  We show that the higher direct images of smooth commutative group schemes
from the Kummer log flat site to the classical flat site are torsion. For (1)
smooth affine commutative schemes with geometrically connected fibers, (2)
finite flat group schemes, (3) extensions of abelian schemes by tori, we give
explicit description of the second higher direct image. If the rank of the log
structure at any geometric point of the base is at most one, we show that the
second higher direct image is zero for group schemes in case (1), case (3), and
certain subcase of case (2). If the underlying scheme of the base is over
$\mathbb{Q}$ or of characteristic $p>0$, we can also give more explicit
description of the second higher direct image of group schemes in case (1),
case (3), and certain subcase of case (3). Over standard Henselian log traits
with finite residue field, we compute the first and the second Kummer log flat
cohomology group with coefficients in group schemes in case (1), case (3), and
certain subcase of case (3).
