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    Sections of upper-ocean mean equatorward velocity υ for the control run, across 9.3°N, 9.3°S, and the modeled Indonesian Throughflow at 1.9°S

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    (a) Annual mean equatorward pycnocline transports PN and PS across 9.3°N and 9.3°S for the control run (thin lines) and the three warming runs (thick lines). (b) Decadal mean transports for the control run (thin lines) and one warming run (thick lines). The observation-based results of MZ for 1956–99 are indicated in both panels

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    Standard deviations for PT, computed in a sliding 21-yr window. Thin curves represent individual warming runs, and the thick curve the ensemble mean. The solid lines represent a least squares piecewise linear fit to the ensemble mean

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    (a) Mean control run equatorward pycnocline transports at latitudes between 20°S and 20°N; (b) transport anomalies about this mean for the control run; (c) as in (b), but for the warming run

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    Linear regression patterns for decadally averaged PT and (a) SST and τ for the control run; (b) SST, based on observational results of MZ and the HadISST 1.1 dataset; (c) SST and τ for a warming run; (d) mean sea level pressure for the control run. Units are °C, N m−2, and kPa per Sv decrease in PT

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    Control run regression pattern for Ekman pumping–induced upwelling. The symbols mark longitudes of high anomalous upwelling at 9.3°S and 9.3°N where PS and PN are computed. Large values within ±5° of the equator are suppressed

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    Regression pattern for equatorward velocity against PT on surfaces at 9.3°N, 9.3°S and 1.9°S, as in Fig. 1. The symbols represent longitudes where anomalous Ekman pumping–induced upwelling is especially large, as in Fig. 6

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    Annual mean PT (thin) and Niño-3 (thick) for 100 yr of the control run. Note the inverted scale for Niño-3

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    Lagged cross correlations: (a) PT vs Niño-3; (b) PN (solid) and PS (dashed) vs Niño-3. Lags are relative to Niño-3. Note the inverted scale

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    Coherency spectra of (a) PN vs Niño-3; (b) PS vs Niño; (c) PN vs PS. Raw spectra have been smoothed across 20 frequency bins. Note the inverted scale for (a) and (b)

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    Lagged cross correlation of Ekman divergence vs pycnocline convergence PT across 9.3°N and 9.3°S. Lag is relative to PT

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    Regression pattern for equatorward temperature flux ρcpυT into the equatorial control volume, against net heat transport h into the volume

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    For the control run, (a) mean equatorward temperature flux ρcpυT across 9.3°N, and corresponding regression patterns of temperature flux against h arising from (b) υT, and (c) arising from υT ′

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    Components of (a) annual mean and (b) decadal mean heat transport h into the equatorial control volume, corresponding to υT (solid), υT ′ (dashed), and υT& prime; (dotted), for 100 yr of the control run

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    (a) Regression of T with anomalies h′ of heat transport into the control volume, plotted on the mean σθ = 24.5 isopycnal surface. (b) Regression following the σθ = 24.5 surface of T with h′. Decadal means are considered in each case. Here, T anomalies in the former instance include contributions due to vertical migration of the thermocline, whereas in the latter they reflect T anomalies propagating along the isopycnal

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    (a) Histogram of differences between successive decadal averages of pycnocline convergence PT for the control run (thin), warming runs for 1950–2000 (thick), and MZ results (circles); (b) as in (a), except differences are across 20-yr intervals

  • View in gallery

    Fig. A1. Values of σ2T computed in a sliding 21-yr window and plotted against σ2N + σ2S for one warming run. Thick lines indicate maximum and minimum realizable values of σ2T for given σ2N + σ2S

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Variability of Upper Pacific Ocean Overturning in a Coupled Climate Model

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  • 1 Canadian Centre for Climate Modelling and Analysis, Meteorological Service of Canada, Victoria, British Columbia, Canada
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Abstract

Variability of subtropical cell (STC) overturning in the upper Pacific Ocean is examined in a coupled climate model in light of large observed changes in STC transport. In a 1000-yr control run, modeled STC variations are smaller than observed, but correlate in a similar way with low-frequency ENSO-like variability. In model runs that include anthropogenically forced climate change, STC pycnocline transports decrease progressively under the influence of global warming, attaining reductions of 8% by 2000 and 46% by 2100. Although the former reduction is insufficient to fully account for the apparent observed decline in STC transport over recent decades, it does suggest that global warming may have contributed to the observed changes. Analysis of coupled model results shows that STC transports play a significant role in modulating tropical Pacific Ocean heat content, and that such changes are dominated by anomalous currents advecting mean temperature, rather than by advection of temperature anomalies by mean currents.

Corresponding author address: Dr. William Merryfield, Canadian Centre for Climate Modelling and Analysis, University of Victoria, P.O. Box 1700, Victoria, BC V8W 2Y2, Canada. Email: Bill.Merryfield@ec.gc.ca

Abstract

Variability of subtropical cell (STC) overturning in the upper Pacific Ocean is examined in a coupled climate model in light of large observed changes in STC transport. In a 1000-yr control run, modeled STC variations are smaller than observed, but correlate in a similar way with low-frequency ENSO-like variability. In model runs that include anthropogenically forced climate change, STC pycnocline transports decrease progressively under the influence of global warming, attaining reductions of 8% by 2000 and 46% by 2100. Although the former reduction is insufficient to fully account for the apparent observed decline in STC transport over recent decades, it does suggest that global warming may have contributed to the observed changes. Analysis of coupled model results shows that STC transports play a significant role in modulating tropical Pacific Ocean heat content, and that such changes are dominated by anomalous currents advecting mean temperature, rather than by advection of temperature anomalies by mean currents.

Corresponding author address: Dr. William Merryfield, Canadian Centre for Climate Modelling and Analysis, University of Victoria, P.O. Box 1700, Victoria, BC V8W 2Y2, Canada. Email: Bill.Merryfield@ec.gc.ca

1. Introduction

The subtropical cells (STCs) of the Pacific, Atlantic, and Indian Oceans are shallow, wind-driven overturning circulations consisting of equatorward geostrophic flow within the pycnocline, upwelling at the equator, and poleward surface Ekman transport (e.g., McCreary and Lu 1994). At higher latitudes where STCs are fed by subduction, these circulations appear to be largely unclosed (e.g., Johnson 2001).

Because STCs transport mass and water properties between the Tropics and subtropics on approximately decadal time scales, they have been viewed as possible agents of decadal climate variability, especially in the Pacific. At least two hypotheses have been advanced for how STCs might induce such variability. Both view STCs as modulating the equatorward heat flux, which scales as the product υT of meridional velocity and temperature. The hypothesis of Gu and Philander (1997) postulates that the STCs convey thermal anomalies from subduction regions in the eastern subtropics to the equator, where they upwell to warm or cool the surface waters, primarily in the central and eastern equatorial Pacific. The resulting changes in zonal temperature gradient modify the equatorial easterly winds, which in turn modulate the atmospheric transport of heat to the extratropical ocean, closing the cycle. According to this picture, the decadal time scale is fixed by the time necessary for subducted water to reach the Tropics. The potential for such a cycle to generate climate variations was demonstrated using a simple box model. Because the mechanism relies on advection of thermal anomalies by the mean flow to modulate equatorward heat flux, it has been termed the vT ′ hypothesis, where here and elsewhere, overbars denote temporal means and primes denote anomalies from the mean.

