Two sources of uncertainty in estimating tephra volumes from isopachs: perspectives and quantification

Calculating the tephra volume 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 isopach areas. In this work, we study two sources of uncertainty in estimating tephra volumes based on isopachs. The first is model uncertainty. It occurs because no fitted curves perfectly describe the tephra thinning pattern, and the fitting is done based on log-transformed square root of isopach area. The second source of uncertainty occurs because thickness must be extrapolated beyond the available data, which makes it impossible to validate the extrapolated thickness. We demonstrate the importance of the two sources of uncertainty on a theoretical level. We use six isopach datasets with different characteristics to demonstrate their presence and the effect they could have on volume estimation. Measures to better represent the uncertainty are proposed and tested. For 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 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 and 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 uncertainty in the volume estimate.