  The balloon-borne HiCal radio-frequency (RF) transmitter, in concert with the
ANITA radio-frequency receiver array, is designed to measure the Antarctic
surface reflectivity in the RF wavelength regime. The amplitude of
surface-reflected transmissions from HiCal, registered as triggered events by
ANITA, can be compared with the direct transmissions preceding them by O(10)
microseconds, to infer the surface power reflection coefficient $\cal{R}$. The
first HiCal mission (HiCal-1, Jan. 2015) yielded a sample of 100 such pairs,
resulting in estimates of $\cal{R}$ at highly-glancing angles (i.e., zenith
angles approaching $90^\circ$), with measured reflectivity for those events
which exceeded extant calculations. The HiCal-2 experiment, flying from Dec.,
2016-Jan., 2017, provided an improvement by nearly two orders of magnitude in
our event statistics, allowing a considerably more precise mapping of the
reflectivity over a wider range of incidence angles. We find general agreement
between the HiCal-2 reflectivity results and those obtained with the earlier
HiCal-1 mission, as well as estimates from Solar reflections in the
radio-frequency regime. In parallel, our calculations of expected reflectivity
have matured; herein, we use a plane-wave expansion to estimate the
reflectivity R from both a flat, smooth surface (and, in so doing, recover the
Fresnel reflectivity equations) and also a curved surface. Multiplying our
flat-smooth reflectivity by improved Earth curvature and surface roughness
corrections now provides significantly better agreement between theory and the
HiCal 2a/2b measurements.
