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OCR for page 52
North Atiantic Sea Level and Circulation
KEITH R. THOMPSON
Dalhousie University, Canada
ABSTRACT
Monthly sea levels are examined from 25 North Atlantic tide gauges for the period 1950 to 1975.
The influence of local wind forcing is first quantified, using multiple regression techniques, and
some of the gains are interpreted in teens of recent theoretical and numerical modeling studies.
Three distinct regions of sea-level variability remain after removal of the local meteorological
effects, namely, (1) the eastern boundary of the North Atlantic, (2) the western boundary, south of
Cape Hatteras, and (3) the western boundary, north of Cape Hatteras. Along the eastern boundary,
a statistically significant relationship is obtained between sea level and Ekman pumping of the North
Atlantic. It appears that wind-forced changes in ocean circulation can significantly affect the eastern
boundary sea level. A similar result could not be found for the western boundary. Examination of
the seasonal cycle, however, suggests that the Gulf Stream and an upper-slope boundary current,
north of Cape Hatteras, may be important influences.
The value of "correcting" annual sea-level series, in order to detect small changes in their long-
term trend, is discussed. An example is given for the easteIn boundary of the North Atlantic, where
the effect of slow changes in wind-forced circulation is removed from the Newlyn sea-level record.
The standard error of the trend estimate is halved, from 0.4 to 0.2 mm/yr, on removal of the
meteorological effects.
INTRODUCTION
Interest in the rate of rise of global sea level has been
stimulated recently by predictions of a change in air tem-
perature associated with the increasing concentration of
atmospheric carbon dioxide. Tide-gauge records have
played a key role in determining the sea-level rise this
century, mainly because of their length (some exceed 100
yr) and accuracy. Rossiter (1972), for example, showed
52
that an annual mean sea level can be considered accurate
to within about 1 mm, certainly less than the variability
due to meteorological forcing or steric changes. Hicks
(1978) showed that the standard deviation of detrended
annual means (CIa) is about 3 cm along the western bound-
ary of the North Atlantic. This implies that at least 35 yr
of data are required to determine a linear trend to within
1 mm/yr, with 95 percent confidence, along this boundary.
If 6a could be halved, by removing the effect of local
OCR for page 53
NORTH ATLANTIC SEA LEVEL AND CIRCULATION
wind for example, only 22 yr of data would be required to
achieve the same accuracy in estimating the linear trend.
Clearly this procedure could be applied to short records
from other regions and so allow them to usefully contrib-
ute to the global picture of sea-level rise. Apart from an
improved linear trend estimate, an accelerating sea-level
rise could also be detected more readily in long "cor-
rected" series.
Rossiter (1967) was one of the first to correct annual
sea level in his study of secular trends on the northwest
European shelf. [See Lisitzin (1974) for an historical
review of this topic.] Rossiter used linear combinations of
air pressures to implicitly represent the joint effect of air
pressure and wind forcing over shelf seas and the North
Atlantic. Multiple regression techniques are also employed
in this chapter to model meteorological and density effects
on North Atlantic monthly sea level. One major differ-
ence between this study and Rossiter's is in the choice of
independent variables for the regression model; only those
variables that correspond to a direct physical influence
(e.g., local wind stress, wind-forced ocean circulation) are
used here (see also Thompson, 19861. The advantages are
twofold. First, physically motivated regression models
contain useful oceanographic information on shelf/ocean
circulation. Second, it is important to know what is being
removed when forming the corrected annual series; many
geophysical time series are dominated by low-frequency
variations that could mistakenly be interpreted as the cause
of the sea-level trend when in fact there is no physical
connection.
In the next section, the main features of North Atlantic
sea-level variability (e.g., variance, power spectra, sea-
sonal cycle, and space scales) are described. In following
sections, the relevant forcing functions and the regression
analysis (with physical interpretation) are discussed. The
correction of long annual series is then finally illustrated
with an example from the eastern boundary of the North
Atlantic.
OBSERVED SEA-LEVEL VARIABILITY
The monthly sea levels used in this study were recorded
by 25 North Atlantic gauges over subperiods of 1950 to
1975 (Table 2.1~. The data were obtained from the Perma-
nent Service for Mean Sea Level. An earlier empirical
orthogonal function (EOF) analysis of a more extensive
array showed that there are three distinct groupings of tide
gauges in the North Atlantic (Thompson, 1981, 1986~.
