Effect of Atlantic Meridional Overturning Circulation Changes on

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Effect of Atlantic Meridional Overturning Circulation Changes on Tropical Atlantic Sea Surface Temperature Variability: A 2½-Layer Reduced-Gravity Ocean Model Study CAIHONG WEN* AND PING CHANG Department of Oceanography, Texas A&M University, College Station, Texas

RAMALINGAM SARAVANAN Department of Atmospheric Sciences, Texas A&M University, College Station, Texas (Manuscript received 20 January 2009, in final form 1 July 2009) ABSTRACT Previous coupled climate model simulations reveal that a dipole-like SST pattern with cooler (warmer) temperature over the north (south) tropical Atlantic emerges in response to a slowdown of the Atlantic meridional overturning circulation (AMOC). Using a 2½-layer reduced-gravity ocean model, a systematic investigation into oceanic processes controlling the tropical Atlantic sea surface temperature (SST) response to AMOC changes by varying the strength of northward mass transport at the open boundaries was conducted. It is found that the North Brazil Current (NBC) reverses its direction in response to a shutdown of the AMOC. Such a circulation change causes a decrease in upper equatorial ocean stratification and warming in the Gulf of Guinea and off the coast of Africa. These findings point to the importance of oceanic dynamics in the equatorial SST response to AMOC changes. Sensitivity experiments further show that the SST response relates nonlinearly to AMOC changes. The strength of the SST response increases dramatically when the AMOC strength falls below a threshold value. This nonlinear threshold behavior depends on the position of a subsurface temperature gradient forming along the boundary between the northern subtropical gyre and the tropical gyre that interacts with the western boundary current. The analysis suggests that, in order for the oceanic dynamics to have a dominant influence on tropical Atlantic SST in response to AMOC changes, two conditions must be satisfied: 1) the AMOC must weaken substantially so that the NBC flows equatorward, permitting water mass exchange between the northern subtropical and tropical gyres, and 2) the subsurface temperature front must be located in an optimal location where subsurface temperature anomalies induced by AMOC change are able to enter the equatorial zone.

1. Introduction Paleoproxy records show evidence that a substantially weakened Atlantic meridional overturning circulation (AMOC) is concurrent with global-scale abrupt climate changes on centennial-to-millennial time scales during glacial and interglacial periods (e.g., Broecker et al. 1985; Haug et al. 2001). A popular hypothesis explaining

* Current affiliation: NOAA/Climate Prediction Center, Camp Springs, Maryland.

Corresponding author address: Caihong Wen, Room 605-A, WWB, 5200 Auth Rd., NOAA/NWS/NCEP/Climate Prediction Center, Camp Springs, MD 20747. E-mail: [email protected] DOI: 10.1175/2009JCLI3042.1 Ó 2010 American Meteorological Society

this connection is that rapid freshening of the North Atlantic due to the melting of continental ice sheets during deglaciation leads to a significant reduction of strength or even collapse of the AMOC, which in turn causes the abrupt climate change documented in the paleoproxy records (Broecker et al. 1985). Inspired by this hypothesis, a number of ‘‘water hosing’’ experiments have been extensively conducted with coupled ocean–atmosphere general circulation models (GCMs) to investigate the impact of the AMOC on climate. In these experiments, a freshwater source is artificially added to the high-latitude North Atlantic of the climate models to mimic meltwater input. The modeling studies reveal a robust climate response in the tropical Atlantic accompanied by a weakened AMOC that includes a dipolelike SST pattern with cooler (warmer) temperature

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over the north (south) tropical Atlantic and a southward shift in the intertropical convergence zone (e.g., Zhang and Delworth 2005; Stouffer et al. 2006). A question that begs an answer is why is there such a strong linkage between the tropical Atlantic and AMOC changes? Attention has been drawn to oceanic pathways in search of teleconnection mechanisms, because the upper tropical Atlantic Ocean is located right above the return flow of the AMOC. Many studies focus on the idea of how the AMOC modulates oceanic meridional heat transport. For example, Yang (1999) proposed that a change of AMOC can affect the interhemispheric SST gradient by modulating cross-equatorial heat transport through planetary wave adjustment (Kawase 1987). Following Yang’s reasoning, Johnson and Marshall (2002) suggested an equatorial buffer mechanism where the Southern Hemispheric response to a sudden change in deep-water formation at the northern high latitude lags the Northern Hemispheric response and the asynchronous response between the two hemispheres results in convergence or divergence of heat transport, producing a SST change in the equatorial region. Recently, Chang et al. (2008) proposed an alternative oceanic teleconnection mechanism. They showed that a substantially weakened AMOC could induce a tropical SST response by altering the pathway of the subtropical cells (STCs). In a coupled GCM water-hosing experiment, they observed that the warming in the south equatorial Atlantic develops in two stages—a weak warming within the first two decades followed by a more dramatic warming. The initial warming is caused by planetary wave adjustment, while the second warming has a different dynamic origin. It occurs when the AMOC is weakened below a threshold, causing the North Brazil Current (NBC) to reverse direction and carry warm northern subtropical gyre water to the south equatorial region. The NBC region has been previously shown to be a region where interactions between the return branch of the AMOC and wind-driven STCs are particularly strong (Fratantoni et al. 2000; Jochum and Malanotte-Rizzoli 2001). Chang et al. (2008) hypothesize that these interactions play an important role in equatorial Atlantic SST response to AMOC changes. In contrast with the aforementioned studies, other investigations focus on the importance of atmospheric teleconnection mechanisms. Chiang and Bitz (2005) showed that cooling in high latitudes can be readily transmitted to the tropics through intensifying northeasterly trade winds and its thermodynamic interactions with the oceanic mixed layer. The latter is often referred to as the wind– evaporation–SST (WES) feedback (Chang et al. 1997; Xie 1999). In a follow-up study, Chiang et al. (2008) suggested that atmospheric processes are the primary cause for

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cooling in the high-latitude North Atlantic, induced by a weakened AMOC spread into the tropics. The relative importance of oceanic versus atmospheric processes in transmitting changes in the high-latitude North Atlantic to the tropics deserves further study, as the issue has a potential bearing on abrupt climate change prediction. In particular, it is important to understand whether the ocean plays an active or passive role in the tropical SST response to high-latitude oceanic changes. Assuming that the role of the ocean is active, it is then important to know how oceanic dynamics control SST responses in the tropical Atlantic and where the oceanic control is most prominent. Although Chang et al. articulated an oceanic teleconnection mechanism, it was not clear how the mechanism could operate under different strengths of the AMOC. Moreover, their analysis was based on a fully coupled GCM simulation in which both atmospheric and oceanic processes were at work. Thus, it was difficult to isolate the oceanic influence from air–sea interaction processes and identify areas that are most critical to oceanic processes. The primary objective of this study is to further elucidate oceanic processes in linking tropical SST response to AMOC changes with a particular emphasis on examining the mechanism proposed by Chang et al. (2008). This mechanism builds on the finding of earlier modeling studies that the pathway of the northern STC to the equatorial zone is blocked by the AMOC return flow along the western boundary under the present climate condition (Fratantoni et al. 2000; Jochum and Malanotte-Rizzoli 2001; Zhang et al. 2003). Chang et al. (2008) hypothesized that, if during a major climatic event, such as the Younger Dryas, the AMOC strength would decrease beyond a critical value, the pathway could then open, leading to warming in the equatorial Atlantic. In this study, we shall take a systematic look at the dependency of the pathway on AMOC strength and its effect on SST response. We shall examine whether there is a threshold behavior of the tropical SST response to AMOC changes, as proposed by Chang et al. We shall also explore the sensitivity of the mechanism on oceanic parameters that affect the water mass exchange between the subtropical gyre and tropical gyre. We shall conduct our investigation within a framework of a 2½-layer reduced-gravity ocean (RGO) model. Such a model is perhaps the simplest and yet most effective dynamic ocean model that is capable of resolving interactions between the return flow of the AMOC and the wind-driven circulation. The simplicity of the model and its computational efficiency allow us to carry out a large suite of numerical experiments to obtain a clear mechanistic understanding of the oceanic processes. A similar

