Pooling strength amongst limited datasets using hierarchical Bayesian analysis, with application to pyroclastic density current mobility metrics

Abstract

In volcanology, the sparsity of datasets for individual volcanoes is an important problem, which, in many cases, compromises our ability to make robust judgments about future volcanic hazards. In this contribution we develop a method for using hierarchical Bayesian analysis of global datasets to combine information across different volcanoes and to thereby improve our knowledge at individual volcanoes. The method is applied to the assessment of mobility metrics for pyroclastic density currents in order to better constrain input parameters and their related uncertainties for forward modeling. Mitigation of risk associated with such flows depends upon accurate forecasting of possible inundation areas, often using empirical models that rely on mobility metrics measured from the deposits of past flows, or on the application of computational models, several of which take mobility metrics, either directly or indirectly, as input parameters. We use hierarchical Bayesian modeling to leverage the global record of mobility metrics from the FlowDat database, leading to considerable improvement in the assessment of flow mobility where the data for a particular volcano is sparse. We estimate the uncertainties involved and demonstrate how they are improved through this approach. The method has broad applicability across other areas of volcanology where relationships established from broader datasets can be used to better constrain more specific, sparser, datasets. Employing such methods allows us to use, rather than shy away from, limited datasets, and allows for transparency with regard to uncertainties, enabling more accountable decision-making.

Towards Quantitative Volcanic Risk of Pyroclastic Density Currents: Probabilistic Hazard Curves and Maps Around Somma‐Vesuvius (Italy)

“…Other sources of parametric uncertainty may include the δ V ratio and the stopping time (Yu et al, ). Theoretical uncertainty : Incomplete knowledge on theoretical assumptions. It has been quantified in terms of the (negative) correlation between PDC volume and bed friction angle (e.g., Ogburn et al, ; Spiller et al, ). Another source of theoretical uncertainty is related to the conceptualization of the column‐collapse process into the setup for the TITAN2D model. Structural uncertainty : Incomplete knowledge reflected in the PDC model.…”

“…Regarding the bed friction angle ( ϕ bed ), we also choose Uniform PDFs because of the scarcity of data available but also because it has been demonstrated that worldwide data on PDC mobility (Ogburn, ) are not fully incompatible with the Uniform distribution (Tierz, Sandri, Costa, Zaccarelli, et al, ). Previous TITAN2D‐based probabilistic hazard assessments of BAFs have used (a) fixed values of ϕ bed (Bayarri et al, ); (b) ϕ bed values distributed as a Uniform PDF (Dalbey et al, ); or (c) ϕ bed values that are stochastically correlated to the value of PDC volume (Spiller et al, ); that is, the bed friction angle and the PDC volume are modeled as inversely correlated (e.g., Hayashi & Self, ; Ogburn, ; Ogburn et al, ) but the specific correlation function is taken as uncertain and explored within the probabilistic hazard analysis. In our parameterization of the Uniform PDFs for ϕ bed at Somma‐Vesuvius, we derive the lower and upper limits of the distributions for each eruption size from the aforementioned eruptions.…”

“…In particular, we calculate maximum and minimum values of arctan(Δ H / L ) ∼ ϕ bed from maximum and minimum runouts measured from the PDC deposits of each eruption and maximum and minimum estimated total height drops (see Table ). We select the upper limits of the medium‐size and large‐size PDFs to be 30° and 25°, respectively, to ensure that ; that is, small‐size PDCs are less mobile than larger PDCs (e.g., Hayashi & Self, ; Ogburn et al, ; Tierz, Sandri, Costa, Zaccarelli, et al, ). In addition, even though some estimated bed friction values are lower than 5°, we set the lower limit of the Uniform PDFs at ° because the thin‐layer problem becomes especially acute beyond this value and the TITAN2D outputs may show unrealistic jumps during dense‐PDC propagation (e.g., Figure 4A in Procter et al, ).…”

TephraProb: a Matlab package for probabilistic hazard assessments of tephra fallout

“…In most cases, eruption scenarios are constructed based on a few studied eruptions representing common eruptive styles and/or often relating underlying geologic processes with analogue eruptive events (Sheldrake 2014). Eruption databases such as the Global Volcanism Program of the Smithsonian Institute (GVP; Siebert et al 2010;Simkin and Siebert 1994) or the Large Magnitude Explosive Volcanic Eruptions (LaMEVE; Crosweller et al 2012, Ogburn et al 2016 can prove useful in acquiring a global picture of eruptive history. TephraProb includes a module to access and explore the Holocene eruptive history as recorded in the GVP database.…”

“…Eruption scenarios reflect the typical eruption styles at a given volcano and are characterized by ranges of eruption source parameters (ESP) such as plume height, erupted mass, mass eruption rate (MER) and total grain-size distribution (TGSD). Eruption scenarios are constrained by the completeness of the eruptive record, as well as an understanding of the range of past activity observed at analogous volcanic systems (Marzocchi et al 2004;Ogburn et al 2016). Highlystudied systems result in eruption scenarios describing precise eruptive episodes, whereas poorly-known systems can often only be characterized by generic eruption scenarios based on analogue systems.…”