The Effect of Ocean Currents on Sea Surface Temperature Anomalies

2340 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 31

OLWIJN LEEUWENBURGH* Geodetic Department, Kort & Matrikelstyrelsen, Copenhagen, Denmark

DETLEF STAMMER Physical Oceanography Research Division, Scripps Institution of Oceanography, La Jolla, California

(Manuscript received 17 April 2000, in ®nal form 30 November 2000)

ABSTRACT Global and regional correlations between observed anomalies in sea surface temperature and height are investigated. A strong agreement between the two ®elds is found over a broad range of latitudes for different ocean basins. From a global frequency spectrum, a mean SST damping timescale of 2±3 months was found with westward and eastward propagating anomalies contributing more or less equally to the total variance. Time± longitude plots and wavenumber±frequency spectra show a signi®cant advective forcing of SST anomalies by a ®rst-mode baroclinic eddy or wave ®eld on spatial scales down to 400 km and timescales as short as 1 month. A scaling analysis of forcing terms in a mixed layer temperature model suggests that Ekman terms are expected to be smaller in magnitude. Even though the magnitude of the mean background temperature gradient determines the effectiveness of the forcing, there is no obvious seasonality that can be detected in the amplitudes of SST anomalies. Instead, individual wavelike signatures in SST can be followed for several months, in some cases even up to two years. The phase lag between SST and SSH anomalies is dependent upon frequency and wavenumber and displays a general decrease toward higher latitudes where the two ®elds come into phase at low frequencies. Linear feedback coef®cients, estimated for an intermediate-scale advective-forcing model, generally increase with latitude. They are much higher than previous estimates for atmospheric damping processes and suggest the importance of ocean mixing processes for the evolution of SST. Estimates of atmospheric feedback on small scales were obtained by matching simultaneous transient features in both SST and surface heat ¯ux ®elds, yielding values of 30±40 W mϪ2 for several zonal sections in the North Paci®c.

1. Introduction by turbulent ¯uxes of momentum and buoyancy (heat On the annual period, large-scale sea surface tem- and freshwater) at the sea surface, entrainment processes perature (SST) is primarily controlled by local air±sea at its lower boundary, and by other advective and dif- ¯uxes of heat (Gill and Niiler 1973). However, details fusive processes within the mixed layer itself. The ver- about processes governing SST anomalies on intrasea- tically integrated heat and salt content of the mixed layer sonal, and interannual to decadal periods are less well varies signi®cantly from one season to the next, as does understood (Kushnir and Held 1996; Frankignoul 1999). its vertical extent. Away from the tropical regions, the On these longer timescales a substantial fraction of the mixed layer depth reaches a maximum at the end of a memory of the climate system must reside in the ocean, cooling season characterized by strong winds and low and knowing how the ocean interior communicates with air temperatures, and reaches its minimum in summer the surface layers and the overlaying atmosphere is an under reversed conditions. important issue to be resolved in climate research. The general assumption was that the mixed layer is In the most general terms, changes in SST are gov- nearly decoupled from the interior ocean during the erned through the heat balance in the so-called surface warming phase, extending through late summer. Con- mixed layer of the ocean, which is strongly in¯uenced sistent with that picture would be that the deep ocean is largely dynamically shielded from the atmosphere and, consequently, that the interaction of anomalous * Current af®liation: Scripps Institution of Oceanography, La Jolla, California. subsurface ocean structures with the atmosphere is limited primarily to winter months (Cayan 1992; Kushnir 1994). Although some effects of interior variability on Corresponding author address: Detlef Stammer, Scripps Institution SST were observed and studied already in the early of Oceanography, 9500 Gilman Dr., MS 0230, La Jolla, CA 92393- 0230. 1980s, they were assumed to be small in magnitude and E-mail: [email protected] were mostly treated as small-scale noise. Instead, strik-

᭧ 2001 American Meteorological Society

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FIG. 1. Ten-day averaged maps of sea surface height and SST anomaly ®elds from the period 12±21 Jul 1996 (T/P repeat cycle 141). Both ®elds represent anomalies relative to a 4-yr mean seasonal cycle of the data. They were smoothed in time by a 30-day moving average window, and in space using a Shapiro low- pass ®lter, which removes all energy on the 2Њ grid spacing. Units are in centimeters for SSH and degrees Celsius for SST.

ing large-scale correlations have been reported between observations is then given in section 5 where we focus SST and sea surface height (SSH) ®elds (e.g., see Nerem on the importance of ocean advection on the SST ®elds. et al. 1999; Leuliette and Wahr 1999) leading to serious questions regarding our understanding of processes re- 2. Global description of SSH and SST variability sponsible for observed SST and SSH variations, their relation to surface heat ¯uxes, changes in the oceanic a. Data and preprocessing heat content, and ocean dynamics. We will begin with a comparison of SST anomalies To gain further insight into the role the ocean plays TЈ, as they emerge from the Reynolds and Smith (1994) in setting observed SST patterns, we will investigate analysis, with anomalies in SSH, ␩Ј, resulting from the here 1) the relation between Reynolds and Smith (1994) TOPEX/Poseidon altimeter dataset. TOPEX/Poseidon SST data and TOPEX/Poseidon SSH data, 2) the rela- data from the period October 1992 through the end of tion of variations in both ®elds to local surface forcing 1998 were processed in a standard manner as described and ocean dynamics, and 3) implications of those re- by Stammer and Wunsch (1994) and King et al. (1995). lations for our understanding of processes governing Data from each individual nominal 10-day repeat cycle SST and SSH changes and air±sea coupling mecha- (in practice the repeat cycle is 9.92 days) were gridded nisms. ona2Њϫ2Њ spatial grid. The Reynolds and Smith We will start in section 2 with a global comparison (1994) analysis ®elds were obtained from the National of SST and SSH anomalies and a description of global Centers for Environmental Prediction (NCEP) on a 1Њ SST frequency and wavenumber spectra. In section 3 ϫ 1Њ global grid. This product is based on Advanced we will then present regional observations of SST and Very High Resolution Radiometer images of skin tem- SSH along various zonal sections. In section 4 we will perature, that were combined with ship and buoy data summarize some of the theory that we will need to into weekly estimates of the surface bulk temperature understand these observations and identify the impor- using an objective analysis procedure (we will refer to tant dynamics. A discussion and interpretation of the these temperatures as SST). We interpolated these week-