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model has been successfully used by Fratantoni et al. (2000) to study the dynamic aspects of the interaction between the AMOC and the wind-driven circulation. In this study, we shall extend their work to include thermodynamic effects and focus our investigation on the role of AMOC and STC interactions in tropical Atlantic SST variability. As in Fratantoni et al., our model does not directly simulate AMOC. We simply prescribe mass transport at the northern and southern boundaries of the model domain to mimic the return flow of AMOC. This modeling approach provides a simple control of the strength of the AMOC return flow in the model. We believe that this is a viable approach to gain mechanistic understanding of the role of the AMOC in Atlantic climate variability. We also discuss the potential drawbacks of the approach. The remainder of this paper is organized as follows: section 2 gives a brief description of the model and an overview of the model performance. In section 3, we examine the sensitivity of SST response to changes in the AMOC and explore oceanic processes contributing to the SST response. In section 4, the dependence of SST response on subsurface thermal conditions will be discussed. Our major results will be summarized and discussed in section 5.

2. Model description and simulations for the control run a. Model description The 2½-layer RGO model used in this study consists of two active layers that represent the surface mixed layer and the seasonal thermocline layer. The abyssal ocean below the thermocline layer is assumed to be motionless, resulting in a reduced-gravity ocean. The dynamic and thermodynamic equations for the model closely follow McCreary and Yu (1992), except for the vertical mixing scheme and open boundary treatment. Both entrainment and detrainment processes are included in this model. The former is estimated using a modified version of the KT model (Krauss and Turner (1967), which is based on the turbulent kinetic energy budget. The latter is parameterized following McCreary et al. (1993), which takes large-scale conditions into consideration. Open boundary conditions (OBCs) developed by Marchesiello et al. (2001) are adopted in our RGO model at the northern and southern boundaries. This OBC not only allows perturbations generated by the model to propagate out of the domain, but also is capable of incorporating external forcing (i.e., AMOC) into the model by fixing the volume transport at the open boundaries. Horizontal mixing processes are expressed as a Laplacian diffusion with a spatially varying

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diffusivity formulated according to Smagorinsky (1963, 1993). A detailed description of the model is provided in the appendix. The model covers the tropical Atlantic basin from 308S to 308N, 1008W to 208E with realistic coastal lines. The northern and southern boundaries are open. Noflux conditions are applied for temperature and layer thicknesses at all boundaries. For flow velocities, no-slip boundary conditions are employed only at wall boundaries. SST at the open boundaries is relaxed to a climatological annual cycle within a sponge layer with a damping time scale of 5 days. The numerical equations were discretized using a second-order enstrophy-conserving finite difference scheme on an Arakawa C grid in space and a leapfrog scheme in time. The dynamic core of the model is based on the numerical code developed by Lee and Csanady (1999). The model resolution is 0.258 in both longitude and latitude. To remove the computational mode produced by the leapfrog scheme, an averaging scheme proposed by Shuman (1957) is applied twice consecutively every 48 time step. The model is driven by the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA40) monthly mean wind stress climatology (Uppala et al. 2005). The surface heat flux forcing consists of shortwave radiation, longwave radiation, latent heat flux, and sensible heat flux. Shortwave and longwave radiation are specified and are taken from the Southampton Oceanographic Centre (SOC) dataset (Josey et al. 1998, 1999). Latent heat flux and sensible heat flux are computed from air temperature and wind speed based on the standard bulk formulas described by Lee and Csanady (1999). The air temperature is derived from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis product (Kalnay et al. 1996) and the wind speed is derived from the ERA-40 product. One special treatment of our model is the temperature in the thermocline layer, as the mechanism proposed by Chang et al. (2008) is sensitive to the subsurface temperature distribution. In the observation, there is a salient front forming along the boundary of the north Atlantic subtropical gyre and tropical gyre in the subsurface, separating the saltier and warmer subtropical gyre water from the fresher and colder tropical-gyre water. As can be seen from Fig. 1a, the temperature along the 1026.45 kg m23 density surface increases from 148C south of 68N to 178C north of 108N across the front. The formation of the front is likely attributed to the subduction process that injects saltier and warmer surface water in the northeastern subtropical Atlantic into the ocean interior along isopycnal surfaces. The subducted water flows

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FIG. 1. (a) Temperature (grayscale) and salinity (contour) changes on the 1026.45 kg m23 density surface derived from the Levitus dataset. (b) Idealized temperature front used in the thermocline of the model with temperature variation from 148C in the southern edge to 218C in the northern edge of the front. The location of front in expts L15NG7C (dash), L10NG7C (solid), L7NG7C (dot–dash), and L3NG7C (dotted) are shown. The solid line also presents the front position of the CTRL run.

southwestward to the western boundary where it bifurcates into a westward branch and an equatorward branch (return branch of the northern STC). The latter is counteracted by the northward-flowing NBC as a part of the AMOC return flow. Since the NBC is stronger than the STC return flow under the current climate condition, the equatorward pathway is blocked (Fratantoni et al. 2000; Zhang et al. 2003), keeping the warmer and saltier water to the north of the front. This is a key aspect of the mechanism proposed by Chang et al. (2008) and must be

treated carefully in the model in order to test this mechanism. Given that the model used in this study has only two active layers and salinity changes in each layer are not explicitly computed, subduction processes cannot be fully accounted for by the simplified physics. We, therefore, adopt a simple approach to maintain an idealized temperature front around 108N in the thermocline layer of the model. Across the idealized temperature front, the temperature increases from 148C near the equator to 218C north of 158N. The temperature front is maintained

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FIG. 2. Monthly averaged SST (contours, 8C) and entrainment rate (grayscale, 1026 m s21) in February, June, and October from the CTRL run.

by adding a specified heat source term in the thermocline layer temperature equation; that is, Q2 5 Qh1 1 Qcre , where Q2h1 is the downward flux at the mixed layer base and Qcre is the source term, which is determined by first restoring the model thermocline temperature to the temperature front during a spinup run and then taking an average over the last 10 years of the spinup. This correction term is computed prior to the start of the model experiments described below and does not depend on the model solutions once determined. This approach is essentially similar to the anomaly flux cor-

rection method widely used in climate modeling studies (e.g., Seager et al. 2001).

b. Control simulation In the control run (CTRL), a 14 Sv (Sv [ 106 m3 s21) mass transport is specified at the northern and southern boundaries to mimic the return flow of AMOC. The model is integrated for 20 years and approaches a steady solution after an 8-yr simulation. The model climatology is computed from the last 10 years of the simulation. The simulated entrainment and SST are shown in Fig. 2. Entrainment starts to increase after February in the eastern tropical Atlantic. Then, within a couple of months, it extends to the center of the basin and strengthens rapidly.

