Preliminary analysis of acceleration of sea level rise through the twentieth century using extended tide gauge data sets (August 2014)

Abstract

This work explores the potential for extending tide gauge time series from the Permanent Service for Mean Sea Level (PSMSL) using historical documents, PSMSL ancillary data, and by developing additional composite time series using near neighbor tide gauges. The aim was to increase the number, completeness, and geographical extent of records covering most or all of the twentieth century. The number of at least 75% complete century-scale time series have been approximately doubled over the original PSMSL data set. In total, over 4800 station years have been added, with 294 of these added to 10 long Southern Hemisphere records. Individual century-scale acceleration values derived from this new extended data set tend to converge on a value of 0.01 ± 0.008 mm/yr². This result agrees closely with recent work and is statistically significant at the 1 sigma level. Possible causes of acceleration and errors are briefly discussed. Results confirm the importance of current data archeology projects involving digitization of the remaining archives of hard copy tide gauge data for sea level and climate studies.

Key Points

• Sea level acceleration from extended tide gauge data converges on 0.01 mm/yr²
• This value is more uniform geographically than previously reported
• This refines and confirms previous estimates of sea level acceleration

1 Introduction and Summary of Previous Work

Quantifying any long-term nonlinear variations (such as acceleration) in sea level rise (SLR) is an important step toward understanding the mechanisms of SLR. Woodworth [1990] using the PSMSL data set up to 1988 found no statistically significant acceleration in sea level rise (SLR) since 1870, but noted that a robust but small value of 0.008 mm/yr² emerged when using the longest time series from Europe. Douglas [1992], in another much cited paper, analyzed 23 essentially complete and widely distributed tide gauge records covering an 80 year period up to 1985 and concluded that whilst global SLR over this period was estimated to be 1.8 mm/yr, any acceleration component was again statistically insignificant. Woodworth also suggested that by early in the 21st century any acceleration due to global warming would probably be evident. In the twenty odd years since, the observational evidence base related to sea level rise has broadened and deepened. Estimates of average coastal sea level rise from tide gauges have now converged on a value of 1.7 ± 0.4 mm/yr for the twentieth century [Rhein et al., 2013]. A wealth of proxy data-based estimates of local sea level variation, albeit with lower temporal resolution [Barlow et al., 2013] indicate that rates of sea level rise were somewhat less than this in the few centuries preceding the twentieth [Gehrels and Woodworth, 2012; Kemp et al., 2011]. The composite satellite altimetry record, comprising continuous direct measurements of sea level over almost the entire ocean surface, gives an estimate of global SLR of 3.2 ± 0.4 mm/yr averaged over the past 20 years. Taken together, these data imply acceleration in rate of SLR over the industrial period. However, the coverage and level of uncertainty associated with the satellite data is impossible to achieve using tide gauge data alone over any equivalent 20 year span. This makes it difficult to state with certainty that the current global rate of change is unprecedented in historical times, though there are indications of similar rates of rise in the period 1930–1950 [Woodworth et al., 2009].

To evaluate whether there has been acceleration most approaches either derive a quadratic fit to the overall time series or split the time series into segments and compare gradients. Several studies using the longest time series and a large number of tide gauges give acceleration values close to 0.01 mm/yr² [Woodworth et al., 2011; Wahl et al., 2013]. In some cases, the result was statistically significant [Church and White, 2011; Jevrejeva et al., 2009; Olivieri and Spada, 2013]. Ray and Douglas [2011] arrived at a value close to zero using a start date of 1900, but note that adding nineteenth century data produces a positive value. Other scientists who have limited either the full spatial or temporal extent of the data have arrived at acceleration values which are inconsistent at a regional level (for example, Cole [2011] for New Zealand) or statistically insignificant (Houston and Dean [2011] using U.S. data from 1930, and Watson [2011], for Australia). This has given rise to debate about whether significant acceleration has occurred during the twentieth century, a period during which atmospheric CO₂ levels increased from 300 to 370 ppm [Keeling et al., 2001] and average global surface temperatures rose by 0.9°C [Hartmann et al., 2013]. It is noteworthy that all of the studies are based on subsets of the same tide gauge data.

