Midlatitude Ocean-Atmosphere Interaction in an. Idealized Coupled Model. Department of Atmospheric Sciences and

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1 Midlatitude Ocean-Atmosphere Interaction in an Idealized Coupled Model S. Kravtsov 1 and A. W. Robertson Department of Atmospheric Sciences and Institute of Geophysics and Planetary Physics University of California, Los Angeles 45 Hilgard Ave. Los Angeles, CA Submitted to J. Phys. Oceanogr. November 7, 2 1 Corresponding author sergey@atmos.ucla.edu

2 ABSTRACT Interannual-to-interdecadal ocean-atmosphere interaction in midlatitudes is studied using an idealized coupled model consisting of eddy-resolving two-layer quasigeostrophic oceanic and atmospheric components with a simple diagnostic oceanic mixed layer. The model solutions exhibit structure and variability resembling many aspects of the climate over the North Atlantic. The atmospheric climatology is characterized by a zonally-modulated climatological jet. The single basin oceanic climatology consists of a midlatitude double jet, representing the Gulf Stream and Labrador currents, which are parts of the subtropical and subpolar gyres respectively. The leading mode of the atmospheric low-frequency variability consists predominantly of meridional displacements of the zonal jet, with a local maximum over the ocean. This mode is found not to be aected by oceanic coupling. Its variability is shown to determine the structure of the sea surface temperature variability both regionally near the western boundary and on the basin scale. The former is due to a delayed modulation of the baroclinic time-dependent boundary currents in response to the slowest components of the atmospheric forcing, with synchronous variations in the two oceanic jets. This forced response dominates vastly over the oceanic intrinsic regional variability, associated with baroclinic eddies. The rst basin scale mode of SST has largely one polarity and is similar in structure to the observed interdecadal mode identied by Kushnir (1994). A warm SST anomaly is accompanied by anomalously low atmospheric pressure, an intensied model Gulf Stream and a weakened Labrador current. In the western part of the basin, this pattern is shown to be forced by the atmospheric surface wind anomaly primarily through its inuence on the baroclinic oceanic circulation. The resulting anomalous currents advect mean SST and produce the SST anomaly 1

3 described above. The response in the east is found to be dominated by local atmospheric forcing. Basin scale intrinsic oceanic variability consists of a damped oceanic oscillatory mode in the baroclinic pressure eld that is excited by the atmospheric noise. Its period is around 5:5 yr, but it has a negligible inuence on the evolution of sea surface temperature. Important for this mode's excitation is the meridional position of the atmospheric center of action relative to the ocean gyres. 2

4 1 Introduction Ocean-atmosphere interaction in midlatitudes is a potential source of interannual-tointerdecadal climate predictability, based on the midlatitude ocean's long intrinsic time scales. However, the existence of signicant coupled modes of variability has not been unambiguously established. In this paper we investigate interactions between the wind-driven ocean gyres and modes of midlatitude atmospheric variability using a coupled mode of intermediate complexity. Figure 1: (a) The dierence between annual mean SST averaged from 195 to 1964 (warm years) and annual mean SST averaged from 197 to 1984 (cold years), contour interval is :2 C; (b) as in (a) but for SLP (contours) and winds (arrows), contour interval :5, arrow scale in m s?1 is indicated below the panel. Shading marks statistical signicance levels as a distribution of a t-variable: light for t=2-2.5, medium for t=2.5-3, and dark for t= A t value of 2.18 would indicate statistical signicance at 95% level (taken from Kushnir 1994). Observations of interdecadal sea surface temperature (SST) anomalies over the North Atlantic (e.g., Bjerknes 1964, Kushnir 1994) do suggest a coupled mode. Here the SST pattern 3

5 lacks the distinctive local relationship with atmospheric sea level pressure (SLP) seen on the interannual timescales, where the atmosphere is known to largely drive SST through anomalous heat uxes and Ean currents (Bjerknes 1964, Wallace et al. 199). Fig. 1 (taken from Kushnir 1994) presents an example of spatial patterns over the North Atlantic, obtained by taking the dierence between the 'positive` and 'negative` phases of an interdecadal anomaly that occurred during the periods 195? 1964 and 197? 1984 respectively. The interdecadal SST structure (panel (a)) has one polarity over most of the North Atlantic ocean, except near the western boundary between the Gulf Stream and the Labrador current. There are two primary positive SST anomalies, located northeast of Bermuda and in the Labrador Sea respectively. Kushnir has argued that anomalously low SLP (panel b) is a baroclinic response of the atmosphere to a heat source over the Labrador Sea, so that the ocean drives the atmosphere on the interdecadal timescales in the North Atlantic region (see also Rodwell et al. 1999). Oceanic temperature anomalies in the upper 1 m of the ocean have been found to have a similar spatial structure to the SST anomaly in Fig. 1a (Levitus 1989a,b) and to be accompanied by an intensication of the Gulf Stream (Greatbatch et al. 1991), suggesting that the ocean plays an active role. Modeling studies provide a means of isolating the roles of processes intrinsic to either the atmosphere or ocean, versus the coupling between them. Steadily-forced eddy-resolving quasigeostrophic (QG) models can themselves generate vigorous internal oceanic variability with interannual and interdecadal timescales (e.g., Cessi and Ierley 1995, Ierley and Sheremet 1995, Berlo and McWilliams 1999). In the realistic weak friction limit, modeled oceanic internal variability crucially depends on the ability of the model to capture baroclinic instability (Meacham and Berlo 1997a,b, Berlo and Meacham 1997,1998, Dijkstra and Katsman 1997, Ghil et al. 2). The dierence between the reduced gravity and two layer quasigeostrophic models comes primarily from the changes in the inertial recirculation dynamics when baroclinic eddies are included (e.g., Spall 1996). Simple coupled models have tended to support the importance of ocean dynamics in determining SST variability (Liu 1993, Jin 1997, Weng and Neelin 1998, Munnich et al. 1998, Cessi 2). However, these models have been limited to 4

6 linear one layer or reduced gravity oceans coupled to ad-hoc or highly simplied atmospheric parameterizations. General circulation model (GCM) studies have given conicting results, providing no consensus as to whether coupled modes of midlatitude variability are important or not. Some of them produce behavior interpreted as a coupled mode (Latif and Barnett (1994, 1996), von Storch (1994), Robertson (1996), Grotzner et al. (1998)). Other suggest that midlatitude coupling is of limited importance to decadal climate variability (Kushnir and Lau (1992), Ferranti et al. (1994), Peng et al. (1995), Saravanan (1998), Danabasoglu (1998), Saravanan et al. (2)). The aim of this study is to ll the gap between the rather ad-hoc simple coupled models of midlatitude ocean-atmosphere interaction and GCMs. The model of an intermediate complexity consists of an eddy-resolving two-layer QG ocean in a rectangular basin representing the North Atlantic ocean, coupled to a two-layer channel QG atmosphere. An explicit diagnostic oceanic mixed layer is included. This is the rst time, to our knowledge, that a simple eddy-resolving ocean model has been coupled to a dynamically-consistent atmospheric model. After discussing the model formulation in Section 2, we start by investigating the uncoupled variability that is intrinsic to the atmosphere and ocean components separately in Section 3. The model atmosphere's variability is due to nonlinearities in atmospheric dynamics. It is stochastic in time and is characterized by a preferred spatial pattern situated over the ocean. In the oceanic integration forced by the history of the atmosphere from the uncoupled atmospheric run, the ultra-low frequency component of this pattern is shown to directly drive the leading order oceanic variability. The intrinsic oceanic variability, which dominates in the steadilyforced ocean-only integration, is found to be weaker than the atmospherically-forced variability. The models are then coupled together in Section 4. Here we nd that the behavior of a coupled model diers little from that of the stochastically forced ocean-only case. The eect on the model atmosphere of prescribing an SST anomaly from the coupled run is investigated in Section 4.3, where it is shown to be weak. The summary and discussion can be found in Section 5. Details of the model are given in the appendix. 5

7 2 Model Formulation The model geometry is depicted in Fig. 2, with a zonal crossection through the model on the top and a plan view at the bottom. The ocean basin is meant to represent a midlatitude portion of the Atlantic ocean and extends longitudinally from X W = 352 to X E = 864 (approximately 6 wide at 45 N) and latitudinally from Y S =?32 to Y N = 24 (16 N to 66 N) with y = corresponding to the 45 N latitude. Atmospheric latitudinal H a ATMOSPHERE h mix LAND H o η D o1 D o2 LAND X aw X w X e X ae Y an Y n OCEAN Y as X aw X w X e X ae Figure 2: Model geometry, see text. 6

8 boundaries are situated at Y a S = Y S and Y a N = 32, i.e., at 16 N and 74 N respectively. The longitudinal atmospheric boundaries at Xa W = and Xa E = 248 (a bit less than the length of the zonal circle at 45 N) are open, and periodic conditions are assumed. The atmosphere overlies the ocean and land. The interior oceanic and atmospheric depths are H o and H a. The mean depth of the lower oceanic layer is D o2. A rigid lid is assumed, so the mean thickness of the upper oceanic layer is D o1 = H o? D o2. On the top of the ocean there is a mixed layer of the constant thickness h mix = 3 m. The equations governing the dynamical modules of the model are standard two-layer quasigeostrophic. The ocean-atmosphere coupling occurs through the mixed layer, where the geostrophic and Ean currents, as well as local ocean-atmosphere heat exchange can aect SST. The latter, in turn, inuences the atmosphere. All the vertical heat uxes in the model are parameterized through SST and a vertically-averaged atmospheric temperature, which is proportional to the atmospheric baroclinic streamfunction. There is no surface heat ux dependence on the wind speed. The exact forms of the equations we employ are given in the appendix. Although the components of the model above have been used before in addressing dierent questions concerning oceanic and atmospheric physics, their combination in a coupled model of this character is unusual. Since the quasigeostrophic dynamics is decient in both high and low latitudes, we should pay attention only to midlatitude processes that are decoupled from those in polar and tropical regions. Indeed, we will see that, whatever is happening near the latitudinal boundaries of our model has little eect on the dynamics of the central region. Additional measures have been taken to assure that this is the case. An extra damping of the oceanic ow close to the zonal boundaries has been used to avoid excessive activity of the extratropical and subpolar circulations. While close to the North Pole this is justiable as a parameterization of the oceanic topography, in the tropics it is just a preventive procedure not to distort the midlatitude dynamics. The model is one of the simplest midlatitude climate process models that retains a fairly complete set of the relevant physics. The quasigeostrophic formulation in the atmosphere is 7