One group is found along the eastern boundary; apart from
the seasonal cycle, the coherence is weak between sea-
level changes on opposite sides of the North Atlantic. The
other two groups are found along the western boundary
and are separated by Cape Hatteras. The split at Cape
53
TABLE 2.1 Positions of the Tide Gauges and the Number
of Monthly Sea Levels Used in This Study
Station
Latitude Longitude a, 02
(°N) (°W) Months (cm) (cm)
GULF OF MAINE AND SCOTIAN SHELF
Halifax 44.7 63.6 300
Yarmouth 43.8 66.1 95
Bar Harbour 44.4 68.2 307
Portland 43.7 70.3 312
Portsmouth 43.1 70.8 228
Boston 42.4 71.1 312
Cape Cod 41.8 70.5 235
MID-ATLANTIC BIGHT
Nantucket 41.3
Woods Hole 41.5
Buzzards Bay 41.7
Newport 41.5
New London 41.4
Montauk 41.1
Sandy Hook 40.5
Atlantic City 39.4
Cape May 39.0
Lewes Harbour 38.8
Kiptopeke Beach 37.2
Virginia Beach 36.9
70.1
70.7
70.6
71.3
72.1
72.0
74.0
74.4
75.0
75.1
76.0
76.0
125
272
229
302
300
283
312
294
84
276
280
102
SOUTH ATLANTIC BIGHT
Morehead City 34.7 76.7 110
Charleston 32.8 79.9 312
Fort Pulaski 32.0 80.9 288
Mayport 30.4 81.4 300
Miami 25.8 80.1 276
4.3
4.1
5.5
4.3
4.4
3.3
3.9
5.0
3.5
3.4
3.6 3.0
4.0 3.3
3.9 3.0
4.1 3.1
5.0 3.8
6.0
5.2
4.7
4.0
6.0 5.1
5.8 4.8
5.9 5.1
4.6 4.5
EASTERN BOUNDARY OF NORTH ATLANTIC
Newlyn 50.1 5.6 312 7.0 3.1
Note: All data was for the period 1950 to 1975; the exact
coverage can be obtained from the data publications of the Per-
manent Service for Mean Sea Level.
The last two columns are the standard deviation of deseason-
alized monthly sea level (art) and residual from the multiple
regression model (~2), both based on data from the common
period 1961 to 1970.
Hatteras immediately suggests that the circulation of the
North Atlantic may be affecting the coastal sea levels.
[Blaha (1984) inferred variations in the strength of the
Gulf Stream from the South Atlantic Bight data.]
Western Boundary
To avoid swamping the text with statistics (e.g., EOFs
and cross spectra), three typical series are shown in
OCR for page 54
54
BOSTON
~: \~r 4~ - _ ~ ~
SANDY HOOK
CHARLESTON I A ~
196C
197C
FIGURE 2.1 Typical monthly mean sea-level series for the
South Atlantic Bight (Charleston), mid-Atlantic Bight (Sandy
Hook), and Gulf of Maine (Boston), 1950 to 1975.
Figure 2.1 to illustrate some of the main features of the
sea-level variability. tA more detailed description is given
by Thompson (1986~.] There is a clear seasonal cycle at
Charleston (~10 cm, South Atlantic Bight) that is attenu-
ated as one moves north to Sandy Hook (~5 cm, mid-
Atlantic Bight) and Boston (~2 cm, Gulf of Maine). These
series are regionally representative, as confirmed by the
JUL ~ n
~ \.
\
OCT
· MID - ATLANTIC BIGHT |
O GULF OF MAINE
· SCOTIAN SHELF
. JAN
FIGURE 2.2 Amplitude and phase of the annual cycle in ob-
served sea level, north of Cape Hatteras. Tick mark corresponds
to a maximum on the fifteenth of each month. The tide-gauge
positions are listed in Table 2.1. The two Scotian Shelf gauges
are Halifax and Yarmouth; the former has the largest amplitude.
KEITH R. THOMPSON
amplitude/phase plot of the annual cycle of sea level in
Figure 2.2. [See Blaha (1984) for a description of the ~7
cm seasonal oscillation in the South Atlantic Bight.] The
coastal sea-level gradient between the South Atlantic Bight
and the Gulf of Maine varies over the year by at least 2 x
10 cm/1500 km (=1.4 x 1O-7~. Also from Figure 2.2, the
sea-surface slope varies by at least 2 x 6 cm/200 km (=6 x
10-7) between the Scotian Shelf and Gulf of Maine. These
are dynamically significant slopes of the sea surface;
Csanady (1976), for example, had to impose a long-shelf
gradient of 1.4 x 1O-7 to correctly model the mean circula-
tion of the mid-Atlantic Bight.
