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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
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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
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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.
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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)
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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.
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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
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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.
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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
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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. REFERENCES Anderson, D. L. T., K. Bryan, A. E. Gill, and R. C. Pacanowski (19791. Transient response of the North Atlantic: Some model studies, J. Geophys. Res. 84, 4795-4815. Barnett, T. P. (1983a). Recent changes in sea level and their possible causes, Climatic Change 5, 15-38. Barnett, T. P. (1983b). Long-term changes in dynamic height, J. Geophys. Res. 88, 9547-9552. Blaha, J. P. (19841. Fluctuations of monthly sea level as related to the intensity of the Gulf Stream from Key West to Norfolk, J. Geophys. Res. 89, 8033-8042. Bunker, A. F. (19801. Trends of variables and energy fluxes over the North Atlantic Ocean from 1948 to 1972, Mon. Weather Rev. 108, 720-732. Csanady, G. T. (1976~. Mean circulation in shallow seas, J. Geophys. Res. 81, 5389-5399. Csanady, G. T. (19791. The pressure field along the western margin of North America, J. Geophys. Res. 84, 4905-4915. Csanady, G. T. (19821. Circulation in the Coastal Ocean, D. Reidel, New York, 279 pp. Drinkwater, K., B. Petrie, and W. H. Sutcliffe (19791. Seasonal geostrophic volume transports along the Scotian Shelf, Estu- arine Coast. Mar. Sci. 9, 17-27. Garrett, G. J. R., F. Majaess, and B. Toulany (1985~. Sea level response at Nain, Labrador, to atmospheric pressure and wind, Atmosphere-Ocean 23~2), 95-1 17. Gill, A. E., and P. P. Niiler (19731. The theory of the seasonal variability in the ocean, Deep-Sea Res. 20, 141-177. KEITH R. THOMPSON Hicks, S. D. (19781. An average geopotential sea level series for the United States, J. Geophys. Res. 83, 1377-1379. Lisitzin, E. (19741. Sea-Level Changes, Elsevier Oceanography Series 8, Elsevier, Amsterdam, 273 pp. Maul, G. A., F. Chew, M. Bushnell, and D. A. Mayer (1985). Sea level variation as an indicator of Florida Current volume transport: Comparison with direct measurements, Science 227, 304-307. Meade, R. H., and K. O. Emery (1971). Sea level as affected by river runoff, eastern United States, Science 173, 425-428. Miller, S. P., and C. Wunsch (1973~. The pole tide, Nature 246, 98-102. Noble, M., and B. Butman (19791. Low-frequency w~nd-induced sea level oscillations along the east coast of North America, J. Geophys. Res. 84, 3227-3236. Pattullo, J., W. Munk, R. Revelle, and E. Strong (1955~. The seasonal oscillation in sea level, J. Mar. Res. 14, 88-155. Roemmich, D., and C. Wunsch (19841. Apparent changes in the climatic state of the deep North Atlantic Ocean, Nature 307, 447-450. Rossiter, J. R. (1967~. An analysis of annual sea level variations in European waters, Geophys. J. Roy. Astron. Soc. 12,259-299. Rossiter, J. R. (19724. Sea level observations and their secular variation, Phil. Trans. Roy. Soc. London, A 272, 131-139. Smith, P. C., and B. Petrie (1982~. Low-frequency circulation at the edge of the Scotian Shelf, J. Phys. Oceanogr. 12, 28-46. Thompson, K. R. (1981~. Monthly changes of sea level and the circulation of the North Atlantic, Ocean Modelling 41, 6-9. Thompson, K. R. (1986~. North Atlantic sea level and circulation, Geophys. J. Roy. Astron. Soc. 87, 15-32. Thompson, K. R., and M. G. Hazen (1983~. Interseasonal changes of wind stress and Ekman upwelling: North Atlantic, 1950-80, Canadian Technical Report of Fisheries and Aquatic Sciences, No. 1214. Wright, D. G., D. Greenberg, J. Loder, and P. C. Smith (1986~. The steady state response of the Gulf of Maine to a surface wind stress, J. Phys. Oceanogr. 15, 947-966.
Representative terms from entire chapter: