  We examine a new family of global analytic solutions for optically thick
accretion disks, which includes the supercritical accretion regime. We found
that the ratio of the advection cooling rate, $Q_{\rm adv}$, to the viscous
heating rate, $Q_{\rm vis}$, i.e., $f=Q_{\rm adv}/Q_{\rm vis}$, can be
represented by an analytical form dependent on the radius and the mass
accretion rate. The new analytic solutions can be characterized by the
photon-trapping radius, $\rtrap$, inside which the accretion time is less than
the photon diffusion time in the vertical direction; the nature of the
solutions changes significantly as this radius is crossed. Inside the trapping
radius,
  $f$ approaches $f \propto r^0$, which corresponds to the advection-dominated
limit ($f \sim 1$), whereas outside the trapping radius, the radial dependence
of $f$ changes to $f \propto r^{-2}$, which corresponds to the
radiative-cooling-dominated limit. The analytical formula for $f$ derived here
smoothly connects these two regimes. The set of new analytic solutions
reproduces well the global disk structure obtained by numerical integration
over a wide range of mass accretion rates, including the supercritical
accretion regime. In particular, the effective temperature profiles for our new
solutions are in good agreement with those obtained from numerical solutions.
Therefore, the new solutions will provide a useful tool not only for evaluating
the observational properties of accretion flows, but also for investigating the
mass evolution of black holes in the presence of supercritical accretion flows.