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FIG. 3. Monthly averaged currents (m s21) in the (left) mixed layer and (right) thermocline layer in January and September from the CTRL run.

After reaching its peak in June, the entrainment begins to decrease and its center retreats back to the eastern basin. Following the entrainment, a cold water tongue is quickly developed in June and reaches its maximum in August. Development of the pronounced annual cycle of SST in the eastern equator agrees well with the observations (e.g., Philander 1990). The model reproduces a quite realistic seasonal circulation pattern in the upper tropical Atlantic, as shown in

Fig. 3. The North Brazil Undercurrent (NBUC) overshoots into the Northern Hemisphere along the western boundary and then retroflects at about 58N, turning southeastward to feed the Equatorial Undercurrent (EUC). The simulated retroflection latitude varies seasonally from 48N in March to 98N in September, which is consistent with observations (Molinari and Johns 1994). The EUC water is entrained into the mixed layer and then flows westward as part of the South Equatorial Current (SEC).

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TABLE 1. List of sensitivity experiments. Integration name CTRL L10NG7C_0Sv L10NG7C L15NG7C L7NG7C L3NG7C L10NG4C L10NG2C

Experimental design Thermal front located around 108N, cross-front temperature difference 78C, northward mass transport set to 14 Sv at the northern and southern boundaries Thermal front located around 108N, cross-front temperature difference 78C, northward mass transport set to zero at the northern and southern boundaries Thermal front located near 108N off the coast of South America, cross-front temperature difference 78C, northward mass transport at the open boundaries decreased systematically from 14 Sv to 0 Sv Thermal front located around 158N off the coast of South America, other settings as for L10NG7C Thermal front located around 78N, other settings as for L10NG7C Thermal front located around 38N near the equator, other settings as for L10NG7C Cross-front temperature difference 48C, other settings as for L10NG7C Cross-front temperature difference 28C, other settings as for L10NG7C

A majority of the SEC water mass merges with the NBC at the western boundary and flows northward. The NBC continues to 58–98N where it retroflects seasonally into the North Equatorial Countercurrent (NECC) during May–December. The simulated seasonal variation of the NBC–NECC system compares quite well with the observations (Richardson and McKee 1984; Richardson and Walsh 1986). Overall, the model successfully captures the major features of the SST and circulation pattern in the upper tropical Atlantic.

3. Sensitivity of SST response to changes in AMOC In this section, we perform a set of sensitivity experiments to test the hypothesis that changes in AMOC strength can have an effect on tropical Atlantic SST response by altering the pathway of the STCs. First, we will simulate the response of the tropical Atlantic to a total shutdown of the AMOC. Then, we will systematically explore the sensitivity of the tropical Atlantic circulation and SST to the northward mass transport imposed at the open boundaries. As will be demonstrated below, the equatorial SST responds nonlinearly to changes in AMOC strength. A prominent equatorial warming occurs when the AMOC is weakened below a threshold value. Note that we name all experiments conducted in this study, except for the aforementioned CTRL run, according to the latitude of the subsurface temperature front, temperature gradient, and the strength of AMOC. For example, ‘‘L10NG7C_0Sv’’ indicates that in the experiment the subsurface temperature front is located at 108N, the temperature front gradient is 78C, and the strength of AMOC is zero.

a. SST response to a shutdown of the AMOC In the tropical Atlantic Ocean, the wind-driven circulation interacts with the return flow of the AMOC. In this section we test the possibility that a substantially weakened AMOC may trigger SST warming in the equa-

torial South Atlantic by reorganizing the pathways of the STCs, as suggested by Chang et al. (2008). We performed the experiment L10NG7C_0Sv, in which where everything is identical to the CTRL simulation described in section 2b except that the northward mass transport is set to zero at the open boundaries. The configurations of the experiment are summarized in Table 1. The CTRL run, which is forced by a ‘‘realistic’’ combination of wind stresses and AMOC, represents the ‘‘current climate state.’’ In contrast, the L10NG7C_0Sv run is only driven by the winds and gives a representation of the climate state when the AMOC is totally shutdown. A comparison of the two experiments allows us to assess the extent to which the tropical ocean circulation system can be modified by the absence of the AMOC and how these circulation changes affect SST. Both experiments were integrated from the same initial conditions and ran for 20 years. The climatology of both experiments is constructed from the last 10 years of the model integrations. Unless stated otherwise, all anomalies shown below are defined as the difference between the mean state of the L10NG7C_0Sv run and the CTRL run. Figure 4 compares the annual mean current and temperature of the L10NG7C_0Sv and CTRL runs. In the presence of a full strength AMOC, the model captures many of the salient features of the observed upper tropical Atlantic circulation (top panel). In the thermocline layer, a major portion of subducted water in the subtropical North Atlantic flows westward to the western boundary where it feeds directly into the western boundary current. A small portion flows equatorward, but it is weaker than the northward western boundary current resulting from the AMOC return flow. Therefore, the return branch of the northern STC is invisible in the thermocline layer, and the Atlantic STCs are highly asymmetric about the equator with the water mass supplying the EUC mainly from the Southern Hemisphere (right top panel) (see also Zhang et al. 2003).

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FIG. 4. Simulated annual mean currents (vectors, m s21) and temperature (contours, 8C) in the (left) mixed layer and (right) thermocline layer: (top) CTRL (wind driven 1 AMOC), (middle) L10NG7C_0Sv (wind driven only), and (bottom) L10NG7C_0Sv 2 CRTL. Note that the bottom panels are plotted in a different scale.

