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Large-Scale Coherence of Sea Level at Very Low Frequencies W. STURGES Florida State University ABSTRACT The coherence of sea level has been examined between a number of widely distributed stations having the longest data sets, such as at San Francisco, where the data begin in 1855. The sea-level signals in the eastern Pacific appear to be dominated by propagating Rossby waves, so that the variability, having periods of 5 to 8 yr (e.g., between San Francisco and Honolulu) is coherent but out of phase by several years. Sea level is coherent on opposite sides of the Atlantic at periods of about 6 yr, but this may be the result of direct atmospheric forcing rather than of wave propagation. From the Pacific to the Atlantic, coherence is also found at the most energetic periods (6 to 8 yr). At the longest periods detectable to 50 yr the sea-level signals have amplitudes of 5 to 15 cm and are "visually coherent" between the west coasts of the United States and Europe. The amplitude of these extremely long-period signals is the same as the apparent "rise of sea level over the past century," although the rate of rise from these fluctuations is larger. Because there is so much variability at extremely long periods, the sea-level data must be treated carefully in space as well as in time to avoid contaminating the "sea-level rise" signal by propagating signals. If the data were adjusted, or "corrected" for these signals, the signal-to-noise ratio might be substantially improved, allowing better estimates of the observed rise of sea level, but the forcing mechanisms are not well known at the longer periods. Until the data are so corrected, changes in the rate of rise of sea level, on time scales of about 10 to 50 yr, cannot be distinguished from the background "noise." INTRODUCTION One of the difficulties in addressing the sea-level rise problem by using tide-gauge data is that the signals are noisy. Many geophysical processes contribute vigorous time-dependent signals to the data; yet, we wish to extract the very small background sea-level trend in the midst of 63 this variability. The purpose of this chapter is to use the longest tide-gauge records to see if there is hope for im- proving the signal-to-noise ratio. The answer is "yes." Barnett (1984) found that the observed rise of sea level, averaged over middle and low latitudes, has been approxi- mately 10 cm in the last century. Lambeck and Nakiboglu (1984) conclude that roughly half of this rise is the result
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64 of continuing, long-term response to glacial unloading, i.e., with no addition of water from (high-latitude) gla- ciers. A major concern, however, comes from the possi- bility that much of this rise has taken place preferentially in the past 50 yr. If it should turn out that the rise is caused by recent CO2 addition to the atmosphere, the rate of rise could increase because of increasing input of additional CO2 and other gases. It is extremely difficult to determine whether the aver- age sea-level rise is caused by the much-publicized "car- bon dioxide effect," the long-term response of the Earth to glacial unloading, or other causes. If the primary cause of sea-level rise is the CO2 increase, we would expect to see an increasing rate of sea-level rise. However, if the ob- served rise is primarily the result of continuing adjustment since the last deglaciation, we would expect the sea-level rise to be a simple linear trend when viewed on appropri- ate time scales. Local tectonic effects, such as the differ- ences between the east and west coasts of the United States, are not addressed here. Because it seems important to try to understand this problem, it is natural that many workers will examine sea- level data, particularly over the past few and the next few decades, in an attempt to determine whether the rate of rise of sea level is increasing. Such analyses will be difficult, as the data have "red spectra." That is, the spectral energy keeps rising at low frequencies. More- over, the variability at the lowest frequencies we can re- solve is the same order as or larger than the rise of sea- level "signal." The point of view taken in this chapter is that, although there is substantial regional variability (as found by Bar- nett and others), we should expect the effects of a nearly global sea-level rise to be coherent and in phase over the appropriate regions of the globe. It seems useful, there- fore, to examine the longest available tide-gauge records to ask: At what frequencies are widely separated gauges coherent, and at what frequencies are they not? Such results might prove useful in telling us what frequencies are (or are not) appropriate for examining the basic prob- lem of "sea-level rise." If there are coherent, large-scale signals, the data can be adjusted for such effects. Most studies take the point of view that the analysis is limited by the time base over which a