1. J. M. Gregory,* 1,2 W. J. Ingram, 2 M. A. Palmer, 3 G. S. Jones, 2 P. A. Stott, 2 R. B. Thorpe, 2 J. A. Lowe, 2 T. C. Johns, 2 and K. D. Williams 2 *j.m.gregory@reading.ac.uk; (1) Centre for Global Atmospheric Modelling, Department of Meteorology, University of Reading, UK; (2) Hadley Centre for Climate Prediction and Research, Met Office, Exeter, UK; (3) Sub-department of Atmospheric, Oceanic and Planetary Physics, University of Oxford, UK Geophysical Research Letters, 31, L03205, doi:10.1029/2003GL018747, 2004 Introduction The concepts of radiative forcing and climate sensitivity are commonly used in analysis of climate change simulated by general circulation models (GCMs), because they are useful in comparing the size of response by different models and to different forcings (greenhouse gases, aerosols, solar variability, etc.). If the imposed forcing is F and the radiative response caused by climate change is H, N=F-H is the net downward heat flux into the climate system. It is found that in any given GCM H= ΔT, where ΔT is the global average surface air temperature change and the climate response parameter, which indicates the strength of the net feedback of the climate system. It is assumed that the real climate system has some constant, which is presently not known. Different GCMs have very different. By definition, a steady-state climate requires that N=0, so that no heat is being taken up by the climate system. In the initial steady state F=H=0 and ΔT=0. In a perturbed steady state F=H= ΔT ΔT=F/. The equilibrium climate sensitivity ΔT 2 eqm is defined as the steady-state ΔT due to a doubling of the CO 2 concentration. If this gives forcing F 2, then ΔT 2 eqm =F 2 /. The usual method to evaluate from a climate model is to run to a steady state with known forcing, and compute =F/ ΔT. This method is practicable with a slab'' model (an atmosphere GCM coupled to a mixed- layer ocean), because such models 10-20 take only years to reach a steady state. Coupled atmosphere-ocean GCMs (AOGCMs), however, take millennia, making this method computationally very expensive. Also, you need F, which is not straightforward to obtain. We propose a new and simple method for estimating F and. In a climate experiment when the forcing agent has no interannual variation, we assume that the forcing is constant on timescales of years and longer. Since N=F-H=F- ΔT, if we plot the variation of N(t) against ΔT(t) as the run proceeds (using annual means or longer), we should get a straight line whose N-intercept is F and whose slope is -. The ΔT-intercept will be F/, equal to the equilibrium ΔT. This method can be applied to any experiment that has time-variation, whether with a slab model or an AOGCM, and it is unnecessary to run the experiment to a steady state. In fact, it is the time- development before the steady state which is of interest. The method does not require a separate knowledge of F. We argue that the N-intercept will be the sum of all forcings that appear quickly (say, less than a year) compared with the rate at which the climate system can respond (cf. Shine et al., 2003). This includes not only the instantaneous effect of the radiative forcing agent, but also forcings which take some time to appear, such as the stratospheric adjustment caused by CO 2 and the indirect forcing that arises from the effects of aerosol on clouds. Starting from its control, we imposed an instantaneous quadrupling of CO 2 on HadSM3 (Williams et al., 2001), which comprises the atmosphere GCM HadAM3 coupled to a slab ocean 50 m deep. We plot N against ΔT. The evolution starts at the top left, where N is large (initially equal to F) and ΔT small, and moves down and right as ΔT rises and N declines. There is scatter resulting from the internally generated variability of the climate system. It reaches a new perturbed steady state where N=0, at the ΔT-intercept. We note that the net downward radiation at the tropopause does not quite reach zero. This is because there can be sensible and latent heat exchange across the tropopause, and apparently there is an increase of 0.5 W m -2 upwards in these arising from climate change. At the top of the atmosphere (TOA), however, there can only be radiative heat exchange, so the TOA net radiative heat flux must equal N. Hence we use TOA fluxes in our method. This avoids the need to diagnose the tropopause, an arbitrary and possibly systematically biased procedure (cf. Shine et al., 2003). Using the TOA instead of the tropopause makes very little difference to the forcing F (the N-intercept), which is 7.2 0.3 W m -2. This implies F 2 =3.6 0.2 W m -2, statistically consistent with though less precise than the value of 3.74 0.04 W m -2 diagnosed by other procedures. Our method is much simpler, requiring no special diagnostics, and it includes stratospheric adjustment. The regression slope for N against ΔT gives =0.99 0.07 W m -2 K -1. Using the steady state for years 21-30 we obtain ΔT=7.18 0.05 K =1.04 0.01 W m -2 K -1. The two are consistent. The precision could be improved by using an ensemble of integrations; for our method, this would be a better use of CPU time than running out to a steady state. In experiments 2S and 4S, N varies linearly with ΔT as in HadSM3 with 4 CO 2. However, the values of 1.2 W m -2 K -1 from these experiments are significantly larger than from HadSM3 i.e. the climate sensitivity to CO 2 is smaller