Since the vT ′ hypothesis was advanced, several observational and modeling studies have found that subducted thermal anomalies are unlikely to reach the equator with appreciable amplitude (e.g., Schneider et al. 1999; Hazeleger et al. 2001). An alternative hypothesis argues that equatorward heat flux is modulated by variations in the equatorward circulation; this has been termed the v′T hypothesis. In an intermediate coupled model with a 3 1/2-layer ocean and a statistical atmosphere, Kleeman et al. (1999) found that a decrease in subtropical wind stress reduces surface Ekman flow away from the equator, and hence the volume of cold water that upwells there. The resulting increase in equatorial SST drives an atmospheric teleconnection to the extratropics, which closes the cycle. By switching off ocean–atmosphere coupling in various regions, this feedback was shown to occur mainly in the northeast subtropical Pacific. An extension of this study by Solomon et al. (2003) found that a similar oscillation, as well as a purely extratropical decadal mode, was present when an atmosphere-to-ocean coupling parameter was sufficiently strong. Yang et al. (2004) found that the Southern Hemisphere contributes more to equatorial variability than the Northern Hemisphere, both via the v′T and the vT ′ mechanisms.

The idea that STC variations might play a role in low-frequency Pacific variability has received observational support from the finding of McPhaden and Zhang (2002); hereafter MZ) that equatorward pycnocline transport across 9°N and 9°S has undergone substantial interdecadal variation, including a decline of nearly 50% from the 1970s to the 1990s. Equatorial upwelling was estimated to have declined approximately 25% over the same period, accompanied by a surface Ekman transport decrease and an equatorial SST increase consistent with the Kleeman et al. (1999) v′T mechanism. Because there is an overall trend in their short (<50 yr) record, MZ raise the possibility that anthropogenically forced climate change might have contributed to the observed STC overturning decrease.

In this paper, we examine STC transport variations in a fully coupled climate model, both in a control run without anthropogenic forcing and in runs that include anthropogenic greenhouse gas and aerosol effects. Questions addressed include the following: (i) are the long–time scale STC transport variations found by MZ the result of natural variability, anthropogenic forcing, or both, (ii) what are the relative roles of thermal and circulation anomalies in modulating STC heat transports, and (iii) are STC variations a passive response to climate variability generated by other processes in the climate system, or do they play an active role in generating climate variability?

2. STC dynamics and pathways

Investigations by McCreary and Lu (1994) and Liu (1994) established fundamental aspects of STC dynamics using layered thermocline models. Among their main findings were that 1) STCs are driven by, and their strength is largely determined by, off-equatorial easterly wind stress; 2) water reaching the equator via the STC originates in the northeast (NE) subtropics; and 3) there are two pathways to the equator, via low-latitude western boundary currents or an interior path that directly links the NE subtropics to the central Tropics. Although the former tends to dominate, the importance of the latter increases with increasing basin width and easterly wind stress.

Additional investigations have refined and generally reinforced these conclusions. A principal theme has been to quantify subtropical-to-tropical transports. For example, based on a regional general circulation model with assimilation of temperature data and forcing by observed surface heat and momentum fluxes, Huang and Liu (1999) estimated equatorward STC transports of 17 Sv (1 Sv ≡ 106 m3 s−1) at 10°N and 26 Sv at 10°S, of which 3 and 11 Sv are attributable to interior pathways. From hydrographic data, Johnson and McPhaden (1999) deduced an upper limit of 5 Sv of interior pathway transport at low northern latitudes, versus about 15 Sv at low southern latitudes, in rough agreement with Huang and Liu. The relatively weak transport via the northern interior pathway has been ascribed to the presence of the intertropical convergence zone (ITCZ), beneath which upwelling creates a potential vorticity (PV) barrier that must be circumvented by equatorward flows (Lu and McCreary 1995; Johnson and McPhaden 1999). Additional evidence for an interior pathway is provided by high tritium concentrations observed in the central equatorial Pacific (McPhaden and Fine 1988; Liu and Huang 1998).

A second theme of STC investigations has been the delineation of source regions associated with the various pathways. By computing Lagrangian particle trajectories in general circulation models, it has been shown that the interior pathways originate in the far eastern subtropics, and the western boundary pathways in adjacent regions immediately to the west. In both cases, transit times are of order 10 yr. Parcels that originate still farther west recirculate in the subtropical gyres (Liu et al. 1994; Rothstein et al. 1998; Huang and Liu 1999). The “exchange windows” linking the subtropical and tropical oceans coincide roughly with the high-subduction formation regions of eastern subtropical mode waters (ESTMW) in the NE and southeast (SE) subtropical Pacific (Hautala and Roemmich 1998; Ladd and Thompson 2000; Hosoda et al. 2001; Wong and Johnson 2003). While subduction in these regions supplies the equatorward limbs of the STCs, STC transports reaching the Tropics are determined by the magnitude of low-latitude easterly wind stress rather than by the amount of subduction (Liu 1994; McCreary and Lu 1994). Subducted water in excess of the permitted equatorward transports recirculate in the subtropical gyre.

A further theme of STC investigations has been to quantify the sensitivity of STC transports to changes in wind stress. For example, Liu and Philander (1995) found that STC transport in a general circulation model scales (though not linearly) with low-latitude easterly wind stress, but is insensitive to the strength of the subtropical westerlies as predicted by Liu (1994). Klinger et al. (2002) confirm these sensitivities in steady experiments using a layer model and, in transient experiments, find that pycnocline transport adjusts more slowly than surface Ekman transport to changes in wind stress. Changes in pycnocline transport thus tend to lag changes in equatorial upwelling, which in turn lag variations in surface Ekman transport. Similarly, Nonaka et al. (2002) find that equatorial SST anomalies that accompany off-equatorial Ekman transport variations lag behind by about 2 yr those driven directly by equatorial wind changes.

3. The CCCma coupled model

The results described here are obtained from the CCCma global coupled model CGCM2, which is an evolution of an earlier version CGCM1 described in Flato et al. (2000) and used for climate change simulation (Boer et al. 2000a; Boer et al. 2000b). CGCM2 differs modestly from CGCM1 in its parameterization of ocean mixing and sea ice dynamics as described in Flato and Boer (2001). Long control climate integrations and simulations of global warming for the twentieth and twenty-first centuries have been carried out with both models. The overall climate sensitivity (equilibrium warming for a doubling of CO2) is 3.5°C in both models, and the transient climate response (warming at the time of CO2 doubling) is 1.96° and 1.93°C, respectively. The temperature response patterns are also very similar, especially in the Tropics.