Unauthenticated | Downloaded 09/24/21 06:15 PM UTC 2342 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 31 ly ®elds onto the 10-day TOPEX/Poseidon cycles to c. Global SST spectra match the SSH time sampling. Because our emphasis is on anomalies not associated In Fig. 3 we show a global average estimate of the with the average large-scale seasonal heating and cool- SST frequency±wavenumber spectrum as it follows ing cycle, the annual and semiannual harmonics were from 15 years worth of SST data between 1985 and removed from both datasets to obtain anomalies TЈ and 1997. The spectrum was calculated as described in ␩Ј. The seasonal cycle in SST is very pronounced, rep- Wunsch and Stammer (1995) on the basis of a spherical resenting 95% of its variance. It represents about 55% harmonic decomposition of global SST maps. As before, of the variance in SSH observations and masks most of the seasonal cycle was removed from the ®elds prior to the midlatitude dynamical ocean signal. The seasonal the computations since it would otherwise dominate the cycle in SSH represents mostly a steric effect associated ®gure. Clearly the spectrum is red and depicts highest with a changing heat content of the surface layers above energy on very long wavelength and periods. Moreover, the seasonal thermocline. However, in some locations, the ®gure illustrates the small amount of energy on small notably the North Paci®c, a seasonal cycle in SSH is time and space scales due to ®lter effects of the Reynolds also related to a mass redistribution due to changing and Smith (1994) objective analysis procedure. wind stress ®elds (e.g., compare Stammer 1997), but The spectral procedure allows separation of the en- which is not of further interest here. ergy of the globally averaged spectrum into eastward and westward moving components (see Wunsch and Stammer 1995 for details). The global average fre- b. Comparison of SSH and SST anomalies quency spectrum obtained from Fig. 3 by summing over Typical examples of ®elds of the anomalies of ␩Ј and all wavenumbers is shown in Fig. 4a separately for east- TЈ as they result from the 10-day period 12±21 July ward and westward traveling components. The respec- 1996 [TOPEX/Poseidon (T/P) repeat cycle 141] are tive global averaged wavenumber spectra are given in shown in Fig. 1. Pointwise cross correlation coef®cients Fig. 4b. In both one-dimensional spectra observed en- between the two anomaly ®elds over time were com- ergy is roughly divided into equal parts between east- puted from the ®rst 4 years of data, thus excluding the ward and westward propagating anomalies. However, 1997±98 El NinÄo (Fig. 2a). Correlations of up to 0.6 there are some noteworthy exceptions. On long wave- are found over large parts of the world oceans, most lengths enhanced energy associated with the peak notably the equatorial Paci®c, but also the eastern mid- around a 5-yr period can be found moving eastward. In latitude North Atlantic and part of the South Paci®c. contrast, the short wavelength part of the spectrum dis- Note also the strong negative correlation between both plays persistently more energy moving westward. On ®elds south of the Antarctic Circumpolar Current, which periods shorter than the annual cycle the spectral slope was already reported by Stammer (1997). is close to Ϫ3/2, while on longer periods it is about Figures 1 and 2a show that there is agreement in both Ϫ2/3. spatial and temporal structures of positive and negative Frankignoul (1999) interpreted a similar SST fre- TЈ and ␩Ј anomalies. Observed SST anomalies are of quency spectrum from the North Atlantic in terms of a order 1ЊC. If representing the upper 200-m depth of the ®rst-order autoregressive Markov process (Frankignoul ocean, this would be associated with steric changes in and Hasselman 1977), 0 SSH, ␩sЈ ϭ #Ϫh ␣(z)TЈ(z) dz (␣ being the thermal ex- (tATЈϭFЈϪ␭TЈ, (1ץ pansion coef®cient), of about 2 cm. Over the bulk of the ocean this is approximately observed. However, in whereFЈA represents white-noise atmospheric forcing several regions, notably the Southern Ocean, SSH and ␭ is a net atmospheric feedback parameter (being changes are much larger, suggesting that processes other positive for negative feedbacks). The corresponding fre- than just changes in the upper-ocean heat content are Ϫ1 quency spectrum can be approximated for ␴ K t F , with in¯uencing observed variability in sea level there. t being the atmospheric forcing timescale, by To test the hypothesis that the general circulation is F manifested in TЈ primarily during winter when the ⌽F(0) mixed layer extends to great depth, we divided the data ⌽T(␴) ϭ , (2) ␴ 22ϩ ␭ into two sets: one consisting of all data north of 50ЊS

(leaving out the region around the Antarctic Circum- where ⌽F(0) is the level of the ``white'' forcing in the Ϫ1 polar Current) and another of all data north of 20ЊN (the frequency band ␴ K t F . latter representing boreal seasons) and computed the We have also included in Fig. 4a the spectrum fol- temporal cross correlations between TЈ and ␩Ј over lowing from (2), based on a globally average decay those regions as a function of time (Fig. 2b). From a timescale for SST anomalies, ␭Ϫ1, of 2 months. conventional point of view one would expect to see The global spectrum in Fig. 4a exhibits a red energy higher correlations in the latter data during boreal win- distribution up to the longest resolved periods where it ter. However, little such enhancement is seen, and it thus con¯icts with the characteristics of a ®rst-order appears that TЈ anomalies persist throughout the year. Markov process. Frankignoul (1999) found similar be-

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FIG. 2. (a: top) Local cross-correlation between the time series of TЈ and ␩Ј from 156 coincident averages over T/P cycles. (b: bottom) The correlation coef®cient between ®elds of TЈ and ␩Ј, such as shown in Fig. 1, plotted as a function of time. The solid line represents data from north of 20ЊN, while the dotted line is based on all data north of 50ЊS.

havior in spectra for the ®rst two EOF modes from the months in low latitudes down to a month or shorter at North Atlantic. various midlatitude locations. Our results from the east- In order to investigate to what extent the global mean ern North Atlantic are in general agreement with pre- decay timescale is related to the averaging procedure, vious estimates (e.g., Frankignoul et al. 1998). The sim- we also computed regional estimates of ␭Ϫ1 as e-folding ple model (1) was found to do well in this area. But timescales estimated from monthly mean SST anomalies substantially longer persistence is found at most low- by ®tting the autocorrelation function appropriate for a latitude locations as well as in the subpolar gyres of the ®rst-order Markov process, North Paci®c and North Atlantic. To gain some insight into the character of observed R (⌬t) ϭ eϪ␭ | ⌬t | (3) T midlatitude SST anomaly decay, Fig. 6 depicts examples Ä Ä at each individual geographical position (Fig. 5). During of TЈ, R, and ⌽T from two midlatitude locations. At the the ®t the observed autocorrelations RÄ were weighted location (30.5ЊN, 330.5ЊE) SST variability is character- by a factor 1/⌬t3 for time lag ⌬t Ͼ 0, to give most ized by a fairly short decorrelation time ␭Ϫ1 of 2.1 weight to small lags. The ®gure clearly shows substan- months, similar to what may be expected from atmo- tial geographical variations in the decorrelation time- spheric feedback (damping) processes. The leveling off scale and yields numbers ranging from more than 10 of the spectrum at low frequencies is as predicted by

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FIG. 3. Global frequency±wavenumber spectrum of sea surface temperature, computed from a spherical harmonic expansion.

