2:30 PM - 2:45 PM
[SVC30-04] A probabilistic hazard mapping method combining numerical simulations of pyroclastic density currents with a frequency function of eruption magnitudes
Keywords:Pyroclastic density current (PDC), Run-out area, Probabilistic hazard map, Numerical simulation, Eruption magnitude, Frequency function
During volcanic eruptions, a mixture of volcanic particles and gas is ejected from the volcanic vent and can flow on the ground surface as a pyroclastic density current (PDC). PDCs are a frequent and hazardous process, and predicting the run-out area of PDCs is an important issue for volcanic disaster mitigation. The run-out area of PDCs strongly depends on eruption conditions (especially, eruption magnitude) and topography; numerical PDC models to evaluate their effects have been developed. In the field of volcanic disaster mitigation, the hazard maps, where the results of such PDC models are plotted, are widely used for decision making, risk assessment, and disaster mitigation education. A method to make hazard maps is shown in the Guideline for Volcanic Hazard Mapping (provided mainly by the Cabinet Office of Japan in 2013), but it is not sufficient. In particular, even though the eruption magnitude M (=log10(erupted mass [kg])-7; Hayakawa, 1993, Kazan; Pyle, 1995, Geophys. Res. Lett.) varies greatly from ~0 to ~8 depending on the events and significantly changes the run-out area of PDCs, the treatment of M differs among hazard map authors. To eliminate arbitrariness in the treatment of M, we propose a probabilistic hazard mapping method that combines a frequency function of M (N(M)) with the results of numerical PDC simulations.
Our probabilistic hazard mapping method consists of the following four procedures.
[Procedure 1] The lower and upper limits of M are determined; then, in this range, the values of M are sampled as Mi at intervals dM i±1/2=|Mi-Mi±1|.
[Procedure 2] For each of the sampled values Mi, a numerical simulation of PDCs is conducted to predict the run-out area of PDCs; the scores of 1 and 0 are given to each grid of simulation area in the run-out area and the other grids, respectively.
[Procedure 3] The scores for each Mi are weighted by multiplying the probability distribution of M: Ni/Σi(Ni) (or the frequency distribution Ni), where Ni=0.25{N(Mi)+N(Mi-0.5dMi-1/2)}dMi-1/2+0.25{N(Mi)+N(Mi+0.5dMi+1/2)}dMi+1/2.
[Procedure 4] The weighted scores are summed up for all of Mi and its result is plotted on the map.
These procedures produce a probabilistic hazard map that combines the run-out area of numerical PDCs and the frequency function N(M) for the set range of M. Compared with existing methods (e.g., the Monte Carlo-type sampling-based approaches), our method has the advantage that we can restart from [Procedure 3] when performing hazard mapping with a different N(M). This means that we can save a lot of time because we do not need to redo the numerical simulations (i.e., [Procedure 2]) every time we perform hazard mapping with different N(M).
As an example, we made a probabilistic hazard map of the run-out area of PDCs generated from the Showa Crater of Sakurajima volcano. The lower and upper limits of M were set to 1 and 3.5, respectively, and the values of M were sampled at equal intervals of 0.5. In the numerical simulations, a dense granular flow model was used to describe the dynamics of the dense basal region of PDCs (Shimizu, 2021, Volcanological Society of Japan Fall Meeting), and a high-resolution digital elevation model provided by NHK was used for generating the surface mesh. The frequency function N(M) is assumed to be two distributions: one is a uniform distribution (N=const), and the other is an empirical power-law distribution (N∝-0.75M; Nakada, 2015, Kazan), which is valid for each volcano on a geological time scale. Compared with the case of N=const, the hazard map with N∝-0.75M strongly reflects the general tendency that small-scale PDCs with narrow run-out areas occur at high frequency and large-scale PDCs with wide run-out areas occur at low frequency. In the future, we will sophisticate our method by introducing a method to set the lower and upper limits of M and by evaluating also the frequency functions of eruption conditions other than M (e.g., location of the volcanic vent).
Our probabilistic hazard mapping method consists of the following four procedures.
[Procedure 1] The lower and upper limits of M are determined; then, in this range, the values of M are sampled as Mi at intervals dM i±1/2=|Mi-Mi±1|.
[Procedure 2] For each of the sampled values Mi, a numerical simulation of PDCs is conducted to predict the run-out area of PDCs; the scores of 1 and 0 are given to each grid of simulation area in the run-out area and the other grids, respectively.
[Procedure 3] The scores for each Mi are weighted by multiplying the probability distribution of M: Ni/Σi(Ni) (or the frequency distribution Ni), where Ni=0.25{N(Mi)+N(Mi-0.5dMi-1/2)}dMi-1/2+0.25{N(Mi)+N(Mi+0.5dMi+1/2)}dMi+1/2.
[Procedure 4] The weighted scores are summed up for all of Mi and its result is plotted on the map.
These procedures produce a probabilistic hazard map that combines the run-out area of numerical PDCs and the frequency function N(M) for the set range of M. Compared with existing methods (e.g., the Monte Carlo-type sampling-based approaches), our method has the advantage that we can restart from [Procedure 3] when performing hazard mapping with a different N(M). This means that we can save a lot of time because we do not need to redo the numerical simulations (i.e., [Procedure 2]) every time we perform hazard mapping with different N(M).
As an example, we made a probabilistic hazard map of the run-out area of PDCs generated from the Showa Crater of Sakurajima volcano. The lower and upper limits of M were set to 1 and 3.5, respectively, and the values of M were sampled at equal intervals of 0.5. In the numerical simulations, a dense granular flow model was used to describe the dynamics of the dense basal region of PDCs (Shimizu, 2021, Volcanological Society of Japan Fall Meeting), and a high-resolution digital elevation model provided by NHK was used for generating the surface mesh. The frequency function N(M) is assumed to be two distributions: one is a uniform distribution (N=const), and the other is an empirical power-law distribution (N∝-0.75M; Nakada, 2015, Kazan), which is valid for each volcano on a geological time scale. Compared with the case of N=const, the hazard map with N∝-0.75M strongly reflects the general tendency that small-scale PDCs with narrow run-out areas occur at high frequency and large-scale PDCs with wide run-out areas occur at low frequency. In the future, we will sophisticate our method by introducing a method to set the lower and upper limits of M and by evaluating also the frequency functions of eruption conditions other than M (e.g., location of the volcanic vent).