The Nitrogen Risk Assessment Model for Scotland (NIRAMS) has been developed for prediction of streamwater N concentrations draining from agricultural land in Scotland. The objective of the model is to predict N concentrations for ungauged catchments, to fill gaps in monitoring data and to provide guidance in relation to policy development. The model uses nationally available data sets of land use, soils, topography and meteorology and has been developed within a Geographic Information System (GIS). The model includes modules to calculate N inputs to the land, residual N remaining at the end of the growing season, weekly time-series of leached N and transport of N at the catchment scale. This paper presents the methodology for calculating N balances for different land uses and for predicting the time sequence of N leaching after the end of the growing season. Maps are presented of calculated residual N and N leaching for the whole of Scotland and the spatial variability in N leaching is discussed. The results demonstrate the high variability in N leaching across Scotland. The simulations suggest that, in the areas with greatest residual N, the losses of N are not directly proportional to the amount of residual N, because of their coincidence with lower rainfall. In the companion paper, the hydrological controls on N transport within NIRAMS are described, and results of the full model testing are presented.