When the AMOC is disabled, the STCs become more symmetric about the equator. This is particularly evident in the northern STC where the southward western boundary current just north of the equator is intensified substantially (right middle panel), allowing a portion of the subducted water to feed the EUC via the western boundary current pathway from the Northern Hemi-

sphere. This result is consistent with the previous findings by Fratantoni et al. (2000) and Jochum and MalanotteRizzoli (2001). Near the surface the NBC is reduced as a result of the absence of the AMOC (left middle panel). The difference of the annual-mean circulation between the L10NG7C_0Sv run and the CTRL is shown in the bottom panel. As expected, the dominant feature of the

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FIG. 5. Hovmo¨ller diagrams of the subsurface temperature anomaly along the (a) WB path and (b) EQ path; contour interval is 18 and 0.38C, respectively. The paths are marked in the bottom of (b). The distance DS is in the unit of 18 and DS 5 0 starts from the northern western boundary. The trajectory following the seasonal climatological mean flow speed along the paths (thick solid line) is plotted.

difference is a narrow and continuous southward western boundary current that is associated with the upper return flow of the AMOC (Fratantoni et al. 2000). We next examine how the circulation change affects the SST response. As described above, removal of the interhemispheric flow causes the western boundary current along the northeastern coast of South America (the return branch of the northern STC) to reverse direction from poleward to equatorward. This circulation change gives rises to a rapid increase in subsurface temperature near the strong temperature gradient front. The warm anomaly first flows equatorward along the western boundary; then a portion of the warm water flows eastward along the North Equatorial Undercurrent (NEUC) and the other portion enters the equatorial zone and finally spreads along the EUC. To investigate what processes are responsible for the temperature propagation, we present Hovmo¨ller diagrams for the temperature anomaly along the western boundary and the equator (Fig. 5). It shows that temperature anomaly near the temperature front increases rapidly within the first 5 months and then reaches an equilibrium state in 2 yr. The variation of the

warm anomaly displays a remarked seasonal cycle, associated with seasonal variation of the NBC–NECC system (Fig. 3). It takes approximately 4 months for the warm anomaly to travel along the western boundary from its source to the equator. The estimated propagating speed along the western boundary is about 0.22 m s21 (Fig. 5a), which is very close to the mean western boundary current velocity of 0.23 m s21 in the L10NG7C_0Sv run. After the warm anomaly enters the equatorial zone, it moves eastward along the equator at a nonuniform speed with a faster propagation during boreal summer when the EUC is strongest (Fig. 5b). The seasonal variation of the currents is affected by the equatorial wave adjustment, which then affects the advection of the temperature anomaly. To further verify that the movement of the temperature anomaly can be explained by the advection in the western boundary current and the EUC, we computed Lagrangian movement of a water parcel along the path indicated by the insert map in Fig. 5b. This was done by integrating the velocity along the path with respect to time. The resultant trajectory is shown by the thick solid line in Fig. 5. It is evident that the Lagrangian

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FIG. 6. Annual mean heat budget (8C month21) of the mixed layer in the CTRL run (solid line with markers) and L10NG7C_0Sv (markers only) in the vicinity of the equator (58S–58N). All quantities shown in the figure are zonally averaged across the Atlantic basin. Net surface heat fluxes (triangles), entrainment cooling (open squares), and zonal (plus signs), meridional (closed circles), and horizontal diffusion (open circles) are denoted.

trajectory tracks closely to the movement of the temperature anomaly, suggesting that the spread of the warm anomaly in the thermocline layer is mainly through the advective process. The subsurface warming leads to substantial surface warming, [O(0.68C)]. The warming is largest on the equator and in the eastern side of the basin along the upwelling zones (Fig. 4, left bottom panel). Heat budget analysis reveals that the SST warming is primarily due to the reduction of the upwelling-induced cooling in the equatorial Atlantic. Figure 6 shows the mean mixed layer heat budget in the vicinity of equator. In the CTRL run, the dominant balance is between the heat input from the atmosphere (solid line with triangles) and the entrainment cooling by the ocean (solid line with open squares). When the AMOC is disabled (L10NG7C_0Sv), entrainment cooling decreases substantially owing to reduction of the vertical temperature gradient (open squares only). As a result, the oceanic heat uptake from the atmosphere is reduced (triangles only). The large subsurface warming along the boundary between the subtropical and tropical gyres and the surface warming along the equator and the African coast in response to a shut-down AMOC is consistent with coupled GCM water-hosing simulations (Dahl et al. 2005;

Stouffer et al. 2006; Chang et al. 2008; Wu et al. 2008). In contrast, the strong surface cooling in the Northern Hemisphere simulated by the coupled GCMs is absent in our stand-alone ocean model simulation, suggesting that the surface cooling is largely attributable to atmospheric processes, which are excluded in this study. Therefore, the direct influence of the AMOC-induced circulation change on SST is confined to the equatorial South Atlantic Ocean. This finding supports the results of previous modeling studies that the atmospheric boundary layer processes and their interaction with the ocean mixed layer are mainly responsible for transmitting the surface cooling from the high-latitude North Atlantic to the tropics (Chiang et al. 2003; Chiang et al. 2008), whereas the oceanic teleconnection is responsible for the warming in the equatorial South Atlantic (Chang et al. 2008; Wu et al. 2008). As in the coupled GCM studies, we find that substantial subsurface warming has a major effect on the equatorial SST seasonal cycle. The effect on the SST seasonal cycle is strongest during boreal summer and fall (Fig. 7). This is because the SST change is mainly forced by the mean upwelling acting on the reduced vertical temperature gradient. The upwelling-induced cooling is most effective during boreal summer and fall when the

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FIG. 7. Simulated seasonal variation of SST along the equator in (a) CTRL (wind driven 1 AMOC), (b) L10NG7C_0Sv (wind driven only), and (c) difference of SST between L10NG7C_0Sv and CTRL.

equatorial cold tongue develops in the Gulf of Guinea. Figure 7 shows that the equatorial cold tongue SST increases by more than 1.58C during July–September in response to a total shutdown of the AMOC. This change in the equatorial SST seasonal cycle can have an important influence on the African monsoon (Vizy and Cook 2002; Chang et al. 2008). The change in upperocean stratification can also have important impact on the ‘‘Atlantic El Nin˜o’’ activity during boreal summer (Haarsma and Hazeleger 2007; Chang et al. 2008).

b. SST response to different strength of AMOC To explore the sensitivity of the SST response to changes in the AMOC, we carried out a set of sensitivity experiments, L10NG7C, in which the imposed northward mass transport at the open boundaries is decreased systematically from 14 Sv to 0 Sv (see Table 1 for details of the experiment configurations). We are particularly interested in examining questions, such as, does the SST respond linearly or nonlinearly to AMOC changes? Is there a threshold value in the AMOC strength below

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which the SST response becomes more sensitive? The CTRL run with a 14 Sv imposed interhemispheric flow (CTRL), serves as a reference for all other sensitivity experiments. To gauge SST response sensitivity, we define two indices: T1a is taken as the SST averaged over an equatorial box of 38S–38N, 208–58W from each experiment and then subtracted by the SST from the control run; T2a is the same as T1a except that it is taken from the thermocline layer. Figure 8 shows the two indices in response to different strengths of the AMOC. Both T1a and T2a indicate clear nonlinear behavior. For small decreases in AMOC strength (13 Sv–10 Sv), the subsurface and surface temperature response is weak and insensitive to the change in AMOC strength. As the AMOC strength continues to weaken, the temperature response becomes more sensitive. If we define the response sensitivity as temperature change per unit change in AMOC strength (8C Sv21), that is, the slope of T1a and T2a, then one finds that the sensitivity of the temperature response increases drastically when the AMOC strength is decreased below a threshold value of about 8 Sv. What mechanism is responsible for such nonlinear behavior in the SST response and what oceanic conditions determine the threshold value? Figure 8c displays the integrated western boundary current transport at 58N in the thermocline layer. It reveals that the NBC starts to reverse direction from northward to southward when the AMOC is weakened below 8 Sv. The fact that the critical AMOC value for NBC reversal coincides with that of the temperature sensitivity change suggests that the nonlinear temperature response is associated with the interplay between the wind-driven northern STC and the AMOC. As illustrated in Fig. 4 (right bottom panel), the AMOC return flow interacts with wind-driven circulation mainly via the western boundary current. The net transport of the NBC is given by the superposition of the equatorward return flow of the northern STC and the northward western boundary current associated with the AMOC. When the AMOC is strong, the NBC of Southern Hemisphere origin penetrates into the Northern Hemisphere and essentially blocks the return branch of the northern STC (Fig. 8c). As the AMOC weakens, the strength of the northward western boundary current decreases. When the imposed AMOC strength is below 8 Sv, the northward western boundary current becomes weaker than the northern STC return flow, causing the NBC to reverse direction. The southward NBC is strengthened as the AMOC strength continues to decrease. Mass transport analysis suggests that, for our model, 8 Sv is the threshold value at which the strength of the northern STC is approximately equal to the AMOC. Figure 9 sketches out the zonally integrated annual-mean meridional circulation

