1. Introduction

The increase in atmospheric concentrations of CO₂ and other greenhouse gases (GHGs) impacts the climate system significantly. The ocean plays a major role in determining the warming rate induced by GHGs and shaping its spatial pattern (Hoffert et al. 1980; Bryan et al. 1982, 1988; Thompson and Schneider 1982; Harvey and Schneider 1985; Schlesinger et al. 1985; Stouffer et al. 1989; Power and Hirst 1997; Manabe and Stouffer 2007). The climate response to radiative forcing is delayed by the ocean owing to its enormous heat capacity. Meanwhile, the heat absorbed by the ocean prolongs the warming effect on climate.

Although GHG increase is nearly uniform in space, pronounced spatial variations emerge in the sea surface temperature (SST) response. The magnitude of spatial deviations is as large as the tropical-mean value (Xie et al. 2010). Furthermore, tropical annual rainfall changes follow the pattern of SST warming, consistent with the hypothesis that rainfall increases where SST warming exceeds the tropical mean value (Xie et al. 2010; Lu and Zhao 2012; Chadwick et al. 2013a). Chadwick et al. (2013a) analyzed tropical precipitation and atmospheric circulation changes in models from phase 5 of the Coupled Model Intercomparison Project (CMIP5) (Taylor et al. 2012) and pointed out that part of the dynamical contribution (the weakening circulation) opposes the thermodynamic contribution to tropical rainfall change, rendering the SST warming pattern effect prominent. The SST pattern is also found to be important in explaining both the multimodel ensemble-mean distribution and intermodel variability of rainfall change (Ma and Xie 2013). Observations suggest that the Walker circulation slowdown for the past six decades is driven by the SST warming pattern of the tropical Indo-Pacific Oceans (Tokinaga et al. 2012). Modest changes in the tropical Pacific may impact the global climate prominently (Karnauskas et al. 2009).

Wind–evaporation–SST (WES) (Xie and Philander 1994) feedbacks are important for the tropical SST pattern (Xie et al. 2010; Lu and Zhao 2012). In the extratropics, ocean heat transport is influential on SST pattern formation mainly through ocean circulation change (Xie et al. 2010). The dominant mechanism for temperature pattern change may differ at different stages of global warming. Over the tropical Pacific, surface heat flux adjustments dominate the surface warming pattern during the transient stage, while horizontal advection is more important during the equilibrium stage (Yang et al. 2009). Indeed, the slow evolution of ocean currents and the thermohaline circulation in response to global warming may lead to a time-varying spatial distribution in surface warming that differs from the equilibrium response (Manabe et al. 1991). This study examines the time-dependent response of SST with a focus on ocean dynamical effects.

Global-mean surface air temperature (SAT) response to the radiative forcing shows clearly short and long time scales in the atmosphere–ocean general circulation models (Olivié et al. 2012). For an abrupt CO₂ doubling, the global-mean SST displays at least two prominent time scales: the fast response of the ocean mixed layer (OML) and the slow response of the deeper ocean (Dickinson 1981; Manabe et al. 1990). The time scale of the former is several years, while the latter is hundreds of years or longer (Stouffer 2004). Jarvis (2011) revealed a third, shorter time scale to the ocean response of just over one year that regulates the global-mean surface temperature in a climate model. Note that fast and slow responses in the ocean are different from those in the atmosphere (Andrews et al. 2010).

Held et al. (2010) isolate the fast and slow components of global warming experimentally by returning GHG forcing abruptly to the preindustrial level. The response of surface temperature shows an initial fast exponential change (fast component) and leaves behind a residual (slow component) that evolves slowly. The two components display distinct spatial patterns. While successful, this method requires costly numerical experiments using coupled climate models. The formation mechanisms and climate impacts of the spatial patterns of the fast and slow components have not been investigated.

