A long-term trend, fluctuations and probability of the sea level at the southern Baltic coast

Transcription

1 Journal of Coastal Research SI pg - pg 259 ICS2011 (Proceedings) Poland ISSN A long-term trend, fluctuations and probability of the sea level at the southern Baltic coast B. Wiśniewski and T. Wolski Faculty of Navigation, Faculty of Geosciences Maritime University, University of Szczecin, 70- Szczecin, Poland 70-8 Szczecin, Poland natal@univ.szczecin.pl natal@univ.szczecin.pl ABSTRACT Wiśniewski B. and Wolski T., A long-term trend, fluctuations and probability of the sea level at the southern Baltic coast Journal of Coastal Research, SI 64 (Proceedings of the 11th International Coastal Symposium),. Szczecin, Poland, ISSN It is of utmost importance to monitor sea level fluctuations so that processes and effects in the coastal zone are understood, their adverse consequences are adequately forecast, and appropriate preventive measures be taken, if possible The aim of the study was the analysis of the series of data on sea levels on the Polish coast. The least squares is used to identify trends in multi-annual variability of the sea level. Fourier spectral analysis one used for the determine of cycles of water levels oscillations. In analyses of the probability of maximum sea levels one used Gumbel and Pearson III the type distribution The Polish Baltic coast shows a variability in the rate of mean sea level changes. In the recent 60 years of continuous observations ( ), the differences between the rates determined for different parts of the coast ranged from 1.0 (western part) to 2.5 mm/yr (eastern part). The variability in the rate of sea level changes at the Polish coast is evidenced also by the spectral analysis revealing considerable fluctuations and cyclicities: a distinct -yr cycle and somewhat weaker cycles of,, and years. The obtained results theoretical sea levels and their probabilities of occurrence can be considered reliable because of the long observation series of sea levels. ADDITIONAL INDEX WORDS: Sea level rise, Cycles, Gumbel s distribution INTRODUCTION As proposed in the current climatological literature, the global climate is rapidly warming, and effects are made to pinpoint anthropogenic effects (increased atmospheric concentration of CO 2 and other glasshouse gases via fossil fuel combustion) as the underlying causes. Evidence of the changes is sought also in areas other than the global atmospheric temperature increase, a rise in the sea level being used as such additional support. The report published by the Nongovernmental International Panel on Climate Change (NIPCC 2008) has summarised opinions on the causes of the sea level rise presented by the four IPCC reports of 1990, 1995, 2001, and All those reports refer to meltdown of mountain glaciers, small icecaps, gigantic icecaps of Greenland and Antarctic, and thermal expansion. The reports contain the following, gradually decreasing, maximum estimates of the sea level rise by 20: 67 (IPCC of 1990), 124 (IPC of 1995), 77 cm (IPCC of 2001), and 59 cm (IPCC of 2007). The Commission on Sea Level Changes and Coastal Evolution of the International Union for Quaternary Research (INQUA) has presented different forecasts of changes in the sea level. As shown by measurements taken in Europe, the sea level was raising by 1.1 mm/yr between 1850 and 1940, but the increase stopped after 1940 by 20, the sea level may increase by 5- cm (Mörner 2004). In the publication one analysed series of data on sea levels on the Polish coast. A research purpose of the work is the identify of trends in multi-annual variability of the sea level for marine and lagoons Polish watergauge stations. A second, additional purpose of the work is separation of cycles mean and maximum sea levels and the determine of the occurrence probability of maximum sea levels on the Polish coast. MATERIALS AND METHODS Uniform series of data on the sea level, used in this work, were collected at the Polish coastal water gauge stations in Świnoujście, Kołobrzeg, Ustka, Władysławowo, Hel, Gdynia, and Gdańsk. Additionally, the analysis includes data from shore stations in the lagoons (Tolkmicko in the Vistula Lagoon and Trzebież in the Szczecin Lagoon) as well as from Szczecin, as changes in water level at those stations may be associated with effects of sea level variability. Analysed data are annual mean and maximum annual sea levels from different time series of data put together by Wiśniewski and Wolski (2009) on the basis published in Poland of bulletins and yearbooks of the Institute of Meteorology and Water Management. For the purpose of this work, the data were standardised to a single water-level gauge datum, i.e., - cm N.N. (normal zero) for the Polish coast. The least squares is used to identify trends in multiannual variability of the sea level. Fourier spectral analysis one used for the determine of cycles of water levels oscillations. In analyses of the probability of maximum sea levels one used Gumbel s and Pearson s III the type distribution. 255