9 implemented to describe both the climatology and variability around it, which allows us to use a specied heat ux at the top of the atmosphere as the natural forcing function of the climate. Diabatic physics is explicitly included in the quasigeostrophic ocean. However, a lot of potentially important physics is simply missing from the model: the geometry is highly simplied, there is only one ocean basin, there is no orography on land, the land model itself is very crude, etc. These will have an eect on the model climate, making it dierent from what is inferred from observations. The model has a potential for overestimating the sensitivity of the climate to the ocean-atmosphere coupling, because a single temperature represents the entire atmospheric column, and enters the bulk formula parameterization of the air-sea heat exchange. Therefore, the sensitivity of the model atmosphere to surface boundary condition is overestimated. Our approach in pursuit of elucidating the coupled ocean-atmosphere eects in midlatitudes is to start from this extreme case, where the coupling is likely to be exaggerated. Experiment Forcing A1 (atmosphere-only) xed SST according to (1) O1a (ocean-only) O1b ('control` or 'idealized` ocean-only) CO (coupled) A2 (atmosphere-only) O2a (ocean-only) O2b ('additional` or 'adjusted` ocean-only) A3 (atmosphere-only) atmospheric climatology of A1 atmospheric history of A1 fully coupled experiment SST climatology of CO atmospheric climatology of CO atmospheric history of CO climatological SST + leading SST anomaly of CO TABLE 1. Summary of the experiments 8

10 3 Uncoupled results 3.1 Atmospheric climate and variability The summary of the experiments we have done is given in Table 1. We rst specify the SST distribution as T s = 12:4 + 17: sin(2y=a e ) (1) and perform a 75 yr-long atmospheric integration (experiment A1 of Table 1). Eq. (1) ts well the observed annual mean temperature prole (e.g., North et al. 1981). Displayed in Fig. 3 is the time-averaged distribution of the zonally-averaged zonal velocity in each of the atmospheric layers. It shows a well-centered midlatitude westerly atmospheric jet in both layers 25 U upper (solid), U lower (dashed) 2 15 m/s Y () Figure 3: Time-mean zonally-averaged barotropic zonal wind from the atmosphere-only integration (A1 of Table 1). Solid line - upper layer; dashed line - lower layer. y = corresponds to 45 N. 9

11 with a realistic meridional structure. The amplitude of the upper layer jet is slightly weaker than observed and the lower layer winds at the sides of the atmospheric channel are distorted due to deciencies of the quasigeostrophic formulation Time averaged elds Spatial distributions of the time-averaged atmospheric elds are shown in Fig. 4. In panel (a), isotachs of the zonal barotropic component of the wind are plotted along with the turbulent barotropic kinetic energy (shading). Panel (b) shows the distributions of the atmospheric temperature and its variance (shading). There is no stationary wave in the model atmosphere due, most likely, to the absence of mountains in the model. Maximum zonal winds occur over land, unlike reality, where a strong jet extends further into the ocean and the jet break is situated over land. The atmospheric jet break in the model is right above the ocean. The reason for this behavior is clearly evident from the temperature distribution characteristics shown in Fig. 4b. In the oceanic region, the atmospheric temperature is anchored to SST by a strong relaxation law, which models the ocean-atmosphere heat ux. The ocean-atmosphere heat ux directly aects the baroclinic structure of the model atmosphere, so that the sensitivity of the atmospheric circulation to SST is exaggerated. In the land region, where an insulation condition is imposed, the north-to-south temperature contrast is aected directly by the solar forcing and the resulting temperature gradient is steeper. By the thermal wind relation, the wind shear is stronger over land than over the ocean, which explains the longitudinal structure of the atmospheric jet in the model Variance The model produces a clear storm track. The temperature variance (constructed using unltered daily data) has a maximum slightly downstream of the maximum winds location (Fig. 4b) and can be shown to be dominated by the high frequency baroclinic disturbances. The barotropic wind variance (Fig. 4a), which is dominated by the lower frequencies, is maximum even further downstream, closer to the exit of the jet and slightly to the north of the jet axis. 1

12 3 3 3 Barotropic U and TKE (shading) (a) x 1 4 T and its variance (shading) a (b) x Figure 4: Atmospheric climatology of the atmosphere-only integration (A1 of Table 1). (a) Time-mean barotropic zonal velocity (contours, every 3 m s?1 ); total turbulent eddy kinetic energy (shading, every 2 m 2 s?2 ); (b) time-mean atmospheric temperature (contours, every 3 C); atmospheric temperature variance (shading, every 5 K 2 ). Thick line marks oceanic boundaries, small rectangle within the ocean will be referred to in later analyses (see text). Although the position of the mean jet relative to the ocean is not reproduced correctly, the relative locations of the jet break, storm track and maximum low-frequency barotropic activity are realistic. The amplitudes of the variances also agree with observations. The atmospheric temperature variability over the ocean (Fig. 4b) is weak partly because of the direct eect of the damping to SST mentioned above, and partly because the weaker atmospheric jet over the ocean is more baroclinically stable. However, this should not seriously impact the coupled 11

13 behavior because the ocean tends to be insensitive to the high frequency content of the atmospheric variability. In contrast, there is a vigorous barotropic wind variability over the ocean (Fig. 4a). Oceanic variability and ocean-atmosphere coupled behavior are likely to be associated primarily with, and sensitive to, the time-dependent structure of the barotropic wind, since it is here that the atmospheric low frequences almost entirely reside EOFs To analyze the spatial structure of the atmospheric variability further, we perform a standard EOF analyses of the atmospheric elds (unltered daily data). In Fig. 5, we plot the rst EOF of the barotropic streamfunction, accounting for approximately 35% of the total variance. The EOF x 1 4 Figure 5: Leading atmospheric EOF of the barotropic streamfunction for the atmosphere-only run (A1 of Table 1), which accounts for 35% of total variance, contour interval 1 6 m 2 s?1, negative contours dashed, zero contour omitted. zonally-averaged structure of this EOF corresponds to the meridional shifts of the jet and is qualitatively similar to that obtained by Koo et al. (2) in an atmospheric model without asymmetries at the lower boundary. Just as important, however, is the zonal distribution of the EOF. It exhibits a nontrivial zonal modulation over the midlatitude ocean, which is similar to the observed midlatitude structure of the North Atlantic Oscillation (NAO) and to Kushnir's (1994) interdecadal atmospheric pressure anomaly. This anomaly is capable of introducing a 12