The present study examines the time-dependent response of SST to global warming with a focus on geographic distribution. The effects of the SST pattern on the atmosphere are also investigated. Our study is mainly based on the Geophysical Fluid Dynamics Laboratory (GFDL) Climate Model, version 2.1 (CM2.1), CO₂ quadrupling experiment (1%4×CO₂). We show that spatial variations in SST slightly decrease after the radiative forcing is stabilized, while the global-mean SST continues to increase. We develop a diagnostic method to divide the evolution of SST into fast and slow responses. The method is then applied to all coupled climate model simulations, and its validity is confirmed by the agreement with the experimental results of Held et al. (2010) and our analysis of the representative concentration pathway 4.5 (RCP4.5) extension experiment in CMIP5. The fast and slow response of SST shows distinct patterns and displays opposite zonal mean and horizontal structures in most oceans. The atmospheric circulation and deeper ocean are also found to display distinct patterns between the fast and slow response. The pattern formation mechanisms, especially ocean dynamical effects, are investigated. Furthermore, we examine the influence of SST patterns on precipitation in CMIP5 and show that the tropical annual precipitation change follows the SST warming pattern in both the fast and slow response. The present study extends previous ones of fast and slow response with a close look into ocean–atmosphere patterns in space and by developing a method that can be applied diagnostically to any long climate change simulation.

The rest of the paper is organized as follows. Section 2 describes the model simulations. Section 3 discusses the physical basis so as to isolate the fast and slow response based on evolution of the global-mean response. Sections 4 and 5 present spatial patterns of the surface response and vertical structure of the ocean temperature response, respectively. Sections 6 and 7 analyze the SST responses and their effect on precipitation in the CMIP5 multimodel ensemble simulations, respectively. Section 8 is a summary.

2. Models

The output of preindustrial control and 600-yr 1%4×CO₂ experiments of CM2.1 is analyzed. In the latter, CO₂ is increased 1% yr⁻¹ from the preindustrial level to quadrupling that at year 140 and held constant thereafter. The atmospheric component of CM2.1, AM2.1, builds on a finite volume atmospheric dynamical core and has a resolution of 2° latitude × 2.5° longitude. The ocean component, OM3.1, has a resolution of 1° latitude × 1° longitude with meridional grid spacing decreasing to ⅓° toward the equator. It has 50 vertical levels, 22 of which are in the upper 220 m. A detailed description of CM2.1 is provided by Anderson et al. (2004) and Delworth et al. (2006).

We also use simulations from nine coupled climate models (Table 1) in CMIP5 for a multimodel perspective. These nine models are selected because their RCP4.5 simulations extend to 2300, long past the radiative forcing stabilization. Both historical (twentieth century with all forcing for 1850–2005) and the RCP4.5 (2006–2300, approximately with a radiative forcing of 4.5 W·m⁻² around year 2100) simulations are used. The spatial resolution varies among models. To facilitate comparison, we interpolated all model output onto a common grid of 2.5° latitude × 2.5° longitude. For each model only one member run (r1i1p1) is analyzed.

Table 1.

List of the nine models from CMIP5 analyzed in this study.

3. Physical basis and global-mean response

a. Physical interpretation of the fast and slow response

Consider a simple two-box model to help understand the global-mean SST response on fast and slow time scales (Gregory 2000; Held et al. 2010):

for the mixed layer

for the deeper ocean

Here is the global-mean SST change, the deeper ocean temperature change, the imposed climate forcing, the SST damping rate, the mixing coefficient between the ocean mixed layer and deeper ocean, and and are the heat capacity of the OML and deeper ocean, respectively. The deeper-ocean response is much reduced because ≫ (Gregory 2000).

A quasi-equilibrium state of the OML can be achieved when a gradual radiative forcing on a time scale longer than the fast OML adjustment time is imposed. For that we can neglect the term involving and thus obtain

The SST change, , at any time is the sum of two terms: the fast OML adjustment to the radiative forcing change

and the slow evolution of the deeper ocean

Substituting (3) into (2) yields the slow evolution equation for the deeper ocean:

The response time scale of the deeper ocean

is far greater than that of the OML, . The equilibrium state of the deeper ocean temperature is achieved when :

The deeper ocean warming is mainly through mixing and ventilation, which are represented by (the mixing coefficient between the OML and deeper ocean). In reality, varies geographically, for example, large in upwelling regions (Clement et al. 1996). Large acts to damp the fast component of the SST response, causes more deeper ocean warming, and enhances the slow component, while small has the opposite effect. As a result, the geographic distribution of can create spatial variations in SST change.

