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  • View in gallery

    The annual mean precipitation (mm day−1) (gray shading), surface wind field (arrows), and SST (°C) (contours) for the control run: LOW.

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    The annual-mean zonal component of velocity (m s−1) along 125°W (color). Also shown is the potential density (contour interval 0.25 g m−3). The black contours indicate σ = 23 and 23.8 (kg m−3), the bottom surface of the two layers examined in Fig. 4. (top) Observations (Johnson et al. 2002), (middle) LOW, and (bottom) HIGH.

  • View in gallery

    The meridional streamfunctions (a) ψz and (b) ψσ for the control run, contour interval 2 Sv. Gray shading indicates negative values.

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    Diapycnic velocity wσ (m s−1) across the bottom of the given density layer (color); the isopycnic volume transport, uhσ (vectors, scale arrow indicates 10 m2 s−1); and depth of the density layer for the control run (top) σ = 22.9 and (bottom) σ = 23.7 (kg m−3).

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    Diapycnic mass transport as a function of potential density averaged over the area 8°S–8°N, 140°–80°W: total transport (thick solid line), averaged over positive wσ only (thin solid line), and averaged over negative wσ only (dashed line) for the (left) LOW and (right) HIGH runs.

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    Differences in surface properties between the HIGH and LOW runs: surface temperature (color; contour interval of 0.5°C) and near-surface winds (vectors) for (top) March and (bottom) October climatologies in the (left) fully coupled and the (right) ocean-only experiments.

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    Differences in the annual cycle of surface properties between the HIGH and LOW runs, averaged between 2°S and 2°N, as a function of longitude: surface temperature (gray shading, contour interval 0.5°C) and near-surface winds (vectors).

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    Differences in the (top left) annual mean precipitation (mm day−1), (top right) surface shortwave radiation QSW (W m−2), (lower left) surface latent heat flux QLA (W m−2), and (lower right) surface temperature (°C) and surface wind (scale arrow over South America indicates 2 m2 s−1) between the HIGH and LOW runs. The gray boxes on the surface temperature plot indicate the regions over which the heat budget is calculated.

  • View in gallery

    The annual-mean surface wind stress curl (N m−2) for (top)–(bottom) LOW, HIGH, and QuikSCAT.

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    The depth-integrated zonal transport, M, averaged between 4°N and 10°N (black lines) and the Sverdrup estimate, MS, (gray lines) as a function of longitude for expts LOW (solid lines) and HIGH (dashed lines).

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    The velocity averaged over the upper 30 m (arrows) in the eastern tropical Pacific for the (left) LOW and (right) HIGH runs. Also shown is the SST (contour interval 0.5°C).

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Vertical Mixing in the Ocean and Its Impact on the Coupled Ocean–Atmosphere System in the Eastern Tropical Pacific

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  • 1 International Pacific Research Center, University of Hawaii at Manoa, Honolulu, Hawaii
  • 2 Frontier Research Center for Global Change, Yokohama, Japan
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Abstract

The zonal and meridional asymmetries in the eastern tropical Pacific (the eastern equatorial cold tongue and the northern intertropical convergence zone) are key aspects of the region that are strongly influenced by ocean–atmosphere interactions. Here the authors investigate the impact of vertical mixing in the ocean on these asymmetries, employing a coupled ocean–atmosphere regional model. Results highlight the need to study the impact of processes such as vertical mixing in the context of the coupled system.

Changes to the vertical mixing in the ocean are found to produce large changes in the state of the system, which include changes to the surface properties of the ocean, the ocean currents, the surface wind field, and clouds and precipitation in the atmosphere. Much of the strength of the impact is through interactions between the ocean and atmosphere. Increasing ocean mixing has an opposite effect on the zonal and meridional asymmetries. The zonal asymmetry is increased (i.e., a colder eastern equatorial cold tongue and increased easterly winds), whereas the meridional asymmetry is decreased (a reduced north–south temperature difference and reduced southerlies), with the impact being enhanced by the Bjerknes and wind–evaporation–sea surface temperature feedbacks.

Water mass transformations are analyzed by consideration of the diapynic fluxes. Although the general character of the diapycnic transport remains relatively unchanged with a change in ocean mixing, there are changes to the magnitude and location of the transport in density space. Oceanic vertical mixing impacts the balance of terms contributing to the heating of the ocean surface mixed layer. With reduced mixing the advection of heat plays an increased role in areas such as the far eastern tropical Pacific and under the intertropical convergence zone.

Corresponding author address: Kelvin Richards, International Pacific Research Center, University of Hawaii at Manoa, 1680 East-West Rd., Honolulu, HI 96822. Email: rkelvin@hawaii.edu

Abstract

The zonal and meridional asymmetries in the eastern tropical Pacific (the eastern equatorial cold tongue and the northern intertropical convergence zone) are key aspects of the region that are strongly influenced by ocean–atmosphere interactions. Here the authors investigate the impact of vertical mixing in the ocean on these asymmetries, employing a coupled ocean–atmosphere regional model. Results highlight the need to study the impact of processes such as vertical mixing in the context of the coupled system.

Changes to the vertical mixing in the ocean are found to produce large changes in the state of the system, which include changes to the surface properties of the ocean, the ocean currents, the surface wind field, and clouds and precipitation in the atmosphere. Much of the strength of the impact is through interactions between the ocean and atmosphere. Increasing ocean mixing has an opposite effect on the zonal and meridional asymmetries. The zonal asymmetry is increased (i.e., a colder eastern equatorial cold tongue and increased easterly winds), whereas the meridional asymmetry is decreased (a reduced north–south temperature difference and reduced southerlies), with the impact being enhanced by the Bjerknes and wind–evaporation–sea surface temperature feedbacks.

Water mass transformations are analyzed by consideration of the diapynic fluxes. Although the general character of the diapycnic transport remains relatively unchanged with a change in ocean mixing, there are changes to the magnitude and location of the transport in density space. Oceanic vertical mixing impacts the balance of terms contributing to the heating of the ocean surface mixed layer. With reduced mixing the advection of heat plays an increased role in areas such as the far eastern tropical Pacific and under the intertropical convergence zone.