The common atmospheric component is described in McFarlane et al. (1992) and is a spectral model with T32 triangular resolution with an associated 96 × 48 transform grid (3.75° in latitude and longitude) and 10 levels in the vertical. The atmospheric general circulation model (AGCM) has a comparatively sophisticated representation of radiative transfer (including annual and diurnal cycles), surface heat and moisture budgets, and clouds and cloud optical properties. The surface hydrology budget includes a runoff term by which freshwater is transferred from river drainage basins to the ocean at the location of river mouths.

The oceanic component of the model is a version of the Geophysical Fluid Dynamics Laboratory (GFDL) modular ocean model (MOM; Pacanowski et al. 1993). For each grid box of the AGCM’s transform grid of 96 × 48 Gaussian grid points there are four oceanic grid boxes giving an ocean resolution of 1.875° × 1.875° × 29 levels. Ocean mixing is parameterized by uniform vertical and isopycnal diffusion with coefficient values 0.3 × 10−4 m2 s−1 and 1 × 103 m2 s−1, together with the eddy-stirring parameterization of Gent and McWilliams (1990). Sea ice is represented thermodynamically as a single layer, possibly topped with snow, and dynamically using the cavitating fluid rheology of Flato and Hibler (1992). Details of the coupling and initialization procedures are provided in Flato et al. (2000).

The results from a long 1000-yr control simulation and three independent transient climate change simulations from 1900 to 2100 are used in this study. The simulations begin at the nominal date of 1850 and proceed to 2100 with analysis data retained from 1900–2100. The effective greenhouse gas and aerosol forcing used in these simulations follows that of Mitchell et al. (1995) and is a modified version of the Intergovernmental Panel on Climate Change 1992 scenario (Houghton et al. 1996). These forcing scenarios are discussed in Boer et al. (2000b).

4. Pacific overturning variability

The Pacific STC circulations in CGCM2 are evident in Fig. 1, which shows equatorward velocity into a control volume encompassing the equatorial Pacific. Basic STC features are present such as poleward surface Ekman transport, equatorward flow within the pycnocline, and eastward shoaling of the pycnocline in accordance with geostrophy. (Also seen are western boundary currents and flow through a strait representing the Indonesian Throughflow at approximately 1.9°S, 130°E.) To facilitate comparison, pycnocline transports in CGCM2 are quantified in a manner similar to that employed by MZ, who considered transports across 9°S and 9°N. Transports in the model are calculated across the nearest velocity grid latitudes at approximately 9.3°S and 9.3°N. Equatorward transports are integrated from the eastern boundary to approximately 145°E in the Northern Hemisphere and 160°E in the Southern Hemisphere in order to exclude the western boundary currents, visible as strong equatorward flows in Fig. 1. Whereas MZ define the vertical integration limits according to density class, we integrate over depth from 50 m, which excludes the poleward Ekman flow that is dominant in the uppermost layer, to 605 m, which encompasses the deepest portions of the pycnocline. Because both techniques capture the relatively shallow “core” of the STC that dominates transport they should give similar results.1

We adopt a slightly different sign convention than MZ, defining both Southern Hemisphere (PS) and Northern Hemisphere (PN) equatorward pycnocline transports as positive (in MZ PN is negative). Pycnocline convergence thus is defined as PT = PS + PN.

a. Control run

Annual mean equatorward pycnocline transports from the first 200 yr of the 1000-yr control run are shown in Fig. 2a, together with observation-based values from MZ. Results from the ensemble of warming simulations for the years 1900–2100 are also shown. Transports are in Sverdrup units. Mean equatorward transport near 9°S is 14.1 Sv in the control run, compared to the 13.7-Sv average of MZ. Near 9°N, the 14.1-Sv mean equatorward transport in the control run is substantially larger than the 8.0-Sv mean found by MZ. The difference is likely related to the relative weakness in the model of the PV barrier beneath the ITCZ, which constricts the interior pathway near 10°N as discussed in section 2. Whereas the peak of the climatological PV ridge at 160°W on the 25.0 kg m−3 isopycnal surface is 10 × 10−10 m−1 s−1, for example (cf. MZ, their Fig. 1b), the corresponding peak in the model is only 4.6 × 10−10 m−1 s−1. This is due to an unrealistically diffuse thermocline, as is common in coarse resolution models, and to the coarseness of the grid itself, as when climatological fields are averaged to the model grid, the peak weakens from 10 × 10−10 m−1 s−1 to 7.5 × 10−10 m−1 s−1.

The control run transports exhibit natural variability, with standard deviations based on annual mean values of σS = σN = 1.6 Sv for PN and PS and σT = 3.0 Sv for PT (Table 1). Interannual variations of PN and PS are correlated at r = 0.74, so that equatorward transports at 9°N and 9°S tend to strengthen and weaken together. The maximum and minimum annual mean values of PN, PS, and PT differ by more than a factor of 2, and short term variations of nearly this magnitude can occur, as between (nominal) years 1951 and 1953, where PT decreases from 33.0 to 17.8 Sv.

Decadal averages of control run transports are shown in Fig. 2b. Corresponding standard deviations are σN = 0.6 Sv, σS = 0.7 Sv, and σT = 1.2 Sv, and decadal PN and PS exhibit the same correlation, r = 0.74, as for annual means. Maximum and minimum decadal PT differ by 6.9 Sv, considerably less than the 13.0 Sv maximum difference in the four averaging periods of MZ.

b. Warming runs

McPhaden and Zhang (2002) find a decrease of nearly 50% in decadally averaged pycnocline transports from the 1970s to the 1990s. No comparable variation is found in the 1000-yr control run, and here we examine whether anthropogenically induced climate change could be contributing to the observed trend. Indeed, the three warming runs in Fig. 2 exhibit a prominent warming-related decrease, particularly in the twenty-first century. To quantify this decrease, the ensemble mean yearly transports, smoothed by a 10-point boxcar filter, were fit via a least squares procedure to separate linear trends in the twentieth and twenty-first centuries, with the constraint that the trend lines coincide at 2000. This yields an 8% decrease in transport by 2000, and a 46% decrease by 2100, which suggests that anthropogenically induced climate change may be a significant, though not dominant, contributor to the changes noted by MZ.

