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We detail a new prediction-oriented procedure aimed at volcanic hazard assessment based on geophysical mass flow models constrained with heterogeneous and poorly defined data. Our method relies on an itemized application of the empirical falsification principle over an arbitrarily wide envelope of possible input conditions. We thus provide a first step towards a objective and partially automated experimental design construction. In particular, instead of fully calibrating model inputs on past observations, we create and explore more general requirements of consistency, and then we separately use each piece of empirical data to remove those input values that are not compatible with it. Hence, partial solutions are defined to the inverse problem. This has several advantages compared to a traditionally posed inverse problem: (i) the potentially nonempty inverse images of partial solutions of multiple possible forward models characterize the solutions to the inverse problem; (ii) the partial solutions can provide hazard estimates under weaker constraints, potentially including extreme cases that are important for hazard analysis; (iii) if multiple models are applicable, specific performance scores against each piece of empirical information can be calculated. We apply our procedure to the case study of the Atenquique volcaniclastic debris flow, which occurred on the flanks of Nevado de Colima volcano (Mexico), 1955. We adopt and compare three depth-averaged models currently implemented in the TITAN2D solver, available from https://vhub.org (Version 4.0.0 – last access: 23 June 2016). The associated inverse problem is not well-posed if approached in a traditional way. We show that our procedure can extract valuable information for hazard assessment, allowing the exploration of the impact of synthetic flows that are similar to those that occurred in the past but different in plausible ways. The implementation of multiple models is thus a crucial aspect of our approach, as they can allow the covering of other plausible flows. We also observe that model selection is inherently linked to the inversion problem.

Plume-SPH provides the first particle-based simulation of volcanic plumes. Smoothed particle hydrodynamics (SPH) has several advantages over currently used mesh-based methods in modeling of multiphase free boundary flows like volcanic plumes. This tool will provide more accurate eruption source terms to users of volcanic ash transport and dispersion models (VATDs), greatly improving volcanic ash forecasts. The accuracy of these terms is crucial for forecasts from VATDs, and the 3-D SPH model presented here will provide better numerical accuracy. As an initial effort to exploit the feasibility and advantages of SPH in volcanic plume modeling, we adopt a relatively simple physics model (3-D dusty-gas dynamic model assuming well-mixed eruption material, dynamic equilibrium and thermodynamic equilibrium between erupted material and air that entrained into the plume, and minimal effect of winds) targeted at capturing the salient features of a volcanic plume. The documented open-source code is easily obtained and extended to incorporate other models of physics of interest to the large community of researchers investigating multiphase free boundary flows of volcanic or other origins.The Plume-SPH code (https://doi.org/10.5281/zenodo. 572819) also incorporates several newly developed techniques in SPH needed to address numerical challenges in simulating multiphase compressible turbulent flow. The code should thus be also of general interest to the much larger community of researchers using and developing SPH-based tools. In particular, the SPH−ε turbulence model is used to capture mixing at unresolved scales. Heat exchange due to turbulence is calculated by a Reynolds analogy, and a corrected SPH is used to handle tensile instability and deficiency of particle distribution near the boundaries. We also developed methodology to impose velocity inlet and pressure outlet boundary conditions, both of which are scarce in traditional implementations of SPH.The core solver of our model is parallelized with the message passing interface (MPI) obtaining good weak and strong scalability using novel techniques for data management using space-filling curves (SFCs), object creation time-based indexing and hash-table-based storage schemes. These techniques are of interest to researchers engaged in developing particles in cell-type methods. The code is first verified by 1-D shock tube tests, then by comparing velocity and concentration distribution along the central axis and on the transverse cross with experimental results of JPUE (jet or plume that is ejected from a nozzle into a uniform environment). Profiles of several integrated variables are compared with those calculated by existing 3-D plume models for an eruption with the same mass eruption rate (MER) estimated for the Mt. Pinatubo eruption of 15 June 1991. Our results are consistent with existing 3-D plume models. Analysis of the plume evolution process demonstrates that this model is able to reproduce the physics of plume development.