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FIG. 8. Changes in (a) SST index T1a, (b) thermocline temperature index T2a, and (c) the western boundary current transport across 58N in the thermocline layer as a function of AMOC strength for the L10NG7C experiment. T1a and T2a are defined as the SST anomaly and thermocline temperature anomaly averaged over 38S– 38N, 208–58W, respectively. The AMOC threshold value (8 Sv) marks the increase of the sensitivity of the temperature response to AMOC changes. In (c) the northward transport takes a positive value.

between 88S and 88N in three model simulations, with imposed northward transports of 0 Sv, 8 Sv, and 14 Sv. The dark pathways are the northern and southern STCs, which are wind-driven and self balanced with the same amount of water flowing poleward in the mixed layer as equatorward in the thermocline layer. The gray-dashed pathways indicate the upper branch of the AMOC in the model. As shown in Fig. 8c, the decrease of western boundary current transport is proportional to the changes in AMOC strength. It shows that, in the annual mean sense, the upper circulation solution of our ocean model can be well approximated by a linear superimposition of the wind- and the AMOC-forced solutions. When the AMOC is disabled, the northern STC (6 Sv) is slightly stronger than the southern STC (4 Sv) in the model (Fig. 9a). With an 8 Sv imposed transport at the boundaries, the 6 Sv AMOC water that enters the thermocline layer is equal to the strength of the northern STC, leaving no mass transport across 88N (Fig. 9b) in that layer. When the imposed AMOC transport is set at 14 Sv, the north-

ward western boundary transport is much stronger than that of northern STC return flow, resulting in a net northward mass transport at 88N (Fig. 9c).

4. Sensitivity to the subsurface temperature condition The results described in the previous section suggest that there are two key elements controlling the tropical SST response to AMOC changes: 1) the western boundary current system along the northeastern coast of the South atlantic, that is, NBC, and 2) the thermal front along the boundary of the subtropical and tropical gyres. In this section, we will examine how sensitive the SST response is to the properties of the thermal front, including its location and strength. To test the effect of thermal front location on the SST response, in addition to the experiment L10NG7C discussed in section 3b, we carried out three sets of experiments in which the center of the front was systematically

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FIG. 9. Schematic of the zonally integrated mass transport in the upper tropical Atlantic Ocean with (a) 0 Sv (wind driven only), (b) 8 Sv, and (c) 14 Sv imposed AMOC transport at the open boundaries for the L10NG7C experiment. Solid routes represent the wind-driven flows associated with the northern and southern STC. Light-dashed routes represent the return flow of the AMOC. Numbers marked on each route indicate the strength of the circulation component. Numbers in the black circle represent the total mass transport, which consist of the contributions from the winddriven circulation and the AMOC in each layer. Note that the strength of the northern STC is equal to that of AMOC in the thermocline layer, resulting in no mass transport across 88N (b).

displaced from a location near 158N off the coast of South America to a location near the equator (see Fig. 1b for the exact locations of the front). In each set of experiments, the AMOC strength is systematically decreased from 14 Sv to 0 Sv. We refer to these sets of experiments as L15NG7C, L7NG7C, and L3NG7C with L15NG7C having the front location farthest from the equator (see Table 1 for experimental configurations). Note that the

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location of the temperature front in the L10NG7C experiment is close to the observed subsurface temperature front derived from the Levitus (1994) dataset (Fig. 1a). Admittedly, such an idealized setting is unrealistic because changes of thermal structure in reality are associated with changes in circulation structures because the two are dynamically linked through geostrophic constraint. In our simplified model, the thermal front is maintained by the heat flux correction, as discussed in section 2a. In a sense, we can view our model as an anomaly model where its mean temperature in the thermocline layer is specified and only departures from the mean temperature are simulated. Our purpose here is not to simulate a realistic mean circulation of the ocean, but rather to elucidate mechanisms governing changes of the ocean in response to AMOC changes. With these caveats in mind, we discuss the results of our sensitivity experiments. Figure 10 shows the temperature response to different AMOC strengths in each set of experiments. When the temperature front is displaced farthest to the north (L15NG7C), the equatorial thermocline temperature response represented by T2a is very weak and the SST response T1a is almost nonexistent. When the front shifts equatorward to about 108N (L10NG7C), it is evident that the temperature responds nonlinearly to changes in AMOC strength, as discussed in the previously section. With the location of the front moving closer to the equator (L7NG7C and L3NG7C), the nonlinear behavior of the temperature response appears to be weakened. This is seen more clearly in the L3NG7C experiment where the front location is very close to the equator (squares in Fig. 10). There are two important factors that can affect anomalous warm water entering the equatorial thermocline. The first is the bifurcation latitude of the NEC, which is determined by the wind-driven circulation and is around 108–128N. The second is the retroflection latitude of the NBC–NBUC, which is around 68–78N (Fonseca et al. 2004). The former does not depend on the strength of the AMOC, but the latter does. As the AMOC weakens, the NBC–NBUC retroflection retreats equatorward. The nonlinear behavior is determined by the distance required for the subsurface temperature anomaly to travel from its source to the NBC–NBUC retroflection latitude. This distance is more than 1000 km in the L10G7C case, and thus the reversal of the NBC– NBUC is required in order to transport the warm water over a significant distance before it can be advected into the EUC system. This gives rise to the nonlinear behavior of the SST response. In contrast, the distance in the L7NG7C case is considerably shorter than that in the L10G7C case and is only about 100–200 km. Therefore, even without the reversal of the NBC–NBUC, some of

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FIG. 10. Equatorial temperature changes as a function of AMOC strength for L15NG7C (dots), L10NG7C (circles), L7NG7C (pluses), and L3NG7C (squares): the subsurface meridional thermal front location is varied. The positions of the thermal front in each experiment are displayed in Fig. 1b. The definitions of the (left) SST index T1a and (right) subsurface temperature index T2a are as in Fig. 8.

the warm anomaly can be brought into the EUC system by the NBC–NBUC retroflection current. This explains the weakly nonlinear behavior. In the L3NG7C case, the warm anomaly is within the NBC–NBUC retroflection, and thus the response is essentially linear. We further examine the impact of the strength of the subsurface temperature front on the behavior of model temperature response. We repeated the sensitivity experiments by reducing the cross-front temperature difference from 78 to 48C and then to 28C in the L10NG4C and the L10NG2C experiments (see Table 1 for experimental configurations). Results of these experiments are summarized in Fig. 11. It shows that the temperature responses in both layers behave nonlinearly to AMOC changes, although the SST response is significantly weakened by the weak temperature front. Therefore, we conclude that the nonlinear behavior of the equatorial temperature response to AMOC changes depends more on location of the thermal front than the strength of the front.

