Although 35 isn't really ultra-wide, Sigma's 35 1.4 is supposed to be really good, and substantially cheaper than Canon's 35 1.4L. Autofocus might not be quite as accurate, but I imagine for storm pictures, it wouldn't be as noticeable as indoor action sports photos.
If you want wide, and not too expensive, and f/4 is fast enough, also consider the 17-40. That'll get you wider, just as much light, and I do believe a fair amount less distortion, although corner sharpness at f/4 might not be quite as good as the 24-105...
also also, what 16 1.4L II are you referring to? There's a 14 f/2.8L II, and a 16-35 f/2.8L II, that I am aware of...