2 A long-term trend, fluctuations and probability of the sea level at the southern Baltic coast Fourier spectral analysis Spectral analysis is used to explore the harmonic structure of a time series. It decomposes a complex time series, containing cyclic components, into a number of basic sine and cosine functions with defined wavelengths (frequencies) to identify those particularly strong or important. The sine and cosine functions are independent of each other (orthogonal); therefore, to obtain a periodogram, squared coefficients for each frequency (period) can be added. Values of the periodogram used were calculated as: P k = sin 2 k * cos 2 k * N/2 (1) where: P k is a value of periodogram at frequency k and N is the length of the series. The analysis was preceded by elimination of linear trend and arithmetic mean from the observation series, as the two effects, potentially strong, might have masked the more interesting periodic changes Occurrence probability of theoretical, maximum sea levels Calculations of exceedance probability of water levels consist in appropriate selection of theoretical probability distributions and next in assumption of estimation s of parameters of a selected distribution, with the use of statistical data. Credibility of such estimation depends both on length of water level observation series and representativeness of a chosen theoretical probability distribution function. Hence for Kołobrzeg the observed water levels from the years of were at one s disposal, for Świnoujście from the years of , for Gdańsk from the years of Confirmation of the fact whether the distribution has been properly selected can be obtained by using the tests of goodness of fit, proposed in the literature. Calculation results are given together with a confidence interval within which real variable value can be found with a given probability. In this work Pearson s distribution and Gumbel s one was used and from among the applied s the quantile one and that of highest likelihood was selected as recommended for the determining of occurrence probability of extreme hydrological phenomena such as water flow rates and water levels In this work consistency of the assumed theoretical distribution with empirical one was examined with the use of Kołmogorow consistency test. (Kaczmarek 1970, Massel 1992,). The Gumbel s distribution The Gumbel s distribution density function is based on statistical distributions of extreme values, which occur in certain larger sets of values. For instance it can be maximum values of sea levels considered in this paper. The Gumbel s distribution density function is double exponential and described by the formula (Gumbel 1958): 1 x bˆ x bˆ f (x) = e e (2) aˆ aˆ a where: â - scale parameter (it determines dispersion of the distribution along x- axis), bˆ - location parameter (it determines location of the distribution on x-axis) e - Napierian base Essence of estimation of the assumed distribution against given measurement data is to determine estimators of the distribution parameters â and bˆ. Pearson s distribution of type III. In hydrology Pearson s distribution is used most often. Its type III has found the widest application to equalization of series of numerical features of hydrological phenomena. The density function of Pearson s rd type distribution is of the following form (Kaczmarek 1970): f (x) = λ α Γ(λ) e α(x ε) ( ) λ x ε 1 where: α, ε, λ distribution parameters which should satisfy the following conditions: x ε (lower limitation of the distribution), α> 0, λ > 0 Γ(λ) gamma function of the variable λ RESULTS AND DISSCUSION Secular mean sea level trends in Świnoujście, Kołobrzeg, and Gdańsk The secular trends in changes and fluctuations of sea level at the Polish coast is well represented in a series of annual mean sea levels in: Świnoujście from the years , Kołobrzeg from the years of and Gdańsk from the years of These are the longest series of observation data at the Polish coast. Secular trends can be identified at other stations as well, but there they are based on shorter observation data series. From calculated values of trends results the sea level rise is 0.45 mm/yr in Świnoujście, 0.5 mm/yr in Kołobrzeg and 1.6 mm/yr in Gdańsk. The trends obtained turned out to be repeatedly lower, of the optimistic scenario of the coastal protection strategy developed for the Polish coast (Cieślak 2005). In addition to the differences in the magnitude of the increase, of interest is the appearance of cyclic fluctuations in the sea levels, observed with 11-yr moving averages assigned to the consecutive terms of the observation series of the annual mean sea levels. One can suppose, with exists the cycle year, next year and last year (Figure 1) which then the cycle appears on all stations (Figure 2). This cycle has distinct coherences showing on their probable common reason which are climatic changes. Results shown in Figure 1 for Świnoujście may also be interpreted differently: the >0-yr cycle of is more important, and it may be repeated in , but the confirmation is postponed until the 200s Świnoujście () y = x R 2 = Figure. 1. Changes of the mean sea level in Świnoujście in (straight line - linear trend; curve - 11-yr moving average) 256

