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Simulations have demonstrated that high-energy neutrinos (E > 10¹⁷ eV) are detected cost-efficiently via the Askaryan effect in ice, where a particle cascade induced by the neutrino interaction produces coherent radio emission that can be picked up by antennas installed below the surface. A good knowledge of the near surface ice (aka firn) properties is required to reconstruct the neutrino properties. In particular, a continuous monitoring of the snow accumulation (which changes the depth of the antennas) and the index-of-refraction profile are crucial for an accurate determination of the neutrino's direction and energy. 14 months of data of the ARIANNA detector on the Ross Ice Shelf, Antarctica, are presented where a prototype calibration system was successfully used to monitor the snow accumulation with unprecedented precision of 1 mm. Several algorithms to extract the time differences of direct and reflected (off the surface) signals (D'n'R time difference) from noisy data (including deep learning) are explored. This constitutes an in-situ test of the neutrino vertex distance reconstruction using the D'n'R technique which is needed to determine the neutrino energy. Additionally, an in-situ calibration system is proposed that extends the radio detector station with a radio emitter to continuously monitor the firn properties by measuring D'n'R time difference. In a simulation study the station layout is optimized and the achievable precision is quantified.