  Let $(E,\overline{\partial}_E,\theta)$ be a stable Higgs bundle of degree $0$
on a compact connected Riemann surface. Once we fix the flat metric
$h_{\det(E)}$ on the determinant of $E$, we have the harmonic metrics $h_t$
$(t>0)$ for the stable Higgs bundles $(E,\overline{\partial}_E,t\theta)$ such
that $\det(h_t)=h_{\det(E)}$. We study the behaviour of $h_t$ when $t$ goes to
$\infty$. First, we show that the Hitchin equation is asymptotically decoupled
under the assumption that the Higgs field is generically regular semisimple. We
apply it to the study of the so called Hitchin WKB-problem. Second, we study
the convergence of the sequence $(E,\overline{\partial}_E,\theta,h_t)$ in the
case where the rank of $E$ is two. We introduce a rule to determine the
parabolic weights of a "limiting configuration", and we show the convergence of
the sequence to the limiting configuration in an appropriate sense. The results
can be appropriately generalized in the context of Higgs bundles with a
Hermitian-Einstein metric on curves.
