Sea Level Variations at the Latvian Coastal Hydrologic Stations

GEODESY AND CARTOGRAPHY ISSN 2029-6991 / eISSN 2029-7009 2016 Volume 42(2): 31–38 http://dx.doi.org/10.3846/20296991.2016.1198564

UDK 528.024.8

SEA LEVEL VARIATIONS AT THE LATVIAN COASTAL HYDROLOGIC STATIONS

Diāna HARITONOVA Institute of Geodesy and Geoinformatics, University of Latvia, 19 Raina Blvd., LV 1586 Riga, Latvia Faculty of Civil Engineering, Riga Technical University, 6A/6B Kipsalas street, LV 1048 Riga, Latvia E-mail: [email protected] Received 15 March 2015; accepted 05 June 2016 Abstract. The objective of this paper is to analyse water level variations of the Baltic Sea on the Latvian coast. This is important because the Baltic Sea exhibits a number of remarkable phenomena. One of them is the sea level variations due to winds, complicated by the shape of the gulfs and islands. Under this influence the range of the sea level variations can reach 3 m on the coasts of gulfs. However, the tidal variations of the Baltic Sea range in the order of centimetres only. In the frame of this study, using hourly time series of the sea level records from 7 Latvian coastal hydrologic stations and employing spectral analysis, it has become feasible to identify diurnal and semi-diurnal tide existence both in the Gulf of Riga and in the Baltic Sea at the Latvian coast. Totally 4 main tidal constituents (O1, K1, M2, S2) have been identified. Additionally, non- tidal frequency of 5 cycles per day has been detected in the sea level time series of the stations located in the Gulf of Riga. Keywords: sea level, tide gauge, harmonic analysis of tide.

Introduction shape of the gulfs and islands (Lisitzin 1959; Wübber, Latvia has 500 km long coastline of the Baltic Sea. The Krauss 1979). west coast of Latvia is washed by the open sea up to According to Ekman (2009), the general picture North (Cape Kolka), where meets waters of the Gulf of of the sea level variations in the Baltic Sea can be sum- Riga. The Gulf of Riga is shallow semi-enclosed basin marized in the three following items: separated by Estonia’s Saaremaa Island and connect- (1) short-term sea level variations (on the time ed to the Baltic Sea with two major cannels towards scale of days) – to a limited extent caused by North and West. air pressure variations producing an inverted As the Baltic Sea is a permanently stratified sys- barometer effect; tem, a key physical feature is the deep-water circula- (2) short-term sea level variations (on the time tion and its implications for the overall dynamics. scale of days) – to a larger extent caused by There are still a lot of gaps in understanding of the winds redistributing water within the Baltic physics of the Baltic Sea deep-water dynamics. This Sea, what mainly affects the northern, eastern subject was discussed by several authors, but has been and south-western shores of the Baltic; treated in only a few more recent studies (Elken, Mat- (3) long-term sea level variations (on the time thäus 2008; Matthäus 2006; Meier 2006). The main scale of months and years) – caused by per- problems are different inflows and stagnation periods, sistent winds redistributing water between the water exchange between basins, diapycnal mixing, ed- Atlantic Ocean (the North Sea) and the Baltic dies and entrainment (Omstedt et al. 2014). Sea, what affects the Baltic as a whole. The Baltic Sea mass variation contains a rich The short-term effect on the Baltic Sea level spectrum of different oscillation phenomena (Ruots- caused by a temporary wind is shown in Figure 1a alainen et al. 2015). The wind-driven free oscillation and the long-term effect caused by a persistent wind patterns on the sea surface are complicated by the is depicted in Figure 1b. It should be noted, that the

