  We study the degeneration of semipositive smooth hermitian line bundles on
open complex manifolds, assuming that the metric extends well away from a
codimension two analytic subset of the boundary. Using terminology introduced
by R. Hain, we show that under these assumptions the so-called height jump
divisors are always effective. This result is of particular interest in the
context of biextension line bundles on Griffiths intermediate jacobian
fibrations of polarized variations of Hodge structure of weight -1, pulled back
along normal function sections. In the case of the normal function on M_g
associated to the Ceresa cycle, our result proves a conjecture of Hain. As an
application of our result we obtain that the Moriwaki divisor on \bar M_g has
non-negative degree on all complete curves in \bar M_g not entirely contained
in the locus of irreducible singular curves.
