The Gaussian model is frequently used for modelling environmental loads, e.g. sea elevation, wind loads and road profiles. However, the Gaussian model is often only valid for short sections of the load. For example, for roads profiles, short sections of roads, say 100 m, is well modelled by a Gaussian process, whereas longer sections of roads, say 10 km, typically contain shorter sections with high irregularity, and the variability between sections is higher than what can be explained by the stationary Gaussian model. This phenomenon can be captured by a Laplace process, which can be seen as a Gaussian process with randomly varying variance. Thus, the Gaussian process is a special case of the Laplace process. Further, the expected damage can be computed from the parameters of the Laplace process. We will give examples of modelling road profiles using Laplace models. Especially, it will be demonstrated how to reconstruct a road profile based on sparse road roughness measurements, such as a sequence of IRI (International Roughness Index) for 100 metre road sections. Further, IRI data from the Finnish road network will be evaluated.