Non-exhaust traffic induced emissions are a major source of particle mass in most European countries. This is particularly important in Nordic and Alpine countries where winter time road traction maintenance occurs, e.g. salting and sanding, and where studded tyres are used. In this paper, Part 1, the road dust sub-model of a coupled road dust and surface moisture model (NORTRIP) is described. The model provides a generalised process based formulation of the non-exhaust emissions, with emphasis on the contribution of road wear, suspension, surface dust loading and the effect of road surface moisture (retention of wear particles and suspended emissions). The model is intended for use as a tool for air quality managers to help study the impact of mitigation measures and policies. We present a description of the road dust sub-model and apply the model to two sites in Stockholm and Copenhagen where seven years of data with surface moisture measurements are available. For the site in Stockholm, where studded tyres are in use, the model predicts the PM10 concentrations very well with correlations (R-2) in the range of R-2 = 0.76-0.91 for daily mean PM10. The model also reproduces well the impact of a reduction in studded tyres at this site. For the site in Copenhagen the correlation is lower, in the range 0.44-0.51. The addition of salt is described in the model and at both sites this leads to improved correlations due to additional salt emissions. For future use of the model a number of model parameters, e.g. wear factors and suspension rates, still need to be refined. The effect of sanding on PM10 emissions is also presented but more information will be required before this can be confidently applied for management applications.