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INTRODUCTION Recent Changes in Sea Level A Summary TIM P. BARNETT Scripps Institution of Oceanography The purpose of this chapter is to review the behavior of sea level over the past century. This review is prompted by recent interest in global warming and the CO2 problem and the possible increase in ocean level that might accompany such a warming (e.g., Hansen et al., 1981~. The change in sea level in such a scenario is due to both an increase in ocean temperature and a decrease (melting) of landbound ice. This change in relative sea level (RSL) will, in the absence of compensating factors, be global in nature (Barrett and Baker, 1981), although the variations need not be uniform over the globe (e.g., Farrell and Clark, 1976; Clark and Lingle, 19771. The review is organized as follows. The next section summarizes research over the past 20 yr on changes in sea level. Next, the data used to study these changes are examined critically. Two different approaches to estimat- ing RSL change are then reviewed using specific case studies. These sections are intended to point out the nonuniqueness in estimates of RSL change, plus the ap- parent fact that sea level has not been rising at all points in the world's oceans over the past century. The next section summarizes some of the possible causes of RSL change and thus provides an introduction to other chapters of this volume. A concluding section summarizes briefly the 37 status of research on RSL. Given the review nature of this chapter, it has been convenient to rely heavily on two articles (Barrett, 1983a, 1984a) that will serve as basic reference for the discussion of the two different approaches to estimating RSL change and will offer abundant refer- ences for readers interested in delving further into the subject. SOME PRIOR STUDIES OF "GLOBAL" SEA LEVEL Sea-level stations are located mainly on coastal mar- gins and a few islands. Over the vast interior of the world's oceans there are no sea-level data. Thus any analysis of mean sea-level (MSL) data that claims to rep- resent a "global" condition is already attended by consid- erable assumption regardless of the results of the analysis. An effort is made throughout the text to remind the reader of this fact. At least six different estimates of the "eustatic increase" in mean "global" sea level were made between 1940 and 1961. These estimates are summarized by Lisitzin (1974) and are presented in Table 1.1. Perhaps the most notable aspect of these early analyses is that all values agree remarkably well, even though they were obtained by sev- eral different methods and data sets (e.g., sea level or cryological information). All of these studies were se

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38 TABLE 1.1 Estimates of Mean Global Sea-Level Increase Author Rate (mm/yr) Method Thorarinsson (1940) Gutenberg ( 1941 ) Kuenen (1950) Lisitzin (1958) Wexler (1961) Fairbridge and Krebs (1962) Emery (1980) 0.5 1.1 +0.8 1.2to 1.4 1.12 + 0.36 1.18 1.2 3.0 Gornitz et al. (1 982)a 1.2 Barnett ( 1 983a) 1.51 + 0. 15 Barnett (1984a) 1.43 to 2.27 Cryologic aspects Sea level (many stations) Different methods combined Sea level (six stations) Cryologic estimates Selected sea level stations Sea level (many stations) and selected stations Sea level (many stations) Selected sea level stations Sea level (many stations) aThe authors attempt a correction for crustal motion and find . mm/yr. The 1.2 mm/yr is without this correction. verely limited by geographic extent, time span, and accu- racy. A second notable aspect of the early analysis pointed out by Lisitzin was the existence of an apparent "break" in temporal behavior of sea level. Prior to about 1890 to 1900, she found little or no trend in sea level. After that time, however, sea level begins a slow, monotonic rise. Fairbridge and Krebs (1962) attempted to create an estimate of"global" sea-level change between 1860 and 1960. They paid careful attention to station location and data quality. In addition, they showed the high correlation that exists between nearby sea-level stations, thus allow- ing one station to represent a large area. Their final esti- mates show an increase for RSL of 1.2 mm/yr, although they note the estimate is biased by an overabundance of North Atlantic data. Their world sea-level curve shows, as suggested by Lisitzin (1974), a period between 1890 and 1910 of little change. Unfortunately, they never stated exactly how their"global" curve was obtained. Emery (1980) used data from selected stations in the worldwide tide gauge net to estimate a rise in "global" sea level of 3 mm/yr over the past 40 yr. (Note: this is roughly three times the rate estimated by earlier workers; see Table 1.1.) He pointed out that his study is hampered by lack of data in the Southern Hemisphere. As noted above, this problem attends all studies of "global" sea level. Emery also found that the rate of sea-level rise between 1970 and 1974 is almost five times the longer-term value. Unfortunately, a number of problems arise in obtaining these estimates: (1) the erratic distribution and strong clustering of stations, plus the analysis method, make the above number strongly biased to several specific regions and individual stations exhibiting strong MSL increases; (2) the recent estimates of RSL rise have not been cor TIM P. BARNETT reeled for atmospheric effects; simple interannual changes In sea-eve pressure (aim) could easily cause part of the observed change; and (3) the 5-yr averaging time (1970 to 1974) is a time scale typical of short-term climate change and regimes. Changes in ocean temperatures and circula- tion, for example, associated with these epochs, could also account for much of the observed RSL trend (cf. Fair- bridge and Krebs, 1962~. Etkins and Epstein (1982) accepted the 3-mm/yr RSL increase and assumed it applies globally. They then tried to explain the increase in terms of ocean temperature change and discharge from the polar ice sheets. Perhaps their most interesting result relates the observed change in rota- tion rate of the Earth to the estimated change in the polar ice caps. The apparent agreement so obtained in this comparison would be much less impressive, however, if they had not used the 3-mm/yr RSL rise figure of Emery. They also did not discuss the fact that the rotation rate of the Earth increased between 1900 and 1930, and so the length of day decreased. Sea-level arguments, such as they presented, would dictate an increase in length of day (see Etkins and Epstein, 1982, reference 8~. The entire problem of the effect of sea level and ice-cap melting on Earth's rotation characteristics has been described well in the l950s. Further discussion of this subject is deferred to a later section in this chapter. Additional