Systematic uncertainties in air shower measurements from high-energy   hadronic interaction models
  Hadronic interaction models at cosmic ray (CR) energies are inherently uncertain due to the lack of a fundamental theoretical description of soft hadronic and nuclear interactions and the large extrapolation required from collider energies to the range of the most energetic cosmic rays observed ($>10^{20}$ eV). Model uncertainties are evaluated within the QGSJET-II model, by varying some of the crucial parameters in the limits allowed by collider data, and between QGSJET-II and other models commonly used in air shower simulations. The crucial parameters relate to hard processes, string fragmentation, diffraction and baryon production. Results on inelastic cross sections, on secondary particle production and on the properties of air showers measured by ground detectors from energies of $10^{12}$ to $10^{19}$ eV are presented. 
R.D. Parsons, C. Bleve, S.S. Ostapchenko, J. Knapp
astro-ph.HE