The standard deviations of the deseasonalized monthly
series (al' Table 2.1) show that the most energetic stations
are found in the South Atlantic Bight (~ ~ 6 cm); further
north, in the mid-Atlantic Bight and Gulf of Maine, cut ~ 4
cm. Changes of monthly sea level are similar at Boston
and Sandy Hook but distinct from those at Charleston
(Figure 2.1), in agreement with the EOF analysis described
above. Note, for example, the anomalous 10- to 20-cm
drop in both the mid-Atlantic Bight and the Gulf of Maine
in early 1950s. This change was not recorded by the South
Atlantic Bight gauges. An upward trend of sea level is
evident in all three series in Figure 2.1. Note, for example,
the 10-cm change in the mean level from 1950 to 1960
through 1970 to 1975 at Sandy Hook. This corresponds to
a mean rate of rise of 5 mm/yr, considerably larger than
the global average of 1.5 mm/yr obtained by Barnett
(1983a). tHicks (1978) suggested that the gauge at Sandy
Hook may be subject to localized subsidence.] The (typi-
cal) spectrum of Boston sea level shows that half of the
energy in this record is at periods between 7 months and
11 yr (Figure 2.3~. There is also a sharp spectral peak at 6
months and a broad peak at 12 to 15 months that will be
related in part to the pole tide in a later section.
Eastern Boundary
A detailed description of the sea level along the eastern
boundary is given by Thompson (19861. The main point
to note here is that, in contrast to the western boundary,
the standard deviation of the deseasonalized series (cat)
increases poleward. This coincides with an increase in the
variance of wind and air pressure at the more northerly
stations and suggests that local meteorological forcing of
sea level may be important.
FORCING FUNCTIONS
A very brief description of some of the more important
influences on sea level is given below in order to motivate
the regression analysis and aid in its physical interpreta-
tion.
OCR for page 55
NORTH ATLANTIC SEA LEVEL AND CIRCULATION
200
00
00 r
w~t ~ :~ HA
! ,.,
POWER ll
(cm2/cpm) 1 ~ Pa
~ ~ K~~_,
50:
SEA sever (~) Wind Stress
arX+ bTY
it, , ~
0 0.1 0.2 0.3 0.4 0.5
FREQUENCY (cpm)
FIGURE 2.3 Power spectra of Boston monthly sea level, air
pressure (1 mbar is equivalent to 1 cm), and contribution of local
wind stress according to Eq. (2.8), 1950 to 1975. The spectra
have been smoothed by "Hamming," and there are 12 degrees of
freedom to each spectral estimate.
Air Pressure
The well-known inverse barometer law relates local air
pressure (Pa) and sea level ~ according to the relationship
Pgll Pa Pat (2.1)
where Pa is the average pressure over the world's oceans.
Pattullo et al. ( 1955) showed that Pa has a surprisingly
large mean annual range of 2.1 mbar and included it in
their study of the seasonal oscillation of sea level. It is
unlikely however that Pa has a significant trend and its
effect can probably be ignored on a decadal time scale.
EFor example, Figure 3 of Bunker (1980) shows that the
average air pressure over the Atlantic (1948 to 1972, 40°S
to 70°N) has a trend of only 0.01 mbar/yr.] The time taken
for a shelf sea to adjust to changes of Pa is complicated by
stratification and topography. However the spin-down
time under bottom friction is probably a controlling factor
55
on the wide, tidally energetic shelf north of Cape Hatteras.
This implies a response time of several days and suggests
that Eq. (2.1) is valid for monthly means.
The (typical) air pressure spectrum for Boston shows
that Eq. (2.1) cannot account for much of the low-fre-
quency sea-level variability, although it is an important
contributor at the annual and shorter periods (Figure 2.3~.
Assuming a typical standard deviation of 5 mbar for monthly
Pa in mid-latitudes, a white Pa spectrum implies that the
standard deviation of annual and decadal means Of Pa
would be 1.4 and 0.5 mbar, respectively.
Both observation and theory confirm that wind stress
acting over the shelf can have an important effect on sea
level. Csanady (1982) described some simple analytical
models and showed that the coastal sea-level response to a
steady longshore wind stress CAYS can be written in the
form
pug/= fL/r, (2.2)
where L is the cross-shelf scale of the wind-driven coastal
boundary current. This scale is a function of the Coriolis
parameter (f), linear bottom friction coefficient (r), bot-
tom slope, and the spatial structure of BY. The time taken
to achieve a steady state is again complicated by stratifica-
tion and topography, but it is probably less than the pres-
ent averaging period of 1 month. tWright et al. (1986)
calculated an e-folding time of 20 hr for the spin-up of
their barotropic model of the Gulf of Maine.] The re-
sponse has therefore been assumed quasi-steady on a
monthly time scale in this chapter, and the empirically
determined gains of sea level on longshore stress have
been used to obtain estimates of L. This is described in the
next section. The combined contribution of longshore and
cross-shore winds at Boston is shown in Figure 2.3 to
illustrate the magnitude of the wind effect. (The results of
the regression analysis have been anticipated in order to
define the gains.) Wind stress effect is similar in magni-
tude to that of air pressure at Boston; it is not a major
contributor to the low-frequency changes of sea level.
