Calculating the probability of compound events: a risky proposition

The following is a guest post from Dr Michael Leonard, a research associate at the University of Adelaide.

Hurricane Sandy in late October 2012 was widely noted to involve the alignment of a tropical storm with an extra tropical storm, and a cold air mass moving from the northwest helped push the storm onshore in the vicinity of New Jersey. The manner in which all these factors combined to produce the flood impact was strongly emphasized in the media discussions following the event, and here the term ‘compound event’ (following the Intergovernmental Panel on Climate Change Special Report on Extremes) could be used to refer to such situations. The unique combination of factors might lead to the conclusion that this event was exceptional and therefore unlikely to recur.

Rather than emphasize that only some events such as Hurricane Sandy are exceptionally coincidental, however, I suggest that all extreme climate events of importance to society should be considered as compound events. This view helps to counteract the perception that any disaster recently experienced was somehow unique and unforeseeable, since although this perception may excuse our lack of foresight, it also will lead us to underestimate the potential of similar events happening again. In other words, we need to view combinations of interacting variables as the norm for understanding the risk of extreme events. This is a major departure from the manner in which planners and engineers usually conceive of such events.

To further the assertion that all events are compound events, consider a different event: the 2011 flooding of Queensland, but focused on the Brisbane region. In June 2010, La Niña conditions were established which lead to a number of catastrophic events over the summer period. The significance of these events takes on different meanings for different stakeholders (individuals or organisations who are affected by the flooding). Consider the nested boxes of the figure above.

  1. Flooding in the Ipswich City region can be due to flooding in the Brisbane River alone, the Bremer River alone or a combination of the two. Thus flooding depends on the correlated tributary flows arising from the coincidence of rainfall on the respective subcatchments.
  2. Wivenhoe Dam sits at the base of the Upper Brisbane catchment so that flows down the Brisbane River are highly dependent on the overall volume of rainfall over a period of days. Planning for sequences of separate storms complicate the operations policy for this dam. What is the probability that the reservoir is full at a time when another extreme rainfall event occurs over the catchment?
  3. Flooding in the downstream region of the catchment requires the ocean boundary (tide, storm surge, wind setup) to be considered jointly with any catchment runoff. For example, what is the probability that the peak catchment runoff will occur during a king tide plus a storm surge?
  4. Regional emergency services are concerned with multiple occurrences of flooding over a wider region, such as flash floods in Toowoomba which occurred shortly before the Brisbane floods. What is the probability of another extreme event will occur in another part of Queensland when emergency services are already fully committed to addressing an existing flood?
  5. Across the wider state multiple cyclones (Tasha, Yasi, Anthony) and widespread flooding caused a number of impacts such as ruining crops, interrupting mining activity and isolating towns and highways. The combined effect of these events is of concern to governments, insurers and industry, who are concerned by the aggregated impact of multiple events occurring over a period of months or years. For example what is the probability of an insurance company having to pay a given amount in claims due to multiple events occurring over a financial year?

At each scale the combination of events that may be seen as “the perfect storm” in the eyes of stakeholders at that scale. Each scenario involves the interaction of variables and events across a range of scales, where each meteorological event is not necessarily extreme, but in combination they produce an extreme impact. Risk modelling of compound events is therefore a challenging undertaking as it requires the realistic combination of many input variables and their interactions. However such modelling will become increasingly important as we learn more about how common the interactions such as those which produced hurricane Sandy really are.

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