Natural hazards, such as tornados and hurricanes, are generally described to have different intensities. In general, high-intensity hazards are much more rare than low-intensity hazards. For example, a Category 5 hurricane may strike Boston every 200 years or so, but a Category 3 may strike several times a century. On the other hand, a Category 5 hurricane would cause much more damage. These differences in the hazard intensity and the hazard probability have to be taken into account in any risk/loss calculation for natural hazards. This is commonly done by calculating and summing the risks associated with hazards of different intensities. Below is a table which shows the probabilities that a coastal town will experience a hurricane of different Categories in any given year. A second column shows the predicted losses caused by wind damage for each of the different Categories of hurricane intensity. Hurricane intensity Yearly probability Predicted loss per incident Category 1 0.20 $0 Category 2 0.10 $1,000,000 Category 3 0.05 $4,000,000 Category 4 0.02 $8,000,000 Category 5 0.01 $16,000,000 Consider this information in the context of the equation risk = hazard x vulnerability. The hazard is the probability of the physical event, the vulnerability is the loss (cost) if such an event happened, and the risk is the average loss per year. (a) What is the total risk (in $/year) from severe winds in any given year associated with Category 4 or weaker hurricanes? What is the total risk associated with all hurricanes (including also Category 5)? Various mitigation measures are available. An investment of $1,000,000 in building-strengthening measures will eliminate the vulnerability to intensities less than Category 5, but will not reduce the vulnerability to stronger winds. The investment of an additional $1,000,000 will reduce the vulnerability to Category 5 winds by half. (b) Calculate the annual benefit (the risk reduction) for the first and the second million invested. What is the ratio between annual risk reduction (the benefit) and the investment (the cost) if only the first million is spent? What is the total benefit/cost ratio if both millions are spent? What is the marginal benefit/cost ratio for the second million spent? (Marginal here referring to the incremental benefit and cost for the second million spent.) Comment on the result. Natural hazards, such as tornados and hurricanes, are generally described to have different intensities. In general, high-intensity hazards are much more rare than low-intensity hazards. For example, a Category 5 hurricane may strike Boston every 200 years or so, but a Category 3 may strike several times a century. On the other hand, a Category 5 hurricane would cause much more damage. These differences in the hazard intensity and the hazard probability have to be taken into account in any risk/loss calculation for natural hazards. This is commonly done by calculating and summing the risks associated with hazards of different intensities. Below is a table which shows the probabilities that a coastal town will experience a hurricane of different Categories in any given year. A second column shows the predicted losses caused by wind damage for each of the different Categories of hurricane intensity. Hurricane intensity Yearly probability Predicted loss per incident Category 1 0.20 $0 Category 2 0.10 $1,000,000 Category 3 0.05 $4,000,000 Category 4 0.02 $8,000,000 Category 5 0.01 $16,000,000 Consider this information in the context of the equation risk = hazard x vulnerability. The hazard is the probability of the physical event, the vulnerability is the loss (cost) if such an event happened, and the risk is the average loss per year. (a) What is the total risk (in $/year) from severe winds in any given year associated with Category 4 or weaker hurricanes? What is the total risk associated with all hurricanes (including also Category 5)? Various mitigation measures are available. An investment of $1,000,000 in building-strengthening measures will eliminate the vulnerability to intensities less than Category 5, but will not reduce the vulnerability to stronger winds. The investment of an additional $1,000,000 will reduce the vulnerability to Category 5 winds by half. (b) Calculate the annual benefit (the risk reduction) for the first and the second million invested. What is the ratio between annual risk reduction (the benefit) and the investment (the cost) if only the first million is spent? What is the total benefit/cost ratio if both millions are spent? What is the marginal benefit/cost ratio for the second million spent? (Marginal here referring to the incremental benefit and cost for the second million spent.) Comment on the result