near-global data set is available. Here, by contrast, we maximize the length of the record available, and deal with a correspondingly much smaller set of stations. Before we explore these low- frequency data, however, it should be noted that a study by Sturges (1987) was made of sources of errors in the usual data. One hopes, of course, to learn something about the ocean in a study such as this. The primary aim of this W. STURGES chapter, therefore, is twofold. First, sea-level studies obviously must contend with noisy data. The analysis can be improved if as much of this "noise" as possible can be understood, and treated appropriately as signal. It is found here that substantial parts of the low-frequency signals are coherent over basin-wide scales. By averaging many such stations, therefore, one may not necessarily reduce the noise although by understanding the physical mechanisms involved one can adjust the data for such effects. A second point is that in the longest data sets (beginning in the middle to late 1800s) fluctuations rather like the "rise of sea level since the 1930s" appear to be part of the normal background variability of sea level but at periods too long to resolve with statistical reliability. The prob- lem, then, is not one so much of measuring the present rate of rise as of separating it (if possible) from the low-fre- quency background variability. SEA LEVEL ALONG A SINGLE COAST Useful and convenient summaries of tide-gauge data around U.S. coastlines have been prepared by Hicks and Crosby ( 1974) and Hicks et al. ( 1983~. Their figures show both. the yearly values and the lower frequency trends. Simply by lining up the highs and lows "by eye," it is apparent that, on these time scales, the major features of sea-level variability are coherent along a single coast line. These effects have been studied elsewhere at great length (e.g., Brooks, 1979; Enfield and Allen, 1980; Chelton and Davis, 1982~. The large scale of this coherence may be partly the result of the large scale of the forcing, but is primarily the result of the efficiency of wave propagation alone coastlines. This coherence along the U.S. coasts is widely known. The Hicks and Crosby figures show that the major highs and lows are coherent along the east coast, just as along the west coast. The details vary, but from Miami and Key West to Atlantic City and New York, the major features at these low frequencies are remarkably similar, and they extend into the Gulf of Mexico. On the Pacific coast, the E1 Nino events are a major forcing phe- nomenon, whereas variations in the large-scale wind field and the Gulf Stream are Atlantic coast counterparts (e.g., Blaha, 1984; Thompson, Chapter 2, this volume). There is some question as to whether the oceanic response to large- scale atmospheric forcing is deterministic. That is, the response may be found only in an averaged, spectral sense. See, for example, the discussion by White (1985~. Because the lowest frequencies are coherent along the entire coastline, it seems plausible that, at the longest periods, a few gauges having the longest records can be examined in detail and assumed to be representative of the whole coast.
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LARGE-SCALE COHERENCE OF SEA LEVEL AT VERY LOW FREQUENCIES SEA LEVEL AT SAN FRANCISCO AND CASCAIS From the results of previous studies we know that the rate of sea-level rise appears to increase after about 1930. One is naturally curious about what the longest available data sets show. Figure 3.1 is a"background" figure. It was prepared to show the frequency bands where the PER 100 - MONTHS - - cn ~ . I _ Z _ O e;, - * 2 (N. * * ~ _% - - Ln - ~o x - ~63 Lo _ * _% Cal, Ln 65 energetic variations occur in nature. In the lower part of the figure, the central peak a result of wind forcing is seen to be at periods less than a month. Figure 3.2 shows yearly mean data at San Francisco and Cascais, Portugal. The data have been heavily filtered to suppress the ener- getic fluctuations at periods less than about 10 yr. The slope of the long-term trend at both stations, 12 cm/cen |22 ta' Ale ~0~: i0-2 ~-s = \ . TV -v h/` 1 1 . - 1 1 1 "'I 10-3 10-2 10-1 l02 101 102 la3 FRECUENCY - CYCLES/MONTH PER I CD - MONTHS ,0, 120 , .... c;, 10- 103 l02 ~ . 1 0- 1 1 2-2 = 7~ it, IV 63 63 \~- 10 ~ .., ...,, . . 10-3 1 0-2 1 0-1 L 00 101 FREGU;N:Y - CYCLES/MONTH ..... 102 103 FIGURE 3.1 A composite sea-level spec- trum based on data processed in a variety of ways, shown in the normal method above and the variance-preserving form below. Highest frequencies are computed from hourly data at St. Petersburg, Florida, smoothed with three Hanning passes. The intermediate periods, from 1 month to 10 months, are based on S-hourly filtered data, smoothed with three Hanning passes. Monthly data at San Francisco are used for periods longer than 10 months and are smoothed with five Hanning passes. From Sturges (1987), J. Physical Oceanography (American Meteorological Society).