We consider a simple radiative forcing pathway: it gradually increases (t > 0) and then stabilizes at time t_c. In the first epoch, the increase in is dominated by the fast component. In the second epoch (t > t_c), increases only due to the slow component. Figure 1 shows the temporal variation of the global-mean SST and its fast and slow components based on the preindustrial control and 1% yr⁻¹ CO₂ increase to doubling (1%2×CO₂) experiments. In the 1%2×CO₂ run, while CO₂ concentration stabilizes after 70 years, the eventual equilibrium state is achieved in thousands of years (Stouffer 2004). For our two-box model, the equilibrium SST response to CO₂ doubling is 2.2°C, with = 1.7 and = 2 W m⁻² K⁻¹. For t < t_c, the SST change is mainly due to the fast component,

For t > t_c, the slow component T_s dominates further changes in SST:

In the first epoch, the OML heats the deeper ocean and evolves much slowly than , resulting in an increase in ocean stratification (). When t > t_c, with the stabilization of the radiative forcing, warms faster than , acting to warm SST gradually. As a result, the sign of the heat flux change between the OML and deeper ocean is downward in the first epoch and turns upward in the second epoch. We expect that SST warming will display opposite spatial structures between the two stages due to the sign reversal of the subsurface heat flux change. This transition is especially large where is large, causing the SST pattern to reverse sign significantly between the two stages.

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Schematic for temporal variations of global-mean SST change (°C): its fast and slow components in the 1%2×CO₂ run with respect to the preindustrial control run, with = 1.7 and = 2 W m⁻² K⁻¹. The thicknesses of the mixed layer and deeper layer are chosen to be 50 and 3300 m, respectively.

Citation: Journal of Climate 27, 1; 10.1175/JCLI-D-13-00297.1

We adopt a convenient relationship to diagnose the ocean storage/heat transport effect on SST (), which is balanced by the net surface flux to first order: (Xie et al. 2010).

b. Global-mean response

Figure 2 displays near-global (60°S–60°N) annual mean changes of several variables in the 1%4×CO₂ experiment, referenced to the preindustrial control run in CM2.1. Near-global-mean SST (Fig. 2a) displays two distinct rates of growth before and after t_c = 140 yr. The transition of SST growth from the fast to slow rate is delayed by a few years relative to the CO₂ concentration stabilization, owing to the adjustment time of the OML. Spatial variations of SST warming increase with SST in the fast response but then level off after CO₂ is stabilized, despite a continued increase in SST, indicative of different response processes between the two stages. The slow growth of SST after the CO₂ stabilization results from heating by the deeper ocean warming.

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Evolution of near-global ocean (60°S–60°N) annual-mean changes in the 1%4×CO₂ run with respect to the preindustrial control run in CM2.1: (a) SST (red line, °C) and its spatial standard deviation (spatial std; green line, °C), (b) scalar wind speed (m s⁻¹), (c) surface air–sea temperature difference (SAT − SST) (red line, °C) and relative humidity (RH) (green line, %), and (d) net heat flux Q_net (red line, W m⁻²) and precipitation (green line, mm month⁻¹). In (a) and (c) different colors and scales of the ordinate on each side are used for different variables. The dotted vertical line stands for the year when the CO₂ concentration reaches quadrupling; an 11-yr running mean is applied in each panel.

Citation: Journal of Climate 27, 1; 10.1175/JCLI-D-13-00297.1

Along with SST, surface scalar wind speed (Fig. 2b) and surface relative humidity and stability (Fig. 2c) all display a clear transition around year 140. Net heat flux (Q_net; Fig. 2d) into the ocean increases with the CO₂ rise for t < t_c and then decreases for t > t_c. Near-global-mean precipitation (Fig. 2d) over the ocean follows the trajectory of temperature and the transition at t = t_c is unclear.

c. Diagnostic method

In light of the two stages that the climate response displays, we propose a diagnostic method to isolate spatial patterns of the fast and slow response. The fast response is evaluated by subtracting the preindustrial climatology from the year 101–150 average in the 1%4×CO₂ run. An additional 10 yr after CO₂ stabilization is included due to the delay of the OML response. The slow response is defined as the changes after CO₂ stabilization, computed by subtracting the year 151–200 average from the year 551–600 average in the 1%4×CO₂ run. These time periods for averaging are chosen based on the global-mean response, which is dominated by the fast component when the radiative forcing increases and by the slow component when the radiative forcing stabilizes. Although the fast and slow components cannot be separated precisely by this method as the time scales of these two components may vary with time and regions, the method yields a good approximation of the fast and slow response.

Figure 3 shows the depth–time sections of the near-global-mean ocean temperature change. In the total response, the vertical maximum of the ocean warming always appears in the upper ocean. A prominent subsurface maximum (about 50–3000 m) warming develops in the slow response (Fig. 3b) where the subsurface warms faster than the upper ocean. Consequently, the temperature gradient between the OML and deeper ocean decrease for t > t_c (Xu et al. 2013), consistent with the simple model.