This study goes some way to reconcile these previous results by creating a database of tide gauge time series which have been systematically extended or infilled where appropriate data is available (and where this can be objectively justified). The aim is to increase the statistical robustness of estimates of acceleration derived directly from tide gauge data over as wide a geographical extent as possible. Simple methods for extending times series are discussed, as are various methods of accounting for vertical land motion. As pointed out by Pouvreau [2008] and Talke and Jay [2013], significant amounts of tide data were collected in the nineteenth and early twentieth centuries and are unrepresented in analyses of SLR. Recovering this data would help improve estimates of sea level acceleration. A significant amount of data for this study is taken from published contemporary analyses of original tide gauge records which in some cases may be lost. Many of these old studies have been uncited in recent work.

2 Low-Frequency Variability

Apart from obvious tidal and seasonal effects, sea level at any tide gauge is influenced by a number of other factors over a wide range of time scales. Variations in meridional redistribution of the high proportion of global thermal energy accumulated in tropical upper ocean layers, the exchange of fractions of this energy with the atmosphere, and the interrelated atmospheric pressure gradients and resultant wind patterns as well as evaporation, precipitation and temporary water storage on land all contribute to regional sea level variability. For example, a significant recurrent climate pattern, represented by the El Niño Southern Oscillation (ENSO), is associated with interannual to decadal SLR variations with local amplitudes of 10 s of mm to several decimeters in the equatorial Pacific [Wyrtki, 1977]. Although the effects of ENSO are large enough to modulate global surface temperatures and sea level [Nerem et al., 1999], when averaged over increasingly long periods, these regional redistributions of water [Thompson and Merrifield, 2014] and heat content will have progressively less impact on any century-scale secular sea level trends related to global cooling or warming driven by long-term planetary thermal energy imbalance [IPCC, 2013, AR5 chapter 3]. Nevertheless, as the estimated global increase in sea level is only around 170 mm during the twentieth century, these variations can still confound attempts to derive consistent trends or acceleration terms from all but the longest individual tide gauge records, and consideration must be given to start (or end) times [Haigh et al., 2014].

The tide gauge network becomes increasingly sparse when extended backward in time, leading to potential coverage problems when deriving global century-scale trends. However, as individual time series get longer, then the spatial extent over which their behavior can be considered representative of longer term variations (coherence scale) gets larger [Douglas, 1992]. Relative sea level data from closely spaced tide gauges is highly correlated even at short time scales. At decadal time periods, correlation can still be seen between data from tide gauges hundreds or even thousands of km apart [Enfield and Allen, 1980; Papadopoulos and Tsimplis, 2006]. If a relatively uniform secular trend and low-order components are indeed common globally, then these should become apparent at time scales approaching the length of the longest tide gauge records. Indeed, if the global SLR trend of 1.7 mm/yr is assumed to be geographically uniform, then subtracting local tide gauge trends from this to estimate vertical land motion gives the closest agreement with both GPS and DORIS-derived values [Bouin and Wöppelmann, 2010]. This prompted Ostanciaux et al. [2012] to state “It is difficult to envision another explanation than a fortunate sampling bias for this result.”

It follows that even a few additional years of data added to individual time series could result in improved estimates of trends and reduced uncertainty. The Sydney and San Francisco PSMSL revised local reference (RLR) monthly tide gauge data (both of which are composite series) give an illustrative example. Correcting these series for vertical land motion (using values from Ostanciaux et al. [2012]), it can be seen that the sea level at each location, separated by almost 12,000 km, appears to be modulated by opposing interannual variations (Figure 1). These are related to the complex thermodynamic effects associated with ENSO, and its atmospheric component, the Southern Oscillation Index (SOI) [Bromirski et al., 2011; Merrifield et al., 2012]. Although inverse barometer corrections can to a small extent compensate for these variations, when trends are derived from these series starting at locally opposing peaks (e.g., 1908) then even though both time series have a span of 105 years in this example, the derived quadratic trends appear markedly divergent. The derived acceleration value for San Francisco is −0.012 mm/yr² whilst for Sydney it is 0.020 mm/yr².

Figure 1

PSMSL data from 1908 for Sydney and San Francisco corrected for glacial isostatic adjustment (GIA), with pentadal averages in red (Sydney) and blue (San Francisco), with quadratic trends fitted in yellow (Sydney) and white (San Francisco).

