Global sea-level rise is one of the emerging topics in present climate change research (Woodworth, 2006; Rahmstorf, 2007; Church et al., 2008; Domingues et al., 2008), as a large number of coastal megacities, populations and regions are threatened by a rising sea level (Bindoff et al., 2007). Assessment, hindcasting and projections of the mean sea level, either from tide gauges, satellite altimetry or coupled atmosphere-ocean climate models, have been investigated in a number of global studies. An importance of regional atmospheric and ocean processes and patterns for present trends and future sea-level projections has been raised too (Sasaki et al., 2008; Timmermann et al., 2010). However, sea-level extremes, although a generator of major flooding events (Bindoff et al., 2007), have been only marginally examined on global (Woodworth and Blackman, 2004), regional or local levels (Storch and Reichardt, 1997; The WASA Group, 1998; Bijl et al., 1999; Pirazzoli et al., 2006; Cayan et al., 2008; Marcos et al., 2009).
The non-existence of high-frequency sea-level data is an obstacle in ocean-wide estimates of extreme sea levels, which are, therefore, not even mentioned in the Intergovernmental Panel on Climate Change (IPCC) assessment reports (Bindoff et al., 2007). One of the rare global studies (Woodworth and Blackman, 2004) documented an increase in extreme high ocean waters after 1975, but that analysis covered only 25 years. Similar conclusions have been drawn for the severe atmospheric processes that induce extreme sea levels, such as tropical cyclones and hurricanes (Webster et al., 2005; Elsner et al., 2008; Hassim and Walsh, 2008). An increase in the intensity of these events has been observed in the last decades over the most of the tropical oceans. However, the number and intensity of tropical formations and hurricanes may have been underestimated prior to the satellite era (Chang and Guo, 2007), potentially resulting in an artificial trend in tropical cyclone activity. Such a consideration should be examined cautiously, given that there are a large number of regional studies that are documenting an absence or decrease in sea-level extremes (Bromirski et al., 2003; Marcos et al., 2009) and overall storm track activities on an ocean-basin scale (Chang and Fu, 2003).
Our approach for this study was somewhat different in that we did not analyse overall global extreme sea levels, but rather extracted and analysed sea-level variability at different frequency bands. Digital filters were applied to sea-level series data to estimate the mean variability in amplitude over different frequency bands and seasons. Such an approach enabled long-term tracking of sea-level variability over different spatial scales, as well as the assessment of the various processes that contribute to extremes over different timescales. The selected timescales encompass most sea-level variations related to direct atmospheric forcing over a range of local, regional and hemispheric processes. Thus, an assessment of long-term sea-level variability trends may also unveil long-term changes in generative atmospheric processes.
2. Materials and methods
We chose 29 tide gauge stations located worldwide (Figure 1) that have operated quasi-continuously from at least 1970 until 2007 and recorded hourly sea-level data that satisfied the requirements of the analyses. Some stations were excluded because of their proximity to other stations, with only the highest quality and longest running stations being considered in these cases. The analysis requirements included the quality and continuity of the data, as the time series are subjected to digital filters at various frequency bands. All data were taken from the University of Hawaii Sea Level Center's research quality database (http://uhslc.soest.hawaii.edu), except for the Ceuta and Antalya data, which were taken from the European Sea Level database (http://www.eseas.org), and the Lerwick and Newlyn data, which were taken from the British Oceanographic Data Centre (http://www.bodc.ac.uk).
