  Surface detector arrays are designed to measure the spectrum and composition
of high-energy cosmic rays by detecting the secondary particle flux of the
Extensive Air Showers (EAS) induced by the primary cosmic rays. Electromagnetic
particles and muons constitute the dominant contribution to the ground detector
signals. In this paper, we show that the ground signal deposit of an EAS can be
described in terms of only very few parameters: the primary energy E, the
zenith angle theta, the distance of the shower maximum X_max to the ground, and
a muon flux normalization N_mu. This set of physical parameters is sufficient
to predict the average particle fluxes at ground level to around 10% accuracy.
We show that this is valid for hadronic air showers, using the two standard
hadronic interaction models used in cosmic ray physics, QGSJetII and Sibyll,
and for primaries from protons to iron. Based on this model, a new approach to
calibrating the energy scale of ground array experiments is developed, which
factors out the model dependence inherent in such calibrations up to now.
Additionally, the method yields a measurement of the average number of muons in
EAS. The measured distribution of N_mu of cosmic ray air showers can then be
analysed, in conjunction with measurements of X_max from fluorescence
detectors, to put constraints on the cosmic ray composition and hadronic
interaction models.
