Power Distribution and Probabilistic Forecasting of Economic Loss and Fatalities due to Hurricanes, Earthquakes, Tornadoes, and Floods in the United States

Traditionally, the size of natural disaster events such as hurricanes, earthquakes, tornadoes, and floods is measured in terms of wind speed (m/sec), energy released (ergs), or discharge (m3/sec). Economic loss and fatalities from natural disasters result from the intersection of the human infrastructure and population with the natural event. This study investigates the size versus cumulative number distribution of individual natural disaster events in the United States. Economic losses are adjusted for inflation to 2014 United States Dollars (USD). The cumulative number divided by the time over which the data ranges is the basis for making probabilistic forecasts in terms of the Number of Events Greater Than a Given Size Per Year and it\u27s inverse, Return Period. Such forecasts are of interest to insurers/re-insurers, meteorologists, seismologists, government planners, and response agencies. Plots of size versus cumulative number distributions per year for economic loss and fatalities are well fit by power scaling functions of the form P(x) = Cx-ß; where, P(x) is the cumulative number of events per year with size equal to and greater than size x (or probability of occurrence), C is a constant which measures the activity level, x is the event size, and ß is the scaling exponent. Power distributions have a property referred to as self-similar or scale free, so that any sample of the distribution at any scale is statistically identical to the whole distribution. Economic loss and fatalities due to hurricanes, earthquakes, tornadoes, and floods are well fit by power functions over one to five orders of magnitude in size. Economic losses for hurricanes and tornadoes have greater scaling exponents, ß = 1.1 and 0.9 respectively, whereas earthquakes and floods have smaller scaling exponents, ß = 0.4 and 0.6 respectively. The value of the scaling exponent determines the petitioning of losses between larger and smaller sized events. All of the data sets exhibit a roll-off for smaller economic loss events. The roll-off below a certain size is attributed to either under estimating the economic losses or to a transition away from a power function below which the cumulative number is independent of size. Fatalities for tornadoes and floods have greater scaling exponents, ß = 1.5 and 1.7 respectively, whereas hurricanes and earthquakes have smaller scaling exponents, ß = 0.4 and 0.7 respectively