1. Introduction
The familiar linear zero-dimensional energy balance model is a useful tool for summarizing and analyzing the response of global mean surface temperature to radiative forcing in simulations of forced climate change. Once tuned to a target atmosphere–ocean general circulation model (AOGCM), the hope is that the simple model can be used to predict how the AOGCM would respond to a large range of forcings (e.g., Solomon et al. 2007; Meinshausen et al. 2008).
The equilibrium climate sensitivity of the linear energy balance model is one of the key parameters adjusted to mimic the target AOGCM. However, rather than the equilibrium sensitivity, which is usually estimated using an atmosphere–slab-ocean model, an “effective sensitivity” (Murphy 1995) is often used for this exercise, determined from a transient run of the AOGCM (Solomon et al. 2007, Table S8.1), in an attempt to avoid inconsistencies between AOGCM and slab-ocean sensitivities. The effective sensitivity is obtained by scaling up the transient temperature response by the factor R/(R − N), where R is the radiative forcing and N is the top-of-atmosphere heat uptake (we refer to this informally as the ocean heat uptake in the following since the two are nearly the same on the time scales of interest here). The great majority of AOGCMs with available data in the Intergovernmental Panel on Climate Change (IPCC) third and fourth assessment reports (Houghton et al. 2001; Solomon et al. 2007) have effective sensitivities less than their equilibrium sensitivities. However, several researchers have noted an increase in the effective sensitivity over the course of long climate change simulations (Senior and Mitchell 2000; Gregory et al. 2004), although this result is not universal (Watterson 2000; Boer and Yu 2003). The increase in effective sensitivity is expected as a model with an effective sensitivity less than its equilibrium sensitivity approaches equilibrium.
Williams et al. (2008) examined the relationship between the top-of-atmosphere (TOA) fluxes and the surface temperature change in the stabilized-CO2 section of 1% CO2 increase experiments and defined an “effective forcing” by extrapolating this relationship back to a zero temperature change. Six of the eight models they investigated had effective forcings that were less than the traditionally defined radiative forcings. They argue that this is evidence for a direct CO2 effect on clouds, with fixed ocean temperatures, which modifies the “forcing” in analogy to the familiar direct stratospheric response. Gregory and Webb (2008) discuss an analogous analysis of slab-ocean models; however, the time scale of forcing adjustment in Williams et al. (2008) is on the order of decades, implicating oceanic adjustment as an important factor and favoring a feedback interpretation.
In this study, we propose an alternative interpretation of “effective forcing” and the time variation of “effective sensitivity.” We are inspired by Hansen et al. (2005), who noted that different forcing agents resulting in the same global mean radiative forcing can elicit different global mean temperature responses and accounted for this by introducing an efficacy factor associated with each forcing (see also Solomon et al. 2007, section 2.8.5). In this paper we note that an efficacy can also be applied to ocean heat uptake. It might seem perverse to treat ocean heat uptake as a forcing rather than a feedback when it is clearly internal to the climate system and likely varies with global mean temperature change. One way of rationalizing this approach is to consider a slab-ocean model in which one attempts to mimic the fully coupled system by specifying the heat flux exchanged between the deep ocean and the slab, putting aside the question of how the heat uptake is determined. A linear zero-dimensional model of this system would have as its inputs the heat uptake as well as the radiative forcing, leading one to consider the possibility of nonunitary efficacy of the heat uptake. We argue in the following that nonunitary efficacy of ocean heat uptake is a useful alternative to thinking in terms of effective forcings or the time variation of effective sensitivity.
In section 2, we present a model comparison that motivates the need for an ocean heat uptake efficacy and demonstrate that the feedbacks that apply to ocean forcing can be significantly different from those that apply to CO2 forcing. In section 3, we define nondimensional quantities that allow us to compare efficacies when radiative forcing and equilibrium sensitivity vary in time and between models. In section 4 we look at the ability of ocean heat uptake efficacy to characterize the time evolution of the climate state in a particular model—the Geophysical Fluid Dynamics Laboratory (GFDL) Climate Model version 2.1 (CM2.1). The distribution of efficacies in the IPCC multimodel ensembles of idealized transient climate change experiments is discussed in section 5. The results are summarized in section 6.