(2). Advection is expected to be small here but may associated large-scale patterns such as those present in cause somewhat smaller estimates of ␭Ϫ1 for small-scale Fig. 1 across the North Paci®c as being the signature SST anomalies. East of New Zealand at Ϫ40.5ЊN, of a ®rst-mode Rossby wave originating from an earlier 180.5ЊE, where mean circulation maps indicate an in- ENSO event. The fact that similar patterns emerge also tense boundary current, a similar decay behavior is from SST suggest that those ␩Ј structures are instead found for short time lags. But on longer periods, SST locally driven through air±sea ¯uxes, or that the SST is signi®cantly affected there by low-frequency pro- ®elds at least to some extent show clear signals of large- cesses. These results were insensitive to prior spatial scale wave dynamics. Westward-traveling signals in the smoothing of all scales smaller than 1000 km and were SST anomalies could be an important indication for the similar for other locations near major current systems, impact of ocean currents on observed SST. thus indicating a signi®cant effect of internal ocean dy- To further highlight the latter possibility, we inves- namics on the character of SST variability. Similar plots tigate here time±longitude sections of both SST and for equatorial locations (not shown) suggest that a ®rst- SSH from various latitudes in the North Paci®c between order Markov model is not appropriate at these latitudes. 5.5ЊN and 37.5ЊN. The zonal sections of sea surface height were obtained from altimetric data by space±time 3. Regional observations of SSH and SST optimal interpolation onto the SST 1Њ grid. The resulting anomalies ␩Ј sections are characterized by westward propagating, relatively small-scale features (top panels of Fig. 7) a. Time±longitude sections while SST anomalies (top panels in Fig. 8) are domi- Although anomalous heating (cooling) forces the wa- nated by high-frequency ¯uctuations on near basinwide ter column to expand (contract), much of the low-fre- scales although some westward propagation is clearly quency variability in surface elevation appears to be in evident even in the SST anomalies. Similar analyses the so-called ®rst vertical dynamical mode, representing were performed for zonal sections in the South Paci®c the bulk vertical motion of the deep isotherms (see (Fig. 9) and North Atlantic (Fig. 10). Note that the west- Wunsch 1997), and much of that motion in turn can be ern part of the 15.5Њ North Atlantic section is actually represented as the propagating free planetary Rossby an extension into the Caribbean. In general terms, the wave in the ocean. As an example, Jacobs et al. (1994) characteristics of SST and SSH anomalies from these

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the Loess smoother described in Schlax and Chelton (1992)] with high-pass ®ltering in longitude and low- pass ®ltering in time using a cutoff wavelength of 4000 km and cutoff periods of 24, 45, 60, and 90 days, respectively, for the four sections. This procedure allows for shorter periods at lower latitudes in recognition of the dispersion relation for linear Rossby wave dynamics. The resulting ``small-scale'' anomalies are displayed in the lower panels of Figs. 7±10. The ``large-scale'' ␩Ј and TЈ residuals (the difference between the original and the small-scale ®elds) from the North Paci®c are shown in the middle panels of Figs. 7 and 8. Quite clearly, both ®elds show substantial large-scale and high-frequency ¯uctuations at various latitudes. Large- scale fast perturbations in SSH have been discussed re- cently in Stammer et al. (2000) in terms of their relation to fast barotropic ¯uctuations of the ocean due to time- varying wind stress ®elds. Consistent with their study, those signals are large in the North Paci®c, but are actually present throughout the World Ocean. It is quite surprising to see a very similar signal here also in SST suggesting that the barotropic ¯ow component of the ocean has a potential impact on SST through lateral (meriodional) advection. From the small-scale North Paci®c anomaly ®elds (Figs. 7 and 8) several general observations can be made: 1) In both ®elds there are pronounced westward moving anomalies with similar phase speeds. However, structures are clearly not homogeneous in space and time and are seemingly localized in space for SST at various latitudes. 2) At 5.5ЊN, propagating features show up in both ®elds in the eastern part of the section during various periods of the data record, predominantly in late fall. These phenomena look strikingly similar in both ®elds and show about the same interannual variability in strength and zonal extension. Chelton et al. (1999, manuscript submitted to J. Phys. Ocean- ogr.) discuss the relation of these ␩Ј features to tropical instability waves, while Allen et al. (1995) report similar observations from SST data. In agreement with these earlier discussions we observe here ap- parent interannual modulation of the wave genera- FIG. 4. (a: top) Global average frequency spectrum of SST,obtained by summing over all wavenumbers separately for eastward-propa- tion, most notably their disappearance during the gating (thin line) and westward-propagating (bold line) components. 1997±98 El NinÄo. In the South Paci®c (Fig. 9), trop- The dashed line is the spectrum for a ®rst-order Markov process ®tted ical instability waves are observed as well but they to the high-frequency part of the total spectrum. (b: bottom) Global appear to be nearly absent in the North Atlantic data. average wavenumber spectrum, obtained by summing over all frequencies and plotted separately for the eastward (thin line) and west- 3) Along 15ЊN, SST anomalies are very pronounced ward (bold line) propagating components. near the eastern boundary, while the SSH appears strong over the entire width of the section. At higher latitude, SSH and SST are both more enhanced on basins are similar to those in the North Paci®c. Note the western side. that the 1997±98 El NinÄo signal is evident both in the North and South Paci®c SSH and SST ®elds along the The presence of westward propagating features in al- 5.5ЊN/S and 15.5ЊN/12.5ЊS sections. timetric sea level ®elds has by now been well docu- To gain further insight into the existence of propa- mented. Less common have been reports of their pres- gating signals we bandpass ®ltered both ®elds [we used ence in satellite-based SST ®elds. Most early studies

