation series at the other gauges.

The intensities of the tidal constituents have been determined from the time series of the sea level by means of the harmonic analysis. The FFT method has been used to numerically perform the spectral analysis. It is necessary, also, to separate the relatively small magnitudes of tidal constituents in the spectrum of the sea level fluctuations from non-harmonic meteorological influence. This filtering has been performed by moving average filtering method with the characteristic period of 36 hours (longer than period of the lowest tidal frequency (period 25.87 hours)).

Amplitudes of tidal constituents as well as total effective amplitude of sea level fluctuations are obtained from intensities by means of relationship , where A is amplitude (cm) of oscillation, I is intensity (cm²) of oscillation. Intensity of tidal constituent is calculated from spectral intensities of spectral bins with the frequencies close to the frequency of tidal constituent. Number of spectral bins used for such averaging depends on data set. We used averaging over 5 neighbouring bins for the 131072 data points in the dataset.
 

3. Discussion

There are several factors that determine magnitude of the tidal wave in the semi-enclosed water basin. The latitude of the water basin, the type of connection of it with the World Ocean and the shape of the water body are the most important. The semidiurnal tidal components dominate in the low latitudes [1]. With increasing the latitude the diurnal components become dominant [1,2,4,5]. The same should be true also for the Baltic Sea [1].

Two types of tides exist in the semi-enclosed water basins like the Baltic Sea. The first is the induced tide that penetrates from the World Ocean. The second is the tide that is formed inside the water basin itself [6]. The highest magnitudes of the tides are observed when the period of tide is nearly equal to resonance period of the water basin. The Baltic Sea is weakly connected with the North Sea, but its size is large enough to develop its own tidal system. Long-term measurements allow us to perform a spectral analysis of the data to determine even very small tidal harmonic oscillations in the total spectrum of sea-level changes.

The spectrum of the sea-level changes consists of non-harmonic oscillations produced by meteorological factors, harmonical tidal and non-tidal constituents (Fig.1.).

Fig.1. Spectrum of sea level fluctuations at the Latvian coast of the Baltic Sea (Liep?ja).

The obtained intensity of tidal constituents is about 0.5% from the intensity of total sea-level fluctuations. The amplitudes of tidal constituents calculated from obtained intensities (see section 2) for 4 gauging stations are shown in Table 1.
 

Table 1. Magnitudes (cm) of principal tidal constituents at selected observation gauges.
Tidal constituent		Magnitudes, cm
		Post of observation
Name	Period, h	Lielupe	Daugavgriva	Skulte	Liepaja
O1	25.82	1.44	1.67	1.53	0.67
P1	24.07	0.63	0.69	0.44	0.32
S1	24.00	1.03	1.04	0.80	0.47
K1	23.93	1.31	1.55	1.18	0.66
M2	12.42	0.46	0.57	0.46	0.16
S2	12.00	0.14	0.19	0.20	0.15
N2	12.66	0.06	0.11	0.02	0.12
T2	12.02	0.02	0.11	0.02	0.05
2N2	12.91	0.00	0.02	0.02	0.13
K2	11.97	0.02	0.06	0.02	0.08
Other constituents		0.05	0.30	0.05	0.00
Total magnitude		2.34	2.69	2.20	1.14
Magnitude of the total sea level oscillations		37.20	37.70	38.30	33.00

There are higher amplitudes of the tidal oscillations at the Gulf of Riga (Lielupe, Daugavgriva, Skulte) than at the coast of the Baltic Sea (Liepaja, see Table1). There are two explanations of it. (1) The water elevation at the coast of the Baltic Sea is more dependent on meteorological forcing than at the coast of the Gulf of Riga. Spectral noise produced by this forcing does not allow determination of true magnitudes of the tidal oscillations. (2) The tidal wave in the semi-enclosed basins can be higher than in the neighbouring sea or ocean [1,2,6] under some circumstances.

The spectrum of semidiurnal oscillations at the Daugavgriva is shown in Fig.2.

Fig.2. The spectrum of semidiurnal constituents in the Gulf of Riga (Daugavgriva).