discussion of the Etkins and Epstein paper is given by Robuck (1983~. Gornitz et al. (1982) also attempted to develop an esti- mate of "global" MSL change. They developed large area averages of sea level, thus avoiding the clustering problem that plagued Emery. They generally ignored regions that do not show an increasing trend (e.g., Alaska) and eventu- ally ended up with a 1.2-mm/yr increase as a "global" number. They also attempted to remove vertical crustal motion based on geologic data and to find a RSL trend of 1 mm/yr on a "global" basis. Review of the references supporting the development of their land motion estimate suggests that their correc- tions may be highly unstable. Indeed, the corrections are generally major, relative to the uncorrected trend, and unstable from millennium to millennium (Newman et al., 19801. It may thus be fortuitous that the two global-trend estimates come out as close as they do. There are other problems in their analysis. (1) Eight of the 13 regions used in the global average border the Atlantic Ocean, a fact that biases their estimates of RSL changes to past variability in that ocean. (2) The regional time series are not temporally homogeneous; thus, for instance, the "global" average between 1880 and 1900 is dictated al- most entirely by European data. (3) The use of raw aver- age trends for each region to develop a "global" trend allows a few active regions to dominate the global number (cf. Table 1 of Gornitz et al., 1982~. _ _ _ _ 1 _ _ _ 1 _ _ _ _ _ ~ ~ ~N 1 1 1

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RECENT CHANGES IN SEA LEVEL: A SUMMARY THE DATA Sources and Distribution Sea-level data have been taken routinely since at least 1808 (Brest, France) and even before, e.g., Amsterdam, 1682 (R. Fairbridge, Columbia University, personal com- munication). These data have been organized by The Per- manent Service for Mean Sea Level, Institute of Oceano- graphic Science, England (Lennon, 1975-1978), and are available in printed volumes and on magnetic tape. The distribution of stations is shown in Figure 1 of Emery (19801. That illustration shows the highest station densi- ties in the United States and western Europe followed by Japan. Long-term records from the Southern Hemisphere, e.g., South America and Africa, are few in number. Long- term records from islands in the open ocean far from land are almost nonexistent. Hence, any attempts to infer "global" changes in sea level from this data set are at- tended by substantial assumption-the distribution of data is simply not adequate to represent global coverage. Instruments Interestingly, little was found in the literature that de- scribed the instrumental methods. However, Lennon (1970) provided a good overview of current instruments and their possible problems and there were many. Most modern tide data come from instrumental mea- surement (e.g., a float in a "stilling well") with the mea- surements continually recorded by a pen and ink device. In recent years the data recording mode has become digi- tal. Before 1900, however, the measurement methods varied considerably. The long-term San Francisco record was obtained in the above manner, even though the actual measurement site was moved four times (S. Hicks, NOAA, personal communication). The old MSL records from India (e.g., Bombay) were obtained by human "tide parties" whose members made frequent visual sightings on a gradu- ated staff inserted in the water (B. Zetler, Scripps Institu- tion of Oceanography, personal communication). Need- less to say, the risk associated with the data increases considerably as one reaches back beyond 1900. Potential Problems The sea-level data have numerous potential difficulties. Some of these are listed below. [See also Fairbridge and Krebs (1962) for additional problems.] 1. Station locations were subject to position change, for example, as harbors developed through the century. 39 These changes can add discontinuity to the time series and, if undetected, can induce apparent long-term trends. 2. Instrument position changes can be accommodated if the old and new locations are tied to a common geodetic reference point. It is often difficult to discover if this was done. But even the leveling (reference) operation is not without difficulty (see below). 3. Tectonic uplift/subsidence of the land mass on which the gauge sits will induce an apparent sea-level change. In some parts of the world (e.g., Alaska and Scandinavia), this signal is as large or larger than any possible oceano- graphic change (e.g., Hicks and Shofnos, 1965~. [Note: this effect is most pronounced in regions of glacial re- bound (high latitudes) and near the mouths of large rivers (e.g., in the Gulf of Mexico) where heavy sedimentation causes subsidence.] 4. Mean sea level is affected by a variety of physical processes (e.g., Lisitzin, 1974; Namias and Huang, 1972), including changes in water temperature and salinity, river runoff, local and nonlocal currents, wind, waves, and atmospheric pressure. All of these can change sea level in conflicting ways, and these changes can be as large as the signal under study. Since all of the variables mentioned above are subject to climatological variations, they char- acteristically have "red spectra," which means they can contribute to estimates of trends in sea level. 5. Geodetic leveling between sea-level stations appar- ently cannot be used to remove relative vertical motion of the land, if the stations are more than a few hundred kilometers apart. Sturges (1966) showed that the 500-mm north-south sea-level difference inferred from leveling data to exist along the Atlantic seaboard was inconsistent with oceanographic data. The same situation was found along the west coast of the United States. More shockingly, Balazs and Douglas (1979) reviewed five different at- tempts between 1969 and 1978 to obtain the relative eleva- tion difference between San Francisco and San Pedro, California (about 700 km apart). According to those sur- veys, the two cities had a relative vertical displacement rate of 70 mm/yr. The RSL trend between the two was 2.1 mm/yr the difference is a factor of nearly 35. Thus, the leveling data for both coasts of the United States may well contain serious errors of unknown origin when the separa- tion distance exceeds a few hundred kilometers. 6. The possible instrumental problems are legion. The ability to speculate in this area far exceeds the available information. Lennon (1970) gave a good overview of possible problems with "modern" equipment. Errors of 180 mm or more are possible in sea-level measurement, and they may be virtually impossible to detect in the data. Contrasting this error with an often stated RSL rise of 1 mm/yr gives one an appreciation for some of the poten- tial uncertainties in sea-level studies.