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Time–depth sections of near-global-mean (60°S–60°N) ocean temperature anomalies (°C) in CM2.1: (a) the total and (b) slow response. Depth coordinates are on logarithmic to highlight the upper ocean, with an 11-yr running mean applied in each panel. (c)The total background temperature (preindustrial climatology) of (a), and (d) the slow background temperature (151–200 mean in 1%4×CO₂) of (b).

Citation: Journal of Climate 27, 1; 10.1175/JCLI-D-13-00297.1

Zonal-mean SST displays opposite structures between the fast and slow response (Figs. 4a,b): regions of enhanced warming appear equatorward of 45°S/N in the fast response but move to higher latitudes in the slow response. We have performed empirical orthogonal function (EOF) analysis of zonal-mean anomalies for the fast and slow response. The pair of the first EOF modes of SST are negatively correlated at −0.6 in space. As discussed in the simple model, the sign reversal of the heat flux change between the OML and deeper ocean contributes to this opposite meridional structure. The opposite structures are especially pronounced in high latitudes (Fig. 4c) where ocean dynamics/storage, as measured by (Fig. 4d), is important. There, ocean dynamics/storage is a cooling effect and suppresses SST warming for the fast response but turns into a warming effect and intensifies SST warming for the slow response. In the fast response (Fig. 4a), zonal-mean SST features an equatorial peak because of the weak evaporative damping (Liu et al. 2005), and the warming is greater in the northern than southern subtropics owing to the WES mechanism (Xie et al. 2010). The latter interhemispheric asymmetry is somewhat opposite in the slow response mainly due to the reversed trade wind change, as will be presented later.

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Time section of zonal-mean SST (°C): (a) the fast and (b) slow response. First EOF modes (EOF1) of the fast and slow response for (c) SST and (d) ocean heat transport (), with the first EOF modes of SST normalized by their tropical (20°S–20°N) mean values.

Citation: Journal of Climate 27, 1; 10.1175/JCLI-D-13-00297.1

4. Global pattern

For convenience, we only show the time difference results for the fast and slow response. The results are highly consistent with EOF analyses in spatial patterns (not shown here). Indeed, the fast and slow response patterns that we obtain are similar to those obtained by the experimental method of Held et al. (2010, their Fig. 7). Similar regional patterns between these two sets of results include the enhanced equatorial Pacific warming in both fast and slow spatial patterns and the opposite warming structures between the fast and slow spatial patterns in the southern subtropics in all three ocean basins and the Southern Ocean. Both Held et al. (2010) and the present study show the sign reversal of the banded structure of warming in the midlatitude Northern Hemisphere (NH) between the fast and slow spatial patterns. Furthermore, fast response patterns in both of these studies display an Indian Ocean dipole (IOD)-like warming, and slow response patterns display broad reduced warming along the Kuroshio Extension (KE). The consistency with Held et al. (2010) validates our diagnostic method of decomposing the SST change into the fast and slow response.

a. Fast response pattern

Figure 5 shows the fast response pattern of SST, , surface wind velocity, and scalar wind speed in CM2.1. SST warming displays several pronounced regional patterns that are robust among models in earlier studies, including the enhanced equatorial Pacific warming (Knutson and Manabe 1995; Meehl et al. 2000; Liu et al. 2005), subtropical southeast Pacific minimum (Meehl et al. 2007; Vecchi and Soden 2007a; Lu and Zhao 2012), and the IOD-like warming in the tropical Indian Ocean (Vecchi and Soden 2007b; Du and Xie 2008; Xie et al. 2010). Besides, the greater warming in the northern than southern subtropics in all three ocean basins, banded structures in the midlatitudes, and minimum warming in the Southern Ocean are also consistent with the study of Xie et al. (2010).

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Annual-mean fast response pattern (year 101–150 mean in the 1%4×CO₂ run minus the preindustrial climatology) in CM2.1: SST [colors, °C; with values larger (smaller) than the tropical (20°S–20°N) mean shaded by warm, red (cool, blue) color], along with (a) [white contours, contour interval (CI) is 8 W m⁻²] and (b) surface wind velocity (vectors, m s⁻¹) and scalar wind speed (white contours, CI is 0.3 m s⁻¹). Zero contours omitted for clarity.

