Antarctic surface reflectivity calculations and measurements from the ANITA-4 and HiCal-2 experiments

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 R. The first HiCal mission (HiCal-1, Jan. 2015) yielded a sample of 100 such pairs, resulting in estimates of R at highly glancing angles (i.e., zenith angles approaching 90°), with measured reflectivity for those events which exceeded extant calculations [P. W. Gorham et al., Journal of Astronomical Instrumentation, 1740002 (2017)]. The HiCal-2 experiment, flying from December 2016-January 2017, provided an improvement by nearly 2 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 [D. Z. Besson et al., Radio Sci. 50, 1 (2015)]. 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-2 measurements.