Currently, the use of numerical models for reproducing the evolution of river systems and landscapes is part of the day-by-day research activities of fuvial engineers and geomorphologists. However, despite landscape evolution modelling is based on a rather long tradition, and scientists and practitioners are studying how to schematize the processes involved in the evolution of a landscape since decades, there is still the need for improving the knowledge of the physical mechanisms and their numerical coding. Updating past review papers, the present work focuses on the frst aspect, discussing six main components of a landscape evolution model, namely continuity of mass, hillslope processes, water fow, erosion and sediment transport, soil properties, vegetation dynamics. The more common schematizations are discussed in a plain language, pointing out the current knowledge and possible open questions to be addressed in the future, towards an improvement of the reliability of such kind of models in describing the evolution of fuvial landscapes and river networks.
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