Corresponding author address: Kelvin Richards, International Pacific Research Center, University of Hawaii at Manoa, 1680 East-West Rd., Honolulu, HI 96822. Email: rkelvin@hawaii.edu

1. Introduction

In assessing the impact of a particular physical process in the ocean–atmosphere system it is important that the assessment is done in the proper context. Vertical mixing in the equatorial ocean is a good example. A number of studies have shown that the magnitude and time evolution of El Niño–Southern Oscillation events depends very much on the state of the ocean (see, e.g., Neelin 1991; Jin and Neelin 1993; Timmermann et al. 1999; Meehl et al. 2001). For instance, Meehl et al. (2001) find an increase in the amplitude of ENSO activity in a coupled numerical model when the vertical mixing is reduced (resulting in a sharpening of the thermocline).

Recognizing the importance of the ocean state, numerous studies have focused on improving the performance of ocean general circulation models (OGCMs) in the tropics by testing and refining the parameterization of vertical mixing in such models. A list of studies, which is by no means all inclusive, includes Pacanowski and Philander (1981), Rosati and Miyakoda (1988), Blanke and Delecluse (1993), Chen et al. (1994), Yu and Schopf (1997), Li et al. (2001), and Noh et al. (2005). All of the cited works describe experiments in which an ocean model is forced with a prescribed atmospheric forcing. What this numerical experimentation strategy does not allow for is a feedback from a changed ocean, caused by a change in the ocean physics, to the atmosphere. The result is a possible inconsistency across the ocean–atmopshere interface. The limitations of experiments using ocean-only models as opposed to fully coupled models to study ocean processes has been known for some time (see, e.g., Guilyardi and Madec 1997). A prime example is the Bjerknes feedback [Bjerknes (1969): a colder SST in the eastern Pacific, possibly brought about by increased mixing, drives stronger easterlies, which in turn produce stronger upwelling and cooling]. Choosing between parameterization schemes on the basis of a “better” SST field therefore may be misleading. Another factor that should not be forgotten, although not explored here, is the interplay between processes. For instance, Maes et al. (1997) find the rate of vertical mixing in their model changes as the level of lateral mixing is changed.

The focus of the present study is on the eastern tropical Pacific. Mitchell and Wallace (1992) and Kessler (2006) describe the features of the atmospheric climatology and ocean circulation, respectively. The coupled dynamics of the region are reviewed by Xie (2004). The region plays an important role in ENSO dynamics through, in particular, the state of the eastern cold tongue and the Bjerknes feedback described above. The purpose of the present paper is twofold. The first is to identify where and at what rate diapycnic fluxes are occurring. The utility of estimating water mass transformations by considering the flux across density surfaces dates back to Walin (1982); see also Marshall et al. (1999) and references therein. These studies have concentrated on the transformations in the surface mixed layer and seasonal thermocline. Sun and Bleck (2006) extend the analysis to the deep ocean. Here we employ the technique presented by Sun and Bleck, which projects model variables onto discrete density layers and calculates the implied fluxes between layers. This produces a different, and we argue more correct, picture than that produced by simply calculating the Eulerian averaged vertical velocity field, which can be misleading (see Hazeleger et al. 2001). The second and main purpose is to investigate the sensitivity of the coupled system to changes in the prescribed vertical mixing. Our intent is not to choose between vertical mixing schemes (in fact, we use a relatively simple parameterization scheme) but to highlight the inherently coupled nature of the response of the system to changes in the mixing. As we will see, changing the level of ocean mixing in a coupled model produces significantly larger changes to SST than those produced in ocean-only experiments. The coupling also produces substantial changes to the ocean currents that can radically alter the balance of terms affecting the heat content of the ocean mixed layer.

The tool used in this study is a regional coupled ocean–atmosphere model configured for the eastern tropical Pacific (Xie et al. 2007). Advantages of using a regional coupled model are that the local processes are isolated and the coupling ensures consistency between the oceanic and atmospheric components. In our particular case, we use a moderately high horizontal resolution (0.5° in both the atmosphere and ocean), which for the atmospheric component means that the model atmosphere is able to resolve and respond to relatively small horizontal scale changes in SST.

The rest of the paper is structured as follows: Details of the regional coupled model are briefly described in section 2. The methodology and results of the analysis of diapycnic fluxes are described in section 3. The impact of changing the level of vertical mixing in the coupled model is investigated in section 4. An analysis of the balance of terms affecting the heat content of the ocean mixed layer is presented in section 5. Section 6 provides some concluding remarks.

2. Regional coupled model

The model we use is the International Pacific Research Center (IPRC) Regional Ocean Atmosphere Model (IROAM) configured for the eastern tropical Pacific. The atmospheric component is the IPRC Regional Atmospheric Model (RAM) (Wang et al. 2003) configured for the region from 35°S to 35°N, 150° to 30°W. The oceanic component is the Geophysical Fluid Dynamics Laboratory Modular Ocean Model version 2 (MOM2) (Pacanowski 1995) configured for the Pacific basin from 35°S to 35°N. The oceanic and atmospheric components each have a horizontal resolution of 0.5° × 0.5°. The vertical discretization is 28 sigma levels in the atmosphere and 30 z levels in the ocean with enhanced resolution close to the lower and upper boundary, respectively. The two components are coupled from 150°W to the American coast and from 30°S to 30°N. Outside this domain, over the western part of the Pacific Ocean, the oceanic component is forced by prescribed surface fields from the daily National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kistler et al. 2001) with turbulent fluxes computed using the bulk formula of Fairall et al. (2003). The temperature and salinity at the closed northern and southern boundaries of the ocean are relaxed back to the Levitus (1982) climatology. For the atmospheric component the SST over the Atlantic sector is prescribed by the weekly SST product of Reynolds et al. (2002). The lateral boundaries of the RAM are nudged toward the NCEP–NCAR reanalysis. Full details of the model can be found in Xie et al. (2007).