If the comparison now uses the full extent of each monthly time series (back to 1855 for San Francisco and 1886 for Sydney) then the second-order trends tend to converge as in Figure 2, resulting in acceleration values of 0.013 mm/yr² for San Francisco and 0.015 mm/yr² for Sydney. The matching of linear trends is of course dependent on the choice of correction for vertical land movement. Here the GIA correction [Ostanciaux et al., 2012] is derived from analysis of altimeter and tide gauge data. As the low-frequency variations are coherent, but for the most part of opposite phase along the entire East coast of Australia and the West coast of the U.S., respectively, covering a significant number of tide gauges, this highlights issues with attempting to derive global trends without wider geographical context and reference to the longest regional time series available. For example, this would be relevant to any analysis of the records from San Diego or Honolulu, which have data available from 1906 and 1905, respectively, and follow a similar multidecadal pattern to the San Francisco record.

Figure 2

Full extent PSMSL data for Sydney and San Francisco corrected for GIA, with pentadal averages in red (Sydney) and blue (San Francisco), with quadratic trends fitted in yellow (Sydney) and white (San Francisco).

If acceleration has occurred in all regions, then it would be expected that time series which started at a later date would, on average, show progressively larger linear trends in SLR. Apart from the problem of increased uncertainty associated with shorter time series, another complication with this approach is that all individual trends must be corrected for vertical land motion, in order to mitigate any regional bias and reduce the variability that may be caused by regional uplift or tectonic activity. Nevertheless, the GIA or GPS-corrected sea level rates do on average show higher value trends as we move the start dates of the series forward in time, but the covarying increase of spread in trend values means that it is difficult to extract acceleration values which are statistically significant.

This work avoids the requirement to derive absolute linear trends in order to combine closely spaced time series, and also avoids the issues of uncertainty in GIA correction [Douglas, 1992] by comparing individual acceleration values derived from a large sample of independent time series.

3 Methods

Clearly, it is desirable to use as many observations as possible over as long a period as possible. To cover the period 1900–2000, time series extending before 1900 (and after 2000) are needed to derive representative multidecadal averages and nonlinear trends. The number of relatively complete quality-controlled tide gauge time series in the PSMSL data set which stretch back over 100 years is just over 50, and extending this to 120 years reduces the number to just over 20. Many of these are in Northern Europe which would bias any result of simple global averaging of data toward this region. There are additional data sets (including the PSMSL “metric” data) where the datum information is not strictly quality controlled, benchmarks have been lost, or where the time series have gaps, but in some cases data can still be used with due care. In many cases the PSMSL time series from individual sites are themselves composites, as tide gauges have been replaced, or moved, over time, for example the Battery, New York [Talke et al., 2014]. In these cases, for the RLR data, accurate recording of tide datum information and standard leveling procedures can allow continuity of the time series. Where tide gauges are close, but not colocated, it is still possible to combine the data from two (or more) nearby gauges into an extended composite time series, provided that any vertical land motion is common, or known at both locations with sufficient precision, so that any offset between mean sea level at the different locations can be minimized [Ray and Douglas, 2011]. As the distance between gauges increases, the probability of differential vertical land motion or divergence caused by low-frequency variations would also be expected to increase. Any acceleration component is independent of the linear trend, and it is assumed that vertical land motion (at least from GIA or slow subduction) is occurring over a long enough term that at multidecadal scale it is effectively linear [Woodworth et al., 2009; Woodworth, 2011]. This means that if data from the two tide gauges have an overlap period of sufficient length, then by minimizing differences between the two series in the overlap period using least squares, static offsets and differential linear trends can be accounted for to allow the two data series to be combined. In many cases, this method accounts for linear differences in vertical land motion and allows an estimate of regional relative sea level acceleration over a longer period.