5. Summary and discussion In this study, we advance an oceanic mechanism linking AMOC changes to the tropical Atlantic SST

changes proposed by Chang et al. (2008). Using a simple 2½-layer RGO model that includes key dynamic and thermodynamic processes, we conducted a systematic investigation into the oceanic processes controlling the SST response to AMOC changes. The modeling approach that we adopted is, in many ways, similar to that of Fratantoni et al. (2000), where a northward interhemispheric flow is specified at the northern and southern open boundaries of the model, mimicking the return flow of the upper limb of the AMOC. Different from Fratantoni et al., our emphasis is on the effect of AMOC changes on the tropical Atlantic SST response. By varying the strength of the imposed interhemispheric flow, we conducted a large number of numerical simulations to shed light on the detailed oceanic processes controlling the tropical Atlantic SST response and its sensitivity. As in Fratantoni et al. (2000), we found that the most significant circulation change in the upper tropical Atlantic in response to a total AMOC shutdown occurs in the NBC–NBUC region. In the absence of the AMOC, the NBC flows equatorward and the Atlantic STCs become more symmetric about the equator. We further show that this circulation change causes a pronounced subsurface warming that is initiated along the gyre boundary of

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FIG. 11. As in Fig. 10 but the front location is fixed as in L10NG7C (circles) and the crossfront temperature difference is reduced to 48C (L10NG4C, diamonds) and 28C (L10NG2C, triangles).

the northern subtropical and tropical gyres and then spreads into the equatorial South Atlantic, giving rise to warm SST anomalies in the Gulf Guinea and along the African coast. The surface warming is strongest during boreal summer and fall when the upwelling is at its peak. This finding supports the hypothesis proposed by Chang et al. (2008). In contrast to the water-hosing experiments carried out using coupled climate models, our ocean-only model simulation shows no prominent SST change in the northern tropical Atlantic, suggesting that the surface cooling in the Northern Hemisphere is primarily attributable to atmospheric processes and the oceanic teleconnection mechanism is mainly responsible for SST changes in the equatorial South Atlantic. These findings are in line with recent modeling studies (Chang et al. 2008; Chiang et al. 2008; Wu et al. 2008; Wan et al. 2009). We further note that the surface warming in our model is generally weaker than those reported in the coupled GCM experiments. This is probably due to the lack of ocean–atmosphere feedbacks in our model in which the SST anomaly is damped by the use of bulk formulations. In subsequent studies, we shall use the same ocean model coupled to an atmospheric general circulation model to address the issue of how air–sea interaction may affect the tropical Atlantic SST response to AMOC changes.

A major objective of this study is to assess the sensitivity of the tropical Atlantic SST to changes in AMOC strength through a set of sensitivity experiments where the imposed northward transport at the open boundaries is varied decrementally from 14 Sv to 0 Sv. An important finding that emerges from these experiments is that, although interactions between the STC and AMOC can be essentially described as a linear superposition of two opposing western boundary currents driven by winds and thermohaline circulation off the northern Brazilian coast, as shown by Fratantoni et al. (2000), the tropical SST response to AMOC changes behaves nonlinearly. The sensitivity of the SST response increases drastically when the AMOC strength decreases below a threshold value of about 8 Sv. This threshold behavior is attributed to the reversal of the NBC owing to the weakened northward western boundary current associated with the AMOC. Sensitivity experiments reveal that the nonlinear threshold behavior depends primarily on the position of subsurface temperature front and is less sensitive to changes in the strength of the subsurface temperature gradient between the northern subtropical and tropical gyres. If the subsurface thermal front is located sufficiently close to the equator, the nonlinear behavior is substantially weakened as the anomaly generated near the subsurface thermal front is readily brought into the

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EUC system by the NBC–NBUC retroflection current, causing changes in the thermocline in the eastern equatorial Atlantic. Our analysis suggests that in order for the oceanic teleconnection mechanism to operate, two conditions must be satisfied: 1) the AMOC reduction must be substantial enough to allow the NBC to reverse direction and thus permit water mass exchange between the northern subtropical and tropical gyres and 2) the gyre boundary where the subsurface thermal front is located must be situated in an optimal location. If the front is too far away from the equator, the subsurface temperature anomaly generated by AMOC changes is unable to enter the equatorial zone and the SST response to AMOC changes is negligible. On the other hand, if the AMOC reduction is not strong enough, the subsurface warm anomaly will be trapped near the gyre boundary and will not be able to enter the equatorial zone; consequently, no strong SST response will take place. This implies that prominent equatorial warming can only occur during strong climatic events, such as the Younger Dryas when substantial AMOC reductions occurred. The result also suggests that climate models must accurately simulate the gyre boundary and the associated temperature gradient in order to simulate abrupt climate changes in the tropical Atlantic sector. If the gyre boundary and the temperature front are located too close to the equator, the warm anomaly can readily be brought into the EUC system by the NBC–NBUC retroflection current even if the NBC does not reverse its direction. In this case, models may overestimate the sensitivity of the tropical SST response to AMOC changes. The conclusions of the study are based on a relatively simple ocean model that does not simulate the AMOC. Instead, the effect of the AMOC is realized through changes at the open boundaries. Concerns are naturally raised about the robustness of these findings. To discuss these concerns, we reference a recent study by Wan et al. (2009) in which a set of similar experiments were conducted with a tropical channel ocean general circulation model (OGCM) from 308S to 308N where the open boundary conditions were derived from a set of global OGCM water-hosing runs. The results of Wan et al. show a similar SST response that is attributed to AMOC–STC interaction. Furthermore, we have done a series of global Modular Ocean Model, version 3 (MOM3) water-hosing experiments where different water-hosing strength is specified in the North Atlantic. The results reveal a basinwide warming in the tropical Atlantic to a substantially weakening in the AMOC, which bears a close resemblance to the simple ocean SST response (Fig. 4). A detailed analysis shows that the AMOC–STC interaction is responsible for the SST response (Wan 2009). Finally, the