The level of interannual variability also decreases with global warming as can be seen visually in Fig. 2a. This is quantified by calculating the standard deviation of PT within a sliding 21-yr window, as shown in Fig. 3. The standard deviation exhibits a decline of about 50% between 1900 to 2100, and this decline is steeper in the twentieth century than the 21st century. We show in the appendix that PN and PS are largely coherent and that weak and strong periods of PT variation are the result of PN and PS strengthening and weakening together rather than their being in or out of phase

c. Latitudinal variation of pycnocline transport

Latitudinal structure of pycnocline transport magnitude, variability and anthropogenically induced change is examined in Fig. 4. Figure 4a shows latitudinal structure of mean equatorward pycnocline transport over tropical latitudes in the control run. These transports resemble those inferred from the National Centers for Environmental Prediction (NCEP) ocean model by Huang and Liu (1999) in several respects, including minima near 10°S and 10°N, maxima at low (≲5°) northern and southern latitudes, and strong transport reduction very near the equator. (The modeled transport near 10°N is larger than that deduced by Huang and Liu for reasons discussed in section 4a.) Temporal variations about this mean profile in the control run are shown in Figs. 4b and 4c. The transport variations tend to peak near latitudes 5°S and 5°N where mean transports are largest, and are generally in phase, spanning the entire latitude range while showing no obvious sign of latitudinal propagation. Variations at 15°S and 15°N are comparable to those at 9°S and 9°N, in accordance with results of MZ. Under global warming, Fig. 4c shows reductions in transport and variability over a broad range in latitude.

5. Climate variability and pycnocline transport

This section examines connections between variations in Pacific pycnocline transport and broader patterns of climate variability in view of the hypothesized role of STC variations in driving Pacific decadal variability. Connections between pycnocline transport PT and other climate variables x are quantified in terms of associated regression patterns X(λ, ϕ) as
i1520-0442-18-5-666-e1
by minimizing ϵ2 to give X(λ, ϕ) = and λ, ϕ are longitude and latitude. Regressions indexed separately against PN and PS do not differ substantially from those for PT. We adopt the sign convention that positive X is associated with negative P′T, that is, decreased pycnocline transport as in MZ. The regression patterns X have units of x per Sv. For consistency with MZ, decadal averages are considered.

a. SST regression patterns

Figure 5a shows the regression pattern of decadally averaged SST for the 1000-yr control run. As described above, the values shown correspond to temperature change per Sv weakening of STC transport. The pattern is similar to that of the positive phase of ENSO, with equatorial warming in the eastern and central Pacific extending wedge like into the northeastern and southeastern subtropics, and cooling to the west in a region extending from the central subtropics to the eastern tropical Pacific. Higher latitude effects, such as warming in the Gulf of Alaska and the western Pacific sector of the Southern Ocean, also are evident. This pattern is similar to that of a regression based on annual means, except that extratropical features are accentuated in the decadal case. Qualitatively similar differences between patterns of Pacific interannual and decadal SST variation are seen in observations (Zhang et al. 1997). SST variations in the central and eastern tropical Pacific are of order 0.1°C per Sv decrease in PT, corresponding to a range of about 0.5°C for a typical ±2σT ≈ 5 Sv range of variation of PT (cf. Fig. 2b).

For comparison, Fig. 5b shows the SST regression pattern using the observation-based HadISST 1.1 dataset and PT from the MZ results. Although based on only four approximately decadal averaging periods, Fig. 5b exhibits Pacific SST anomalies having remarkably similar signs, locations and magnitudes as those in Fig. 5a; this SST pattern is similar to the 1990–99 minus 1970–77 differences shown in Fig. 3a of MZ. To provide an indication as to whether the similarities and differences between Figs. 5a and 5b are significant in light of the limited sample considered by MZ, model regressions were performed by sampling the same years as MZ in six consecutive centuries. Each of these six regressions exhibits the main features of Fig. 5a, namely a wedge of warming in the Tropics between the coast of South America and the date line, including a concentration in the central equatorial Pacific not seen in Fig. 5b, and opposing cooling in the central midlatitude North and South Pacific.

In the warming runs, SST variations are decomposed as x = x + x′ = x + x′m + x″ where x is the long-term mean, x′m is a 21-yr running mean of x′, and x″ is variability about the running mean; PT is decomposed similarly. The SST regression pattern that accompanies the gradual PT decrease associated with warming was isolated as in (1) by regressing the running means of SST and PT. The resulting pattern is shown in Fig. 5c, where the contour interval is the same as in Fig. 5a, but the shadings have been shifted to compensate for the overall warming trend. In the tropical Pacific, the SST pattern for x′m in the warming simulation has qualitatively the same spatial pattern as that obtained for x′ for the control run. Higher latitudes, particularly in the North Pacific, exhibit features that are similar to those in the control run, but are accentuated even more strongly relative to the interannual case.

The SST regression pattern corresponding to the variability about the gradually warming climatic mean is obtained by regressing with the departures x″ from the 21-yr running means. These closely resemble the result in Fig. 5a for the control run, and are not shown.

b. Wind stress and sea level pressure

Figure 5a also shows the regression pattern for the control run wind stress τ. As for SST, the pattern is distinctly ENSO like, featuring westerly anomalous tropical winds and southeasterly anomalous winds in the South Pacific convergence zone (e.g., Wallace et al. 1998). The τ pattern is similar to the difference between 1990–99 and 1970–77 wind stresses shown in Fig. 3a of MZ, particularly in the central and western tropical Pacific, although the model result in Fig. 5a shows particularly strong westerly τ anomalies between 10° and 20°N just west of the date line.

The sea level pressure regression pattern in Fig. 5d resembles the Southern Oscillation pattern, with a dipolar shift across the Pacific, centers of anomalously high pressure in the northwestern and southwestern tropical Pacific, and centers of anomalously low pressure in the northeastern and southeastern extratropical Pacific (e.g., Wallace et al. 1998). These anomalous low pressure centers, which occur at somewhat lower latitudes than the observed anomalous pressure centers associated with ENSO, coincide with the cyclonic gyres of anomalous wind stress seen in Fig. 5a.

c. Ekman pumping and meridional velocity

Figure 6 shows the regression pattern for the upwelling velocity curlτ/ρ0f due to Ekman pumping for the control run. It is seen that when PT is weak, wind stress anomalies straddling the equatorial Pacific give rise to anomalous upwelling in both hemispheres. This is in accord with Fig. 3b of MZ, which shows significant shallowing of the pycnocline between 1970–77 and 1990–99 near these regions, in addition to an overall relaxation of pycnocline tilt due to weakened trade winds. McPhaden and Zhang (2002) note that the shoaling of the western Pacific pycnocline from the 1970s to the 1990s, together with anomalous deepening farther east, opposes the ambient geostrophic tilt, consistent with the observed reduction in equatorward pycnocline transport.

