Abstract. The enhancement of the stratospheric sulfate aerosol layer has been proposed as a method of geoengineering to abate global warming. Previous modelling studies found that stratospheric aerosol geoengineering (SAG) could effectively compensate for the warming by greenhouse gases on the global scale, but also that the achievable cooling effect per sulfur mass unit, i.e. the forcing efficiency, decreases with increasing injection rate. In this study we use the atmospheric general circulation model LMDZ with the sectional aerosol module S3A to determine how the forcing efficiency depends on the injected amount of SO2, the injection height, and the spatio-temporal pattern of injection. We find that the forcing efficiency may decrease more drastically for larger SO2 injections than previously estimated. As a result, the net instantaneous radiative forcing does not exceed the limit of –2 W m−2 for continuous equatorial SO2 injections and it decreases (in absolute value) for injection rates larger than 20 Tg S yr−1. In contrast to other studies, the net radiative forcing in our experiments is fairly constant with injection height (in a range 17 to 23 km) for a given amount of SO2 injected. Also, spreading the SO2 injections between 30∘ S and 30∘ N or injecting only seasonally from varying latitudes does not result in a significantly larger (i.e. more negative) radiative forcing. Other key characteristics of our simulations include a consequent stratospheric heating, caused by the absorption of solar and infrared radiation by the aerosol, and changes in stratospheric dynamics, with a collapse of the quasi-biennial oscillation at larger injection rates, which has impacts on the resulting spatial aerosol distribution, size, and optical properties. But it has to be noted that the complexity and uncertainty of stratospheric processes cause considerable disagreement among different modelling studies of stratospheric aerosol geoengineering. This may be addressed through detailed model intercomparison activities, as observations to constrain the simulations of stratospheric aerosol geoengineering are not available and analogues (such as volcanic eruptions) are imperfect.