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Ultra-high energy cosmic rays generate extensive air showers in Earths atmosphere. A standard approach to reconstruct the energy of an ultra-high energy cosmic rays is to sample the lateral profile of the particle density on the ground of the air shower with an array of surface detectors. For cosmic rays with large inclinations, this reconstruction is based on a model of the lateral profile of the muon density observed on the ground, which is fitted to the observed muon densities in individual surface detectors. The best models for this task are derived from detailed Monte-Carlo simulations of the air shower development. We present a phenomenological parametrization scheme which allows to derive a model of the average lateral profile of the muon density directly from a fit to a set of individual Monte-Carlo simulated air showers. The model reproduces the detailed simulations with a high precision. As an example, we generate a muon density model which is valid in the energy range 1e18 eV < E < 1e20 eV and the zenith angle range 60 deg < theta < 90 deg. We will further demonstrate a way to speed up the simulation of such muon profiles by three orders of magnitude, if only the muons in the shower are of interest.
Radio detection of inclined air showers currently receives special attention. It can be performed with very sparse antenna arrays and yields a pure measurement of the electromagnetic air-shower component, thus delivering information that is highly co
The Tunka Radio Extension (Tunka-Rex) is a digital antenna array for the detection of radio emission from cosmic-ray air showers in the frequency band of 30 to 80 MHz and for primary energies above 100 PeV. The standard analysis of Tunka-Rex includes
With the Auger Engineering Radio Array (AERA) of the Pierre Auger Observatory, we have observed the radio emission from 561 extensive air showers with zenith angles between 60$^circ$ and 84$^circ$. In contrast to air showers with more vertical incide
Radio detection of inclined air showers is currently receiving great attention. To exploit the potential, a suitable event reconstruction needs to be developed. The first step in this direction is the development of a model for the lateral distributi
We describe the method devised to reconstruct inclined cosmic-ray air showers with zenith angles greater than $60^circ$ detected with the surface array of the Pierre Auger Observatory. The measured signals at the ground level are fitted to muon densi