To begin, we removed the tides from the sea-level series separately at intervals of 6 years (or less if specific analysed segments were shorter) using a t-tide software package (Pawlowicz et al., 2002). Although the downloaded data were carefully inspected for errors, we additionally applied a number of quality-check algorithms to further reduce the errors detected during the inspection of the investigated dataset. A common problem with data, especially for historical series, is time shifts and drifts due to malfunctions and imprecise measurements of the clocking and recording devices. These malfunctions result in leakage of tidal energy into residual sea-level series (i.e. ‘false’ tides), especially at the stations with strong tidal oscillations. In fact, this problem contributes to the overall sea-level variability and extremes by preventing the proper extraction of super-diurnal (0–1 d) residual sea-level oscillations, as these are highly contaminated by diurnal, semidiurnal and higher ‘false’ tides (Vilibić and Šepić, 2010). Another problem embedded in high-frequency sea-level series is the effect of long-term changes in morphological or other conditions in harbours where most of the tide gauges are situated. Changes in harbour bathymetry and shape (e.g. through sedimentation or by adding piers), as well as in mean sea-level rise, result in different harbour or bay seiche periods and energies (Lionello et al., 2005; Rabinovich, 2009). However, most of this effect is removed or strongly reduced by removing the super-diurnal sea-level variability through filtering procedures. Additionally, noise may be introduced to the series by different tide gauge operators (Woodworth and Player, 2003), which is recognizable in the hourly sea-level series (Vilibić, 2006). Finally, a difference in quality control procedures between data centres (e.g. in handling gaps and spikes) may introduce noise to hourly series data. This should not be relevant in this study as we applied additional quality control procedures to minimize eventual errors.
The next quality check involved despiking as unrealistic spikes were visually detected at some stations. A spike was defined as the value that differs from the neighbouring values by more than 20 cm (positive spike) or less than − 20 cm (negative spike). We set such a high threshold value because there are real processes on hourly scales that may be present in the records (e.g. meteotsunamis; Monserrat et al., 2006). All spikes were removed, and resulting missing values were linearly interpolated from the neighbouring data. Additionally, short data gaps (i.e. several days) occurred frequently at some stations, thus preventing application of digital filters on continuous series. We filled gaps shorter than 7 d by linearly interpolating between bordering residual values. The band-pass filter with cut-off periods of 10 and 100 d prevented us from analysing short time series, so we only analysed the continuous fragments of time series that were 1 year or longer. The dataset available for this analysis is shown in Figure 1.
The data were filtered at three frequency bands with the Chebyshev band-pass filter (Otnes and Enochson, 1972) of orders 5, 4 and 3 for cut-off periods of 1–3, 3–10 and 10–100 d, respectively. The 1–3-d filter was, in fact, a 28–72-h filter, where the lower cut-off period was moved far from the diurnal tidal periods to prevent the embedding of ‘false’ tides into residual sea levels. The first 30 d in all filtered series were removed due to the boundary effects of the filters. The quality of the filtering procedure was verified by reconstructing the original time series from the filtered and residual series. The envelope (i.e. moving amplitude) of the filtered series was computed by applying the procedure developed for the analysis of seismograms (Farnbach, 1975), which has been applied in other oceanographic studies (Cerovecki et al., 1997). The method is based on the linear separation of the amplitude information from the angle in a complex plane, where amplitudes (envelopes) are more amenable to visual interpretation than the real signal itself. All analyses and results presented later in the article relate to the filtered series of amplitudes (envelopes).
In order to make easier a connection between the filtered data and dominant processes which are driving sea-level variability in these frequency bands, we assumed for the purpose of this article that the first frequency band (1–3 d) contains most of the surges excited by short-scale (temporal and/or spatial) synoptic disturbances and tropical formations (depressions, cyclones). The second frequency band (3–10 d) is supposed to encompass mostly long-living surges generated by quasi-stationary atmospheric patterns at synoptic scales (e.g. slow cyclones and anticyclones). The third frequency band (10–100 d) primarily includes sea-level oscillations forced by atmospheric planetary waves or planetary processes (e.g. Madden–Julian oscillation) and sea-level changes driven by ocean circulation changes. As a result, three different time series of amplitudes were created for each station. It is difficult to separate the different types of processes embedded in these frequency bands because they differ in intensity and frequency in different parts of the ocean (e.g. haline-driven changes are relevant in regions influenced by large rivers but negligible over the open waters). However, proper and detailed explanation of driving processes is beyond the scope of this study, which may be followed by in-depth studies focused on processes rather than on frequency bands. The upper period limit of 100 d was chosen to prevent the inclusion of semi-annual cycle energy to our analyses. The semi-annual cycle is quite strong in the World Ocean, especially in the tropics (Vinogradov et al., 2008) and semi-enclosed basins (Marcos and Tsimplis, 2007), and would significantly bias our analyses. Unfortunately, this also meant losing some oceanic processes relevant to sea-level variability (e.g. Rossby waves that may occur over 200–300 d).
