Uncertainty assessment and applicability of an inversion method for
volcanic ash forecasting
Authors: Steensen Birthe Marie , Kylling Arve , Kristiansen Nina Iren , Schulz Michael 
Published: January 2017

Abstract. Significant improvements in the way we can observe and model volcanic ash clouds have been obtained since the 2010 Eyjafjallajökull eruption. One major development has been data assimilation techniques, which aim to bring models in closer agreement to satellite observations and reducing the uncertainties for the ash emission estimate. Still, questions remains to which degree the forecasting capabilities are improved by inclusion of such techniques are and how these improvements depend on the data input. This study exploits 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 and a priori emissions with dispersion model data. Two major ash episodes over four days in April and May of the 2010 Eyjafjallajökull 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 range from 26 % and 47 % of the a posteriori reference estimate for the same two periods. Varying the assumptions made in the satellite retrieval therefore translates into uncertainties in the calculated emissions and the modelled ash column loads. By further exploring the weighting of uncertainties connected to a priori emissions and the other-than-size uncertainties in the satellite data, the uncertainty in the a priori estimate is found to have an order of magnitude more impact on the a posteriori solution compared to the other-than-size 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 input data is shown to compensate each other. Because of this an inversion based emission estimate in a forecasting setting needs well tested and 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 Eyjafjallajökull ash emissions. We show that the initially too high a priori emissions are reduced effectively when using just 12 hours of satellite observations. More satellite observations (> 12 h), in the Eyjafjallajökull 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 hours of the a posteriori emission. Using this emission for a forecast simulation performs better 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 connected to both the satellite observations and the a priori estimate to perform a more confident forecast in both amount of ash released and emission heights.