Quantifying uncertainty in probabilistic volcanic ash hazard forecasts, with an application to weather pattern based wind field sampling

Probabilistic forecasting of volcanic ash dispersion involves simulating an ensemble of realistic event scenarios to estimate the probability of a particular hazard threshold being exceeded. Although the number of samples that make up the ensemble, how they are chosen, and the desired threshold all set the uncertainty of (or confidence in) the estimated exceedance probability, current practice does not quantify and communicate the uncertainty in ensemble predictions. In this study, we use standard statistical methods to estimate the variance in probabilistic ensembles and use this measure of uncertainty to assess different sampling strategies for the wind field, using the example of volcanic ash transport from a representative explosive eruption in Iceland. For stochastic (random) sampling of the wind field, we show how the variance is reduced with increasing ensemble size and how the variance depends on the desired hazard threshold and the proximity of a target site to the volcanic source. We demonstrate how estimated variances can be used to compare different ensemble designs, by comparing stochastic forecasts with forecasts obtained from a stratified sampling approach using a set of 29 Northern European weather regimes, known as Grosswetterlagen (GWL). Sampling wind fields from within the GWL regimes reduces the number of samples needed to achieve the same variance as compared to conventional stochastic sampling. Our results show that uncertainty in volcanic 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.