1. Introduction

Most studies of sea level changes in the past century, and of potential changes in the next 100 yr, have focused on changes in mean sea level (MSL) rather than in extreme high waters, although it is the latter that results in the most impact at the coast (Woodworth et al. 2003). For example, one can note the relatively small number of publications on changes in extremes quoted in scientific reviews, such as that of Church et al. (2001). In this paper, we have made use of a tide gauge dataset, which provides a “global sampling” (if not a comprehensive global coverage) of extreme high waters, to address two main questions.

The first question is consideration of whether there is any evidence for recent increases in extreme high waters, over and above the much-studied topic of MSL change. There has been a considerable amount of anecdotal evidence (newspaper reports, etc.) of record extreme levels in different parts of the world. However, it is not always clear whether the increasing extremes are primarily due to interannual or long-term MSL change or to a different time series behavior of the high-water values on top of the MSL caused by, for example, an increasing occurrence of storms. A second question is concerned with whether the interannual variability in extremes is dependent upon variations in regional climate, which are represented often by indices such as the Southern Oscillation Index (SOI) and North Atlantic Oscillation (NAO).

2. Sea level datasets

Most sea level data recorded by tide gauges are obtained from the sampling of water levels at hourly or greater frequencies. See Pugh (1987) for a description of tide gauge measurement techniques and for an explanation of how MSL and other tidal parameters are computed. In this study, we have standardized the use of hourly values, which make up the majority of our records, by subsampling any available higher-frequency data. This will mean that in some cases the extreme high-water levels are underestimated slightly.

The majority of our data come from the Research Quality Data Set (RQDS) of the University of Hawaii Sea Level Center (UHSLC; Caldwell 2000). This extensive dataset of hourly values originated from work during tropical Pacific research programs, but has since expanded to include higher latitudes and other ocean areas and is now one of the main research products of the Global Sea Level Observing System (GLOSS) (IOC 1998).

Although the RQDS contains several long records of hourly values, it consists primarily of data from the last 20–30 yr. Therefore, our studies of changes in extremes are necessarily restricted to recent decades. The RQDS also contains several major gaps in its geographical coverage. For example, it contains few data from Europe even though copious data exist. We supplemented the RQDS in Europe by obtaining information directly from a number of national sea level agencies. This proved to be a slow process, with data readily available from some countries but not all, and with many different sampling periods and formats. This situation should improve radically in the future through the work of the recently formed European Sea Level Service (Plag 2002). Other major RQDS gaps occur in Africa and other regions, which are being addressed through network-development initiatives of GLOSS and other programs.

Figure 1 shows the geographical distribution of the 141 time series at our disposal, with stations required to have at least 18 yr of sea level data during the period 1975 onward, with each selected year of data required to be at least 75% complete.

3. Percentile time series analysis

The method chosen to study changes in extreme high-water levels over and above changes in MSL was percentile time series analysis. This method determines changes in the frequency distribution of measured sea levels and has been used extensively in sea level research. For example, Woodworth and Blackman (2002) employed percentiles in a study of changes in high waters at Liverpool, northwest England, during the last 230 yr, and Hunter (2002) used similar methods in an investigation of the reasons for recent flooding at Funafuti, Tuvalu, in the central tropical Pacific.

In a normal year with no data gaps there will be 8760 hourly measurements, which can be ordered in terms of their observed sea level, and, which can be used to compute percentile levels for the year. We chose to calculate percentile values at 19 levels (0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 80, 90, 95, 98, 99, 99.5, 99.8, 99.9, 99.95 percentiles). The 50th percentile (the median) will correspond to MSL to a good approximation, while the 0.1th and 99.9th percentiles will correspond approximately to the levels of the eight lowest and highest hourly sea level values, respectively. If one subtracts the 50th percentile from each individual percentile, one obtains a measure of the distribution of hourly sea levels during the year relative to MSL for that year.

There are two reasons why reduction of the percentiles to MSL might be desirable. The first is scientific: extreme high (or low) waters might be the result of the same atmospheric and/or oceanic forcings that cause MSL change. In this case, the time series of the higher percentiles will have similarities to those of MSL, as would be demonstrated in the reduction to MSL by the removal of the common signal. Alternatively, if the extremes have forcings that are different than those of MSL, or have the same forcings but to a different extent, then the reduction will demonstrate the difference. An example of each case is shown in Fig. 2.

