| Summary: | Poor knowledge of dispersion model source parameters related to quantities such as the total fine ash mass emission rate, its effective spatial distribution, and particle size distribution makes the provision of quantitative forecasts of volcanic ash a difficult problem. To ameliorate this problem, we make use of satellite-retrieved mass load data from 14 eruption case studies to estimate fine ash mass emission rates and other source parameters by an inverse modelling procedure, which requires multidimensional sampling of several thousand trial simulations with different values of source parameters. We then estimate the dependence of these optimal source parameters on eruption height. We show that using these empirical relationships in a data assimilation procedure leads to substantial improvements to the forecasts of ash mass loads, with the use of empirical relationships between parameters and eruption height having the added advantage of computational efficiency because of dimensional reduction. In addition, the use of empirical relationships, which encode information in satellite retrievals from past case studies, implies that quantitative forecasts can still be issued even when satellite retrievals of mass load are not available in real time due to cloud cover or other reasons, making it especially useful for operations in the tropics where ice and water clouds are ubiquitous.
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