in HadCM3 than in HadSM3. When we plot N against ΔT for experiment 4R we find that they are not linearly related. The flattening of the gradient as ΔT rises means that the strength of the climate feedback is changing as the climate evolves. The physical mechanisms responsible for this are under investigation. The clear-sky longwave component of N varies linearly with ΔT; the deviations from linearity are found mainly in the cloud feedbacks. A standard technique to estimate climate sensitivity from AOGCM time-dependent experiments is to compute =H/ΔT=(F-N)/ΔT. The dotted red line has a slope (F-N)/ΔT for year 1000. Evaluated this way, is often expressed as the effective climate sensitivity ΔT 2 eff =F 2 /, to permit comparison with ΔT 2 eqm. Because the climate feedback strength is changing in experiment 4R, ΔT 2 eff rises with time, in a similar way to that found by Senior and Mitchell (2000) for HadCM2. For year 1000, ΔT 2 eff =4.1 0.1 K, larger than of HadSM3. Since the climate feedback is not constant, we cannot reliably predict ΔT 2 eqm without running the experiment out to a steady state. However, we can estimate it by extrapolating ΔT to N=0 (dashed red line). This gives ΔT=10.0 K, indicating ΔT 2 eqm 5 K, which should be taken as a lower limit, since the slope may show a continuing tendency to flatten. It is evident from the slow rate of temperature rise in the later part of the experiment that it would take a very long time to reach this steady state. Because of that, an exponential fit to the timeseries to obtain ΔT 2 eqm (Voss and Mikolajewicz, 2001) might be relatively poorly constrained. Variations in solar irradiance could produce a significant radiative forcing, with magnitudes on decadal and century timescales estimated to be a few tenths W m -2. We have undertaken three experiments to evaluate the climate sensitivity to solar forcing: (1) Reduction of the solar irradiance in HadSM3 by 0.55%, at the upper end of the range of estimates for the difference in irradiance between the Maunder minimum and the present day. (2) Increase to the solar irradiance in HadSM3 by ten times its anomaly for 1989 from the timeseries of Lean et al. (1995), in which 1989 has the largest value. (3) As (2), imposed on HadCM3. Regression of N against ΔT in the HadSM3 experiments gives values ~1.5 W m -2 K -1 for, in agreement with the value calculated from the steady-state warming. These values are significantly larger than for CO 2, but such a size of difference is consistent with other studies (Hansen et al., 1997; Joshi et al., 2003). However, the HadCM3 =2.0 0.3 W m -2 K -1 is larger still, suggesting a climate sensitivity about 60% smaller than the HadCM3 sensitivity to CO 2. It is also clear that the extrapolation of the HadCM3 experiment will give a smaller warming than that realised in the corresponding HadSM3 experiment. These differences require an explanation. References Gordon, C., C. Cooper, C. A. Senior, et al. (2000), The simulation of SST, sea ice extents and ocean heat transports in a version of the Hadley Centre coupled model without flux adjustments, Clim. Dyn., 16, 147-168. Hansen, J., M. Sato, and R. Reudy (1997), Radiative forcing and climate response, J. Geophys. Res., 102(D6), 6831-6864. Joshi, M., K. Shine, M. Ponater, et al. (2003), A comparison of climate response to different radiative forcings in three general circulation models: Towards an improved metric of climate change, Clim. Dyn., 20, 843-854, doi:10.1007/s00382-003-0305-9. Lean, J., J. Beer, and R. Bradley (1995), Reconstruction of solar irradiance since 1610: Implications for climate change, Geophys. Res. Lett., 22(23), 3195-3198. Senior, C. A., and J. F. B. Mitchell (2000), The time dependence of climate sensitivity, Geophys. Res. Lett., 27(17), 2685-2688. Shine, K. P., J. Cook, E. J. Highwood, et al. (2003), An alternative to radiative forcing for estimating the relative importance of climate change mechanisms, Geophys. Res. Lett., 30(20), 2047, doi:10.1029/ 2003GL018141. Voss, R., and U. Mikolajewicz (2001), Long-term climate changes due to increased CO2 concentration in the coupled atmosphere-ocean general circulation model ECHAM3/LSG, Clim. Dyn., 17, 45-60. Williams, K. D., C. A. Senior, and J. F. B. Mitchell (2001), Transient climate change in the Hadley Centre models: The role of physical processes, J. Clim., 14, 2659-2674. Experiments with an instantaneous doubling (experiment 2S, S'' for sudden', not shown above) and quadrupling (4S) of CO 2 have been run with the HadCM3 AOGCM (Gordon et al., 2000) starting from its control. Because of the much larger heat capacity of the ocean, these approach equilibrium more slowly than HadSM3. In the ninth decade HadCM3 4S has ΔT=4.9 K, about 70% of the steady-state of HadSM3. A longer HadCM3 4 CO 2 experiment (4R, R'' for ramp'') has been done whose initial state was obtained by ramping up CO 2 from its control value. Following stabilisation of CO 2, ΔT rises for many centuries as the deep ocean slowly takes up heat (cf. Senior and Mitchell, 2000; Voss and Mikolajewicz, 2001), passing the steady-state ΔT for the HadSM3 experiment. Averaged over years 1100-1200 the rate of temperature rise is 10 -3 K yr -1. A clearer indication of continuing disequilibrium is that N=0.7 W m -2. CO 2 forcing in a slab model CO 2 forcing in an AOGCM Solar forcing A new method for diagnosing radiative forcing and climate sensitivity