  Gaia DR1 Tycho-Gaia Astrometric Solution parallaxes, Tycho-2 photometry and
reddening/extinction estimates from nine data sources for 38074 giants within
415 pc from the Sun are used to compare their position in the
Hertzsprung-Russell diagram with theoretical estimates, which are based on the
PARSEC and MIST isochrones and the TRILEGAL model of the Galaxy with its
parameters being widely varied. We conclude that (1) some systematic errors of
the reddening/extinction estimates are the main uncertainty in this study; (2)
any emission-based 2D reddening map cannot give reliable estimates of reddening
within 415 pc due to a complex distribution of dust; (3) if a TRILEGAL's set of
the parameters of the Galaxy is reliable and if the solar metallicity is
Z<0.021, then the reddening at high Galactic latitudes behind the dust layer is
underestimated by all 2D reddening maps based on the dust emission observations
of IRAS, COBE, and Planck and by their 3D followers (we also discuss some
explanations of this underestimation); 4) the reddening/extinction estimates
from recent 3D reddening map by Gontcharov, including the median reddening
E(B-V)=0.06 mag at |b|>50 deg, give the best fit of the empirical and
theoretical data with each other.