Figure 7 shows the regression patterns of meridional velocity against PT at 9.3°S and 9.3°N. The pycnocline transport changes are seen to be concentrated in the western Pacific, in regions where mean pycnocline velocities are relatively small (cf. Fig. 1). The symbols in Fig. 7 mark regions of high Ekman pumping–induced upwelling and correspond to similar markings in Fig. 6, indicating a close association between changes in meridional transport and wind stress. Decreased geostrophic convergence is compensated by decreased Ekman divergence, and by anomalous western boundary convergence. The tendency for anomalous western boundary convergence to oppose that in the pycnocline is discussed by Springer et al. (1990), and was noted in a data-forced ocean circulation model by Lee and Fukumori (2003), who found western boundary current variability to be concentrated in the uppermost 200 m, much as in Fig. 7.

d. Surface fluxes

Regression patterns of anomalous surface heat fluxes also are ENSO like. Though not shown here, these patterns closely resemble the modeled response to anthropogenic forcing shown in Fig. 4 of Yu and Boer (2002). For example, anomalous shortwave fluxes in the central and western equatorial and subtropical Pacific are negative due to increased and brighter cloudiness that accompanies the warmer SSTs in these regions. Anomalous longwave surface fluxes are such as to warm the surface in these regions, partially offsetting the decreased shortwave heating. Anomalous latent heating in the central equatorial Pacific acts to cool the surface due to increased evaporation associated with warmer temperatures, and anomalous sensible heating is weak and generally acts to warm the surface (i.e., decreasing heat flux from the surface), due in part to reduced easterly winds.

Yu and Boer (2002) found that convergence of oceanic heat flux was an important contributor to the modeled warming of the central equatorial Pacific under anthropogenic forcing. Such convergence may be expected to accompany variations in PT, and its nature and influence are investigated in section 6.

e. Interannual variability

The regression patterns linking modeled variations in decadal means of PT and those of SST, sea level pressure, wind stress, wind stress curl, and surface heat flux resemble those of ENSO. Shorter time-scale relationships in terms of annual means of PT and other quantities are now considered.

Figure 8 shows a 100-yr record of annual mean PT in the control run, together with SST in the Niño-3 region (5°S–5°N, 90°–150°W; note the inverted scale for Niño-3). The two quantities are highly anticorrelated, with r = −0.89. Individually, r = −0.74 for PN and −0.92 for PS. The lagged cross correlations of these quantities are shown in Fig. 9. In each case, the correlation function is largest (negative) at zero lag. The peak values, if estimated as the extrema of parabolic fits to the three points nearest the annually-resolved peaks, occurs with PT leading by 0.8 months, PN leading by 1.9 months, and PS lagging by 0.3 months (Table 2).

Figure 8 conveys the impression that PT undergoes more high-frequency variability than Niño-3. This is borne out in power spectra (not shown), which indicate that PN in particular exhibits more high-frequency power at periods ≲4 yr than Niño-3. This result is consistent with the PT anomalies being primarily wind driven, as discussed in the next section, and with a tendency for modeled and observed low-latitude wind stress anomalies to have higher frequency content than equatorial SST anomalies at interannual to decadal periods (e.g., Wittenberg 2004). Figure 8 also suggests that correlations between PT and Niño-3 diminish at higher frequencies. This tendency is seen in the coherency spectra of Figs. 10a–b, which show that PN and PS are highly anticorrelated with Niño-3 at periods ≳8 years, especially in the case of PS. Equatorward transports PS and PN are positively correlated at all frequencies (Fig. 10c), though less so at higher frequencies.

6. Variability of STC heat transport

In the previous two sections, natural and anthropogenically driven variations in equatorward pycnocline transport in CGCM2 were diagnosed and shown to be closely associated with ENSO-like patterns of climate variability. This section examines physical connections between PT and ENSO-like variability that arise through variations in heat transported by the STC.

STC dynamics play a significant role in the modulation of tropical heat transports. On interannual time scales, westerly trade wind anomalies rapidly (on an inertial time scale) decelerate surface Ekman flows, leading to anomalous convergent heat flux in the surface layers. Because compensating adjustments to the underlying geostrophic circulation occur only after Rossby waves driven by anomalous wind stress curl reflect from the western boundary as equatorial Kelvin waves, heat builds up at the equator until adjustment is achieved roughly six months to a year later (Springer et al. 1990), after which the accumulated heat is released. Because such wave adjustments also cause the El Niño warming itself, this anomalous divergence tends to coincide with the positive phase of El Niño, as found observationally by Sun and Trenberth (1998). In the model, interannual variations in Ekman divergence and pycnocline convergence across 9.3°N and 9.3°S are related in just such a manner (Fig. 11 and Table 2), exhibiting a peak cross correlation of 0.71 when the former leads by 0.8 yr, as estimated from annually averaged data using the method described in section 5e.

For interdecadal changes, the picture is quite different because the delay between anomalous Ekman divergence and pycnocline convergence is much smaller relative to the time scale of variation, as illustrated in Fig. 6 of Klinger et al. (2002). Hence adjustment of the STC to anomalous τ is more nearly in phase, so that anomalous low-latitude westerlies are accompanied by overall slowing of the STC. This should reduce the transport of heat away from the equator by the STC, and indeed at the very long time scales associated with global warming such an anomalous convergence has been noted (Yu and Boer 2002), in contrast to the El Niño correlated convergence found by Sun and Trenberth (1998).

The relation between interdecadal changes in modeled equatorward pycnocline transport and heat transport is examined by calculating advective heat fluxes into a control volume bounded by latitudes 9.3°N, 9.3°S and a section at 1.9°S across the modeled Indonesian Throughflow. In the control run the mean throughflow volume flux is 15.1 Sv exiting the control volume, and is largely compensated by 16.1 Sv entering the control volume at 9.3°S (Fig. 1). Balancing this net volume import is a mean northward export of 1.0 Sv across 9.3°N. Net heat flux convergence h into the control volume is computed as
i1520-0442-18-5-666-e2
where υ is meridional velocity with the sign convention that velocities into the control volume are positive; T is potential temperature; dAi refer to bounding surfaces where N, S and I refer to the northern, southern, and Indonesian throughflow surfaces described above, each extending from the ocean surface to the bottom; and ρ = 1026 kg m−3 and cp = 3996 J m3 kg−1 K−1 are standard reference values for density and specific heat. Because the flux f = ρcpυT depends on the choice of temperature scale, we follow the usual practice of referring to f as a “temperature flux” and expressing temperature in degrees Celsius. By contrast, h does not depend on this choice due to the vanishing of 〈υ〉, and can be considered a heat transport. In the control run, h = −1.23PW, corresponding to a net oceanic heat export from the control volume; this value is comparable to heat exports from the low-latitude Pacific inferred from hydrographic sections (Ganachaud and Wunsch 2000) and a data-constrained circulation model (Stammer et al. 2003).

The variability of h in the control run is characterized by an interannual standard deviation of 0.17 PW, and an interdecadal standard deviation of 0.024 PW (Table 1). Regression patterns of decadal mean temperature flux f(λ, ϕ, z, t) against decadal mean h(t) for each of the three bounding surfaces are plotted in Fig. 12, which shows that positive h′—that is, anomalous heat import—is associated with anomalous convergent temperature flux in the surface layers at 9.3°N and 9.3°S, consistent with reduced Ekman divergence due to weakened trade winds. Anomalous divergent heat flux in the interior pycnocline is concentrated where equatorward pycnocline velocities are most variable (cf. Fig. 7). This anomalous divergence is opposed by anomalous western boundary current convergence, much as was found on interannual time scales by Springer et al. (1990). In the Indonesian Throughflow, positive h′ is associated with strong anomalous heat flux into the control volume.