Figures 2a and 2b show percentiles before and after removal of the median (or MSL) using data from Tuvalu in the central South Pacific (9°S, 179°E), which have recently been discussed in detail by Hunter (2002). Figure 2a shows the median time series to contain several large negative spikes, which are known to be associated with ocean circulation changes during El Niño events (Luick 2002), and, which are also represented in the higher-percentile series. Subtraction of the median (Fig. 2b) largely removes this common signal, and one would conclude that the extremes are not linked to El Niño (e.g., via storms) other than by what are known to be intraseasonal and longer thermohaline changes in the MSL. Figures 2d and 2e show an opposite example from Stockholm, Sweden, in the Baltic Sea. MSL changes at this station (Fig. 2d) and at neighboring sites in the eastern North Sea and the Baltic are known to be closely associated with fluctuations in the air pressure and wind fields represented by the wintertime NAO index (Andersson 2002; Wakelin et al. 2003). Figure 2e shows the same information, with each percentile reduced to the median value (or MSL). A first observation is that the spread of the higher percentiles is greater than that of the lower percentiles. This asymmetric feature is observed in many mid- and high-latitude records, and is primarily a consequence of the asymmetries in air pressure data and in the wind fields associated with highs and lows. Pugh (1987) discusses several examples from North Sea locations. A second observation is that the higher percentiles in Fig. 2e have a similar time dependence to that of the median (or MSL) in Fig. 2d. In other words, the extreme high waters have a greater response to wintertime NAO than does MSL.

A second reason why MSL reduction might be desirable is concerned with errors in the control of the datum of the sea level time series. By choosing to study the time series of percentiles relative to the median, one is not affected by considerations of vertical land movement or of datum uncertainties, which dominate the discussion of MSL change (Church et al. 2001).

In studies of the higher percentiles, and especially in studies of annual maxima [which would correspond to the (100 − 100/8760) percentile], there has to be more attention paid to data quality control and the absence of instrumental bias around high waters than is often applied within investigations of MSL. A monthly or annual MSL calculation will be relatively immune to a small number of incorrectly measured hourly values, but a study of annual maxima could be corrupted significantly if those errors occur around high water [see appendix 1 of Woodworth and Blackman (2002) for further discussion on this point]. However, in a percentile analysis with percentage levels selected such that the calculated percentile levels are not affected by a small number of incorrect hourly values, then the influence of measurement errors will be less. For this reason, we have chosen to use two percentile levels (99th and 99.9th) for most discussion in this paper. The latter corresponds to the level of the most extreme 8 h of data each year, and, therefore, should provide the information on extremes we require, but is more susceptible to corruption by data errors than the 99th percentile series. Conversely, the 99th percentile corresponds to the level of the top 88 h of data, which could differ somewhat from the real annual extremes but is relatively immune to data errors.

An important complication, if changes in percentile levels are to be interpreted in terms of factors, such as increased storm surge activity during the past few decades, concerns the role of the ocean tide. The distribution of high-water levels due to the tide is not the same each year, and popular perceptions of an increase in extreme flood events during the past few years could as easily stem from the tide as from changing surge levels. For example, in the highest percentile time series for Tuvalu (Fig. 2b) one can see the important role of perigean tides with a quasi-4.4-yr periodicity. A smaller nodal (18.6 yr) component is also present. These features of extreme tidal levels are well known (Cartwright 1974; Amin 1979) and exist in almost all records, except for stations such as Stockholm, where the ocean tide is small. Without consideration of the tide, any observer of the high-percentile levels, or of annual maxima, might misinterpret such changes as being due to meteorological or oceanic forcings.

In order to remove the complication of the tide from the analysis, a further set of percentiles, each reduced to their medians, was calculated for each station-year of data. This was obtained by subjecting each year of hourly values to a tidal harmonic analysis (Pugh 1987), using a standard set of 63 constituents, with the determined tidal component of the hourly time series for the year used to compute a set of “tidal percentiles.” The 19 time series of tidal percentile values for each station were then subtracted from the corresponding 19 time series from the observed data, providing time series of percentile differences that are reduced to medians and are free from tidal effects. (The difference series must not be interpreted in the sense of “surge percentiles;” large positive and negative surges can occur throughout the observed and tidal percentile spectra.)

