Aerosol-cloud interaction is the most uncertain mechanism of anthropogenic radiative forcing of Earth's climate, and aerosol-induced cloud water changes are particularly poorly constrained in climate models. By combining satellite retrievals of volcano and ship tracks in stratocumulus clouds, we compile a unique observational dataset and confirm that liquid water path (LWP) responses to aerosols are bidirectional, and on average the increases in LWP are closely compensated by the decreases. Moreover, the meteorological parameters controlling the LWP responses are strikingly similar between the volcano and ship tracks. In stark contrast to observations, there are substantial unidirectional increases in LWP in the Hadley Centre climate model, because the model accounts only for the decreased precipitation efficiency and not for the enhanced entrainment drying. If the LWP increases in the model were compensated by the decreases as the observations suggest, its indirect aerosol radiative forcing in stratocumulus regions would decrease by 45%.