Genesis 9:16

"Whenever the rainbow appears in the clouds, I will see it and remember the everlasting covenant between God and all living creatures of every kind on the earth."  Genesis 9:16

Here he is pointing out that this promise from God is everlasting.  He didn't say "I won't destroy all life by flood for the next 10 years or even for the next millennia," but he promised that he would never again destroy all life by flood.

When God says "I will see it," the Qbible translates this as "I will look at it."  So he's not going to just notice it out of the corner of his eye as an after thought, but he's going to actively look at the rainbow and remember his promise.  God will actively remember and keep his promises.

Genesis 9:14-15

"Whenever I bring clouds over the earth and the rainbow appears in the clouds, I will remember my covenant between me and you and all living creatures of every kind.  Never again will the waters become a flood to destroy all life."  Genesis 9:14-15

In the previous verses God told Noah that he was making a promise to mankind and all the creatures and all the future generations, and now he is telling what that pledge is - he will never again destroy all living creatures and people with flood waters.  The rainbow in the sky reminds both us and God of his promise.  And this is a promise he has kept, no matter how displeasing we are or how much our world rejects him, God has not brought forth another flood.

Genesis 9:12-13

 "And God said, 'This is the sign of the covenant I am making between me and you and every living creature with you, a covenant for all generations to come:  I have set my rainbow in the clouds, and it will be the sign of the covenant between me and the earth.'"  Genesis 9:12-13

Now that God has made his pledge to Noah and his descendants and all the living land creatures, not to destroy the whole world by flood again, he is putting up a sign as a reminder.  Every time we see a rainbow, we know that God promised us.  And he has kept that promise - never since then has there been a global flood that wiped out all life on the land.