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FIG. 5. Persistence of sea surface temperature anomalies de®ned as e-folding decay time, computed for each 1Њϫ1Њ grid box from 10-day averages. have focused on areas characterized by strong eddy var- 5 points was applied in the frequency±wavenumber do- iability and pronounced frontal structures where sharp main, thereby increasing the number of degrees of free- water mass contrasts reach to the sea surface (Legeckis dom for each estimate from 2 to 50 (however, only every 1975; Bernstein et al. 1977), whereas others concen- ®fth frequency and wavenumber estimate is therefore trated on the North Atlantic subtropical convergence, independent). which has been the focus of extensive ®eld experiments Quite noticeable along all latitudes is the enhanced (Voorhis et al. 1976; Halliwell et al. 1991). Wavelike energy in both ®elds near the theoretical dispersion structures were also reported from a regional study of curve (plotted as solid lines) for the linear ®rst-mode SST and SSH slopes in the North Atlantic (Cipollini et baroclinic Rossby waves corresponding with the re- al. 1997). It is obvious from Figs. 1 and 7±10, however, spective latitude. The curves are based on the Rossby that wavelike patterns are a truly global phenomenon deformation radius estimates of Chelton et al. (1998). in both TЈ and ␩Ј ®elds. In particular, the maximum energy along 5.5ЊN asso- Along various sections, most notably 5ЊN and 5ЊSin ciated with the instability waves coincides with the max- the Paci®c, eastward traveling TЈ anomalies can be de- imum frequency possible for this mode at the upper tected that seem to emerge from the western boundary. turning point of the dispersion relation. The substantial They suggest a re¯ected wave signal, but are only weak- amount of eastward propagating energy in the SST ®elds ly indicated here in ␩Ј [more tuned ®ltering, however, is quite obvious from the SST spectra but is lacking will bring out this signature more clearly, as in Fig. 6 from the SSH spectra at most latitudes. Among others, in Chelton et al. 1999, manuscript submitted to J. Phys. Chelton and Schlax (1996) investigated the agreement Oceanogr.)]. A complex atmosphere±ocean interaction of SSH observations with the theoretical Rossby wave is possibly involved in the creation, propagation, and dispersion curve, and noted that resolved wavenumber± ultimately the decay of these anomalies [see also Fran- frequency combinations show a tendency to depart from kignoul (1985) for more details]. the dispersion curve towards higher frequencies (c.f. also Zang and Wunsch 1999). We obtain a similar result b. Zonal frequency±wavenumber spectra here for SST data. Halliwell et al. (1991) noted this Zonal frequency±wavenumber power density spectra energy shift relative to the theoretical dispersion curve of SSH and SST were computed from the time±longi- in their SST analysis of the western North Atlantic, tude sections of Figs. 7±9 by applying a 2D Fourier which they explained partly in terms of the effect of a transform. We show here the autospectra for the North nonzero mean ¯ow ®eld on the Rossby wave phase Paci®c (Fig. 11) and South Paci®c (Fig. 12). We selected speed. To test their suggestion, we have plotted in Figs. only those parts of the sections for which the time± 11 and 12 the dispersion curve following from a re- longitude plots suggest a correlation between SSH and duced-gravity model of a dynamically active upper layer SST on the smaller wave scales but required a minimum overlying an inactive layer. The zonal mean upper-layer zonal span of 50 degrees. The resolved zonal wave- currents were based on estimates of monthly mean zonal numbers differ slightly between the sections due to re- surface velocities from ship drift data (Richardson and sulting differences in the total zonal span and to the Walsh 1986). While some improvement can be seen for decrease in the zonal sampling interval with latitude. the 15ЊN and 12.5ЊS latitudes (and especially the 15ЊN With the frequency de®ned to be positive, positive and North Atlantic section, not shown), the estimated effect negative wavenumbers indicate eastward and westward of the mean ¯ow ®eld does not seem to generally remove propagation. In order to increase the con®dence level the discrepancy between the observed and theoretical of the estimates, a moving averaging window over 5 by energy distribution. However, the accuracy of the mean

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FIG. 6. SST, its autocovariance, and power spectral density for two locations in the midlatitude North Atlantic and South Paci®c.

¯ow velocity estimates, as well as the simple manner bility wave regime that dominates the small-scale en- in which we tried to account for them, are debatable. ergy spectrum at this latitude. The squared coherency reaches maximum values of more than 0.8 for a few frequency±wavenumber combinations, implying that c. Coherence spectra more than 80% of the observed SST variance can be The squared coherence, phase lag, and gain between explained as a linear function of SSH. The phase dif- SSH and SST, computed from the cross-spectra for each ference is close to 180Њ (a mean of 166Њ) for wave- section, are shown in Fig. 13. The phase difference be- number±frequency combinations where the squared co- tween SSH and SST might give insight into the linking herency is larger than 0.7. mechanism between both ®elds. In addition, the squared At 15.5ЊN, signi®cant coherence values with a max- coherence can be interpreted as the fraction of variance imum larger than 0.6 are found for waves with periods in SST that can be explained as a linear function of of about half a year and wavelengths of approximately SSH. 900 km. Reduced coherence values are found for the The highest coherence values are found at 5.5ЊN for two northernmost North Paci®c sections, with maximum the frequency band corresponding to the tropical insta- values close to 0.5 for 37.5ЊN. Coherences between SSH

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FIG. 7. Time±longitude sections of ␩Ј along various latitudes in the North Paci®c: 5.5ЊN, 15.5ЊN, 25.5ЊN, and 37.5ЊN. and SST are generally lower in the South Paci®c but temperature anomalies can be approximated by (see, show the same decreasing tendency poleward. e.g., Frankignoul 1985) Most noticeable in both North and South Paci®c phase ١ThЈ ´ lags is the difference between the 5.5Њ north and south (hu)Ј Tץ TЈϭϪ Ϫ(ϩu١ץ) sections and the other three sections. As in the North tthh Paci®c, a phase difference of nearly 180Њ is found at [⌫(w )w (T Ϫ T )]Ј QЈϪQЈ 5.5ЊS for frequency±wavenumber combinations asso- Ϫϩee h h ciated with the tropical instability wave regime. The h ␳chp phase lag between SSH and SST for the other sections 2 (appears to decrease with increasing latitude. In the North ϩ ␬ٌ TЈ, (4 Paci®c a decrease is observed from about 70Њ at 15.5ЊN where T and u represent temperature and horizontal cur- to almost 0Њ at 37.5ЊN. For the three southernmost sec- rent velocity vertically integrated over the depth h of tions the phase lag of SST with respect to SSH yields the mixed layer, ␳ is the density of seawater, cp is the (poleward) 29Њ,26Њ, and 15Њ, respectively. speci®c heat of seawater at constant pressure, we denotes the entrainment velocity at its lower boundary, with (w ) 1 for w 0 and (w ) 0 otherwise, and 4. Dynamics of SST anomalies ⌫ e ϭ e Ͼ ⌫ e ϭ ␬ is the eddy diffusivity, representing mixing on all un- In order to interpret and understand the observed SST resolved scales. The net heat ¯uxes through the sea sur- anomalies described above, and their relation to SSH face and through the bottom of the mixed layer are anomalies we need to go back to theoretical consider- denoted Q and Qh, respectively. ations of processes governing changes of the near-sur- If we neglect mixed layer depth anomalies and heat face SST ®eld. De®ning primed terms as the anomalies ¯uxes through the mixed layer base, and approximate relative to a seasonally varying mean background state, the mean temperature gradient by its meridional com- denoted by an overbar, the evolution of mixed layer ponent, Eq. (4) can be rewritten as

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FIG. 8. Time±longitude sections of TЈ along various latitudes in the North Paci®c: 5.5ЊN, 15.5ЊN, 25.5ЊN, and 37.5ЊN.