Citation: Journal of Climate 27, 1; 10.1175/JCLI-D-13-00297.1

In the midlatitude NH, the annual-mean SST warming displays meridional banded structures that are highly correlated with ocean heat transport () anomalies: SST warming strengthens where is positive and weakens where is negative (Fig. 5a). In the midlatitude Southern Hemisphere (SH), zonal banded structures of SST are also highly correlated with the change of . In the Southern Ocean and subpolar North Atlantic Ocean where bottom-water/deep-water forms, strong dynamical cooling suppresses SST warming. The correlation between and spatial variations in SST (with the area mean removed) between 60° and 20°S (20° and 60°N) is 0.48 (0.58). Also, is important for SST changes in the tropical Indian Ocean and for the zonal minimum (around 140°–110°W) in SST over the equatorial Pacific Ocean.

In the SH subtropics, a clear meridional SST minimum (Fig. 5b) is found in all three ocean basins, accompanied by the intensified southeast trades. Both the northeast trades and westerlies weaken in the NH with a slightly weakened Aleutian low, sustaining a warming that is generally greater than the tropical mean value. The greater warming in the northern than southern subtropics mainly results from the interhemispheric asymmetry of wind speed change. The reduced wind speed in the tropical Atlantic and northern Indian Ocean also leads to intensified SST warming, similar to the enhanced warming south of Hawaii where positive ocean heat transport is also favorable for SST increase. The correlation between wind speed change and spatial deviations of SST (with the area mean subtracted) is −0.66 between 25°S and 20°N. Generally, enhanced SST warming follows a decreased wind speed change in the tropics and subtropics, and vice versa. This is consistent with previous studies that, on the basin scale, the WES mechanism is important in the tropical SST pattern formation (Xie et al. 2010; Lu and Zhao 2012). The reduced SST warming and enhanced wind speed in the subtropics of the SH may be triggered by suppressed SST warming in the high latitudes. Ocean–atmosphere interactions may propagate it to the subtropics by the WES footprinting mechanism (Vimont et al. 2003; Wu et al. 2007; Xie et al. 2010).

b. Slow response pattern

Figure 6 displays the slow response pattern to be compared to the fast response (Fig. 5). The SST warming displays several distinct features from the fast response: the El Niño–like warming in the eastern tropical Pacific, suppressed warming in the equatorial Atlantic and northern Indian Oceans, broad reduced warming along the Kuroshio and Kuroshio Extension, greater warming in the southern than the northern subtropics in all three ocean basins, reversed banded structures in warming in the northern subtropics, and enhanced warming in the Southern Ocean.

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Annual-mean slow response pattern (year 551–600 mean minus year 151–200 mean in the 1%4×CO₂ run) in CM2.1: SST (colors, °C), along with (a) (white contours, CI is 4 W m⁻²) and (b) surface wind velocity (vectors, m s⁻¹) and scalar wind speed (white contours, CI is 0.1 m s⁻¹). Zero contours omitted for clarity.

Citation: Journal of Climate 27, 1; 10.1175/JCLI-D-13-00297.1

Tropical and subtropical SST warming patterns appear to be positively correlated in space with ocean heat transport change over most regions, in contrast with the fast response pattern. Local SST warming and are highly correlated over the midlatitudes in the slow response, especially in the North Atlantic and Southern Ocean. The correlation between and spatial deviations of SST (with the area mean subtracted) in the extratropics south (north) of 20°S (20°N) is 0.71 (0.78), higher than that in the fast response.

Wind speed is reduced in most oceans. The eastern Pacific Ocean north of the equator is an exception where the wind speed increase is collocated with a local minimum warming. The correlation between wind speed change and spatial deviations of SST warming (with the area mean subtracted) between 25°S and 20°N decreases from −0.66 in the fast response to −0.37 in the slow response. Similar to the fast response, wind speed change also contributes to the SST warming pattern formation in the tropics but with a reduced importance in the slow response.

Atmosphere circulation change is also almost opposite to the fast response. The most pronounced atmosphere circulation change is the deceleration of the southeast trade winds in all three ocean basins, opposite to the fast response. The enhanced Aleutian low in the slow response is another prominent feature that may be associated with a broad reduced warming in the KE region and enhanced warming in the subpolar North Pacific. Westerly wind anomalies almost disappear in the Southern Ocean, replaced by anomalous easterlies at most longitudes. Similar to the fast response pattern, we speculate that the enhanced warming in the southern subtropics originates from high latitudes via the WES footprint mechanism, especially in the Pacific where dynamical warming suggests an origin from the Southern Ocean (Fig. 6b).

