We present TError, a Matlab package designed to quantify systematically the uncertainty associated with the characterization of tephra deposits, in which the most commonly used methods to quantify eruption source parameters are implemented. Inputs of the code are a range of field-based, model-based and empirical parameters (i.e., clast diameter, crosswind and downwind ranges, thickness measurement, area of isopach contours, bulk deposit density, empirical constants and wind speed), for which the user defines an uncertainty and an associated distribution. The TError package contains two main functions. The first function deterministically varies one input parameter at a time and quantifies the sensitivity of each Eruption Source Parameter (ESP; i.e., plume height, erupted volume, mass eruption rate) 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 physical parameters of explosive eruptions in a systematic way. For both functions, comprehensive reports and sets of figures assist the user in the interpretation of the results. As an example, the TError package was applied to Layer 5 of Cotopaxi volcano. Using the median, the 2nd percentile and the 98th percentile as central value, lower bound and upper bound respectively, a new quantification of the ESP suggests a plume height of $30 +/- 1 km a.s.l, a mass eruption rate of 1.8 (-0.2, +0.3) x 108 kg s-1 and a tephra volume between 0.23 (-0.04, +0.13) and 0.43 (-0.06, 0.08 km3, depending on the empirical model used.



TError_code.zip (487 kB)
Source code

sensitivity.xlsx (39 kB)
Sensitivity result, Layer 5 of Cotopaxi

gaussian.xlsx (14 kB)
Propagation result using a Gaussian distribution of error, Layer 5 of Cotopaxi

uniformR.xlsx (14 kB)
Propagation result using a uniform random distribution of error, Layer 5 of Cotopaxi

gaussian_wind.xlsx (14 kB)
Propagation result using a Gaussian distribution of error with wind input, Layer 5 of Cotopaxi