Copyright © 2016 Vilnius Gediminas Technical University (VGTU) Press 31 http://www.tandfonline.com/tgac 32 D. Haritonova. Sea level variations at the Latvian coastal hydrologic stations short-term variations are mainly internally driven to redistribute mass gives to ocean tides their own dy- variations, with maximum amplitudes in the far north namics. Ocean tide behaviour on any spot on the coast and the far south, and a nodal line close to Stockholm is strongly affected by the shape of the coastline and in the middle. Thus short-term sea level variations are the profile of the seabed. The ocean tides have there- nearly eliminated at this site (Ekman 2009). fore the same spectrum as solid Earth tides, but differ- For example, the range of non-tidal variation is ent amplitude and phase (Doan, Brodsky 2006). up to 2–3 m on the coasts of the Gulf of Bothnia and Ocean tide models are required to calculate the Gulf of Finland (Virtanen, Mäkinen 2003a). However, loading response at a point. Some of them are based the tidal variations of the Baltic Sea range in the order on hydrodynamic modelling and some are based on of centimetres only. satellite altimetry observations. In general, satellite altimetry based ocean tide models are best in open 1. Effect of the ocean tides ocean areas, while models based on sea level station Ocean tides are generated by the same gravitational data and hydrodynamic modelling are best near coast- forces as solid Earth tides, but the ability of the ocean al areas (Khan 2005).

a) b)

Fig. 1. The short-term effect on the Baltic Sea level caused by a temporary wind (a) and the long-term effect caused by a persistent wind (b): continuous line – south-west wind and dashed line – north-east wind (Ekman 2009)

Fig. 2. Diurnal and semi-diurnal tidal groups shown with the frequency axis warped to make each of the groups equal in size. The two lines below the groups show the amplitude spectrum of tidal harmonics in both linear and logarithmic amplitude (Agnew 2013) Geodesy and Cartography, 2016, 42(2): 31–38 33

Ocean tide models are typically developed and gaps in the observation series for desired 3-year pe- distributed as gridded maps of tide height amplitudes. riod – from year 2013 to 2015. Locations of the select- These models provide in-phase and quadrature ampli- ed stations are shown in Figure 3; five stations (Kolka, tudes of tide heights for main tidal frequencies (of 11 Mērsrags, Lielupes grīva, Daugavgrīva and Salacgrīva) tidal constituents: K2, S2, M2, N2, K1, P1, O1, Q1, Mf, are located on the coast of the Gulf of Riga, and two Mm, Ssa) on a variable grid spacing over the oceans (Liepāja and Ventspils) – on the west coast of Latvia, (Petit, Luzum 2010). washed by the open sea. Ocean tide model can be represented as a sum of Sea level data used for this analysis are mean harmonic constituents, which are determined by their values of hour last 15 minutes, in this way having 24 frequencies ωi, amplitudes Ai and phases φi. The total values for each day. Of course, during 3-year period tidal variation is a sum of all the tidal harmonics. The there were some short gaps in the time series of each ocean tide height can be defined as sea level station, mostly 1–3 hour long. To perform NN spectral analysis data were interpolated. In the case of HHot=∑∑ i, ot = A icos( ω i t +ϕ i ) , (1) long gaps, data of whole year have not been used. ii=11 = The Fourier transform with Parzen window w(k) where N is the total number of tidal constituents. has been applied to perform spectral analysis. Sea Figure 2 shows decomposition of diurnal and level time series have been detrended separating non- semi-diurnal constituents and their amplitude spec- harmonic influence. trum. The spectrum of tidal amplitudes on a linear The common formula for computation of the scale indicates higher amplitudes for main diurnal: smoothed spectral density function is Q , O , P , K , and semi-diurnal tidal constituents: − 1 1 1 1 L 1 πlk N2, M2, S2, K2. Rxx ( l) =2 1+= 2∑ rxx ( kwkcos) ( ) , l 0,1 , … , F , k=1 F (2) 2. Data selection and processing where L – window bandwide, Hydrological observations in Latvia are carried out by ck( ) = xx the Latvian Environment, Geology and Meteorology rkxx ( ) (3) cxx (0) Centre (LEGMC). It is maintaining totally 9 coastal is the sample autocorrelation function with the autoco- hydrologic stations on the Latvian coast, which pro- variance function estimate vide continuous observations. nk− For this study observations from 7 sea level sta- 1 cxx ( k) =∑ ( xt −− xx)( t+ k x) . (4) tions have been used. Data from two other stations n t=1 (Roja and Skulte) are not used because there are great For more details refer to (Jenkins, Watts 1968).