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66 100 FIGURE 3.2 Sea level at San Francisco (upper curve) and at Cascais, Portugal (lower curve). The means have been sub tracted; the curve at Cascais is offset by 100 mm; and a linear trend (12 cm/cen tury) has been removed from each. The data have been filtered to suppress the '0O energetic signals at 5 to 8 yr; half the signal remains at periods of about 6.5 yr (less than 10 percent at 4 yr, over 90 per cent at 16 ye). From Sturges (1987), J. Physical Oceanography (American Me teorological Society). fury, has been removed. The second digit is scarcely significant, however, as changing the length of the record by about 10 yr can change the mean slope by about 1 cm/ century. In the San Francisco data a noticeable, qualitative fea- ture is an "event" between approximately 1860 and 1900. In other words, there is a "signal" in this record having a period of approximately 40 yr, and an amplitude essen- tially the same as that observed in the "mean rise of sea level" since about 1930. Likewise, sea level at Cascais was high in the late 1800s, low around 1920, and rose again after then, showing a pattern similar to, but slightly out of phase with, the San Francisco record. Clearly, these records are not long enough for statisti- cally significant calculations at periods of 40 to 50 yr. Nevertheless, one cannot help but notice the obvious "visual correlation" between the longest-period variability in the two records- from different continents and different oceans. The essential idea is that the data contain a sub- stantial amount of energy at periods of many decades. The "observed rise of sea level" since 1930 takes place in a frequency band that has energy from many sources. In terms of what the data actually show, the "mean sea-level rise" could fairly be described as low-frequency variabil- ity having a peak-to-peak signal of at least 10 cm and a period of at least 100 yr. On the basis of the data in Figure 3.2, one finds it difficult to argue for any significant change in sea-level behavior beginning in the 1920s. Given this variability, assigning a "beginning date" at which a linear trend should be fit to the data is quite difficult, unless the records could be prefiltered to remove the energetic 40- to 50-yr vari- ability. These two sea-level records are coherent, in a statisti- cally significant sense, at periods on the order of years to decades. Before we discuss this result, however, it seems appropriate to discuss the idea that sea levels are coherent, on large scales, within a single ocean. o I v 1850 1900 Yeor W. STURGES A 1950 SEA-LEVEL SIGNALS FROM PROPAGATING OCEAN WAVES In an attempt to be quantitative about the longest pos- sible periods, I have computed cross spectra between sea level at a number of locations, using mean monthly data for some of the calculations and mean yearly data for others. For the details and some hand wringing, see Sturges (1987~. Pacific Ocean Figure 3.3 shows cross spectra between sea levels at San Francisco and Honolulu. The principal results are twofold. First, for periods of about 5 yr and longer, where the power is found, the records are highly coherent. Sec- ond, there is a substantial phase difference; San Francisco leads. While this is clearly a straightforward result in terms of Rossby wave propagation, it has important impli- cations for the "sea-level rise problem," as discussed in a later section. The gain factor (or frequency-response function) shows that the (coherent portion of the) ampli- tude at Honolulu is essentially the same as that at San . . . ~ranclsco. It is standard practice to introduce an artificial delay into one of a pair of records to allow for the energy travel time between the two. Such a technique enhances the signal-to-noise ratio, and is also known to improve the accuracy of the phase estimates (e.g., Jenkins and Watts, 1968, p. 396ff). Because it is known that the Rossby wave energy takes several years to travel these distances, an artificial delay was induced between the records for the calculations shown in Figure 3.3. The maximum coher- ence was found with delays of 2 to 3 yr (a reasonable result, as shown below). The propagation of low-frequency waves across the ocean has been studied extensively. White (1985) reported agreement between observations and models of wind
