Statistical theory of probabilistic hazard maps: a probability distribution for the hazard boundary location

Abstract

Abstract. The study of volcanic mass flow hazards in a probabilistic framework centers around systematic experimental numerical modelling of the hazardous phenomenon and the subsequent generation and interpretation of a probabilistic hazard map (PHM). For a given volcanic flow (e.g., lava flow, lahar, pyroclastic flow, etc.), the PHM is typically interpreted as the point-wise probability of flow material inundation. In the current work, we present new methods for calculating spatial representations of the mean, standard deviation, median, and modal locations of the hazard's boundary as ensembles of many deterministic runs of a physical model. By formalizing its generation and properties, we show that a PHM may be used to construct these statistical measures of the hazard boundary which have been unrecognized in previous probabilistic hazard analyses. Our formalism shows that a typical PHM for a volcanic mass flow not only gives the point-wise inundation probability, but also represents a set of cumulative distribution functions for the location of the inundation boundary with a corresponding set of probability density functions. These distributions run over curves of steepest ascent on the PHM. Consequently, 2D space curves can be constructed on the map which represent the mean, median and modal locations of the likely inundation boundary. These curves give well-defined answers to the question of the likely boundary location of the area impacted by the hazard. Additionally, methods of calculation for higher moments including the standard deviation are presented which take the form of map regions surrounding the mean boundary location. These measures of central tendency and variance add significant value to spatial probabilistic hazard analyses, giving a new statistical description of the probability distributions underlying PHMs. The theory presented here may be used to construct improved hazard maps, which could prove useful for planning and emergency management purposes. This formalism also allows for application to simplified processes describable by analytic solutions. In that context, the connection between the PHM, its moments, and the underlying parameter variation is explicit, allowing for better source parameter estimation from natural data, yielding insights about natural controls on those parameters.

Toward Next‐Generation Lava Flow Forecasting: Development of a Fast, Physics‐Based Lava Propagation Model

“…Indeed for the Mauna Loa test, the model could be run many times (even in series) over a range of input parameters and still produce a timely forecast. If high‐performance computing resources are available, hundreds or thousands of runs could be produced in parallel, drawing input parameters from best‐estimate distributions, which could then be combined (e.g., Bevilacqua, Patra, et al., 2019; Hyman et al., 2019) to produce timely probabilistic hazard maps for lava flow inundation. Because the flow is most sensitive to vent location, eruption rate, viscosity, thermal diffusivity, and yield strength (either of the core or crust), producing an ensemble forecast over many samples of these parameters would be most beneficial for early forecasting.…”

Assessing minimum pyroclastic density current mass to impact critical infrastructures: example from Aso caldera (Japan)

“…However, these intermediate values would be associated with a lower chance of marker site incursion when the topography is considered and a relatively low kinetic energy budget at the marker site. These bounding effects may be further studied through statistical methods that analyze the edge of the inundated region once 2D or 3D models are applied (Hyman et al, 2019).…”