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Significant improvements in the way we can observe and model volcanic ash clouds have been obtained since the 2010 Eyjafjallajokull eruption. One major development has been the application of data assimilation techniques, which combine models and satellite observations such that an optimal understanding of ash clouds can be gained. Still, questions remain regarding the degree to which the forecasting capabilities are improved by inclusion of such techniques and how these improvements depend on the data input. This study explores how different satellite data and different uncertainty assumptions of the satellite and a priori emissions affect the calculated volcanic ash emission estimate, which is computed by an inversion method that couples the satellite retrievals and a priori emissions with dispersion model data. Two major ash episodes over 4 days in April and May of the 2010 Eyjafjallajokull eruption are studied. Specifically, inversion calculations are done for four different satellite data sets with different size distribution assumptions in the retrieval. A reference satellite data set is chosen, and the range between the minimum and maximum 4-day average load of hourly retrieved ash is 121% in April and 148% in May, compared to the reference. The corresponding a posteriori maximum and minimum emission sum found for these four satellite retrievals is 26 and 47% of the a posteriori reference estimate for the same two periods, respectively. Varying the assumptions made in the satellite retrieval is seen to affect the a posteriori emissions and modelled ash column loads, and modelled column loads therefore have uncertainties connected to them depending on the uncertainty in the satellite retrieval. By further exploring our uncertainty estimates connected to a priori emissions and the mass load uncertainties in the satellite data, the uncertainty in the a priori estimate is found in this case to have an order-of-magnitude-greater impact on the a posteriori solution than the mass load uncertainties in the satellite. Part of this is explained by a too-high a priori estimate used in this study that is reduced by around half in the a posteriori reference estimate. Setting large uncertainties connected to both a priori and satellite mass load shows that they compensate each other, but the a priori uncertainty is found to be most sensitive. Because of this, an inversion-based emission estimate in a forecasting setting needs well-tested and well-considered assumptions on uncertainties for the a priori emission and satellite data. The quality of using the inversion in a forecasting environment is tested by adding gradually, with time, more observations to improve the estimated height versus time evolution of Eyjafjallajokull ash emissions. We show that the initially too-high a priori emissions are reduced effectively when using just 12 h of satellite observations. More satellite observations (>12 h), in the Eyjafjallajokull case, place the volcanic injection at higher altitudes. Adding additional satellite observations (>36 h) changes the a posteriori emissions to only a small extent for May and minimal for the April period, because the ash is dispersed and transported effectively out of the domain after 1-2 days. A best-guess emission estimate for the forecasting period was constructed by averaging the last 12 h of the a posteriori emission.

Using this emission for a forecast simulation leads to better performance, especially compared to model simulations with no further emissions over the forecast period in the case of a continued volcanic eruption activity. Because of undetected ash in the satellite retrieval and diffusion in the model, the forecast simulations generally contain more ash than the observed fields, and the model ash is more spread out. Overall, using the a posteriori emissions in our model reduces the uncertainties in the ash plume forecast, because it corrects effectively for false-positive satellite retrievals, temporary gaps in observations, and false a priori emissions in the window of observation.