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LARGE-SCALE COHERENCE OF SEA LEVEL AT VERY LOW FREQUENCIES forced, baroclinic Rossby waves. Price and Magaard (1983) found a peak in energy in thermocline motions in the Pacific associated with Rossby waves at periods consistent with the peak shown in Figure 3.3. He found that the energy is almost all in the first baroclinic mode; so we expect to see it in sea-level fluctuations. Mysack (1983) studied Rossby waves at the annual period (an energetic band suppressed in the present work) traveling away from the U.S. west coast. In his model, the waves are generated by fluctuations in coastal currents rather than directly by wind. The important feature to note, for this application, is that the group velocity is toward the southwest (toward the Hawaiian Islands). The phase, however, propagates toward the northwest. At the o PERIDO - YERPS to Id, ~ 02 m Hi: ~ 56N rRR~C\5CO 1: /r,/~, A ~ \ ~ Or V\ ; ' of\\ lo-2 18_1 108 FREQUENCY - CYCLES/YEPR PER I OD - YEARS __ 99 ss 92 80 50 67 annual period the waves are still dispersive. Using Mysack's values (his Eq. 3.10), but for a 7-yr period, long enough to be nondispersive, the group velocity is esti- mated to be about 2.5 cm/s. Thus, in the 4500 km between San Francisco and Honolulu, the travel time for energy would be about 6 yr. We compared Balboa (Canal Zone) with San Francisco. It is well known (e.g., Enfield and Allen, 1980) that sea- level signals propagate to the north along the west coast of North America. Chelton and Enfield (1986) showed typi- cal amplitudes greater than 10 cm. Chelton and Davis (1982) found that the dominant signal [their first empirical orthogonal function (EOF)] accounted for about 40 per- cent of the energy and represented a fairly uniform rise PER ~ DO - YERRS Lo On CE I .%,,, \ -at `, \ :` mI_ ~ % '`,,, ~% C '., - : Lit o _ Lit o Z a: CL tD or . .,,, ·: ·, 10-1 108 FREQUENCY - CYCLES/VERR PERIOD - YERPS 108 LLJ z o CL LL At: z to 11 to ~ _ N 1 ., ~ lo-2 10-' 10. ,o-2 10-1 12' FREQUENCY - CYCLES/YERR FREQUENCY - CYCLES/YERR FIGURE 3.3 Cross spectra between sea level at San Francisco and Honolulu: yearly data are given for 1905 through 1971 at San Francisco, and beginning in 1907 at Honolulu. The Hon- olulu data are delayed by 2 yr for increased coherence (see text). The spectral amplitudes, upper left, are shown in the variance- preserving form; coherence is shown in lower left. Frequency- response curve, lower right, shows the ratio of the coherent power at Honolulu to that at San Francisco. On the phase plot, upper right, the 90 percent confidence intervals are shown. Smoothing is by five Hanning passes. From Sturges (1987), J. Physical Oceanography (American Meteorological Society).
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68 and fall of sea level along the whole coast. They found that low-frequency signals traveled up the coast at about 40 cm/s. Hence, at low frequencies, the signals should be essentially in phase between Balboa and San Francisco. Most of the low-frequency signals at Balboa lead those at San Francisco. At periods near 6 yr, however, the computed result is in the other direction, although the energy level at Balboa is low. The phase error bars (at 90 percent confidence limits) reach to zero; thus, in a statisti- cal sense, this result may not be repeatable but for the present data the phase calculation is correct. From this we conclude that the phase difference along the coast must be at least partly the result of the distribution of forcing, and not simply of wave propagation. Atlantic Ocean A similar set of calculations was done between sea- level records in the Atlantic. On the basis of results in the Pacific, we anticipate that wave energy will propagate generally toward the southwest, suggesting comparison between Cascais and Mayport, Florida. Figure 3.4 shows that coherence is high for the band of energy near 5 to 6 yr. These data overlap, after filtering, for only 38 yr. There is a data segment from 1897 to 1924 at Fernandina, Florida (near Mayport). Because there is not a reliable benchmark connection between the Fernandina and Mayport data, and because there is a 5-yr gap between the two data sets, it seemed risky to try to form a single, long, interpolated data set from the two. It is possible, however, to compare Cascais with Fernandina data, and on the basis of 25 yr of overlapping data, the results were consistent with the Cascais-Mayport calculations. A most surprising result, however, is found in these comparisons. The coherence is about 90 percent confi- dence (periods of 6 to 7 yr) when the data are adjusted to introduce a 2- or 3-yr lead into the Cascais data to be consistent with ocean wave propagation. The coherence is highest, however, when a 3- to 4-yr lead is introduced into the Mayport data-which is in the "wrong