[⌫(wee)w (T Ϫ T h)]Ј Levitus et al. (1994) salinity climatologies, which yield ١T Ϫ Ϫ6 Ϫ1( tgETЈϩu١TЈ ഠ Ϫ(uЈϩuЈץ yThϳ 5 ϫ 10 ЊCm and ϳ 60 m. Typical meanץ h velocities (u ,␷ ) are assumed to be on the order of 10 QЈ Ϫ1 . ϩϩ␬ٌ2TЈ, (5) cm s ␳chp From a comparison of the ®rst terms on the left- and where the velocity in the ®rst right-hand-side term in right-hand sides of (5) we ®nd that advection by anom- (4) was split into a quasigeostrophic eddy ¯ow ®eld u alous geostrophic currents is of the same order as the g Ϫ7 Ϫ1 and an anomalous time-varying ageostrophic Ekman ve- observed local change (␴TЈϳ3 ϫ 10 ЊCs ), that yT/ f. At the same time we ®nd that ␴ץis, ␴TЈϳgk␩ locity uE ϭ (␶Јϫk)/(␳fh), where ␶ is the wind stress vector and f is the Coriolis parameter. ϳ ku, which implies that the advection of SST anom- In the following we will use scaling arguments to alies by the zonal mean (geostrophic and Ekman) current estimate the relative importance of the terms in Eq. (5) is of the same order as typical local temperature changes. of the mixed layer temperature on the ``small'' scales. In other words, for the lower to midlatitudes, the mean To do so, we inferred the dominant spatial and temporal current velocityu is of the same order as the wave speed scales of interest from the wavenumber±frequency pow- ␴/k. However, near major boundary currents and at high er spectra (Figs. 11 and 12) to be typically k/2␲ ϳ 1/ latitudes, the mean current can become larger. 1500 cyc kmϪ1 and ␴/2␲ ϳ 2 cycles per year for the Eddies and waves may also change the SST by ver- three most poleward sections. Values differ slightly with tical advection across the mixed layer base. Assuming latitude but separate estimates for the three sections did a temperature jump across the mixed layer base of ⌬T not signi®cantly alter the results of the analysis pre- ϭ 0.5ЊC (this corresponds with a density change of sented here. Typical amplitudes for SST and SSH of the approximately 0.125 kg mϪ3, commonly used to de®ne order of ␩Јϳ15 cm, TЈϳ0.75ЊC are found from the the mixed layer depth) and assuming furthermore that ®ltered time±longitude plots. Monthly mean meridional baroclinic waves are associated with vertical oscillations temperature gradients and mixed layer depths were com- of the thermocline on the order of A ϳ 100 m (such puted from Levitus and Boyer (1994) temperature and that the vertical velocity wЈ within the thermocline will

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FIG. 9. Time±longitude sections of ␩Ј and TЈ along various latitudes in the South Paci®c: 5.5ЊS, 12.5ЊS, 25.5ЊS, and 37.5ЊS. vary with an amplitude ␴A), the ratio of the horizontal anomalies induced by horizontal advection would be to vertical advection terms is then approximately about 1.13ЊC, thus more than 3 times as large. yTh/ f )/(A␴⌬T/)ϳ 1, implying that it is both the With a small-scale zonal wind stress anomaly of ␶ ϳץgk␩) horizontal advection and the vertical movement of the 2.5 ϫ 10Ϫ2 NmϪ2, the term representing anomalous isopycnals that contribute to the observed SST vari- Ekman currents acting on the mean temperature gradient Ϫ8 Ϫ1 yTh)/(␳f ) ϳ 2.5 ϫ 10 ЊCs , about an order ofץability. However, this is most likely an upper bound is (␶ since the amplitude of vertical oscillation at the depth magnitude smaller then the local change. Similarly, of the mixed layer base is very likely smaller than the based on characteristic wind stress curl amplitudes in one assumed above (amplitudes decrease toward the sur- NCEP ®elds [curl(␶) ϳ 1 ϫ 10Ϫ7 NmϪ3] we ®nd that face with a factor of order 102±103). Stevenson (1983) the vertical Ekman pumping term (with values for ⌬T found that for typical Mid-Ocean Dynamics Experiment andhhh as used earlier) wE⌬T/ ഠ curl(␶)⌬T(␳f ) ϳ 1 conditions SST modi®cations due to vertical advection ϫ 10Ϫ8. had an amplitude of about 0.35ЊC. With the scaling val- In summary, we obtained estimates of individual ues assumed here, and in agreement with estimates by terms of (5) according to O(10Ϫ7) ϩ O(10Ϫ7) ϭ O(10Ϫ7) Frankignoul (1985), we ®nd that the amplitude of SST ϩ O(10Ϫ8) ϩ O(10Ϫ8) ϩ O(10Ϫ7) ϩ diffusion. This is

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FIG. 10. Time±longitude sections of ␩Ј and TЈ along various latitudes in the North Atlantic: 3.5ЊN, 15.5ЊN, 28.5ЊN, and 35.5ЊN.

also the main result from Fig. 14, which displays time± 5. Discussion longitude sections along 25.5ЊN in the North Paci®c of the various terms in the temperature equation (5): 1) Based on the scaling results from the previous section local SST changes, 2) advection of the mean SST by we will try and interpret the observations presented ear- anomalous geostrophic current, 3) advection by anom- lier by invoking the following a simpli®ed heat balance: ␩Јץ Tץ TЈ gץTЈץ alous horizontal Ekman currents, 4) anomalous Ekman pumping, and 5) heat ¯uxes. All ®elds were ®ltered prior ϭϪu ϪϪ␭TЈ, (6) t xfy x ץ ץ ץ ץ to the compilation using the same ®lter parameters that were used for the SSH and SST ®elds. We used the that is, a balance between local changes in TЈ, advection time-averaged mixed layer depths and temperature gra- by the mean current, and meridional advection through dients since seasonally varying terms were found to an eddy or wave ®eld acting on the background tem- produce seasonal modulations that are not seen in the perature gradient in the presence of dissipation, which temperature or in the temperature tendency. we represent by a linear feedback coef®cient ␭. Note that

