The children travel in five stages: Sun Land, Magic Forest, Ice Land, Cloud Mountain and finally the Hinterworld. That order is not the cycle of the world - which is exactly the point.
Heat from the sun moves the air. The air carries warmth to the Ice Land and the ice melts. The water irrigates the Magic Forest. Rivers and moisture return to the Sun Land. In short: fire, air, water, earth, fire. The children only see the connection in the fifth book.
Very long ago, a high culture of antique character built an enormous structure at Cloud Mountain. Its engineers set out to solve a problem with rational engineering, and they did solve it - but their solution threw the whole system off balance. Today the barrier is weathered and overgrown and looks like a mountain. It blocks an old wind corridor. That is why the warm downslope wind is missing, why the water land freezes, why the forest dries out and why the Sun Land loses its rivers.
An eccentric outsider everyone takes for a madman.
The president, the highest leader in the land.
An outlaw nobody recognises as a guardian any more.
A real dragon nobody believes in.
In the end the Sun Land stays hot, the Ice Land stays cold, the forest stays a forest and Moon Land stays lunar. They are simply connected again.