  Recent observations have detected excess H$\alpha$ emission from young
stellar systems with an age of several Myr such as PDS 70. One-dimensional
radiation-hydrodynamic models of shock-heated flows that we developed
previously demonstrate that planetary accretion flows of $>$ a few ten km
s$^{-1}$ can produce H$\alpha$ emission. It is, however, a challenge to
understand the accretion process of proto-giant planets from observations of
such shock-originated emission because of a huge gap in scale between the
circumplanetary disk (CPD) and the microscopic accretion shock. To overcome the
scale gap problem, we combine two-dimensional, high-spatial-resolution global
hydrodynamic simulations and the one-dimensional local radiation hydrodynamic
model of the shock-heated flow. From such combined simulations for the
protoplanet-CPD system, we find that the H$\alpha$ emission is mainly produced
in localized areas on the protoplanetary surface. The accretion shocks above
CPD produce much weaker H$\alpha$ emission (approximately 1-2 orders of
magnitude smaller in luminosity). Nevertheless, the accretion shocks above CPD
significantly affect the accretion process onto the protoplanet. The accretion
occurs at a quasi-steady rate, if averaged on a 10-day timescale, but its rate
shows variability on shorter timescales. The disk surface accretion layers
including the CPD-shocks largely fluctuate, which results in the time-variable
accretion rate and H$\alpha$ luminosity of the protoplanet. We also model the
spectral emission profile of the H$\alpha$ line and find that the line profile
is less time-variable, despite the large variability in luminosity.
High-spectral resolution spectroscopic observation and monitoring will be key
to reveal the property of the accretion process.