direction." The most plausible explanation is that direct atmospheric forc- ing is more important in these records than is ocean wave propagation. This lag direction for maximum coherence is also supported by the comparisons between San Francisco and Cascais, as discussed in the next section. It is likely that the mid-Atlantic ridge system interferes with the oceanic wave propagation, making the coherence lower here than between the U.S. west coast and Hawaii. As in the Pacific, we find significant phase shifts. At periods near 6 to 7 yr, the observed phase shift is about 135°, and for periods near 19 yr the phase difference is about 45° on the basis of records beginning in 1929. We should note that, while the statistical reliability of coher W. STURGES PER ~ 00 - YERRS 63 ID 392 10 -1 ' ' ' ' ' ' - ' ' ' lo 0 53 ~ in ~ - LL ~ Z 0 1 CL ~ can LL Z LL - Lo A: LL 108 90 80 , ~, , , ~ l0-2 10-, ~FREQUENCY - CYCLES/YERR _ , _ An\ ._ Ila-2 1a-1 FREDUENCY - CYCLES/YERR 10° 10. FIGURE 3.4 Coherence (upper) between sea level at Mayport, Florida, and Cascais, Portugal, and gain (lower), based on 38 yr of yearly mean data beginning in 1938. An artificial delay of 4 yr was introduced into the Cascais data. From Sturges (1987), J. Physical Oceanography (American Meteorological Society). ence of periods this long is beyond the limits of the data, the observed phase difference, as calculated, is a valid result and is potentially important in the context of the present work. Sturges and Summy (1982) found large-scale coherent waves in the central Atlantic thermocline whose energy propagated toward the west southwest. On the basis of their results for group velocity we expect that it should take the energy about 3 yr to propagate across the Atlantic Ocean. It was found that introducing an artificial delay of 3 yr into the records, in the sense of the direction of energy propagation, resulted in increased coherencies. Thus we find that the lagged coherence has maxima for an induced delay of 2 to 3 yr in one direction or 3 to 4 yr in the other. This is consistent with the idea that the 6- to- 7-yr period energy has highest coherence. One cannot tell (simply from these calculations) whether the secondary
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LARGE-SCALE COHERENCE OF SEA LEVEL AT VERY LOW FREQUENCIES maximum, consistent with ocean wave propagation, is merely the effect of atmospheric forcing offset by one period. Further work is required to distinguish between the two mechanisms. On the east coast of the United States, we compared New York with Mayport. The long-period fluctuations are marginally coherent (about 80 percent or higher) for peri- ods longer than about 4 yr, with New York leading, as expected. The much higher coherence typical of the U.S. west coast, however, is not evident. On the eastern side of the Atlantic, the coherencies were surprisingly low. Other than Cascais the longest records seem to be at Brest, France, and Takoradi (5°N, 2°W) on the coast of Ghana. For periods longer than a few years coherence was low between Cascais and Brest. At the energetic periods found at Cascais (about 7 to 8 yr) there is little power in the Brest record. Similar lack of coherence was found between Takoradi and Cascais. While there is significant energy in the near- 6-yr band at Takoradi, it was marginally coherent (not quite 80 percent confidence level) with that at Cascais. Energy having periods near 3.5 yr, however, was barely coherent between the two stations. The direction of phase propagation for this signal, however, was from Cascais to Takoradi, suggesting that the phase difference is a result of the forcing, rather than simple wave propagation (or that this result is from aliasing). SAN FRANCISCO TO CASCAIS San Francisco and Cascais are located at similar lati- tudes and positions in the Pacific and Atlantic. Because it is known that the sea-level signals on the U.S. coasts are strongly coherent with atmospheric forcing, and because atmospheric signals at low frequencies have very large scales, it seemed reasonable to calculate coherence be- tween sea level observed at San Francisco and Cascais. That is, in the example of San Francisco and Honolulu, the observed coherence results from oceanic wave propaga- tion. Any coherence between San Francisco and Cascais, however, would be attributed presumably to coherence in atmospheric forcing if the coherence is found in a fre- quency range where atmospheric signals are present. Figure 3.5 shows, first, that there is high coherence at resolvable periods. Second, the energetic signals in the two oceans