Satellite-based observations during the Arctic winter of 2009/2010 provide firm evidence that, in contrast to the current understanding, the nucleation of nitric acid trihydrate (NAT) in the polar stratosphere does not only occur on preexisting ice particles. In order to explain the NAT clouds observed over the Arctic in mid-December 2009, a heterogeneous nucleation mechanism is required, occurring via immersion freezing on the surface of solid particles, likely of meteoritic origin. For the first time, a detailed microphysical modelling of this NAT formation pathway has been carried out. Heterogeneous NAT formation was calculated along more than sixty thousand trajectories, ending at Cloud Aerosol Lidar with Orthogonal Polarization (CALIOP) observation points. Comparing the optical properties of the modelled NAT with these observations enabled a thorough validation of a newly developed NAT nucleation parameterisation, which has been built into the Zurich Optical and Microphysical box Model (ZOMM). The parameterisation is based on active site theory, is simple to implement in models and provides substantial advantages over previous approaches which involved a constant rate of NAT nucleation in a given volume of air. It is shown that the new method is capable of reproducing observed polar stratospheric clouds (PSCs) very well, despite the varied conditions experienced by air parcels travelling along the different trajectories. In a companion paper, ZOMM is applied to a later period of the winter, when ice PSCs are also present, and it is shown that the observed PSCs are also represented extremely well under these conditions.