Variations in parameters of extreme value distributions of water level along the eastern Baltic Sea coast

Time series of water level at several sites of the eastern Baltic Sea contain statistically almost impossible outliers. Their presence may considerably modify the appearance of the relevant extreme value distributions. We analyse systematically the variation in the parameters of the Generalised Extreme Value (GEV), Gumbel and Weibull distributions for extreme water levels along a 600 km coastal stretch in the north-eastern Baltic Sea. The parameters of the distributions are evaluated using a) three different methods, b) the output of two different ocean models and c) two versions of block maxima (for calendar years and for stormy seasons), and compared with similar parameters retrieved for measured water level time series at five sites. The location and scale parameters of GEV and Gumbel distributions vary smoothly by about +/- 30% from their average values. The variation is modest along the open shores of the Baltic Sea proper. All these parameters increase almost linearly along the southern coast of the Gulf of Finland. The absolute values of the shape parameter of the GEV distribution are mostly < 0.2. Different methods for evaluation lead to values of the same magnitude but with a different sign on the open shores of the Baltic Proper. This feature indicates that extreme water levels may follow radically different extreme value distributions in different locations of semi-enclosed seas.