have peaks that are at slightly different periods, but the differences are small in a spectral sense (i.e., within 90 percent confidence limits). Third, the most energetic fluc- tuations are out of phase by several years. At the longest periods resolvable (about 30 yr) the records are also out of phase by about 3 yr. There is some evidence that atmospheric fluctuations at low frequencies tend to advance from south to north, at 69 periods of order about 2 yr, so the east-west phase differ- ence may be a result of the slope of phase lines, rather than simple east-west propagation. So far as we are aware, however, comparisons of this type at the longer periods have not been done with the atmospheric data (J. M. Wallace, University of Washington, personal communica- tion). It was not clear whether an easterly or westerly phase lead was more likely, and so the phases were com- puted with lags in both directions. Assigning the lead to Cascais gives a slightly broader band of coherence at periods from 5 to 8 yr. Assigning the lead to San Francisco gives a slightly higher coherence, but the results are not very sensitive to the choice. DISCUSSION Several people have suggested a possible connection between the low-frequency sea-level perturbations shown in Figure 3.2 and the length-of-day (l.o.d.) record shown in Figure 3.6. The l.o.d. variations show striking correla- tion with atmospheric angular momentum (e.g., Morgan et al., 1985~. The l.o.d. variations shown by Barnett (1983) and by Morgan et al. have the same amplitudes but are at enormously different periods. Brosche and Sondermann (1985) examined the transfer of angular momentum be- tween the solid earth and the ocean; they find that variabil- ity in the Antarctic Circumpolar Current can account for the observed discrepancy in the semiannual angular momentum budget of the Earth and atmosphere, and that the amplitudes are comparable. Thus there is reason to suspect that at very long periods, there may be a rational connection between oceanic circulation and the angular momentum of the Earth hence the l.o.d. signal. Because the sea-level record at Brest is rather unlike the record at Cascais at the longest periods, one suspects that these variations have to do with changes in the gyre-scale circu- lation. Although it is perhaps speculative to suggest a connec- tion between variations in the l.o.d. and sea level at peri- ods of many decades, it may be important to point out such a possibility in the context of this chapter. That is to the extent that the variability in these records can be ascribed to known forcing mechanisms, the uncertainty in deter- mining the rate of any real, global sea-level rise may be improved significantly. There is a natural temptation to invoke the climate variability of the 1800s in an attempt to explain the lowest frequency variability of Figure 3.2. Stommel and Stom- mel (1983) showed a temperature record from England beginning in 1740, in which the January temperatures show the most variability at periods of roughly 40 to 50 yr. To "prove" a causality between the forcing mechanism and the observations, however, one must overcome three in
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70 PERIOD - YERRS On CY ~* =, ~ _ I. * - ~* ~- to ~ ~ te~Ci5 In\ ~ ,^ :,~; C~sc~5 , ,,, ,, 1 l ~1 of 1 o-2 FREQUENCY - CYCLES/YERR PER I OD - YERRS 101 . . . . . . . . . . . . . . . FREQUENCY - CYCLES/YERR 99 ss 90 82 50 10. FIGURE 3.5 Cross spectra between sea level at San Francisco and Cascais using 90 yr of data beginning in 1884. The phases are computed using data that are delayed by 4 yr at Cascais. The dashed curve on the coherence plot is for data delayed by 2 yr at timidating hurdles. The records are not very long, com- pared with the periods involved; the events took place during a time that was "historical but prethermometric" (in the words of Stommel and Stommel); and, finally, as Chelton and Davis (1982) pointed out, on scales as large as the subtropical gyres, almost all the observed signals are coherent, making it difficult to distinguish between a variety of reasonable hypotheses. CONCLUSIONS The dominant sea-level signals at periods of 5 to 10 yr and longer are coherent between the U.S. Pacific coast and Hawaii, and on both sides of the Atlantic. The amplitudes, W. STURGES PERIOD - YERPS FREQUENCY - C)'CLES/YERR PERIOD - YERRS LLJ cn Z _ o ~ in to LO CY LO N - 186 102 101 108 ~ . · . . = ~ 1 10-1 10. FREDUENCY - CYCLES/YERR San Francisco (see text). Smoothing is by five Hanning passes. From Sturges (1987), J. Physical Oceanography (American Meteorological Society). at