Economic Value of Weather and Climate Forecasts, Richard W. Katz and Allan H. Murphy, editors, 1997 includes some hard core math. But the idea explored is straightforward enough, and much of each paper included is spent on the considerations which direct the mathematics, so you needn't be up on the math to gain from the reading.
Fundamentally, a forecast has zero economic value if it can't be, or isn't/won't be, used to increase a profit or reduce a loss. The value lies in the decisions which can be (and are) made based on the forecast, and not the forecast's accuracy (abstractly considered) itself.
On an extreme example, the value of climate forecasts to James Inhofe is zero. There is nothing, given his public statements, he would do in response to a climate forecast (regardless of how good) differently than with no information. Also limited value of hurricane forecasts 5 days ahead to Rush Limbaugh, who dismissed (September 5th, 2017) the (extremely accurate, as it turned out) forecast of Hurricane Irma's landfall in Florida on the 10th. On the 5th (follow link to news story with the details), he was dismissing the forecast as fake news / liberal conspiracy, and advising his listeners to ignore the forecast. On the 8th, just 2 days ahead of the storm, he evacuated from Florida. Given his listeners and advertisers, it may well have profited him to delay response. People who couldn't evacuate because they listened to him for too long, different matter.
But it illustrates a different issue -- lead time and actions. If you don't (can't, won't) do anything differently with 5 days' lead time than with 2 days' lead time, there's no value to you in the extra lead time for the forecast. Scientists, of course, are very interested in the difference -- the better we understand hurricanes, the better (farther ahead) we can predict them. But that's hard to put a dollar value to. For me, certainly, 5 days lead time in knowing a hurricane is coming is far better than 2 days. It gives me time to prepare the house for the winds and waters, and to make a considered retreat (meaning no traffic jam) outside the range of the hurricane. With just 2 days warning, that becomes hard to do. On the other hand, it would be no more helpful to me to know of a hurricane coming in August 16, 2019 than to know of one coming August 16, 2018. And August 16th is probably no more useful to me than July 16th (from my vantage of June 3rd).
There are people and interests other than me and mine, however. Home supply and repair stores, for instance, might profit greatly from knowing that they'll need a large stock of material and staff prior to a particular date. Or even just that odds are higher than usual that their area will have a hurricane.
What are some weather or climate decisions you make? How much difference does the accuracy of the prediction make? How far ahead does it matter for your decisions to have the prediction?
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