A potential criticism of this method is that trends derived from a short overlap period can be biased by interannual sea level variations, but as these variations are highly correlated in closely spaced tide gauge data, any interannual bias will be common mode, minimizing impact. Another possible issue is the assumption of constant vertical land motion over the period of interest. For example, there are a large number of long (>100 years) time series from the Baltic, where the postglacial rebound from the melting of the Fennoscandia ice sheet at the onset of the current interglacial period is still ongoing, and over centennial scales this could have small second-order components. Longer term Continuous Global Positioning System (CGPS) and standard leveling techniques are used to measure these uplift rates, where the first-order terms can be comparable with or even exceed current global SLR. There are also a number of time series where rate of change of relative sea level has been significantly affected by nonlinear land motion, often from subsidence due to greatly increased groundwater extraction in growing population centers. In some cases, the apparent rise in sea level shows a marked inflexion point coincident with the onset of rapid development of the ports or surrounding area, and this can lead to anomalously high acceleration values in the tide gauge records spanning this period, for example, Manila [Raucoules et al., 2013], Yangon, Calcutta, and Bangkok. On the other hand, there is evidence from high-latitude tide gauges and colocated CGPS stations that some regions (Greenland, Alaska, West Antarctic Peninsula) have experienced measurable changes in rate of upward land movement in response to recent accelerated land ice mass loss [Sasgen et al., 2013]. This would lead to relative sea levels which have a deceleration component over decadal time scales [Tamisiea and Mitrovica., 2011; Spada and Gallass, 2012], though data from most of these high-latitude tide gauges does not span more than a few decades and so is not used in this analysis. In other cases seismic activity can significantly affect the tide gauge data (as in Onahama, Japan or Kodiak, Alaska), although even large step changes can in some cases be accounted for (e.g., Port Blair after the Sumatra-Andaman earthquake in 2004).

Basic quality control procedures such as buddy checks with nearby tide gauge time series can usually highlight outliers, datum shifts (e.g., Vlissingen in 1884, Kabelvag in 1988), or anomalous nonsea level-related behavior. For this study, several extended composite time series were created. In each case, the difference between the two series (and other nearby series) was examined to ensure they were correlated and help remove outliers (buddy check), before matching the linear trends and zeroing any offsets [Burgette et al., 2013]. Large gaps in the time series can also degrade trend analysis, so in most cases, records or composites which are more than 75% complete (up to 2010) were used. Inverse barometer (IB) correction of tide gauge data was not used for the bulk of the analysis, as although this reduces the standard deviation and interannual variations in some individual time series, in most cases, the effect on overall acceleration was small. Altimeter data (using nearest valid 1° cell) were used with similar qualifications to fill recent small gaps in a small number of tide gauge time series where other tide gauge data were unavailable. Before linear trend matching was used to subtract effects of local vertical land motion, IB correction of the tide gauge data were necessary in the overlap period to avoid bias, as the altimeter data set used here (University of Colorado) was already IB corrected.

Acceleration here is defined as twice the second-order term of a quadratic fit to the data. This is not necessarily a realistic model for sea level rise, but rather it is used as a simple indicator of long term increase or decrease in trend, and gives a means of convenient comparison with previous studies.

4 Data Sources

First, the PSMSL monthly and annual data sets as of mid-2013 [Holgate et al., 2012; PSMSL, 2013], CGPS tables [e.g., Santamaría-Gómez et al., 2012; Rudenko et al., 2013], Glacial Isostatic Adjustment (GIA) tables (Peltier ICE-5G, and Ostanciaux et al. [2012]), and 2013 gridded altimeter sea level trends from Colorado University (http://sealevel.colorado.edu/content/interactive-sea-level-time-series-wizard) and Aviso (http://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level.html) were accessed. Some series were updated where appropriate with daily values from University of Hawaii Sea Level Centre (UHSLC). Seasonal variations in the time series were accounted for by using annual average values. Many of the annual time series were extended using the ancillary tide gauge series available from PSMSL [Spencer et al., 1988] updated from the Publication Scientifiques from the International Association for Physical Oceanography (IAPO), e.g., No. 5 [Proudman et al., 1939]. Research into historical sources has resulted in (for example) a new complete monthly time series for Honolulu from 1901 to 1904 [Lyons, 1901–1904), a corrected annual series from Sydney stretching back to 1873 [Russell, 1885], early monthly and complete annual data for Newcastle NSW from 1892 to 1916 [Russel, 1898, 1904; Coghlan, 1914, 1917], additional monthly data from Port Adelaide from 1892 to 1902 [Chapman and Inglis, 1902], and annual data from Buenos Aires from 1890 to 1896 [Dobson, 1899]. Other sources gave data from sites including Keelung [Hirayama, 1911; Omori, 1911], Kaohsiung [Hirayama, 1911], Bombay [Burrard, 1912; Parkes, 1868], Karachi [Parkes, 1868], New York [Tuttle, 1904; Burr et al., 1904; Schureman, 1934], Boston [Freeman, 1903; Schureman et al., 1928], Halifax, Quebec [Dawson, 1917], Victoria, Vancouver, Point Atkinson, Prince Rupert [Dawson, 1923], Buenos Aires [Bateman, 1871], and Amsterdam [van Veen, 1945]. Data from more recently published long time series were also included: Hansweert, Ternuezen [Kuijper and Lescinski [2013], and Rijkswaterstaat), Ostende [Lebbe et al., 2008], Keelung, Kaohsiung [Tseng et al., 2010], Key West [Maul and Martin, 1993], Stockholm [Ekman, 2003], Wellington [Bell and Hannah, 2012], Auckland [Hannah et al., 2010], San Francisco [Breaker and Ruzmaikin, 2011], Cadiz [Marcos et al., 2011], Leixoes [Araújo et al., 2012], Kronstadt [Bogdanov, 2000], Pertuis d'Antioche [Gouriou et al., 2013], Delfzijl and Den Helder [Wahl et al., 2013], Tallin [Suursaar et al., 2011], Kolobrzeg [Zorita and Hünicke, 2010], Aburatsubo, Hosojima, Wajima (from Geospatial Information Authority of Japan, updated 2013) and Brest [Woppelmann et al., 2008]. Some of these are not in the PSMSL data set, and some may not be subject to the same quality control, but it is hoped that the quantity of time series will still allow meaningful statistics to be derived. In general, for the purposes of deriving acceleration, only time series with a span of greater than 80 years were considered, as prescribed by Douglas [1992], but most of the final results here are based on records with at least a 100 year span.

