In the 1970s I was flying copilot on charter flights between San Francisco and Honolulu, Boeing 707s and 747s. We carried an extra pilot so we could fly round trip. In April 1977 a large storm was approaching the California coast. We would have to cross it both going and returning that day. During an hour break in Honolulu, I obtained this satellite full disk infra-red view of the Earth. (Only the top half here.)
The Pacific water is cold off the CA coast, and we got through it both ways with just light turbulence. It did dump record breaking rainfall on some California cities.
Crossing the Intertropical Convergence Zone, ITCZ, would become an every trip occurrence for me in the 1990s flying to South America. Thunderstorms need a lifting mechanism to get them going and the convergence of trade winds from the north and south near the Equator supply constant lifting. The ITCZ is there every day, more or less. They do not form hurricanes because of a lack of Coriolis force.
CONVECTION
Convection is the movement caused within a fluid by warmer and less dense material to rise, and colder, denser material to sink. Movement of the air in a cumulous cloud is vertical. Any cloud that looks like the top of a cauliflower is bumpy, towering cumulous very bumpy and cumulonimbus, (thunderstorms), extremely turbulent to catastrophic. Pilots deal with these on many flights. (From Miami to South America, every flight.)
The power of storms comes from the energy involved with the change of state of water from liquid to gas, (vapor), and back. A thunderstorm gathers humid air, (water vapor), at the bottom and lifts it up to higher altitudes where the atmosphere cannot hold so much moisture and forces it to change back to a liquid, releasing a huge amount of energy. Search the acronym CAPE, Convective Available Potential Energy.