the use od once

navigator,

The second sentence is not right because it implies a control over the rain by someone.

For example:

I will return to playing with my toys only after the neighbor kid is executed, said the petulant prince.

"Is executed" as in "is executed by someone", a passive construct.

The rain is not controlled and is not able to be stopped.

"I'd like to go for a walk once the riot is quelled" would be correct, but it doesn't work with rain.

It has stopped. = It stopped prior to now, and the present perfect tense gives it a connection to now, the connection being that: it is not raining now.

It is stopped. = Simple present usually describes habitual or characteristic qualities, as in "she is a happy person" or "she is routinely bedded by the football team" or "he is probed by ailens on a daily basis".

The latter are passive tenses in the simple present that indicate that an entity has performed the action.

With rain, no such entity stops it.

Alternately, it would not be uncommon in American English to say: "I'd like to go for a walk once the rain stops."

It just doesn't work with "is stopped" too well, as it sounds like a use of a passive construct that means something or someone stopped it.

"Is stopped" in a construct meaning the state of "stop", as in "not raining" does not work.

It stops and then has stopped (the present perfect lends to the present the connection that it is currently still "stopped") but does not engage in the state of "stop".

I hope that's not too confusing.