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40 - ''-~ -(- 4~ fat ~ ~ ::: FIGURE 1.1 Location of primary (~) and secondary (x' stations versus estimates of vertical crustal motion for the period 1000 to ESTIMATES OF RELATIVE SEA-LEVEL CHANGE: KEY STATION APPROACH Methods One approach to estimating change in global RSL is to analyze data from key stations, arguing that changes at these stations are representative of changes in RSL in large (1000+ km) regions surrounding the stations. Ex- amples of such analyses are found in Table 1.1 (e.g., Fairbridge and Krebs, 1962; Barnett, 1983a). The latter work is summarized here. The use of the key station approach imposes the follow- ing series of constraints on the data to be analyzed. 1. High-quality, continuous measurement that reveals no sudden shifts suggestive of station movements should be used. The records should be as long as possible. 2. Station locations should be away from areas of strong tectonic movement (e.g., separated from areas of major deposition/uplift). 3. Stations should be unaffected by spurious physical TIM P. BARNETT - -_ ~_-~_ 12 ~_ TO -2; ~ ~ ~~ _~1 ~ ~- 1000-2000 yr BP `~;] J.~'\-\\ WAX ~ ) 1 I' / _ 2000 yrBP. Contours are in millimeters per year. After Newman et al. (1980). processes (e.g., gauge exposed to strong freshwater inva- sions). 4. The spatial density of stations by oceans should be proportional to the relative areas of the respective oceans, e.g., 2.4/1.5/1.0, for the Pacific/Atlantic/Indian (cf. Sverdrup et al., 1942~. The stations should be synchronous in time. Such a distribution will allow equal weight to be given to all oceans and years in the subsequent analysis, thereby avoiding biasing problems. 5. Finally, the selected stations must represent large . . . geographic regions. The locations of a set of stations that generally satisfy these criteria are shown in Figure 1.1 and are listed in Table 1.2. A method of inferring, quantitatively, the existence of a signal that is coherent over all portions of a data field using empirical orthogonal function (EOF) analysis (cf. Backus and Preisendorfer, 1978; Barnett, 1978) was ap- plied to the primary key station set and to the secondary station set to check sensitivity of the results to data pertur- bations. The sea-level data at position i are represented by

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RECENT CHANGES IN SEA LEVEL: A SUMMARY hi(t), i = 1, 2, . . in the study. Define and . NP, where NP is the number of stations hi = (hift)>t' o2=,, (1.1) where ~ >, denotes a time averaging operation. The data were normalized to have unit variance and zero mean, i.e., h (t)- h h' (t) = i I . ( 1.2) csi This is a crucial step for later interpretation of the results, for now each station will have equal weight in the subse- quent analysis. This, coupled with equal time and area weighting in the key station selection, ensures a more or less equal geographic weighting for the analysis. Next form the correlation matrix: Cij = (`h if t~h~(t)~. (1.3) Denote the eigenvectors and eigenvalues of Eq. (1.3) by Bni and An, respectively, and the associated principal com- ponents: Antt) = ~Bni h'(t) (1.4) Finally, it follows that 1 h (t) = MA n (t)Bni ~ 1 .5 n Special properties of the (Bn, An) are given in the above references. The EOF representation of the RSL field is interpreted as follows: Results 41 Figures 1.2 through 1.5. For the longer time period, the B all have the same sign (Figure 1.2), indicating the exis- tence of a coherent pattern of variation in the data set. Note all stations analyzed are not contributing equally to this pattern since all By are not the same size. Figure 1.3 shows that the coherent change is associated with increas- ing RSL. Further, the time variation appears well fit by a simple linear trend ( 1.51 + 0.15 mm/yr). Analysis of the more recent period suggests RSL is not rising uniformly within the data set analyzed (Figure 1.41. Indeed the implied decrease in RSL in the eastern Asian region TON is supported by independent hydrographic observations (e.g., White et al., 1979~. The implied RSL trend in Figure 1.5 is 1.79 + 0.22 mm/yr. (Note that neither of the temporal reconstructions suggests an accel- erating rate of RSL in recent years.) Consideration of the results and the data shows that the EOF analysis is being dominated by temporal trends. Stations with positive trends have B. components of one sign; those with negative trend have By components of the opposite sign. The analysis method is extracting a single trend common to all stations that accounts for as much of the total field variance as possible. Extraneous noise, which would normally contaminate study of data from individual stations, is therefore effectively filtered out of data prior to trend estimation. TABLE 1.2 Sea-Level Stations Station PRIMARY San Francisco Honolulu Tonoura, Japan Balboa, C.Z. Sydney Bombay Baltimore Cristobal, C.Z. Cascais, Port. Takoradi 1. The Bni represent average patterns of spatial covari ability between the NP-members of the sea-level field. If all members are fluctuating in unison, as would be the case for a global change in RSL, then all components of Bit, the first, most energetic eigenvector, will have the same sign. 2. The Angst) modulate, in time, the intensity of the spatial patterns of By . For instance, a secular trend in the hi coherent at all stations will be manifested by a secular trend in Alit). 3. Using Eq. (1.5) and an average value of the Hi from SECONDARY Eq. (1.1), it is possible to reconstruct the behavior of Ketchikan global sea-level change if such a creature exists. Hosojima Aden Aberdeen Helsinki Montevideo Ystad The results of the above analysis for two different time periods, 1903 to 1969 and 1930 to 1975 are shown in Missing Abbreviation Start End Years SFO HNL TON BCZ SYD BOM BAL CRS CAS TAK MON 1862 1874 1905 1975 1894 1975 1908 1969 1897 1977 1878 1964 1903 1975 1909 1969 1882 1975 1930 1975 1 1 4 1 1919 1975 1894 1977 1879 1960 45 1862 1965 1 1879 1970 1938 1970 1887 1974

