The principle of air-shower universality yields a method of understanding extensive air showers
of UHECRs as a superposition of different particle components whose spatial and temporal
distributions follow individual analytical profile functions. We present a model of the expected
densities of particles in time and space that uses the depth of the shower maximum, $X_\text{max}$ , and the
relative muonic content of the shower, $R_\text{µ}$ , as input parameters besides the shower geometry and
energy. The model is parametrized using simulated showers using different hadronic interaction
models. Furthermore, we present results for the reconstruction of $X_\text{max}$ and $R_\text{µ}$ that allow for
an event-by-event estimation of the mass of the primary particle, based on the responses of the
water-Cherenkov and scintillator surface detectors of the Pierre Auger Observatory.