14 spatially-coherent forcing on the oceanic circulation through the associated Ean pumping, which has a maximum amplitude in the center of the anomaly. The corresponding PC has a red spectrum without any localized peaks (Fig. 6a). This power spectrum was computed by dividing the timeseries into overlapping 55-d segments and averaging over the 1 periodograms so obtained. In Fig. 6b, we plot in more detail the 1 4 PC 1 spectrum 1 3 PC 1 spectrum 1 2 power power (a) frequency (day 1 ) (b) frequency (year 1 ) Figure 6: Atmospheric power spectrum of the atmosphere-only run (A1 of Table 1), constructed from PC1 of the barotropic streamfunction. (a) Full spectrum; (b) low-frequency portion. Smooth solid line - red noise (AR(1)) t to the spectrum, dashed line - 9% condence level, dotted line - 95% condence level. low-frequency portion of the spectrum. In this case, 2-d means of the PC timeseries were used to construct a multi-taper spectrum with 5 tapers (Dettinger et al. 1995), describing the lowfrequencies in more detail. The spectrum is very weakly red. Note the lack of the power in the ultra-low frequency range due to the nite length of the sample timeseries. Also plotted in Fig. 6b are 9% and 95% condence intervals (Mann and Lees 1996). There is no known physical mechanism able to support ultra low-frequency oscillatory behavior in the atmosphere, so the seemingly signicant peaks seen in the spectrum are most likely due to sampling variations. 13

15 3.2 Oceanic climate and variability Climatology and time-dependent behaviors We next perform two uncoupled 375 yr long oceanic experiments analyze the last 3 yr of these integrations. The rst run (hereafter steadily-forced run, O1a of Table 1) is forced by the climatological values taken from the atmosphere-only integration. The second oceanic integration (stochastically-forced, O1b of Table 1) uses the daily-stored output from the atmospheric run. The atmospheric run is only 75 yr long, so we use the atmospheric data repeatedly 5 times. Steady forcing The oceanic climatology of the steadily-forced experiment (not shown) is very similar to that of the stochastically-forced run (see below). Due to the use of the coastal friction parameterization, which is very similar to the no-slip boundary condition (see appendix), this climatology is characterized by the presence of a double jet near the western oceanic boundary (cf. Haidvogel et al. 1992). The variability in the model has a spectrum dominated by lowfrequency baroclinic motions with most intensity in the region of the western boundary currents separation. These motions have a scale of the oceanic internal Rossby deformation radius and form vortex-like structures similar to those found in many other quasigeostrophic models (e.g., Berlo and McWilliams 1999). An EOF analysis (not shown) indicates that the variabilities of the two jets are independent (or decoupled) of each other. Stochastic forcing The climatology of the stochastically-forced oceanic run is shown in Fig. 7. The barotropic transport is plotted in panel (a), oceanic interface height relative to the boundary in panel (b) and SST distribution in panel (c). The maximum value of the barotropic transport found in the subtropical gyre recirculation region is realistic at about 6 Sv. The structure of the baroclinic circulation shown in panel (b) and of the SST eld (panel (c)) are also reasonable (cf. Cessi 2). Although the climatologies of the two runs are similar, the variability of the stochasticallyforced run is dramatically dierent from that of the steadily-forced run. The EOFs of the 14

16 Transport η SST (a) (b) (c) Figure 7: Ocean climatology of the ocean-only integration (O1b of Table 1) forced with dailysampled atmospheric timeseries from the atmosphere-only integration (A1 of Table 1). Later EOF analyses will be performed in the small rectangle within the ocean; negative contours dashed, zero contours omitted. (a) Barotropic transport, contour interval 1 Sv; (b) interface displacement relative to the boundary, contour interval 4 m; (c) SST, contour interval 3 C oceanic elds for the stochastically forced integration are plotted in Fig. 8. Only the data from a small rectangle in Fig. 7 has been used for the EOF analysis, corresponding to the region of most intense oceanic variability in the model. The upper three panels (a,b, and c) show the rst EOF of barotropic transport, interface displacement and SST respectively, constructed using the unltered oceanic data. In the lower panels (d, e and f), the EOFs of 5 yr low-pass ltered elds are plotted. The lter (Otnes and Enochson 1978) is applied to 2 d means of the data timeseries. In all cases the leading EOF is well separated from the second EOF, and accounts for a signicant portion of the oceanic variability (percentages of variance are given in Fig. 8). The rst EOF of the unltered barotropic transport (Fig. 8a) shows a pattern, similar to that of the rst EOF of the atmospheric barotropic streamfunction (Fig. 5). It is clearly directly forced by the atmospheric wind, and we verify this below. An interesting feature of the oceanic baroclinic pressure variability (Fig. 8b) is a synchronous and large scale (larger than the oceanic 15