2. The need for ocean heat uptake efficacy
Figure 1 shows the global warming and net TOA flux anomalies for the two models forced with 1% yr−1 CO2 increase to doubling. Counter to (1), the MPI model has more heat uptake than the GFDL model. The heat uptake difference between the two models is evidently responding to the temperature change difference between the two models rather than forcing it, since the warmer model has more heat uptake. The twenty-first century simulations of the two models under Special Report on Emission Scenarios (SRES) B1, A1B, and A2 forcing scenarios show similar relationships (not shown). Raper et al. (2002) noted this tendency for models with larger transient warming to simulate larger heat uptake, relating the two quantities linearly with a constant of proportionality, which they term “ocean heat uptake efficiency.”
Equation (4) is a generalization of (2), which is its ε = 1 special case. By applying a factor to the ocean heat uptake in (4) we have not sacrificed conservation of energy. As (3) shows, ε modifies the feedback operating on ocean heat uptake. It is simply a matter convenience to attach it as a factor to N.
Hansen et al. (1997) show that the geographical structure of a radiative forcing is an important source of nonunitary efficacy. They show that forcings focused at the surface at high latitudes have the greatest impact on temperature and therefore the larger efficacy. The ocean heat uptake occurs at the surface, of course, and it is largest in the subpolar oceans. Figure 2 compares the doubled CO2 radiative forcing with the ocean heat uptake at doubling in the 1% yr−1 CO2 increase experiment with the GFDL model. It is clear that the ocean heat uptake is enhanced at high latitudes while CO2 forcing is somewhat larger in the tropics. Therefore, the expectation is that ocean surface heat flux will tend to have an efficacy greater than 1.
While the first 70 years of the 1% yr−1 CO2 increase to doubling experiment contains responses to changes in both radiative forcing and heat uptake, the subsequent stabilization period gives us an opportunity to look at the response to changing ocean heat uptake in isolation. This experiment has been run for 600 years with the GFDL model and its global mean warming over the 530-year stabilization period is about the same as in the initial CO2 increasing period. The efficacy in the stabilization period is about 2—the model is twice as sensitive to ocean heat uptake as it is to CO2 forcing, implying that that the feedback parameter for ocean heat uptake, λ/ε, is one-half that for CO2 forcing, λ [Eq. (3)]. To determine the sources of this difference, we evaluate feedbacks for the transient run stabilization period and the atmosphere–slab-ocean doubled CO2 experiment using the kernel method of Soden and Held (2006) and the GFDL model radiative kernel. The results are shown in Table 1. The total feedback is about −1 W m−2 K−1 for CO2 forcing and −0.5 W m−2 K−1 for ocean heat uptake. The 0.5 W m−2 K−1 difference comes from the increased positive cloud and albedo feedbacks and a decreased negative temperature feedbacks in response to ocean forcing. Several studies show that water vapor and temperature feedbacks are tightly coupled through the maintenance of constant relative humidity (Zhang et al. 1994; Soden and Held 2006). This motivates combining of the temperature and water vapor feedback in Table 1 to avoid cancellation of large terms of opposite sign. The sum of these two increases the ocean heat uptake efficacy somewhat more than does the albedo feedback difference but less than the cloud feedback difference. Thus, the reasons for ocean heat uptake efficacy are distributed among the individual feedbacks with cloud feedback making the largest contribution, about 50% of the total difference in feedback, after combining temperature and water vapor feedbacks.
Having obtained the equilibrium SST response in this way we can use it to obtain the response forced by ocean heat uptake. Consistent with Eq. (3), this is simply the transient response (Fig. 3, bottom panel) minus the equilibrium response and is shown in the middle panel of Fig. 3. Both ocean and CO2 forcing induce SST responses that are amplified in the subpolar regions. However the ocean forcing induces a stronger subpolar response so that the total response has a minimum of warming in these regions where the ocean forcing is dominant. This pattern is a common feature of transient simulations and appears in the Solomon et al. (2007) multimodel mean. The pattern was noted by Manabe et al. (1991) who showed that the deep mixed layers and large isopycnal mixing in the Southern Ocean and in the North Atlantic lead to minima in the ratio of transient to equilibrium response in those regions.
3. Ocean heat uptake efficacy with variable forcing and sensitivity
The difference in efficacy of the two models discussed in the last section was apparent because the models had similar equilibrium climate sensitivities and similar radiative forcings. We would also like to compare models with different sensitivities and also evaluate the efficacy in a single model, over time. For this purpose, we define the climate state, as illustrated schematically in Fig. 4, as consisting of the transient temperature change T relative to the equilibrium value TEQ on the x axis, and the net heat uptake N relative to the radiative forcing R on the y axis.