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42 ho 1 o o x 2O m 50 So 1O o 40 ~ 1 ~ ~ ~ 1 t ~20 O J Z ~J C) ~ J ~t0 Y Z - 1= Z O Cal >a O Of ~As ~ 0 - of) I ~m ~ Co m Cry ~ ~ : ~m l o PACIFIC {INDIAN; ATLANTIC 20 STATION FIGURE 1.2 Mode 1 eigenvector components by station for the analysis period 1903 to 1969. If all stations contribute equally to the pattern, then all eigenvector components would have value (NP)-s. From Barrett (1983a), Climate Change (American Meteorological Society). In conclusion, it appears that a large coherent pattern of increasing RSL exists over much of the globe where data are available. The rate of increase is rather uniform spa- tially (Bit - (NP)-s) except in the westem and Indo-Pa- cific regions in the past 3 to 4 decades. These results are qualitatively unaltered by substantial perturbation of the original set or method of normalization. ESTIMATES OF RSL CHANGE: AREA AVERAGE APPROACH Methods Selection of one or more unrepresentative stations in the key station approach can introduce spurious inforrna- tion into the resulting analysis. An obvious way around this potential problem is to average a large number of - - z z o z A: 0~) - 5 LO - " . ~ . . ~ _. . . ~- 1111111 1!111 ~l11111111111111111111111111!111111111111111111illllll 1 910 1920 1930 1940 1950 1960 Tl ME FIGURE 1.3 The principal component for the first eigenvector of the analysis period 1903 to 1969 scaled to give estimated RSL trend in real units (centimeters). The solid line represents a least squares fit to the data. From Barnett (1983a), Climate Change (American Meteorological Society). TIM P. BARNETT -30 o LO En J z c:, at 0 >a ~en J en Y A: A: c: ~ PAC I F I C ~ I N DIAN ~ ATLANT IC STAT I ON FIGURE 1.4 As in Figure 1.2 but for analysis period 1930 to 1;975. From Barnett (1983a), Climate Change (American Mete- orological Society). stations within a region to get a representative estimate of RSL in that area. Examples of this approach may be found in Hicks (1978), Emery (1980), Gornitz et al. (1982), Barnett (1984a), and Aubrey (1985~. Unfortunately, this apparently simple procedure is not without its problems as we shall see below. One way of objectively obtaining a quantitative area average was proposed by Bamett (1984a). Denote by hints the time history of RSL at station i in a predetermined region and form Ci. as in Eq. (1.3~. Again denote the first eigenvector of Cij {y Bit. It turns out that for most of the sea-level data studied, this first mode accounts for the - E OCR for page 37
RECENT CHANGES IN SEA LEVEL: A SUMMARY majority of the non-noise variability in the hilts. Under these conditions, the B,i provide a set of weights that can be used to average the hi over the domain of analysis. Thus one measure of a regional average would be Rk (t) = A I,BIi hints, (1.6) where A = >,B7i and Rk is average sea level for the kth i region and i= 1, 2, . . . NP. Note Ri is comparable to a principal component except for the normalizing factor A. The latter is necessary if the hints do not all begin and end at the same time. One may use only values Of B,i with the same sign in Eq. (1.6~. This ensures that the signal coherent and in like phase at the NP stations is included in Rk. Alternatively, all elements of B,,i could be used in Eq. (1.6) to obtain a different version of the area average. Results The results of applying the above methods to the six regions shown in Figure 1.6 are given in Figure 1.7. The 43 regional results are much the same as those suggested in Figures 1.2 and 1.4. RSL seems to be increasing generally in most of the study areas. The exception (also seen in Figure 1.4) occurs along the east coast of Asia (Region 4), where RSL is seen to have been decreasing since the mid- 1950s. Note also the highly differential behavior of the regional trends. For instance, in Region 1, RSL seems essentially static from 1880 to 1920, after which time it begins to increase. By contrast the east coast of North America (Region 3) shows a rather steady increase since 1900 (the beginning of the data). For the reasons noted previously, the estimation of "global" sea-level change does not appear possible with present data. However, it is of interest to estimate the average of the data we do have available. With this in mind, the analysis using the area average method was performed on the objectively defined regional averages shown in Figure 1.7. Use of Eq. (1.6), then, gives an "overall average" (Ro), provided the hi represent the re- gional averages defined earlier and the By ale the mode-1 eigenvector components of the regional analysis. Note that the distribution of regional averages is roughly area representative of the respective oceans. Prior to the early 1900s, however, the temporal representativeness is biased to the Atlantic and Indian oceans. The EOF analysis of the regional data (not illustrated) i (~9)~;~/~/664 i I "hi;-Jo; ~ 6 f ~ ; - - r\ - T i - ~ rI rat ~ ( ~ ,,~,,,,, ,,,,,,,,, , - ,, ,,,,,~., . . . . ~ V ,. ~ .r . W \ -jet Wt: -- ~ ~ Al ~ ~ \ ; ~ If, , 4-\ ''eel 1 1 i , 1 lo-.. ~, ! 1 1 / / '' _. ,.,, ,./, ~ A/' - = ~ FIGURE 1.6 Station and region location chart. The upper number of each pair refers to region numbers. The numbers in parentheses indicate the number of individual stations in the region. From Barnett (1984a) with permission from the Ameri- can Geophysical Union.