5 Results

Extending the data set allows a significant increase in the number of long (>100 years) and relatively complete annual time series. In Figure 3, the extent of some of the PSMSL and extended time series (in station number order) is represented. There are of course many more time series available in the PSMSL, but for clarity only the first 215 are shown here. Station number 215 is the approximate transition point to records with <100 year start dates in the PSMSL database. As the PSMSL data set index is approximately in order of time series start date, a majority of the original longer (>100 year) time series are thus represented. As might be expected, there are still a disproportionately large number of long records from the midlatitude Northern hemisphere, although modest gains have been made in the Southern hemisphere (294 station years added to ninth century-scale time series), along the Canadian coasts, and also around the Indian Ocean (187 station years added to sixth century-scale records).

Figure 3

Representation of some of the extended data series. Blue represents the original PSMSL RLR data extent and red represents data series extension or infill.

For example, the PSMSL record from Aden, Yemen, starts in 1880 but with large gaps. Accepting the data (as at May 2013), the derived acceleration would be −0.036 mm/yr². Annual data from the ancillary files is available for the period 1894–1920, and this can be offset for RLR and used to fill the 22 year gap between 1894 and 1916 in the RLR annual time series. This highlighted a datum issue with the 1880–1894 section of the original RLR series, which has now been adjusted in a recent PSMSL update (P. L. Woodworth, personal communication, 2013) to rectify the improbable step in 1894. The new series, essentially complete up to 1969, gives acceleration values of 0.011 mm/yr² (Figure 4). Similarly for Karachi, the PSMSL tide gauge record (1916 onward) again contains large gaps. The unadjusted acceleration trend is high at 0.052 mm/yr². If the ancillary annual time series for Karachi is added (1868–1920) and offset to RLR then this extends the time series back by 48 years, leading to a reduced acceleration value of 0.018 mm/yr². If this new series is buddy checked against the long time series of Mumbai, the long term correlation greatly improves. Further buddy checking with nearby tide gauge data and cross checking with altimeter data reveals the need to deal with a datum offset across the gap between the later section of the data recorded at Manora Island up to 1994 and the data from the new tide gauge setup in 2005. Research into other old records [Tennant, 1856; Parkes, 1868] has uncovered additional MSL values for 1855 and 1857 with known datum information. Further monthly data between 1922 and 1933 can be extracted from The Survey of India Geodetic reports and Indian Tide Tables.

Figure 4

Examples of extended annual series. Arbitrary vertical datum offsets are added for clarity. Dashed sections indicate extended or infilled data. The long series from Fremantle is also shown.

The time series for New York (Figure 4) uses data from Sandy Hook N.J. to infill the 1879–1892 period [see also Talke et al., 2014], with corrections from analyzing the long-term differential trends in SLR at Sandy Hook and the New York harbor sites including Willets Point, and relative offsets adjusted by comparing benchmark elevations and MSL data in the period of data overlap [Tuttle, 1904; Schureman, 1934].

