The most straightforward measurements of sea level are made by tide gauges. These instruments, usually placed on piers, measure the height of the sea relative to a nearby geodetic benchmark. A resurvey, commonly done annually, is made to determine if settling of the pier has occurred. New surveys are also needed if gauges are moved or replaced, so that sea level series taken at a site can be referred to a common datum in spite of disturbances of the instrument or its platform. Gauges for which such surveys have not been made are of no use for establishing long-term trends of sea level. See Spencer and Woodworth [1993] for an extended discussion.
Beyond such instrument platform effects, at any specific location the rate of relative sea level rise is modified by subsidence or emergence of the land in the area or region. This fact greatly complicates the problem of determining a value for the overall global rate of sea level change from tide gauge data.
The most ubiquitous source of regional submergence/emergence at tide gauge sites is the Post Glacial Rebound (PGR) that continues from the last deglaciation. It is manifest over the entire planet, not just at locations ice-covered at the last glacial maximum. Vertical crustal movements due to PGR at most sites are of approximately the same magnitude as the global (eustatic) rise. Peltier and Tushingham [1989] provide an excellent short summary of their ICE-3G model for PGR, and a particularly clear treatment of the relevance of PGR to the sea level problem. An exhaustive treatment of PGR and the basis of the ICE-3G model is found in Tushingham and Peltier [1991]. A general overview of the phenomenon of PGR can be found in Lambeck [1991].
As particular examples of the effect of PGR, consider Baltimore, Maryland, and Stockholm, Sweden. The long-term (order 100 years) sea level rise of approximately 3.5 mm per year at Baltimore (and everywhere else in the Chesapeake region) is about twice the global rate because of subsidence due to the peripheral bulge collapse from the last deglaciation [ Tushingham and Peltier, 1991]. In contrast, sea level at Stockholm falls by about 4 mm per year as land in the region continues to emerge in response to the disappearance of the ice there during the last deglaciation. It is clear that the effect of sea level change in the Baltic is very different than in the Chesapeake Bay. In general, however, falling sea levels from land emergence only occur at places deeply ice covered at the start of the last deglaciation 18,000 years ago. For most of the world's coastal population, sea level rise remains the practical issue.
It is obvious that any attempt at estimating global sea level rise from tide gauge data must take PGR into account, as well as other vertical crustal movements. As we shall see below, the nearly score of estimates published in the last few decades can be separated into distinct groups based on how PGR and other vertical crustal movements were considered.
Estimates of the rate of global sea level rise determined from tide gauge records have been summarized by Gornitz [1994] in a comprehensive and valuable review paper. The range of published estimates based on tide gauge data is about 1 to 3 mm per year. The data used for these estimates were supplied to investigators by the Permanent Service for Mean Sea Level (PSMSL) [ Spencer and Woodworth, 1993], so that differences of estimates reflect the authors' approach to the problem, and not the data.
Of estimates made prior to 1989, all but one were less than 1.5 mm per year. After eliminating the extreme value, both the mean and median of the 12 remaining values quoted by Gornitz [1994] are 1.2 mm per year. Since 1989, the five new estimates published have been rather larger, also with a single exception. After eliminating that extreme value, the mean value of the recent estimates is 1.9 mm per year, and the median, 1.75. As Gornitz [1994] has noted, the recent estimates are different from the prior ones in that they have accounted for PGR. Thus Peltier and Tushingham [1989, 1991], Trupin and Wahr, [1990]; Wahr and Trupin, [1990]; and Douglas, [1991] all explicitly corrected their estimates of sea level trend for isostatic adjustment at the tide gauge sites. However, the PGR values used by these authors were in fact all computed by Peltier and his colleagues, so it could be argued that the agreement of the recent papers is fortuitous. The estimate of Nakiboglu and Lambeck [1991] also allowed for glacial rebound, but by an ad hoc method, and resulted in an estimate of eustatic rise (1.15 mm per year) more in line with earlier values.