Wind-Forced Ocean Circulation
Recent theoretical and numerical modeling studies (e.g.,
Anderson et al., 1979) show that the initial response of a
mid-latitude, baroclinic ocean to an imposed wind stress is
essentially barotropic. Away from the western boundary,
the quasi-steady barotropic response can be approximated
by the bottom-modified Sverdrup relationship, i.e.,
Jay, f/h) = k · Vx(~/ph), (2.3)
OCR for page 56
56
where ~ is the stream function and J denotes Jacobian.
The associated sea-level slopes are given implicitly by
gJ(h/f, ~) = We' (2.4)
where g is acceleration due to gravity and we is the Ekman
pumping [i.e., k · Vx(~/ph)~. The sea-sudace topography
can be determined, up to an arbitrary constant, by integrat-
ing Eq. (2.4) from the eastern boundary along f/h con-
tours. To calculate the arbitrary constant of integration,
the ocean is assumed closed and conservation of mass is
applied, i.e.,
i1 = 0, (2.5)
where the overbar denotes a basinwide average and ~ is
measured relative to the undisturbed level. (Note that the
contribution to ~ from the western boundary region is
assumed relatively small and ignored.) The longshore
momentum equation for the eastern boundary and Eqs.
(2.4) and (2.5) then give the interior change in sea level. If
it is assumed for simplicity that h is a constant and that
wind setup is negligible along the eastern boundary, then
the sea level along the eastern boundary is
Tie f2 ~XW ~ (2.6)
where x = 0 on the western boundary and increases east-
ward.
If all the dissipation is assumed to occur in a narrow
western boundary current, then the sea-level head along
the shoreward edge of the western boundary current (but
still in deep water) is approximately given by
w
by = pgh + J k · Vx ~ oh ~ tie ~(2.7)
where W is the width of the ocean. (Again h is assumed
constant, but the results can be readily generalized to in-
clude bottom topography.)
How big are the sea-level changes predicted by Eqs.
(2.6) and (2.7~? Clearly the results depend on h. If
variations in ~ are slow compared to the time taken for a
baroclinic Rossby wave to cross the ocean (i.e., decades),
then h can be approximated by the mean thermocline depth
and bottom topography plays no part (Anderson et al.,
1979~. For shorter periods (i.e., months), h is the ocean
depth. The sea-level response therefore depends on the
frequency of wind forcing. Power spectra of monthly we
were calculated for 55°N, 35°W and 35°N, 35°W in the
manner outlined by Thompson and Hazen (1983~. The
spectra were white, apart from an annual peak. The stan-
dard deviations of the monthly changes were 15 x 10-7 and
8 x 10-7 m/s at 55°N and 35°N, respectively. If typical
values are assumed of we = 5 x 10-7 m/s and W = 5000 km,
KEITH R. THOMPSON
then fle = 2 cm (for h = 4 km, initial barotropic) and 8 cm
(for h = 1 km, final baroclinic). Thus the large-scale wind
field becomes increasingly important on longer time scales.
Similarly, sea-surface slopes along the western boundary
are 0.6 x 10-8 (initial barotropic) and 2 x 10-8 (final baro-
clinic) if the same values for W and we are taken and By is
assumed to be 0.1 Pa.
Thermohaline Changes
Fluctuations of the local heat and salt content of the top
200 m of the ocean are responsible for a pronounced
seasonal oscillation in sea level (Figure 2.41. The ampli-
tude of this oscillation in the deep water adjacent to the
mid-Atlantic Bight and Scotian Shelf is about 8 cm (Fig-
ure 2.4~. Csanady (1979) extrapolated the deep-ocean
steric field to the coast of North America under the as-
sumption that the geostrophic velocity is zero at the seafloor
(Figure 2.5~. His topography for spring shows a well-
defined surface geostrophic flow along the 1000-m iso-
bath; the difference between summer and spring shows
that this current has a strong seasonal variation. This
seasonal difference in sea level (Figure 2.5b) is consistent
with Figure 2.4 in deep water but shows that the deep-
ocean amplitude (~10 cm) is attenuated at the coast (~2
cm, mid-Atlantic Bight; O cm, Gulf of Maine).
The influence of thermohaline changes is not limited to
the annual period. Roemmich and Wunsch (1984) identi-
fied decadal changes in the large scale temperature field of
"r:
1 ,.~
r rid Act ~
1 fit Q 1 14
FIGURE 2.4 Co-rallge lines of the annual cycle of North Atlan-
tic sea level (centimeters) as calculated by Gill and Niiler (1973);
an annual wave was fitted to the sum of contributions given in
their Figure 3. The individual boxed values are the amplitudes
(centimeters) of the annual steric oscillation calculated by Pattullo
et al. (1955). The maximum sea level generally occurs in August
throughout the North Atlantic.
