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The precise determination of the arrival direction of cosmic rays is afundamental prerequisite for the search for sources or the study of theiranisotropies on the sky. One of the most important aspects to achieve anoptimal measurement of these directions is to properly take into account themeasurement uncertainties in the estimation procedure. In this article wepresent a model for the uncertainties associated with the time measurements inthe Auger surface detector array. We show that this model represents well themeasurement uncertainties and therefore provides the basis for an optimaldetermination of the arrival direction. With this model and a description ofthe shower front geometry it is possible to estimate, on an event by eventbasis, the uncertainty associated with the determination of the arrivaldirections of the cosmic rays.

A model for the time uncertainty measurements in the Auger surface detector array