Observational satellite data and the model-predicted response to human influence have a common latitude/altitude pattern of atmospheric temperature change. The key features of this pattern are global-scale tropospheric warming and stratospheric cooling over the 34-year satellite temperature record. We show that current climate models are highly unlikely to produce this distinctive signal pattern by internal variability alone, or in response to naturally forced changes in solar output and volcanic aerosol loadings. We detect a “human influence” signal in all cases, even if we test against natural variability estimates with much larger fluctuations in solar and volcanic influences than those observed since 1979. These results highlight the very unusual nature of observed changes in atmospheric temperature.