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