The mean temperature flux f = across 9.3°N is shown in Fig. 13a. Decomposing anomalous temperature flux f ′ = ff as
i1520-0442-18-5-666-e3
and its covariance with heat flux convergence h as
i1520-0442-18-5-666-e4
we plot regression patterns versus h′ of the υT and υT ′ temperature flux components in Figs. 13b–c. The υT component dominates the υT ′ component by at least an order of magnitude (note the factor of 10 difference in contour interval between Figs. 13b and 13c). The υT ′ contribution is an additional order of magnitude smaller and is not plotted. This comparison is to some extent arbitrary because the magnitude of spatial variations in υT depends on the temperature scale adopted; as discussed above, we employ the conventional practice of expressing T in degrees Celsius. However, one might equally plausibly express T in K, in which case the differences between Figs. 13b and 13c would be accentuated.
To obtain a more physical comparison of υT and υT ′ effects, we decompose h′ = hh as in (3):
i1520-0442-18-5-666-e5
where angle brackets denote integration over lateral boundaries of the control volume as in (2). It can be shown that hυ = ρcpυT〉 is independent of the zero of the temperature scale by representing T as an average TA over the bounding surfaces of the control volume, plus a remainder T+ that varies spatially but has zero mean: then 〈υT〉 = 〈υ〉〈TA〉 + 〈υT+〉, and the desired result follows from 〈υ′〉 = 0 and the lack of dependence of T+ on the zero of the temperature scale.
Figure 14 shows 100-yr time series of the components of hυ, h′T and h′υT based on decadal averages (lower panel) and annual averages (upper panel). The magnitudes of hυ, h′T h′υT have roughly the same ordering as their spatially dependent counterparts (cf. Fig. 13), with respective standard deviations of 0.173, 0.017, and 0.006 PW under annual averaging and 0.033, 0.007, and 0.005 PW under decadal averaging (Table 1). To further quantify this ordering, temporal variances are computed as
i1520-0442-18-5-666-e6
where h′res, which represents terms of third and fourth order in the primed quantities, is calculated as a residual. Fractional contributions to based on annual (decadal) averages are 1.014 (1.170) for h′2υ, 0.010 (0.061) for h′2T, −0.021 (−0.255) for , and −0.003 (0.024) for . Note that the variance of hυ exceeds that of h′ because of the negative covariance between hυ and h′T.

The warming runs exhibit a decline in mean heat export from the control volume, in accordance with the anomalous convergence of ocean heat transport under global warming found by Yu and Boer (2002), and consistent with the gradual slowing of STC circulation discussed in section 4b. The decline in heat export is approximately 2% at 2000 and 17% (or ≈0.2 PW) at 2100. To ascertain the presence of any secular changes in the above fractional contributions to , the above procedure was repeated using averages computed within a sliding 21-yr window. No obvious secular changes to these balances were evident.

In the above calculations T ′ is computed at fixed depth, and therefore includes contributions both from temperature anomalies on isopycnals and from vertical migration of the thermocline. The relative magnitudes of these contributions can be assessed by comparing (i) T regressed against h and then interpolated to mean isopycnal surfaces, with (ii) T on the same (time-dependent) isopycnal surfaces, regressed against h. Such a comparison for the σθ = 24.5 surface in the tropical midthermocline is shown in Fig. 15. It is seen that depth-regressed T ′ (Fig. 15a) mainly reflects ENSO-like changes in the tropical thermocline: when h′ is positive, so that heat export from the control volume is reduced, STC transports are low (cf. Table 2) and ENSO-like conditions prevail (Fig. 5), with a tropical thermocline that is deeper leading to warmer temperatures in the eastern Pacific, and shallower leading to cooler temperatures in the western Pacific. However, when T ′ is computed following the isopycnal (Fig. 15b), contributions from vertical migration of the thermocline are eliminated. The remaining signal consists primarily of cold anomalies that appear to have been advected westward and equatorward from subduction regions in the subtropical North and South Pacific. The Southern Hemisphere anomalies are stronger as they approach the equator than the Northern Hemisphere anomalies, as in ocean models forced by observed fields (Giese et al. 2002; Yang et al. 2004). Overall, the σ-regressed anomalies are substantially weaker than the depth-regressed anomalies, especially in the eastern half of the basin where geostrophic υ is largest. Thus, contributions to h′ strictly from T anomalies on isopycnals—that is, via the Gu and Philander (1997) mechanism—are likely to be as small or smaller than the already small vT ′, in Figs. 1314.

Overall, the clear implication by all measures is dominance of the vT mechanism—that is, of anomalous velocities—in STC heat transport variability.

7. Discussion

In this section the questions posed in the introduction are revisited in light of the above results. First, are the STC transport variations found by MZ a result of natural variability, anthropogenic forcing, or both? As discussed in section 4a, the interdecadal changes in equatorward pycnocline transports found by MZ are considerably larger than typical interdecadal changes in the coupled model control run. However, at least two factors complicate this comparison. First, the level of ENSO-like variability on decadal time scales is moderately less in the model than in the historical record. Quantitatively, the standard deviation of decadally averaged Niño-3 over the 1000-yr control run is 0.146°C, compared to the observed value of 0.168°C based on decadal averages for 1860–1999 of Niño-3 from the blended Kaplan et al. (1998) and NCEP analyses. Variability in recent decades has been larger still (mainly because of an upward trend since the mid-1970s), and the Niño-3 standard deviation for the four averaging periods considered by MZ is 0.242°C. Furthermore, interannual ENSO variability in the model is substantially weaker than observed, and if processes operating on those time scales influence STC variability this could further affect the comparison. The second complicating factor is that the shortness of the MZ record makes it difficult to determine if the variability found by MZ is “typical” or a statistical sampling fluctuation.

