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

Abstract

Abstract. 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.

Statistical theory of probabilistic hazard maps: a probability distribution for the hazard boundary location

“…This is done primarily because the flow boundary is easily definable and conceptualized in these models, giving a consistent intuition to the complicated mathematical quantities discussed here. However, these con-cepts extend to many other types of hazard models where a particular threshold is of interest in defining the region impacted by a hazard in volcanology and other fields including concentration thresholds in volcanic clouds (Bursik et al, 2012), thickness thresholds in tephra fallout (Sandri et al, 2016), ballistic ejecta impact count thresholds (Biass et al, 2016), pyroclastic density current invasion (Bevilacqua et al, 2017), lava flow inundation (Gallant et al, 2018), tsunami run-up thresholds (Geist and Parsons, 2006;Grezio et al, 2017), ground-shaking thresholds in seismic hazards (Kvaerna et al, 1999), hurricane wind speed thresholds (Splitt et al, 2014), and many others. All of these examples can be cast in the same mathematical formulation that we detail below.…”

“…Following from the previous application of the PHM statistics to a simple flow, here we present a more advanced application: construction and analysis of a PHM for a more complex flow over natural topography. This example consists of numerical modeling detailed in Bevilacqua et al (2019) of the 1955 volcaniclastic debris flow which destroyed the village of Atenquique at the base of Nevado de Colima, Mexico. On 16 October 1955, at 10:45 LT, residents of Atenquique experienced the arrival of an 8-9 m high debris flow wave front that subsequently destroyed much of the town's buildings and infrastructure and caused more than 23 deaths (Ponce Segura, 1983;Saucedo et al, 2008).…”

“…The debris flow was initiated by landsliding in the upper reaches of the Atenquique, Arroyo Seco, Los Plátanos, and Tamazula fault ravines, with a minimum initial volume of 3.2 × 10 6 m 3 (Rupp, 2004;Saucedo et al, 2008). In the simulation of this flow, this volume was increased by 10 %-50 % to give volumes of V = 4.25 ± 0.75 × 10 6 m 3 (Bevilacqua et al, 2019).…”

“…We analyze an ensemble of TITAN2D simulations of this flow that were generated by Bevilacqua et al (2019) using a physically realistic rheology for a debris flow, the Voellmy-Salm (VS) rheology. This rheology is parameterized by a bed friction coefficient µ VS and a velocity-dependent friction parameter ξ which approximates turbulence-induced dissipation and is uncertain over several orders of magnitude.…”

“…The distribution is propagated by a physical model to yield a space of hazard distributions which put probabilistic constraints on quantities that would be fixed in a deterministic, scenario-based modeling framework. In practice this has typically been accomplished by accumulating the statistics of the processes through deterministic modeling over an en-D. M. Hyman et al: Statistical theory of probabilistic hazard maps semble of model inputs (Neri et al, 2015;Biass et al, 2016;Bevilacqua et al, 2017;Gallant et al, 2018;Patra et al, 2018b). Polynomial chaos approximations and Gaussian model surrogates can provide fast algorithms to obtain these statistics (Bursik et al, 2012;Madankan et al, 2012;Stefanescu et al, 2012;Spiller et al, 2014;Bayarri et al, 2015;Tierz et al, 2018).…”