4. Time evolution of efficacy in the GFDL CM2.1
We now focus on the time variation of the climate state in a single model, the GFDL CM2.1. This model has the largest efficacy at CO2 doubling of any model in the IPCC ensemble presented in the next section. We employ the time-varying radiative forcing and equilibrium temperature change as scalings for the net TOA flux and transient temperature change, respectively, as in (8), to show the evolution of climate state over two 600-year experiments with a 1% yr−1 CO2 increase to doubling and to quadrupling. The results are shown in Fig. 5. The two experiments pass through a similar arc of states that have increasing efficacy over time, more rapidly at first, and then more gradually. There is a somewhat narrower band of efficacies in this arc in the 1% to 4 times CO2 experiment, presumably because of the larger signal-to-noise ratio. The scatter is larger in the transient forcing period of the experiments for the same reason. The two experiments are in reasonable agreement in this normalized climate state space, even in the band of states where the 1% to doubling experiment has stabilized forcing but the 1% to quadrupling experiment forcing is still increasing. The efficacy does not appear to be very sensitive to forcing history. The convergence of the model state on the lower right corner of Fig. 5 is an indication of the agreement of the coupled and slab-ocean equilibrium sensitivities since the slab-ocean value has been used to normalize the temperature axis.
The descent from the ε = 1 line in the 1% yr−1 CO2 increase experiments is seen to occur in the early pentads, while the forcing is ramping up. It should be noted that forcing increases alone do not induce efficacy—nonunitary efficacy develops as a climate response to forcing changes. To explore this early adjustment further, we also show the ensemble mean of four instantaneous CO2 doubling experiments with the same model. The first four pentads of this ensemble mean are denoted on Fig. 5 with the numbers 1 through 4. These show that the efficacy approaches a value near two within the first two decades. During this period a pattern is established of sea surface temperature change with reduced warming, and even some areas of cooling, in the subpolar North Atlantic and Southern oceans as the competing cooling effect of ocean heat uptake overcomes the radiatively forced response in these areas. The ocean warming that occurs in this early adjustment period is confined to the mixed layer and nearby regions.
Figure 5 also shows the mean state of a five-member ensemble of twentieth-century runs of CM2.1 averaged over the period 1980 to 1999 relative to an 1860 control run. The forcing is calculated as the change in top-of-atmosphere flux between two ensembles of fixed SST experiments, one with time-varying forcing agents and one with tine-invariant forcing agents. The late-twentieth-century climate state indicates that this model’s high efficacy is applicable to the historical period as well as to idealized forcing experiments. An important implication is that accurate measurements of the temperature change, forcing and ocean heat uptake associated with anthropogenic forcing in the current climate will not be sufficient to determine the equilibrium climate sensitivity and the committed warming if the actual heat uptake efficacy is significantly different from unity, as it is in this model.
The 600-year time series of pentadal and global mean temperature changes for the CM2.1 1% yr−1 to doubling experiment is shown in Fig. 6. This time series shows that about half of the total warming occurs in the CO2-stabilized portion of the run. If we use Eq. (8) for the fit, taking the heat uptake from the model itself, with an efficacy of 1, there is too much warming in the CO2 increasing period and not enough in the CO2 stabilized period although this fit seems to be approaching the AOGCM’s temperature at the end of the experiment. If we use an effective sensitivity in place of the equilibrium sensitivity in the equation, as is commonly done in reduced model fits to AOGCMs, a similar but smaller bias is apparent early in the run. Although this fit works reasonably well in the first two centuries, it has insufficient temperature increase in the final 400 years of the experiment.
The use of an efficacy allows us to fit both the CO2 increasing and CO2 stabilized portions of the time series. However, applying the efficacy naively to all time scales has the effect of increasing the amplitude of short-term temperature variations. This suggests that these short-term variations in N are not subject to the same efficacy as the longer-term variations, as would be plausible if these are not as concentrated in high latitudes as the long-term evolution of N–El Niño Southern Oscillation (ENSO) variability for example. An efficacy parameter should be useful in the simple models that are fit to AOGCMs when it is desirable to capture the long-term behavior of the AOGCM.
5. Multimodel transient efficacies at CO2 doubling
Table 3 shows that the radiative forcing has little correlation with transient and equilibrium warming. The methodology for computing radiative forcings in not fully standardized, and it is likely that the intermodel spread of forcing values would be smaller with more standardization, so it is encouraging that the mean and standard deviation of efficacy in the models is not altered substantially if one substitutes a uniform value of the forcing for the tabulated values. Some of the lowest values of efficacy are eliminated if one uses a uniform forcing, however.