17 Transport EOF 1 η EOF 1 SST EOF (a) (b) (c) Transport LP filtered EOF 1 η LP filtered EOF 1 SST LP filtered EOF (d) (e) (f) Figure 8: Leading oceanic EOFs of the ocean-only stochastically-forced integration (O1b of Table 1), constructed using the data within the small rectangle of Fig. 7. Upper panels use raw data in the EOF analysis, 5 yr low-pass ltered data used in the lower panels. (a, d) Barotropic transport (35% and 5% of total variance), contour interval 5 Sv; (b, e) internal interface displacement (28% and 63% of total variance), contour interval 1 m; (c, f) SST (27% and 44% of total variance), contour interval :2 C. Negative contours dashed, zero contours omitted. 16

18 internal Rossby radius) variability in the double jet region. Undoubtedly, this synchronization is realized through atmospheric connections, because it is absent in the steadily-forced run. The spatial regularities of the baroclinic and barotropic modes time-dependencies sum to produce a large amplitude ( 1:5 C) large scale ( 1 ) meridionally aligned SST dipole (Fig. 8c, cf. Deser and Blacon 1993), potentially capable of aecting the atmospheric circulation. However, we show below that this does not happen and the eect of this SST mode on the atmospheric variability in the coupled integration is negligible. 4 η PC 1 (t 2.75) (dashed), P a PC 1 (solid), corr(η(t 2.75),P a )= time(years) Figure 9: Time evolution of the stochastically forced ocean run (O1b of Table 1). Solid line: 5 yr low-pass ltered timeseries of the atmospheric PC 1 (corresponding to the EOF in Fig. 5), dashed line: 5 yr low-pass ltered P C 1 timeseries of the oceanic interface displacement (corresponding to the EOF in Fig. 8b,e), lagged by 2:75 yr. The lower panels of Fig. 8 show that on interannual-to-interdecadal timescales, the oceanic 17

19 regional variability is dominated by the baroclinic component of the oceanic circulation. The similarity between Fig. 8 (b) and (e) conrms that the baroclinic response of the ocean is dominated by the low frequencies. The baroclinic motions inuence the barotropic eld through nonlinear interaction (cf. Fig. 8 (d) and (e)) and advect SST (Fig. 8f). The low-frequency component of the low-pass ltered SST EOF still retains a large-scale dipolar component evident in Fig. 8c, albeit with a smaller amplitude and smaller scale spatial modulation. It may still be potentially important in inducing an atmospheric response on very long timescales Connection with the atmospheric variability We now show that the oceanic low-frequency variability in the stochastically-forced run involves no dynamically-active internal oceanic mode excited by the atmospheric noise. The ocean simply acts as a low-pass lter on this noise, not feeling the high frequency atmospheric variations and directly following the low-frequency atmospheric history. In Fig. 9, the 5 yr low-pass ltered PC 1 of the oceanic interface displacement (corresponding to the EOF in Fig. 8e and normalized by the standard deviation of the unltered data), lagged by 2:75 yr, is plotted along with the normalized PC 1 of the atmospheric barotropic wind (corresponding to the EOF in Fig. 5). This lag produces a maximum correlation of :7 between the two timeseries, thus illustrating the important point above. The time lag required for maximum correlation can be understood by computing the time, necessary for the oceanic long baroclinic waves to travel across the scale of the atmospheric forcing (L 2 ) to the western boundary of the ocean, where most of the variability occurs. This calculation gives L?1 R?2 d 2:23 yr; which is close to the time lag value above Basin scale oceanic variability The oceanic behavior observed in simple models reviewed in the introduction has a basin scale (e.g., Jin 1997, Cessi 2). We thus construct the EOFs of the oceanic elds by using the 18

20 data from the whole oceanic basin, recorded on a coarser grid The rst EOFs of the barotropic transport, interface displacement and SST are plotted in Fig. 1 (a, b, c) respectively. Comparison with Fig. 8 shows that the structure of the regional portions of the basin scale EOFs is captured by the regional EOF analysis. Examination of the corresponding spectra (not shown) does not show any signicant spectral peaks in any of the elds. As in the regional case, the oceanic variability seen on the basin scale seems to be directly forced by the spatially and temporally structured atmospheric noise. We will return to discussing this very important point in the subsequent analyses of the coupled system behavior. In summary, the low-frequency variability in the stochastically-forced run is a directly-forced oceanic lagged response to the low frequency evolution of a noisy spatially-coherent atmospheric pattern, conducted to the regions of strong currents by the large scale baroclinic Rossby waves. Transport EOF 1 η EOF 1 SST EOF y y y (a) x (b) x (c) x Figure 1: Leading basin-scale EOFs for the stochastically-forced ocean-only run (O1b of Table 1). (a) Barotropic transport (25% of total variance), contour interval 5 Sv; (b) interface displacement (34% of total variance), contour interval 5 m; (c) SST (23% of total variance), contour interval :1 C; Negative contours dashed, zero contours omitted. 19

21 4 Coupled results 4.1 Atmospheric climate and variability We now couple the oceanic and atmospheric models and perform a 5 yr long integration of the full model, analyzing the last 35 yr of this integration (experiment CO of Table 1). The component models were spun up using the uncoupled runs. The coupled model is in statistical equilibrium, i.e., there is no long-term drift of the model variables during the last 35 yr of the integration. The climatological structure of the atmosphere arising in the coupled integration is shown in Fig. 11, which should be compared to that from the uncoupled integration in Fig. 4. The jet in 3 Barotropic U and TKE (shading) (a) x 1 4 T and its variance (shading) a (b) x Figure 11: Atmospheric climatology of the coupled run (CO of Table 1). Details as in Fig. 4. 2