One might ask why it is necessary to perform a tidal analysis separately for each year of data, rather than perform an analysis for 1 yr only (perhaps using a “best year,” which contains no data gaps) and then to compute tidal predictions for all years on the basis of that 1 yr. There are at least two reasons why that would not be satisfactory. The first is that tidal prediction always involves assumptions about the long-term time dependence of individual constituents, of which the 18.6-yr “nodal” dependence of the M2 constituent is the most obvious (M2 being the major twice-daily lunar tide). In the equilibrium tide, the amplitude of the M2 term varies by 3.7% over the nodal cycle (Doodson and Warburg 1941). However, in shallow parts of the real ocean the nodal dependence can be significantly lower (e.g., Amin 1985). Consequently, predictions based on 1 yr of data only will be imprecise. A second reason is that we found examples in the data of stations that have slightly different tidal characteristics in different periods, which are probably due to changes in gauge technology or location. The use of predictions based on a single year of data would once again be inappropriate for such stations.

Figures 2c and 2f present examples of 99th percentile series minus those obtained from tidal analyses of each year for Tuvalu and Stockholm, respectively. In the case of Tuvalu, most of the variability in sea level can be accounted for by the tide, so that, when the two sets of percentile series are subtracted, small percentile differences are obtained with a small, negative trend (Fig. 2c). This is opposite to the impression one would obtain by inspection of the 99th percentile series in Fig. 2b, which suggests a small, positive trend. This reversal can be accounted for by slightly smaller tidal amplitudes (and of sea level variability in general) for the period before and around 1982, compared to later data, which can possibly be instrumental in origin. As a contrast, Fig. 2f shows that the 99th percentile difference series for Stockholm is systematically nonzero, reflecting the fact that sea level variability at this site is large, and is primarily due to the weather and not to the small tide. Consequently, the 99th percentile difference series lies systematically above zero, with reduction to medians being implicit in the tidal removal as described above. The 99th percentile difference series contains possible NAO-related variations, which are referred to below.

4. Significance of trends of the higher percentiles

Figure 1 (top) indicates the measured trends in the observed 99th percentile time series since 1975 for the stations at our disposal. Trends were computed using a simple linear regression with allowance for a perigean component and were sorted by whether they were significantly positive at the 95% confidence level (red), significantly negative (blue), or otherwise (black). Confidence levels were computed ignoring any possible residual serial correlation in the percentile time series.

A first observation is that of the 141 stations, 50 and 7 are shown as red and blue, respectively. This supports the many anecdotal assertions worldwide that extreme high-water levels have increased in recent decades. Groupings of red, blue, and black (or at least of blue or black) can be seen, indicating regional spatial coherence and also inspiring confidence in general data quality. Particularly dense groupings of red can be seen along the Atlantic coast of the United States (cf. Zhang et al. 1997, 2000), parts of the coasts of China and Japan, and across the central and South Pacific. A similar plot for the median values (not shown), derived without the perigean term because it is not relevant for MSL, demonstrates 59 and 10 stations in red and blue, respectively, at essentially the same locations as in Fig. 1 (top).

Figure 1 (middle) also shows the corresponding distribution of trends computed similarly, with each 99th percentile time series reduced to their median values. This map contains a much reduced number of 18 and 9 stations shown in red and blue, respectively, as is to be expected if the trends in the 99th percentiles and medians have the same sign. The formerly red groupings along the U.S. Atlantic coast, and the coasts of China and Japan, have now turned mostly black. The central and South Pacific remains red, although it can be seen that some swapping between red and black has taken place.

Figure 1 (bottom) likewise shows the corresponding distribution with median subtraction as before, with the tidal percentile differencing described above. In this case, trends were computed from the corrected 99th percentiles, using simple linear regression, because the tidal subtraction will have removed any genuine perigean tidal components in the time series. There are now only four and three stations shown in red and blue, respectively, and the central and South Pacific is now largely black. This indicates that much of the observed increase in extremes [Fig. 1 (top)] is, as far as we can tell, within the statistics of short records—either a consequence of the same type of forcing, which produces MSL trends in this period, or an artifact of short-term trends in extreme astronomical tides.

Use of the 99.9th percentiles, instead of the 99th percentiles, allows us to test the sensitivity of these conclusions with a set of higher extreme levels. The main difference found with 99.9th percentiles was that the red points along the U.S. Gulf Coast in Fig. 1 (top) were black, and remained black after median and tide removal. Otherwise, all the general conclusions obtained using the 99th percentiles apply also to the 99.9th percentiles.

