Energy determination in the Akeno Giant Air Shower Array experiment

Using data from more than ten-years of observations with the Akeno Giant Air Shower Array (AGASA), we published a result that the energy spectrum of ultra-high energy cosmic rays extends beyond the cutoff energy predicted by Greisen, and Zatsepin and Kuzmin. In this paper, we reevaluate the energy determination method used for AGASA events with respect to the lateral distribution of shower particles, their attenuation with zenith angle, shower front structure, delayed particles observed far from the core and other factors. The currently assigned energies of AGASA events have an accuracy of $\pm$25% in event-reconstruction resolution and $\pm$18% in systematic errors around 10${}^{20}$eV. This systematic uncertainty is independent of primary energy above 10${}^{19}$eV. Based on the energy spectrum from 10${}^{14.5}$eV to a few times 10${}^{20}$eV determined at Akeno, there are surely events above 10${}^{20}$eV and the energy spectrum extends up to a few times 10${}^{20}$eV without a GZK-cutoff.