1. Introduction

The Intergovernmental Panel on Climate Change (IPCC) provides periodic assessments of the causes and impacts of climate change, as well as possible response strategies. The fourth and most recent Assessment Report (AR4), entitled Climate Change 2007, consists of contributions from three working groups plus a very useful synthesis (Pachauri and Reisinger 2007). Perhaps the foremost conclusion of AR4 is that the warming of the earth’s climate system is unequivocal. It is based largely on the report of Working Group I (Solomon et al. 2007), whose chapters document global average warming of both the land and sea surfaces (Le Treut et al. 2007), of air temperature (Trenberth et al. 2007), and of upper-ocean temperatures (Bindoff et al. 2007), as well as a widespread reduction in snow and ice cover and rising global average sea level (Lemke et al. 2007).

According to Trenberth et al. (2009), there is a near balance at the top of the atmosphere between the incoming solar radiation (≈341 W m⁻²), the reflected solar (≈−102 W m⁻²), and the terrestrial radiation to space at longer wavelengths (≈−239 W m⁻²). The latter is reduced by the presence of greenhouse gases (GHGs) in the atmosphere, so to maintain this radiative balance the earth’s climate is warmer than it otherwise would be. Another major AR4 conclusion is that most of the global average warming over the past 50 years is very likely due to anthropogenic increases in GHGs, such as carbon dioxide and methane as well as any additional water vapor held in the warmer atmosphere (Hegerl et al. 2007). The estimated combined GHG forcing is only about 2 W m⁻², at least some of which should be offset by increasing aerosols (Lemke et al. 2007) (Le Treut et al. 2007).

In the warmer climate, the average surface warming is not uniform and is nearly 50% greater over land than over the ocean (Le Treut et al. 2007). A robust finding of AR4 is that this warming pattern is seen in all future warming scenarios (Meehl et al. 2007). Therefore, there is a need to understand the smaller ocean surface warming and its relation to ocean heat uptake because the less taken up by the ocean, the greater the possible effects on terrestrial climate. However, a key uncertainty is that climate data coverage remains limited in some regions, including remote ocean areas (Bindoff et al. 2007). Although the recent advent of Argo floats (Roemmich et al. 2004) has greatly improved the observational network, significant improvement in this situation will take many years because of the multidecadal time scales of climate change and large natural variability. However, improved reexaminations of existing observations could have immediate beneficial consequences.

For example, the AR4 states that the oceans are warming with the global average temperature above 700-m depth having risen by 0.10°C between 1961 and 2003 (Bindoff et al. 2007). The basic foundation for such estimates of ocean heat content change is the World Ocean Database (Conkright et al. 2002). But, Harrison and Carson (2007) compare warming trends from three analyses of these data and find warming to increase with the degree of interpolation in the analysis. With the least interpolated data, they find that most of the ocean does not have significant 50-yr trends at the 90% confidence level. With first interpolation to standard depths, then horizontal objective analysis, the trend estimates of Levitus et al. (2005) become larger, with striking differences appearing even in regions of their statistically significant trends. Harrison and Carson (2007) suggest that interpolation over the very data sparse areas of the World Ocean may have substantial effects on results. Some other issues with the World Ocean Database are biases in the ocean measurements, the paucity of deep observations and aliasing of signals from mesoscale eddies, the internal tide, and inertial motions.

The purpose of the present work is to bring estimates of global air–sea fluxes (Large and Yeager 2009) to bear on the processes behind the recent increases in sea surface temperature (SST) and to test the underlying assumptions of a Slab Ocean Model (SOM). These fluxes were computed from the forcing developed for the Coordinated Ocean-Ice Reference Experiments (COREs) (Griffies et al. 2009) through a novel analysis and merging of existing data. They include both heat and freshwater fluxes from 1984 through 2006, and the time series of global and ocean basin averages are shown in Large and Yeager (2009). Over these years the climatological global heat flux is about 2 W m⁻², with an uncertainty of about the same magnitude as the 2 W m⁻² GHG forcing, but only on the global scale. This uncertainty grows to tens of watts per square meter on smaller regional scales (Large and Yeager 2009). Therefore, the focus will be on global and basin scales. Furthermore, it will be on changes in annual flux anomalies, both to filter large seasonal signals and to mitigate systematic errors. By only considering changes, the results do not depend on whether there is overall heating or cooling of the global ocean. Implications for upper-ocean temperature change and heat uptake are outlined in section 2, with the role of ocean processes outlined in section 2b. The heat flux and companion SST datasets are presented in section 3. Least squares linear regressions of annual anomaly time series are used in section 4 to estimate the 23-yr (1984–2006) changes in fluxes and in SST that need to be reconciled with SOM assumptions and radiative forcing. Again, it is argued that large basin and global scales are more tractable than smaller regions. Variability relationships on shorter time scales and over the longer 1949–2006 period are also discussed. Finally, section 5 contains a discussion and conclusions.

2. Air–sea interaction and coupling

The ocean and atmosphere directly interact physically through the fluxes of momentum, heat, and freshwater. The latter two fluxes are directly connected through the latent heat flux associated with evaporation. At high latitudes the presence of sea ice often leaves only a fraction of the ocean surface exposed directly to the atmosphere above. Over the remainder the air–sea interaction is indirect through the sea ice. The ocean–ice heat flux is difficult to estimate and small because sea ice is a very effective insulator. Therefore, it is not consider further.

a. Air–sea heat flux

Calculations of the air–sea heat flux into the ocean Q are detailed in Large and Yeager (2009). For present purposes it is instructive to decompose this flux according to direct sources of interannual and decadal variability. The ocean surface albedo is constant on these time scales, so the net solar flux Q_S as well as the downwelling longwave radiation Q_A vary with the properties of the overlying sky, such as clouds. Their sum is given by

View Expanded

The remainder of Q is determined by properties in the atmosphere and ocean planetary boundary layers and is denoted as Q_pbl:

View Expanded

Specifically, Q_pbl is the sum of the turbulent fluxes of latent heat Q_E and sensible heat Q_H plus the blackbody longwave radiation from the ocean surface Q_B. The latter is given by

View Expanded

where σ = 5.67 × 10⁻⁸ W m⁻² is the Stefan–Boltzmann constant and the surface emissivity is taken to be 1.0 to account for the small fraction of Q_A that is reflected (Lind and Katsaros 1986). The bulk formulae parameterize the turbulent fluxes in terms of the near-surface atmospheric state (wind U, potential temperature θ, specific humidity q, and density ρ) and the ocean state (SST and ocean surface current ):

View Expanded

and

View Expanded

where , c_p ≈ 1005 J kg⁻¹ °C⁻¹ is the specific heat of air, Λ_υ ≈ 2.5 × 10⁶ J kg⁻¹ is the latent heat of vaporization, and C_E and C_H are the empirical bulk transfer coefficients. The air at the ocean surface is assumed to be saturated with its specific humidity approximated by the function shown in Fig. 1a:

View Expanded

where the factor 0.98 applies only over seawater.

View Full Size

Some functions of SST: (a) saturation specific humidity (kg kg⁻¹) from (6); (b) negative feedback due to blackbody radiation from the sea surface Q_B (W m⁻² °C⁻¹), as well as from latent heat flux Q_E in (11) and sensible heat flux Q_H in (12), both in units of W m⁻² °C⁻¹ per m s⁻¹ of wind speed.

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00148.1

• Download Figure
• Download figure as PowerPoint slide

In nature any change in SST is expected to affect both q and θ and vice versa. To examine the fluxes associated with these related changes, it is useful to partition Q_pbl into a term, Q_sst, that varies with SST plus a second, Q_air, that varies with air temperature and humidity:

View Expanded

with

View Expanded

and

View Expanded

These two terms depend on the relative wind speed and only changes or differences are physically meaningful. In addition, Q_sst dampens changes in SST by exchanging heat with the atmosphere. Similarly, Q_air dampens changes in air temperature by exchanging heat with the ocean.

An air–sea heat flux coupling coefficient C_as can be defined as the change in Q divided by the associated change in SST. The only component that can be explicitly defined is

View Expanded

This coefficient is negative definite because an increase in SST tends to reduce the heat flux into the ocean from all three terms. The negative feedback of the first term comes from Q_B and is shown in Fig. 1b for SST between 0° and 30°C, where it ranges from about −4.6 to −6.3 W m⁻² °C⁻¹. Figure 1b also shows the feedback from the other two terms. These come from the latent (Q_E) and sensible (Q_H) heat fluxes and are given as the feedback per meter per second of wind speed. The respective functions are given by

View Expanded

and

View Expanded

The Q_B feedback becomes less than the sensible feedback for wind speeds greater than about 4 m s⁻¹. The latent heat term (11) is a strong function of SST and is more than double the sensible feedback (12) for SST greater than about 10°C. It becomes the dominant feedback at high winds and higher SST.

A given change ΔSST over a time interval can be accompanied by changes in the atmospheric state and, in particular, the boundary layer wind, temperature, and humidity, as well as the cloud field. Therefore, the total change in Q is not given by (10), but rather by an effective coefficient . This coefficient can be empirically determined, as can other effective coefficients, such as , and similarly defined , , , and . The values of these effective coefficients empirically include wind speed effects and other correlations. They are expected to vary regionally and with time interval.

b. Sea surface temperature evolution

A prognostic equation for the time evolution of SST, and hence of annual anomalies, was formulated by Stevenson and Niiler (1983) as

View Expanded

where h is an effective mixing depth and the product of ocean density times heat capacity is (ρC_p)_w = 4.1 MJ m⁻³ K⁻¹. In (13) lateral and vertical ocean processes are represented by R_H (e.g., lateral advection over the depth h at all scales) and by R_V (vertical diffusion plus entrainment at h). The heating due to the latter is inversely proportional to h, while the entrainment itself is proportional to an entrainment velocity at h: w_e(−h) = w(−h) + D_th, where D_t represents the total derivative and w(−h) is the vertical velocity at depth h. According to (13) a constant positive (negative) right-hand side would maintain a linear trend of increasing (decreasing) SST.

A slab ocean model simply solves (13) with interannually invariant specified spatial distributions of depth h and of the net heating due to all ocean processes. Under these conditions the addition of an anomalous annual heat flux ΔQ to the balancing heat flux over a time interval Δt of 1 yr would produce an annual temperature change given by

View Expanded

where an effective annual mixing depth could be diagnosed from (14) but cannot, in general, be computed from the specified SOM annual cycle of h.

In a SOM, therefore, a constant positive (negative) heat flux anomaly would produce an increasing (decreasing) linear trend in SST anomaly. Here anomaly means the difference from what is required to balance ocean heating processes. The importance of determining how trends in SST are maintained in nature is magnified by the practice of using SOMs to determine climate sensitivity of atmospheric models. This parameter is perhaps the most important characteristic of climate models. It is defined as the equilibrium increase in global surface temperature to a doubling of carbon dioxide in an atmospheric model coupled to a SOM. As intended, this climate sensitivity depends primarily on the atmospheric model, and neither on the use of a SOM nor on the specified mixing depth h (Danabasoglu and Gent 2009). Instead, h and other ocean model physics determine the time required to reach equilibrium.

According to (8), with all other fluxes and flux parameters being constant, a linear trend in SST would lead to slightly more than a linear decrease in Q_sst and, hence, Q because of the nonlinearity of Fig. 1a. The flux change would be given by

View Expanded

Thus, there is a conflict because with an increasing trend in SST could not be sustained. On climate time scales, a common argument is that increasing radiative fluxes are sufficient to make . However, there are other possibilities. In general h is time varying, especially over the season cycle when it can deepen from O(10 m) in summer to hundreds of meters in winter. It is also highly variable spatially. Therefore, as is evident from (14), annual average SST and its spatial averages can change without a corresponding change in surface heat flux. In the limit ΔQ = 0, we have . Such an example would arise if there was anomalous summer heating in summer when h is shallow, combined with compensating winter cooling when h is deeper. Similarly, a regional average SST would change if heat flux changes differed between shallow and deep mixing regions even if there were no change in the average Q. Therefore, an indicator of such rectification would be a much less negative effective coefficient (e.g., ) based on spatial averages (e.g., ΔQ and ΔSST) compared to the spatially averaged coefficient (e.g., C_as).

3. The SST and heat flux datasets

The Hadley–optimum interpolation (OI) product (Hurrell et al. 2008) provides monthly SST over all of the world’s oceans and has been made compatible with historical sea ice distributions. These data are a merger of the monthly Met Office Hadley Centre Sea Ice and SST dataset, version 1 (HadISST1) and the NOAA weekly optimum interpolation analysis, version 2 (OIv2) (Reynolds et al. 2002). HadISST1 is described and evaluated by Rayner et al. (2003). It includes historical SSTs reconstructed from ship observations beginning in 1871 (Folland et al. 2001). There is evidence (Hurrell and Trenberth 1999) that, for present purposes, the random and sampling error in the SST should be sufficiently reduced in the annual means, that themselves are typically further averaged over large ocean regions using area weighting. Persistent systematic errors are eliminated by analyzing only time changes. There is no evidence of potentially problematic interannually varying large-scale error.

The air–sea heat fluxes are from version 2 of the CORE fluxes (COREv2) described in Large and Yeager (2009). They were computed according to the formulas of section 2a and purposefully exclude all numerical weather prediction, including reanalysis, products that directly involve clouds, such as radiation and precipitation. This CORE judgment is supported by more recent examinations, Bosilovich et al. (2011), for example, of the Modern Era Retrospective-Analysis for Research and Applications (MERRA). Therefore, the radiative components of Q_sky are available only after June 1983 when the International Satellite Cloud Climatology Project flux data (ISCCP-FD) begin. The solar radiation is uniformly reduced by 5% between 50°S and 30°N. For smoothness the reduction is linearly diminished to become zero poleward of 60°S and 40°N. The magnitude of the reduction is based on comparisons with measurements from the Tropical Ocean-Atmosphere (TAO) and Prediction and Research Moored Array in the Tropical Atlantic (PIRATA) surface mooring arrays (Large and Yeager 2009). The geographic extent is suggested by comparisons with zonal means from other over-ocean products shown in Béranger et al. (2000) and in Taylor (2000). Some degree of reduction is consistent with comparisons with the Baseline Surface Radiation Network in Zhang et al. (2004).

The Q_pbl averages are computed onward from 1949 using the atmospheric state from the National Centers for Environmental Prediction reanalysis, but only after making a number of critical adjustments to flux parameters based on a variety of more reliable satellite and in situ measurements. These adjustments and the radiation reduction are time invariant, so have negligible effects on the present analyses of time changes. Although Large and Yeager note that there is little justification for invariance, they also show how unknown time-dependent errors may compensate one another.

The overall effects of the adjustments are faster wind speeds, drier humidities, and reduced radiation. As a result the climatological (1984–2006) global-mean air–sea heat flux becomes 2, down from 30 W m⁻². This lower value plus an expected small ocean heat loss through sea ice is in agreement with the observation of small ocean heat content changes (Harrison and Carson 2007) (Levitus et al. 2000, 2005). However, in regional comparisons Large and Yeager (2009) find an alarming range among alternatives, with more than 40 W m⁻² not uncommon. Although the uncertainty in the CORE heat flux is not believed to be so large, it is at least O(2 W m⁻²), so the sign of the climatological global-mean ocean surface heat flux must be regarded as uncertain. A reassuring finding is that the implied ocean heat transports are within the, albeit large, uncertainty of estimates from ocean observations in both Atlantic and Indo-Pacific basins.

The global air–sea heat fluxes were recomputed over the 1984–2006 period: first, after adding 0.5°C to the Hadley-OI SSTs and, second, after subtracting 0.5°C. The difference between the mean heat fluxes gives the spatial distribution of the SST coupling coefficient C_sst shown in Fig. 2. There are low values at or near zero in polar regions where there is little or no air–sea heat flux because of extensive year-round sea ice coverage. In ice-free regions the coefficient grows more negative toward the equator, mostly with SST according to Fig. 1b. In the subtropics and over the Gulf Stream the latent heat feedback due to the combination of high SST and high winds produces coefficients beyond −60 W m⁻² °C⁻¹. According to Fig. 1b, wind speeds of only about 7 m s⁻¹ are sufficient to produce so negative a coupling when the SST is greater than about 26°C. Elsewhere, the interplay between wind and SST determines the distribution of Fig. 2. The global-mean SST coupling coefficient is about −40 W m⁻² °C⁻¹. It is slightly less negative than the effective coefficient, W m⁻² °C⁻¹ (Table 1), computed from (14) as the ratio of global averages. This difference indicates that little or no warming is due to the rectification effects discussed at the end of section 2.

View Full Size

Global distribution of the SST coupling coefficient C_sst defined by (10).

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00148.1

• Download Figure
• Download figure as PowerPoint slide

Table 1.

Results of linear regressions of annual SST anomalies over the 23 years from 1984 to 2006 and the effective coupling coefficients (W m⁻² °C⁻¹), global and for the predominantly ice-free basins, given by the ratios of Δ₂₃SST to the heat flux changes in Table 2.

View Table

4. Trends and changes (1984–2006)

Annual anomalies of both SST and heat flux have been constructed relative to the means over the 23 years from 1984 to 2006. This period is chosen as a standard baseline because it has a complete set of flux estimates. Throughout these years, satellite measurements are available for input into constructing the SST fields, so the earlier presatellite era problems of consistency and sampling over remote ocean regions are greatly ameliorated. Nevertheless, time series of SST and heat flux anomalies were computed back to 1949 because they suggest a different behavior up to the 1970s.

Linear regressions of annual anomalies over the 1984–2006 period are used to compute trends, which are expressed as the 23-yr changes Δ₂₃ from 1 January 1984 to 31 December 2006. To partition Q_pbl anomalies according to (7), annual SST anomalies at all points are used to estimate

View Expanded

Spatial averages of these estimates reflect the spatial correlation of SST anomalies and the nonlinearities of Fig. 1 that are implicit in the global distribution of C_sst (Fig. 2). Although, Q_sst could be computed from (8), these estimates are sufficient for present purposes because changes in Q_pbl, not its partition, are central.

The spatial distributions of 23-yr changes in SST, Q, Q_sky, and Q_pbl are shown in Fig. 3. The predominant air–sea flux signals are associated with changes in sea ice coverage, but the corresponding SST changes are small. The general reduced coverage of the Arctic margins means that more radiation is absorbed by the open ocean instead of being reflected by sea ice, but Δ₂₃Q_S (not shown) is typically less than 20 W m⁻². Larger changes, greater than 40 W m⁻², are seen in Δ₂₃Q_A (not shown), such that changes in Q_sky along the margins of the Arctic Ocean and Labrador Sea typically exceed 50 W m⁻². A similar situation, but with smaller signals, is seen in the Antarctic between the Ross Sea and the Antarctic Peninsula. However, just to the west of this region there are signals of similar magnitude but opposite sign associated with increased sea ice coverage. The greater Arctic and lesser Antarctic sea-ice-related changes in Q_sky are not evident in Δ₂₃Q (Fig. 3b) because they are largely compensated by changes in Δ₂₃Q_pbl.

View Full Size

Global distributions of the 23-yr changes (1984–2006): (a) Δ₂₃SST (°C), (b) Δ₂₃Q (W m⁻²), (c) Δ₂₃Q_sky (W m⁻²), and (d) Δ₂₃Q_pbl (W m⁻²).

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00148.1

• Download Figure
• Download figure as PowerPoint slide

The SST changes of Fig. 3a are not uniform. Only small regions (e.g., off Baja California) show Δ₂₃SST < −0.5°C. But there is large-scale warming of the North Atlantic south of the ice zone and including the Mediterranean Sea, in the western Pacific of both hemispheres, and in the Indian Ocean. Over most of these regions there is a general reduction in Q_pbl, as expected from C_sst < 0, and this signal is identifiable in Δ₂₃Q (Fig. 3b) because the Q_sky signals (Fig. 3d) are generally smaller in amplitude. The exception in the subpolar gyre of the North Atlantic, where Δ₂₃Q is positive, is due to increases in both Q_sky and Q_pbl. The latter is a result of an increase in Q_air (not shown) dominating the decrease in Q_sst (not shown). Much of the heating (≈1°C) of the subpolar North Atlantic occurred in just 2 years following the winter of 1995. Robson et al. (2012) argue that the rapid heating was caused by a surge in northward ocean heat transport in response to the negative North Atlantic Oscillation (NAO) index of 1995/96 following a prolonged positive phase. The hindcast study of Yeager et al. (2012) finds rapid warming at this time when a reduced surface cooling no longer balances an already strong heat transport. This latter picture is consistent with the increase in Q in this region of Fig. 3b, which is due to changes in both Q_sky and Q_pbl, possibly because of less cloud and weaker winds, respectively, associated with the positive to negative shift in the NAO index. Both studies suggest an important role for ocean heat transport, R_H in (13), at least in the subpolar North Atlantic. Hereafter, such lateral advection signals are minimized by averaging over entire ocean basins or the global ocean.

a. Basin and global changes in SST

Figure 4 shows annual anomalies of the global and basin average SSTs from 1949 through 2006 and the 1984–2006 linear regressions. The global SST (Fig. 4a) is relatively constant until the mid-1970s, then generally rises by about 0.4°C through 2006. Similar behavior is seen in most individual basins so that prior to 1983 all but two annual anomalies (1979 and 1980 Southern Ocean, Fig. 4e) are negative in all basins. The 23-yr differences Δ₂₃SST are given in Table 1. They range from only 0.08°C in the Southern Ocean to 0.48°C in the Atlantic Ocean. As previously noted, the latter is dominated by the North Atlantic SST response (Fig. 3a) to the NAO shift. Significant contributions to the global change of 0.28°C also come from the western Pacific and Indian Oceans.

View Full Size

Annual SST anomalies (°C) relative to the 1984–2006 base period from 1949 through 2006 averaged over (a) the global ocean, (b) the Atlantic basin, (c) the Pacific Ocean basin, (d) the Indian Ocean basin, (e) the Southern Ocean, and (f) the Arctic Ocean. Thick black lines from 1884 through 2006 are the linear regressions over this base period.

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00148.1

• Download Figure
• Download figure as PowerPoint slide

Over the full 58 years (1949–2006) of Fig. 4 the largest SST increase of ~0.7°C is seen in the Indian Ocean basin because of significant warming prior to the mid-1970s. There is similar, though weaker, behavior in the Southern Ocean where the SST increase over the entire record is more than twice its Δ₂₃SST.

This SST analysis is not aimed at ENSO variability, which is highly damped by basin and global averaging and is typically spread over two annual anomalies. Nonetheless, major ENSO events do appear in Fig. 4, particularly in the Pacific. For example, the highest Pacific anomalies appear in 1997/98. In 1998 this signal is reinforced from the Atlantic and Indian Ocean basins to give the largest global anomaly. These warm years are largely offset by the colder years of 1999/2000, so the 23-yr trends are not adversely affected. However, this compensation would not be true even globally of shorter trends—over 1985–98, for example.

b. Basin and global changes in heat fluxes

The datasets do allow Q_sst, Q_air, and Q_pbl heat fluxes to be computed from 1949 through 2006 over the ice free ocean. Figure 5 shows the annual values globally and for the individual basins, except for the Arctic where sea ice coverage can dominate interannual variability (Fig. 3). The Q_sst anomaly time series reflect SST anomalies of Fig. 4 according to (15), depending on the spatial correlation between local SST and heat flux changes that are implied by the coupling coefficient distribution of Fig. 2.

View Full Size

Annual heat flux anomalies of Q_pbl Q_sst and Q_air (W m⁻²) from 1949 through 2006, relative to the 1984–2006 base period, averaged over (a) the global ocean, (b) the Atlantic Ocean basin, (c) the Pacific Ocean basin, (d) the Indian Ocean basin, and (e) the Southern Ocean.

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00148.1

• Download Figure
• Download figure as PowerPoint slide

First, consider the 23 year (1984–2006) changes (Δ₂₃) given in Table 2. Despite very different magnitudes, the general pattern of behavior in the predominantly ice-free basins is similar to the global. An increase in SST is accompanied by a decrease in Q_sst according to (10). About one-half of this decrease is compensated in Q_pbl by an increase in Q_air. Specifically, the response to the global SST increase of 0.28°C is Δ₂₃Q_sst = −12.9°C, giving = −46 W m⁻² °C⁻¹. The corresponding global increase in Q_air is 6.8 W m⁻², such that Δ₂₃Q_pbl is only −6.2 W m⁻², mostly due to evaporation.

Table 2.

Air–sea heat flux changes Δ₂₃ (W m⁻²) from the beginning of 1984 to the end of 2006, estimated from the linear regressions of annual heat flux anomalies over these 23 years. In parentheses are the percent confidence levels that the trends, and hence differences, are nonzero.

View Table

The global and basin effective coupling coefficients are given in Table 1. Consistent with Fig. 2, the Southern Ocean has the weakest basin at −36 W m⁻² °C⁻¹ and the Indian Ocean has the strongest at −53 W m⁻² °C⁻¹. The Atlantic (−44 W m⁻² °C⁻¹) and Pacific (−48 W m⁻² °C⁻¹) fall in between because they span more latitudes. An effective global boundary layer coupling coefficient is = −22 W m⁻² °C⁻¹. Here again, the Indian Ocean has the strongest coupling and the Southern Ocean the weakest at −30 and −12 W m⁻² °C⁻¹, respectively, with the Atlantic and Pacific in between at −20 W m⁻² °C⁻¹. The ratios of this global and the four basin values of to the corresponding are 0.48, 0.57, 0.33, 0.45 and 0.42, respectively. Therefore, about half the decrease in Q_sst is compensated by an increase in Q_air.

Now, consider the full 57 yr of Fig. 5. The compensation of Q_sst by Q_air can be seen on the longest time scales in all basins. However, on decadal time scales the negative correlation sometimes breaks down. In the Indian Ocean (Fig. 5d), the two cycles of large 5 W m⁻² amplitude decadal variability in Q_sst (dotted trace) through the 1950s and 1960s is not seen in Q_air and the 2000s show an increase in Q_air but a more steady Q_sst. In the Atlantic (Fig. 5b), there is a positive correlation between Q_sst and Q_air (dashed trace) from about 1954 through 1961, and the two quantities are not closely coupled from 1984 to 1998.