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nonlinear nature of the SST response caused by AMOC– STC interaction is also consistent with the finding from the Geophysical Fluid Dynamics Laboratory Climate Model version 2 (GFDL CM2) water-hosing experiment described by Chang et al. (2008). All of this evidence suggests that the mechanism presented here is unlikely to be an artifact of the simple model. It is worth pointing out that the tropical SST response to AMOC changes studied here cannot be simply attributed to changes in meridional heat transport that have been widely used as an explanation for warming (cooling) of the South (North) Atlantic when the AMOC is reduced (e.g., Dahl et al. 2005; Fedorov et al. 2006; Barreiro et al. 2008). The meridional heat transportÐis a vertically integrated measure of oceanic heat fluxes VT dz. If we simply divide the ocean into a warm upper layer where MOC return flow takes place and a cold lower layer where the North Atlantic Deep Water outflow occurs, the meridional heat transport can be approximated as V(Tu 2 Tb), where V is the vertically integrated northward flow carried by the AMOC return flow, equal but opposite in sign to the NADW outflow, and Tu(Tb) are the temperature of the upper (lower) layer. An AMOCinduced meridional heat transport change can be simply due to a change in V, that is, DV(Tu 2 Tb), but does not necessarily require an exchange of water masses between gyres, which is demonstrated as a crucial process giving rise to the SST response in this study. We thus argue that the tropical SST change is not simply governed by the meridional heat transport change DV(Tu 2 Tb). To illustrate this point further, we compare the meridional heat transport and temperature response between two sets of simulations. In the first set (case 1), we ran the model with 14 Sv- (CTRL) and 0 Sv AMOC boundary forcing (L10NG7C_0Sv) with a subsurface temperature front of 78C. This set of experiments has been discussed in detail in section 3a. In the second set (case 2), we ran the identical model but set the amplitude of the subsurface temperature front to zero. Figure 12 displays the zonally integrated heat transport and subsurface temperature response in these two cases. In our reducedgravity model, the abyssal layer is assumed to be infinitely deep and motionless. However, the transport of the abyssal layer, the product of velocity and layer thickness, can remain nonzero. Therefore, for a consistent description of the total heat transport, a southward transport of the NADW outflow required to balance the northward mass transport in the upper layers is included in the heat transport calculation. Thus, the total heat transport is defined as V1T1 1 V2T2 2 (V1 1 V2)T3, where V1 and V2 are the mass transport of the mixed layer and the thermocline layer; T1, T2, and T3 are the temperature of the mixed layer, the thermocline layer, and the infinitely

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FIG. 12. Simulated zonal annual mean heat transport (PW) in the upper ocean and subsurface temperature change (8C) in (top) the presence of a subsurface front gradient of 78C (case 1) and (bottom) the absence of a subsurface front gradient (case 2). In each case, the simulation with AMOC forcing is contrasted to the simulation without AMOC forcing. (left) Meridional heat transports for both cases. For both cases, the meridional heat transport without AMOC forcing (dashed lines) is decreased by about 1 PW (dotted lines) compared to that with AMOC forcing (solid lines). (right) Subsurface temperature changes with and without AMOC forcing for both cases.

deep abyssal layer, respectively. In this study T3 is set to be 28C. As shown in Figs. 12a,c, in both cases there is a substantial reduction of northward meridional heat transport O(1 PW) in response to the AMOC shutdown. The majority of this change in the meridional heat transport is a direct result of the change in the circulation strength through DV(Tu 2 Tb). In case 2, for which there is no subsurface temperature gradient, the change in the meridional heat transport is nearly constant at each latitude, resulting in near-zero heat transport convergence– divergence everywhere and thus no temperature changes (Fig. 12d) in spite of the significant reduction in the meridional heat transport. In case 1, in which the subsurface temperature front is present, the heat transport convergence–divergence is near zero south of the equator but is positive north of the equator, suggesting a convergence of heat in the tropical North Atlantic. This positive heat transport convergence is accounted for largely by the subsurface warming in the tropical North Atlantic (Fig. 12b). However, it does not explain why the SST

response shows maximum warming in the equatorial South Atlantic (Fig. 4) because the distribution of convergence of the heat transport would suggest a warming north of the equator. Neither of these cases produces a dipolelike SST response, even though there is a major reduction in the meridional heat transport. This finding is further validated by a similar set of OGCM experiments (Wan 2009). The OGCM experiment results are consistent with the simple model results, suggesting that the result is not an artifact of the simplified physics of our model. We note a similar result from a recent coupled model intercomparison study where 14 different coupled climate model water-hosing experiments are compared (Stouffer et al. 2006). The multimodel ensemble mean meridional heat transport change in 0.1 Sv water-hosing experiments (Fig. 8b of Stouffer et al. 2006) is generally consistent with the simple model result. In particular, it shows a convergence of the heat transport change over the entire tropical ocean from 308S to about 208N, with weaker convergence south of the equator and stronger convergence north of the equator. This change in the meridional

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heat transport again cannot explain the dipolelike SST response in the models (Fig. 7b of Stouffer et al. 2006). Therefore, the study presented in this paper suggests that to understand how the Atlantic SST responds to AMOC changes it is not sufficient to just study meridional heat transport changes. Our results clearly identify that oceanic dynamics play an important role in the tropical Atlantic SST response to AMOC change. The induced SST perturbations may modify the distribution of oceanic heat transport in the coupled system via a set of air–sea interactions. A comprehensive understanding of this issue requires an understanding of interactions between the wind-driven and thermohaline circulations along the western boundary, as well as an understanding of ocean–atmosphere interactions.

Acknowledgments. We would like to acknowledge Dr. Sang-Ki Lee for sharing his model code. We would also like to acknowledge the anonymous reviewers for their comments on the manuscripts. This work was supported by the NSF Grant OCE0623364 and DOE Grant DEFG02-08ER64620.

APPENDIX Equations for Model Simulation The 2½-layer model consists of two active layers—the mixed layer and the thermocline layer. The deep water below the thermocline layer is motionless. The governing equations for the mixed layer are as follows:

›u1 u y 1 ›u21 1 › 1 ›P1 tf vH(v) 1 (u2  u1 ) 1 F f1 , (u1 y1 cosu)  1 1 tanu  2V sinuy 1 5  1 1 1 a cosu ›f a cosu ›u a cosu ›f h1 ›t a r1 h1 (A1) ›y1 u2 1 › 1 › 2 1 ›P1 tu vH(v) (u1 y 1 ) 1 (y 1 cosu) 1 1 tanu 1 2V sinuu1 5  1 1 1 (y 2  y1 ) 1 F u1 , a cosu ›f a cosu ›u a ›u h1 ›t a r 1 h1 (A2)   ›h1 1 › › (u1 h1 ) 1 (y 1 h1 cosu) 5 v, 1 a cosu ›f ›u ›t Q0  Qh ›T 1 u1 ›T 1 y ›T ›2 T 1 vH(v) 1 1 1 1 15  (T 1  T 2 ) 1 Kt =2 T 1 1 Kz ; h1 ›t a cosu ›f a ›u r1 Cp h1 ›z2

(A3)