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44 2O, 1 ~ I ~ I I I REGION I EUROPE/AFRICA o -10 -2C 20t 20 10 . -IC , 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -2G 1900 1920 1940 1960 1980 1900 I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1' ~ REGION 3 EAST COAST NORTH AMERICA 2C 1( -10 ^~ -20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -Cal _ 1900 1920 1940 1960 1980 201 _ 10 _ n -10 _ -20 _ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ! REG ION 5 INDO PACI FIC - 1 1 1 1 1 1 1 1 1 1 1 1 1 ~ 1900 1920 1940 1960 1980 FIGURE 1.7 Regional averages of annual sea-level anomaly. From Barnett (1984a) with permission from the American Geo- physical Union. showed that the first mode components all have the same sign, except for the Southeast Asian region. Thus, to first order, all the regions vary in unison, except the Southeast Asian region. Since the first mode captured approximately 50 percent of the total variance, it contains the dominant signal in the sea-level set. Further, the in-phase eigencom- ponents were all of approximately equal magnitude, sug- gesting the uniformity of the relative sea-level variation associated with this mode. However, since there is a well TIM P. BARNETT I I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 REGION 2 WEST COAST NORT H AME R I CA . . . 1920 1940 1960 1 980 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 REG I ON 4 EAST COAST AS I A 1 1 1 1 1 1 - 1 1900 1920 19401960 1980 20 10 -IC --2G I 1 1 1 1 1 ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 REGION 6 WEST COAST CENTRAL & SOUTH AMERICA - . I ~L_ I ~1 1940 1900 1920 _ 1960 1980 defined area that is not in phase with the other regions, one cannot claim the existence of a uniform pattern fluctuation common to all available sea-level data. The time domain result of the above operations is shown in Figure 1.8 for the periods 1881 to 1980 and 1930 to 1980. The Ro curve of the 100-yr data set has a slope of the trend that is 1.43 + 0.14 mm/yr, a value close to that obtained by other workers. This trend accounts for 81 percent of the total variance in Ro However, it is clear that

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RECENT CHANGES IN SEA LEVEL: A SUMMARY a simple trend is not the best representation for the entire 100-yr set, as it represents a compromise between times of little change (1881 to 1920) and steady increase (1920 to 1980). The analysis for the period 1930 to 1980 is well repre- sented by a trend of magnitude 2.27 + 0.23 mm/yr that accounts for 87 percent of the variance in the Ro series. The larger slope value for the 1930 to 1980 sea-level set is due to omission of the first 50 years of data (1881 to 1930) when little or no trend was apparent. This result empha- sizes the sensitivity of the results to the length of record considered. The past 50 years of data were exceedingly well fit by a simple linear trend. Would a more exotic function give a better fit to the data? The realistic answer is "No." The residual time series for 1930 to 1980, after removal of the trend, was indistinguishable from white noise (zero mean and a standard deviation of 12 mm), based on analysis of its correlation function. Thus higher-order fits, which appear to capture more variance, are likely fictitious and could lead one to an erroneous view of the data. Cautions: Nonuniqueness The selection of the gross regions for EOF analysis was based on geographic considerations. The selection could have been made on the basis of water mass types or rela- tion to specific ocean gyres, for example. Any of these criteria seem reasonable and could be easily rationalized. Using different selection procedures might have changed somewhat the resulting regional definitions. The magni- tude of the Rk certainly would have been affected. A final estimate of global RSL obtained by averaging the Rk will 20 10: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ~ -10 _ 1 1 1 1 1 1 20 1900 1920 1940 1960 1980 45 also clearly depend on the original selection of the gross regions. The EOF analysis was performed on the correlation matrix of the hift). Use of the covariance matrix would have given a different set of weight to use in Eq. (1.6~. It might also be argued that the weighting in Eq. (1.6) should be proportional to B,i2 since the latter represent pattern variance. Both alternatives would concentrate attention on the sea-level data with the highest variance in this case, greatest trend thus guaranteeing a higher value of global RSL change than estimated here. Finally, one might ask, "Why not compute the EOFs of all the stations together?" This will lead to a result biased by regions of highest station density. The resulting global average would thus be, in reality, no more than the RSL changes associated mainly with one ocean, the Atlantic (50 percent of the stations). The point of the above discussion is that there are many valid but rather different ways to estimate "global," even regional, RSL changes. Without an adequate global sea- level network, which is unlikely to exist in the near future, the estimate of "global" RSL change will remain an uncer- tain business. Tests of the different approaches mentioned above to obtain this average suggest that estimates of global change with current data can vary by a factor of 50 percent a scatter induced solely by the analysis method. One should not become too enamored with a single esti- mate of "global" RSL change or depend on it for crucial policy decisions. DISCUSSION: POSSIBLE CAUSES The results of the previous section indicate that on average there has been a rise in RSL along most of the FIGURE 1.8 Estimates of overall average (Ro) of sea-level data for two different time periods. The solid/dashed lines are least squares fits of a linear trend. From Bar- nett (1984a) with permission from the American Geophysical Union.

