In the study of cosmic rays with ground-based particle detectors, controlling systematic uncertainties, especially those arising from secondary particle transport in the atmosphere, is crucial. There are various applications in the High Altitude Water Cherenkov Observatory (HAWC) that require a detailed description of atmospheric effects on the secondary particle flux, for example, in the study of anomalous phenomena that disturb the atmosphere, such as the Hunga Tonga volcano explosion in 2022. Specifically, we propose a characterization of the effects of atmospheric pressure, temperature, and humidity using Monte Carlo simulations of cosmic ray-induced air showers in different atmospheric scenarios, based on meteorological data at the HAWC location. We simulate vertical, very inclined and horizontal air showers in the TeV range using AIRES and CORSIKA, as well as different hadronic interaction models.