Muon rate models play a key role in converting measured data into information on the density distributions of a target. Any given muography measurement, either in transmission or in scattering mode, requires a proper modelization of the muon flux according to the localization and to the atmospheric conditions. Two approaches are commonly used: either through semiempirical models calibrated on existing data or via Monte Carlo simulations. The former requires extrapolations to the field experiment conditions while the latter offers the advantage of tackling down, in a unique way, all relevant parameters such as barometric conditions, geomagnetic field, and atmosphere density. Although significant progress were made in the last decades, precision muography experiments require more and more accuracy on the models, especially for the muons close to the horizon where large disparities still remain. In this paper, we present detailed results obtained with the CORSIKA simulation framework to emphasize and quantify the impact of the environmental conditions on the sensitivity of muography measurements.