3 Wiśniewski and Wolski Świnoujście, Kołobrzeg and Gdańsk Kołobrzeg Świnoujście Gdańsk Figure. 2 Changes of the mean sea level (11-yr moving average) in Świnoujście, Kołobrzeg and Gdańsk in Sea level trends at the Polish coast in Analysis of annual mean and maximum annual sea levels during the observation period of made it possible to include data for more stations along the Polish coast (Table 1). Table 1: The trends value of sea level in the homogenous observation series of at the major observation stations of the Polish coast sea level The trend value [mm/yr] increase [cm] Maximum sea level The trend value [mm/yr] increase [cm] Szczecin Trzebież Świnoujście Kołobrzeg Ustka Władysław Hel Gdynia Gdańsk Tolkmicko Values of the linear trend in the mean annual sea level for the recent 60 years show the level to have been raised by 0.8 mm/yr (8 cm/0 years) in Szczecin to 2.5 mm/yr (25 cm/0 years) in Gdańsk. Generally, the results support the finding, known from the literature, about a slightly accelerated mean sea level rise along the southern Baltic coast in the second half of the 20th century (Dziadziuszko and Jednorał 1988) It is proposed to estimate secular and multi-annual trends also for the maximum and minimum annual sea levels in Świnoujście ( ), Kołobrzeg ( ) and Gdańsk ( ). With respect to the maximum annual sea level, the changes range from mm/yr (Kołobrzeg) to mm/yr in Gdańsk, the changes in the minimum annual sea levels varying from mm/yr (Świnoujście) to 1.56 mm/yr (Gdańsk). However in the recent 60 years ( ), the rate of changes of the maximum sea level clearly accelerated: linear trends of the maximum annual sea level at those stations ranged from 4. mm/yr (Świnoujście) to 5.7 mm/yr (Gdańsk), which is a result of an increasing number of intensity of storm surges (Majewski 1986, Kałas 199, Rotnicki and Borzyszkowska 1999, Wiśniewski and Wolski 2009) In addition to the global warming effect on the sea level, the latter may be also affected by changes in the Earth s geoid, global isostasy, rotational mass distribution in the Earth s interior and in the world s oceans, extensive fluctuations in oceanic currents, sedimentation in the oceans, etc. In addition, local vertical movements of the Earth s crust at the coast may have importantly affected the trends observed as well Significant cycles in sea level changes at the Polish coast Significant cycles in the annual mean and maximum annual sea level in at the observation stations are shown in Table 2 and at the station Kołobrzeg in Figure Table 2: Significant cycles in sea level changes at the Polish gauge stations, as determined for the observation series Szczecin Świnoujście Values of the periodogram Ustka Hel Gdańsk () sea level (4,6) Cycles (years) Maximum sea level Trzebież Kołobrzeg Władysaw. Gdynia Tolkmicko Kołobrzeg Cycles (years) Maximum sea level sea level Period (years) Figure. Spectral analysis of annual mean sea levels in Kołobrzeg in ; values in parentheses denote the length (years) of significant cycles

4 A long-term trend, fluctuations and probability of the sea level at the southern Baltic coast As shown by spectral analysis of annual mean sea levels, all the gauge stations at the Polish coast show a single distinct -yr cycle as well as secondary cycles (of,, and years) which are more or less clearly visible at different stations. However for maximum sea levels appears one distinct cycle 2.- years and secondary cycles -years and -years. Thus, results of the analysis evidence fluctuations in the long-term sea level data series which change the nature of the long-term trend. The frequencies of the cycles identified are consistent with the cyclicity of changes in the Baltic Sea level reported by other authors (Wiśniewski 1978, Wróblewski 1992, Kożuchowski Stolarczuk, Wiśniewski 1994) Results of theoretical maximum sea levels for particular observation stations and probabilities of their occurrence The best adjusted to long-term observation series are the theoretical maximum sea levels and their occurence probability determined by means of the Gumbel s distribution and maximum likelihood. The so-calculated highest theoretical sea levels which can occur once a 00 years, 200 years, 0 years and 50 years are given in detail in Table through 5. From the results it can be concluded that the highest of them will occur and did really occur in Polish west - coast ports, i.e. Kołobrzeg and Świnoujście.. For instance in the station of Kołobrzeg the water level of 750,2 cm, i.e. 2,5 m above the average mean sea level, should be expected once a 00 years (zero points of Polish water level indicators are based on the Amsterdam s zero-level equal to - N.N.). Świnoujście (with 72,6 cm) and Gdańsk (with 716,7 cm) are the successive stations in which the maximum thousandyear levels can be expected. Other occurrence probabilities can be also considered. Graphical representation of the relations is presented in Figure 4 at Gdańsk station. As already mentioned, due to its characteristics Gumbel s distribution has been considered the closest to empirical one. Its advantage results from lack of lower limitation of variability range of the random variable X, among estimated parameters. Estimation of lower or upper limitation of Pearson s distribution (x 0%, or x 0% ) faces serious difficulty due to a subjective way of its determination (Byczkowski A. 1996, Ozga-Zielińska and Brzeziński 1997). Table. Theoretical maximum sea levels and probability of their occurrence at Kołobrzeg observation station in the period of years % % % % % % % % metod - maximum likelihood Table 4. Theoretical maximum sea levels and probability of their occurrence at Świnoujście observation station in the period of years % % % % % % % % Table 5. Theoretical maximum sea levels and probability of their occurrence at Gdańsk observation station in the period of years ] m e v l[c a le se % % % % % % % % Observed Theoret. 