22 the coupled run is slightly weaker and displaced a little bit equatorward (panel (a)), consistent with angular momentum conservation. An increase in temperature variance is clearly seen from comparison of Figs. 11b and 4b. The total barotropic turbulent kinetic energy in the coupled run is also increased (cf. Figs. 4a and 11a). Despite these quantitative changes, the spatial structure of the atmospheric mean values and variances remains similar. The changes in the strength of the atmospheric variability between the coupled and uncoupled runs can be explained as the result of dierences in the climatological SST eld and corresponding adjustments in the strength of the atmospheric ow. To conrm this, we have performed an additional 75 yr long atmosphere-only integration forced by the SST climatology from the coupled run (experiment A2 of Table 1). The spatial pattern and strength of the climatological and time-dependent atmospheric circulation in this run are virtually indistinguishable from that in the coupled run (but see below). The rst EOF of the barotropic streamfunction (Fig. 12) is similar in structure to that in the uncoupled case. An examination of the atmospheric spectra corresponding to the leading EOF x 1 4 Figure 12: Leading atmospheric EOF of the coupled run (CO of Table 1). Details as in Fig. 5; the EOF explains 41% of total variance. EOF of the barotropic wind (Fig. 13) shows that there is no additional regularity introduced to the atmospheric behavior through coupling on the interdecadal timescales. The spectra in Fig. 13 were constructed analogously to those in Fig. 6 (but with lower resolution due to a longer 21

23 timeseries and using 7 tapers instead of 5) and are very similar to those of the uncoupled run. Not more than 5% of frequencies pass the 95% condence level in Fig. 13b, indicating that the spectral peaks seen there are due to sampling variations. Interestingly, the relative power contained in the high and low frequency portions of both coupled (Fig. 13) and uncoupled (Fig. 6) spectra is roughly the same. This also argues that SST variability does not participate in determining the atmospheric circulation. Therefore, the dominance of the low frequencies in the model atmosphere is due to intrinsic atmospheric nonlinearities (cf. James and James 1989). A more careful analyses can be performed by comparing the coupled spectrum with the spectrum (not shown) of the corresponding PC for the atmosphere-only run forced by the climatological SST from the coupled run (A2 of Table 1, see above). In the former, it is possible to identify a very weak, but distinguishable increase in the power contained in the low-frequency portion of the spectrum. This increase is attributable to the decreased thermal damping of the atmosphere in the coupled run due to an ability of SST anomalies to adjust to atmospheric temperature variations, versus that in the uncoupled run, where the oceanic 1 4 PC 1 spectrum 1 3 PC 1 spectrum 1 2 power 1 power (a) frequency (day 1 ) (b) frequency (year 1 ) Figure 13: Atmospheric power spectrum of the coupled run (CO of Table 1). Details as in Fig

24 temperatures are xed (Barsugli and Battisti 1998). In summary, no pronounced coupled mode of the ocean-atmosphere interaction is evident from the analyses of the atmospheric response in our coupled model. 4.2 Oceanic climate and variability Climatology and time-dependent behaviors Changes in climatology The oceanic climatology resulting from the coupled integration is displayed in Fig. 14, which should be compared with analogous uncoupled results in Fig. 7. The qualitative nature of the circulation and SST pattern are similar in the two runs. However, Transport η SST (a) (b) (c) Figure 14: Oceanic climatology of the coupled run (CO of Table 1). Details as in Fig.7. there is a southward displacement of the gyres in the coupled relative to uncoupled case. In addition, the size of the recirculation zone (panel (a)) is dramatically increased in the coupled run, especially in the subtropical gyre region. There is an additional tropical gyre (Fig. 14 a, b) and the mean north-south SST gradient is increased in accordance with a similar increase in the atmospheric temperature gradient (cf. Figs. 4b and 11b). An additional uncoupled oceanic integration forced by the atmospheric history from the coupled run (O2b of Table 1) reproduces all these changes, showing that they are entirely due to an adjustment of the oceanic 23

25 and atmospheric circulations that arise during the rst decade after coupling and, therefore, do not represent a true coupled eect. Regional response We perform a regional EOF analysis of the oceanic elds in the small rectangle in Fig. 14 and compare it with an analogous analysis of the uncoupled elds (Figs. 8 and 9). We nd that in this regional sense, the coupled system behaves exactly as the uncoupled one, i.e., the low frequency response in the region of the boundary currents conuence zone and inertial recirculations is predominantly baroclinic and represents a passive synchronous adjustment of the two jets to the atmospheric anomalies, generated to the east of the western oceanic boundary and carried to this boundary by the large-scale baroclinic Rossby waves. Since the location of the atmospheric anomaly is the same in the coupled and uncoupled runs, the time lag of the oceanic response should be the same as well. Indeed, we nd that this is the case. The lag is again 2:75 yr. An oceanic eigenmode Interesting dierences arise in the analysis of the basin-scale oceanic EOFs. The rst EOF of the interface displacement (Fig. 15a, cf. Fig. 1b) possesses a broad spectral peak around 5:5 yr (Fig. 15b). It has no counterpart in the uncoupled integrations discussed in Section 3. However, this mode is reproduced in an additional ocean-only integration using the atmospheric history from the coupled run as a forcing (O2b of Table 1) and is absent from the ocean-only integration forced by the atmospheric climatology from the coupled run (O2a of Table 1). It thus appears to be an eigenmode of the oceanic circulation that is excited by the atmospheric stochastic forcing. Note that the period of the oscillation is twice the time lag, mentioned in previous paragraph. The ability of the atmospheric noise to excite this mode appears to depend on the relative locations of the oceanic time-mean circulation and atmospheric stochastic forcing, since this is a major change between the control (forced by the atmospheric history from the idealized atmosphere-only integration, O1b of Table 1) and the additional (forced by the atmospheric history from the coupled run, O2b of Table 1) ocean-only integrations. The meridional displacement of the jets does not aect the eigenmodes due to -plane QG approximation, where 24