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46 Earth's coastal margins and in central ocean regions where data have been gathered. Exceptions to this statement occur in areas of known upward crustal motion and in areas where the sense of the vertical motion is not so well known, e.g., east Asia. It is unknown whether similar changes are occurring over the interior of the southern oceans. At any rate, it is tempting to state the results as follows: "Relative sea level is rising 'globally' at a rate of about 1.5 to 2.0 mm/yr." Subject to the numerous caveats and assumptions stated earlier, let us now take this rate as a working hypothesis. How might this hypothesis be ra- tionalized? This section serves to introduce some of the possible answers to this question and comes largely from Barnett (1983a). Other chapters of this volume will deal with these individual possibilities in more depth. Subsidence Argument The average result might simply be due to the fact that all the stations analyzed, plus all the regions they repre- sent, are slowly subsiding because of crustal downthrust and/or sediment compaction. If the Earth is not contract- ing, then the subsequent compensation could occur at high latitudes (glacial rebound?) or in the ocean basins. The work of Hicks (1972) and Newman et al. (1980) suggests that the value for the RSL increase is not inconsistent with the uplift/subsidence rate alone. The above argument is not particularly convincing for the following reason. The spatial scale of observed coher- ent RSL increase, when projected to the regions that the individual stations represent, is substantially larger than the uplift/subsidence spatial scale shown in Figure 1.1. Furthermore, the current stations are rather uniformly distributed among up/down motion areas, at least as they were about 1500 yrBP. In fact, 7 of 11 primary stations are in what were inactive regions. It would be a remark- able coincidence if the current station pattern put all loca- tions in areas of subsidence. Indeed the detailed studies of Clark et al. (1978) suggest this did not happen. However, in this volume, Pettier (Chapter 4) and Bloom and Yo- nekura (Chapter 6) clearly show the potentially strong contaminating effect that crustal motion has on the RSL data. Global Warming Melting the ice caps and warming the oceans due to a global temperature increase would give rise to an increase in global MSL as noted earlier. Assume for the moment that the RSL change is due to this effect. What other evidence might be used to test this hypothesis? Ocean Warming One might simply look at the shape of a global or hemispheric temperature curve since 1900 TIM P. BARNETT and compare it with the time series of coherent RSL and ocean temperature (Figure 1.9~. The air temperature curve rises slowly until around 1940 after which time it drops. The RSL curve shows no such behavior. However, time histories of sea-surface temperature (SST) from the world's oceans show a linear trend (increasing) identical to the RSL curve, although they too show an apparent decrease beginning around 1960 (see also Kukla et al., 19771. The 1C change in SST since 1900, if distributed in the vertical by some type of mixing process as suggested by Cess and Goldenberg (1981), would raise RSL at the rate of about 1.1 mm/yr remarkably close to previous and current estimates. Indeed, Gornitz et al. (1982) concluded that much of the observed RSL can be attributed to this thermal expansion. Roughly one-half of the rise of 1C since 1900 through 1970 can be ascribed, if so desired, to differing instrumen- tal methods, e.g., bucket versus injection temperature (Barrett, 1984b). Also, it is difficult to conceive of the world's oceans warming by 1C and the atmosphere not following suit by a like amount. Part of this inconsistency may be due to the general practice of estimating hemi- spheric temperature from land stations only (Mitchell, NOAA, personal communication). The work by Paltridge and Woodruff (1981) partially overcomes this problem but, in turn, has severe difficulties of its own. At any rate, this "global" temperature curve does not agree with the RSL with regard to phasing, and this is a crucial disparity. Changes in the vertical density structure of the ocean, such as might be associated with warming, have been investigated over time scales of 40 to 60 yr by Robinson (1960) for the Pacific and Barnett (1983b) for the North- ern Hemisphere oceans. Both find no significant change in the density field of the upper 1000 m of the ocean. Both point out the very noisy nature of the hydrographic data they used. Studies of upper ocean variability at time scales of 20 to 30 yr are varied in their conclusion (e.g., Gammelsrod and Holm, 1 98 1; Tabata, 1 98 1 ). Work by Wunsch ~ 1972), Pocklington ~ 1972,1978), and Roemmich (Chapter 13, this volume) suggest that, at least near Ber- muda, warming of the upper ocean can or cannot explain the local RSL change, the result depending on the length of record analyzed. This is clearly an unsatisfactory situ- at~on. In summary, the connection between global atmospheric warming and the behavior of the ocean over the past 70 to 80 yr, while suggestive, is hardly convincing. Astronomical Observations Another possible means of checking indirectly the warming assumption lies in a rich set of scientific work on the theory of the Earth's rotation done in the 1950s. Lambeck (1980) gives an excellent summary to back the discussion, as do Munk and McDonald (1960~.

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RECENT CHANGES IN SEA LEVEL: A SUMMARY 1.0 ~ - o - ~ 0.5 _ At: o z I.3J o LLI ~ - 0.5 111 A4A~NA . _\ -1.0 1 1 1 1 900 1920 1940 YEAR - ~ _ Zz LOLL O 1 - FEZ o Ins to C 1 . .. ./ 5 1900 ~ 1 1 1 1 1 1 920 1940 1960 YEAR ,, 0.5 _ o - o z LLI o a LLJ ~ -0.5 :: 1 1 1 1960 ... .~ |~ ~ INDIAN OCEAN -- 1! 1 gNORTH PACIFIC i air i ~X\ \ ~ i ~\NORTH ATLANTI C i\| / jet/ an/ EQUATORIAL PACIFIC 900 1920 1940 1960 YEAR FIGURE 1.9 Time series of key climatic variables for the period 1900 to 1970. Upper panel: Northern Hemisphere temperature anomalies (after Jones et al., 19821; middle panel: "global" sea- level trend reconstruction (Barrett, 1983a); lower panel: sea surface temperature anomalies averaged over large ocean areas by pentad. From Barnett (1983a), Climate Change (American Meteorological Society). 