Finding a sensible balance for natural hazard mitigation with mathematical models

Society for Industrial and Applied Mathematics: Uncertainty issues are paramount in the assessment of risks posed by natural hazards and in developing strategies to alleviate their consequences. In a paper published last month in the SIAM/ASA Journal on Uncertainty Quantification, the father-son team of Jerome and Seth Stein describe a model that estimates the balance between costs and benefits of mitigation—efforts to reduce losses by taking action now to reduce consequences later— following natural disasters, as well as rebuilding defenses in their aftermath. Using the 2011 Tohoku earthquake in Japan as an example, the authors help answer questions regarding the kinds of strategies to employ against such rare events.

“Science tells us a lot about the natural processes that cause hazards, but not everything,” says Seth Stein. “.... This situation is like playing the card game ‘21’, in which players see only some of the dealer’s cards. It is actually even harder, because we do not fully understand the rules of the game, and are trying to figure them out while playing it.”

...Another conundrum for authorities in such crisis situations is the appropriate amount of resources to direct toward a disaster zone. ...Selecting an optimum strategy, however, depends on estimating the expected value of damage. This, in turn, requires prediction of the probability of disasters.

....To determine the advantages and pitfalls of rebuilding after such disasters, the authors present a deterministic model. Here, outcomes are precisely determined by taking into account relationships between states and events. The authors use this model to determine if Japan should invest in nuclear power plant construction given the Fukushima Daiichi nuclear reactor meltdown during the 2011 tsunami. Taking into account the financial and societal benefits of reactors, and balancing them against risks—both financial and natural—the model determines the preferred outcome.

Such models can also be applied toward other disaster situations, such as hurricanes and floods, and toward policies to diminish the effects of climate change. Stein gives an example: “Given the damage to New York City by the storm surge from Hurricane Sandy, options under consideration range from doing nothing, using intermediate strategies like providing doors to keep water out of vulnerable tunnels, to building up coastlines or installing barriers to keep the storm surge out of rivers. In this case, a major uncertainty is the effect of climate change, which is expected to make flooding worse because of the rise of sea levels and higher ferocity and frequency of major storms. Although the magnitude of these effects is uncertain, this formulation can be used to develop strategies by exploring the range of possible effects.”

How much mitigation is needed? The bottom of a U-shaped curve is a “sweet spot” – a sensible balance. Photo Credit: Jerome Stein and Seth Stein