3.2. Probability density functions
To examine both high- and low water levels and their occurrence in the Rhine–Meuse channel network in high detail, probability density functions of water level records have been calculated. To detect changes inwater level distribution through time, four centroids labeled C1 through C4 were determined corresponding to adjacent segments in a , separated by the two peaks and one local minimum in a pdf of a tidal signal. When the tidal amplitude decreases, the two peaks of the pdf approach each other, and so do the centroids C2 and C3. When tidal amplitudes are negligible, the pdf is single-peaked, and only the two centroids C1 and C4 are calculated. The two centroids in a single peaked pdf are considered to correspond to the two centroids of the segments including the tails of the distributions in the double peaked. Using this method, the characteristics of a pdf can be only substantial, sudden changes in mean water level occur at stations along the Haringvliet, as a result of the closing of the estuary. When looking at of water levels, and the trends in corresponding centroid parameters, two types of changes can be distinguished. Southern stations display a shift in pdf type between 1940 and 2010. Water levels have been severely affected by the closure of the Haringvliet and Hollandsch Diep estuaries. The reduction of tidal influence in the southern estuaries causes the double-peaked pdf to change to a single-peaked,with only two centroids to parameterize the pdf. Therefore, the trends in the position of the centroid have been split in two periods: the first period before closure of the Haringvliet, 1940– 1970, the second period after the closure, 1970–2010. The trends in centroid parameters vary for C1 to C4 and throughout the system (Figs. 7 and 8). For the stations close to sea, the trend in high water parameter for water level C4 can exceed the sealevel rise, meaning that not only water levels increase, but also their occurrence. For inland stations, C4 shows a smaller rate of increase ormay even feature a negative trend, displaying a decrease in level and occurrence of high water. The statistics for two nearby stations can be very different. For example, Hoek van Holland and Rotterdam are located approximately 25 km apart. In Hoek van Holland, C3 and C4 rise fastest, while for Rotterdam C1 and C2 show the largest increase. This result implies that rising mean water levels do not directly translate into rising highor low water levels.