In analyzing any work of cinema, it is important to integrate specific points in the analysis. Identifying and ensuring that your analysis addresses these points are critical. With that in mind, I think that one element that can be addressed is how the film depicts Noah, as a protagonist. The summary of the film is based on the Biblical story of Noah and the Ark. It is from this point that some rather interesting points of analysis can be discussed.
One particular theme that can be addressed is the condition of the divine. Essentially, the film addresses if God is merciful or vengeful. On one hand, the destructive capacity of the divine is a significant part of the narrative. Aaron Aronofsky, the film's director and writer, argues that this is a significant aspect of the narrative:
There’s always been this comedic element to Noah, but I wanted to tell it seriously...It’s the fourth story in the Bible, and God already decides to destroy mankind. To destroy your creation is such a huge emotional moment.
This vengeful anger of the divine is a significant part of the story. A thematic implication of the film is how God demonstrates both anger and redemption. The ending promise from the divine that another flood will not be used as well as the symbolic use of the rainbow helps to convey the mercy of the divine. The exploration of this dynamic that expresses both the anger and redemption of the divine represents a significant aspect of the film's themes:
The story of Noah starts with this concept of strong justice, that the wickedness of man will soon be met with justice, and it ends when the rainbow comes and it says, even though the heart of man is filled with wickedness, I will never again destroy the world...So it ends with this idea of mercy. God somehow goes from this idea of judging the wickedness to mercy and grace. So we decided that was a powerful and emotional arc to go through, and we decided to give that arc to Noah.
Exploring how this characterization impacts the film can be part of your analysis.
I think that another aspect of analysis about Noah would have to be in the titular character. It can be argued that Noah is rather one- dimensional in the Bible. He follows the word of God and does what God asks of him. Aronofsky wanted to alter this type of perception of Noah, offering a different view than “a fable for kids — a nice story about an old man with a beard and some animals, so of course kids gravitate towards it.” A significant trait of Aronofsky's films is how he explores the intricacy of characters. Primary characters are analyzed and seen through different lenses. The result is a psychologically complex portrait in which characters are round and intensely intricate. Noah is shown in a similar manner in Aronofsky's film. Noah struggles with the task in front of him, recognizes the pain in what he must do, and has to face agonizing decisions in terms of what to do and how to live. The result is that Noah is richly developed, a characterization that identifies "the rationale for God’s mercy in some native spark of goodness in Noah that will, viewers hope, make the new, post-flood world more livable than the antediluvian one." This is a complex characterization that emerges in the film and can be part of an analysis of the film.