For minimal surfaces admitting an elliptic fibration over a smooth curve, there is a famous analysis of possible singular fibers and a canonical bundle formula due to Kodaira.

There are two papers of Kenji Ueno, in which he tries to classify the singular fibers of an abelian surface fibration over a smooth curve. But I don't see any formula for the canonical bundle of such threefolds?

Does any body know of any formula for that?

(All the varieties I am talking about are projective)