Lateral mixing in the ocean is prescribed as horizontal Laplacian diffusion with a constant coefficient of 200 m2 s−1. Pezzi and Richards (2003) find the results of experiments with an ocean model configured for an idealized tropical ocean basin are little changed by the form of lateral mixing (isopycnic versus horizontal), or grid resolution, provided a small value is used for the lateral diffusion coefficient (their small value was 400 m2 s−1). The contribution by lateral mixing to the heat balance of the mixed layer in our experiments is found to be negligible (see section 5). We therefore do not expect our results to be unduly affected by the level or form of lateral mixing. Vertical diffusion of tracers, on the other hand, is found to be very influential on the model solution. Vertical mixing is prescribed by the Richardson number–dependent Pacanowski and Philander (1981) parameterization scheme. The minimum (background) value for viscosity is set to 10−4 m2 s−1 to avoid numerical stability issues and is kept the same for all experiments. The background value of the diffusion coefficient of tracers is set to 10−6 m2 s−1 for our control experiment (also referred to as experiment LOW—the effect of changing this value is investigated in section 4). The low value for the background diffusion coefficient is chosen in part because of the observation of low values at low latitudes (Gregg et al. 2003) and in part by numerical experiments that demonstrate that a low value gives an improved zonal current structure in the tropics (R. Furue 2007, personal communication).

In all experiments the ocean component, MOM2, is initialized by setting the tracer fields to Levitus (1982) climatology for January and the velocity to zero. The oceanic component is spun up for five years with NCEP–NCAR reanalysis fluxes across the whole domain, starting in January 1991. The oceanic and atmospheric components are then coupled in January 1996 and the coupled model is run an additional eight years. In terms of the Niño-3 SST, the model tracks both the annual and interannual observed variability very well (Xie et al. 2007). Here we present results averaged over years 2000–03 to avoid the 1997–98 El Niño–La Niña, and we will refer to the average as the annual average. To assess the degree to which the ocean had adjusted to the specified vertical mixing, the stratification in the thermocline was examined in individual yearly averages over the period used in the analysis. No discernable change was detected, except for the change associated with a weaker undercurrent in 2002.

Additional ocean-only experiments were performed. Here the ocean component (MOM2) is forced by the NCEP–NCAR reanalysis over the whole of the tropical Pacific basin.

To demonstrate the fidelity of the model we present the IROAM annual average surface wind field, SST, and precipitation in Fig. 1. Realistic features of the model include the northward displaced intertropical convergence zone (ITCZ), the strength and westward extension of the equatorial cold tongue, and the southeasterly winds over the southeast Pacific. A more thorough comparison of the model’s annual mean and seasonal cycle with observations is presented in Xie et al. (2007); de Szoeke and Xie (2008) evaluate the model performance in comparison with state-of-the-art coupled GCMs. The zonal component of velocity as a function of latitude and depth along 125°W from observations (Johnson et al. 2002) and the control run is shown in the top and middle panels of Fig. 2. The observed structure of the currents is well reproduced by the model. The shape of the model Equatorial Undercurrent (EUC) is good, although its maximum (1.26 m s−1) is approximately 20% greater than that observed and the thermocline is too diffuse. The subsurface countercurrents (SSCCs) centered at 5°S and 4°N are well placed but somewhat too weak, particularly the southern SSCC. The model North Equatorial Countercurrent (NECC) has a maximum of 0.34 m s−1, which is somewhat greater than that observed (0.26 m s−1) and is displaced approximately 1° to the south of the observed maximum.

3. Diapycnic fluxes

We start by considering the meridional overturning circulation. As noted by Hazeleger et al. (2001), calculating the meridional overturning streamfunction by averaging the flow at constant depth, denoted by ψz (shown in Fig. 3a for the control case), produces a misleading result in terms of the ventilation characteristics of the tropics. The streamfunction ψz exhibits strong so-called tropical cells that would imply a downward, diapycnic flux between 3° and 5° north and south of the equator. This misleading, or spurious, result arises from a combination of averaging across the east–west sloping density surfaces and the highly variable flow caused by the tropical instability waves (TIWs) (Hazeleger et al. 2001). Instead, we choose to view the overturning circulation in density space. The streamfunction ψσ (Fig. 3b), where σ denotes potential density, is calculated by first projecting daily averages of the horizontal velocity field (u, υ) onto discrete density layers to obtain the isopycnic volume transport uhσ = (uhσ, υhσ), where u and υ are the eastward and northward components of velocity, respectively, and hσ = h(x, y, σ, t) denotes the thickness of a given density layer. Here we discretize density by increments of Δσ = 0.02 kg m−3. The time-averaged meridional component of the isopycnic mass transport, υhσ, is then integrated zonally to produce ψσ.

The circulation in density space (Fig. 3b) is dominated by the two subtropical cells (STCs) north and south of the equator (cf. McCreary and Lu 1994). The transport of the northern and southern cells, based on the maximum and minimum value of ψσ, is 18 and 16 Sv (Sv ≡ 106 m3 s−1), respectively, with the center of the northern cell at a somewhat lighter density than the southern. Note that the majority of the transport occurs between 30°S and 30°N. There is, however, a modest amount of water mass transformation occurring in the relaxation regions applied to MOM2 poleward of 30° latitude. In the southern cell water is advected south in the surface layer, becoming progressively denser. Subduction occurs around 20°S followed by an approximately adiabatic flow to the equator. A strong diapycnic flux ensues in the vicinity of the equator with this flux being somewhat off the equator for lighter layers. The situation in the northern cell has two important differences. First, there is a significant diapycnic flux from approximately 15°N as water is moved to the equator along the lower (denser) branch of the cell. Second, there is a counterrotating cell centered at 3°N and σ = 23 such that the upwelling is pushed well off the equator. Note that the diapycnic flux (from dense to light) is in the opposite direction, in terms of density, to that implied by the tropical cells found in ψz (Fig. 3a).

The spatial distribution of the diapynic flux can be determined by calculating the diapycnic velocity wσ from the lateral divergence of the isopycnic volume transport,
i1520-0442-22-13-3703-e1
in which wσ+ and wσ refer to the diapycnic velocity at the top and bottom of a given layer, respectively, and we have assumed the tendency term for layer thickness is negligible (which is the case here). The diapycnic velocity across a given interface between layers can be found by taking wσ = 0 at the top and bottom of the water column. Sun and Bleck (2006) use the same method to calculate the geographic distribution of the diapycnic component of the thermohaline circulation in a number of climate models.