Likewise for other locations, extending or infilling the time series tends to result in convergent acceleration values, as can be seen in Figure 5 for a selection of stations, and in Figure 6 for all of the available stations meeting the criteria defined previously.

Figure 5

Variation of multidecadal acceleration (mm/yr²) of sea level rise with start date (5 year steps) for several widely spaced long (>100 year) tide gauge records showing convergence at century time scales and longer.

Figure 6

Three-dimensional plot of number of tide gauges averaged over 5 year intervals and acceleration variation with start date. End year is 2012.

As can be seen by comparing Figures 7a and 7b, the extension of the PSMSL data set to the full extent available for each individual series allows reduction of the variability associated with derived acceleration values for coastal sea level rise covering the twentieth century and before, to the point where a mean value of 0.01 mm/yr² emerges with 90% confidence level. A normal distribution curve with the same mean and standard deviation is shown for comparison. This is a refinement and confirmation of previous results due to convergence of long term trends as local tide gauge data is extended backward (or forward) in time (Figures 5 and 6). To reduce the uncertainty in individual trends derived from each record, and to minimize potential bias due to gaps or an arbitrary start year, the full range of each time series is used, back to a limit of 1850, provided that the span exceeds a given number of years (100 years in the examples shown).

Figure 7

(a) Spread of derived acceleration values (mm/yr²) for the 61 longest time series (>100 years) in the original PSMSL data set as at May 2013. (b) Spread of derived acceleration values for the 117 longest extended and composite time series (all series >100 years and >75% complete as at August 2014) and probability density functions for normal distributions with the same mean and standard deviation.

This result is significant (p < 0.1) if time series with extents greater than around 90 years are considered (Figure 8). This suggests an unambiguous positive century-scale global acceleration in sea level, which is also consistent with values reported previously [Jevrejeva et al., 2009; Church and White, 2011; Olivieri and Spada, 2013]. The spread of data in Figure 7b will contain contributions from all possible error sources as well as any remaining natural or regional variations. If subsidence either through sediment loading at ports associated with rivers, or through intensive local groundwater extraction was significant, then a positive skew might be expected. More detailed site-specific analysis would be required to investigate this. Further analysis using regional groupings could also help address issues of statistical independence due to the regional distribution and close spacing of some tide gauges [Barnett, 1984; Iz et al., 2012; Jevrejeva et al., 2009].

Figure 8

Sea level acceleration mean values (mm/yr²) and standard deviation derived from full extended tide gauge data series, and variation with temporal extent (years before 2012).

The extended data set allows some preliminary insights into hemispheric or regional variations in acceleration. If the large number of long time series from northern Europe (or from >50°N) are excluded from the centennial analysis, then the mean value for acceleration is 0.0097 ± 0.008 mm/yr². This is consistent with the 0.0105 ± 0.0081 mm/yr² for the full data set of 117 (>75% complete) century-scale records, whilst the sample number is roughly halved. If only the 10 long Southern Hemisphere records are used, the value is 0.0133 ± 0.006 mm/yr² (Williamstown is 71% complete from 1900 but is included). For the Pacific Ocean as a whole, the value is 0.0091 ± 0.007 mm/yr² using 26 records. A consistent acceleration value (0.0109 ± 0.006 mm/yr²) also emerges with reduced variability (>95% confidence, p = 0.035) if only the longest local time series from 32 widely distributed (and therefore more statistically independent) tide gauges are compared (Figures 9 and 10). Whilst different arbitrary thresholds can be set on the acceptance criteria for extended time series, the overall result of acceleration values of order 0.01 mm/yr² appears robust.

Figure 9

Location of longest tide gauge time series available in various coastal regions. The Northern Hemisphere is better represented than the Southern Hemisphere (base map courtesy of NASA).

Figure 10

Histogram of derived SLR acceleration values for the longest regional tide gauge time series for 32 widely spaced sites.

6 Discussion

The extension of individual tide gauge time series results in greatly reduced variability between derived centennial-scale SLR acceleration values. Whilst it is of course possible that “a fortunate sampling bias” is responsible for this result, it appears probable that this acceleration is effectively global in extent, and most likely reflects the volume and mass changes influenced by global warming of the oceans and surface which has increased, though not monotonically, during the twentieth century.

