An upper limit of the predictability of atmospheric motions can be determined from observations of the dispersion of tracers in the atmosphere. The range of time P within which the prediction of any numerical model must be erroneous in the grid scale of that model is estimated from the lifetime of fluid particles in the atmosphere which have the size of a mesh cube of the model. A further technique is proposed which allows for an assessment of P from curves of relative particle separation in the atmosphere. The further growth of the prediction error after t = P can be derived from these curves as well. These ideas are tested in a barotropic model atmosphere and, finally, applied to the atmosphere using data of large scale dispersion experiments with constant volume balloons. The obtained upper limit of predictability as a function of scale is felt to be too optimistic for it does not properly take into account the influence of the vertical motions in the atmosphere.