Qingyuan Yang , Susanna F Jenkins

Calculating the volume of tephra erupted is important for estimating eruption intensity and magnitude. Traditionally, tephra volumes are estimated by integrating the area under curves fit to the square root of hand-drawn isopach areas. Previous studies have attempted to quantify the uncertainty in this approach, but not all sources of uncertainty have been well-analyzed or addressed. In this work, we study two such sources of uncertainty in estimating tephra volumes based on isopachs. The first source is model uncertainty. It occurs because no fitted curves perfectly describe the tephra thinning pattern, and the fitting is done based on log-transformed thickness and the square-root of isopach area. This model uncertainty is often omitted or considered compensated for or overridden by the presence other sources of uncertainty. The second source of uncertainty occurs because thickness must be extrapolated beyond the available data (i.e. beyond isopachs), which makes it impossible to validate the extrapolated thickness. It has been pointed out in a previous work, but remains unresolved. We demonstrate the importance of the two sources of uncertainty on a theoretical level. We use six isopach datasets with different features (e.g., spacing, coverage, and number of isopachs) to demonstrate their presence and the effect they could have on volume estimation. Measures to better represent the uncertainty are proposed and tested. For uncertainty arising from the model uncertainty, we propose: i) a better-informed and stricter way to report and evaluate goodness-of-fit, and ii) that uncertainty estimations be based on the envelope (or union thickness) defined by different well-fitted curves, rather than volumes estimated from individual curves. For the second source of uncertainty, we support reporting separately the volume portions that are interpolated between isopachs and those that are extrapolated, and we propose to test how sensitive the total volume is to variability in the extrapolated volume. The two sources of uncertainty should not be ignored as they could introduce additional bias, and lead to under- or over-estimated uncertainty in the volume estimate.