Abstract : The measurement of large scale patterns or anisotropies in the arrival direction of high energy cosmic rays is an important step towards the understanding of their origin. Such measurements rely on an accurate estimation of the detector relative exposure in each direction on the sky : the coverage map. To reach an accuracy on the determination of this map below the one percent level one must properly identify and correct for all the environmental effects that may induce variations in the detector exposure as a function of time. In an approach, similar to the one used in anti-sidereal time analysis, we propose a method to empirically estimate and correct for those effects under the hypothesis that seasonal and diurnal variations can be factorized. We tested this method using a model ground detector of cosmic ray air showers, whose aperture varies due to the dependence of the air shower development on the atmospheric conditions.