Forecasting tephra fallout with an event tree
An event tree can be used to estimate the probable impacts of specific volcanic phenomena, like magnitude of tephra fallout at a specific location. Steps in the sequence, starting at the left and proceeding to the right, are shown by nodes (circles). Each node is connected by a link (line) and there is a transition probability associated with each link. This event tree has more than two links emerging from some nodes, allowing for categorical variables (like VEI).
The conditional probability P[VEI 2-5 | explosion] must be less than or equal to 1. The conditional probability P[T > 10 kg/m2 | VEI] is computed using a separate numerical model, in this case Tephra2. Run Tephra2 Probability Tool to estimate these input values for a specific geographic location you select.
Key Concepts
One can calculate the conditional probability of tephra mass loading exceeding 10 kg/m2 (P[T> 10kg/m2 | eruption]) by summing these probabilities.
Often the geologic record is used to deduce the relative frequencies of eruptions of different magnitudes (VEI). This record might be biased toward larger eruptions that are better preserved in the geologic record, or biased toward more recent, better documented, eruptions. It is important to explore this potential bias by assessing uncertainties in the transition probabilites.
Alternative numerical models or empirical observations can be used to populate event trees. The impact of alternative, or ensemble models on aggregate probabilities is rarely investigated and a wide open area for further research.
Some References
Hill et al., 1998 is an early example of using a survivor function, also called a complementary cumulative distribution function (CCDF) in probabilistic volcanic hazard assessment of tephra fallout.
The event tree used in this exercise was first described in Connor et al., 2001
Accessible articles on event trees in eruption forecasting are: Newhall and Hobblit, 2002 and Marzocchi et al., 2004