How good do natural hazard assessments need to be?

In trying to mitigate natural hazards, society plays a high-stakes game against nature. Often nature surprises us when an earthquake, hurricane, or flood is bigger or has greater effects than expected from detailed natural hazard assessments. In other cases, nature outsmarts us, doing great damage despite expensive mitigation measures. These difficulties are illustrated by the March 2011 earthquake off Japan’s Tohoku coast. The earthquake was much larger than anticipated from hazard maps and generated a tsunami much larger than anticipated, which overtopped coastal defenses, causing more than 15,000 deaths and US$210 billion damage. Similar situations occur in predicting earthquake ground shaking (Stein et al., 2012), river floods (Merz, 2012), and other hazards (Pollack, 2003; Pilkey and Pilkey-Jarvis, 2007). Society faces the challenge of choosing mitigation strategies, given that assessments of potential hazard have large uncertainties. This challenge is similar to that in national defense, involving choosing among expensive weapons and strategies to deal with poorly known future threats. like defense planners, hazard planners must decide how much is enough (enthoven and Smith, 1971; Goda and Hong, 2006). We explore choosing strategies using a simple model comparing the costs and benefits of mitigation options (Stein and Stein, 2012). For example, given the damage to new York City by the storm surge from Hurricane Sandy, options under consideration range from continuing to do little through intermediate strategies like providing doors to keep water out of vulnerable tunnels to building barriers to keep the surge out of rivers. Progressively more extensive mitigation measures cost more but are expected to produce increasing reduction of losses in future hurricanes. In our model, we denote the cost of mitigation as C(n), where n is a measure of mitigation. The scale of a natural event is parameterized by h, such as the height of a storm surge, an earthquake’s magnitude, or the level of the resulting ground shaking. The predicted annual economic loss, L(h,n) increases with h and decreases with n. The annual probability of an event h is p(h), so the present value of the expected loss is