Probabilistic Assessment of Correlations of Water Levels in Polish Coastal Lakes with Sea Water Level with the Application of Archimedean Copulas

Abstract

The hydrology of coastal lakes differs significantly from that of inland water bodies due to the influence of the neighboring sea. Observed climatic changes are expected to enhance the effect of the sea on coastal lake ecosystems, which makes research on sea-lake interactions even more significant. In this study, on the basis of maximum annual and monthly values of water level, dependencies among the water levels of six lakes located along the southern coast of the Baltic Sea in Poland, and the Baltic Sea water levels were analyzed. First, the Spearman rank correlation and the linear regression method were applied. Then, selected copulas were used to find joint distributions of the studied time series. In the next stage, the degrees of synchronous and asynchronous occurrences of maximum water levels in lakes and the sea were calculated. The study revealed that correlations between the maximum annual water levels in coastal lakes and in the Baltic Sea in the selected gauge stations were very strong and statistically significant. These results were confirmed by a synchronicity analysis carried out with the help of a copula function. The highest relationship was detected in the case of Lake Resko Przymorskie (correlation coefficient 0.86, synchronicity 75.18%), while the lowest were observed in Lakes Jamno (0.62 and 58.20%, respectively) and Bukowo (0.60 and 56.82%, respectively). The relation strength between maximum water levels of the sea and coastal lakes may increase in the future due to sea level rises caused by climate warming.Coastal lakes are characterized by complex water circulation related to their location at the interface of two "environments", sea and land, and they supply marine waters and river waters from inland areas. Research on coastal lakes in Poland and in the world has covered issues concerning, among other things, the chemistry/quality of water (including its salinity) [7][8][9][10][11][12][13], the development of lakes in the Holocene [14], the trophic status of lakes in the Holocene [15], biodiversity [16][17][18][19][20], sea water intrusions [4,21,22], and ice phenomena [23]. All of these said studies have confirmed the effect of the sea on the aforementioned properties of lakes.Water level fluctuations in lakes have various characteristics and causes. Water level changes, their scale, dynamics, and change tendencies depend on natural [24][25][26] and anthropogenic [27,28] factors [29]. In the case of coastal lakes, more dynamic changes in water levels are observed than in the remaining lakes. This is related to the effect of the Baltic Sea [30][31][32][33][34]. Research on the water level regime in lakes in North Poland has shown that coastal lakes constitute a separate type [35][36][37]. They are lakes with considerable mean annual amplitudes exceeding 100 cm [35], and according to Reference [36], they show a four-period rhythm of seasonal water level variability determined by atmospheric circulation and the hydrodynamic state of the Baltic Sea. In a classification of lakes through val...

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