Median values of envelopes were estimated for all frequencies and seasons. Medians were used instead of mean values because the former are better correlated with changing atmospheric conditions (The WASA Group, 1998; Woodworth and Blackman, 2004). Seasons were defined as follows: winter (JFM: January, February, March), spring (AMJ: April, May, June), summer (JAS: July, August, September) and autumn (OND: October, November, December). Trends of median values were estimated for all stations, and their significance was tested with a t-test at the 95% confidence level. In order to use a t-test, we also tested the normality of all series with a Lilliefors test (Lilliefors, 1967). The Lilliefors test is a modified version of the Kolmogorov–Smirnov test used to test the null hypothesis that data come from a normally distributed population when the expected value and variance are not specified. Most of median distributions were normal. All trends that did not come from a normal distribution were considered insignificant. We also tested the series for autocorrelations with a Durbin–Watson statistics test (Sargan and Bhargava, 1983). No significant autocorrelations were found in the series.
3.1. Temporal changes in sea-level variability
Figure 2 displays the median values of annual sea-level variability and their trends for selected long-term stations over all considered frequency bands. The purpose of such a presentation is to visualize differences in inter-annual variability over various basins, latitudes and frequency bands.
The sea-level variability over all frequency bands is generally low over the open tropical Pacific (e.g. Honolulu, Pago Pago), although variability increases with decreasing frequency. Equatorial eastern coasts of the Pacific may possess particularly strong sea-level variability over all frequency bands (e.g. La Libertad) due to variability in El Niño appearances. An exceptional maximum at La Libertad at all frequency bands in 1998 resulted from a strong El Niño event (Colas et al., 2009), which provoked significant atmospheric synoptic activity at all analysed frequencies (Douglas et al., 2009) and caused thermally driven variability at 10–100-d periods through Kelvin wave dynamics (Roundy and Gribble-Verhagen, 2010).
Much larger energies were found in the Gulf of Mexico (Galveston), where a number of processes are strengthened by shallow topography and coastal influences. Temporal changes at Galveston were particularly large over the 10–100-d period, presumably being induced by significant changeability in coastal ocean processes (i.e. haline-induced processes driven by large freshwater loads that are modulated by atmospheric forcing, primarily wind; Wang and Justić, 2009). Sea-level variability increased when moving towards the poles (e.g. Stockholm, Ketchikan), especially over 10–100-d periods. Significant inter-annual and multi-decadal variability was also seen in the series at these latitudes. Planetary atmospheric waves are stronger at higher latitudes than in the tropics and subtropics (Hansen and Sutera, 1986; Kravtsov et al., 2009), which presumably affects sea-level variability through related ground air pressure and wind regimes (Pasarić et al., 2000). Sea-level variability series from San Francisco, a representative of the northeastern Pacific coast, revealed moderate inter-annual differences. Peaks in variability were found over 10–100-d periods during strong El Niño events (e.g. 1982/1983, 1997/1998), implying that the Kelvin wave dynamics associated with this sea-level variability can be tracked as far as San Francisco in the north.