long periods, are about 5 to 15 cm. These signals are out of phase, with delays of several years, and are consis- tent in part with baroclinic wave propagation across the ocean. At the longest periods detectable in the records, "signals" having periods of 40 to 50 yr are found with amplitudes of about 10 cm. There is "visual correlation" between records on the U.S. Pacific coast and the west coast of Europe, at the same latitude. Similar periodicities are found in English temperature records, but no causal mechanisms have been established. Because these changes in sea level are coherent on ocean-wide scales, inferences about the "sea-level rise problem" must be treated with this in mind. That is, the longest records appear to be "contaminated" by ocean
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LARGE-SCALE COHERENCE OF SEA LEVEL AT VERY Law FREQUENCIES +4.0 +2.0 ~4 rN f ,6~~ +40 of ~ - _ ~ ~ +2.0 O -20 \,, 1-2.0 -4.0 1 1 1875 1900 FIGURE 3.6 Secular variation in length of day (l.o.d.) in milli- seconds. The line denoted "SL effect" is the change in l.o.d. expected due to the relative sea-level change estimated by Bar- nett (1983), if that change was due to polar melting. The line wave propagation, as well as by regional tectonic motions and other processes. A wave of 10-yr period and 5-cm amplitude has a rate of rise of order 2 cm/yr, which is an order of magnitude larger than the presumed sea-level rise of 10 cm in the past 50 yr. The 40- to 50-yr variations have slopes of about 30 cm/century. Records of shorter duration have a much better geographical distribution, and modern records may have higher precision, but they hide the extent of the low-frequency variability. These conclusions do not mean that there is no "rise of sea level" problem. On the U.S. east coast, the present rise of sea level (about 26 cm/century) is clearly observable. Of the observed mean global low-latitude rise, roughly half is consistent with long-term glacial rebound. The remaining about 6 cm/century is thoroughly buried in a background of low-frequency variability. If we are to make significant comparisons between the rise of sea level and forcing mechanisms, such as increases in atmospheric gases, in order to have any predictive capability, further effort will be required to extract the signal from the nor- mal background variability associated with all geophysi- cal variables. ACKNOWLEDGMENTS During the course of this work, I have benefited from discussions with many people as well as comments from readers of a previous version of this manuscript, including Tim Barnett, John Blaha, Allan Clarke, Nelson Hogg, Jim McCullough, and others. The spectral analysis programs were written by Chris Evans. Data were very kindly provided by Elaine Spencer, Permanent Service for Mean YEAR 1 1 1925 1950 1975 -din denoted "TF" is the change in l.o.d. due to tidal friction. After Barnett (1983), Climate Change, (American Meteorological Society). Sea Level, Bidston Observatory. I also thank Pat Klein for cheerfully revising many versions of the manuscript. This work was partially supported by NSF grant OCE 8416458 and by Florida State University. REFERENCES Barnett, T. P. (1983). Possible changes in global sea level and their causes, Climate Change 5(1), 15-38. Barnett, T. P. (1984). The estimation of "global" sea level change: A problem of uniqueness, J. Geophys. Res. 89, 7980-7988. Blaha, J. P. (1984). Fluctuations of monthly sea level as related to the intensity of the Gulf Stream from Key West to Norfolk, J. Geophys. Res. 89(CS), 8033-8042. Brooks, D. A. (1979~. Coupling of the Middle and South Atlan- tie Bights by forced sea level oscillations, J. Phys. Oceanogr. 9, 1304-1311. Brosche, P., and J. Sondermann (19851. The Antarctic Cireum- polar Current and its influecee on the Earth's rotation tabs.), paper presented at IAMAP/IAPSO Joint Assembly, August 5-16, 1985, Honolulu, Hawaii. Chelton, D. G., and R. E. Davis (1982~. Monthly mean sea level variability along the west coast of North America, J. Phys. Oceanogr. 12, 757-784. Chelton, D. G., and D. B. Enfield (1986~. Ocean signals in tide gauge records, J. Geophys. Res. 91, 9081-9098. Enfield, D. B., and J. S. Allen (19801. On the structure and dynamics of monthly mean sea level anomalies along the Pacific coast of North and South America, J. Phys. Oceanogr 10, 557-578. Hicks, S. D., and J. E. Crosby (1974). Trends and Variability on Yearly Mean Sea Level 1893-1972, U.S. Dept. Commerce NOAA, National Ocean Service, 14 pp.
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Representative terms from entire chapter: