1. Introduction and tropospheric adjustment
In climate models, adjustments in the stratosphere have long been accounted for when determining radiative forcings (Shine et al. 1990). The concept of tropospheric adjustment emerged only recently. Tropospheric effects have been called “fast feedbacks” or “the initial fast features” (Lahellec and Dufresne 2014), “semi-direct effects” (Andrews and Forster 2008), “fast responses,” “rapid adjustments” (Bala et al. 2010), or “direct response to CO2” (e.g., Merlis 2015). The separation between fast tropospheric adjustments and feedbacks partly arises from the approximation of the global radiative response by a feedback term that depends linearly on global temperature anomaly [λT in Eq. (1)]. Tropospheric adjustments, which have short time scales, are included in the effective radiative forcing (ERF; e.g., Boucher et al. 2014; Forster et al. 2013).
From a process point of view, tropospheric adjustment for CO2 happens because directly after the forcing is applied, the radiative imbalance at Earth’s surface is smaller than at the top of the atmosphere (TOA). The middle and lower troposphere warm before the surface temperatures increase, causing increased stability, and reduced evaporation, convection, and precipitation over oceans (Cao et al. 2012; Andrews et al. 2012; Kamae et al. 2015).The tropical upward velocities weaken over the oceans and strengthen over land in all models (Bony et al. 2013). The circulation also weakens—independently of the land–sea warming contrast—due to the spatial pattern of the CO2 radiative forcing acting on the climatological distribution of clouds and humidity (Merlis 2015). Trace gases alone force the stratosphere and upper troposphere to increase the eddy momentum flux, to accelerate stratospheric westerlies, and to displace the tropospheric jets poleward without any sea surface temperature response (Wu et al. 2012; Grise and Polvani 2014a; Staten et al. 2014). Either the reduced surface latent heat flux or the reduced relative humidity at the top of the boundary layer leads to a reduction in low-level cloud cover (Colman and McAvaney 2011; Kamae and Watanabe 2013; Wyant et al. 2012; Watanabe et al. 2012; Tomassini et al. 2013; Zelinka et al. 2013). The cloud response can be attributed to both the aforementioned dynamic and thermodynamic component. Other adjustment effects are the increased transport of heat from the land to the ocean due to enhanced land–ocean heating contrast (Williams et al. 2008; Dong et al. 2009; Webb et al. 2013) and the CO2 physiological effect, which enhances the land warming and moisture transport onto land (Cao et al. 2011; Kravitz et al. 2013; Doutriaux-Boucher et al. 2009; Kamae and Watanabe 2013). Different forcing agents, such as solar or CO2 forcing, show different adjustment processes (Lambert and Faull 2007; Bala et al. 2010; Andrews et al. 2010; Schaller et al. 2013). Overall, the tropospheric CO2 adjustment is also defined as the sum of all processes that happen before the net forcing at the TOA and surface are equal, operating as a measure of the equilibration of the troposphere with the surface (Bala et al. 2010; Lahellec and Dufresne 2014).
Some of the tropospheric adjustment effects are consistent across models, while others are model dependent, or even model version or cloud scheme dependent (e.g., Chung and Soden 2015a). Studies disagree as to how important the different tropospheric adjustment processes are compared to long-term or equilibrium responses. Williams et al. (2008), Andrews and Forster (2008), Gregory and Webb (2008), Bala et al. (2010), Webb et al. (2013), Bony et al. (2013), and Lahellec and Dufresne (2014) find that the ECS or the overall uncertainty to external forcing is influenced, whereas Tomassini et al. (2013), Vial et al. (2013), and Grise and Polvani (2014b) find no statistically significant effect of (their) adjustment processes on the feedback strengths or ECS. Ringer et al. (2014) show a correlation between forcing and feedback, which further complicates the distinction between the two and is discussed further in section 5.
There is no a priori reason why all adjustment processes should be fast, so the distinction between adjustment and surface temperature–mediated response is not clear (Williams et al. 2008; Caldeira and Myhrvold 2013; Zelinka et al. 2013; Sherwood et al. 2014). Some forcing-dependent processes may take place over months or years after the imposition of the forcing, during which the temperature may increase by several degrees, so adjustment and feedback may be taking place simultaneously. An adjustment process influences the local temperatures and heat fluxes, but has little impact on the global mean surface temperature [T in Eq. (1)]. We define the system that is being forced and that experiences adjustments and feedbacks as that which determines T.
Technically, the spatial pattern of a tropospheric adjustment response is determined by either fixed sea surface temperature (SST) runs, in which a climatological SST field is prescribed [used, e.g., in Hansen et al. (2005), Bala et al. (2010), Andrews et al. (2012), Zelinka et al. (2013), and Meraner et al. (2013)] by defining the adjustment as the first year of a 4×CO2 simulation of a coupled model [used, e.g., in Kravitz et al. (2013) and Bony et al. (2013)] or a slab ocean model [used, e.g., in Bony et al. (2013) and Grise and Polvani (2014b)] or by regressing each grid boxes’ variable evolution against the global mean surface air temperature (Gregory and Webb 2008; Andrews et al. 2015). Attempts and problems using radiative kernels to define the tropospheric adjustment response are discussed in Chung and Soden (2015a), Block and Mauritsen (2013), and Larson and Portmann (2015). Forcings are determined by either fixing the global surface temperature (Shine et al. 2003), or—more commonly—fixed-SST simulations, a regression method, which uses Eq. (1) and regresses N, the TOA flux imbalance, against T, the surface temperature response (Fig. 1), or radiative kernels [see Chung and Soden (2015b) for a comparison of the different definitions of radiative forcings].
Global mean net TOA downward radiative flux evolution against global average surface air temperature change of the large abrupt 4×CO2 ensemble. The regression covers the first 150 yr (black line). Small dots depict the 121 ensemble member annual averages, while large dots are ensemble averages—annual until year 100, at ~4.4-K temperature increase, and decadal afterward.
Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-16-0312.1
In this paper, we want to challenge the common understanding of subannual tropospheric adjustment. We find robust multiannual adjustment responses in a large ensemble of coupled simulations introduced in section 2. This response includes mechanisms described above, but we also find the ocean to strongly adjust to the radiative forcing, shaping in turn the tropospheric adjustment processes. We introduce a conceptual framework to show that this response is indeed better described as a time-dependent forcing adjustment than a temperature-dependent feedback (section 3). We then show in the large ensemble that the multiannual adjustment is caused by shortwave cloud radiative effect over the oceans and argue that this is due to the spatial pattern formation of sea surface temperature, ocean heat uptake and loss, and the meridional ocean heat transport (section 4). Finally, since the conventional definitions of radiative forcing only include the adjustment of subannual tropospheric processes, we discuss the consequences of oceanic adjustment for the definition of radiative forcing (section 5).
2. Model and experimental setup
We generate a large initial condition ensemble of abrupt4×CO2 simulations—in which CO2 is quadrupled at the start and then held constant—with the coupled atmosphere–land–ocean–sea ice Community Earth System Model (CESM1.0.4 with a resolution of roughly 2° in the atmosphere and land and 1° in the ocean and sea ice component; Gent et al. 2011; Danabasoglu et al. 2012). Abrupt forcing allows us to study different time scales, and the conclusions also apply for more realistic gradual forcing scenario simulations, which can be thought of as a convolution of infinitesimal abrupt forcing changes (Good et al. 2011, 2013; Geoffroy et al. 2013a). From a several-century-long control run, each January an ensemble member is branched off. In total, 121 different combinations of ocean, sea ice, and atmospheric states are used as initial conditions for the abrupt CO2 forcing. This nearly eliminates internal variability when considering the ensemble average. Simulations starting in months other than January were conducted, but yield similar results. All ensemble members are run for 2 years, 13 members for 100 years, 6 members for 250 years, and one member is run for 1300 years. All atmospheric data shown here are annual anomalies of each ensemble member with respect to the stable annual averaged control run. All oceanic anomalies are the difference of the forced ensemble member and the corresponding years following the control run branch off years, which are up to 100 years apart, to account for the small drift in the control run deep ocean. Ensemble averages are shown, except where noted. Results for other CMIP5 models with a similar experimental setup, but only a few ensemble members are shown by Andrews et al. (2012), Kravitz et al. (2013), Vial et al. (2013), Flato et al. (2014), and Chung and Soden (2015a).
To obtain the forcing, an atmosphere-only control simulation with climatological fixed prescribed SST derived from the coupled control run was run for several decades. Four 30-yr-long quadrupling CO2 simulations are branched off from different initial conditions. The last 10 years of each simulations’ averaged TOA imbalance are depicted as a red cross in Fig. 1. Further, for illustration purpose only, we conduct two more 150-yr step function simulations with 2× and 8×CO2.
3. Forcing adjustment versus time-dependent feedbacks
We solve Eqs. (2a) and (2b) for T with C = 7.3 W yr m−2 K−1 (Geoffroy et al. 2013a), λ = 1.2 W m−2 K−1 for all cases, and F = 3.2, 6.9, and 11.2 W m−2 for the different forcing levels. The estimates are based on the years 20 to 100 regression of the CESM 2×CO2, 4×CO2, and 8×CO2 simulations. Note that F is not proportional to the log CO2 (Gregory et al. 2015, and references therein). For illustrative purposes, we choose fA(T) as 
Illustration of cases A and B, discussed in the text. Scaled temperature anomaly for the illustrative model for (a) case A, (b) case B, and (c) CESM; annual averages are shown by the thin line, and spline fit by the thick line. (d)–(f) As in (a)–(c), but for scaled TOA radiative imbalance. (g)–(i) As in (a)–(c), but for unscaled dT/dN. Gray, red, and light blue depict 2×CO2, 4×CO2, and 8×CO2 forcings, respectively; annual CESM output in (i) is shown in darker colors. The regressions lines (in gray, red, orange, and blue) for different temperature ranges are discussed in the text.
Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-16-0312.1
Because Eq. (2a) is not linear in T, for case A, T1(t) is different from nT2(t) or mT3(t) with the subscripts denoting the use of F1, F2, and F3 (Fig. 2a). The same holds for the TOA radiation imbalance, N1(t) ≠ nN2(t) ≠ mN3(t) (Fig. 2d). Equation (2b) is linear in T, however, so for case B, T1(t) = nT2(t) = mT3(t) (Fig. 2b), and equivalently for N(t) (Fig. 2e). For CESM, the scaled T (Fig. 2c) and N (Fig. 2f) nearly coincide for the three forcing levels. This indicates that case B and Eq. (2b) constitute a good description of the time evolution of N and T.
The evolution of dN/dT behaves similarly: For case A and Eq. (2a), 
In summary, we argue that the curvature in the N–T space for the first few years could be treated as an adjustment problem (case B) rather than a temperature-dependent feedback (case A). This does not imply that later on during the equilibration process the feedback parameter has to be constant, that a combination of cases A and B might not be a better overall description, or that a spatially dependent feedback parameter might be a helpful description (Armour et al. 2013). We now show that the widely used two-box model with an ocean heat uptake efficacy factor conforms to case B, but modifies the forcing on different time scales than fB(t).
A commonly used refinement of the global model of Eqs. (2a) and (2b) is to consider two layers (Gregory 2000; Held et al. 2010; Geoffroy et al. 2013a), with T being the temperature of the upper layer and Tdeep layer that of the deep layer, and a downward heat flux 
The time scales on which the curvature develops are different in the two models: decades to centuries for 
In the next section we show how the shortwave cloud radiative response causes the curvature of dN/dT and how the oceanic adjustments—of meridional heat transport, surface heat fluxes, and SST patterns—might be connected to it. Section 5 will come back to the questions whether an adaptation of Eq. (1) according to case B might be useful.
4. From tropospheric to oceanic adjustment
a. Shortwave cloud radiative response
Most studies point to the shortwave cloud response dominating the tropospheric adjustment and the short-term nonlinearity of feedbacks, mostly focusing on the tropical west Pacific (Bala et al. 2010; Colman and McAvaney 2011; Andrews et al. 2012; Zelinka et al. 2013), but also on the Southern Ocean (Grise and Polvani 2014b). We use the measure of cloud radiative effect (CRE) as a rough indication of the cloud response. The CRE is defined as net TOA all-sky minus net clear-sky response and we consider only the shortwave (SW) component, since the longwave component evolves linearly with temperature and shows cloud masking effects. Its applicability is discussed, for example, by Zelinka et al. (2013) and Kamae et al. (2015). On time scales discussed here the SW CRE is dominated by the low-latitude response so that potential aliasing errors over sea ice would be too small to qualitatively impact our results. Figure 3 shows that in agreement with some other studies the SW CRE over the oceans is positive in the first year, and by extrapolation that it is nonzero at T = 0, indicating tropospheric adjustment (Colman and McAvaney 2011; Zelinka et al. 2013; Andrews et al. 2015). The SW CRE over the oceans declines as the temperature increases, changes sign after 3 to 4 years, and equilibrates after about a decade at a negative value. Models disagree on the temporal evolution and temperature sensitivity of the SW CRE but many models show a different sensitivity during the first decade compared to the century time scale response (Ringer et al. 2014; also, see gray dots for the global SW CRE response in Fig. 3 herein). In our case, oceanic SW CRE it is not linearly dependent on global mean temperature, as one would expect of a climate feedback. Global SW CRE varies first strongly and on decadal to centennial time scales only very slightly with global mean temperature. This behavior could be described either as an inconstant climate feedback parameter (case A above) or as an adjustment on a longer time scale than a few months (case B). SW CRE over land is also positive in the first year and remains roughly constant, so it can be described as a tropospheric adjustment, with no climate feedback. We will argue below that the SW CRE response comes about not only due to the rapid adjustment to the radiation on monthly time scale, but also due to the oceanic adjustment of heat transport within the first few years after the forcing is applied. We cannot exclude that the surface temperature increase of more than 3 K during the first 10 years influences the SW CRE response. However, Fig. 3 suggests that the SW CRE is not sensitive to temperature anomalies beyond 4 K. The four-member fixed-SST ensemble average SW CRE values (in green and orange for the ocean and land, respectively) lie within the range of the coupled ensembles (i.e., at 0.8 and 0.4 W m−2, respectively) with a global surface temperature increase of 0.7 instead of 1.1 K. The standard deviation of the first year’s ocean SW CRE is 0.24 W m−2, which dominates the total TOA ensemble standard deviation of 0.34 W m−2 (Fig. 1). The spatial SW CRE response pattern is discussed in section 4d.
TOA shortwave cloud radiative effect (positive downward) over land (red), oceans (blue), and total (gray) for all 121 ensemble members of the abrupt4×CO2 simulations. Small dots depict individual ensemble annual averages, while large dots are ensemble averages (annual until year 100, at ~4.4-K temperature increase, and decadal afterward).
Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-16-0312.1
b. Surface temperature, surface heat flux, and ocean heat content patterns
Figure 4 shows the anomaly patterns of the surface air temperature (leftmost column), sea surface temperature (middle left), surface heat flux (middle right, positive downward), and the rate of change of ocean heat content overlaid by the wind stress (rightmost column) of the first four years (upper four rows) and the long-term average (bottom row). Local values (in K or global W m−2) are divided by their annual global mean value (lower left box in each panel). The surface air and sea temperature increase includes Arctic amplification, enhanced warming over the Northern Hemispheric continents, and initial cooling in the equatorial Pacific region, especially in the east, which gradually weakens. This La Niña–like cooling pattern is attributed to the increase in upwelled cold waters by anomalous surface wind stress forcing (rightmost column). The deep water was not exposed to the surface warming signal yet and increases the east–west temperature gradient across the Pacific (Clement et al. 1996; Cai et al. 2015). The CMIP5 average shows delayed warming in the east Pacific as well (Andrews et al. 2015). Andrews et al. (2015) showed that the evolving pattern of surface warming is the dominant cause of nonlinearity between N and T in Eq. (1) for the HadCM3 and HadGEM2 atmospheric components and that the pattern of SST changes determines the SW CRE.
Abrupt4×CO2 ensemble and annual mean year one to four and 80–100 for (a)–(e) surface air and (f)–(j) sea temperature anomalies divided by the global response of that year (lower left corner of each panel, in K). Also shown are (k)–(o) surface heat flux anomaly (positive downward) and (p)–(t) rate of change of ocean heat content integrated over the whole water column, again divided by the global value (both W m−2). The difference between the rightmost two columns is the ocean heat transport convergence. Surface wind stress anomaly vectors overlay heat content anomaly contours in the last column.
Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-16-0312.1
Taking this line of thought one step further we show in the remainder of this paper how not only SSTs but also the ocean’s heat content and transport respond on short time scales and impact the tropospheric response. The two right columns of Fig. 4 show the annual and ensemble average surface heat flux anomaly and the vertically integrated rate of change of ocean heat content. The difference between the two columns is the ocean heat transport convergence. The tropical Atlantic loses heat to the atmosphere (blue in Figs. 4k–n) and the subtropical oceans (blue in Figs. 4p–s) and so does the whole eastern and tropical Pacific. Locally, the time evolution of surface fluxes, heat transport, and surface wind stress are rapidly changing (e.g., in the Indian Ocean, equatorial west Pacific, North Atlantic, or over Eurasia). All responses shown in Fig. 4 in the first four rows are as high as or higher than the inter annual standard deviation of the control run, indicating that they are a forced response. Patterns of surface air and water temperatures in the first years differ strongly from the long-term pattern (Figs. 4e,j). The increase in surface heat flux patchiness (Figs. 4k–o) is dominated by the latent heat flux (not shown). After three years the land does not take up heat. The rate of change of ocean heat content anomaly in year 80–100 (Fig. 4t) is very small and multiplied here by 4 to show the distinctively different pattern in all ocean basins, compared with the initial response pattern. Pattern of heat fluxes from the mixed layer to the deep ocean can influence atmospheric feedbacks and the global surface temperature response through SW CRE in slab ocean aquaplanet models (Rose et al. 2014). We argue in the following that meridional ocean heat transport shapes SW CRE on short time scales, on which the mixed layer is still equilibrating. A direct comparison to Rose et al. (2014) is not possible given our transient coupled experimental setup. However, their argument that the SST pattern caused by oceanic heat transport influences the SW CRE is the same as laid out here.
We now describe in more detail the oceanic adjustment processes. They are caused by the tropospheric adjustment of the first few months, as well as the anomalous surface heat fluxes, wind stress pattern, and the land–sea warming contrast of the first few years. Since they respond to the forcing and differ from the surface temperature mitigated ocean patterns of decadal to centennial time scales, oceanic adjustments last longer than tropospheric adjustments but provide the lower boundary conditions for the short-term atmospheric response.
c. Ocean heat transport and circulation response
Figure 5 shows—as a function of latitude and time—the ensemble mean surface heat flux (Fig. 5a), the meridional ocean heat transport convergence (Fig. 5b), and the rate of change of ocean heat content (Fig. 5c; all in Watts per global square meter). As already obvious from Fig. 4, the zonally integrated anomalous surface heat flux is positive at all latitudes for some years and especially high in the Southern Ocean 50°–60°S and the northern subtropics around 30°N (Fig. 5a). There is anomalous divergence of heat out of the equatorial regions and across the Antarctic circumpolar current (blue in Fig. 5b). These two effects lead to a cooling in the equatorial ocean initially, and warming everywhere else, especially in the midlatitudes, where there is downward wind-driven pumping of heat. The meridional heat transport could be one reason why in the Pacific sea surface temperatures emerge faster than expected from scaling global mean warming (Chadwick et al. 2014). Locally, it can take 2 to 4 years until the fluxes reach their highest value (e.g., around 55°S or 40°N).
Abrupt4×CO2 zonally integrated ensemble and annual mean (a) ocean surface heat flux change, (b) ocean meridional heat transport convergence, and (c) rate of change of ocean heat content, all in Watts per global square meter. Positive values indicate ocean heat uptake in (a), heat accumulation through transport in (b), and an increase in ocean heat content in (c).
Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-16-0312.1
In the North Atlantic the short time scale response in surface fluxes leads to a temporary increasing AMOC strength for 2 to 4 years (Fig. 6a), which is statistically different from the year following the branching off in the control run. Based on our simulations we cannot distinguish whether surface freshwater, surface or lateral freshwater fluxes, the wind field anomalies, sea ice edge, or places of convection and deep water formation cause this AMOC response (e.g., Gregory et al. 2005; Smith et al. 2014). All these fields show anomalous patterns in strength and locality compared with the long-term response. The zonally averaged rate of change of ocean heat content the North Atlantic is much smaller than in other locations during the first years and heat reaches depth later (Fig. 7, left minus right column). The wind field anomalies change sign within the first two years (Fig. 4). The small but robust AMOC response shows that even the deep ocean content can be affected by an anomalous surface forcing within a year and local surface conditions can influence volume fluxes elsewhere (e.g., here at 18°S where the overturning response is reversed and delayed for a few years, Fig. 6b). Local surface fluxes and ocean heat uptake efficiency influence the lower boundary condition for the atmosphere to respond to the radiative forcing (Fig. 4) and thus the time scale of tropospheric adjustment and short time scale feedbacks. We trust this surprising result only because of our large ensemble size, with which we can differentiate the response from the control run variability.
Abrupt4×CO2 ensemble and annual mean meridional overturning circulation anomaly at (a) 30°N and (b) 18°S for year 1 (red), year 2 (orange), year 3 (light blue), etc., to year 10 (black) (1 Sv = 106 m3 s−1).
Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-16-0312.1
Abrupt4×CO2 ensemble mean (left) global and (right) Pacific ocean heat content change for (top 4 rows) the end of years 1 to 4 and (bottom) the average of years 80–100 divided by 5 to fit the scale. Stippling indicates that the anomaly is significantly different from the control run variability at the 95% level.
Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-16-0312.1
Changes in the ocean interior temperature result from the changes in ocean heat transport. Figure 7 shows the global (left) and Pacific (right) ocean heat content change in joules—including surface heat flux and transport—for the first four years and the long-term response (lowest row, scaled to compare the patterns and fit the scale). Stippling indicates where the anomalous heat uptake patterns differ from the control run simulation variability at the 95% level. Next to the Pacific subsurface cooling, the nonuniform heating becomes obvious here also with depth. For each location the temperature perturbation reaches depths of 1 km after the first year and in the Southern Ocean the perturbation reaches a depth of 4 km in the second year.
d. Evolution of spatial SW CRE patterns
After having sketched out some processes involved in oceanic adjustment, we now show how the SW CRE responds to the oceanic adjustment. We suggest an interpretation along the lines of case B of section 3.
Figure 8 shows the coupled ensemble average of the first and second year’s and the long-term response (Figs. 8a,b,d), and the difference of the fixed-SST response to the first year of the coupled response (Fig. 8c). The fixed-SST response is averaged over years 10 to 30 of four ensemble members and can be regarded as “year 0.” In the global mean, the fixed-SST and coupled values are nearly the same [cf. also Fig. 3 herein and the discussion in Ringer et al. (2014)]. However, the spatial pattern shows local differences in the order of magnitude of the response itself, also over the land and especially strongly over the Southern Ocean. Throughout the ensemble, locally the strongest response in magnitude (both positive and negative) appears in year 2 (Fig. 8b). Figure 8d indicates that the long-term response pattern is very different from the short-term response, both in high and low latitudes.
Abrupt4×CO2 shortwave cloud radiative effect for the (a) first and (b) second year, and (d) the long-term coupled ensemble average. (c) Difference between the fixed-SST ensemble average of years 10–30 and the average coupled response of the first year. Global values are indicated in the lower left corner of each panel, all in W m−2 for the whole global area.
Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-16-0312.1
To measure the time evolution of the spatial pattern, and thus the potential to influence the nonlinearity of the feedback term, Fig. 9a shows the root-mean-square difference between each year of each coupled ensemble member and the long-term pattern shown in Fig. 8d. Each ensemble member is depicted as a gray line, and the longer ensemble members as colored lines, for the first 20 years of the simulations. The SW CRE pattern differs strongest from the long-term pattern in year 2 in 74% of all simulations. It takes 5 to 10 years to reduce the deviation from the long-term pattern by half. Figure 9b show that the spread between ensemble members for the first year is dominated by the western equatorial Pacific and Indian Ocean, where the ocean heat transport convergence is also very high and the SST influence the low stratocumulus clouds and thus the SW CRE.
Abrupt4×CO2 coupled ensemble member (colors and gray). (a) Root-mean-square deviation of the spatial SW CRE pattern from the long-term ensemble average pattern shown in Fig. 8d. (b) SW CRE standard deviation of coupled ensemble. (c) Root-mean-square deviation of rate of change of ocean heat content from its long-term pattern shown in Fig. 4t. (d) Root-mean-square deviation of rate of SST from its long-term pattern shown in Fig. 4j. Patterns used for (c) and d) are normalized, as in Fig. 4.
Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-16-0312.1
Figures 9c and 9d show again the root-mean-square difference to the long-term pattern of the rate of ocean heat content change and SSTs, which are similar to the response of SW CRE. To remove the global warming signal, the SST and dOHC/dt patterns are normalized with their global values, as in Fig. 4, before the root-mean-square difference is computed. The SW CRE pattern, however, is not normalized, since it does not scale with global mean temperature anomaly as a feedback would do. The time scale of pattern changes of SW CRE, rate of heat content change, and the SST are similar; most changes happen in the first six years. We interpret this as an indication that the SW CRE response over the ocean—after being triggered by the application of the forcing—is shaped by the oceanic adjustment of heat transport to the forcing. Perturbed physics experiments fixing the clouds or ocean heat transport would be necessary to understand this relationship in more detail. The analysis here shows that even very short time scales should be studied in coupled atmosphere–ocean instead of fixed-SST or slab ocean frameworks.
5. Virtual radiative forcing
We have shown in section 4 why fixed-SST simulations do not represent the full magnitude of the adjustment processes and discussed which oceanic processes could play a role in the adjustment process. In section 3 we suggested that the forcing term could be modified to capture the nonlinear evolution of dN/dT. We now propose a formulation of the forcing term, which includes processes of oceanic adjustments and reattributes part of the N–T curvature to the forcing. If fixed-SST simulations do not represent the full tropospheric adjustment magnitude, which forcing do they represent? Figure 1 indicates that the fixed-SST forcing is smaller than the ERF obtained in a regression of the first 150 years. In Flato et al. (2014) 5 out of 10 CMIP5 models, which contributed both the forcing from fixed-SST and the regression method, had smaller or similar forcings obtained by both methods. The brown cross in Figs. 10a and 10b includes the correction suggested by Hansen et al. (2005), using the 150-yr regression (from Fig. 1) to project FfixedSST (red cross) onto the vertical axis. This assumes that the same feedbacks act in a fixed-SST and coupled run and that λ is constant, which is both not the case (e.g., Gregory and Webb 2008). The orange cross adds the land warming of around 0.4 W m−2 to the fixed-SST forcing. Finally as an example, the green cross is the intersection of the vertical axis with the regression of years 10–150 (red line). This somewhat arbitrary time frame takes into account all adjustment and ocean mixed layer processes of the first 10 years.
(a) Annual global mean TOA net downward radiative flux evolution against global average surface air temperature anomaly, regressed for years 10 to 150 (red), and example of 1.4-K wide window to determine the time dependence of Teff, Fvirtual, and λ (blue). (b) Time evolution of Teff (black), Fvirtual (red), and λ (gray) for the time and temperature range indicated by the gray shading in (a). Values and arrows at the right vertical axis are the values of the same method after 150 yr.
Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-16-0312.1
a. Alternative method to obtain F and λ: Moving window regression
To examine the nonconstancy of F and λ in more detail, we now regress the radiative imbalance not over a certain time, but over a limited temperature range. That is equivalent to calculating the local derivative 
We suggest to call a forcing not obtained by regressing the first 150 years, but any other time frame virtual forcing. Virtual since there is no real state that experiences that forcing (Andrews et al. 2015), and since it is not only a radiative forcing but includes the whole state of the coupled system. Certain processes are fully, others only partly, included: for example, the virtual forcing of year 5 (7.6 W m−2) includes the adjustment of the AMOC and the corresponding influence on ocean heat uptake but only (although the main) part of the SW CRE adjustment.
b. Applications and limitations
The virtual forcing could be chosen simply as the forcing value that is most suited to maintain a “linear enough” relationship between N and T in a desired range of temperature or time in order to answer a certain question. While this approach complicates the definition of the forcing term, it might shift the attention to understanding and comparing processes step by step. If the initial curvature in dN/dT is indeed explained through a modified forcing term, the use of a virtual forcing would help to differentiate responses caused by the application of the forcing and the surface temperature increase. Ringer et al. (2014) found a correlation between the forcing term and the SW cloud feedback over 150 years. Folding these processes into the forcing term might be helpful to disentangle forcing and feedback. The concept of virtual forcing also might help to compare models with different degrees of adjustment. Assume that one model X has a strong sea ice response within the first three years, while model Y has a strong west Pacific SW CRE response within the first two years, and model Z shows a perfectly linear N–T relationship over the first few years. Comparing their virtual forcings might be cleaner than comparing their ERF or fixed-SST forcings, leading to a reduced uncertainty in λ and ECS. Given the evolution of λ, F, and ECS term in Fig. 10 it is also unclear which forcing is most suitable to determine ECS from observations (e.g., Otto et al. 2013) and how representative the transient response at any time is not only of equilibrium conditions, but also of any other time frame (Gregory et al. 2015). The virtual radiative forcing has the potential to be more process based than the ERF or fixed-SST forcing. Finally, one might use the virtual forcing for more technical studies: Even in noncoupled simulations one might differentiate with this method between specific atmospheric processes (e.g., by keeping the land surface temperature, certain surface fluxes, or aerosol concentrations fixed) and determine their adjustment time scales.
One obvious limitation becomes clear in Fig. 10b and by recalling the formulation of case B: The description of the time dependency of the adjustment might be more complicated than the exponential illustrative example in section 3. Note that fB(t) does not have an obvious formulation and depends on various very likely strongly model-dependent processes. In the coupled model reality, temperature-dependent processes (either in the form of case A or related to the deep ocean equilibration) can set in while a model is still adjusting. Thus, it is open to which degree the concept described here might be indeed helpful, not only in a model context with clearly defined forcing (here only done for one CO2 level) and a rough understanding of internal variability, but also concerning observational estimates of surface warming and ocean heat uptake.
6. Conclusions
We use a 121-member ensemble of abrupt4×CO2 simulations to overcome initial conditions dependency and internal variability to explore the heat flux through the coupled system within the first few years after an abrupt forcing. After the forcing is applied, the stratosphere and troposphere adjust within a few months. The resulting anomalous surface flux and wind stress force the ocean to take up and transport heat meridionally and vertically. Locally, the meridional ocean heat transport convergence can be even stronger than the surface heat flux, leading to a short-term tropical Pacific cooling. Circulation adjustments include the Atlantic meridional overturning circulation, which increases for some years. These oceanic adjustments of circulation and heat transport set the conditions for local surface fluxes and thus the atmospheric response of the first few years. The SW CRE over the oceans in particular has an adjustment time scale of several years, after which it does not scale with the global mean atmospheric temperature increase like a feedback would do. Instead, the time scale of pattern formation of SW CRE, SST, and ocean heat transport convergence from their initial homogeneous to a spatially stable pattern changing only in magnitude is the same. The time scale discussed here is connected to the fast time scales identified by, for instance, Hasselmann et al. (1993), Held et al. (2010), Caldeira and Myhrvold (2013), or Geoffroy et al. (2013b). Simple energy balance models or fits to coupled model output may capture part of the behavior but might be a less helpful framework to understand processes. We show through scaling an abrupt2×CO2 and 8×CO2 simulation that the coupled model output is better described as a forcing adjustment than as a temperature dependent feedback. In other words, the processes causing the curvature of dN/dT during the first few years proceed with a characteristic time scale in response to the forcing [Eq. (2b)] and do not scale nonlinearly with the global mean temperature [Eq. (2a)].
We define a virtual forcing—a variation of the traditional forcing term, which is defined either as effective radiative forcing or fixed-SST forcing. Virtual forcing is the forcing at a time when the feedback parameter is approximately constant in the time range of interest. Folding adjustment processes into the forcing term might help to compare models with different adjustment processes, to circumvent forcing-feedback correlations, or potentially also to better estimate ECS from observed warming and ocean heat uptake (Otto et al. 2013; Knutti and Rugenstein 2015). However, in principle a model could adjust for a few years through various processes and then either remain linear or display nonlinear feedbacks. At this stage it is unclear whether there is a sufficiently robust behavior across models that the concept can be useful. We do not want to argue that this approach is superior to describing the feedbacks as time or state dependent but simply offer one more approach in the recent discussion of the forcing-feedback framework applicability.
Acknowledgments
We thank three anonymous reviewers, Mike Winton, and Bala Govindasamy for their interest and stimulating in-depth comments.
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