Probabilistic forecasting of plausible debris flows from Nevado de Colima (Mexico) using data from the Atenquique debris flow, 1955

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 depthaveraged
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.