Figure 16a compares modeled and observed PT variability in terms of histograms of the PT difference between consecutive decadal averaging periods (neglecting the fact that the MZ averaging periods are not all contiguous or of the same length):
i1520-0442-18-5-666-e7
where PT,i denotes the ith decadal average. To allow for the lower level of decadal ENSO-like variance as described above, the model δP(1)T values were multiplied by 1.66, the ratio of decadal Niño-3 variance for the periods considered by MZ to that for the control run. Figure 16a shows histograms of δP(1)T, based on sample sizes of 99 for the control run (thin lines) and 3 for the MZ results (circles). In addition, influences of global warming are included by calculating δP(1)T values for 1950–2000 in the three warming runs; thick lines represent the resulting sample of 12. Two of the consecutive MZ differences are large with respect to those found in the model, even when the latter are scaled up as described above and effects of warming are included. However, several of model δP(1)T are of comparable magnitude to the MZ values and one is larger, suggesting that model–data differences could be the result of MZ having sampled a period of unusually large PT variability, albeit one with precedent in the 1000-yr record of the control run. However, doubt is cast on this interpretation by Fig. 16b, which shows histograms of
i1520-0442-18-5-666-e8
which gauges PT changes across 20-yr intervals. The sample size is only 2 for the MZ results, but one of these values is an outlier that has no counterpart in the model’s 1000-yr control or global warming records. This suggests either that PT variability in the model differs from that in nature, or that the ∼50% decrease in PT between the 1970s and the 1990s was an unusual event recurring only on time scales of many millennia.

Second, are STC heat transport variations dominated by advection of temperature anomalies by mean velocity (vT ′) or by velocity anomalies advecting mean temperature (vT)? In section 6 it was found that the vT effect is easily more effective than the vT ′ effect in modulating modeled heat transports into the tropical Pacific. This dominance is approximately a factor of 10 on interannual time scales and a factor of 5 on interdecadal time scales. From Fig. 13b it is evident that positive anomalies in convergent heat transport h (i.e., reductions in oceanic heat export from the equatorial Pacific) due to the vT mechanism are associated with anomalous Ekman convergence and anomalous geostrophic divergence, and thus with reduced STC overturning.

Third, we ask if STC transport variations play an active or a passive role in the generation of decadal climate variations. STC transport variations can be considered to play an active role if they induce significant variability in tropical heat content. We estimate the contribution of modeled STC variations to anomalous decadal heat content variations by assuming that STC water reaching the equator via the interior pycnocline subsequently upwells and is advected poleward in the surface layer, a picture generally supported by investigations of such pathways (e.g., Fukumori et al. 2004). The estimated mean heat transport into the control volume of section 6 due to the STC is then ρcp(TinTout) = −0.89PW, where = 28.2Sv is the mean pycnocline convergence and TinTout = −7.22oC is the transport-weighted mean temperature of water entering the volume and contributing to , minus that of the surface transport exiting the volume. This net heat export is about 70% of the overall mean heat export of −1.23 PW. To estimate the fractional contribution of the STC to anomalous heat flux convergence h′ via the vT mechanism, we must replace by P′T = −29.9Sv PW−1 ,the regression of PT on h′, and difference the mean temperatures of the anomalous STC inflows and outflows, which are distributed differently than the mean STC flows (cf. Figs. 1 and 7). Such a procedure yields TinTout = −6.43oC and ρcpP′T(TinTout) = 0.79 PW PW−1. Similarly, the fractional contribution of the STC to h′ via the vT ′ mechanism is estimated as ρcp(T ′inT ′out) = −0.06PW PW−1, where T ′inT ′out = −0.51oC is the difference between the transport-weighted mean temperature anomalies (determined from regression of T on h′) of the mean STC inflow and outflow. Thus, the vT ′ effect is much smaller than and opposes the vT effect, as for the full transports of section 6, and the net fractional contribution of the STC to h′ (ignoring the vT ′ effect) is ∼70%, comparable to the STC fractional contribution to the mean.

Does this STC-related anomalous heat flux convergence contribute significantly to tropical heat content anomalies? Defining heat content H as the integral of ρcpT over the control volume, we have
i1520-0442-18-5-666-e9
where f ′ is the anomalous flux of heat into the control volume through the ocean surface. The correlation coefficient of decadal-mean H with h′ is 0.64, and with f ′ is −0.65, so that h′ drives anomalous H whereas f ′ is damping. Thus the STC-related heat transports, which compose the bulk of h′, are a primary driver of tropical heat content anomalies in the sense that reduced STC transport induces overall warming of the control volume. To estimate the magnitude of this warming, we suppose that anomalous heat content is concentrated in the uppermost 300 m of the control volume, where almost all of the temperature variability occurs. Taking the STC contribution to H′ as 3.2 × 1021 J (70% of its interdecadal standard deviation of 4.4 × 1021 J), the associated decadal standard deviation of T in the upper ocean is estimated as 0.08°C. This is similar in magnitude to the increase in tropical SSTs associated with a 1 standard deviation decrease in PT (cf. Table 1 and Fig. 5a), pointing to a significant role for STC transports in driving decadal SST variability in the tropical Pacific.

On longer time scales, STC changes appear to play a significant role in the quasi-steady El Niño-like response to global warming found by Yu and Boer (2002). They note that one of the primary contributors to the enhancement of tropical SSTs is strongly convergent anomalous ocean heat flux near the equator. Such a tendency is consistent with the gradual decline in pycnocline transports shown in Fig. 2, which leads to decreased heat export from the tropical Pacific as discussed above.

8. Summary

This study has examined Pacific STC variability in a coupled climate model in light of the dramatic interdecadal changes in Pacific STC overturning deduced by MZ. In the 1000-yr control run, STC pycnocline transports are found to be highly correlated with ENSO-like variations in climate, both on interannual and interdecadal time scales. Interdecadal variations in modeled transports are occasionally as large as the changes found by MZ, although there is no modeled bidecadal variation (i.e., between decadal means separated by 20 yr) as large as that found by MZ, even when the lower level of decadal tropical SST variability in the model is factored in.

In model runs that include anthropogenically forced climate change, STC transports decline (relative to the control run) 8% by 2000, and 46% by 2100. Although in the present epoch this effect is too small to account for the nearly 50% decrease between the 1970s and 1990s found by MZ, this result does suggest that warming may have contributed to the observed change. The pattern of SST change that accompanies forced changes to STC transport under global warming consists of an El Niño-like pattern similar to that associated with unforced, or “natural” STC variability (Fig. 5a), superimposed on an overall warming trend (Fig. 5c). This is in accord with development of a positive El Niño–like pattern of Pacific SST change under global warming as described by Yu and Boer (2002).

The main influence controlling pycnocline transport changes in the model appears to be local variation of wind stress: as Figs. 6 and 7 show, the accompanying meridional velocity changes are concentrated at longitudes where Ekman pumping anomalies are largest. Thus, STC variations in the model appear to be a response to anomalies in low-latitude easterly winds. This atmospheric influence is conveyed to the equatorial upper ocean via STC transport variations, which in the model significantly modulate tropical heat content via the vT mechanism.

Acknowledgments

The authors are indebted to J. Christian, M. McPhaden, B. Yu, D. Zhang, and two anonymous reviewers for helpful comments and suggestions.

