  We present a full model of surface-detector responses to extensive air
showers. The model is motivated by the principles of air-shower universality
and can be applied to different types of surface detectors. Here we describe a
parametrization for both water-Cerenkov detectors and scintillator surface
detectors, as for instance employed by the upgraded detector array of the
Pierre Auger Observatory. Using surface detector data, the model can be used to
reconstruct with reasonable precision shower observables such as the depth of
the shower maximum $X_\text{max}$ and the number of muons $R_\mu$.
