AbstractStratospheric aerosol geoengineering could be used to maintain global mean temperature despite increased atmospheric greenhouse gas (GHG) concentrations, for example, to meet a 1.5 or 2 °C target. While this might reduce many climate change impacts, the resulting climate would not be the same as one with the same global mean temperature due to lower GHG concentrations. The primary question we consider is how long it would take to detect these differences in a hypothetical deployment. We use a 20‐member ensemble of stratospheric sulfate aerosol geoengineering simulations in which SO2 is injected at four different latitudes to maintain not just the global mean temperature, but also the interhemispheric and equator‐to‐pole gradients. This multiple‐latitude strategy better matches the climate changes from increased GHG, while the ensemble allows us both to estimate residual differences even when they are small compared to natural variability and to estimate the statistics of variability. We first construct a linear emulator to predict the model responses for different scenarios. Under an RCP4.5 scenario in which geoengineering maintains a 1.5 °C target (providing end‐of‐century cooling of 1.7 °C), the projected changes in temperature, precipitation, and precipitation minus evaporation (P − E) at a grid‐scale are typically small enough that in many regions the signal‐to‐noise ratio is still less than one at the end of this century; for example, for P − E, only 30% of the land area reaches a signal‐to‐noise ratio of one. These results provide some context for the projected magnitude of climate changes associated with a limited deployment of stratospheric aerosol cooling.