  Some models of coronal heating suppose that convective motions at the
photosphere shuffle the footpoints of coronal magnetic fields and thereby
inject sufficient magnetic energy upward to account for observed coronal and
chromospheric energy losses in active regions. Using high-resolution
observations of plage magnetic fields made with the Solar Optical Telescope
aboard the Hinode satellite, we investigate this idea by estimating the upward
transport of magnetic energy --- the vertical Poynting flux, S_z --- across the
photosphere in a plage region. To do so, we combine: (i) estimates of
photospheric horizontal velocities, v_h, determined by local correlation
tracking applied to a sequence of line-of-sight magnetic field maps from the
Narrowband Filter Imager, with (ii) a vector magnetic field measurement from
the SpectroPolarimeter. Plage fields are ideal observational targets for
estimating energy injection by convection, because they are: (i) strong enough
to be measured with relatively small uncertainties; (ii) not so strong that
convection is heavily suppressed (as within umbrae); and (iii) unipolar, so S_z
in plage is not influenced by mixed-polarity processes (e.g., flux emergence)
unrelated to heating in stable, active-region fields. In this plage region, we
found that the average S_z varied in space, but was positive (upward) and
sufficient to explain coronal heating, with values near (5 +/- 1) x 10^7
erg/cm^2/s. We find the energy input per unit magnetic flux to be on the order
of 10^5 erg/s/Mx. A comparison of intensity in a Ca II image co-registered with
the this plage shows stronger spatial correlations with both total field, B,
and unsigned vertical field, |B_z|, than either S_z or horizontal field, B_h.
The observed Ca II brightness enhancement, however, probably contains a strong
contribution from a near-photosphere hot-wall effect unrelated to atmospheric
heating.