The diapycnic velocity, wσ, at the bottom of two density layers is shown in Fig. 4. A positive wσ indicates a diapycnic flow in the direction of decreasing density (i.e., an upward flow, on the whole). Also shown in Fig. 4 is the depth of the layer and the isopycnic mass flux. The layers have been chosen so that they cut through the centers of the southern STC (bottom panel, σ = 23.7) and the secondary circulation in the northern STC (top panel, σ = 22.9), respectively (see Fig. 3b). On the denser σ = 23.7 layer (bottom panel in Fig. 4), as expected, we see a region of positive wσ on the top of the eastward-flowing EUC where there is high shear and, hence, mixing. We also see, however, regions of positive wσ as the flow peels off and retroflects to join the northern and, in particular, the southern branches of the South Equatorial Current (SEC). This positive flux is consistent with the warming of the SEC as it flows westward. The region of positive wσ in the SEC moves westward as σ decreases. The circulation is closed by the regions of negative wσ as water is cooled while it moves southward in the surface layer. On σ = 23.7 this is occurring along 12°S, whereas it is just starting to appear at 20°N. The regions of negative wσ move equatorward as σ decreases. The isopycnic layer σ = 23.7 is domed along 10°N under the model’s ITCZ and farther east as the Costa Rica Dome. The positive wσ in these regions contributes to the diapycnic flux inferred from the lower limb of a Lagrangian meridional streamfunction (Fig. 3b). It is interesting to note the additional doming of water centered on 7°N, 82°W.

On σ = 22.9 (top panel in Fig. 4) the near-equator vertical flux is dramatically different from that below. The vertical flux is now dominated by bands of negative and positive wσ centered on approximately 2° and 5°N, respectively. The sense of the diapycnic flux is consistent with that required to close the residual circulation induced by the TIWs, as indicated in Fig. 3b, and is such as to recirculate and mix water in the mixed layer between the southern flank of the eastward flowing NECC and the westward flowing water in the northern branch of the SEC. To reemphasize the importance of averaging flow fields in an appropriate way, the vertical component of velocity associated with the northern tropical cell, obtained by averaging fields at a constant depth, is downward along 5°N with a minimum value of around −4 × 10−5 m s−1, which is of opposite sense, in terms of the flux across density surfaces, and a factor of 4 greater in amplitude compared to wσ at this latitude (see Fig. 3b).

The diapycnic transport integrated over the area 8°S–8°N, 100°–140°W is shown in Fig. 5. The transport peaks at 18 Sv at around σ = 23.5. The region captures most of the diapycnic transport at this range of latitude with the maximum transport being 70% of that obtained by integrating over the entire width of the basin. The contributions from regions of positive and negative values of wσ, respectively, are also shown. The peak in the contribution from negative wσ at σ = 22.8 is associated with the TIWs. It is noteworthy, however, that the contribution from negative wσ is significant over the density range shown and indicates that there is appreciably more transformation of water masses than inferred from the net transport alone.

4. Impact of vertical mixing

To assess the impact of vertical mixing in the ocean on the coupled system we consider the effect of changing the vertical diffusivity in the ocean component of the model. The vertical mixing schemes for momentum and tracers in the ocean model are based on Pacanowski and Philander (1981); that is, the vertical viscosity, v, and diffusion coefficient, κz, are given by
i1520-0442-22-13-3703-e2
and
i1520-0442-22-13-3703-e3
where Ri is the gradient Richardson number and v0 and κ0 are the background viscosity and diffusion coefficient, respectively. The constants α and n are set to 5 and 2, respectively (as in Pacanowski and Philander 1981), and the background viscosity, v0, to 10−4 m2 s−1 in all experiments. We consider a change to the background diffusion coefficient alone and take two cases: κ0 = 10−6 m2 s−1 (the control run) and κ0 = 50 × 10−6 m2 s−1. The two model runs are labeled LOW and HIGH, respectively. It should be noted from (3) that changes to κ0 can influence the magnitude of κz through changes to the Richardson number. Indeed, with a weaker stratification and lower Richardson number κz is increased in the thermocline with the maximum value of κz (at the top of the EUC) in HIGH (8 × 10−3 m2 s−1) being approximately twice that found in LOW.

a. Changes in diapycnic fluxes

The general character of the diapycnic fluxes changes little with the change in the background diffusivity. The integrated diapycnic transport of HIGH is compared to that of LOW in Fig. 5. The shape of the transport with respect to density is similar in the two experiments. There are changes, however, to the magnitude and location of the transport in density space. The maximum diapycnic flux in HIGH is 20% greater than that in LOW (22.2 Sv compared to 19.6 Sv, respectively, consistent with the stronger easterlies in HIGH; see later) with the peak being narrower but with the tail reaching to somewhat higher densities. The maxima in the upward and downward diapycnic transports are shifted to lower densities in HIGH compared to LOW. The peak in the net downward transport associated with the TIWs is increased by 60% (−1.9 Sv at σ = 22.8 for HIGH compared to −1.2 Sv at σ = 22.6 for LOW).

b. Changes in surface properties

To characterize the changes to the system brought about by a change in the ocean vertical diffusivity we first consider the change in two surface properties. Figure 6 shows the difference in surface temperature and near-surface wind field between the HIGH and LOW runs for the April and October climatologies (top and bottom panels, respectively). Also shown in Fig. 6 are the results using the ocean-only model (right column), that is, the ocean model forced with NCEP–NCAR reanalysis over the entire domain. For the ocean-only case, the change in SST brought about by increasing κ0 is greatest where and when the mixed-layer depth is shallow. In April the change in SST reaches −1.4°C toward the eastern end of the region, whereas in October the change is much smaller. In the coupled system we find the change in SST is considerably more than in the ocean-only case. In April it reaches −4.0°C in the far east with the signal spreading into the Gulf of Panama. The signal also spreads farther toward the west than in the ocean-only case. Associated also with the cooler SST along the equator is a reduction in the southeasterly winds in the south Pacific, particularly along the South American coast, and a reduction in the gap winds in the Gulfs of Panama and Papagayo (the latter seen in the October climatology). This decrease in the strength of the gap winds is a consequence of the increase in sea level pressure on the Pacific side caused by the cooler SST. In October there is a substantial warming off the coast of South America south of 5°S and a substantial cooling over the eastern side of the South American continent.

