While the idea may sound extreme, a "Frequently Asked Questions" webpage from 2014 on the National Oceanic and Atmospheric Administration website fields a similar question.
The page that appears on The Atlantic Oceanographic & Meteorological Laboratory attempts to answer the question "Why don't we try to destroy tropical cyclones by nuking them?"
In short, Christopher Landsea, a former research meteorologist with the Hurricane Research Division of the Atlantic Oceanographic & Meteorological Laboratory at NOAA, said that aside from the deadly radioactive fallout, there simply isn't enough energy in even a large nuclear explosive to alter a large hurricane.
Additionally, of the 80 or so tropical waves or depressions that form every year, only around five develop into hurricanes. Attempting to bomb each depression would be an inefficient way to prevent possible hurricanes.
Here is the answer as it appears on what appears to be a NOAA FAQ page created in 2014:
"During each hurricane season, there always appear suggestions that one should simply use nuclear weapons to try and destroy the storms. Apart from the fact that this might not even alter the storm, this approach neglects the problem that the released radioactive fallout would fairly quickly move with the tradewinds to affect land areas and cause devastating environmental problems. Needless to say, this is not a good idea.
"Now for a more rigorous scientific explanation of why this would not be an effective hurricane modification technique. The main difficulty with using explosives to modify hurricanes is the amount of energy required. A fully developed hurricane can release heat energy at a rate of 5 to 20x1013 watts and converts less than 10% of the heat into the mechanical energy of the wind. The heat release is equivalent to a 10-megaton nuclear bomb exploding every 20 minutes. According to the 1993 World Almanac, the entire human race used energy at a rate of 1013 watts in 1990, a rate less than 20% of the power of a hurricane.
"If we think about mechanical energy, the energy at humanity's disposal is closer to the storm's, but the task of focusing even half of the energy on a spot in the middle of a remote ocean would still be formidable. Brute force interference with hurricanes doesn't seem promising.
"In addition, an explosive, even a nuclear explosive, produces a shock wave, or pulse of high pressure, that propagates away from the site of the explosion somewhat faster than the speed of sound. Such an event doesn't raise the barometric pressure after the shock has passed because barometric pressure in the atmosphere reflects the weight of the air above the ground. For normal atmospheric pressure, there are about ten metric tons (1000 kilograms per ton) of air bearing down on each square meter of surface. In the strongest hurricanes there are nine. To change a Category 5 hurricane into a Category 2 hurricane you would have to add about a half ton of air for each square meter inside the eye, or a total of a bit more than half a billion (500,000,000) tons for a 20 km radius eye. It's difficult to envision a practical way of moving that much air around.
"Attacking weak tropical waves or depressions before they have a chance to grow into hurricanes isn't promising either. About 80 of these disturbances form every year in the Atlantic basin, but only about 5 become hurricanes in a typical year. There is no way to tell in advance which ones will develop. If the energy released in a tropical disturbance were only 10% of that released in a hurricane, it's still a lot of power, so that the hurricane police would need to dim the whole world's lights many times a year."
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