OCR for page 57
NORTH ATLANTIC SEA LEVEL AND CIRCULATION
SPRING
(cm)
_~
- 11~5.-~
~J~
r ^~
~ /~ ~110
120
150
SUMMER
- SPR I NO
(cm)
Redrawn from Csanady (1979)
_- dLl
_~:
r~J~/ 5
,~AO~,~O~
~ (~(150
FIGURE 2.5 (a) Sea-surface topography during spring (April
through June) calculated by Csanady (1979, Figure 4), under the
assumption that the bottom geostrophic velocity is zero. Values
are in centimeters. (b) Differences in the summer (July through
September) and spring sea-surface topographies, calculated by
Csanady (1979, Figures 4 and 7~.
the North Atlantic. The observed warming of the ocean
between 700 to 3000 dbar, across 24°N and 36°N, results
in a thermal expansion of several centimeters. Roemmich
(Chapter 13, this volume) shows that Bermuda sea level
does reflect such changes in the density field. On a larger
spatial scale, Barnett (1983b) examined slow changes of
dynamic height in the major oceans (0 to 1000 dbar, early
57
1900s to date), but he did not find a significant global
trend.
MULTIPLE REGRESSION ANALYSIS
In this section, multiple regression models based on the
above forcing functions are used to explain some of the
observed features of sea-level variability. The following
model has been fitted to each series in order to quantify the
effect of local meteorology and seasonal changes in den-
sity:
Pg~1 + Pa = am + bay + cat cos~co~t + ¢~)
+ ~2 cos(O2t + ¢2) + £, (2.8)
where co, = 1/12 cpm and m: = 1/6 cpm. The influence of
air pressure has been assumed to follow Eq. (2.1) and has
been removed by adding the local air pressure and sea
level to obtain the total pressure (pan + Pa). Local air
pressure could of course be included as a forcing term in
Eq. (2.8~. However, Pa could alias the influence of wind
stress, and this would complicate our physical interpreta-
tion of the model's coefficients. The influence of local
wind stress ( - , EYE has been modeled by am + boy, where
a and b are regression coefficients to be determined. This
form assumes a quasi-steady response to monthly mean
winds (no lags) and a sinusoidal dependence on wind
direction, i.e., the direction of maximum sea-level response
is given by tan-~(b/a), and there is no response to winds
perpendicular to this direction. tIn contrast to the results
of Noble and Butman (1979), I found no evidence in the
monthly sea levels of an asymmetrical dependence on the
direction of wind forcing.] The influence of seasonal
changes of density has been modeled by the periodic terms
in Eq. (2.84. Unfortunately, there were insufficient hydro-
graphic data to improve on this representation.
Eastern Boundary
There is insufficient space in this chapter to discuss the
seasonal cycles and wind gains for the eastern boundary
Esee Thompson (1986) for a detailed discussion]. One of
the most interesting results from the regression analysis,
however, was that the residual series (£) were still corre-
lated, i.e., the coherent sea-level signal along the eastern
boundary could not be explained by local air pressure and
wind forcing. The influence of North Atlantic circulation
was therefore examined by first calculating a time series
of Tie using Eq. (2.6) and the 3-month mean Ekman
upwelling fields of Thompson and Hazen (1983~. (The
ocean was assumed closed at 30°N, 60°N; the depth was
taken to be 4 km.) The coherence and gain between Tie and
Newlyn residuals (£J are shown in Figure 2.6. (The posi
OCR for page 58
58
COHERENCE
GAIN
Or'
Sr
it=
o.s 1 1.5 2
FREQUENCY (coy)
FIGURE 2.6 Coherence and gain between ale and Newlyn re-
siduals Aid, 1950 to 1975. Seasonal mean values were used.
Confidence intervals are at the 95 percent level. The horizontal
line in the coherence plot is that coherence that is significantly
different from zero at the 0.05 level.
lion of the Newlyn tide gauge is given in Table 2.1; this
series was chosen because it was the longest available
from the eastern boundary.) The gain increases with de-
creasing frequency as expected from the above discussion
of the response of a baroclinic ocean to Ekman pumping.
The coherence also increases with decreasing frequency;
the slight reduction at the lowest frequencies may be due
to the quasi-linear trend in the Newlyn record, due to
eustatic changes and land movement (Rossiter, 1967), which
. . ~
Is not In fly.
Thus it appears that the North Atlantic circulation does
influence sea level along the eastern boundary. Further,
the gain (Figure 2.6) will transform a white we spectrum
into a "redder" ale spectrum and so allow the meteorology
to make a significant contribution to the interannual changes
of sea level. This point is discussed further in the next
section.
Western Boundary
Blaha (1984) recently presented a thorough analysis of
the monthly sea-level variability observed in the South
Atlantic Bight. The following discussion focuses there-
fore on the stations north of Cape Hatteras.