The slow SST response displays a spatial pattern opposite to the fast one in most oceans, explaining why the spatial variations of SST slightly attenuate for t > t_c even though the global-mean SST continues to increase (Fig. 2a). As discussed above, the sign reversal of the heat flux change between the OML and deeper ocean causes the opposite spatial structures between the fast and slow response, especially in regions where the ocean dynamical effect is strong. In the subtropics, the reversed trade winds anomalies also contribute to shaping the opposite spatial SST structures between the fast and slow response.

The slow response displays a spatial pattern very different from the fast one, indicative of importance of the deeper ocean evolution. The fast response pattern has been studied in the literature, while the slow response pattern has not been examined because the magnitude of the latter is considerably smaller than the former in short simulations (<100 yr). The importance of the slow response pattern, however, will increase as climate evolves toward a new equilibrium, as revealed in the results of the 600-yr simulation in CM2.1.

5. Vertical structure of ocean temperature response

Ocean temperature change shows distinct vertical structures between the fast and slow responses (Fig. 7). Overall, the warming is surface intensified in the fast response, whereas it is hidden below the thermocline in the slow response. The zonal-mean distribution in the upper-ocean warming is consistent with the SST warming structures such as the equatorial warming, asymmetric warming between the northern and southern subtropics, and the poleward enhanced warming in the slow response—the last feature extending deep in the vertical due to Southern Ocean ventilation.

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Vertical structure of ocean temperature change (colors, °C) along with background temperature (black contours, CI is 2°C) in CM2.1: zonal mean (a) fast and (b) slow response and equatorial (5°S–5°N) mean (c) fast and (d) slow response. The thick blue and red lines in (c) indicate the equatorial mean thermocline depth of the preindustrial climatology and the year 101–150 mean in the 1%4×CO₂ run, respectively. The thick blue and red lines in (d) indicate the equatorial mean thermocline depth of the year 151–200 mean and the year 551–600 mean in the 1%4×CO₂ run, respectively.

Citation: Journal of Climate 27, 1; 10.1175/JCLI-D-13-00297.1

Along the equator (5°S–5°N mean), ocean temperature displays large warming in the upper ocean and small warming in the deeper ocean in the fast response (Fig. 7c), which is almost reversed in the slow response (Fig. 7d). In the fast response, there is a distinct reduced warming/weak cooling along the thermocline in the equatorial Pacific, especially in the western Pacific (the thermocline depth is defined as the depth of the maximum vertical temperature gradient). Westerly wind anomalies in the equatorial Pacific (Fig. 5b) flatten the thermocline (thick blue and red lines in Fig. 7c) and upwell cold thermocline water to suppress the upper warming, consistent with the results of Vecchi and Soden (2007b). This minimum warming in the thermocline is also evident in the eastern tropical Indian Ocean where easterly wind anomalies act to shoal the thermocline. Such a feature is diminished in the equatorial Atlantic. The shoaling thermocline is a major reason for the reduced warming along the thermocline; other factors such as the influence of subtropical ventilation need to be explored.

The thermocline depth change is the combined effect of thermodynamical and dynamical factors. In the fast response, the former generally shoals the thermocline because of surface-intensified warming, while the latter acts to flatten the thermocline in the equatorial Pacific. In the slow response, the thermodynamical effect due to enhanced subsurface warming (shaded color in Fig. 7d) offsets the dynamical effect induced by the wind anomalies on the equator, making the thermocline depth change much weaker (thick blue and red lines in Figs. 7c,d). Consistent with Chadwick et al. (2013b), equatorial western Pacific thermocline change appears to follow the wind forcing in both responses. In the equatorial eastern Indian Ocean, by contrast, the thermocline slightly deepens in the slow response. The percentage of grid points with increased vertical maximum temperature gradient between 20°S and 20°N decreases from 97.49% in the fast response to 67.94% in the slow response, indicating that the temperature gradient between the upper and deeper ocean is decreased in some regions when the radiative forcing stabilizes. Indeed, the medium thermocline depth change (normalized by global-mean SST change) between 20°S and 20°N decreases from −2.3 m K⁻¹ in the fast response to −0.75 m K⁻¹ in the slow response, suggestive of a thermodynamical effect on the thermocline as the deeper ocean warms faster than the upper ocean.

