Atmospheric parameters, such as pressure (P), temperature (T) and density (ρ∝P/T), affect the development of extensive air showers initiated by energetic cosmic rays. We have studied the impact of atmospheric variations on extensive air showers by means of the surface detector of the Pierre Auger Observatory. The rate of events shows a 10% seasonal modulation and 2% diurnal one. We find that the observed behaviour is explained by a model including the effects associated with the variations of P and ρ. The former affects the longitudinal development of air showers while the latter influences the Molière radius and hence the lateral distribution of the shower particles. The model is validated with full simulations of extensive air showers using atmospheric profiles measured at the site of the Pierre Auger Observatory. ; http://www.sciencedirect.com/science/journal/09276505 ; The Pierre Auger Collaboration. K.B. Barber. J.A. Bellido. R.W. Clay. B.R. Dawson. V.C. Holmes. J. Sorokin. P. Wahrlich. B.J. Whelan. M.G. Winnick. et al.