KEITH R. THOMPSON
Local Wind Effect Wind gains from the regression
model (a, b) are shown in Figure 2.7. To illustrate the type
of information that can be extracted from this figure,
consider the Scotian Shelf, which is relatively straight and
to which Csanady's idealized models are relevant. The
longshore gain at Halifax implies that the cross-shelf scale
of the wind-forced coastal boundary current is about 16
km [L, see Eq. (2.2~. A typical value of 5 x 10 - m/s was
used for r (see Csanady, 1982~. This width is in reason-
able agreement with the value of 23 km obtained from
Csanady's "box-car" forcing model (Csanady, 1982, Eq.
6.53), if we assume (1) r is the same as above; (2) the
longshore wind forcing starts at the deep Laurentian Chan-
nel, the natural "upstream" boundary; and (3) the bottom
slope is 5 x 10-3, a value that is representative of the
inshore bottom topography felt by the boundary current.
The gains for the Gulf of Maine have a stronger on-
shore component than the Scotian Shelf gains, presumably
the result of enhanced wind setup in this wide, semi-
enclosed sea. Recent results from a numerical modeling
study of the Gulf of Maine agree favorably with Figure 2.7
Esee Wright et al. (1986) for a detailed comparison].
Seasonal Cycle The coefficients cat and c2 define the
annual cycle of sea level that is not forced by local wind or
air pressure. This cycle is more regionally coherent than
WIND GAIN
(a,b)
in,;
· ,
Im/Pa ~ ~ ~ ~
~3 '
\
FIGURE 2.7 Wind gains (a, b) of sea level on local wind stress
from Eq. (2.8). The tide-gauge positions are given in Table 2.1.
Several of the gains for the mid-Atlantic Bight have been omitted
to avoid cluttering the figure, but they conform to the overall
pattern. All the gains are significantly different from zero at the
0.05 level except Miami.
OCR for page 59
NORTH ATLANTIC SEA LEVEL AND CIRCULATION
TABLE 2.2 Mean Correlation of Residual
Series Ail, Both Within and Between Tide-
Gauge Groups for the Common Period 1961
to 1970
GMSS MAB SAB
GMSS 0.64
MAB 0.63
SAB 0.26
0.74
0.28 0.70
Note: The groupings are SAB (Miami, May-
port, Fort Pulaski, Charleston); MAB (Kiptopeke
Beach, Lewes, Sandy Hook, Montauk, New Lon-
don, Newport, and Buzzards Bay); GMSS (Cape
Cod, Boston, Portland, Bar Harbour, and Halifax).
the annual cycle in observed sea levels and has a Septem-
ber maximum in both the mid-Atlantic Bight and the Gulf
of Maine (compare Figures 2.2 and 2.8~. The amplitude is
about 4 cm in the mid-Atlantic Bight and about 2 cm in the
Gulf of Maine. These weak seasonal cycles are in favor-
able agreement with the change in coastal sea level, from
spring to summer, predicted by Csanady (1979), i.e., 2 cm
in the mid-Atlantic Bight and 0 cm in the Gulf of Maine.
Both sets of results agree on an attenuated amplitude at the
coast. Thus our sea-level data provide some evidence for
the existence of Csanady's upper slope current that was
calculated under the major assumption that the geostro-
phic bottom velocity was zero. The attenuation and phase
propagation of the annual cycle along the Scotian Shelf
(Halifax-Yarmouth, see Figure 2.8) reflect the seasonal
freshwater discharge from the Gulf of St. Lawrence
(Drinkwater et al., 19791. The maximum westward flow
in winter would correspond (geostrophically) to an in-
creased coastal sea level as observed. (The influence of
the freshwater discharge is also evident in the Csanady's
spring topography shown in Figure 2.5.)
Residuals Empirical orthogonal function analysis of
the residuals (~) showed that the large-scale modes of sea-
level variability remained after removal of the seasonal
cycle and the influence of local meteorology. The results
of the EOF analysis are confirmed by the overall correla-
tion structure of the residuals given in Table 2.2. (The
correlations have been averaged according to the tide-
gauge groupings suggested by the EOF analysis.) The
average correlation is high (~0.7) for station pairs on the
same side of Cape Hatteras. The average correlation be-
tween station pairs on different sides of Cape Hatteras is
much lower (~0.3~. Three typical residual series are shown
in Figure 2.9. Note the similarity of the Boston and Sandy
Hook records (both north of Hatteras). Apparently, the
59
JUL ~ ~ c
\ ~ · ~
| · Ml D - ATLANTIC BIGHT |
3 GULF OF MAINE
j · SCOTIAN SHELF
~fJaN
_ · ~
_ ~ ~
FIGURE 2.8 As in Figure 2.2 but for the annual cycle in the
regression model, i.e., cat and c2, the annual cycle not forced by
local air pressure or wind. The largest amplitude, Scotian Shelf
station, is Halifax.
10-cm anomaly in the mid-Atlantic Bight and Gulf of
Maine in early 1950 was not due to local air pressure or
wind (compare Figures 2.1 and 2.91.
