High energy neutrinos ($E>10^{17}$ 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. We present an in-situ calibration system that extends the radio detector station with a radio emitter to continuously monitor the firn properties by measuring time differences of direct and reflected (off the surface) signals (D'n'R). We optimized the station layout in a simulation study and quantified the achievable precision. We present 14 months of data of the ARIANNA detector on the Ross Ice Shelf, Antarctica, where a prototype of this calibration system was successfully used to monitor the snow accumulation with unprecedented precision of 1 mm. We explore and test several algorithms to extract the D'n'R time difference from noisy data (including deep learning). 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.