About the module

  • Forecasting pyroclastic density currents (PDCs) is critical because of their potential to do great harm. Likely more than one thousand people were killed by PDCs during the 2018 eruption of Fuego volcano (Guatemala) and more than 300 people killed by the 2010 PDCs from Merapi volcano (Indonesia).
  • Volcano scientists have incomplete information when they forecast potential PDCs. Perhaps the volcano shows signs of unrest (earthquakes, increased gas flux). The probability of eruptions must be deduced from these data. As a sequence of events unfolds, the probabilities leading up to those events become 1. The probabilites of future events are less than 1.
  • The visualization uses slider bars to control probabilities on the binary event tree.
  • Try to develop probabilities for the binary event tree for PDCs for future unrest at some specific volcano, using eruption summaries provided by the Smithsonian GVP. Compare your probabilites with others, try to reach a consensus on your average probabilites and document the uncertainties in your probabilites. Develop your own binary event tree for different eruptive scenarios.

Useful Links

Forecasting pyroclastic flows with a binary event tree

A binary event tree summarizes a sequence leading to a specific event, in this case the occurrence of a pyroclastic density current (PDC) on a volcano. 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 probability associated with each link. The tree is binary because only two links emerge from each node.

Each column in the tree corresponds to a step in the sequence leading to PDCs or not. Is the unrest associated with the intrusion of magma or not (y or n)? If so, does this intrusion lead to an eruption or not? If not, can an eruption still occur (e.g., phreatic)? And so on.

The two transition probabilites emerging from each node sum to 1. So, setting one probability, allows the other to be calculated (P[no] = 1 - P[yes]). A branch of the tree is an entire sequence of events, which ends in a leaf, the last node on the branch. The probability of a leaf occurring is the product of all transition probabilities along the branch. On a binary event tree, the probabilities of all the leaves sums to 1.

Adjust the sliders to change the probabilites along specific branches. Check out how the probabilities of different leaves changes as probabilities are adjusted at different points on the tree.

Key Concepts

In this case there is more than one branch leading to PDC leaves (the event: a PDC occurs, which is the end of the branch). The total probability of a PDC is the sum of the probabilities of these leaves. Events that can occur along different branches are sometimes called Moivrean events, or a Moivrean set, after the mathematician Du Moivre.

The transition probabilites might be based on guesses, past frequency of events, an aggregate of expert judgments, model output, or Bayesian estimates, which ideally use a prior probability calculated from current observations and a likelihood calculated from frequency of past events.

One can continue the binary event tree to the left (what is the probability of unrest occurring), or continue the tree to the right (given a PDC, will the run-out reach a specific location?).

One advantage of a binary tree is that it is, well, binary. Perhaps a binary decision needs to be made (evacuate or not?). The steps of the tree leading to this decision are systematic and understandable. This feature makes binary trees very popular in engineering and decision analysis. A disadvantage is that processes are usually more nuanced. One might be concerned about the magntiude of a potential eruption, rather than if an eruption occurs or not.

Some References

Shafer (1996) is a classic text on the concepts of causal reasoning based on event and probability trees. Aspinall and Cooke, 1998 developed a nearly binary event tree (a few nodes have three branches) for the Monteserrat eruption. This article also describes their expert elicictation process.