What are we to make of this? Unfortunately, there are complicating
factors beyond the issue of PGR, and published results reflect a
lack of consensus as to how to deal with them as well. In addition
to whether or not PGR was explicitly modeled, differences between
analyses include data record length, tide gauge station selection
criteria, and analysis method. The inability of investigators to
arrive at a consensus concerning the rate of global sea level rise,
or even how to approach the problem, has led some authors to
conclude that global sea level rise cannot be measured at all.
Barnett [1984] states that ``
it is not possible to uniquely
determine either a global rate of change of sea level or even the
average rate of change associated with the existing inadequate data
set.'' Emery and Aubrey [1991] state that (p. 176) ``At
present, we cannot discover a statistically reliable rate for
eustatic rise of sea level alone
'' Pirazzoli [1993] is the
most pessimistic, declaring that ``
the determination of a single
sea-level curve of global applicability is an illusory task.''
However, the situation for determining eustatic sea level rise may not be quite as hopeless as indicated by these authors. I shall argue in what follows that the differing estimates among authors arises (in addition to how PGR was treated) largely from the use of tide gauge records of inadequate length, and from use of sea level series from sites that suffer large vertical movements because of their proximity to convergent tectonic plate boundaries. In addition, completeness of record plays a very large role. The available long records show that sea level cannot be regarded as a stationary time series; large, unpredictable fluctuations that persist over decades are commonplace [ Douglas, 1992]. These fluctuations severely compromise the use of records with large gaps for estimation of a meaningful or accurate value of long-term sea level rise.
The issue of record length has received some attention by authors
who have made estimates of global sea level rise. Barnett
[1984] selected for his study ``Only stations that had 30 or more
years of data
'' Emery and Aubrey [1991], in Figure 39 on
p. 83 of their book, present the confidence factors (from a t-test)
that the estimated sea level trend for tide gauge records is within
1 mm per year of the true sea level trend. The figure shows a
remarkable coherence of results for sea level records longer than
40-50 years. Inexplicably, they go on to consider records as short
as 20 years to be adequate to suppress true sea level fluctuations,
and thus reveal vertical crustal movements. Gornitz [1994]
also states that ``A time series of at least 20 years, and
preferably longer, is needed
'' The most extreme example of the
use of short records was that of Nakiboglu and Lambeck
[1991], who used 655 stations with record lengths as short as 10
years.
In fact, short (a few decades) tide gauge records are of no use whatsoever for determining an underlying long-term global trend, because of low-frequency fluctuations of sea level. Pugh [1987] on p. 320 gives a compelling graphical example of the problem for 10 year records. He demonstrates that 10-year trends at a site can have different signs, depending on the time interval chosen. Douglas [1991] extended the approach used on 10 year records by Pugh [1987] to 30 year intervals. For San Francisco, the longest continuous record (140 years) in the U.S., he found that 30 year trends computed anywhere in the entire series varied from -2 to +5 mm per year. Since the low frequency spectral content of the San Francisco record is in no way unusual, his analysis established the inadequacy of even 30 year records.
Sturges [1987] also pointed out the existence of interdecadal and longer fluctuations that can markedly influence estimated sea level trends. Finally, Roemmich [NRC, 1990, and in a preprint circulated for a number of years previously] in his analysis of sea level and hydrographic records at Bermuda and Charleston, S.C., showed that coastal and relatively nearby mid-ocean sea level trends can differ markedly over several decades. He concluded from his analysis that 50 year records of sea level and dynamic height are needed to understand the sea level fluctuations at a site.
