About one purpose: to serve as a reminder, not to convince.

8 Then God said to Noah and to his sons with him: 9 “I now establish my covenant with you and with your descendants after you 10 and with every living creature that was with you—the birds, the livestock and all the wild animals, all those that came out of the ark with you—every living creature on earth. 11 I establish my covenant with you: Never again will all life be destroyed by the waters of a flood; never again will there be a flood to destroy the earth.”

12 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: 13 I have set my rainbow in the clouds, and it will be the sign of the covenant between me and the earth. 14 Whenever I bring clouds over the earth and the rainbow appears in the clouds, 15 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. 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.” 17 So God said to Noah, “This is the sign of the covenant I have established between me and all life on the earth.”