Estimation and propagation of volcanic source parameter uncertainty in an ash transport and dispersal model: application to the Eyjafjallajokull plume of 14-16 April 2010

Data on source conditions for the 14 April 2010 paroxysmal phase of the Eyjafjallajokull eruption, Iceland, have been used as inputs to a trajectory-based eruption column model, bent. This model has in turn been adapted to generate output suitable as input to the volcanic ash transport and dispersal model, puff, which was used to propagate the paroxysmal ash cloud toward and over Europe over the following days. Some of the source parameters, specifically vent radius, vent source velocity, mean grain size of ejecta, and standard deviation of ejecta grain size have been assigned probability distributions based on our lack of knowledge of exact conditions at the source. These probability distributions for the input variables have been sampled in a Monte Carlo fashion using a technique that yields what we herein call the polynomial chaos quadrature weighted estimate (PCQWE) of output parameters from the ash transport and dispersal model. The advantage of PCQWE over Monte Carlo is that since it intelligently samples the input parameter space, fewer model runs are needed to yield estimates of moments and probabilities for the output variables. At each of these sample points for the input variables, a model run is performed. Output moments and probabilities are then computed by properly summing the weighted values of the output parameters of interest. Use of a computational eruption column model coupled with known weather conditions as given by radiosonde data gathered near the vent allows us to estimate that initial mass eruption rate on 14 April 2010 may have been as high as 10(8) kg/s and was almost certainly above 10(7) kg/s. This estimate is consistent with the probabilistic envelope computed by PCQWE for the downwind plume. The results furthermore show that statistical moments and probabilities can be computed in a reasonable time by using 9(4) = 6,561 PCQWE model runs as opposed to millions of model runs that might be required by standard Monte Carlo techniques. The output mean ash cloud height plus three standard deviations-encompassing c. 99.7 % of the probability mass-compares well with four-dimensional ash cloud position as retrieved from Meteosat-9 SEVIRI data for 16 April 2010 as the ash cloud drifted over north-central Europe. Finally, the ability to compute statistical moments and probabilities may allow for the better separation of science and decision-making, by making it possible for scientists to better focus on error reduction and decision makers to focus on "drawing the line" for risk assessment.