In Fig. 6 annual anomalies of Q, Q_pbl, and Q_sky are shown for all 23 years (1984–2006) when the latter is available from ISCCP-FD. On shorter time scales within this period, the relationships between SST and the various terms of the surface heat flux fundamentally differ from one period to another as well as from basin to basin. To illustrate, consider the decade centered about January 1991. SST departures from the linear trends in the Atlantic and Indian Oceans (Fig. 4) can be generally described as positive over the first half decade and negative over the second half decade. Accordingly, the Q_sst departures in Fig. 5 are of opposite sign. In the Atlantic Q_air is nearly a constant −3 W m⁻² over the 10 yr, so Q_pbl follows Q_sst with a negative displacement. But Q_sky departures (Fig. 6b) are in phase with the SST and of similar amplitude, so that there is very little signal in Q departures from its trend. In contrast, Fig. 5d shows Q_air in the Indian Ocean basin following the sign of SST and over most of the second 5 yr (1991–95), nearly completely compensating Q_sst, so that there is little signal in Q_pbl other than a small negative departure in 1992. Therefore, Q over this half decade is correlated with Q_sky departures, which are negative in 1991 and 1992 and near zero afterward. There is a different interplay between Indian Ocean terms over the first 5 years (1986–90) of the decade. There is less compensation from Q_air, so Q_pbl departures are generally negative, but these are overmatched by large positive departures of Q_sky that make Q significantly above its linear trend from 1987 through 1989.

View Full Size

As in Fig. 5, but for Q_pbl, Q_sky, and Q over the base period 1984–2006 only.

Citation: Journal of Climate 25, 18; 10.1175/JCLI-D-11-00148.1

• Download Figure
• Download figure as PowerPoint slide

d. The SOM assumptions

According to (14) the observed linear trends in annual SST from 1984 through 2006 could be sustained by a constant positive heat flux, Q. However, Fig. 6 shows that annual Q anomalies are not constant but are themselves decreasing. Although the sign of Q may be uncertain, the decrease in anomalies is robust and quantified in Table 2 by the negative Δ₂₃Q in all basins, and hence globally. Specifically, the CORE fluxes in Fig. 6 indicate that the global anomaly in Q decreases from 1984 through 2006 with Δ₂₃Q = −9.1 W m⁻². Although a decrease due to Q_pbl is expected, the additional decrease given by Δ₂₃Q_sky = −3 W m⁻² is not. This global signal is due to the longwave flux change of Δ₂₃Q_A = −3 W m⁻², and an essentially steady shortwave radiation due to an Atlantic and South Pacific increase balancing a Southern Ocean and North Pacific decrease.

Thus, the data we do have indicate that, as SST increased after 1984, Q_sky did not increase. This result and the then inevitable decrease in Q imply that the slab ocean model assumptions leading to (14) are incorrect. However, the assumption of no heating due in lateral ocean processes, R_H = 0 in (13), is likely valid on basin and global scales. Globally, the heat flux through continental boundaries is essentially zero. On basin scales the assumption is supported by the similarity between the global and basin behavior, despite large difference in magnitude, whereas R_H heating of one basin would mean cooling of another.

A difficult SOM assumption to justify is for h in (13) to remain interannually invariant when both diurnal and seasonal variations are known to be from 10 to 1000 m. Nevertheless, a shoaling of h alone would not seem to explain our results. To illustrate, consider an initia1 heat flux anomaly Q_o and mixing depth h_o. According to (13), at all times a constant linear trend in SST equals h⁻¹Q = h_o⁻¹Q_o. The effective couping coefficient W m⁻² °C⁻¹ can then be used to give the time evolution of h as

View Expanded

Therefore, so as to produce the observed SST warming and decrease in heat flux, in the absence of other ocean processes, the rate of shoaling would need to have been 230 m yr⁻¹. But, there is no evidence of h changing to within even two orders of magnitude of this rate over the 23 years from 1984 to 2006. Instead, from (13) the most likely explanation is that the cooling expected due to vertical ocean processes R_V/h diminished from 1984 to 2006. Unfortunately, the evolution of this term is not observable on basin and global scales, but as a testament to its potential power we note that it is the primary driver of ENSO variability in the equatorial Pacific.

5. Discussion and conclusions

Global datasets (Hurrell et al. 2008) show a rise in SST in all ocean basins from the 1970s onward—in particular, in the North Atlantic, western Pacific, and Indian Oceans. The latter has the largest basin-scale warming and is evident from the 1950s. The SST increase has been much smaller in the Southern Ocean where the effects of sea ice changes are of both signs and largely cancel. Although the basin-scale changes are small (<1°C), satellite observations since the late 1970s have greatly ameliorated consistency and sampling problems so that signals since then are generally believed to be real (Le Treut et al. 2007).

