Dawn phenomenon (this is where your body needs more insulin pre-dawn to wake up);
Middle of the night 'hypo' and subsequent rebound;
Insufficient levemir;
Issues with the injection site (do you rotate your sites?)
Something you ate prior to bed that's included high fat/protein, which has slowed the release of carbs.
Have you had this before?
What's your usual morning BG result?
Have you changed anything (e.g. insulin type / amount / diet / exercise, etc.) in the last few days?