3:30 PM - 3:45 PM
[SVC28-06] Total erupted mass and magma discharge rate estimated from isopach and mean grainsize distribution; an application of MCMC coupled with a GPGPU tephra simulation code TWiCE
Keywords:Tephra, simulation, volcanic ash, MCMC, GPGPU
The total mass released by pyroclastic eruptions such as Plinian has been determined by integrating functions that approximate the relationship between the thickness (S) and area enclosed (A) (hereafter S-A relationship) of iso-mass loading contours (isopachs). However, since the approximation formula had no theoretical background, the estimated mass can differ greatly depending on extrapolation of proximal and distal areas where no measurement point is available. Also, uncertainty of estimated value was hard to be quantified. The magma discharge rate has been calculated using a method proposed by Carey and Sparks (1986), which can determine the plume height (∝ ejection rate) and average wind speed from the width of the isopleth of the largest grain size. However, this method involves arbitrariness in determining the "maximum grain size" of particles deposited at each locality and the assumption that the relationship between the height and width of the eruption plume is constant.
Some studies have attempted to determine eruption parameters by inversion coupled with tephra fall simulation. However, most of these inversions search for the parameter combination that minimizes the residual between observed and calculated massloadings, and it was difficult to quantify uncertainty of the estimated value of parameters the correlation among the different parameters.
The author is developing a framework that use a tephra fall simulation code named TWiCE and the Markov chain Monte Carlo (MCMC) method to overcome the difficulties mentioned above. In this framework, plume parameters are estimated from data obtained by field volcanologists such as S-A relationship. MCMC is a general term for algorithms for sampling the target probability distribution by generating a Markov chain. In this study, the Metropolis method was used. Here, the reciprocal of residual between observations and calculations of the S-A relation are considered as the likelihood and sampled as a function of the plume parameters. TWiCE is a simulation code that calculates the ash fall distribution from plumes bent by wind. Because TWiCE runs on GPUs, it can calculate the mass loadings for numerous points at high speed, which is advantageous to make isopach maps. In this study six parameters were set to be searched for: total eruption mass (M), magma discharge rate (Q), plume thickness (Hp), diffusion coefficient of coarse particle (K), and the mean (Md) and its standard deviation (σ) of the particle size distribution of total erupted assuming a normal distribution.
The MCMC samplings indicate that M is well constrained by the S-A relation while other parameters can hardly be constrained. We thus conducted a parameter search using the relationship between distance from the source vent (d) and mean particle diameter of the deposit (md) (md-d relationship), which is a dataset relatively easy to collect, as a new target for reconstruction. By the parameter search using md-d relationship, Q was weakly constrained. We thus gave M obtained by the previous parameter search using the S-A relation as fixed to the parameter search using md-d relation and Q was reasonably constrained. However, it was not possible to constrain other parameters (Hp, K, Md, σ) well.
Thus, it is possible to obtain the likelihood distribution of the total eruption mass (M) from the conventional isopach maps. If the md-d relation is obtained, the magma discharge rate (Q) can be constrained well. These results suggest the importance of measuring grain size distributions at least several points ranging various distance from the source vent.
Some studies have attempted to determine eruption parameters by inversion coupled with tephra fall simulation. However, most of these inversions search for the parameter combination that minimizes the residual between observed and calculated massloadings, and it was difficult to quantify uncertainty of the estimated value of parameters the correlation among the different parameters.
The author is developing a framework that use a tephra fall simulation code named TWiCE and the Markov chain Monte Carlo (MCMC) method to overcome the difficulties mentioned above. In this framework, plume parameters are estimated from data obtained by field volcanologists such as S-A relationship. MCMC is a general term for algorithms for sampling the target probability distribution by generating a Markov chain. In this study, the Metropolis method was used. Here, the reciprocal of residual between observations and calculations of the S-A relation are considered as the likelihood and sampled as a function of the plume parameters. TWiCE is a simulation code that calculates the ash fall distribution from plumes bent by wind. Because TWiCE runs on GPUs, it can calculate the mass loadings for numerous points at high speed, which is advantageous to make isopach maps. In this study six parameters were set to be searched for: total eruption mass (M), magma discharge rate (Q), plume thickness (Hp), diffusion coefficient of coarse particle (K), and the mean (Md) and its standard deviation (σ) of the particle size distribution of total erupted assuming a normal distribution.
The MCMC samplings indicate that M is well constrained by the S-A relation while other parameters can hardly be constrained. We thus conducted a parameter search using the relationship between distance from the source vent (d) and mean particle diameter of the deposit (md) (md-d relationship), which is a dataset relatively easy to collect, as a new target for reconstruction. By the parameter search using md-d relationship, Q was weakly constrained. We thus gave M obtained by the previous parameter search using the S-A relation as fixed to the parameter search using md-d relation and Q was reasonably constrained. However, it was not possible to constrain other parameters (Hp, K, Md, σ) well.
Thus, it is possible to obtain the likelihood distribution of the total eruption mass (M) from the conventional isopach maps. If the md-d relation is obtained, the magma discharge rate (Q) can be constrained well. These results suggest the importance of measuring grain size distributions at least several points ranging various distance from the source vent.