A comparison of climate feedbacks in general circulation models

Abstract.

A comparison is performed for water vapour, cloud, albedo and lapse rate feedbacks taken from published results of 'offline' feedback calculations for general circulation models (GCMs) with mixed layer oceans performing 2 × CO₂ and solar perturbation experiments. All feedbacks show substantial inter-model spread. The impact of uncertainties in feedbacks on climate sensitivity is discussed. A negative correlation is found between water vapour and lapse rate feedbacks, and also between longwave and shortwave components of the cloud feedback. The mean values of the feedbacks are compared with results derived from model intercomparisons which evaluated cloud forcing derived feedbacks under idealized climate forcing. Results are found to be comparable between the two approaches, after allowing for differences in experimental technique and diagnostic method. Recommendations are made for the future reporting of climate feedbacks.

Appendix 1: Estimation of the lapse rate feedback

1.1 Lapse rate feedback reported, but without an equilibrated stratosphere (GFDL1, 2, BMRC1, CSIRO): Method 1 (following Arking 1991)

All four models also quote instantaneous TOA CO₂ forcing, $\delta R_{CO_2 }$ (which includes both LW and SW forcing), and surface temperature feedback: ${\partial R_{T_\ast} \over \partial T_\ast}.$

Assuming the CO₂ forcing produces a warming of ΔT ₀, with only the surface temperature feedback operating, then:

$$ s = {\partial R_{T_\ast} \over \partial T_\ast} \cdot \Delta T_o - \delta R_{{\rm CO}_2} {\enspace} , $$

where s is the radiative response due to stratospheric cooling. The value of s can then be subtracted from the quoted lapse rate feedback, giving ${\partial R_\Gamma \over \partial T}$ as a residual. Assuming ΔT ₀ = 1.2 K (Hansen et al. 1984), values of the stratospheric cooling response for the models vary from 1.5 to 1.8 Wm^–2 (c.f. Hansen et al. 1997, value of 1.6 Wm^–2).

Based on this range, uncertainty in the final feedback may be roughly ±0.1 Wm^–2 K^–1.

1.2 No lapse rate feedback reported, (although total temperature feedback known) (UKMO, MPI): Method 2

Total temperature feedback is assumed to be the sum of surface temperature (T _*) and lapse rate (Γ) feedbacks plus the effect of stratospheric temperature change (s). The latter (properly regarded as an adjustment, not a feedback) is assumed to be 1.6 Wm^–2 for CO₂ forcing (taken from Hansen et al. 1997, and supported by method 1 calculations). For +2% solar forcing, s is taken as –0.19 Wm^–2 (Hansen et al. 1997). The surface temperature feedback is taken from the mean of the seven models which reported it (BMRC1, 2, GFDL1, 2, GISS1, 2 and CSIRO). The mean value of these is –3.34 Wm^–2 K^–1 with a standard deviation of 0.1 Wm^–2 K^–1 and a range of 0.32 Wm^–2 K^–1. Lapse rate feedback is then calculated as a residual.

Noting the range of these values and the uncertainty in s, uncertainty in the final lapse rate feedback is estimated at approximately ±0.15 Wm^–2 K^–1.

1.3 No temperature feedback reported (LMD1,2): Method 3

The sum of all feedbacks, $\sum\limits_i {{\partial R_i \over \partial T_\ast},}$ can be calculated from Eq. 2 (following Schlesinger 1988), where ΔT ₀ is the temperature change with only surface temperature responses,ΔT _* is the final surface temperature change, and $K = \left( {{{\partial R_{T_* } } \over {\partial T_* }}} \right)^{ - 1} .$

Assuming ΔT ₀ =1.2 (Hansen et al. 1984) and taking K = 0.3 Km²W^–1 from quoted model results, noted in the discussion of method 2, permits calculation of $\sum\limits_i {{\partial R_i \over \partial T_\ast}. }$ Knowing all other feedbacks, permits lapse rate feedback to be calculated as a residual.

Some measure of the potential error associated with this method may be obtained by calculating the lapse rate feedback for these models where it is reported with an equilibrated stratosphere (BMRC2, CCM1). The errors here are 0.06 and 0.01 Wm^–2 K^–1 respectively. Errors for the GISS1 and 2 models are close to zero, as these values are those used to specify the method. Errors in the remaining models (Table 3) are more difficult to estimate as the true value of the lapse rate feedback is not known, but disagreement with method 1 is as large as 0.2 Wm^–2 K^–1 (BMRC1), and with method 2 of 0.5 Wm^–2 K^–1 (MPI).

Table 3. Table showing estimates of lapse rate feedback using methods 1, 2 and 3, as applicable (see text for details of the methods)

From Table 3, and from the results of the BMRC2 and CCM1 an error of ±0.3 Wm^–2 K^–1 is used in Fig. 2. Given the larger error associated with this method, method 1 and 2 values, where available, are used in Fig. 2.