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OCR for page 63
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
OCR for page 64
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.
OCR for page 65
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
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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
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63
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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).
OCR for page 66
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
OCR for page 67
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
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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
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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).
OCR for page 68
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
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LL
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90
80
, ~, , , ~
l0-2 10-,
~FREQUENCY - CYCLES/YERR
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_ 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
OCR for page 69
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
OCR for page 70
70
PERIOD - YERRS
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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
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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
OCR for page 71
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.
OCR for page 72
1
72
Hicks, S. D., H. A., Debaugh, and L. E. Hickman (1983~. Sea
Level Variations for the United States, 1855-1980, U.S. Dept.
Commerce, NOAA, National Ocean Service, 170 pp.
Jenkins, G. M., and D. G. Watts (1968~. Spectral Analysis and
Its Applications, Holden Day.
Lambeck, K., and S. M. Nakiboglu ~ 1984~. Recent global changes
in sea level, Geophys. Res. Lett. 11, 959-961.
Morgan, P. J., R. W. King, and I. I. Shapiro (19851. Length of
day and atmospheric angular momentum: A comparison for
1981-1983, J. Geophys. Res. 90 (B 14), 12645-12652.
Mysack, L. A. (19831. Generation of annual Rossby waves in the
north Pacific, J. Phys. Oceanogr. 13, 1908-1923.
Price, J. M., and L. Magaard (1983~. Rossby wave analyses of
W. STURGES
subsurface temperature fluctuations along the Honolulu-San
Francisco great circle, J. Phys. Oceanogr. 13, 258-268.
Stommel, H., and E. Stommel (1983~. Volcano Weather, Seven
Seas Press, 177 pp.
Sturges, W. (1987~. Large-scale coherence of sea level at very
low frequencies, J. Phys. Oceanogr. 17, 2084-2094.
Sturges, W., and A. Summy (1982~. Low-frequency temperature
fluctuations between Ocean Station Echo and Bermuda, J.
Mar. Res. 40 (Supply, 727-746.
White, W. B. (1985~. The resonant response of interannual
baroclinic Rossby waves to wind forcing in the eastern mid-
latitude North Pacific, J. Phys. Oceanogr. 15, 403-415.
Representative terms from entire chapter:
wave propagation