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FIG. 11. Observed frequency±wavenumber power spectral density ⌽ of sea level (top) and temperature (middle) for each of the four North Paci®c sections. The true spectrum lies within 0.62⌽ and 1.91⌽ with 95% con®dence. The solid line represents the ®rst-mode Rossby wave dispersion curve for a zero mean zonal current. The dashed line shows the effect of including a ship-drift-based estimate of the annual mean zonal ¯ow. Units are cm2/(cyc/year ´ cyc/1000 km) for SSH and ЊC2/(cyc/year ´ cyc/1000 km) for SST. (bottom) Predicted SST power spectral Ä density ⌽T. the meridional geostrophic velocity in (6) was substituted contributions from atmospheric forcing processes may from the zonal altimetric sea surface slope and that in optionally be anticipated by adding a noise term. this formulation we have neglected forcing terms such Plotted in Fig. 15 is the rms variability (in time) of as wind-driven entrainment and SST anomaly advection the small-scale SSH and SST anomalies, as well as the by the mean meridional ¯ow. The presence of small-scale magnitude of the annual mean meridional temperature

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FIG. 12. As in Fig. 11 but for the South Paci®c. y, evaluated from the Levitus and Boyer It should be noted that we observe no obvious seasonalץ/Tץ gradients (1994) SST climatology. For most sections, in good cycle in the relation between the wavelike patterns in ␩Ј agreement with (6), amplitudes of propagating SST and TЈ. Instead, anomalies exist throughout the year (in anomalies are relatively large in those parts of the sec- some cases they can be followed in the SST data over one tions where the (absolute) value of the meridional tem- or two years), apparently quite independently from any perature gradient is enhanced, thus giving rise to a more anomalous interaction with the atmosphere. effective anomaly forcing by the surface wave ®eld. From the previous results it seems plausible that the This is especially clear for the 15.5ЊNP, 12.5ЊSP, and shapes of the observed SST spectra are at least partly the 15.5ЊNA sections. For the Paci®c 5.5ЊN and 5.5ЊS explained through a mixed layer temperature model sections, as well as at 3.5ЊN in the Atlantic, we observe forced by anomalous geostrophic currents as in (6). In a reversal of the temperature gradient as compared to that case, a prediction of the power spectrum of SST, the higher-latitude sections, implying an increase of the ⌽T, can be obtained from the spectrum of SSH, ⌽␩, surface temperature poleward. In the Atlantic this re- through the zonal-time Fourier transform of that equa- versal takes place at a longitude of approximately 10ЊW, tion (Halliwell 1991): which appears to be related to some peculiar behavior ␣22k of the SST anomalies there (Fig. 10). The phase plots ⌽Ä (k, ␴) ϭ⌽(k, ␴), (7) indicate phase lags of approximately 180Њ for these sec- T ␴ 22ϩ ␭ ␩ tions, while much smaller values are found for the high- where er-latitude sections. This phase lag difference with the Tץ other sections cannot be explained in the framework of g a SST variability forced by vertical ¯ow, which would ␣ ϭ . (8) yץ f result in largely identical phase signatures for all the sections, and instead points toward horizontal advection It was assumed here that u ϭ 0. To obtain estimates of as the primary forcing mechanism. ⌽T from ⌽␩, values of the feedback coef®cient ␭ are

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needed. It was suggested by Rahmstorf and Willebrand suggests that rather than a forcing term, heat ¯uxes on (1995) that the feedback might depend on the spatial these scales act as a feedback mechanism in proportion scale and it might then not be possible to ®nd a single to the magnitude of the SST anomaly as in (1) with QЈץ coef®cient valid for the entire range of wavenumbers 1 ␴ ϭ . TЈץresolved here. We chose feedback coef®cients that re- ␳ch sulted in the best possible overall resemblance between p observed and predicted temperature spectrum. Values Focusing on the propagating signal, we ®nd from Fig. chosen for the North Paci®c vary from 22 yrϪ1 at 15ЊN 14 a heat ¯ux signal of about 30 W mϪ2 for TЈ values to 53 yrϪ1 at 37.5ЊN. These values are much higher then of ϳ0.5ЊC leading to a decay time ␭Ϫ1 of approximately may be expected for atmospheric feedback. Halliwell et 45 days if h ϭ 60 m. The atmospheric feedback found al. (1991) suggested that such high values instead com- here is at the high end of estimates for large-scale SST pensate for unmodeled mixing processes that result in anomalies and is not inconsistent with previous indi- a fairly strong damping of SST anomalies. The neglect cations (Frankignoul 1985) that smaller anomalies have of remaining small-scale atmospheric forcing contri- less persistence. A similar procedure for 15.5ЊN and butions may also introduce some bias. Resulting pre- 37.5ЊN (not shown) results in heat ¯ux±temperature Ä pairs of (30 W mϪ2, 0.4ЊC) and (60 W mϪ2, 0.75ЊC), dictions ⌽T for the North Paci®c SST spectra are included in the lower panels in Fig. 11. Although not leading to decay times of 30 days and 35 days, respec- unlike the spectra of the observed temperature anom- tively, with the mixed layer depth used above. alies, the predicted SST power in the North Paci®c is A possible cause for the decrease in coherence be- found at higher wavenumbers than observed, especially tween SSH and SST at higher latitudes is the decrease in low latitudes. in ®rst-mode baroclinic wave speed. For low forcing An alternative to using (7) is to compare the observed frequencies other processes that have largely been ne- gain and phase lags with the gain and phase of the glected here, such as advection by the mean current, transfer function, given by entrainment, recurrence, seasonal modulation, mixed layer depth variability, or even mass redistribution, |␣k| might become important. The forcing model (1) should G(k, ␴) ϭ , and (9) (␴ 2ϩ ␭ 2) 1/2 become more appropriate at midlatitudes, thus increasing the atmospheric contribution, and further decreasing ␭ the coherence between SST and SSH. Goodman and ⌰(k, ␴) ϭ tanϪ1 . (10) Marshall (1999) discuss the large-scale coupling mech- ␴ ΂΃ anism between SST and the oceanic streamfunction ⌿ If ␣k Ͻ 0, then ␲ should be added to the phase. It can supported by their analytical atmosphere±ocean model. be seen from (10) that the presence of feedback mech- They suggest that a maximum in SST should be ob- anisms introduces a phase lag between SST and SSH served at the maximum in ⌿ (depressed thermocline, that would otherwise be zero. Furthermore, the 180Њ or raised sea level), and that slow propagating waves phase shift for sign changes of ␣ explains the observed should create larger SST anomalies. This appears to be phase behavior at the near equatorial sections where we similar to what we observe in our midlatitude sections ®nd phase lags of almost 180Њ. Observed gain and phase on smaller scales where we ®nd small phase differences values at those (k, ␴) combinations where a high co- at low wavenumbers and frequencies. herence is observed, together with relations (9) and (10), In summary, we must conclude that at midlatitudes can also be used to infer appropriate values for the feed- no single forcing term can account for all low-frequency back coef®cient ␭. Values computed using the gain func- small-scale SST variability. Instead, a rather complex tion were often found to be very different from those combination of horizontal and vertical advection and obtained using the phase relation, but estimates were damping terms is responsible for setting observed SST generally similar in magnitude to the high values pre- changes, with Ekman terms apparently being of lesser sented above. The estimated values are larger at higher importance. There remain uncertainties in the estimation latitudes, suggestive of more effective damping there. of some of these terms due to their dependence on pa- h Other than that, no particular interpretation should be rameters such as ⌬T and , while small-scale mixing has been ignored altogether. given to these estimates. A direct estimate of the atmospheric contribution to the feedback can be obtained by using the observation that the heat ¯ux ®eld contains 6. Summary a propagating signal with a signature very similar to In the past the effect of interior variability on SST that of the temperature ®eld itself (see Fig. 14). This was mostly treated as fairly insigni®cant small-scale