The annual variation in the difference in SST and surface wind between HIGH and LOW, averaged between 2°S and 2°N, is shown in Fig. 7 as a function of longitude. An increase in vertical mixing in the ocean causes a reduction in the southerly component of the surface wind throughout the year in the far east, peaking in December–February in the central and western parts of the region. This reduction of the southerly wind at the equator is caused by the meridional asymmetry in the change in SST (Fig. 8), which itself is a consequence of the stronger stratification of the ocean north of the equator compared to that to the south. In the central and western equatorial parts of the region the cooling peaks in April (in excess of 1.5°C) with a strong easterly anomaly in the surface wind. This strong cooling occurs at a time when the equatorial ocean is at its warmest and most strongly stratified. The net effect of increased ocean mixing is to reduce the range of the annual cycle in the equatorial SST by as much as 1.5°C. As the equatorial annual cycle arises from the meridional asymmetry in mean climate (Xie 1994), the reduction in the latter causes the former to weaken. The annual cycle affects ENSO both in phase and amplitude (e.g., Guilyardi 2006; Timmermann et al. 2007).

Increasing the vertical mixing in the ocean is found to increase the zonal asymmetry (a colder cold tongue and stronger easterlies) while reducing the meridional asymmetry (reduced north–south temperature difference and southerly wind). These asymmmetries are key aspects of the eastern tropical Pacific. The sense of the surface wind anomalies shown in Figs. 7 and 8 is indicative of an amplification of the impact of mixing on the zonal and meridional asymmetries of the eastern tropical Pacific through ocean–atmosphere interactions—the Bjerknes feedback (Bjerknes 1969) and the wind–evaporation–SST (WES) feedback (Xie 2004), respectively. In the case of the zonal asymmetry, colder surface water in the east of the equatorial Pacific, brought about by increased vertical mixing, increases the sea level pressure. The increased surface pressure drives stronger easterlies that increases upwelling, leading to a further cooling of the surface ocean. In the case of the meridional asymmetry, the eastward and westward turning of the southerly wind north and south of the equator, respectively, caused by the Coriolis force, means that the reduced southerlies at the equator as ocean mixing is increased is accompanied by an increase (decrease) in the easterly wind north (south) of the equator. This tendency is seen in the annual mean of the change in surface winds (Fig. 8), particularly to the south of the equator. The increased easterlies to the north of the equator tend to increase the latent heat flux and cool the ocean. The opposite occurs south of the equator, leading to a warming of the ocean. The net result is a reduction in the meridional gradient in SST.

The changes to the annual mean latent, QLA, and shortwave, QSW, surface heat fluxes (the two main contributors to the net heat flux) are shown in Fig. 8. A positive flux indicates a tendency to warm the underlying surface. The change in QLA over the ocean broadly reflects the change in SST (latent cooling is reduced over colder SSTs). The exception is 5°–10°S, where the positive change in QLA (decreased cooling) is consistent with the WES feedback described above. Changes to the shortwave radiation are directly related to changes to the model’s low-level cloud (as measured by the total liquid water content below 700 mb), as evidenced by the very similar patterns in the changes to the two quantities (the latter quantity is not shown). The shortwave radiation, and low-level clouds, are increased and decreased off the coast of South America and in the Gulf of Panama, respectively. Both changes are brought about by the positive feedback between the SST and low-level stratus clouds (see Norris and Leovy 1994; de Szoeke et al. 2006). Off South America the reduction in southwesterly winds reduces upwelling and produces a warming of SST. This warming tends to destabilize the atmospheric boundary layer, reducing the stratus cloud, which amplifies the warming of SST. In the Gulf of Panama the reverse is happening, with the increased stratus cloud contributing to the cooling of SST in the region. In the ITCZ and Gulf of Panama the SST cooling, induced by increased ocean mixing, reduces deep convection (increased OLR) and the resultant precipitation [the pattern of changes in model OLR (not shown) and precipitation are very similar but of opposite sign]. In the ITCZ the increase in ocean mixing has led to a 25% reduction in the level of precipitation. The precipitation in the Gulf of Panama is almost completely suppressed.

There is a markedly different relationship between changes in latent heat flux and surface temperature over land compared to the ocean. Over the South American continent there is an increase in precipitation. This is a result of an eastward shift of the edge of the precipitation over the central continent. The reason for the shift is not totally clear but is presumably associated with the reduced pressure gradient across the continent caused by the decreased equatorial SST in the Pacific and the resultant decrease in cross-continent winds. The change in precipitation does have a large effect on the surface temperature through an increase in cooling caused by the increased latent heat release from the moister land surface.

c. Changes in ocean currents

In the coupled system changing the vertical diffusivity can impact ocean currents in two ways: (i) a change in vertical viscosity brought about by a change in the stratification and (ii) a change in the surface wind forcing caused by changes in SST. To highlight the need to study the coupled system in assessing the sensitivity of the system to changes in model parameters, we note that the maximum speed of the EUC remains essentially unchanged with an increase in the diffusivity (1.26 m s−1 in LOW and 1.27 m s−1 in HIGH), suggesting a balance between the effects of the increase in surface stress caused by the Bjerknes effect (mechanism ii) and the retardation by the increased viscosity (mechanism i). This is in sharp contrast to the 15% decrease in the maximum speed of the EUC in the equivalent twin ocean-only experiments with the same increase in vertical diffusivity and fixed wind forcing (mechanism i alone).

As shown in Fig. 2, there is a reduction in the speed of the NECC from LOW to HIGH. The eddy kinetic energy of the tropical instability waves (the eddy component of the flow is defined here as motions with temporal scales less than 45 days) is reduced by 15%, associated with the reduced shear between the SEC and the NECC and a reduced barotropic conversion of energy (cf. Masina et al. 1999) (not shown). The NECC is a result of the meridional asymmetry in the eastern tropical Pacific, with its strength related to the zonal integral of the meridional gradient of curl τ, as discussed below. Changing the meridional asymmetry changes the strength of the NECC.

The annual mean surface wind stress curl, curl τ, for LOW and HIGH is shown in Fig. 9. There are two notable differences between the two cases that impinge on the surface current field. The first is the deeper minimum and greater meridional gradient, from 120° to 85°W, of the zonally oriented minimum in curl τ centered on 4°N in LOW compared to HIGH. The second is the greater positive curl associated with the gap winds in the Gulf of Papagayo and, less prominently, in the Gulf of Panama in LOW compared to HIGH. For reference, the wind stress curl calculated from Quick Scatterometer (QuikSCAT) data is also shown in Fig. 9. The general pattern of the observed wind stress curl is captured by the model. The observed positive curl associated with the Papagayo wind jet and the meridional gradient of the curl in this area is better represented in LOW than in HIGH. There are, however, some distinct differences in both model runs to observations: most notably, the stronger than observed positive curl associated with the Tehuantepec wind jet and the linear feature in negative curl along 2.5°N, associated with the anticylonic turning of the southeasterlies north of the equator, which is less distinct in the observations.

