| Summary: | Probabilistic forecasting of volcanic ash dispersion typically involves simulating an ensemble of realistic event scenarios to estimate the probability of a particular hazard threshold being exceeded. While the ensemble size, the sampling procedure used, and the desired threshold all influence the uncertainty in the probability estimate, current practice does not usually quantify and communicate this uncertainty. We present the application of standard statistical methods to estimate the variance in probabilistic ensembles and communicate confidence intervals, using the example of volcanic ash transport from a representative explosive eruption in Iceland. For stochastic (random) sampling of the wind data, we show how the variance of an exceedance probability depends on the threshold of interest and the ensemble size, and illustrate how we can use the relative variance to compare the uncertainty between estimates of probabilities of different magnitudes. Further, we demonstrate how the variance can be reduced using a stratified sampling approach to ensemble design; in the chosen example we consider a set of 29 Northern European weather regimes known as Grosswetterlagen (GWL). We show that sampling wind fields from within the GWL regimes allows the uncertainty to be quantified just as easily, and reduces the number of samples required to achieve the same variance, compared to stochastic sampling. Our results show that uncertainty in ash dispersion forecasts can be straightforwardly calculated and communicated, and highlight the need for the volcanic ash forecasting community and operational end-users to jointly choose acceptable levels of variance for ash forecasts in the future.
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