Why use the rule of thirds? Because in a 3:2/4:3 landscape orientation it is very effective at giving a sense of balance and being pleasant to the eye. Why are several people in here advocating against it? Well, look at the words they're using:
"The storm is what I want to capture"
"the subject is the storm or tornado"
"The sky is always the story and main subject"
"important to include all of a whole storm"
Documenting a scene accurately conflicts with creating an artistic image. The rule of thirds is one of many composition guidelines to help make your images more aesthetically pleasing. For many chasers, I suspect that the first goal is to document the scene as best possible, and aesthetics take a back seat.
This isn't a bad thing, it's pretty much a necessity to be successful as a chaser. This decision is made even easier because we don't have time to do many of the things that landscape photographers do such as waiting for different lighting, or considering multiple angles. Landscape photography is also typically done at narrower apertures to capture all details, but we can't afford to stop down to f22 when we're under a storm.
Since we can't pick our foregrounds, we are very limited in aperture and shutter speed, and documenting the storm takes priority over aesthetics, the proportions need to be compromised. The truly stunning storm pictures that document the scene *and* are aesthetically pleasing from an artistic perspective are few and far between, and require a small degree of luck. It's like street photography except the subject can kill you, the lighting conditions are horrible, and sometimes there isn't a single person out in the streets.
Let's look at one of Mike H's pics because he's a great photographer, and has seen some great storms:
What's that, a rule of 6ths?
There's some great contrast in there, and blue/orange are very appealing, so it would have been a mistake to crop out too much of that foreground. There are two focal points that some lines converge on, and neither are in optimal position. The focal points/lines are almost wasted because of the intense highlights on the left side of the image that keep drawing the eye over.
Cover up the top half of the image with your hand - there's a lot of contrast and detail, it's an interesting image to look at. Cover up the bottom half of the image with your hand - it's pretty darn boring, banal even. All of this was out of Mike's control for the most part, he could either document the storm from that vantage point, or turn the camera off and wait for that 1% chance of getting a perfect image. So Mike did a few things: he left the top half as part of the image to provide scale, so the viewer really feels the size of this storm. He balanced the highlights on the left so that they were present and provided weight, but kept them minimal. He left just enough ground in to provide a base, some reference, and some good color synergy. Given the scene he was presented with, he did the best he could to make it aesthetically pleasing even if the composition couldn't be perfect. Most importantly he documented the storm.
Now try thinking about all that in your head while an EF-4 is about to cut right in front of you and you're in 50mph inflow. I've seen several dozen tornadoes, taken tons of non-weather pictures, and I still can't do it. Something has to give, and I'd rather document the storm than create art if I'm forced to decide.
