Period estimation and using multivariable data analysis methods in Lake Balaton time-series

The time-series ofδ18O values measured weekly in Lake Balaton gave a chance to estimate the period time. To do this, we used a recently worked-out psd estimation method, the Lomb-Scargle periodogram (Lomb 1976, Press et al. 1992), in which the type of distribution can be given exactly to the power values, so confidence interval can be calculated. The result, however, is only a characteristic mean value of the time-interval examined, so the changes of the period-time were examined by demodulation. The essence of the method is that the process (time-series) is let through a filter that is permeable at merely one frequency, all the other frequency components are filtered out, so the difference from the mean period time can be placed in time. We also examined to what extent the water samples coming from one bay of Lake Balaton are representative of the whole lake. Hierarchical clustering was carried out on the hydrobiological and hydrochemical parameters of water samples coming from ten sites of Lake Balaton to determine the similar sampling sites. After the clustering, part of the sampling sites fell into different groups in the examined 16 sampling times. So the groups were marked in all the 16 sampling times with a code that shows to which group that actual sampling site belongs. In this way, each sampling site was placed in a 16-dimension space. Thus, another clustering became possible, so the grouping related to the given time period could be determined. The result was checked by statistical calculations