Outside of John Calvin, no confessionally Reformed theologian has impacted my theology more than John Murray. His work on Christian Baptism was particularly valuable in my coming to adopt the covenant (infant) baptism position. Before reading that work again, I'm reading through Murray's The Covenant of Grace again.

A couple of Murray's points on the Noahic Covenant and its perpetuity across generations who do not acknowledge it are particular good to recall from time to time,

"The covenant operates from good to such an extent that its benefits are not contingent upon intelligent appreciation of the covenant or of the benefits which are dispensed in terms of it.

...

Furthermore, we may not forget that the covenant purpose and grace were made known to Noah, and the perpetuity of the covenant is continuously attested in order that those capable of understanding may have confidence in the security and perpetuity of the covenant grace bestowed. But we must also observe that the covenant operates on behalf of, and dispenses its blessings to, those who are wholly unaware of its existence. It is a covenant with all flesh." (13)

Futhermore, Murray reflects on the import of the covenant sign being God-centric,

"It is true that the revelatory purpose of the bow in the cloud is not to be forgotten. But the significant fact is that the revelatory purpose is to bear witness to the divine faithfulness. It is the constant reminder that God will not prove unfaithful to his promise. The main point to be stressed now, however, is that this continuance is dependent upon divine faithfulness alone; in anthropomorphic terms, upon the divine remembrance alone. And if we fail to interpret the sign the right, if we regard it simply as a natural phenomenon without any reference to its covenantal meaning, this does not negate or nullify the Divine remembrance and the perpetuity of God's faithfulness." (14)

The rainbow reminds God of His unconditional covenant with all of creation. And as such, it reminds us of God's faithfulness.