The Sverdrup (1947) estimate of the depth-integrated zonal transport is given by
i1520-0442-22-13-3703-e4
where ρ is the density of seawater, β = ∂f/∂y ( f is the Coriolis parameter), and x and y are eastward and northward coordinates, respectively. Yu et al. (2000) find that MS is a good approximation for the total zonal transport in the region of the NECC using results from a numerical model forced with different wind fields. (They also find that the structure of the NECC is also dependent on the near-equatorial zonal component of the wind stress.) Figure 10 compares the depth-integrated zonal transport, M, and the Sverdrup estimate, MS, averaged between 4°N and 10°N. For LOW, from the South American coast to around 95°W, the westward increase in transport in MS is somewhat greater than that of M. Westward of 100°W, however, the two track each other very well. Between 105° and 140°W, the transport, M, in HIGH is reduced compared to that in LOW; a similar, but larger, reduction is seen in MS. Although not conclusive, the results are suggestive that the change in the depth-integrated zonal transport in the model, brought about by the increase in the ocean diffusivity, is through the change in the wind stress curl. The caveat to this result is that the model wind stress curl toward the southern limit of the latitude range considered is somewhat different in amplitude to that observed.

As noted by Kessler (2002), east of approximately 110°W the zonal flow, centered on 6°N, is not a direct continuation of the NECC but is a consequence of the existence of the Costa Rica Dome. This is evident in the depth of isopycnic layers shown in Fig. 4. The flow averaged over the upper 30 m for LOW and HIGH in the far eastern tropical Pacific, superimposed on SST, is shown in Fig. 11. The effect of the stronger positive wind stress curl associated with the Papagayo and Panama wind jets in LOW, compared to HIGH (see Fig. 9), is to produce a stronger doming of water in the Costa Rica Dome and the secondary dome in the Gulf of Panama. This stronger doming produces considerably stronger surface currents in LOW as compared to HIGH. (The cyclonic circulation associated with the doming in the Gulf of Panama is seen in surface drift data, although the circulation in the model is displaced farther to the west than in observations; see Fig. 4 of Kessler 2002) The northern edge of the northern branch of the SEC is displaced somewhat farther south in LOW than in HIGH. The SST in the region is considerably warmer in LOW than in HIGH. The effect of the change of surface currents on the heat balance is examined in the next section.

5. Mixed-layer heat balance

The impact of the changes to the system on the near-surface ocean temperature can be assessed by examination of the terms producing a change in the heat content of the surface mixed layer. Here we average the equation for temperature over the depth of the mixed layer and a 4-yr period. The result is
i1520-0442-22-13-3703-e5
where angled brackets denote an average over the mixed layer depth, h, and an overbar denotes a time average over the specific period (cf. Vialard and Delecluse 1998; Menkes et al. 2006). The temperature T and the three velocity components, u, υ, and w, have been divided into a high-frequency (eddy) component, denoted by a prime and a low-frequency (LF) component, denoted by m. Here we define high frequency as variations with a period shorter than 45 days (increasing this to 90 days does not change the results unduly). The lateral mixing term is represented by Dl. The total heating rate by the atmosphere, Q, is written as the penetrative solar shortwave flux [the difference in the surface shortwave flux, Qs, and that penetrating through the base of the mixed layer, Qsf (h)] and the nonpenetrative flux, Q*. The mixed layer depth is taken to be the depth at which the difference in density from that at the surface is 0.125 kg m−3. This threshold is somewhat greater than used by Menkes et al. (2006). Reducing the threshold does not significantly change the mixed layer depth, and we do not expect the results of the analysis to be unduly sensitive to its value (cf. Menkes et al. 2006).

The various terms in Eq. (5) represent the heating rate of the mixed layer by A: advection by low-frequency currents, B: advection by high-frequency currents, C: vertical diffusion, D: lateral diffusion, and E: the atmosphere. The tendency term over the averaging period is negligible. The terms have been calculated from 1-day averages of the variables. As such, the calculation is not exact. The error (determined by the residual in the summation of all terms), however, is small, except in one case considered below. We have chosen not to further subdivide the advection term into zonal, meridional, and vertical components. As noted by Lee et al. (2004), caution needs to be exercised in the interpretation of the relative importance of the components since the result is dependent on both the form used for the advection term and the reference temperature and the results can be misleading.

We consider three regions (see Fig. 8). The first is a region affected by the TIWs. The heat balance terms are averaged over the area 0°–4°N, 90°–140°W. The northern boundary was chosen to cut through the center of TIW activity. Relatively modest changes to the specification of the region do not change the results significantly. The results for low (LOW) and high (HIGH) diffusion experiments are tabulated in Table 1 (region 1). The total diffusion (terms C + D) is dominated by vertical diffusion, lateral diffusion being approximately 1% of the total. We find that the atmospheric heating (term E) is almost balanced by vertical diffusion (term C). Although the low- and high-frequency advection terms are relatively large, they almost balance each other. A number of authors have analyzed the mixed layer heat budget in the Pacific in the TIW region (e.g., Kessler et al. 1998; Vialard et al. 2001; Menkes et al. 2006; Jochum and Murtugudde 2006) and, on the whole, found similar results as shown here in regard to the relative importance of terms and the balancing of the heat flux by low- and high-frequency advection. Only Menkes et al. (2006) present the total advection of heat. In their case, the total advection produces a net warming of the region, although the balance is still dominated by the atmospheric flux and vertical diffusion.

Increasing the background diffusivity (HIGH) increases the magnitude of both atmospheric heating (E) and vertical diffusion (C) but not the overall balance. In both LOW and HIGH the total advection plays a minor role in the heat balance, although the low- and highfrequency terms are themselves relatively large; the cooling by the low-frequency currents (term A) is more or less balanced by the warming by the high-frequency TIWs (term B), with the magnitude of each little changed between LOW and HIGH (interestingly, although the TIWs of HIGH have a lower eddy kinetic energy than in LOW, the eddy advective heat flux is slightly higher). The residual in the balance of terms is satisfyingly small in both experiments.