47 Change in the length of day (I.o.d.) The change in l.o.d. from 1860 to 1970 is shown in Figure 1.10 (courtesy, T. Van Flandern, U.S. Naval Observatory; also see Brouwer, 1952~. [The l.o.d. data until 1956 were derived from lunar occultation observations of Ephemeris Time minus Uni- versal Time. After 1956 the data came from U.S. Naval Observatory observations (McCarthy, 1976~.] Only after the early 1900s do the data obtain sufficient accuracy to become highly useful (see Lambeck, 1980~. Now a rise in sea level of 1 cm, if due to melting on Greenland and/or the Antarctic continent, will increase the length of day by 0.06 ms (Munk and Revelle, 1952a) as the Earth's rotation rate slows to conserve the change in momentum induced by the net mass redistribution. A 1.5-mm/yr change in RSL is equivalent to a 1 ms/century change in l.o.d. On the other hand, if the increase in sea level is due only to a uniform warming of the oceans (thermal expansion), Munk and Revelle (1952b) showed that there will be negligible impact on the l.o.d. Figure 1.10 shows that the majority of the variance in the l.o.d. must be explained by other processes. Indeed, the rapid decrease in l.o.d. in the early 1900s is exactly opposite to any sea-level induced effect. However, if one considers the secular trend in l.o.d., then the effect of RSL rise due to polar melting cannot be ruled out, but the l.o.d. will also increase as tidal friction slows the Earth's rota- tion rate. The effect is shown on Figure 1.10 and seems to offer an adequate explanation for the scalar trend in l.o.d. (see Lambeck, 1980 for more in this area). Other reasons for increase in l.o.d. are given by Pettier (Chapter 4, this volume). Changes in pole position In a series of papers, Munk and Revelle (1952a,b, 1955) showed that the position of the Earth's instantaneous pole of rotation is highly sensi- tive to small, differential changes in amount of polar ice and its position. They compute the amount the (north) pole will be displaced toward Greenwich (~) and toward 90E of Greenwich (it) depending on relative changes in ice concentration as reflected in RSL changes. A crude history of the long-term migration of the rota- tion pole is shown in Figure 1.11 (Yumi and Yokoyama, 1980; actual data courtesy of D. McCarthy, U.S. Naval Observatory). The quality of data such as these deserves special attention, for they can be attended by numerous sources of error. However, it appears that the general secular trend in the illustration is reasonable, at least with respect to direction and order of magnitude in displace- ment. For further discussion in this area, see Melchior and Yumi (19721. Using the theoretical results from Munk and Revelle (1952b, Table b, one finds a 1.5-mm/yr linear increase in RSL, if due to approximate equal melting on both Green- land and Antarctica, will cause the pole to move (linearly) toward 60W. ELambeck's (1980) version of these results

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48 +40r FIGURE 1.10 Secular variations in length of day (l.o.d.) in milliseconds. The line denoted "sea-level effect" is the change in l.o.d. expected from the RSL change, if that change was induced by polar melting. The line denoted "TF" is the change in l.o.d. caused by tidal friction. From Bar nett (1983a), Climate Change (American -4G Meteorological Society). . +2.0 _ ~ _ ~ O - -2.C (his Table 9.2) is qualitatively the same but has some quantitative differences.] The heavy line bisecting the data is directed towards 70W. The observed (linear) travel distance is approximately 730 cm. This contrasts with 180 cm expected on theoretical grounds. Assuming most of the melting occurred on Greenland would change the theoreti- cally expected direction of motion to approximately 37W and increase displacement to 826 cm. Both possibilities appear clearly within the range and uncertainty of the combined MSL and astronomical data sets. If melting of the landlocked ice sheets is completely responsible for all the RSL change, then this implies that roughly 45,000 km3 of ice (roughly 0.2 percent of the land-ice volume) has melted since about 1900, i.e., the change is glacioeustatic. [Note: this value is about the magnitude that Etkins and Epstein (1982) estimated for the period since 1940.] The astronomical results suggest that this volume would have to come about equally from Greenland and Antarctica or mainly from Greenland alone because the Antarctic ice sheet is not so asymmetric with respect to the mean axis of rotation as Greenland, and hence changes there do not affect the position of the axis as much. In any event, current knowledge suggests that the ice volume of both Greenland and Antarctica is relatively stable (see Chapter 10, this volume). Unfortunately, the residual in such calculations is enough to explain the in- crease in RSL (cf. Lambeck, 1980~. Lambeck states, however, that estimates of this residual are both positive and negative. Accretion of the polar ice would lower RSL-but then the rotation axis would presumably have a secular motion just opposite to that currently observed. The assumption of approximately equal melting at both poles seems in reasonable agreement with the astronomi- cal observations; however, the polar wandering can be explained in terms of other processes that need not affect RSL. Continued rebound effects from the Pleistocene deglaciation could explain the polar wandering (Dickman, 1979; Nakiboglu and Lambeck, 1980, 1981), although there is ample room for argument on the details of these theo- retical calculations and on the appropriate time scale of the effects (Dickman, 198 1; Sabadini et al., 1982~. The posi TIM P. BARRETT ~ _ ~ it= 1 1 1 1875 1900 1925 YEAR ~ +4 O /~_\ 1950 1975 +2.0 _ O _ -2.0 _ ~4.0 lion of the pole also will be affected by continental drift. Given typical drift values (e.g., Minster and Jordan, 1978), the resulting pole displacement will be but 10 to 20 per- cent of that observed (McCarthy, 1972; Mueller and Schwartz, 1972; Dickman, 1977~. These points are con- sidered in depth in Chapter 4, this volume, by Pettier. It is sufficient to say that the astronomical data cannot be used exclusively to explain RSL change. Glacial Retreat Mountain glaciers hold roughly 1 percent of the total land ice (cf. Flint, 1971) and at first thought would seem an unimportant source of RSL change. However, moun- tain glaciers show large variability in time, and one needs only a 20 percent reduction in their volume to obtain the observed RSL increase. Consideration of their retreat rates since 1900 suggests that mountain glaciers could account for a significant fraction of the observed RSL. Because they occur asymmetrically around the Earth at high latitude, their melting will also increase l.o.d. (as goow flu tom) -600 -300 1 1 1974 ~,~6 21944 1920 1908>< 1902 - _ ~950 70 W _ _ '< oo FIGURE 1.11 Observed motion of the mean pole of rotation. Displacements in centimeters toward Greenwich (~) and 90E of Greenwich (it). The solid arrow directed toward 70W indicates the average direction of pole motion between 1900 and 1975. Each data point represents the average of six annual mean posi- tions thereby minimizing biasing effect of the Chandler wobble. From Barnett (1983a), Climate Change (American Meteorologi- cal Society).