(A4)

and for the thermocline layer ›u2 u y 1 ›u22 1 › 1 ›P2 vH(v) (u2 y 2 cosu)  2 2 tanu  2V sinuy 2 5  1 1 1 (u2  u1 ) 1 F f2 , a cosu ›f a cosu ›u a cosu ›f h2 ›t a (A5) ›y2 1 › 1 › 2 u2 1 ›P2 vH(v) (y 2  y 1 ) 1 F u2 , (u2 y2 ) 1 (y 2 cosu) 1 2 tanu 1 2V sinuu2 5  1 1 a cosu ›f a cosu ›u a ›u h2 ›t a   ›h2 1 › › (u h ) 1 (y h cosu) 5 v, 1 a cosu ›f 2 2 ›u 2 2 ›t (A7) ›T 2 u2 ›T 2 y ›T 1 1 2 2 ›t a cosu ›f a ›u 5

Qh

1

r 2 C p h2

1 Qcre 

vH(v) (T 1  T 2 ) h2

› T2 . ›z2

Based on the hydrostatic assumption, the pressure gradient terms are given by 1 h$P1 i 5 ga$[h1 (T 1  T 3 ) 1 h2 (T 2  T 3 )]  gah1 $T 1 , 2 (A9)   h2 $T 2 . h$P2 i 5 ga$[(h1 1 h2 )(T 2  T 3 )]  ga h1 1 2 (A10)

2

1 K t =2 T 2 1 K z

(A6)

(A8)

The horizontal momentum friction terms for the ith layer are (Wajsowicz 1993)

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F fi 5

F ui 5

1 ›(Ai DTi ) 1 ›(Ai cos uDSi ) 1 , a cosu a cos2 u ›f ›u 1 a cosu

›(Ai DS ) i

›f



1 a cos2 u

›(Ai cos2 uDT ) i

›u

(A11)

, (A12)

where horizontal tension:   ›ui ›(y i cosu) 1 DTi 5  yi sinu ,  a cosu ›f ›u

  ›yi ›(ui cosu) 1 1 ui sinf . 1 a cosu ›f ›u

(A14)

The viscosity Ai is determined as (Smagorinsky 1963, 1993) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ai 5 CDxDy (DT2 1 D2S ), i

i

(A16)

The entrainment rate (vk) is estimated using a modified version of the KT model, which is based on the turbulent kinetic energy budget. The net production of turbulent kinetic energy (P) in the mixed layer is parameterized as   P 5 ms u3*  «h1  0.25h1 [(1  n)B(h1 ) 1 (1 1 n)B(h1 ) 1 2m f jV sin(f)ju2*],

(A17)

where u* is the friction velocity [u* 5 (t/r1)1/2], « is a coefficient associated with background dissipation, n is a turbulent mixing coefficient for convection, and mf is introduced to get the correct neutral (zero surface heat flux) equilibrium mixed layer depth (Wallcraft et al. 2003); ms is a wind-stirring coefficient and is function of latitude with strong mixing near the equator (Chang 1994), ms 5 mso (1 1 ey

2

/L2m

hm /h1 ),

 (  ag  Qo 1 Qsol Rp e(g1 h1 ) 1 (1  Rp )e(g2 h2 ) B(h1 ) 5  r1 Cp " #) (g h ) (g h ) 2 Rp (1  e 1 1 ) (1  Rp )(1  e 2 1 )   1  ,  h1 g1 g2 (A19) where Qsol is the downward solar radiation flux at the ocean surface and Rp (g1 and g2) denote the solar radiation penetration (attenuation) coefficient of the solar radiation. When the effect of wind stirring exceeds that of the thermal forcing and background dissipation (P . 0), the entrainment rate of water mass into the mixed layer is given by

(A15)

where C is the Smagorinsky dimensional scaling coefficient and is empirically determined based on details of the model. The total exchange rate (v) of water mass across the base of the upper layer is represented as sum of entrainment rate and detrainment rate (McCreary et al. 1993) v 5 vk H(vk ) 1 vd .

Following Chang (1994), the buoyancy flux B(h1) is given by

(A13)

and horizontal shearing strain: DSi 5

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(A18)

where hm is the depth of the mixed layer at rest and Lm is taken to be 300 km.

vk 5

P . 1/2agh1 (T 1  T 2 )

(A20)

In KT-type bulk models, detrainment is often treated in a simple way: when the stabilized effect of a negative buoyancy flux outweighs that of the wind mixing (P , 0), the mixed layer shoals until it reaches the equilibrium depth (e.g., Krauss and Turner 1967; Schopf and Cane 1983). The mixed layer at the equilibrium state is determined by setting P equal to zero. This approach may be suitable to estimate the one-dimensional mixed layer thickness, as proposed by Kraus and Turner; however, it is not appropriate to determine the two-dimensional mixed layer thickness field, because mixed layer thickness is not only influenced by local processes, but also by largescale factors such as divergence of the mean flow and distribution of surface heat fluxes. Accordingly, the detrainment rate is parameterized as (McCreary et al. 1993) vd 5 

Qo H(Qo ) (h1  hr )2 H(h1  hr ), Qr td h1

(A21)

where hr is a reference equilibrium depth, td is an arbitrary detrainment time scale, and Qr is a scaling parameter with the same order of the mean net heat flux in the tropical Atlantic Ocean. Detrainment occurs whenever the ocean absorbs heat from the air and the mixed layer is thicker than the specified equilibrium depth hr. Note that the entrainment rate vk contributes to the total exchange rate v only when vk is positive; otherwise the mixed layer retreats to the equilibrium depth hr. Variables used in the above equations are defined as follows: ui (y i) are the zonal (meridional) components of

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velocity for layer i, hi is the thickness of layer i, Ti the temperature of layer i; a, f, and u are radius, longitude, and latitude of the earth respectively, V is the angular velocity of the rotation of the earth, ri the density of layer i, g the acceleration of gravity, a the thermal expansion coefficient, Cp the specific heat of water, Kt (Kz) the horizontal (vertical) heat diffusion coefficient, t f(t u) the zonal (meridional) components of the surface wind stress, Qo the downward net heat flux at the surface, Qh the downward heat flux at the base of the mixed 1 layer; Qcre the heat flux correction term for the second layer, and H(x) is the Heaviside step function [H(x) 5 1 if x $ 0; H(x) 5 0 if x , 0]. The OBCs utilized in the ocean model follows Marchesiello et al. (2001). The radiation equation for a prognostic model variable f is given by ›f ›f ›f 1 1 cx 1 cy 5  (f  fext ), ›t ›x ›y g

(A22)

with g 5 g out ,

if

cx . 0

and g 5 gin ,

if

cx , 0,

where fext denotes external information and g is the time scale for nudging. The phase speeds (cx, cy) are projections of the oblique radiation and are calculated as follows: cx 5 

›f ›f/›x 2 2 ›t (›f /› x) 1 (›f2 /›2 y)

(A23)

cy 5 

›f ›f/›y ›t (›f2 /›2 x) 1 (›f2 /›2 y)

(A24)

and

To keep the total mass of the model conserved during the integration, a volume constraint is applied. The basic idea of the constraint is that the total volume transport through the open boundary is adjusted to the balance of the external source (sink) of the seawater (M) by uniformly subtracting (adding) a velocity correction (Vc). The Vc is defined as "ð # 1 (h y 1 h2 y 2 ) dL  M , (A25) Vc [ Sb Lb 1 1 where Sb and Lb are the total intersection surface and total perimeter of the open boundary, respectively.

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