Like other weather-related phobias, ombrophobia often starts in childhood, as a result of a traumatic experience. The fix - like the fix for most phobias - is pretty nasty.
Perhaps the most efficient means of extinguishing a storm phobia is the procedure called "flooding," in which the phobic is exposed directly to the maelstrom and not allowed to escape. When no injury occurs, the fear subsides within an hour or two. Flooding can be harsh, and few would stand for it in this rude form. However, a more humane and common variant is also effective. With graduated exposure, the stimulus is presented in increments of increasing intensity, allowing the person to habituate to one level before the next, more intense element is introduced. Many phobics can be treated in a single, extended session using this modified incremental exposure procedure. (From Diagnosis & Treatment of Phobias)
It sounds good in theory. If you're the one undergoing the treatment, though, it is not so nice. In any "desensitization" demonstrations I've seen, people look like they're dissociating, not like they're actually getting any less scared.
The horror writer in me always asks, "What if that person is right to be scared?"