The second region considered is 5°–15°N, 110°–140°W (Table 1, region 2), situated under the ITCZ. Increasing the vertical diffusion from LOW to HIGH results in a doubling of the cooling caused by the vertical diffusion of heat. The cooling is enhanced by a decrease (23%) in the advection term in HIGH, as compared to LOW, brought about by the weaker surface currents in HIGH, in particular the NECC (see Fig. 2). This combined effect of vertical diffusion and advection in LOW is enough to support a net warming of the atmosphere (term E is negative; see Table 1), leading to enhanced convection and resultant precipitation (compared to HIGH in which E is positive). For the equivalent region centered on 10°S the increased cooling brought about by increasing the vertical mixing is approximately a third of that to the north (the mixed layer and thermocline are considerably shallower in region 2, as compared to the equivalent region to the south). The preferential cooling north of the equator leads to a reduced meridional asymmetry as discussed above.

The third region considered is in the far eastern Pacific from the equator to 10°N and 100°W to the American coast (Table 1, region 3): the southerly half of the area shown in Fig. 11. Now we see a dramatic change in the balance of terms in the heat equation between experiments LOW and HIGH. For HIGH the situation is as in the TIW region; that is, the major balance is between atmospheric heating and vertical entrainment, although now the magnitude of the low- and high-frequency advection terms is relatively much smaller. For LOW a substantially stronger surface circulation increases the net effect of advection in the heat balance. Because of the higher SST the flux from the atmosphere is decreased through an increase in the latent cooling (relative to that in HIGH). There is a marked increase in the total advection term (principally in the low-frequency term), however, so that now its magnitude is approximately 75% of that of the atmospheric term and such that advection is contributing significantly to the heat balance.

Unfortunately, the residual in the sum of the calculated heat balance terms for region 3 of LOW has become uncomfortably large relative to the individual terms; it is approximately 50% of the total advection term. The size of the residual, however, is not large enough, we suggest, to cast too much doubt on our conclusion that advection plays an important role in the heat balance in region 3 when the vertical diffusivity is set to a small value. We note that the 3–4-day-period easterly waves in the atmosphere are enhanced more in IROAM compared to those in the NCEP reanalysis. These waves induce strong vertical velocities in the oceanic component of IROAM that are not properly sampled by the 1-day averages used in the calculation of the heat balance terms.

6. Concluding remarks

The regional coupled model has proved to be a valuable tool in investigating the impact of ocean vertical mixing on the ocean–atmosphere system in the eastern tropical Pacific. The results highlight the need to consider the coupled system when assessing the role of physical processes in such a strongly interacting environment. Here, we find increasing the background tracer diffusion coefficient in the ocean has a marked effect on the surface properties of the ocean, the ocean currents, the surface wind field, and the clouds and precipitation in the atmosphere. Much of the strength of the impact is through interactions between the ocean and atmosphere that tend to amplify the changes to the system brought about by changes to the ocean mixing.

We find that increasing ocean mixing has an opposite effect on the zonal and meridional asymmetries in the eastern tropical Pacific. Increased mixing cools the eastern equatorial ocean. This cooling is further enhanced through the Bjerknes feedback, leading to an increased east–west temperature gradient. Because of the meridional asymmetry the stratification to the north of the region is greater than that to the south. Increasing ocean mixing leads to a preferential cooling to the north, reducing the north–south temperature gradient, convection in the ITCZ, and the meridional asymmetry. Ocean–atmosphere interaction again enhances the impact of the change in ocean mixing, with the wind–evaporation–sea surface temperature (WES) effect tending to reduce the meridional asymmetry still further. A number of studies point to a dominant role of the atmospheric component of coupled models in producing tropical biases (e.g., Schneider 2002; Guilyardi et al. 2004; de Szoeke and Xie 2008). An implication from this work, however, is that the biases relating to the too strong zonal and too weak meridional asymmetries found in many climate models may be improved by consideration of the level of vertical mixing in the ocean.

In the TIW region, the balance of terms in the heat budget for the ocean mixed layer remains relatively unaltered as the background ocean diffusion is changed. The cooler SST in HIGH increases the atmospheric heating by 50% over that in LOW, but this increase is met (at least in the balanced state) by an increased cooling by vertical diffusion. As remarked before, there is little change in the low- and high-frequency advective components. In the far eastern Pacific, on the other hand, the situation is very different. Here the changes in the strength of the surface circulation in the ocean (brought about by a change in the surface wind field) radically alter the balance of heat such that advection is a significant player in the budget for LOW. One may speculate that the response to low-frequency (externally forced) changes may be different in the two systems (LOW and HIGH).

The above puts into question the suitability of seeking “improvements” in ocean-only or atmosphere-only simulations by numerical experimentation if the feedbacks to the other medium are not considered. The schemes used here for the vertical mixing of momentum and tracers in the oceanic component of the model are relatively simple. The use of more sophisticated schemes will undoubtedly change the sensitivity of the system to changes in the background ocean diffusivity through the way that mixing is changed in the thermocline and mixed layer. We suggest, however, that the basic nature of the changes to the ocean–atmosphere interactions will not be changed. Such an assertion, of course, needs to be tested. Equally, convection in the model atmosphere is very susceptible to subtleties in atmospheric convection schemes. Of course, there are issues with regard to the necessary resolution in the horizontal and vertical in both oceanic and atmospheric components of the model required to capture the relevant physics and interactions. Additional numerical experimentation is required, but the impact of changes to the system can only be fully assessed in the context of the coupled system.

The results from IROAM have revealed a strong oceanic response to easterly waves in the model atmosphere. Recent observations have shown the existence of an oceanic response to such waves in the atmosphere (J. Mickett 2007, personal communication). One impact of the higher horizontal resolution in RAM compared to the NCEP–NCAR reanalysis is that the relative vorticity field associated with easterly waves is more intense in the former than the latter. This vorticity drives a strong vertical circulation in the surface layers of MOM2. A detailed analysis of the easterly waves and their impact on the ocean dynamics and thermodynamics is beyond the scope of the present study and warrants a better ocean mixing scheme and probably better resolution than utilized here.

