Jamawami took the words right out of my mouth, so to speak. There isn't much to add. In fact, some storms can be lethal, and if not that, at least harmful if you are caught out unprepared. I use a 10 by 12 polytarp when I bike tour. The part about making a lean-to shelter with a fence line is good.
I have been caught out in some freakish deadly storms, and I weathered all well enough except for one where I got chilled to the bone. That was High Island, Texas across the road from the beach. Later I was told that if I had camped on the beach side of the road where I was, I would have been toasted because there were over 90 lightning strikes all over the beach there.
If you carry a tent, freestanding or other, set it up right away. Usually, the conditions for such storms present themselves before all hell breaks loose. When out in the middle of nowhere, set up your shelter right away just in case. If it storms, you're covered. If it doesn't, pack up and go. All you've lost is a little time, and you're better safe than sorry.
Weather is always a major concern to people who cross oceans in small sailboats such as thirty and forty foot sloops. What they learn to do is read the wind and clouds which presage certain kinds of weather systems. This is an extremely important part of sailing because reefing sails and putting up a storm jib can range between pure hell and impossible to do in a gale. You can do the same weather predicting on land. Read books on sailing and there are usually sections detailing cloud formations which indicate certain types of approaching weather systems. You can get small, light weight, inexpensive radios which have weather radio stations at the flip of a switch. They had them at Big Lots for about $10.00.
The thing about heavy weather is it often goes unreported unless it is a killer storm because people who live in houses and work inside are not to be concerned with it. They stay inside or in their vehicles. Being out there on a bike is a whole different world when the devil comes to visit. That's why weather radio is a good thing.