95% CI Gdansk, Gumbel Distribution, Method F (%) T (yr) Figure. 4 Occurrence probability of maximum yearly sea levels at Gdańsk in the period of years (Gumbel s distribution, maximum likelihood ) On the basis of comparison of both s of estimation and determination of distribution parameters it can be concluded that 258

5 Wiśniewski and Wolski the maximum likelihood makes it possible to obtain more precise results as in this - in contrast to the quantile to use interpolation of distribution parameters is not necessary.consistency of the assumed theoretical distributions and empirical one was checked by means of the Kołmogorow test Results of the test calcultations do not lead to rejection of the assumed hypothesis on consistency of the distributions In Polish subject-matter literature the s of determination of probability of extreme sea levels were described in the publications of Wróblewski, (1975, 1992), Cyberski and Wróblewski (1999), Massel (1992), Wiśniewski and Wolski (2009). From the comparison of the results of the theoretical sea levels for Gdańsk observation station, obtained by these authors by using the maximum likelihood and Gumbel s and Pearson s distributions, with those determined by Wróblewski (1975, 1992), the difference from several up to a dozen or so centimeters for different quantiles, can be observed. The differences are mainly caused by a different way of determination of the lower limitation of the distribution and also the different length of observation series. CONCLUSION 1. The observation series of annual mean sea levels in Świnoujście, the longest at the Polish coast, shows the secular trend for to amount to 0.44 mm/yr, i.e., the sea level was rising by about 4.5 cm/0 years. In Kołobrzeg, the secular linear trend of mean annual sea level was 0.5 mm/yr in , 1.57 mm/yr being the trend in Gdańsk during The Polish Baltic coast shows a variability in the rate of annual mean sea level changes. In the recent 60 years of continuous observations ( ), the differences between the rates determined for different parts of the coast ranged from 1.0 (western part) to 2.5 mm/yr (eastern part). For next of 0 years the sea level at the Polish coast probably will increase from to 25 cm 2. Analysis of the relatively long observation series on annual extreme sea levels in Świnoujście, Kołobrzeg, and Gdańsk showed the amplitude between the maximum and minimum annual sea levels to have increased, the secular linear trend of the maximum sea level increasing by 0.6 to 2. mm/yr. However in the recent 60 years ( ), the rate of changes of the maximum sea level clearly accelerated: linear trends of the maximum annual sea level at those stations ranged from 2. mm/yr (Tolkmicko) to 5.7 mm/yr (Gdańsk), which is a result of an increasing number of intensity of storm surges. The variability in the rate of mean annual sea level changes at the Polish coast is evidenced also by the 11-yr moving average (which follows a cycle of rise and drop) and by the spectral analysis revealing considerable fluctuations and cyclicities: a distinct -yr cycle and somewhat weaker cycles of,, and years; perhaps also a half-century and 0 yr. cycles occur as well. However for maximum annual sea levels appears one distinct cycle 2.-years and secondary cycles - years and -years 4. The obtained results can be considered reliable because of the long observation series of sea levels, especially those for Kołobrzeg ( ), Świnoujście ( ) and Gdańsk ( ),. Once a 00 years the sea levels: cm in Kołobrzeg, 72.6 cm in Świnoujście and 71 cm in Gdańsk should be expected. Large (upper) values of the observed sea level series are due to storm swellings and their impact on sea coast. The occurrence probability of high sea levels determined in this work for polish stations (ports) Kołobrzeg, Świnoujście,, and Gdańsk can be used in designing the coastal hydro-engineering buildings as well as in managing the costal zone and inudation areas during storm and flood phenomena. LITERATURE CITED Byczkowski A., Hydrology. Vol. I, Warszawa, Wydawnictwo SGGW, p.416 [in Polish] Cieślak A., The strategy of the protection of shore In: FURMAŃCZYK K. (ed.) ZZOP w Polsce, - stan obecny i perspektywy. Szczecin, Wyd. IN PLUS, pp [in Polish] Cyberski J., Wróblewski A., Recent and forecast changes in sea level along the Polish Coast during the period In: Quaternary Studies in Poland, Special issue, OWN Poznań pp Dziadziuszko Z. Jednorał T., Variations of sea level at the polish Baltic coast. Studia i Materiały Oceanologiczne, 52, [in Polish with Engl. summ.] Gumbel, E.J Statistics of Extremes. New York: Columbia University Press, 95p. 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