Quantifying Uncertainties in Tephra Thickness and Volume Estimates

Characterization of explosive volcanic eruptive processes from interpretations of deposits is a key to assessing long-term volcanic hazards and risks, particularly for large explosive eruptions which occur relatively infrequently and others whose deposits, particularly distal deposits, are transient in the geological record. Whilst eruption size - determined by measurement and interpretation of tephra fall deposits - is of particular importance, uncertainties for such measurements and volume estimates are rarely presented. In this study, we quantify the main sources of variance in determining tephra volume from thickness measurements and isopachs in terms of number and spatial distribution of such measurements, using the Fogo A deposit, São Miguel, Azores as an example. Analysis of Fogo A fall deposits show measurement uncertainties are approximately 9 % of measured thickness while uncertainty associated with natural deposit variability ranges between 10 % and 40 % of average thickness, with an average variation of 30 %. Correlations between measurement uncertainties and natural deposit variability are complex and depend on a unit's thickness, position within a succession and distance from source and local topography. The degree to which thickness measurement errors impact on volume uncertainty depends on the number of measurements in a given dataset and their associated individual uncertainties. For Fogo A, the consequent uncertainty in volume associated with thickness measurement uncertainty is 1.3 %, equivalent to a volume uncertainty of 1.5 × 0.02 km3. Uncertainties also arise in producing isopach maps: the spatial relationships between source location and different deposit thicknesses are described by contours subjectively drawn to encompass measurements of a given thickness, generally by eye. Recent advances in volume estimation techniques involve the application of mathematical models directly to tephra thickness data. Here, uncertainties in tephra volumes derived from isopach maps were investigated by modelling raw thickness data as bicubic splines under tension. In this way, isopachs are objectively determined in relation to the original data. This enables limitations in volume estimates to be identified in previously published maps where a mathematically formal fitting procedure was not used. Eruption volumes derived using these spline isopachs are in general smaller than published traditional estimates. Using the bicubic spline method, volume uncertainties are correlated with number of data points and decrease from as much as 40 % relative to the mean estimate for a case with 30 measurements to 10 % when 120 measurements or more are available. Thus the accuracy of volume estimation using this method depends on the number of data points, their spatial distribution and their associated measurement uncertainties, and the estimate reliability can be fully quantified on these terms; comprehensive uncertainty assessment is not feasible for most conventional tephra volume estimates determined using hand drawn isopachs.