3.2. Trends and coherent patterns
Figure 3 shows sea-level variability trends in annual median values over different frequency bands, with trends significant at 95% being bolded. We included all data in this analysis, although different series lengths affected the trends and their significances differently. This is known to be the likely scenario when significant multi-decadal or secular variability is present in the series (Llovel et al., 2009; Tourre et al., 2010). The most perceptible pattern spread over the Pacific was characterized by negative 1–3- and 3–10-d trends. This was significant at a large number of stations. As some of these trends were estimated from centennial time series, such a coherent pattern indicates a long-term decrease in high-frequency sea-level variability over the region. Simultaneously, in the atmosphere, either no change or a decrease in the overall intensity and frequency of the southern (Hassim and Walsh, 2008) and northern (Chan and Xu, 2009; Kubota and Chan, 2009) tropical Pacific cyclones and hurricanes has been found when assessing centennial time series. In fact, a clear positive trend of hurricane intensity has been found only in the Atlantic according to some recent studies (Kossin et al., 2007; Bromirski and Kossin, 2008). That is presumably the reason why positive 1–3-d sea-level variability trends are found in the western tropical Atlantic (Galveston; Figure 3(a)). In addition, extratropical atmospheric variability has also been found to have non-significant trends over the Pacific (Chang and Fu, 2003; Wang et al., 2006), resulting in non-significant extratropical 1–3-d sea-level variability trends. Additionally, one should be aware that our definition of sea-level variability includes all processes at a certain frequency band (i.e. weak storms and their influence on sea level are also included but were not followed by any tropical storm analysis). Therefore, an overall decrease in sea-level variability energies over the tropical and subtropical Pacific was found for the synoptic scale frequencies (1–3 and 3–10 d). However, we found no significant trends over the Pacific on the planetary-scale frequencies (10–100 d), indicating long-term cumulative steadiness of generating processes (e.g. the Madden–Julian oscillation; Zhang, 2005) and ocean circulation variability at these frequencies.
Other recognizable coherent patterns were found in the extratropical regions. A shift in storm tracks towards the poles (Giorgi and Coppola, 2007) is suggested from the northern Atlantic, Pacific and Mediterranean Sea-level variability trends. A decrease in atmospheric storm track activity has been found at latitudes at approximately 50°N and below (Weisse et al., 2005; Bengtsson et al., 2006; Trigo, 2006) that affects sea-level variability primarily at the 1–3-d periods. This also includes the Mediterranean Sea, where the decrease in sea-level variability was found mostly over synoptic frequencies (1–3 and 3–10 d). Unfortunately, similar conclusions cannot be drawn for the Southern Ocean from the available tide gauge records because there are no long-term operating tide gauge stations south of 35°S, although poleward storm track shift has been found there (Biastoch et al., 2009).
While some changes may have been observed, the coherent patterns in median sea-level variability trends over the last 37 years (1970–2007) mostly followed the patterns observed for the entire dataset (Figure 4). Some very long series (e.g. Honolulu and Johnson over 10–100-d periods) contained differences between their total data set and 1970–2007 trends because multi-decadal and secular processes modulate these trends. An overall steadiness in the 1970–2007 trends versus the trends in the entire series was seen over 1–3-d periods, but an increase in the former versus the latter variability trends was observed over 3–10-d periods. An increased spatial difference between all data and the 1970–2007 trends can also be seen over the 10–100-d periods, giving this frequency band the highest multi-decadal variability among all analysed bands. This was confirmed by the analysis of variance of the respective series. This implies that there are different contributions from the different frequencies to the worldwide increase in sea-level extremes, which has been closely related to changes in regional climate after the 1970s (Woodworth and Blackman, 2004).
Coherent sea-level variability trend patterns were not persistent over the course of a year and varied seasonally. For example, the strongest negative 1–3-d variability trends over the Pacific were found in the boreal spring (AMJ). These trends were found to be significantly negative at a 1.2 Pacific station during boreal winter (JFM), summer (JAS) and autumn (OND). A general decreasing trend over most of the European Seas at latitudes lower than approximately 50°N was detected. Such a trend followed the northward movement of the planetary waves' intensity, jet stream and cyclones (Strong and Davis, 2007).
The trends in some regions were significantly dissimilar over different frequency bands. For example, an intercomparison of 3–10- and 10–100-d boreal spring trends (Figure 5) shows that, while the 3–10-d trends in the southern sea-level stations (30–35°S) were weak, they become strongly negative over the planetary-scale frequencies. Although only the trend at Port Nolloth was significant at 95%, the difference between the 3–10- and 10–100-d trends was significant at 95% at the majority of the stations. Another change in trends over the frequencies is shown in Figure 5. The western coast of the North Atlantic primarily had strong, positive 10–100-d sea-level variability trends, while the 3–10-d variability trends were weaker and insignificant.
