The storm Lear endures symbolizes his emotional state through mirroring his inner turmoil. Lear's compounding madness is symbolized through the storm's power and turbulent nature. One can parallel the storm's physical "anger" as being a representation of what is going on inside Lear himself.
King Lear is facing an inner storm, because he is trying to decide what to do about his children. He says he wants to choose the one who loves him more.