One fundamental objective in geomorphometry is to extract signatures of geomorphologic processes on different spatial scales from digital terrain models (DTMs) and to describe the complexity of landforms as the synthesis of those individual imprints. We present an approach for characterizing land surfaces on multiple, spatially varying local scales. We approximate terrain surfaces locally to calculate surface derivatives at different window sizes. Local scale behaviour diagrams are used to define dominant scale ranges and multiple curvatures for each surface point. Multi-scale landform analysis leads to improved models of surface derivatives and new landform classifications, applicable in geomorphology, soil science and hydrology.