A comprehensive system of definitions of land surface (topographic) curvatures, with implications for their application in geoscience modelling and prediction

Current use of land surface curvatures (LSCs) is in a confused state as a large gap has opened up between applications and theoretical work. LSCs exercise important control on changes of gravity potential energy and the equilibrium of the surface, and they are increasingly used in geosciences but they are not consistently defined. This paper offers a comprehensive theoretical framework for definition, classification and interpretation of LSCs. Systematization of known and newly derived relationships between LSCs is followed by extension of the traditional scheme for interpretation. A new comprehensive system of LSCs starts with the basic trio: profile, plan and twisting curvatures, and includes their slope-dependent sub-forms, combinations and imitations. Analysis of their influence on changes of gravitational potential energy available for mass flows is crucial for their understanding, and leads to a new interpretation of difference curvature. The systematic evaluation of LSCs as expressions of slope disequilibrium offers a further interpretation: zero values of LSCs can be considered as important theoretical attractors of landform development. LSCs are increasingly employed for analyses of landslide, flood, snow avalanche, forest fire, soil erosion, mass balance, ground water, digital soil mapping, individual landform identification and land surface segmentation, modelling of landscape development, classification of LIDAR data and visualization of terrain features. Important improvement of LSC use in all these spheres is possible. They are mostly computed in geographical information systems with limited capabilities: the performance of ArcGIS, SAGA, GRASS, LandSerf, Surfer and MICRODEM is compared here. The important interrelations of DEM resolution, accuracy and generalization are demonstrated in relation to the nested hierarchy of land forms and processes. The best interpretable LSCs, and challenges of future progress, are specified at the close of the paper.