A summary of all noteworthy coherent sea-level variability trend patterns extracted from this analysis is given in Figure 6.
4. Discussion and conclusions
Our approach in assessing long-term trends in sea-level variability was somewhat different from other approaches, which commonly use the overall extremes and investigate their variability and trends (Woodworth and Blackman, 2004). We split high-resolution sea-level series data into three frequency bands of 1–3, 3–10 and 10–100 d. This implies that we removed mean sea-level changes from the analyses. We estimated their envelopes and seasonal and yearly median envelope values and then investigated trends in median sea-level variability over the frequency bands. This is a unique benefit to our study, and these results may be used to assess changes in climate and long-term trends in extreme sea levels by supplementing a number of mean sea-level studies to achieve a more comprehensive picture of sea-level changes. We are aware that an arbitrary selection of frequency cut-offs may create problems in interpretation of the results. Some relevant processes (e.g. Rossby waves) are not properly included in the analyses, and others are not bordered by fixed frequency cut-offs. However, upper and lower frequency limits were based on the presence of strong periodical signals. Tidal signals are still present because diurnal tides are not adequately removed due to poor data quality and because semi-annual signals are quite strong in most of the world's ocean. A complementary solution could be based on long-term analyses of running spectra or wavelets to gather more information.
Our results show non-uniform patterns of high-frequency sea-level variability trends that are presumably connected to changes in regional climate, as suggested by Woodworth and Blackman (2004). For example, significant negative trends over most of the open Pacific at periods of 1–10 d oppose the trends found in the tropical Atlantic that followed the behaviour documented for tropical cyclones (Trenberth et al., 2007). Climate projections predict an overall decrease in tropical storms of up to 30%, except in the North Atlantic (Oouchi et al., 2006), which is consistent with our sea-level variability trends. Moreover, positive trends at the northernmost stations (Lerwick and Ketchikan) and negative trends over most of the mid-latitude stations over 1–10-d periods indicate a poleward shift in storm and synoptic activity that has been found to be significant in future climate change scenarios (Meehl et al., 2007).
Our study raises a variety of questions to be answered in future studies, including quantification of the atmospheric and oceanic processes to the attained sea-level variability values over different frequencies. This may be achieved through correlation studies between sea-level variability and global surface meteorological fields (e.g. wind, air pressure and precipitation) available from global atmospheric data, e.g. National Centers for Environmental Prediction (NCEP) or European Centre for Medium-Range Weather Forecasts (ECMWF) global reanalysis fields. A quantitative study of the contribution of sea-level variability over different frequencies to the overall sea-level extremes would also be important as the total extreme impact would likely be devastating to coastal areas. Our approach could also be used with modelled climate sea-level projections to quantify the coherence in sea-level variability trends with human-induced climate change. Finally, this approach may be downscaled to regions with dense, long-term, high-frequency sea-level data to assess regional sea-level changes and patterns over different frequency bands.
Knowledge of sea-level variability trends should be included in any assessment of global sea-level changes because disastrous flooding situations are a consequence of processes that occur over the temporal scales examined herein. In addition, knowledge of long-term changes in driving forces would contribute to a large number of different studies (e.g. tropical storms, hurricanes or extratropical storm tracks). The sparseness of long-term, high-frequency, sea-level data is a major obstacle in obtaining more reliable coherence patterns, especially in the Southern Ocean and polar regions, but the coherence in sea-level variability trends can still unveil general patterns in climate changes, which are relevant for assessing sea-level threats in regions like the tropical and subtropical Pacific.
We would like to thank all of our sea-level data providers, particularly the University of Hawaii Sea Level Center. The comments and suggestions raised by two anonymous reviewers are appreciated. We thank the Ministry of Science, Education and Sports of the Republic of Croatia (Grant 001-0013077-1122) for financial support.