←

FIG. 13. Squared coherence and phase lag and gain between SSH and SST for the wavenumber±frequency combinations with the highest signi®cant coherence. The lines again represent the ®rst-mode Rossby wave dispersion curves.

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FIG. 14. Time±longitude plots at 25.5ЊN in the North Paci®c of the small-scale contributions from the different terms in the mixed Ј tT Ј), anomalous geostrophic ¯ow ®eld (Ϫ␷ gTThy), Ekman pumping (Ϫwe⌬ / ), temperature (TЈ), Ekmanץ) layer temperature tendency Ϫ1 .(transport (Ϫue١Th), and net surface heat ¯ux (QЈ/(␳cp )). Units are ЊCs , except for the temperature (ЊC noise. However, much resemblance can actually be that is acted on by the wave's meridional velocity com- found between SST and SSH anomalies on small spatial ponent. However, this process for dynamically creating scales and low frequencies, indicating a greater impact SST anomalies becomes less ef®cient towards high lat- of ocean surface currents on observed SST than pre- itudes, where wave phase speeds decrease substantially, viously anticipated. thus allowing for more ef®cient atmospheric damping Typically one-third of the rms SST variability outside of induced SST anomalies, and where changes in the the seasonal cycle can be associated with wavelengths wind will also result in changes in local oceanic dy- smaller than 1000 km, and at many latitudes small-scale namics, heat ¯ux divergences, and redistribution of features are closely related to free ®rst-mode baroclinic mass. Rossby waves. These waves create a signature in the Damping coef®cients estimated from the phase lags SST ®eld that in some cases can be followed for over between SSH and SST anomalies result in values of 20± a year, thus exceeding persistence times of atmospher- 30 yrϪ1 with some estimates far exceeding these num- ically forced anomalies at midlatitudes (Frankignoul et bers. These numbers are much larger than those ex- al. 1998). Dynamically coupled anomalies in SSH and pected for atmospheric feedback in midlatitudes, and SST have been reported earlier in limited regions (Hal- Halliwell et al. (1991) suggested that they rather rep- liwell et al. 1991; Cipollini et al. 1997). We show here resent the damping effect of ocean mixing processes. that these features can be detected in all ocean basins From our analysis there is evidence that there is a extending from near-equatorial to midlatitudes. It ap- signi®cant coupling in the horizontal between the sur- pears that a necessary condition for the existence of face mixed layer and the underlying layers through oce- Rossby wave±like SST anomalies is the existence of a anic currents associated with a baroclinic wave ®eld. nonzero meridional background temperature gradient Moreover, Fig. 6 suggests a signi®cant in¯uence of low-

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FIG. 15. Root-mean-square variability in time of sea level (dashed line) and temperature (thin line). Units are on the left-hand axis with a conversion factor to obtain values for the temperature (ЊC) between brackets above the graph. Annual mean meridional temperature gradient (bold line); units are on the right-hand axis. frequency modulation of SST by ocean variability near and 0.3 monthsÐroughly an order of magnitude smaller all major current systems. than those found for the large-scale anomalies. A global (area weighted) average of local decorre- The main conclusion of this paper is that a signi®cant lation scales in Fig. 5 yields an estimate of 3 months. fraction of the low-frequency variability of SST is con- This is slightly larger than the global mean value esti- nected to dynamical processes that extend over the entire mated from the spectra given in Fig. 4a, possibly be- oceanic water column. Understanding of the joint evo- cause the ®t of the autocorrelation functions is partly lution of the coupled ocean±atmosphere, which de®nes in¯uenced by the low-frequency energy, while the spec- much of the climate system, will therefore necessarily trum was chosen to match only the high-frequency part. require accounting for oceanic circulation structures and Both numbers are considerably larger than damping variability not now represented in models. As the da- timescales obtained for ``small-scale'' transient anom- tasets lengthen and known or suspected errors in them alies, which instead yield decay timescales between 0.2 are removed, a fuller description of the air±sea coupling