Fig. 3. Latvian sea level stations: Liepāja, Ventspils, Kolka, Mērsrags, Lielupes grīva, Daugavgrīva and Salacgrīva 34 D. Haritonova. Sea level variations at the Latvian coastal hydrologic stations

3. Results and discussion More representative picture of the sea level dynamics at the Latvian coast is given by Figure 5, where Time series of the sea level for the mentioned 3-year differences between sea level maximum and minimum observation period are shown in Figure 4. The sea level at the appropriate station are given. Stations in a graph data are given above the gauge zero. As one can see are in consecutive order starting with station Liepāja from this figure, sea level ranging diapason is quite and continuing along the coast till station Salacgrīva. high; it runs up to 2 meters during one year. One more One can observe that sea level differences are obvious fact is that the time series have distinct in- mostly increasing with every next station. Stations crease in the amplitude during the winter season; with Liepāja, Ventspils and Kolka have smallest sea level increasing sea level in early winter and decreasing sea differences in a background of other station data for level in late winter. all 3 years. It can be explained by the fact that sta- This effect was pointed out by Ekman (1998). tions have direct connection to the open sea and Comparing the sea level data with wind data from the their locations are close to the nodal line of the sea Baltic entrance for the whole period 1825–1984 he level variations as in the case of Stockholm station. found that the main origin of the amplitude increase In spite of strong impact of the open sea flows due to is a secular change in the winter wind conditions, wind, short-term variations are nearly eliminated, and with increasing south-westerly winds in early winter long-term sea level variations have mean values as de- and decreasing south-westerlies in late winter (Ekman scribed before and depicted in the Figure 1. 2009).

Fig. 4. Sea level time series of the Latvian coastal hydrologic stations Liepāja, Ventspils, Kolka, Mērsrags, Lielupes grīva, Daugavgrīva and Salacgrīva from year 2013 to 2015

Fig. 5. Differences between sea level maximum and minimum values at 7 Latvian coastal hydrologic stations given for 3 years Geodesy and Cartography, 2016, 42(2): 31–38 35

Additionally, differences between sea level maxi- Totally 4 main tidal waves (O1, K1, M2, S2) have mum and minimum at the stations Liepāja, Ventspils been identified in the spectrum of sea-level changes. and Kolka have more pronounced annual changes in The magnitudes of tidal constituents are given in Ta- comparison with other station data. Explanation of ble 1. this could be annual meteorological conditions of the One can observe that obtained magnitudes Baltic Sea, whose changing is more observable in the of the tidal oscillations at the Gulf of Riga (Kolka, open sea. Mērsrags, Lielupes grīva, Daugavgrīva, Salacgrīva) are According to Wübber, Krauss (1979) the Gulf of higher than at the west coast of Latvia (Liepāja and Riga is of considerable importance for the seiches of Ventspils). Similar results were published by Keruss, the Baltic Sea. The sea level variations in the interi- Sennikovs (1999), where they used considerably lon- or areas of the gulfs behave like standing waves; this ger sea level time series from 4 Latvian coastal hydro- holds for the Gulf of Riga as well. It exhibits the high- logic stations. The explanation of this effect is follow- est amplitudes, what seems to be due to a cooscillating ing: sea level changes at the coast of the Baltic Sea are mode of this basin. Sea level stations Lielupes grīva, more dependent on meteorological forcing than at the Daugavgrīva and Salacgrīva are more eastern stations coast of the Gulf of Riga; spectral noise produced by of the Gulf of Riga. Sea level differences at these sta- it prevents from identifying of true magnitudes of the tions show the highest values, what absolutely corre- tidal oscillations. sponds to the previous statement. As can be seen from the Table 1 magnitudes of Results obtained after spectral analysis are shown tidal constituents are not the same comparing values in Figures 6 and 7. There spectral density functions for each year. This also can be explained by changing for time series of the sea level at the Latvian coastal meteorological conditions of the Baltic Sea, which af- hydrologic stations for each year are depicted. fected sea level time series.

