Relating the mass eruption rate (MER) of explosive eruptions to column height in the atmosphere is key to reconstructing past eruptions and forecasting volcanic hazards. Using 134 eruptive events from the Independent Volcanic Eruption Source Parameter Archive (IVESPA v1.0), we explore the canonical MER-height relationship for four measures of column height: spreading level, sulfur dioxide height, and top height from both directly observed plumes and those reconstructed from deposits. These relationships show significant differences and should be chosen carefully for operational and research applications. The roles of atmospheric stratification, wind, and humidity remain challenging to assess across the large range of eruptive conditions in this database, ultimately resulting in empirical relationships outperforming analytical models that account for atmospheric conditions. This finding reveals the complexity of the height-MER relation that is difficult to constrain based on available heterogeneous observations, which reinforces the need for improved datasets to develop eruptive column models.

Tephra fallout hazard assessment is commonly undertaken with the development of probabilistic maps that rely on numerical models. Among the steps for map production, the definition of input parameters of the model (including atmospheric conditions), the physical approximations of the numerical simulations, and the probabilities of occurrence of different eruption types in specific time frames are among the most critical sources of uncertainty. In this paper, we present a tephra fallout hazard assessment study for two volcanoes (Cotopaxi and Guagua Pichincha) in Ecuador. We utilize the coupled PLUME-MoM/HYSPLIT models, and we develop a procedure for uncertainty quantification where: i) we quantify the uncertainty on eruptive source parameters and eruption type occurrence through expert elicitation; ii) we implement a new procedure for correlations between the different parameters, and iii) we quantify the uncertainty of the numerical model by testing it with past eruptions and by deriving coefficients of mean model overestimation/underestimation. Probability maps of exceedance, given a deposit thickness threshold, and thickness maps, given a probability of exceedence, are produced for eruption of sub-Plinian and Plinian types, which are then merged into single maps concerning the next eruption. These are described according to the uncertainty distribution of eruption type occurrence probabilities, in terms of their 5th percentile, mean and 95th percentile values. We finally present hazard curves describing exceeding probabilities in 10 sensitive sites within the city of Quito. Additional information includes the areal extent and the people potentially affected by different isolines of tephra accumulation.