Other quantitative analyses of the role of record length on estimated values of sea level have been made by Peltier and Tushingham [1989], and Douglas [1992]. Peltier and Tushingham [op. cit.] argued that for their selection of tide gauge records, the best balance between number of stations and spatial coverage was achieved at record lengths of 40-50 years. Douglas [1992] investigated the role of record length by computing the trend and acceleration for all sea level records longer than 10 years available from the Permanent Service for Mean Sea Level [ Spencer and Woodworth, 1993]. The acceleration estimate is just a measure of the ability of a quadratic function to absorb the low-frequency component of each series. Figure 1, taken from Douglas [1992], shows that the low-frequency variations of sea level dominate the estimate of acceleration for records shorter than about 50 years. This result is entirely consistent with a straightforward interpretation of Emery and Aubrey's [1991] Figure 39. It is interesting that no obvious reason exists for why the coherence of trends and accelerations so strikingly increases for records longer than 50 years. This matter certainly deserves further investigation.
The conclusion that can be drawn from all of this is that 50 years is the absolute minimum sea level record length that should be considered in an analysis of global sea level rise or acceleration from tide gauge data alone. Fortunately, more long records are becoming available in many parts of the world because of the large number of tide gauges installed in the years following World War II. In addition, we shall see below that it may be possible to compute from other data much of the troublesome interdecadal sea level ``noise,'' and eliminate it from the signal. The next 10 years should see much progress in the problem of separating vertical crustal movements at tide gauge locations from interdecadal fluctuations of sea level.
There are other factors affecting estimates of global sea level rise beyond record length. Statistically significant disagreements remain even among those studies that use only long time series. This has probably occurred because many long sea level series are contaminated by local crustal movements and/or data problems. Unfortunately, most of these tainted records have been used in published investigations.
One of the most striking examples of an unsuitable long sea level series is that of Seattle, Washington. The record of sea level there is continuous since 1899. There are a number of other tide gauges in the immediate area, and geodesists have made good use of the highly discordant differential sea level trends in this region of converging tectonic plate boundaries to monitor vertical crustal movements. Obviously, a tide gauge record cannot serve both geodesy and global sea level analysis simultaneously. In this particular case, geodesy is the appropriate application. This is so because the low frequency periodic variations of sea level are practically the same at all of the sites due to the small size of the region.
Douglas [1991] identified other unsuitable long tide gauge records, including Manila (Philippines), Tonoura (Japan), Bombay (India), and others. He did find a total of 23 long (60 years minimum, 76 years average) records in 10 oceanographic regions, free of obvious tectonic effects and severe data gaps or defects. After correction for glacial rebound using the model results of Peltier and Tushingham [1989], the trends for these 10 regions averaged 1.8 mm per year with a root-mean-square (rms) variation about this mean of only 0.3 mm per year.
Finally, the question of distribution of tide gauge stations over the sphere must be addressed. Groger and Plag [1993] and others have rightly made much of this matter, but have failed to consider a critical factor; the longer the period of signal variation, the greater the spatial extent of that signal. Thus very long records do not require the coverage needed by shorter ones to establish a value for global change. On the scale of the era of the continuously recording tide gauge (about 150 years), Douglas [1991, 1992] has shown that widely separated tide gauge records show very consistent trends and (lack of) acceleration. Woodworth [1990] also observed the latter. Thus on the 100 year temporal scale, the lack of uniform global coverage appears to be much less important than usually supposed.
Assuming now that an average value of global sea level rise can be, and has been, determined for about the last 100-150 years, the next consideration is whether or not this value has undergone significant change over that time. Fortunately, determining acceleration of sea level change is less formidable than the linear problem, at least in regard to PGR and tectonic plate boundary effects. The reason is that PGR is linear over the tide gauge record, as are vertical crustal movements at plate boundary locations with long earthquake recurrence times. Thus both of these effects drop out in the calculation of acceleration. Woodworth [1990], and Gornitz and Solow [1991] have found weak evidence of acceleration in long European records, but no conclusive evidence of a global acceleration of sea level. Douglas [1992] carried out a systematic global analysis of sea level acceleration, and arrived at a similar result that no acceleration of global sea level has occurred over the last 150 years that is statistically significantly different from zero at the 95 authors have bounded any acceleration that might have occurred in the last 150 years at an order of magnitude or more less than that predicted to accompany global warming in the future [ Houghton et al., 1990].