The quantities TEQ, ε, and N are well correlated with T, the transient climate response and the sign of the correlations is such that TEQ and ε variations enhance the intermodel TCR differences while N variations damp them. Of these, TEQ is the most difficult to diagnose. Because (13) defines ε, it would be possible for ε to capture spurious variance from misdiagnosis of TEQ. The lack of correlation between the two parameters allays this concern. We conclude that efficacy is an important driver of intermodel TCR variance in addition to, and relatively independent of, the equilibrium sensitivity.
While λ affects TCR through TEQ as well as through the degree of equilibration, ε and γ have their impact on the TCR entirely through the degree of equilibration. Table 4 shows the correlation of these three parameters with T/TEQ. The signs of the correlations are consistent with (15). Efficacy has the largest correlation with TCR/TEQ but little correlation with the efficiency γ. The correlation of ε with N (Table 3) is apparently accounted for by its correlation with TCR after assuming (14). In this view, the anticorrelation between ε and N comes about because efficacy reduces warming by enhancing the cooling effect of heat uptake; the reduced warming, in turn, feeds back to reduce heat uptake.
Equation (15) expresses the simple idea that equilibration is decreased by a large ratio of γ, deep-ocean–surface climate coupling, to λ/ε, the coupling of the resultant anomalies to space. The degree of equilibration in the multimodel global mean is a little >0.5, indicating that this ratio is near 1, the strength of coupling to space and to the deep ocean are about the same. Mathematically, efficacy and efficiency enter as a product in (15) and Fig. 8 shows the impact of their intermodel variation on the product. The variations in efficacy are responsible for most of the variation in the product, so that, as expected from the correlations in Table 4, it has a larger influence on the degree of equilibration.
The implication of our simple model interpretation is that one would be more effective in reducing AOGCM uncertainties in transient climate sensitivity by reducing uncertainty in the radiative response to ocean heat uptake than in the relationship of the uptake magnitude to the surface climate perturbation. Uncertainty in radiative feedbacks substantially impacts not only the simulated equilibrium response but also the trajectory toward equilibrium for which ocean processes might have been thought dominant.
6. Conclusions
We argue that simple energy balance model fits to AOGCMs should make use of the concept of the efficacy of ocean heat uptake. This is equivalent to, but we believe more physically intuitive than, the concept of “effective forcing” since the adjustments that establish efficacy or effective forcing take place on a decadal scale, favoring interpretation as a response rather than a forcing. We also show that efficacy is more parsimonious than “effective sensitivity” since a considerable part of the time dependence of effective sensitivity can be captured with a time-invariant efficacy. The efficacy factor is variable across the AOGCMs used for IPCC assessments but is generally larger than 1 with an average value between 1.3 and 1.4, and can approach 2. Thus for most models the simulated warming is more sensitive to ocean heat uptake than to CO2 radiative forcing. Amongst the models, the transient climate response is better correlated with the efficacy than it is with the equilibrium climate sensitivity. The efficacy and climate sensitivity have little correlation, indicating that they represent different model characteristics. An understanding of the reasons for the differences in efficacy amongst the models should be useful for resolving the differences in the magnitude of transient climate change simulated in these models.
The use of an efficacy, or its equivalent, is necessary to fit the global mean temperature in both the forcing-increasing and forcing-stabilized sections of a 1% yr−1 CO2 increase experiment with the GFDL CM2.1. The potential significance of high efficacy in slowing the warming is well illustrated by this model and by an analysis of models utilized in the third and fourth IPCC assessments. The stabilized forcing warming commitment inherent in a given level of ocean heat uptake is magnified by the efficacy. High efficacy implies a greater fraction of the equilibrium response will occur after stabilization. Therefore uncertainty about efficacy poses a difficulty for determination of the equilibrium climate sensitivity from observations of forcing, temperature, and ocean heat uptake.
Plattner et al. (2008) and Solomon et al. (2009) have presented the long-term response to CO2 emissions in intermediate complexity models. In these experiments, there is a near cancellation between the warming effect of reduced ocean heat uptake and the cooling effect of reduced radiative forcing as carbon enters the ocean in the millennium following a cessation of carbon emissions, leading to a global temperature that declines only slightly. Our study indicates that radiative feedbacks play an important role in the impact of the ocean heat uptake reductions and that different AOGCMs may give differing results because of differences in the efficacy of heat uptake. A larger heat uptake efficacy would imply a more durable temperature response to CO2 emissions as reduction in radiative forcing accompanying oceanic CO2 uptake experiences a relatively larger warming offset from reduced ocean heat uptake. Our results suggest that the AOGCMs, which contain the most comprehensive simulations of radiative feedbacks and efficacy, should be applied to this long-term emissions commitment problem.
