Abstract. Depending on the magnitude of their eruptions, volcanoes impact the atmosphere at various temporal and spatial scales. The volcanic source remains a major unknown to rigorously assess these impacts. At the scale of an eruption, the limited knowledge of source parameters, including time variations of erupted mass flux and emission profile, currently represents the greatest issue that limits the reliability of volcanic cloud forecasts. Today, a growing number of satellite and remote sensing observations of distant plumes are becoming available, bringing indirect information on these source terms. Here, we develop an inverse modelling approach combining satellite observations of the volcanic plume with an Eulerian regional chemistry-transport model (CHIMERE) to characterise the volcanic SO2 emissions during an eruptive crisis. The May 2010 eruption of Eyjafjallajökull is a perfect case study to apply this method as the volcano emitted substantial amounts of SO2 during more than a month. We take advantage of the SO2 column amounts provided by a vast set of IASI (Infrared Atmospheric Sounding Interferometer) satellite images to reconstruct retrospectively the time series of the mid-tropospheric SO2 flux emitted by the volcano with a temporal resolution of ~2 h, spanning the period from 1 to 12 May 2010. We show that no a priori knowledge on the SO2 flux is required for this reconstruction. The initialisation of chemistry-transport modelling with this reconstructed source allows for reliable simulation of the evolution of the long-lived tropospheric SO2 cloud over thousands of kilometres. Heterogeneities within the plume, which mainly result from the temporal variability of the emissions, are correctly tracked over a timescale of a week. The robustness of our approach is also demonstrated by the broad similarities between the SO2 flux history determined by this study and the ash discharge behaviour estimated by other means during the phases of high explosive activity at Eyjafjallajökull in May 2010. Finally, we show how a sequential IASI data assimilation allows for a substantial improvement in the forecasts of the location and concentration of the plume compared to an approach assuming constant flux at the source. As the SO2 flux is an important indicator of the volcanic activity, this approach is also of interest to monitor poorly instrumented volcanoes from space.