Quantifying uncertainties in the measurement of tephra fall thickness

Abstract

The uncertainties associated with tephra thickness measurements are calculated and implications for volume estimates are presented. Statistical methods are used to analyse the large dataset of Walker and Croasdale J Geol Soc 127:17-55, 1971 of the Fogo A plinian deposit, São Miguel, Azores. Dirichlet tessellation demonstrates that Walker and Croasdale's measurements are highly clustered spatially and the area represented by a single measurement ranges between 0.5 and 10 km2. K-means cluster analysis shows that lower thickness uncertainties are associated with closely spaced measurements. Re-examination and analysis of Fogo A fall deposits show thickness uncertainties are about 9% for measured thickness while uncertainty associated with natural variance ranges, between 10 and 40%, with an average error of 30%. Correlations between measurement uncertainties and natural variance are complex and depend on a unit's thickness, position within a succession and distance from source. Normative error increases as tephra thickness decreases. The degree to which thickness measurement error impacts on volume uncertainty depends on the number of measurements within a given dataset and their associated uncertainty. The uncertainty in volume associated with thickness uncertainty calculated herein for Fogo A is 1.3%, equivalent to a volume of 0.02 km3. However uncertainties associated with smaller datasets can be much larger; for example typically exceeding 10% for less than 20 data points.