The extended data set also gives additional information regarding global multidecadal variations. Despite the likelihood of relative phases of long-term variations and inflexion points of any decadal-scale global components in individual tide gauge data being biased by regional interannual variations, a broad multidecadal “W”-shaped pattern, superimposed on the upward trend of SLR during the twentieth century is evident in many individual long records [e.g., Fadil et al., 2013]. This pattern is clearly represented in several large-scale global reconstructions [e.g., Church and White, 2011]. This implies higher rates of SLR in the periods roughly from 1930 to 1950, and from 1985 to the present, plus lower rates over the decades covering the start of the twentieth century and after 1960. This pattern is qualitatively similar to the global Sea Surface Temperature (SST) record over the same period, which is highly correlated with ocean heat content in the upper layers, and suggests a strong link [Vermeer and Rahmstorf, 2009]. It is clear that due to these lower-frequency components, the length of record and choice of start and end times of any trend analyses are again critical. When considering regional MSL changes, then the tide gauge records should be long relative to natural decadal fluctuations as reflected in SST-based climate indices such as the PDO (Pacific Decadal Oscillation). An examination of the Church and White [2011] global GMSL reconstruction makes it evident that an 80 year analysis starting around 1930 (as in Houston and Dean [2011]) is more likely to show a lower acceleration value than an analysis starting in 1900 or 1950 [Rahmstorf and Vermeer, 2011]. This work shows similar inflexion points if the acceleration values from the extended time series are simply averaged (using 71 stations up to 55°N to mitigate effects of bias from the large number of Northern European tide gauges; Figure 11) with a progressively increasing start date. The difference after around 1925 between the findings of using averaging as in this study and the Church and White EOF approach is likely to be due to the different method.

Figure 11

The effect of varying the start date of the analysis on overall acceleration (mm/yr²) [after Rahmstorf and Vermeer, 2011]. The red curve is mean value from long time series in this study as compared with the equivalent values (blue) from a similar analysis of the Church and White [2011] global results. Error bars are 1 standard deviation.

Similarly, if the end year of the analysis is stepped backward in time from 2012, then the average acceleration value reduces to close to zero as the end date moves through the early 1980s, which is consistent with the Douglas [1992] result (Figure 12).

Figure 12

As in Figure 11, but showing the effect of varying the end date of the analysis on overall averaged acceleration (mm/yr²) with a fixed start date of 1850, from this study. Error bars are 1 standard deviation.

This multidecadal coherence of regional sea level variations, or basin wide multidecadal variations about a secular sea level rise have prompted questions of quasi-60 year oscillations in the various ocean basins or indeed in the global sea level (for a recent discussion, see Chambers et al. [2012]). Although the possibility of a global phase locked approximate 60 year cyclical mechanism can not be discounted, much longer records are required to confirm this. High-resolution proxy data suggest similar variability in the past but little evidence of 60 year periodicity [e.g., Saenger et al., 2009]. The question arises if these multidecadal variations in rate of rise and the overall relatively low centennial value for acceleration can be adequately explained by updated estimates of variations in radiative forcing components [Otto et al., 2013] and the effect on ocean temperature, volume, and mass.

Various satellite missions since the mid-1970s have allowed Infrared measurement of SST at high spatial resolution, augmenting the standard vessel and buoy-measured SST data which extends back into the nineteenth century. The Argo network of instrumented floats, plus more sparse coverage by earlier instruments give measurements of Ocean Heat Content (OHC) in the upper ocean layers back to the mid-1950s [Lyman and Johnson, 2013]. These measurements confirm a significant steric component of sea level rise over this period. The absolute sea surface height has been measured globally at high resolution with overlapping satellite-based radar altimeters since 1992, thus allowing global sea level to be measured and volume changes to be estimated. With the addition of the GRACE satellite missions in 2002, it has been possible to measure the mass change of land-based ice, stored water, and mass redistribution in the oceans. Recent refinements in these measurements have allowed closure of the sea level budget within error bounds from 2005 onward [Schuckmann et al., 2013; Chen et al., 2013], and from these observations a much clearer understanding of the overall processes contributing to recent sea level rise and regional variations is emerging [Gleckler et al., 2012; Church et al., 2013b]. This in turn allows more confident estimates of the factors contributing to the historical sea level budget [Gregory et al., 2013a]. The scale and overall variation in rate of SLR are consistent with outputs of process-based models which account for known volcanic eruptions and effects of aerosols as well as Green House Gases (GHG) [Church et al., 2013a]. SLR is driven mainly by the nonmonotonic increase in global heat content, with more than 90% of this extra heat energy accumulating in the Oceans [Abraham et al., 2013], combined with increased transfer of mass from land-based ice to the oceans. The steady increase in noncondensing GHG combined with anthropogenic aerosol effects and temporally clustered volcanic eruptions in the late nineteenth and second half of the twentieth century [Stenchikov et al., 2009] gives a deterministic explanation of much of the variation and the relatively gentle overall twentieth century SLR acceleration [Church et al., 2013cc]. Further work on extended tide gauge data could allow improved estimates of the effect of major eruptions such as Krakatoa in 1883 on global sea level [Gleckler et al., 2006]. The temporary downturn in rate of SLR after that time in a reconstruction using extended data from this study (Figure 13) is suggestive of a Krakatoa-related signal of order 5 mm as discussed by Church et al. [2005]. This signal appears much larger in the high-latitude Northern Hemisphere (above 50°N using 67 century-scale records).

