The fundamental problem with this analogy is that it amounts to Modalism.
H2O can be expressed in three states--a solid, a liquid, and a gas. This is not analogous to three Hypostases or Persons sharing together in the one Essence; but is analogous to God as a single agent expressing Himself through three masks or faces.
Water does not exist simultaneously as a gas and a solid, for example; that is the same molecules will not simultaneously be a gas as well as a solid. Whereas the Father, the Son, and the Holy Spirit exist simultaneously--the Father, Son, and Holy Spirit love one another, there is a conversation that can exist when Jesus prays to the Father and the Father says "Here is My beloved Son"; Jesus can point beyond Himself to the Father who sent Him, and speak of the Holy Spirit as "another comforter" that He will send, who comes from the Father.
Jesus is not talking to Himself, God the Son is speaking to God the Father, God the Father is speaking to God the Son; God the Father and God the Son send God the Holy Spirit. God relates to God, God is with God, God sends God.
This is a monumental difference.
"We believe in one God,
the Father almighty,
maker of heaven and earth,
of all things visible and invisible.
We believe in one Lord Jesus Christ,
the Only Begotten Son of God,
born of the Father before all ages.
God from God, Light from Light,
true God from true God,
begotten, not made, consubstantial with the Father;
through him all things were made.
For us men and for our salvation
he came down from heaven,
and by the Holy Spirit was incarnate of the Virgin Mary,
and became man.
For our sake he was crucified under Pontius Pilate,
he suffered death and was buried,
and rose again on the third day
in accordance with the Scriptures.
He ascended into heaven
and is seated at the right hand of the Father.
He will come again in glory
to judge the living and the dead
and his kingdom will have no end.
We believe in the Holy Spirit, the Lord, the giver of life,
who proceeds from the Father [and the Son],
who with the Father and the Son is adored and glorified,
who has spoken through the prophets.
We believe in one, holy, catholic and apostolic Church.
We confess one Baptism for the forgiveness of sins
and we look forward to the resurrection of the dead
and the life of the world to come. Amen."
-CryptoLutheran