The standard deviations of the residuals (CJ27 Table 2.1)
show that the most energetic stations are in the South
Atlantic Bight, even though the influence of local meteor-
ology has been removed (62 ~ 5 cm). Further north, ~2 iS
-vatted ~ ~ a ~MA ~ ,ir ~' ~ 4t >~7 I v ;' , ~ ~ ~VIA ~ ~ ~ t~ ~ ~ ~t ~ ' -
R0STON I
SANDY HOOK
Y A ~ A ~ WA I ~ ~ \ A rid ;
4- ~ V-l Y ~ it u ~ . .~.~)J ;~ ~e ~v
C~ ~ Al F~TnN
Im
FIGURE 2.9 Typical residual (£) series for the South Atlantic
Bight (Charleston), mid-Atlantic Bight (Sandy Hook), and Gulf
of Maine (Boston), calculated from Eq. (2.8) for the period 1950
to 1975.
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60
POWER
DENSITY
cm2/cpm
too
o
~~-~~'V~~
0.1 0.2 0.3 0.4 0.5
FREQUENCY(cpm)
FIGURE 2.10 As in Figure 2.3 but for Boston residual series,
1950 to 1975. The 95 percent confidence interval is given for the
pole tide peak.
about 4 cm. The proportion of sea-level variance that can
be accounted for by local air pressure end wind(1 -~22/~2)
is everywhere less than 42 percent along the western
boundary, in contrast to 80 percent at Newlyn on the
eastern boundary (Table 2.1~. The power spectrum of the
Boston residuals (Figure 2.10) shows that the regression
model has been able to account for about half of the
energy at periods less than 1 yr but is noticeably less
successful at lower frequencies (compare Figures 2.3 and
2.10~. The pronounced peak in the residual spectrum at
14.7 months is presumably due to the pole tide. Miller and
Wunsch (1973) also detected a weak pole tide in the Boston
monthly sea-level record but did not attempt to reduce the
background noise by removing the variations coherent
with the meteorology. This analysis suggests that such a
procedure would significantly improve the chances of
detecting such a small signal.
What causes the large-scale residual variations north
and south of Cape Hatteras? Given the EOF split at Cape
Hatteras and the higher residual variance in the South
Atlantic Bight, one obvious possibility is the Gulf Stream.
I attempted to relate the residuals to monthly fluctuations
in the Sverdrup transport across f/h contours (i.e., trans-
ports were calculated from Eq. (2.3) using North Atlantic
bathymetry). No significant relationships were found. It
was also impossible to explain the difference in sea level
between the mid-Atlantic Bight and South Atlantic Bight
using the pressure head from Eq. (2.7~. In short, no rela-
tionship could be found between the residual variations
along the western boundary and the large-scale wind field
KEITH R. THOMPSON
over the North Atlantic. It is however still likely that
fluctuations in the surface current of the Gulf Stream
contribute significantly to the sea-level variability in the
South Atlantic Bight, particularly as its influence has been
so clearly demonstrated at Miami on shorter time scales
(Maul et al., 1985~. If this is indeed true, then monthly
changes in the surface current are not dominated by the
bottom modified Sverdrup transport of the North Atlantic
or by the local wind field.
Some statistically significant relationships were obtained
between residuals and changes in shelf hydrography north
of Hatteras. (Temperature and salinity data from U.S.
lightships were used from the well-mixed time of year,
October to March, 1956 to 1971.) The correlations, how-
ever, are so low (~0.3) that it seems unlikely that local
hydrographic changes are the main cause of the coherent
month to month variations in the residuals. Comparison of
the time series of sea level and salinity did suggest, how-
ever, that density may be important on time scales exceed-
ing 1 yr.
SECULAR CHANGES OF SEA LEVEL
We have seen that wind stress and air pressure are only
small contributors to the interannual changes of sea level
along the western boundary of the North Atlantic. Shelf
salinity and baroclinic boundary currents may be impor-
tant, but further work is required to quantify their effect on
sea level. Thus it has not been possible to correct the
western boundary records and so obtain a "cleaner" signal
for detecting a change in the rate of rise of sea level.
Along the eastern boundary, however, the large-scale
wind field does appear to exert a significant influence on
the low-frequency changes of sea level. The combined
influence of local wind, air pressure, and ale has been
subtracted from an extended annual series for Newlyn by
means of a multiple regression model. The marked reduc-
tion in the variability about the trend after "correction" is
clear from Figure 2.11. The trends in the observed and
residual records are 1.0 + 0.5 and 1.4 + 0.2 mm/yr, respec-
tively. The standard errors clearly indicate the increased
confidence that can be placed in the latter estimate. Per-
haps more important than the reduced standard error is the
possibility of detecting a change in the trend more readily
in the residual, rather than observed, series (Figure 2.11~.
There is no evidence for an increasing rate of rise in the
Newlyn record.