6. CMIP5 multimodel ensemble results

Here, we apply the diagnostic method to nine models in the CMIP5 RCP4.5 simulations. The fast response is computed by subtracting the average of 1956–2005 (historical run) from the average of 2051–2100, and the slow response by subtracting the average of 2101–50 from the average of 2251–2300 in RCP4.5. The RCP4.5 simulations have much weaker radiative forcing ( ~ 4.5 W m⁻² at 2100) than the 1%4×CO₂ run ( ~ 7.42 W m⁻² at year 140). This, along with the difference in the length of integration, causes the spatial distribution and magnitude of climate response to differ between the two experiments. The agreement between the two experiments would indicate the robustness of the diagnostic method.

The CMIP5 ensemble-mean results produce fast and slow response patterns of SST (Figs. 8 and 9) that are consistent with the CM2.1 results, including the equatorial warming in the Pacific and Indian Oceans, southern subtropical and Southern Ocean warming, and banded structures in warming in the SH. Indeed, the correlation for the fast (slow) SST response pattern, normalized by the tropical man, between CM2.1 and CMIP5 is 0.89 (0.57). Furthermore, the correlations of SST (with the area mean subtracted) with and wind speed change are also well produced (Table 2). Specifically, the tropical Indian Ocean SST warming in CMIP5 is highly correlated with ocean heat transport as in the CM2.1 in the fast response. The decreased role of wind speed in the tropical SST pattern formation from the fast to slow response is also evident. The general reversal of the fast and slow response patterns in SST and atmosphere circulation is also produced, especially in the southern subtropics and Southern Ocean. The robust response patterns confirm the utility of the diagnostic method to separate the fast and slow response.

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Annual-mean fast response pattern (2051–2100 mean in RCP4.5 minus 1956–2005 mean in the historical run) in CMIP5: SST (colors, °C), along with (a) (white contours, CI is 2 W m⁻²) and (b) surface wind velocity (vectors, m s⁻¹) and scalar wind speed (white contours, CI is 0.1 m s⁻¹). Zero contours omitted for clarity.

Citation: Journal of Climate 27, 1; 10.1175/JCLI-D-13-00297.1

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Annual-mean slow response pattern (2251–2300 mean minus 2101–50 mean in RCP4.5) in CMIP5: SST (color shaded, °C), along with (a) (white contours, CI is 1 W m⁻²) and (b) surface wind velocity (vectors, m s⁻¹) and scalar wind speed (white contours, CI is 0.03 m s⁻¹). Zero contours omitted for clarity.

Citation: Journal of Climate 27, 1; 10.1175/JCLI-D-13-00297.1

Table 2.

Correlations with SST deviations (T*) from area means: changes in ocean heat transport effect (), scalar wind speed (W), and percentage precipitation change (dP/P) in CM2.1 and CMIP5 for the fast and slow responses.

There are some differences between the CM2.1 and CMIP5 results. In the CMIP5 fast response, the banded SST warming structures in the North Pacific is less clear, likely due to averaging across models. A broad enhanced SST warming appears in the high latitude of the North Pacific accompanied by negative ocean heat transport changes. Major differences in the CMIP5 slow response include the weak banded structures in the North Atlantic and reduced minimum warming in the KE region. The enhanced SST warming band in the North Pacific appears farther north in the CMIP5 than in CM2.1 in the slow response. Besides, the Aleutian low change in the CMIP5 slow response is weak. Generally, disagreements between these two sets of patterns are larger in the NH than in the SH.

7. Precipitation response

Percentage precipitation change (dP/P) in the CMIP5 ensemble shows distinct fast and slow response patterns (Fig. 10) that follow the SST response. In the fast response pattern (Fig. 10a), there is a pronounced band of robust dP/P increase over the equatorial Pacific, anchored by the maximum SST warming. The enhanced warming in the tropical north Indian Ocean causes an increase in dP/P, while the decrease in dP/P is apparently in the southern subtropics, associated with the reduced SST warming in all three ocean basins. In the tropical North Atlantic Ocean, the local minimum warming anchors a broad decrease in dP/P. The correlation between the dP/P and relative SST (deviations from the tropical mean) within 20°S–20°N is 0.6.

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Percentage precipitation change (dP/P) (green/gray shade and white contours) along with SST change [contours, °C; with value larger (smaller) than tropical (20°S–20°N) mean contoured by warm (cool) color] in CMIP5 RCP4.5: (a) the fast response pattern (SST CI is 0.1°C) and (b) the slow response pattern (SST CI is 0.04°C). White contour intervals for dP/P change are 4% in (a) and 2% in (b).