26 all latitudes away from the boundaries are dynamically equivalent. The leading atmospheric variability pattern in the coupled run is 'more realistic`, since the atmospheric and oceanic circulations here are dynamically consistent. There is no apparent signature of this mode in the barotropic transport and SST elds. Thus, the heat ux due to advection of the mean SST by a baroclinic eld anomaly is weak compared to other components of the total heat ux. This is due to the spatial structure of the η EOF y (a) x η PC spectrum power (b) frequency (year 1 ) Figure 15: (a) Leading EOF of the ocean interface displacement for the coupled run (CO of Table 1), (34% of total variance), contour interval is 5 m. Negative contours dashed, zero contour omitted; (b) power spectrum of the PC timeseries corresponding to the EOF in panel (a). 25

27 mode whose current vectors lie almost perpendicular to SST gradients at least in the locations where the latter are strong. Since the only way for the ocean to aect the atmosphere is through SST, the internal oceanic mode cannot inuence the atmosphere, which is consistent with the red noise structure of the atmospheric variability. Basin scale response of SST to atmospheric forcing Other oceanic basin-scale EOFs do not exhibit any signicant peaks in the spectra of the corresponding PCs. In Fig. 16, we plot the rst EOF of the barotropic transport in (a), the second EOF of the interface displacement in (b) and the rst EOF of SST in (c). These EOFs are constructed using 2 d means of the oceanic elds. In panels (d), (e) and (f), the rst EOFs of the three elds constructed using 5 yr low-pass ltered data are plotted. The rst EOF of SST (Fig. 16c) has a structure that is similar to that observed by Kushnir (1994; our Fig. 1). Positive temperature anomalies with realistic amplitude are seen in the most of the northern model ocean, with the two centers of action situated near the western boundary. They are separated by a negative anomaly, whose boundary coincides with the location of the two climatological jets, which are considered to be model 'Gulf Stream` and 'Labrador` currents. Two other centers are located toward the eastern boundary, where a positive anomaly is seen in the north and a negative anomaly in the south. However, the amplitude of the negative anomaly is much larger than that of the weak observed anomaly in the tropics, due probably to the oversimplied mixed layer model. Just as in observations (Kushnir 1994), the SST pattern in Fig. 16c is concurrent with a negative atmospheric pressure anomaly over the ocean (Fig. 12). The timeseries of the leading PCs of the atmospheric streamfunction and SST are highly correlated (correlation of.7) at zero lag (recall that the sampling interval we use is 2 d). Correlating the PCs of the other oceanic elds and atmospheric pressure anomalies shows that the patterns plotted in Fig 16a, b, c occur approximately simultaneously (correlation of.5). The same behavior is obtained in the ocean-only integration using the atmospheric history from the coupled run as a forcing (O2b of Table 1). All of this argues that the spatial structures obtained represent a passive response of the ocean to the low frequency evolution of the atmospheric ow. A negative atmospheric pressure anomaly accompanies a warm basin scale SST pattern (Fig. 16c), intensied model 26

28 'Gulf Stream` and reduced amplitude of the model 'Labrador current` (Fig. 16a, b). These features have also been alluded to in observations of interdecadal variability in the North Atlantic (Levitus 1989a, b, Greatbatch et al. 1991). Transport EOF 1 η EOF 2 SST EOF y y y (a) x Transport EOF, 5 yr LP data (b) x η EOF, 5 yr LP data (c) x SST EOF, 5 yr LP data y y y (d) x (e) x (f) x Figure 16: Leading oceanic EOFs of the coupled run (CO of Table 1), using 2 d-binned data (upper panels) and 5 yr low-pass ltered data (lower panels). (a, c) EOF 1 of the barotropic transport (26% and 58% of total variance), contour interval 2 Sv; (b) EOF 2 of the interface displacement (26% of total variance), (e) EOF 1 of the interface displacement (42% of total variance), contour interval 5 m; (c, f) EOF 1 of SST (24% and 35% of total variance), contour interval :1 C. Negative contours dashed, zero contour omitted. 27