Unauthenticated | Downloaded 09/24/21 06:15 PM UTC 2358 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 31 as a function of position, as well as of time and space King, C., D. Stammer, and C. Wunsch, 1994: The CMOP/MIT TO- scales, will become possible. PEX/Poseidon altimeter data set. Center for Global Change Sci- ence, Massachusetts Institute of Technology Tech. Rep. 30, 45pp. Kushnir, Y., 1994: Interdecadal variations in North Atlantic sea sur- Acknowledgments. Charmain King helped with some face temperature and associated atmospheric conditions. J. Cli- of the computations. Helpful discussions with Carl mate, 7, 141±157. Wunsch and Claude Frankignoul are gratefully acknowl- ÐÐ, and I. M. Held, 1996: Equilibrium atmospheric response to edged. D.S. was supported by Contract JPL-68571, and North Atlantic SST anomalies. J. Climate, 9, 1208±1220. Legeckis, R. V., 1975: Application of synchronous meteorological by Contract NAGW-7857 and NAG5-8901 with NASA. satellite data to the study of time dependent sea surface tem- O.L. acknowledges support by the Danish Research perature changes along the boundary of the Gulf Stream. Geo- Council, Program in Earth Observation and the hospi- phys. Res. Lett., 2, 435±438. tality of EAPS, MIT. Contribution to GEOSONAR and Leuliette, E. W., and J. M. Wahr, 1999: Coupled pattern analysis of sea surface temperature and TOPEX/Poseidon sea surface WOCE. height. J. Phys. Oceanogr., 29, 599±611. Levitus, S., and T. P. Boyer, 1994: World Ocean Atlas 1994. Vol 4: Temperature, NOAA Atlas NESDIS 3, 117 pp. REFERENCES ÐÐ, R. Burgett, and T. P. Boyer, 1994: World Ocean Atlas 1994. Allen, M. R., S. P. Lawrence, M. J. Murray, C. T. Mutlow, T. N. Vol. 3: Salinity, NOAA Atlas NESDIS 3, 97 pp. Stockdale, D. T. Llewellyn-Jones, and D. L. T. Anderson, 1995: Nerem, S., D. P. Chambers, E. W. Leuliette, G. T. Mitchum, and B. Control of instability waves in the Paci®c. Geophys. Res. Lett., S. Giese, 1999: Variations in global mean sea level associated 22, 2581±2584. with the 1997±1998 ENSO event: Implications for measuring Bernstein, R. L., L. Breaker, and R. Whritner, 1977: California Cur- long term sea level change. Geophys. Res. Lett., 26, 3005±3008. rent eddy formation: Ship, air and satellite results. Science, 195, Rahmstorf, S., and J. Willebrand, 1995: The role of temperature feed- 353±359. back in stabilizing the thermohaline circulation. J. Phys. Ocean- Cayan, D. R., 1992: Latent and sensible heat ¯ux anomalies over the ogr., 25, 787±805. northern oceans: Driving the sea surface temperature. J. Phys. Reynolds, R. W., and T. M. Smith, 1994: Improved global sea surface Oceanogr., 22, 859±881. temperature analysis using optimum interpolation. J. Climate, 7, Chelton, D. B., and M. G. Schlax, 1996: Global observations of 929±948. oceanic Rossby waves. Science, 272, 234±238. Richardson, P. L., and D. Walsh, 1986: Mapping climatological sea- ÐÐ, R. A. deSzoeke, M. G. Schlax, K. El Naggar, and N. Siwertz, sonal variations of surface currents in the tropical Atlantic using 1998: Geographical variability of the ®rst baroclinic Rossby ra- ship drifts. J. Geophys. Res., 91, 10 537±10 550. dius of deformation. J. Phys. Oceanogr., 28, 433±460. Schlax, M. G., and D. B. Chelton, 1992: Frequency domain diag- Cipollini, P., D. Cromwell, M. S. Jones, G. D. Quartly, and P. G. nostics for linear smoothers. J. Amer. Stat. Assoc., 87, 1070± Challenor, 1997: Concurrent altimeter and infrared observations 1081. of Rossby waves propagating near 34ЊN in the northeast Atlantic. Stammer, D., 1997: Steric and wind-induced changes in large-scale Geophys. Res. Lett., 24, 885±24 892. sea surface topography observed by TOPEX/POSEIDON. J. Frankignoul, C., 1985: Sea surface temperature anomalies, planetary Geophys. Res., 102, 20 987±21 009. waves, and air±sea feedback in the middle latitudes. Rev. Geo- ÐÐ, and C. Wunsch, 1994: Preliminary assessment of the accuracy phys., 23, 357±390. and precision of TOPEX/POSEIDON altimeter data with respect ÐÐ, 1999: Sea surface temperature variability in the North Atlantic to the large scale ocean circulation. J. Geophys. Res., 99, on monthly to decadal time scales. I. Beyond El NinÄo: Decadal 24 584±25 604. and Interdecadal Climate Variability, A. Navarra, Ed., Springer- ÐÐ, ÐÐ, and R. Ponte, 2000: De-aliasing of global high frequency Verlag, 25±47. barotropic motions in altimeter observations. Geophys. Res. ÐÐ, and K. Hasselmann, 1977: Stochastic climate studies, II: Ap- Lett., 27, 1175±1178. plication to sea-surface temperature variability and thermocline. Stevenson, J. W., 1983: The seasonal variation of the surface mixed- Tellus, 29, 284±305. layer response to the vertical motions of linear Rossby waves. ÐÐ, A. Czaja, and B. L'Heveder, 1998: Air±sea feedback in the J. Phys. Oceanogr., 13, 1255±1268. North Atlantic and surface boundary conditions for ocean mod- Voorhis, A. D., E. H. Schroeder, and A. Leetmaa, 1976: The in¯uence els, J. Climate, 11, 2310±2324. of deep mesoscale eddies on sea surface temperature in the North Gill, A. E., and P.P.Niiler, 1973: The theory of the seasonal variability Atlantic subtropical convergence. J. Phys. Oceanogr., 6, 953± in the ocean. Deep-Sea Res., 20, 141±177. 961. Goodman, J., and J. Marshall, 1999: A model of decadal middle- Wunsch, C., 1997: The vertical partition of oceanic horizontal kinetic latitude atmosphere±ocean coupled modes. J. Climate, 12, 621± energy and the spectrum of global variability. J. Phys. Ocean- 641. ogr., 27, 1770±1794. Halliwell, G. R., Jr., Y. J. Ro, and P. Cornillon, 1991: Westward- ÐÐ, and D. Stammer, 1995: The global frequency±wavenumber propagating SST anomalies and baroclinic eddies in the Sargasso spectrum of oceanic variability estimated from TOPEK/POSEI- Sea. J. Phys. Oceanogr., 21, 1664±1680. DON altimeter measurements. J. Geophys. Res., 100, 24 895± Jacobs, G., H. E. Hurlburt, J. C. Kindle, E. J. Metzger, J. L. Mitchell, 29 910. W. J. Teague, and A. J. Wallcraft, 1994: Decadal-scale trans- Zang, X., and C. Wunsch, 1999: The observed dispersion relationship Paci®c propagation and warming effects of an El NinÄo anomaly. for North Paci®c Rossby wave motions. J. Phys. Oceanogr., 29, Nature, 370, 360±363. 2183±2190.

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