Fig. 6. Spectral density functions for time series of the sea level at the Latvian coastal hydrologic stations: Liepāja, Ventspils and Kolka (cpd – cycles per day) 36 D. Haritonova. Sea level variations at the Latvian coastal hydrologic stations

Fig. 7. Spectral density functions for time series of the sea level at the Latvian coastal hydrologic stations: Mērsrags, Lielupes grīva, Daugavgrīva and Salacgrīva (cpd - cycles per day)

Table 1. Magnitudes (cm) of main tidal constituents at the Latvian coastal hydrologic stations. Frequency is given in cycles per day.

Tidal constituent O1 K1 M2 S2 Frequency, cpd 0.930 1.002 1.932 2.000 Years 2013 2014 2015 2013 2014 2015 2013 2014 2015 2013 2014 2015 Liepāja 0.52 0.69 0.61 0.51 0.48 0.75 0.20 0.19 0.28 0.18 0.19 0.18 Ventspils 0.60 0.72 0.67 0.58 0.42 0.61 0.53 0.53 0.59 0.18 0.15 0.14 Kolka 1.36 1.35 – 1.04 0.87 – 0.39 0.37 – 0.11 0.09 – Mērsrags 1.50 1.47 1.53 1.22 0.96 1.49 0.53 0.56 0.55 0.18 0.16 0.15 Lielupes grīva 1.38 – 1.49 1.08 – 1.51 0.47 – 0.51 0.14 – 0.06 Daugav-grīva 1.50 1.49 1.63 1.22 1.18 1.66 0.53 0.57 0.62 0.18 0.11 0.11 Salacgrīva 1.55 1.58 – 1.23 1.01 – 0.33 0.38 – 0.14 0.10 – Geodesy and Cartography, 2016, 42(2): 31–38 37

Fig. 8. Magnitudes of main tidal constituents at the Latvian coastal hydrologic stations