5. Correlations with regional climate indices

In order to investigate how extreme high-water levels might be affected by regional climate changes, we have made use of a set of indices selected from the Web sites of the Climatic Research Unit University of East Anglia (online at http://www.cru.uea.ac.uk), the Joint Institute for the Study of the Atmosphere and Ocean University of Washington (online at http://jisao.washington.edu/main.html), the National Oceanic and Atmospheric Administration (online at http://www.cpc.ncep.noaa.gov/data/indices/), and the Japan Marine Science and Technology Center (online at http://w3.jamstec.go.jp). Although there is potentially a long list of such indices, we selected nine of the major ones. Six are based on air pressure data [wintertime (January, February, December) NAO, annual NAO, SOI, Arctic Oscillation (AO), Pacific–North American index (PNA), and Antarctic Oscillation (AAO)], and three are based on sea surface temperatures [Niño-3, Indian Ocean dipole (IND DIPOLE), and Pacific decadal oscillation (PDO)]. Each index was employed in annual mean form, apart from the wintertime NAO.

Figure 3a shows the sites for which the 99th percentile time series have a correlation (red), or anticorrelation (blue), with the indices significantly different from zero at 95% confidence level. (Correlations were computed at zero lag using detrended time series, with percentile and index values for each year assumed to be independent.) Of particular note are the especially strong correlations between extremes at Pacific stations with indices connected to El Niño (SOI, Niño-3, PDO) (cf. Tuvalu discussion above), while stations in the western Pacific and Southeast Asia show significant anticorrelation with IND DIPOLE. A grouping of several northwest European stations indicates a correlation of extremes with the wintertime and annual NAO index (cf. Stockholm discussion above), while all North American sites plotted have significant anticorrelation with PNA.

Figure 3b shows a similar set of maps but with the 99th percentile time series reduced to their medians. In the Pacific, much of the large-scale El Niño–related correlations have now disappeared, except for a grouping along the coasts of the United States and Canada (SOI) and at several stations along the Pacific American coastline (PDO). In the western Pacific, the density of correlations is either much reduced (SOI, IND DIPOLE) or reverses sign (Niño-3, PDO); this reversal is connected to the close timings of El Niño events and high perigean tides, as will be mentioned below. In northwest Europe, the correlations with the NAO are maintained for several stations.

Figure 3c shows a similar set of maps but with the 99th percentile time series reduced to their medians, and with the tidal contributions to the percentiles removed as described above. The tidal removal could be expected to affect the El Niño–related correlations in particular, owing to similarity in the timings of El Niño events and of peak astronomical tide during the late 1980s and 1990s. Figure 3c shows that several groupings of correlations remain such as with SOI and Niño-3 at certain sites along the Pacific–American coastline, with wintertime NAO in northwest Europe.

The number of stations plotted on the nine maps of Figs. 3a–c total 205, 83, and 102, respectively. This suggests that, while there may have indeed been significant variability in extreme high-water levels in recent years and while that variability can certainly be linked to variations in regional climate, much of the observed variability is common to that in MSL (i.e., does not infer different physics at work) and, in certain locations, can be confused with variations in astronomical tidal variations. Nevertheless, there are some locations at which the extremes do suggest a separate, or enhanced, linkage to regional climate.

The sensitivity of these conclusions to the choice of extreme level can be studied by using the 99.9th percentile time series instead of the 99th percentiles. The corresponding sets of maps contain 160, 71, and 72 stations, respectively, with geographical distributions largely similar to those of Fig. 3. Differences include weaker anticorrelations with IND DIPOLE and PDO in the western Pacific. In addition, all correlations in northwest Europe with wintertime NAO are less significant.

6. Conclusions

We conclude that, within the limitations of the “global” dataset of 141 stations at our disposal, if one considers the generality of the sea level information, then there is indeed evidence for an increase in extreme high-water levels worldwide in the period since 1975, and that the variations in extremes in this period are related to changes in regional climate. Examples can be found of the time series of extremes having a different character, or different amplitude of variability, to that of MSL change. However, in most cases, the secular changes and the interannual variability in extremes are similar to those in MSL during the same period, and are, therefore, consistent with having the same magnitude and type of atmospheric and/or oceanic forcing.

This is an important finding with regard to studies of the impacts of coastal sea level changes (Woodworth et al. 2003). If variations in extremes were to be a consequence of “different physics” to those in MSL, then uncertainties in the occurrence of extremes in future might be expected to be even larger than those in the mean levels, which are themselves considerable. Such differences require a considerably greater range of study using both real data and climate model information, as Church et al. (2001) have emphasized. However, on the evidence of data from the past quarter-century at least, one can say that no systematic difference can be found on a worldwide basis.