Citation: Journal of Climate 27, 1; 10.1175/JCLI-D-13-00297.1

In the slow response, dP/P increases in the tropical Pacific with the enhanced SST warming, while it decreases over the broad reduced warming in the tropical western Pacific Ocean (Fig. 10b). The enhanced SST warming in the southern subtropics of all three ocean basins creates clear bands of increase in dP/P. The correlation between dP/P and relative SST (deviations from the tropical mean) within 20°S–20°N is 0.52. Generally, tropical precipitation change is locally positive correlated with relative SST in both the fast and slow response. Rainfall increases (decreases) where SST warming exceeds (falls below) the tropical mean value, indicative of the “warmer get wetter” mechanism. The opposite SST warming patterns cause rainfall patterns to be opposite between the fast and slow response . As a result, the rate of increase in spatial variance of annual tropical precipitation slows from 6.2 during 2006–2100 when the radiative forcing increases to 5.7 after the radiative forcing stabilization. This is an important result since precipitation change is to first order spatially variable.

8. Summary

We have investigated the fast and slow response of SST in global warming and their influence on the atmosphere, mainly based on a 1%4×CO₂ simulation with CM2.1. While global-mean SST continues to increase at a reduced rate after CO₂ stabilization, spatial variations of the SST warming are attenuated. We have developed a diagnostic method, as opposed to the experimental method of Held et al. (2010), to divide the SST change into two stages and isolate the respective spatial patterns: the fast response, where the OML is in quasi equilibrium with both the atmosphere and deeper ocean, and the slow response, where the slow evolution of the deeper ocean gradually heats the ocean mixed layer and atmosphere after radiative forcing stabilizes. We have applied the method to a CMIP5 multimodel ensemble simulation and obtained spatial patterns of the fast and slow response similar to those from the CM2.1. The consistency between these two sets of results confirms the utility of the method, which separates the fast and slow response diagnostically.

Spatial patterns of the fast and slow SST response are distinct. The SST warming pattern tends to be opposite between two stages of the response, especially in regions where the ocean dynamical effect is strong. This is due to the sign reversal of the heat flux change between the OML and deeper ocean, as indicated by the change in vertical structure of ocean temperature. The deeper ocean retards the SST warming in the fast response as in the Southern Ocean and North Atlantic bottom-water/deep-water formation regions. The deeper ocean reverses to heat the OML in the slow response, an effect most apparent in the above bottom-water/deep-water formation region. The equatorial Pacific is an exception, featuring enhanced warming in both the fast and slow response. There the equatorial peak warming is due to the weak evaporative damping in the fast response (Liu et al. 2005; Xie et al. 2010), whereas it seems to result from the positive upward heat flux change in the slow response (Figs. 6a and 7b,d). Besides ocean dynamics/storage, wind speed change is also important for SST pattern formation in the tropics, especially for the fast response. In the CMIP5 ensemble, spatial variations of SST warming exert an important effect on tropical precipitation in both the fast and slow response, with rainfall increasing (decreasing) where SST warming exceeds (falls below) the tropical mean.

The slow response will become important when CO₂ mitigation is implemented. Chadwick et al. (2013b) conducted coupled experiments to explore spatial patterns of the climate response to CO₂ increase and decrease. Surface temperature changes display a slow-response-like pattern in the CO₂ ramp down compared to the CO₂ ramp up (their Figs. 2c,d), including the El Niño–like warming, intensified southern subtropical and Southern Ocean warming, banded structures in the NH, and broad reduced warming along the Kuroshio Extension. The difference between the CO₂ ramp up and down (Figs. 2e,f of Chadwick et al. 2013b) resembles the slow response in the spatial pattern (our Fig. 6). The fast component is diminished when the radiative forcing first increases and is then reduced back to its origin value. The difference is dominated by the slow component. This is a good example of how the slow response influences the surface warming patterns.

Our study has highlighted the differences in the SST pattern between the fast and slow response to global warming. Further investigations into pattern formation dynamics and related atmospheric and oceanic processes are needed: specifically, that the Southern Ocean dynamics/heat storage effect shifts from reducing to enhancing the local SST warming as the climate evolves from the fast to slow response (Fig. 4). We note that this is associated with a change in the cross-equatorial gradient of SST warming between the northern and southern subtropics in a way consistent with a coupled ocean–atmosphere energetics argument (Kang et al. 2008; Fučkar et al. 2013). How the extratropical influence takes place and the wind–evaporation–SST footprint mechanism mediates this adjustment needs to be examined.