Our time series contained several data gaps. Small gaps of at most one data point were filled by linear interpolation. Larger gaps could not be filled by interpolation without affecting the results. Therefore, we calculated separate wavelet power spectra for all subsets of the time series with a sufficient number of consecutive data points. Wavelet analysis can accurately detect periodicities up to ,25% of the length of a time series [28]. Subsets of time series were therefore included in the analysis only if they contained .100 consecutive hours for the hourly averaged data, and .60 consecutive days for the daily averaged data. Global wavelet power spectra of time series were obtained by averaging the local wavelet power spectra at each individual time point over all time points included in the analysis [27]. Results The Data Time series of water level, chlorophyll, SPM, nitrate, light intensity, temperature and salinity all displayed strong variability at several different time scales (Fig. 2; Figs. S2, S3, S4, S5, S6, S7, S8, S9). Water level fluctuated at the 12 hour 25 min periodicity of the semidiurnal tidal cycle and the 15-day periodicity of the spring-neap cycle (Fig. 2A). The spring-neap cycle is further illustrated by the time series of the tidal range (difference between high and low tide; blue line in Fig. 2A). SPM concentrations showed considerable within-day variability as well as biweekly fluctuations associated with the spring-neap tidal cycle (Fig. 2B). At the seasonal time scale, SPM concentrations reached higher values in winter than in the summer months. Likewise, the chlorophyll concentration also displayed daily and biweekly fluctuations. The chlorophyll concentration gradually built up over several spring- neap tidal cycles in March-April, resulting in a spring bloom when the SPM concentration strongly declined in mid May (Fig. 2B). The phytoplankton species composition was determined once per month, and consisted of a wide variety of diatoms, dinoflagellates and small flagellates (including Phaeocystis). Most abundant were chain-forming diatoms (e.g. Chaeotoceros, Skeletonema, Paralia, Guinardia and Eucampia), and benthic diatoms (e.g. Cylindrotheca, Plagiogrammopsis and Navicula). Light intensity (PAR) at 1 m depth followed the expected seasonal pattern, but with distinct daily and biweekly variation (Fig. 2C). High light intensities coincided with low SPM concentrations at neap tide. The light attenuation coefficient (Kd), calculated from PAR measurements at 1 m and 2 m depth, fluctuated in phase with the SPM concentration (Fig. S10). Hence, the SPM concentration can be used as proxy of the turbidity of the water column. The nitrate concentration was highest in winter and early spring, was depleted during the spring bloom in mid May, and remained relatively low during summer (Fig. 2C). Salinity displayed considerable interannual variability (Figs. S2, S3, S4, S5, S6, S7, S8, S9). The timing of the reductions in salinity coincided with neap tides and often with enhanced nitrate concentrations (Fig. 2C,D), indicative of an enhanced influence of nutrient-rich freshwater from the river Thames. Temperature showed a clear seasonal pattern, superimposed by short-term temperature vari- ability (Fig. 2D). The time series all showed several gaps. During these periods observations were lacking or unreliable, due to technical problems or fouling of the sensors. The Tidal Cycle We first analyzed the tidal data measured at station Sheerness (Fig. 3). In line with expectation, wavelet analysis reveals a significant 12-hour periodicity in water level throughout the year (Fig. 3B). This is further illustrated by the global wavelet power Dancing with the Tides spectrum, which has a pronounced peak at a 12-hour periodicity (Fig 3C). The tip of the peak is located at a periodicity of 12 hours 25 min. The peak exceeds the 95% confidence level of red noise (dashed line, Fig. 3C), confirming that the semidiurnal tidal cycle of the North Sea is, indeed, highly significant. The spring-neap cycle is clearly visible in the time series of the tidal range (Fig. 3D). Close inspection of this time series reveals additional variation in the spring-neap cycle. The tidal range alternates between strong and weak spring tides in May – July, and between strong and weak neap tides in March – April and August – October (Fig. 3D). This pattern is caused by the apogee-perigee cycle. Wavelet analysis of the tidal range confirms the significance of the 15-day periodicity of the spring-neap cycle, while the 28-day periodicity of the apogee-perigee cycle is at the edge of significance (Fig. 3E,F). Analysis of Hourly-averaged Time Series Wavelet analysis of the hourly-averaged chlorophyll concentra- tion of the year 2007 reveals significant periodicities of 6 hours 12 min and 12 hours 25 min during most of the year, and an additional 24-hour periodicity in late spring and summer only (Fig. 4A). Likewise, SPM also fluctuated at significant periodicities of 6 hours 12 min and of 12 hours 25 min (Fig. 4C), with highest power at 6-hour periodicity. This is consistent with the 6-hour periodicity in tidal current speeds and, hence, tidal mixing. Conversely, salinity and water temperature showed predominantly 12-hour periodicity (Figs. 4E, G), in agreement with the 12-hour periodicity in the horizontal displacement of water by the tides. There was no significant 24-hour periodicity in water temperature, which indicates that temperature fluctuations due to diel heating and cooling were small compared to fluctuations due to horizontal transport. Analysis of the entire dataset of 2001–2009, summa- rized in the global wavelet spectra (Figs. 4B, D, F, H), shows the same dominant periodicities as the results for 2007. Comparison with the tidal data reveals that chlorophyll concentrations consistently peaked a few hours before high tide and a few hours before low tide (Fig. 5A). The timing suggests that the chlorophyll peaks are generated by enhanced tidal mixing due to high tidal current speeds. To investigate this hypothesis, we calculated the rate at which the water level (W) increased or decreased as a simple proxy of the tidal current speed (TC): TC * dW dt Taking the absolute value (vertical bars) transforms the 12 hour 25 min periodicity of the water level to a 6 hour 12 min periodicity in tidal current speed. Indeed, the rate of change in chlorophyll concentration seems to fluctuate in phase with tidal current speed (Fig. 5B). This phase relationship can be tested by wavelet coherence analysis, which displays the coherence (colors) and phase angles (arrows) between two fluctuating time series. Bold black lines delineate areas of significant coherence. Arrows pointing to the right indicate in-phase fluctuations. This confirms that the rate of change in chlorophyll concentration fluctuated in phase with tidal current speed at a significant 6-hour periodicity (Fig. 5C). In other words, chlorophyll concentrations increased during high tidal and decreased during low tidal current speeds. Calculation of all significant phase angles in the entire time series of 2001–2009 reveals a dominant phase angle of 310–330u (Fig. 5D), corre- sponding to a minor phase delay of ,45 minutes between tidal PLOS ONE | www.plosone.org 4 November 2012 | Volume 7 | Issue 11 | e49319