Figure 8 represents mean magnitudes of tidal of Riga and in the Baltic Sea. 4 main tidal waves (O1, constituents obtained from values given in the Table 1. K1, M2, S2) have been identified. Magnitudes of the The magnitude of diurnal constituent O1 is the highest tidal oscillations in the Gulf of Riga are higher than in for all stations. Close to it is the magnitude of diurnal the open sea. Furthermore, the power at the frequency constituent K1, excepting two stations Salacgrīva and of 5 cpd has been detected for stations in the Gulf of Kolka, which are more northern Latvian stations in Riga, which could represent some local effect. the Gulf of Riga. Interesting that magnitude of diurnal Spectral analysis of one year sea level data allows constituent K1 is practically equal to the magnitude of determination of 4 main tidal waves. To identify more semi-diurnal constituent M2 at the station Ventspils. tidal constituents it is necessary to use long-term sea Comparing semi-diurnal constituents, magnitude of level observations. M2 is 3–5 times higher than magnitude of S2, but not in the case of station Liepāja, where these magnitudes References are sub-equal. Agnew, D. C. 2013. Baytap08 User’s Manual. Additionally, spectral density functions in Fig- Doan, M.-L.; Brodsky, E. E. 2006. Tidal analysis of water level ure 7 show explicit power at the frequency of 5 cpd. in continental boreholes, version 2.2. Santa Cruz: University This frequency doesn’t correspond to the tidal fre- of California. quency. Magnitude of this oscillation is not consid- Ekman, M. 1998. Secular change of the seasonal sea level varia- erable; it is about 1 mm, but interesting that this is tion in the Baltic Sea and secular change of the winter cli- typical only for stations Mērsrags, Lielupes grīva and mate, Geophysica 34: 131–140. Daugavgrīva. As these sea level stations are located Ekman, M. 2009. The changing level of the Baltic Sea during 300 years: a clue to understanding the earth. Summer Institute for relatively close together in the Gulf of Riga, the power Historical Geophysics. could represent some local effect. Elken, J.; Matthäus, W. 2008. Annex A: physical system descrip- tion, in The BACC Author Team (Ed.). The BALTEX As Conclusions sessment of climate change for the Baltic Sea basin. Springer- Verlag, 379–398. Observations of 3-year long period have shown that Jenkins, G. M.; Watts, D. G. 1968. Spectral analysis and its ap- the sea level ranging diapason is quite high in the Gulf plications. Holden-Day.Keruss, M.; Sennikovs, J. 1999. De- of Riga; it runs up to 2 meters during one year at the termination of tides in Gulf of Riga and Baltic Sea, in Pro ceedings of International Scientific Colloqium ‘Modelling of Salacgrīva station. In the case of stations located on the Material Processing’, 28–29 May 1999, Riga, Latvia. west coast of Latvia (Liepāja and Ventspils) and sta- Khan, S. A. 2005. Surface deformations analyzed using GPS time tion Kolka this diapason is not so high, but differences series: Thesis for PhD degree. University of Copenhagen, between sea level maximum and minimum here have Niels Bohr Institute for Astronomy, Physics and Geophysics. more pronounced annual changes in comparison with Lisitzin, E. 1959. Uninodal seiches in the oscillation system Bal- tic proper, Gulf of Finland, Tellus 4: 459–466. other station data. Matthäus, W. 2006. The history of investigation of salt water in The spectral analysis of the sea level data from flows into the Baltic Sea – from the early beginning to recent the Latvian coastal hydrologic stations has shown di- results. Marine Science Reports, 95. Baltic Sea Research In- urnal and semi-diurnal tide existence both in the Gulf stitute, Warnemünde, Germany. 38 D. Haritonova. Sea level variations at the Latvian coastal hydrologic stations

Meier, H. E. M. 2006. Baltic Sea climate in the late twenty-first Diāna HARITONOVA. Researcher at the Institute of Geodesy century: a dynamical downscaling approach using two glob- and Geoinformatics, University of Latvia, 19 Raina Blvd., Riga, al models and two emission scenarios, Climate Dynamics LV 1586, Latvia (Phone: +371 67034435), e-mail: diana.hari- 27(1): 39–68. http://dx.doi.org/10.1007/s00382-006-0124-x [email protected]. (Mg.sc.ing. 2012). PhD student at Riga Tech- Omstedt, A.; Elken, J.; Lehmann, A.; Leppäranta, M.; Mei- nical University, the Faculty of Civil Engineering. Research er, H. E. M.; Myrberg, K.; Rutgersson, A. 2014. Progress interests: analysis of GNSS station time series, Earth’s surface in physical oceanography of the Baltic Sea during the displacements, harmonic tidal analysis. 2003–2014 period, Progress in Oceanography 128: 139–171. http://dx.doi.org/10.1016/j.pocean.2014.08.010 Petit, G.; Luzum, B. 2010. IERS Conventions (2010). Technical Note No. 36, IERS Conventions Centre. Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie. Ruotsalainen, H.; Nordman, M.; Virtanen, J.; Virtanen, H. 2015. Ocean tide, Baltic Sea and atmospheric loading model tilt comparisons with interferometric geodynamic tilt observation – case study at Lohja2 geodynamic station, southern Finland, Journal of Geodetic Science 5: 156–162. http://dx.doi.org/10.1515/jogs-2015-0015 Virtanen, H.; Mäkinen, J. 2003a. The effect of the Baltic Sea level on gravity at the Metsähovi station, Journal of Geody namics 35(4–5): 553–565. http://dx.doi.org/10.1016/S0264-3707(03)00014-0 Wübber, Ch.; Krauss, W. 1979. The two-dimensional seiches of the Baltic Sea, Oceanologica Acta 2(4): 435–446.