Comparison of amplitudes of semidiurnal tidal constituents shows (see Table1) that tidal constituent M₂ in the Gulf of Riga is much higher than other semidiurnal constituents. The semidiurnal constituents in the Baltic Sea, contrary, are nearly equal. It is possible that there exists own M₂ tidal system of the Gulf of Riga. This system is influenced by the M₂ system of the Baltic Sea in such a way that the magnitude of this constituent becomes higher in the Gulf of Riga.

The spectrum of diurnal oscillations at the Daugavgrîva is shown in Fig.3. The amplitude of lunar diurnal constituent (O₁) is the highest among other diurnal constituents at all gauging stations. Nearly equal (except Skulte) to it is the amplitude of lunisolar diurnal constituent (K₁). It was also possible to detect diurnal constituents S₁ and P₁. Their amplitudes are 1.4 to 2 and 2 to 3 times smaller than amplitude of O₁, respectively.

Fig.2. The spectrum of diurnal constituents in the Gulf of Riga (Daugavgriva).

The total intensity of the diurnal constituents is higher than total intensity of semidiurnal constituents by factor 14 (Liepaja) to 22 (Skulte). This factor is higher in the Gulf of Riga than in the Baltic Sea. Ratio of corresponding amplitudes is from 3.7 to 4.7.

The magnitudes of tidal constituents are obtained by summing spectral power in the spectral bins with frequencies near the peak frequency. Accuracy of the results depends on the spread of harmonic oscillations among neighbouring spectral bins. There are higher spectral dissipation rates of the Baltic Sea level fluctuations due to the meteorological factors. Therefore the accuracy of determination the tidal amplitudes in the Gulf of Riga is higher than in Baltic Sea. The lower estimate of tidal intensity can be obtained from the spectral intensity of the spectral bin with frequency exactly equal to frequency of tidal constituent. The upper estimate cannot be directly estimated. We assume that standard deviation of amplitudes from the obtained values is equal to difference between these obtained values (see Table 1) and their lower estimates. Taking above-mentioned reasoning into account the overall obtained tidal magnitudes are 2.5± 0.5 cm in the Gulf of Riga and 1.0± 0.5 cm at the Latvian coast of the Baltic Sea.

The occasional measurements of a temperature at a constant depth in the Gulf of Riga revealed presence of the internal wave with the period equal to semidiurnal tidal period [11]. Simple comparison of internal and surface oscillations according to density difference considerations shows that amplitude of semidiurnal surface tidal component should be about 2 cm. This result corresponds with the magnitudes obtained in the present study from completely different considerations.
 

Conclusions

We can draw the following conclusions about the tidal oscillations in the Gulf of Riga and the Baltic Sea from the present study:

• The tides exist both in the Baltic Sea and the Gulf of Riga. It is impossible to detect these tides in a way of direct sea level measurements due to influence of the meteorological factors. The only possibility is to use the long-term sea level measurement data and to process this data employing spectral analysis.
• The obtained intensity of tidal constituents is about 0.5% from the intensity of total sea-level fluctuations. Effective amplitudes of all tidal water surface level fluctuations are 2.5± 0.5 cm in the Gulf of Riga and 1.0± 0.5 cm at the Latvian coast of the Baltic Sea.
• Intensity of surface tidal oscillations in the Gulf of Riga is higher than in the Baltic Sea.
• Total intensity of diurnal constituents is 14 to 22 times higher than total intensity of semidiurnal constituents. Ratio of corresponding amplitudes is about 4.
• The tidal constituents O₁ and K₁ are the highest among the diurnal constituents both in the Gulf of Riga and the Baltic Sea.
• The amplitude of lunar semidiurnal constituent M₂ are much higher than amplitudes other semidiurnal constituents in the Gulf of Riga. Contrary, at Liepâja (coast of Baltic Sea) the amplitudes of semidiurnal constituents M₂, S₂, N₂, 2N₂ are nearly equal.

Authors owe Viesturs Berzins for the possibility to use the data of the measurements of internal waves in the Gulf of Riga.