Indirect aerosol forcing, quasi forcing, and climate response

The component of the indirect aerosol effect related to changes in precipitation efficiency (the second indirect or Albrecht effect) is presently evaluated in climate models by taking the difference in net irradiance between a present-day and a preindustrial simulation using fixed sea surface temperatures (SSTs). This approach gives a "quasi forcing,'' which differs from a pure forcing in that fields other than the initially perturbed quantity have been allowed to vary. It is routinely used because, in contrast to the first indirect (Twomey) effect, there is no straightforward method of calculating a pure forcing for the second indirect effect. This raises the question of whether evaluation of the second indirect effect in this manner is adequate as an indication of the likely effect of this perturbation on the global-mean surface temperature. An atmospheric global climate model (AGCM) is used to compare the evaluation of different radiative perturbations as both pure forcings (when available) and quasi forcings. Direct and indirect sulfate aerosol effects and a doubling of carbon dioxide (CO(2)) are considered. For evaluation of the forcings and quasi forcings, the AGCM is run with prescribed SSTs. For evaluation of the equilibrium response to each perturbation, the AGCM is coupled to a mixed layer ocean model. For the global-mean direct and first indirect effects, quasi forcings differ by less than 10% from the corresponding pure forcing. This suggests that any feedbacks contaminating these quasi forcings are small in the global mean. Further, the quasi forcings for the first and second indirect effects are almost identical when based on net irradiance or on cloud-radiative forcing, showing that clear-sky feedbacks are negligible in the global mean. The climate sensitivity parameters obtained for the first and second indirect effects (evaluated as quasi forcings) are almost identical, at 0.78 and 0.79 K m(2) W(-1), respectively. Climate sensitivity parameters based on pure forcings are 0.69, 0.84, and 1.01 K m(2) W(-1) for direct sulfate, first indirect, and 2 x CO(2) f forcings, respectively. The differences are related to the efficiency with which each forcing excites the strong surface-albedo feedback at high latitudes. Closer examination of the calculations of the first indirect effect as a forcing and quasi forcing shows that, although they are in reasonable agreement in the global mean, there are some significant differences in a few regions. Overall, these results suggest that evaluation of the globally averaged second indirect effect as a quasi forcing is satisfactory.