Andrew Goodwin's theory.

Andrew Goodwin's theory states that traditional narrative does not apply to pop videos, as pop videos approach narrative from a different angle in comparison to novels and films. There are several reasons for this: pop videos are built around songs – and usually songs do not follow the traditional narrative.. structures (normality – problem – resolution). Also, the artist plays both the narrator and character within the pop video. Moreover, the singer often looks directly at the camera, this enhances the performance and the audience in more involved.

Some videos are autonomous, which gives you the power to do your own thing. Some video’s offer a visual pleasure that encourages repeated viewing and promotes the music at the same time. Whereas other videos might also be promoting other medias such as films.

Overall there are three types of relations between songs and videos: 
Illustration: when the video tells the story of the lyrics

Britney Spears' video for Circus i think is an illustration video because it has many literal connotations to the lyrics plus the song is called "Circus" and the location is a circus tent. Her lyric "Im like the ring leader" is supported by her wearing a top hat and tails and later taming the lions which is traditionally done by the ring leader. Also she often sings "Spotlight on me" and this is supported by her soley being lit by a spotlight and/or her being infront of the light with it strobing into the camera. She also sings "the dancefloor is my stage" and then goes to perform a dance in the circus ring as if it were a stage.
Amplification: when there is additional meaning to the lyrics visually

In the case of Rihanna's Disturbia video i think it fits into the category of amplification because of its use of mise-en-scene, cinematography, costume and make up. The song is quite dark lyrically and so is the video with many jump cuts creating jerked movements. Most things in the video are out of the ordinary and there is alot of black with the only light being streamed from the background.

Disjuncture: when there is little or no link between the image and lyrics

Adeles Rolling in the Deep music video i think is disjunctured because there is nothing in it that supports the lyrics and music and also for a country song it doesn't contain many of stereotypes that would follow. She is sat in a room singing and there is also a contemporary dance which doesn't support what the lyrics are saying.