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BET_EF

BET_EF

One of the main challenges of modern volcanology is to provide the public with robust and useful information for decision-making in land-use planning and in emergency management. From the scientific point of view, this translates into reliable and quantitative long- and short-term volcanic hazard assessment and eruption forecasting.
Because of the complexity in characterizing volcanic events, and of the natural variability of volcanic processes, a probabilistic approach is more suitable than a deterministic modeling when eruption forecasts or hazard assessment are needed. In this view, two probabilistic codes have been developed for quantitative short- and long-term eruption forecasting (BET_EF) and volcanic hazard assessment (BET_VH). Both of them are based on a Bayesian Event Tree (BET), in which volcanic events are seen as a chain of logical steps of increasing detail. At each node of the tree, the probability is computed by taking into account different sources of information, such as geological and volcanological models, past occurrences, expert opinion, numerical modeling of volcanic phenomena, and monitoring measurements. Since they are based on a Bayesian inferential procedure, the output probability is not a single number, but a probability distribution accounting for aleatory (intrinsic) and epistemic (due to lack of knowledge) uncertainty.

The software package implementing BET_EF is available at http://bet.bo.ingv.it for free downloading, along with the help manual. The core program is written in Fortran 77, while the GUI is written in Visual Basic, although a new GUI (in Python) will be released soon

BET fig1 BET_EF (Figure 1) is designed to provide short- and long-term probability at different nodes of the event tree, representing different potential outcomes related to the uncertain evolution of a pre-eruptive phase, such as volcanic unrest, magmatic unrest, eruption, vent location and eruption size. Therefore it can be useful in many practical aspects, from volcanic emergency management to land use planning.
In short-term applications, the output probabilities are mostly based on the information from monitoring measurements that are believed relevant by the user, i.e. those monitored parameters that are indicative of unrest, magmatic unrest and eruption. This is based on the assumption that upward movements of magma at a volcano will produce detectable changes in the monitored parameters at the surface. The relevant monitoring measurements are treated through a fuzzy approach; it means that, for a given relevant monitored parameter, in order to decide if one of its measures is anomalous or not, a range of values of increasing degree of anomaly can be identified, rather than a sharp and single threshold value (Figure 2).
The identification of the relevant monitored parameters and the related fuzzy thresholds can be based on recorded time series of the various parameters and/or (especially if time series are not available) on expert elicitation procedures.
 BET fig2

RELEVANT REFERENCES
Marzocchi W., Sandri L., Gasparini P., Newhall C.G., and E. Boschi (2004).
Quantifying probabilities of volcanic events: the example of volcanic hazard at Mount Vesuvius
J. Geophys. Res., DOI:10.1029/2004JB003155, 109:B11201
Marzocchi W., Sandri L., and J. Selva (2008).
BET_EF: a probabilistic tool for long- and short-term eruption forecasting
Bull. Volcanol., 70:623–632,  DOI:10.1007/s00445-007-0157-y
Sandri L., Guidoboni E., Marzocchi W., and J. Selva (2009)
Bayesian Event Tree for Eruption Forecasting (BET_EF) at Vesuvius, Italy: a retrospective forward application to 1631 eruption
Bull. Volcanol., 71:729-745, DOI: 10.1007/s00445-008-0261-7
Lindsay J., Marzocchi W., Jolly G., Constantinescu R., Selva J., and L. Sandri (2010).
Towards real-time eruption forecasting in the Auckland Volcanic Field: application of BET_EF during the New Zealand National Disaster Exercise 'Ruaumoko'.
Bull. Volcanol., 72:185-204, DOI: 10.1007/s00445-009-0311-9
 

GALES

GALES - GAlerkin LEast Squares

MODEL
Transient 2D dynamics of multicomponent multiphase homogeneous fluid mixtures in the compressible-to-incompressible flow regimes. GALES solves the mass conservation of components, and the momentum and energy equations of the multiphase mixture. Mixtures are made of gas, liquid and dispersed solid particles. Phase and mixture properties are computed as a function of local P-T-X conditions, with embedded advanced constitutive equations for melt-gas mixtures (e.g., SOLWCAD).
ALGORITHM
Weak form of the transport equations is discretized on ustructured grids with advanced stabilized space-time, time discontinuous, Finite Element Method using Langrangian space-time shape functions. Least squares and discontinuity capturing terms prevent spurious oscillations of the solution with minor smoothing of sharp gradients. The non-linear transport equations are linearized with a Taylor series expansion. Time marching algorithm is of predictor-multicorrector type.
IMPLEMENTATION
The code is implemented and organized as a C++ object oriented library, with an extensive use of design patterns and template meta programming paradigms. GALES is a parallel computation MPI-based software employing the Trilinos package (developed by the Sandia Laboratories). Trilinos provides high-level representation for distributed dense and sparse matrices and vectors, as well as efficient tools for parallel computation (matrix multiplication, GMRES linear system iterative solver, etc...).

gales fig1 Fig 1. Distribution of computed composition and vertical velocity for a magmatic plume rising  through a  gravitationally unstable magmatic system. Initially two different magmas are placed in contact at the connection between the bottom dike and the upper magma chamber. The lower magma is richer in volatiles components H2O and CO2, thus lighter than the upper magma, originating the gravitational instability
 gales fig2 Fig. 2. Distribution of composition and density after 3000 s of simulation of a gravitationally unstable  magmatic system. Initially two different magmas are placed in contact at the connection between the bottom dike and the upper magma chamber. The lower magma is richer in volatiles components H2O and CO2, thus lighter than the upper magma, originating the gravitational instability. A series of light magma plumes develop and invade the magma chamber. Light magma progressively accumulates at the top of the chamber
RELEVANT REFERENCES
Numerical simulation of the dynamics of fluid oscillations in a gravitationally unstable, compositionally stratified fissure.
Longo A., D. Barbato, P. Papale, G. Saccorotti and M. Barsanti.
From: LANE, S. J. & GILBERT, J. S. (eds) Fluid Motions in Volcanic Conduits: A Source of Seismic and Acoustic Signals, Geological Society, London, Spe. Vol. 307, pp: 33-44, 2008
Numerical simulation of convection and mixing in magma chambers replenished with CO2-rich magma
Longo A., Vassalli M. , Papale P. and M. Barsanti
Geophys. Res. Lett. 33, 2006
doi: 10.1029/2006GL027760
Magma convention and mixing dynamics as a source of Ultra-Long-Period oscillations.
Longo A., Papale P., Vassalli M., Saccorotti G., Montagna C.P., Cassioli A., Giudice D. and E. Boschi
Bull. Volcanol.,2011
doi: 10.1007/s00445-011-0570-0
 

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