29 The temporal correlations between the timeseries of the oceanic and atmospheric elds are even higher (correlation of.7) if we use the 5 yr low-pass ltered data (Fig. 16d, e, f). The internal oceanic mode discussed in the previous paragraph gets ltered out and the second EOF of the unltered interface dispacement becomes the rst EOF for the ltered signal. As can be seen from comparison of the upper and lower panels of Fig. 16, all the basic features of the oceanic elds survive upon ltering Mixed layer dynamics We now investigate the dynamics behind the SST pattern in Figs. 16c,f. The analysis below shows that the dynamics are dierent in dierent parts of the basin. To demonstrate this, we compute the SST (T ) anomaly evolution associated with the atmospheric and oceanic circulation EOFs in Figs. 12 and 16d,e together with their corresponding PC time dependences. The mixed layer equation (A15) in this experiment is nite dierenced on a coarse grid. Dynamically important terms in this equation are shown to be @x (u g + u e (v g + v e ) T + o c P o h mix T a + E + ::: ; (2) where an overbar denotes a time mean eld, u g ; v g are the geostrophic velocity anomalies in the upper oceanic layer, u e ; v e are the Ean velocity anomalies, T a is the atmospheric temperature anomaly associated with the circulation pattern in Fig. 12 and E is an anomalous entrainment heat ux at the base of the mixed layer. Note that there is no dependence of the surface heat ux on wind speed in the coupled model. In the geostrophic eld, we will also distinguish between barotropic and baroclinic components of the ow. The entrainment heat ux parameterization in our mixed layer model is highly nonlinear (see (A15)). To determine E, we take the timeseries of the atmospheric wind anomaly (Fig. 12), the timeseries of the modeled SST anomaly (Fig. 16f), mean atmospheric wind and mean SST, and compute the time mean entrainment heat ux as in (A15). In the integration of (2), we rst compute an entrainment heat ux using the same data with an exception of SST, which is now computed (T ). E is then computed as a dierence between this instantaneous value and previously determined time mean. The results from this integration are summarized in Fig. 17. In panel (a), we plot the rst 28

30 SST EOF 1 ; full ML model SST EOF 1 ; no T a y y (a) x SST EOF ; baroclinic adv (b) x SST EOF ; barotropic adv y y (c) x (d) x Figure 17: Leading EOF of SST obtained in the dierent versions of the mixed layer integration (see text). Contour interval :3 C. (a) Full mixed layer model; (b) no forcing by the anomalous atmospheric temperature; (c) only the advection of the mean SST by the anomalous baroclinic current is included; (d) only the advection of the mean SST by the anomalous barotropic current is included. 29

31 EOF of the SST anomalies, resulting from the mixed layer run with all the terms included. The pattern obtained is reasonably close to that in Fig. 16c away from the zonal boundaries, given that the time-dependent elds used to force the mixed layer model are not perfectly correlated. The amplitude of the anomaly is slightly weaker than that from the coupled model integration (note dierent contour interval), which can be due to coarse spatial and temporal resolution used in the mixed layer model. Our mixed layer model is potentially more justiable in the midlatitude region, than in the tropical or polar regions, where signicant changes in the mixed layer depth and convective activity occur. The quantitative dierences with the observed interdecadal temperature signal in the very north and in the tropics (Fig. 1) may be due to deciencies of our mixed layer formulation. Panel (b) shows the results from the integration with the T a anomaly neglected. There are some quantitative dierences throughout the basin, but the general structure survives. It is interesting that the heat ux associated with the atmospheric temperature anomaly generally tends to damp the SST anomaly, rather than to reinforce it (cf. Robertson 1996). It shows that the anomalous atmospheric surface heat ux does not force the SST mode in our model. Essential for the SST pattern to exist is the atmospheric equivalent barotropic anomalous circulation. Dramatic changes take place when we remove the eects of the anomalous Ean and entrainment heat uxes. In Fig. 17c, the only term retained in (2) is the advection of the mean temperature by the anomalous baroclinic current. Comparing panels (c) and (a) shows that near the western boundary, the anomalous SST structure is primarily determined by that heat transport. The barotropic contribution (panel (d)) has a similar structure, but a somewhat smaller amplitude. In the rest of the basin, the SST anomaly is predominantly caused by the anomalous Ean and entrainment transports, conditioned by the uxes associated with the atmospheric temperature anomaly. In summary, the leading low frequency SST behavior in our model is directly forced by spatially coherent atmospheric noise. The structure of this mode has similarities with that observed (Kushnir 1994; our Fig. 1). In the western part of the basin, the SST response is caused largely by anomalous baroclinic advection of the mean SST. These changes in oceanic 3

32 circulation passively follow the low frequency atmospheric wind anomaly. In the rest of the basin, the SST response is almost entirely due to anomalous Ean and entrainment heat uxes in the mixed layer, and thus is again directly forced by the atmosphere. This qualitative picture is consistent with the GCM results of Seager et al. (2) and Reason (2) Comparison of the two ocean-only integrations In this section, we discuss in more detail the dierences between the two ocean-only integrations. The run forced by the atmospheric history resulting from the idealized steady SST forcing atmosphere-only experiment was discussed in detail in Section 3. We will refer to it henceforth as the idealized run (experiment O1b of Table 1), since the atmospheric forcing used had no information about the oceanic behavior. The second run is analogous to the rst one, but uses the atmospheric history from the coupled model integration. We will thus call it the adjusted run (experiment O2b of Table 1). As discussed above, important aspects of the coupled integration are reproduced in the adjusted run, which allowed us to deduce that we are dealing with the eects caused by the spatial and temporal structure of the atmospheric noise and not with any intrinsic oceanic or truly coupled eects. The principal dierences between the two runs are: 1) The gyres are located 5 farther to the north in the idealized ocean-only run, consistent with the distribution of the climatological Ean pumping (not shown), while the meridional shift of the atmospheric variability center is negligible (cf. Figs. 5 and 12). 2) The recirculation zone is much larger in the adjusted run than that in the idealized run. 3) An oceanic eigenmode with a 5:5-yr period is present in the adjusted run, but absent from the idealized run. 4) The basin scale EOF of SST in the idealized run (Fig. 1c) does not have a pronounced contribution from the anomalous baroclinic advection of mean temperature (cf. Fig. 16c). The relative meridional location of the climatological oceanic circulation and atmospheric wind anomalies appears to be responsible in each case. In the idealized run, the anomalous currents and mean SST are not spatially compatible, because the latter does inuence the 31