DISCUSSION
What has been learned about the sea level and circula-
tion of the North Atlantic? Ekman pumping of the North
Atlantic may be causing significant changes in sea level
OCR for page 61
NORTH ATLANTIC SEA LEVEL AND CIRCULATION
IOcm
A :: ~
'a 1:,' ~
RESIDUALS ~
~1
1950 1960 1970 1980
FIGURE 2.11 Annual mean sea level at Newlyn, before and
after removal of the effect of local Pa, I, and Me with a multiple
regression model. The linear trends (+ standard error) are 1.0 +
0.5 and 1.4 + 0.2 mm/yr before and after correction, respectively.
along the eastern boundary. Clearly, more work is re-
quired to check this hypothesis because of the arbitrary
closing of the ocean at 30°N. One check would be to
compare Ekman pumping data for the North Atlantic with
changes in the observed density field. Sea-level differ-
ences between island stations, notably, Bermuda, and the
eastern boundary could also be compared with Ekman
pumping. It would be worthwhile, using the Panulirus
data, to first remove the effect of density changes below
the main thermocline (and so probably not directly wind
forced) from the Bermuda sea-level record.
Local wind stress is a significant contributor to sea-
level variability at all tide gauges except Miami, although
it does not explain the EOF split at Hatteras. Along the
Scotian Shelf, the longshore wind gain implies that the
quasi-steady, wind-forced coastal boundary current is
trapped to within about 16 km of the coast. This value is
in good agreement with the inclined beach model of
Csanady (1982) if the longshore wind forcing is assumed
to start at the deep Laurentian Channel. In the Gulf of
Maine, the gains are in favorable agreement with a nu-
merical modeling study (Wright et al., 1986), thereby
adding credibility to the gains further south. The most
useful oceanographic application of these empirical analy-
ses is probably the provision of such checks on numerical
and analytical models. Ideally, the gains should be based
on hourly data and made frequency dependent. This can
lead to estimates of the spin-down time of shelf circulation
(Garrett et al., 1985) and possibly the influence of nonlo-
cal winds.
61
Changes in the intensity of the surface Gulf Stream are
believed to dominate the seasonal oscillation of Miami sea
level; it is also probable that the surface Gulf Stream
makes a significant contribution to the aperiodic sea-level
variability at Miami and the South Atlantic Bight as a
whole. If coastal sea levels are assumed to be a measure
of the intensity of the surface Gulf Stream, then my failure
to relate the sea-level residuals to bottom-modified Sver-
drup transport requires some other forcing mechanism for
monthly fluctuations in the surface Gulf Stream. North of
Cape Hatteras, the seasonal oscillation of sea level sug-
gests the importance of baroclinic current variations, spe-
cifically the upper-slope current identified by Csanady
(1979) from hydrographic data. Smith and Petrie (1982)
recently showed that the surface position of the shelf/slope
water boundary along the Scotian slope exhibits large-
scale, submonthly onshore translations that appear related
to changes in the longshore current in deep water and at
the shelf break. This suggests that aperiodic variations in
the upper-slope current may make a significant contribu-
tion to the monthly sea-level variability north of Hatteras.
A comparison of coastal sea level with some of the long-
term current records now available for the shelf break and
slope is required.
Long and precise tide-gauge records will probably
continue to play a key role in determining the rate of rise
of global sea level. One of the objectives of this chapter
has been to show how more reliable trends can be obtained
by first removing meteorological effects from the tide-
gauge records. We have seen that meteorological forcing
is relatively unimportant to the interannual changes of sea
level along the western boundary. Salinity variations may
be important, but further work is required to quantify their
effect. Fluctuations in the Gulf Stream, and perhaps the
upper-slope current, probably contribute to the sea-level
variability, but their effect is difficult to quantify.- Thus in
the absence of any effective independent variables for the
regression analysis, it has not been possible to "correct"
the western boundary sea-level series. [Meade and Emery
(1971) showed that river discharge can account for only 7
to 13 percent of the annual sea-level variance.]
However, the variance of the annual sea-level series
from Newlyn (eastern boundary) was reduced significantly
by removing the influence of local wind, air pressure, and
Ekman pumping of the North Atlantic. The standard error
of the trend in the record was thus halved from 0.4 to 0.2
mm/yr. Perhaps more important than the reduced error
bars on the trend is the possibility of detecting changes in
the trend more readily by using the corrected series. Given
the present concern about an accelerating rise of sea level,
and the shortage of long series from important areas of the
globe, it appears worthwhile to develop similar regression
models for other strategic locations.
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62
ACKNOWLEDGMENTS
I would first like to thank the Permanent Service for
Mean Sea Level for providing all the sea-level data used in
this study. Both Chris Garrett and Adrian Gill made some
useful suggestions during the course of this work for which
I am grateful. Thanks also to Sara Bennett for reviewing
a draft version of this chapter.
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Representative terms from entire chapter:
north atlantic