Acknowledgments
The authors thank Ron Stouffer, Geoff Vallis, Rong Zhang, and four anonymous reviewers for helpful comments on the manuscript. The authors also thank Brian Soden for the use of the GFDL CM2.1 radiative kernel. The authors acknowledge the international modeling groups for providing their data for analysis, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the model data, the JSC/CLIVAR Working Group on Coupled Modeling (WGCM) and their Coupled Model Intercomparison Project (CMIP) and Climate Simulation Panel for organizing the model data analysis activity, and the IPCC WG1 TSU for technical support. The IPCC Data Archive at Lawrence Livermore National Laboratory is supported by the Office of Science, U.S. Department of Energy.
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(top) Global mean temperature anomaly and (bottom) net TOA radiation anomaly for the GFDL CM2.1 and MPI ECHAM5 AOGCMs forced with the 1% yr−1 CO2 increase to doubling. Anomalies are taken relative to the mean of the first century of the preindustrial control runs. The equilibrium temperature change and radiative forcing are taken from Solomon et al. (2007).
Citation: Journal of Climate 23, 9; 10.1175/2009JCLI3139.1
Zonal mean doubled CO2 radiative forcing and ocean heat uptake at doubling in the 1% yr−1 CO2 increase experiment of GFDL CM2.1.
Citation: Journal of Climate 23, 9; 10.1175/2009JCLI3139.1
(top) SST equilibrium response (°C) to a CO2 doubling estimated from a long coupled model run of a 1% yr−1 CO2 increase to doubling experiment using Eq. (5), (middle) ocean heat uptake forced component of the transient response at CO2 doubling, and (bottom) the transient response at CO2 doubling, which is sum of the (top) and (middle).
Citation: Journal of Climate 23, 9; 10.1175/2009JCLI3139.1
Schematic relationships between radiative forcing R, equilibrium climate sensitivity TEQ, effective climate sensitivity TEF, effective forcing REF, and ocean flux efficacy ε, on a plot of global mean temperature T, against net TOA heat flux N, which is nearly equal to the net ocean heat flux over climatological time scales. If the climate state traverses the thick gray line between [0,R] and [TEQ, 0], REF = R, ε = 1, and TEF = TEQ; TEF, REF, and ε are different ways of accounting for deviations of the climate state from this path.
Citation: Journal of Climate 23, 9; 10.1175/2009JCLI3139.1
A scatterplot of scaled global mean temperature T/TEQ against scaled TOA net heat flux N/R for the 1% CO2 increase to doubling and quadrupling experiments with the GFDL CM2.1 climate model. All points are pentadal averages. The first three pentads of the 1% yr−1 experiments fall outside the box due to smallness of the forced response early in the experiments. The numbers represent pentadal and four-member ensemble means from the first 20 years of an instantaneous CO2 doubling experiment with the same model. The green circle shows the mean state of five-member ensemble of twentieth-century runs between 1980 and 1999.
Citation: Journal of Climate 23, 9; 10.1175/2009JCLI3139.1
Time series of pentadally averaged global mean temperature change in the 1% yr−1 CO2 increase to doubling experiment of the GFDL CM2.1 climate model. The plot also shows estimates of the transient temperature change using Eq. (8) with an efficacy of 2 and Eq. (9) with an effective climate sensitivity of 2.28°C.
Citation: Journal of Climate 23, 9; 10.1175/2009JCLI3139.1
Scatterplot of global mean temperature at CO2 doubling scaled by the equilibrium temperature change (T/TEQ) against net TOA heat flux scaled by the doubled CO2 radiative forcing (N/R) for 22 climate models used in the IPCC third and fourth assessment reports. Twenty-year means centered on year 70 of the 1% yr−1 CO2 increase to doubling experiments are used for the estimates.
Citation: Journal of Climate 23, 9; 10.1175/2009JCLI3139.1
Scatterplot of the ocean heat flux efficacy against efficiency for 22 climate models used in the IPCC third and fourth assessment reports. The product of the two scattered quantities reduces the equilibration of the surface climate TCR/TEQ.
Citation: Journal of Climate 23, 9; 10.1175/2009JCLI3139.1