Calculating the diapycnic model fluxes has proved to be illuminating in terms of determining the spatial distribution of the flux and in providing a quantitative measure of water mass transformation. We find that increasing the vertical diffusivity changes the portrait of diapycnic mass transport in density space. In terms of the water mass properties, changing the vertical diffusion in the ocean component of the model, therefore, not only changes the thickness of the thermocline but also the water mass transformations. The diapycnic transport is an integral part of the overturning circulation of the subtropical cells. The changes to the diapycnic transport found here are modest. It is unclear how large an impact these changes make by themselves; however, it is an aspect that needs to be taken into account when comparing different vertical mixing schemes or other parameterizations in ocean models.

We encourage the use of the diapycnic flux as a useful diagnostic in modeling studies and as a target for observational programs. In terms of the model, the calculated diapycnic flux is the total diapycnic flux and therefore includes not only the flux due to the explicit vertical mixing in the model but also from the flux due to horizontal mixing across sloping density surfaces (the “Veronis effect”; Veronis 1975). Estimating the magnitude of this effect is difficult. Employing a numerical scheme that approximates isoneutral diffusion (Griffies et al. 1998) will minimize spurious mixing but not totally remove it.

Finally, there is often an interplay between physical processes. Maes et al. (1997) note the interplay between lateral and vertical mixing: when the former is reduced, the latter is enhanced in their OGCM. Unresolved processes such as interleaving (Richards and Edwards 2003), which can produce significant lateral and vertical mixing and also depends on the large-scale flow, may feed back to the large-scale flow itself. The interplay between processes in the coupled environment is yet to be fully explored.

Acknowledgments

We wish to thank Pierre Dutrieux and Simon de Szoeke for help with the coding of the diagnostic analysis of the model output; K. Horuichi, Sharon DeCarlo, and Y. Shen for maintaining the data servers in Yokohama and the IPRC, which hold the model output; and Shan Sun for discussions on diapycnic fluxes. The computation was carried out on the Earth Simulator, Yokohama, Japan. This work was supported by the Ministry of Education, Culture, Science and Technology (Project Kyosei-7 RR2002), the Japan Agency for Marine–Earth Science and Technology, and the U.S. National Oceanic and Atmospheric Administration.

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Fig. 1.
Fig. 1.

The annual mean precipitation (mm day−1) (gray shading), surface wind field (arrows), and SST (°C) (contours) for the control run: LOW.

Citation: Journal of Climate 22, 13; 10.1175/2009JCLI2702.1

Fig. 2.
Fig. 2.

The annual-mean zonal component of velocity (m s−1) along 125°W (color). Also shown is the potential density (contour interval 0.25 g m−3). The black contours indicate σ = 23 and 23.8 (kg m−3), the bottom surface of the two layers examined in Fig. 4. (top) Observations (Johnson et al. 2002), (middle) LOW, and (bottom) HIGH.

Citation: Journal of Climate 22, 13; 10.1175/2009JCLI2702.1

Fig. 3.
Fig. 3.

The meridional streamfunctions (a) ψz and (b) ψσ for the control run, contour interval 2 Sv. Gray shading indicates negative values.

Citation: Journal of Climate 22, 13; 10.1175/2009JCLI2702.1

Fig. 4.
Fig. 4.

Diapycnic velocity wσ (m s−1) across the bottom of the given density layer (color); the isopycnic volume transport, uhσ (vectors, scale arrow indicates 10 m2 s−1); and depth of the density layer for the control run (top) σ = 22.9 and (bottom) σ = 23.7 (kg m−3).

Citation: Journal of Climate 22, 13; 10.1175/2009JCLI2702.1

Fig. 5.
Fig. 5.

Diapycnic mass transport as a function of potential density averaged over the area 8°S–8°N, 140°–80°W: total transport (thick solid line), averaged over positive wσ only (thin solid line), and averaged over negative wσ only (dashed line) for the (left) LOW and (right) HIGH runs.

Citation: Journal of Climate 22, 13; 10.1175/2009JCLI2702.1

Fig. 6.
Fig. 6.

Differences in surface properties between the HIGH and LOW runs: surface temperature (color; contour interval of 0.5°C) and near-surface winds (vectors) for (top) March and (bottom) October climatologies in the (left) fully coupled and the (right) ocean-only experiments.

Citation: Journal of Climate 22, 13; 10.1175/2009JCLI2702.1

Fig. 7.
Fig. 7.

Differences in the annual cycle of surface properties between the HIGH and LOW runs, averaged between 2°S and 2°N, as a function of longitude: surface temperature (gray shading, contour interval 0.5°C) and near-surface winds (vectors).

Citation: Journal of Climate 22, 13; 10.1175/2009JCLI2702.1

Fig. 8.
Fig. 8.

Differences in the (top left) annual mean precipitation (mm day−1), (top right) surface shortwave radiation QSW (W m−2), (lower left) surface latent heat flux QLA (W m−2), and (lower right) surface temperature (°C) and surface wind (scale arrow over South America indicates 2 m2 s−1) between the HIGH and LOW runs. The gray boxes on the surface temperature plot indicate the regions over which the heat budget is calculated.

Citation: Journal of Climate 22, 13; 10.1175/2009JCLI2702.1

Fig. 9.
Fig. 9.

The annual-mean surface wind stress curl (N m−2) for (top)–(bottom) LOW, HIGH, and QuikSCAT.

Citation: Journal of Climate 22, 13; 10.1175/2009JCLI2702.1

Fig. 10.
Fig. 10.

The depth-integrated zonal transport, M, averaged between 4°N and 10°N (black lines) and the Sverdrup estimate, MS, (gray lines) as a function of longitude for expts LOW (solid lines) and HIGH (dashed lines).

Citation: Journal of Climate 22, 13; 10.1175/2009JCLI2702.1

Fig. 11.
Fig. 11.

The velocity averaged over the upper 30 m (arrows) in the eastern tropical Pacific for the (left) LOW and (right) HIGH runs. Also shown is the SST (contour interval 0.5°C).

Citation: Journal of Climate 22, 13; 10.1175/2009JCLI2702.1

Table 1.

Terms contributing to the heating rate of the ocean surface mixed layer (°C month−1) for the LOW and HIGH runs. Eddy is defined as processes that have temporal scales less than 45 days; low frequency (LF) is defined as the remainder. Region 1: 0°–4°N, 90°–140°W; region 2: 5°–15°N, 110°–140°W; and region 3: 0°–10°N, 100°W to the American coast.

Table 1.

* International Pacific Research Center Publication Number 560 and School of Ocean and Earth Science and Technology Publication Number 7586.

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