A simple semi-empirical approach to model thickness of ash-deposits for different eruption scenarios

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Abstract
The impact of ash-fall on people, buildings, crops, water resources, and infrastructure depends on several factors such as the thickness of the deposits, grain size distribution and others. Preparedness against tephra falls over large regions around an active volcano requires an understanding of all processes controlling those factors, and a working model capable of predicting at least some of them. However, the complexity of tephra dispersion and sedimentation makes the search of an integral solution an almost unapproachable problem in the absence of highly efficient computing facilities due to the large number of equations and unknown parameters that control the process. An alternative attempt is made here to address the problem of modeling the thickness of ash deposits as a primary impact factor that can be easily communicated to the public and decision-makers. We develop a semi-empirical inversion model to estimate the thickness of non-compacted deposits produced by an explosive eruption around a volcano in the distance range 4–150 km from the eruptive source. The model was elaborated from the analysis of the geometric distribution of deposit thickness of 14 world-wide well-documented eruptions. The model was initially developed to depict deposits of potential eruptions of Popocatépetl and Colima volcanoes in México, but it can be applied to any volcano. It has been designed to provide planners and Civil Protection authorities of an accurate perception of the ash-fall deposit thickness that may be expected for different eruption scenarios. The model needs to be fed with a few easy-to-obtain parameters, namely, height of the eruptive column, duration of the explosive phase, and wind speed and direction, and its simplicity allows it to run in any platform, including a personal computers and even a notebook. The results may be represented as tables, two dimensional thickness-distance plots, or isopach maps using any available graphic interface. The model has been tested, with available data from some recent eruptions in México, and permits to generate ash-fall deposit scenarios from new situations, or to recreate past situations, or to superimpose scenarios from eruptions of other volcanoes. The results may be displayed as thickness vs. distance plots, or as deposit-thickness scenarios superimposed on a regional map by means of a visual computer simulator based on a user-friendly built-in computer graphic interface.

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