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Ultra high energy neutrinos ($E_\nu > 10^{16.5}$eV$)$ are efficientlymeasured via radio signals following a neutrino interaction in ice. An antennaplaced $\mathcal{O}$(15 m) below the ice surface will measure two signals forthe vast majority of events (90% at $E_\nu$=$10^{18}$eV$)$: a direct pulse anda second delayed pulse from a reflection off the ice surface. This allows for aunique identification of neutrinos against backgrounds arriving from above.Furthermore, the time delay between the direct and reflected signal (D'n'R)correlates with the distance to the neutrino interaction vertex, a crucialquantity to determine the neutrino energy. In a simulation study, we derive therelation between time delay and distance and study the correspondingexperimental uncertainties in estimating neutrino energies. We find that theresulting contribution to the energy resolution is well below the natural limitset by the unknown inelasticity in the initial neutrino interaction. We presentan in-situ measurement that proves the experimental feasibility of thistechnique. Continuous monitoring of the local snow accumulation in the vicinityof the transmit and receive antennas using this technique provide a precisionof $\mathcal{O}$(1 mm) in surface elevation, which is much better than thatneeded to apply the D'n'R technique to neutrinos.

Neutrino vertex reconstruction with in-ice radio detectors using surface reflections and implications for the neutrino energy resolution