AshCalc–a new tool for the comparison of the exponential, power-law and Weibull models of tephra deposition

Matthew L Daggitt,Stephen Page,David M Pyle,Tamsin A Mather

doi:10.1186/2191-5040-3-7

Matthew L Daggitt, Stephen Page + Show 2 more

Open Access

https://doi.org/10.1186/2191-5040-3-7

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Abstract

This paper presents a new tool, AshCalc, for the comparison of the three most commonly used models for the calculation of the bulk volume of volcanic tephra fall deposits: the exponential model, the power law model and the Weibull model. AshCalc provides a simple and intuitive tool to speed up the analysis of tephra deposits and compare and contrast the fits for each model. Two improvements in terms of computational performance are implemented in AshCalc for the estimation of the parameters for the Weibull model. The first is an analytic method for reducing the number of free parameters, whilst the second exaggerates the minima in parameter space, leading to a more robust solution. We show that AshCalc provides volume estimates in line with other previously published estimates and hence can be used with a high degree of confidence. We include the open source python code for Ashcalc with the intention that it can be used both as a stand-alone program and integrated into other python projects.

Highlights

Studying the variation in thickness of tephra fall deposits has long been used as a key tool for estimating the volumes of explosive volcanic eruptions (Pyle, 1989)
In order to assess the accuracy of AshCalc, the program’s outputs were compared to published values for four eruptions
AshCalc has the potential to be a powerful tool for volcanologists to calculate and compare the various models for tephra deposits as matches for their data and calculation of volumes

Summary

Introduction

Studying the variation in thickness of tephra fall deposits has long been used as a key tool for estimating the volumes of explosive volcanic eruptions (Pyle, 1989). By fitting multiple exponential segments to the data, the exponential law is capable of modelling deposits which have a variable rate of thinning with distance away from the vent–a feature which is common to many well constrained deposits (e.g. Pyle, 1989; 1990; Fierstein and Nathanson, 1992; Bonadonna and Houghton 2005; Watt et al 2009). This approach lends itself to a variety of simple approximations, for example to determine the minimum volume of a deposit from sparse information Taking the log of both sides linearises the equation and the parameters, c and m, are found by applying least squares regression

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