The net heat flux into the ocean between 1984 and 2006 is highly uncertain and cannot be said to differ from zero by more than its uncertainty plus the cooling through sea ice. This viewpoint is consistent with estimates of little, if any, ocean heat content changes (Harrison and Carson 2007). On basin scales the distribution of mean heat flux is consistent with observationally based estimates of ocean heat transport (Large and Yeager 2009), but the transport uncertainties are large too. Therefore, it must reemphasized that the present results say nothing about the absolute magnitude of the heat flux into the ocean. Instead, they depend only on changes in annual anomalies. The time invariant adjustments of section 2 have negligible impact on these changes. For example, the solar radiation reduction alters the Table 2 values of Δ₂₃Q_S by only 0.005 W m⁻² globally and by at most 0.15 W m⁻² on basin scales. Although unknown time-dependent errors could affect these changes, there is nothing known to suggest anything significant, and the data used here represent the current state of knowledge. The downwelling longwave flux is the most suspect, so it was examined in section 4c and found to be consistent with Stephens et al. (2008).

The global increase in SST from 1984 through 2006 on its own would be expected to reduce the heat flux into the global ocean by about Δ₂₃Q_sst = −13 W m⁻². The anticipated compensation by Q_air is now quantified in Table 2 as being about one-half or Δ₂₃Q_air = 6.8 W m⁻² globally, and this behavior is similar in other basins, though magnitudes differ substantially. Therefore, the rough agreement between Δ₂₃Q_sst and the present finding of Δ₂₃Q ≈ −9 W m⁻² is only a fortuitous consequence of the increase in Q_air (7 W m⁻²) being partly balanced by a decrease in Q_sky (−3 W m⁻²). This latter signal is due to a small decrease in Q_A over these 23 years, which is counter to the increase expected over longer time scales in response to increases in atmospheric GHG composition. Therefore, the ISSCP-FD time series suggest that this 23-yr period is too short to be representative of long-term climate change in response to O(1 W m⁻²) anthropogenic GHG forcing plus counteracting aerosol effects.

A strong conclusion is that from 1984 through 2006 the upper ocean did not behave as a slab ocean model because increasing SST and decreasing heat flux are inconsistent with SOM behavior. If Q_sky truly decreased, or even increased by less than Q_pbl decreased, then (13) says that ocean processes must have been active in the SST increase. The most likely way for this to happen is if the warming strengthened the upper-ocean stratification so that cooling by vertical ocean processes became less, perhaps with some shoaling of the mixing depth. Indeed, heat flux anomalies would be expected to warm SST faster than subsurface temperatures, increasing the stratification and inhibiting entrainment mixing of cold water to the surface. Although consistent, there are also other factors at work, such as the wind and freshwater forcing, including sea ice melt, not considered here. The inference for a dominant role for vertical ocean processes is indirect because their time evolution is not known. However, it is supported by the data, by their dominant role in ENSO variability, and by arguments that lateral processes must be small globally and seem to be so on basin scales too, and that changes in mixing depth would need to be too large to play an important role on their own.

Clearly, the 1984–2006 SST and Q trends are not sustainable indefinitely. The implication is that natural variability dominates the SST and the O(10 W m⁻²) heat flux signals over the 1984–2006 period, with a significant contribution from the 1995–96 shift from positive to negative NAO index. Also supportive of this possibility are the different ways SST and the various heat flux anomalies behave on decadal and shorter time scales. Although incomplete, the apparent much more steady behavior of SST and heat flux through the 1950s and 1960s is also consistent.

A curious observation is the tendency for the radiative flux Q_sky particularly the longwave component, to counter SST increases. This effect is quantified by , globally and in most basins. If this negative feedback is more generally true, then an interesting speculation is that it may be more difficult for nature to warm SST than believed on the basis of Q_sst and Q_pbl only.

The nonsolar feedback of W m⁻² °C⁻¹ is more than twice as strong as the −14.6 W m⁻² °C⁻¹ estimated by Doney et al. (1998) from an early coupled climate model. Just alone is about 50% stronger, suggesting that some climate models may have a weaker negative heat flux feedback to SST changes than estimated here for the 1984–2006 period. In particular, during late-twentieth-century warming in the latest Community Climate System Model, version 4 (CCSM4), Q_pbl provides little or no negative feedback (Bates et al. 2012), in contrast to the large negative values of in Table 2. The suggestion, following from the discussion of warming in section 4c, is that there may be more surface warming due to increasing Q_air in these models than found in observations of the 1984–2006 period.