Costs and Benefits of Hurricane forecasting

Even though hurricane conditions affect only 100 miles of coastline on average, forecasters generally raise warnings on >400 miles. The additional 300 miles of warning area are a buffer that allows for uncertainty in the track forecast. Forecast errors have decreased by ~30% since the late 1960s, but ---contrary to the expectation--- the length of warning areas has nearly doubled. The more-extensive warnings have coincided with a >30% increase in lead time. Thus, each time forecasters raised warnings, they made an informal cost–benefit calculation that implicitly valued increases in lead time more than reductions in warning area.

Forecast errors increase approximately linearly with duration. If one were willing to accept 12 h lead time instead of the present 24 h, it would be feasible to halve the buffer to 150 miles and warn a total of 250 miles of coast with the same degree of risk. Doubling of forecast accuracy would also allow halving of the buffer. Given an average cost of $0.6M per mile for preparation, the smaller buffer size would reduce overwarning cost from $240M to $150M.

In contrast with the linear increase of overwarning cost, the value of the next hour of lead time decreases with total duration because of the law of diminishing returns. Citizens and enterprises complete the higher-priority actions first. After a time, they simply run out of worthwhile preparations. Exponential decrease is an appealing model. After some "half life" ½ of potential actions are incomplete. After two half lives 1/4 remain, after three half lives 1/8.... A reasonable value for the half life, based upon experience, is twelve hours. Measures undertaken "in extremis" such as protecting openings of buildings or evacuation of aircraft and vessels, have limited effectiveness, say for the sake of argument 25% of the total damage. One might reduce the average $3000M damage expected from a Category 3 hurricane by $750M if one had a long time to prepare. At 12 h preparation time, the reduction would be $375M, at 24 h it would be $563M, at 36 h it would be $656M, and so forth. Clearly, a minimum exists where the marginal cost of raising warnings an hour earlier and warning an additional 12.5 miles of coastline just balances the savings realized by actions undertaken in that same hour. In this case, the minimum occurs at 31 h, when the warning cost is $292M and the value of damage mitigated is $625M, for a net savings of $332M.

Factors that favor long lead time are: 1) more accurate forecasts or cheaper preparations, which reduce overwarning costs; 2) greater total damage as a result of either more property at risk or a more intense hurricane; and 3) slower or (paradoxically) more effective actions to reduce damage.