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RECENT CHANGES IN SEA LEVEL: A SUMMARY observed). Their melting should also cause the axis of rotation to wander. Preliminary calculations by Lambeck (1980) suggest that this deglaciation plays a role in the variations of ~ and it, although it does not dominate the observations. Mountain glacial retreat has been studied in more depth by Meier (Chapter 10, this volume), who concludes that a significant fraction of the observed RSL change could be accounted for by this mechanism. Ocean Circulation Changes It is well known that RSL is intimately involved with the oceanic circulation systems (e.g., Reid and Mantyla, 1976~. Sea level roughly tends to be higher in the central parts of the ocean's gyres because of the general geostro- phic balance of the clockwise circulation of the current systems (counterclockwise in the Southern Hemisphere). The reverse situation applies for counterclockwise gyre systems. A unique pattern of reduction/increase in the general circulation of the oceans could give a RSL change at the coastal boundaries as observed and a subsequent change in the central gyres where, generally, we have no information. The above ideas could be checked through an exhaus- tive analysis of the historical hydrographic data. The available superficial studies of these data, however, sug- gest that the effect, if real, may not be important. For instance, the resulting magnitude change in the ocean cir- culation systems would have been noticed, at least qualita- tively. Further, White and Hasanuma (1980) and White et al. (1979) showed that coherent dynamic height variations occur throughout the edges and center of the Pacific gyre. If the circulation change idea was correct, the fluctuations in the western edge should have been out of phase with those of the central ocean. Also, Robinson (1960) and Barnett (1983b) showed no statistically significant differ- ences in limited hydrographic data below 100 m depth obtained from nearly identical sites between 1824 and 1958 and between the 1920s and the 1970s, respectively. Finally, it may be noted that circulation changes would have no appreciable effect on the Earth's rotation (Munk and Groves, 1952~. Chapters 2 and 3 in this volume by Thompson and Sturges, respectively, deal with the circula- tion mechanism in more depth. CONCLUSIONS Numerous diverse studies over the past four decades have been directed at the problem of sea-level change. These studies have suggested that, on average (over the available data set), RSL is increasing. Notable exceptions to this statement occur around Scandinavia, Alaska, and 49 parts of eastern Asia. All studies have been attended by serious limitations, which include the following: 1. The lack of data in the Southern Hemisphere and mid-ocean regions means one must accept a substantial risk in interpreting the results in terms of global changes. 2. The effect of vertical crustal motion induces a "sig- nal" in each station's data that cannot reliably be removed. Hence, it is possible, but highly unlikely, that vertical motions of the crust are responsible for almost all of the RSL change. New geophysical measurement systems, e.g., very-long-baseline interferometers, may remove this problem in the future. 3. A coherent global signal can be detected in a relative sense. Attributing a magnitude to it, however, is subject to the problems included in 2 above plus many others. Given the limitations noted above, the following state- ments characterize our current knowledge regarding RSL change: 1. The average rate of increase, according to the exist- ing sea-level data set, is roughly 1 to 2 mm/yr. Different methods of analysis alone can cause variations on the order of 50 percent in these estimates. 2. The existence of a "globally" coherent pattern of RSL increase has not been confirmed with existing data and analysis techniques. Neither is the existence of an ac- celerating rate of RSL increase in recent years. 3. It is not possible, at this time, to explain the reasons why RSL seems to be increasing at many stations. It is possible, but unlikely, that a large part of the RSL change observed is due to vertical crustal motion alone. Fortu- nately, there are a number of other interesting hypotheses that could explain the RSL change. The current data are not adequate to unambiguously test these ideas. However, many of these possible explanations can be rigorously tested, and the approaches for doing so are discussed in Chapter 14 (this volume). REFERENCES Aubrey, D. G. (1985~. "Recent sea levels from tide gauges: Problems and prognosis, in Glaciers, Ice Sheets, and Sea Level: Effects of a CO2-Induced Climate Change, Polar Research Board, National Academy Press, Washington, D.C., pp. 73-91. Backus, G., and R. W. Preisendorfer (19781. On the positive components of the first eigenvector of a positive symmetric matrix, Appendix in Barnett (1978). Balazs, I., and B. Douglas (19791. Geodetic Leveling and the Sea Level Slope along the California Coast, NOAA Tech. Memo., NOS NGS 20, National Geodetic Survey, Rockville, Md. Barnett, T. P. (19781. Estimating variability of surface air tem perature in the Northern Hemisphere, Mon. Weather Rev. 106, 1 353-1 367.

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RECENT CHANGES IN SEA LEVEL: A SUMMARY Nakiboglu, S. M., and K. Lambeck (19811. Corrigendum, Geo- phys. J. Roy. Astron. Soc. 64, 559. Namias, J., and H. Huang (19721. Sea level at Southern Califor- nia: A decadal fluctuation, Science 177, 351-353. Newman, W., L. J. Cinquemani, R. R. Pardi, and L. F. Marcus (19801. Eustasy and deformation of the geoid: 1,000-6,000 radiocarbon years BP, in Earth Rheology, Isostasy and Eu- stasy, N-A. Morner, ea., Wiley, New York, pp. 555-567. Paltridge, G., and S. Woodruff (19811. Changes in global sur- face temperature from 1880 to 1977 derived from historical records of sea surface temperature, Mon. Weather Rev. 109, 2427-2434. Pocklington, R. (19721. Secular changes in the ocean off Bermuda, J. Geophys. Res. 77, 660~6607. Pocklington, R. (19781. Climatic trends in the North Atlantic, Nature 273, 407. Reid, J. L., and A. W. Mantyla (19761. The effect of the geostro- phic flow upon coastal sea elevations in the Northern Pacific Ocean, J. Geophys. Res. 81, 3100. Robuck, A. (19831. Global mean sea level: Indicator of climate change? Science 219, 996. Robinson, M. K. (1960~. Statistical evidence indicating no long- term climatic change in the deep waters of the North and South Pacific Oceans, J. Geophys. Res. 65, 2097-2116. Sabadini, R., D. Yuen, and E. Boschi (19821. Polar wandering 51 and the forced responses of a rotating, multilayer viscoelastic planet, J. Geophys. Res. 87, 2885-2903. Sturges, W. (1966~. Slope of Sea Level Along U.S. Coasts, Ph.D. thesis, Johns Hopkins University, Baltimore, Maryland, 89 pp. Sverdrup, J., J. Johnson, and R. Fleming (1942~. The Oceans, Prentice-Hall, New York, 515 pp. Tabata, S. (1981~. Oceanic time series measurements from sta- tion P and along line P in the Northeast Pacific Ocean, in Proceedings of the Meeting on Time Series of Ocean Measure- ments (Tokyo, Japan), World Meteorological Organization. Thorarinsson, S.: (1940~. Present glacier shrinkage and eustatic changes in sea level, Geogr. Ann. 12, 131-159. Wexler, H. (1961~. Ice budget for Antarctica and changes of sea level, J. Glaciol. 3, 867-872. White, W., and K. Hasanuma (1980~. Interannual variability in the baroclinic gyre, J. Mar. Res. 38~4), 651-672. White, W., K. Hasanuma, and G. Meyers (1979~. Large-scale secular trend in steric sea level over the Western North Pacific from 195~1974, Geodetic Soc. Jpn. 25, 49-55. Wunsch, C. (1972~. Bermuda sea level in relation to tides, weather, and the baroclinic fluctuations, Rev. Geophys. Space Phys. 10, 1~9. Yumi, S., and K. Yokoyama (1980~. Results of International Polar Motion Service in a Homogeneous System 1899.9-1979.0, Publ. Cent. Bureau, International Polar Motion Service, 15 pp.