Figure 13

Preliminary SLR reconstruction from integrating annual-averaged 15 year SLR rates from all individual century or longer tidal records, similar to Holgate [2007]. Ice core-derived sulfate level estimates in kg/km² from significant volcanic eruptions on right vertical scale [Sigl et al., 2013]. The integrated MSL is the mean of averages in four broad latitude bands in order to minimize the impact of a northern European bias in decadal SL variations due to simple averaging. The acceleration derived from the quadratic fit 1878–2008, shown by the black curve, is 0.008 mm/yr².

It follows that the century-scale acceleration in SLR is somewhat less than might be expected from GHG radiative forcing alone [Woodworth, 1990; Church et al., 2005; Gregory et al., 2013b]. It is therefore probable that SLR will continue at the current relatively high rate in line with ongoing land ice mass loss and increasing OHC [Balmaseda et al., 2013] unless natural (or anthropogenic) aerosol effects intervene.

7 Conclusions

The main objective of this study was to evaluate whether extending the annual time series in the PSMSL offered potential for improving trend estimates for SLR. One result is that global SLR acceleration values converge more closely on a value of 0.01 mm/yr².

Most recent studies including comprehensive attempts to correct land motion with CGPS also suggest convergence of SLR over the twentieth century of 1.7 mm/yr. Regional SLR values as measured by altimetry over the past 20 years compared with the spread in CGPS-corrected SLR trend estimates over the past century suggests current regional decadal rates higher or lower than the global average are likely to be transient at multidecadal time scales [Merrifield et al., 2012]. The spread of differences between pre and post-1950 year sea level trends within individual long time series from this study (multidecadal trend differences are again unaffected by an assumed constant GIA) is small relative to the spread in overall twentieth century GPS or GIA-corrected sea level trends using the same time series. This would be unlikely to be the case if recent (post-1950) local anthropogenic subsidence was the greatest cause of accelerated relative SLR, or if natural regional variations were significantly biasing longer term results. This observation is consistent with localized vertical land motion in most areas being relatively constant over century time scales, but with residual trend errors remaining in a significant number of the vertical corrections, whether the corrections are from state of the art GIA models or from reprocessed data from CGPS stations located at or near the tide gauge. These results are also consistent with a century-scale increase in rate of sea level rise, or acceleration, which appears more geographically uniform than previously reported. It is hoped that the results from this “first pass” using extended data will be updated and refined further as more results from current data archeology efforts become available [Talke and Jay, 2013; Caldwell, 2013] and that this approach can provide improved historical constraints for global sea level reconstructions as well as for modeling projections in SLR.

Acknowledgments

The author is indebted to the various workers at the PSMSL and to Philip Woodworth for constructive advice and encouraging words, and the many others in the sea level monitoring community who helped with data contributions and their time. Also, the reviewers who have helped improve the paper, and the many who indirectly contributed through maintaining data archives and digitizing historical documents in order to make these valuable records more widely accessible. The new data sets, composite time series, and offset factors resulting from this study, and notes, will be permanently lodged with the PSMSL. Historical sources of the original data can be found in the references. Data and RLR factors from Spencer 1988, which is used extensively in this work can be found at: http://www.psmsl.org/data/longrecords/ancill_rep.htm.