(a) Time series of OBS (black), ATM (blue) and RES (red) at the tide gauge of Cuxhaven over the period from 1871 to 2011. The location of the tide gauges is shown in (b) with Cuxhaven marked in red. Wavelet coherence plots (Morlet wavelet) of ATM and RES versus OBS are shown in (c,d). The black lines show the 5% significance level using the red noise model. The corresponding global power spectra for OBS, ATM and RES inferred from a fast Fourier transformation are shown in (e,f). Fluctuation functions estimated with DFA2 for OBS, ATM and RES, respectively. The grey dotted lines mark the time window (13≤s≤423 months) for which the Hurst exponents α were estimated. The black dotted line marks a Hurst exponent α of 0.5, that is, uncorrelated noise.