TError: towards a better quantification of the uncertainty propagated during the characterization of tephra deposits
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Abstract
NOTE The code is now maintained on GitHub: https://github.com/e5k/TError
Follow updates on: https://e5k.github.io/
Eruption Source Parameters (ESP; e.g. plume height, erupted volume/mass, mass eruption rate, eruption duration) inferred from tephra deposits are associated with large degrees of uncertainty, as also demonstrated by recent work (e.g. Biass and Bonadonna, 2011; Bonadonna and Costa, 2013; Burden et al., 2013; Burden et al., 2011; Engwell et al., 2013; Klawonn et al., 2014a; Klawonn et al., 2014b; Le Pennec et al., 2012; Maeno et al., 2014). However, such uncertainties are rarely reflected in the published literature where ESPs are still often reported as a single value rather than a confidence interval. A new package of Matlab functions (TError) was designed to help characterize tephra deposits and provide a framework for a systematic quantification of ESP uncertainty.
TError takes ranges of field-based, model-based and empirical parameters as inputs, for which the user defines an uncertainty and an associated distribution (i.e., clast diameter, crosswind and downwind ranges, thickness measurement, area of isopach contours, bulk deposit density, empirical constants and wind speed). The TError package contains two main functions; the first function deterministically varies one input parameter at a time and quantifies the sensitivity of each ESP to the variability of input parameters; the second function propagates input parameters as stochastic distributions of noise through all ESPs. The resulting distributions can then be used to express the uncertainty of ESPs in a systematic way. For both functions, comprehensive reports and sets of figures assist the user in the interpretation of the results.
The package contains an implementation of the following methods for the quantification of ESPs:
- Plume height and wind speed from Carey and Sparks (1986);
- Mass eruption rate from Wilson and Walker (1987), Mastin et al. (2009) and Degruyter and Bonadonna (2012);
- Erupted volume from Fierstein and Nathensen (1992), Bonadonna and Houghton (2005) and Bonadonna and Costa (2012).
More details can be found in the associated paper recently published in Statics in Volcanology (Biass et al. 2014): http://scholarcommons.usf.edu/siv/vol1/iss1/2/
References:
Biass, S., Bagheri, G.H., Aeberhard, W. and Bonadonna, C., (2014). TError: towards a better quantification of the uncertainty propagated during the characterization of tephra deposits. Statistics in Volcanology.
Biass, S. and Bonadonna, C., 2011. A quantitative uncertainty assessment of eruptive parameters derived from tephra deposits: the example of two large eruptions of Cotopaxi volcano, Ecuador. Bulletin of Volcanology, 73(1): 73-90.
Burden, R.E., Chen, L. and Phillips, J.C., 2013. A statistical method for determining the volume of volcanic fall deposits. Bulletin of Volcanology, 75(6).
Burden, R.E., Phillips, J.C. and Hincks, T.K., 2011. Estimating volcanic plume heights from depositional clast size. Journal of Geophysical Research-Solid Earth, 116.
Engwell, S.L., Sparks, R.S.J. and Aspinall, W.P., 2013. Quantifying uncertainties in the measurement of tephra fall thickness. Journal of Applied Volcanology, 2(5).
Klawonn, M., Houghton, B.F., Swanson, D.A., Fagents, S.A., Wessel, P. and Wolfe, C.J., 2014a. Constraining explosive volcanism: subjective choices during estimates of eruption magnitude. Bulletin of Volcanology, 76(2).
Klawonn, M., Houghton, B.F., Swanson, D.A., Fagents, S.A., Wessel, P. and Wolfe, C.J., 2014b. From field data to volumes: constraining uncertainties in pyroclastic eruption parameters. Bulletin of Volcanology, 76(7).
Le Pennec, J.-L., Ruiz, G.A., Ramon, P., Palacios, E., Mothes, P. and Yepes, H., 2012. Impact of tephra falls on Andean communities: The influences of eruption size and weather conditions during the 1999-2001 activity of Tungurahua volcano, Ecuador. Journal of Volcanology and Geothermal Research, 217: 91-103.
Maeno, F., Nagai, M., Nakada, S., Burden, R.E., Engwell, S., Suzuki, Y. and Kaneko, T., 2014. Constraining tephra dispersion and deposition from three subplinian explosions in 2011 at Shinmoedake volcano, Kyushu, Japan. Bulletin of Volcanology, 76(6).
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