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APPENDIX

Effect of Warming on Pycnocline Transport Variability

We examine here the gradual decline in interannual PT variability in the warming runs, evident in Figs. 2 and 3. In Fig. 3 this variability is measured by the variance σ2T of annual mean PT calculated in a sliding 21-yr window. In terms of the variances σ2N and σ2S associated with PN and PS, σ2T can be written
i1520-0442-18-5-666-ea1

Whether the decline in σT is caused by changes in σN and σS or in r is addressed in Fig. A1, which plots σ2T against σ2N + σ2S. Realizable values of σ2T are bounded by heavy solid lines having slopes 2 and 0. If r > 0, then from (A1) the PN and PS variations add constructively, and σT lies above the dotted r = 0 line. If r < 0, then PN and PS variations add destructively, and σT lies below this line. If r and σN/σS remained constant in time, then all points would lie along a straight line intersecting the origin. Conversely if changes in σ2T were caused by changes in r alone (i.e., constant σN and σS), then the points would lie along a vertical line. The essential coherence of the STC transports as a tropical transequatorial phenomenon is clear from the fact that r is always positive; that is, the north and south transports are never in opposition during a 21-yr period. Moreover, the correlations are largest when σ2T is large, and smallest when σ2T is small. In other words, when equatorward STC convergence varies strongly during a 21-yr period, correlation is high implying that both PN and PS strengthen and weaken together and vice versa. Hence, both of the aforementioned effects—that is, changes in σ2N + σ2S and changes in r—contribute to reductions in σ2T. From Fig. A1 it is seen that changes in r effect changes in σ2T that are less than a factor of 2, since in all instances r remains positive, whereas σ2N + σ2S ranges over more than a factor of 5. The amplitude effect is thus the main contributor to σT variability.

The preceding analysis assumes constant σN/σS ≈ 1, as in the control run. In the warming runs there is a tendency for σN/σS to increase from unity in the twentieth century to ≈1.4 by late in the twenty-first century. From (A1) it follows that this tendency reduces σ2T from its maximum realizable value σ2max ≡ 2(σ2N + σ2S) at most (for r = 1) by a factor σ2T/σ2max = ½ + (σN/σS)/[1 + (σN/σS)2]. This implies changes of <5% in the present case, and is therefore a small effect.

Fig. 1.
Fig. 1.

Sections of upper-ocean mean equatorward velocity υ for the control run, across 9.3°N, 9.3°S, and the modeled Indonesian Throughflow at 1.9°S

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 2.
Fig. 2.

(a) Annual mean equatorward pycnocline transports PN and PS across 9.3°N and 9.3°S for the control run (thin lines) and the three warming runs (thick lines). (b) Decadal mean transports for the control run (thin lines) and one warming run (thick lines). The observation-based results of MZ for 1956–99 are indicated in both panels

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 3.
Fig. 3.

Standard deviations for PT, computed in a sliding 21-yr window. Thin curves represent individual warming runs, and the thick curve the ensemble mean. The solid lines represent a least squares piecewise linear fit to the ensemble mean

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 4.
Fig. 4.

(a) Mean control run equatorward pycnocline transports at latitudes between 20°S and 20°N; (b) transport anomalies about this mean for the control run; (c) as in (b), but for the warming run

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 5.
Fig. 5.

Linear regression patterns for decadally averaged PT and (a) SST and τ for the control run; (b) SST, based on observational results of MZ and the HadISST 1.1 dataset; (c) SST and τ for a warming run; (d) mean sea level pressure for the control run. Units are °C, N m−2, and kPa per Sv decrease in PT

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 6.
Fig. 6.

Control run regression pattern for Ekman pumping–induced upwelling. The symbols mark longitudes of high anomalous upwelling at 9.3°S and 9.3°N where PS and PN are computed. Large values within ±5° of the equator are suppressed

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 7.
Fig. 7.

Regression pattern for equatorward velocity against PT on surfaces at 9.3°N, 9.3°S and 1.9°S, as in Fig. 1. The symbols represent longitudes where anomalous Ekman pumping–induced upwelling is especially large, as in Fig. 6

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 8.
Fig. 8.

Annual mean PT (thin) and Niño-3 (thick) for 100 yr of the control run. Note the inverted scale for Niño-3

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 9.
Fig. 9.

Lagged cross correlations: (a) PT vs Niño-3; (b) PN (solid) and PS (dashed) vs Niño-3. Lags are relative to Niño-3. Note the inverted scale

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 10.
Fig. 10.

Coherency spectra of (a) PN vs Niño-3; (b) PS vs Niño; (c) PN vs PS. Raw spectra have been smoothed across 20 frequency bins. Note the inverted scale for (a) and (b)

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 11.
Fig. 11.

Lagged cross correlation of Ekman divergence vs pycnocline convergence PT across 9.3°N and 9.3°S. Lag is relative to PT

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 12.
Fig. 12.

Regression pattern for equatorward temperature flux ρcpυT into the equatorial control volume, against net heat transport h into the volume

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 13.
Fig. 13.

For the control run, (a) mean equatorward temperature flux ρcpυT across 9.3°N, and corresponding regression patterns of temperature flux against h arising from (b) υT, and (c) arising from υT ′

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 14.
Fig. 14.

Components of (a) annual mean and (b) decadal mean heat transport h into the equatorial control volume, corresponding to υT (solid), υT ′ (dashed), and υT& prime; (dotted), for 100 yr of the control run

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 15.
Fig. 15.

(a) Regression of T with anomalies h′ of heat transport into the control volume, plotted on the mean σθ = 24.5 isopycnal surface. (b) Regression following the σθ = 24.5 surface of T with h′. Decadal means are considered in each case. Here, T anomalies in the former instance include contributions due to vertical migration of the thermocline, whereas in the latter they reflect T anomalies propagating along the isopycnal

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Fig. 16.
Fig. 16.

(a) Histogram of differences between successive decadal averages of pycnocline convergence PT for the control run (thin), warming runs for 1950–2000 (thick), and MZ results (circles); (b) as in (a), except differences are across 20-yr intervals

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

i1520-0442-18-5-666-f21

Fig. A1. Values of σ2T computed in a sliding 21-yr window and plotted against σ2N + σ2S for one warming run. Thick lines indicate maximum and minimum realizable values of σ2T for given σ2N + σ2S

Citation: Journal of Climate 18, 5; 10.1175/JCLI-3282.1

Table 1.

Standard deviations of annual and decadal time series for the 1000-yr control run. Pycnocline transports PT, etc., are defined in section 4; anomalous heat transports h′, etc., in section 6; and heat content H in section 7

Table 1.
Table 2.

Correlations between pairs of annual and decadal time series for the 1000-yr control run. Lags of peak |correlation| for the annual case are determined by quadratic polynomial interpolation

Table 2.

1

 This correspondence was tested by repeating the transport calculation using the MZ method for the first 200 yr of the model run. The mean isopycnal-based transports were found to be 12% smaller than the depth-based transports in the Northern Hemisphere, and 7% smaller in the Southern Hemisphere, whereas the correlation coefficients for the isopycnal- and depth-based time series were >0.98 in the Northern Hemisphere and >0.99 in the Southern Hemisphere.

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