Physical geomorphometry for elementary land surface segmentation and digital geomorphological mapping

By interpretations related to energy, elementary land surface segmentation can be treated as a physical problem. Many pieces of such a view found in the literature can be combined into a synthetic comprehensive physical approach. The segmentation has to be preceded by defining the character and size of searched units to result from the segmentation. A high-resolution digital elevation model (DEM) is the key input for this task; it should be generalized to the resolution best expressing information about the searched units. Elementary land surface units can be characterized by various parts of potential gravitational energy associated with a set of basic geomorphometric variables. Elevation above sea level (z) represents Global Geomorphic Energy (GGE). Regional and Local Geomorphic Energy (RGE and LGE) are parts of GGE, represented respectively by relative elevation above the local base level (zrel) and local relief (elevation differential in a moving window Delta z). Derivation (change) of elevation defines the slope inclination (S), determining the local Potential Energy of Surface (PES) applicable to mass flow. Normal slope line (profile) curvature (kn)s and normal contour (tangential) curvature (kn)c express change in the PES value (Delta PES(kn)s, Delta PES(kn)c), responsible for acceleration/deceleration and convergence/ divergence of flow. Mean curvature (kmean) determines the Potential Energy of Surface applicable to Diffusion (PESD). Energetic interpretation of basic geomorphometric variables enables their direct comparison and systematic evaluation. Consequently, the homogeneity of basic geomorphometric variables defines a hierarchy of states of local geomorphic equilibria: static equilibrium, steady state, and non-steady state dynamic equilibrium. They are local attractors of landform development reflected in the geomorphometric tendency to symmetry (horizontality, various types of linearity, and curvature isotropy, together expressed by gravity concordance). Nonequilibrium and transitional states can be characterized by the PES excess (PESe) determined by difference curvature (kd), by gravity discordant change of the PES characterized by twisting curvature (tau g)c, and by Integral Potential Energy of Surface Curvature (IPESC) expressed by Casorati curvature (kC) (general curvedness). Excluding zrel and Delta z, all these energy-related geomorphometric variables are local point-based. Local area-based and regional variables such as Glock's Available Relief, Melton Ruggedness Number, Stream Power Index, Openness, Topographic Position Index, Topographic Wetness Index, and Index of Connectivity also have energetic interpretations although their definition is more complex. Therefore we suggest exclusive use of the local point-based variables in designs of elementary land surface segmentation. The segmentation should take notice of natural interconnections, the hierarchy of geomorphometric variables, elements of Local Geomorphic Energy, and (dis)equilibria states, so that elementary segments are clearly interpretable geomorphologically. This is exemplified by Geographic Object-Based Image Analysis (GEOBIA) segmentation of Sandberg, a territory on the boundary of the Carpathians and Vienna Basin with a complex geomorphic history and marked morphodynamics. Compared with expert-driven field geomorphological mapping, the automatic physically-based segmentation resulted in a more specific delineation and composition of landforms. Physical-geomorphometric characteristics of the elementary forms enabled the formulation of their system and subsequent improvement of the expert-based qualitative genetic analysis, with interpretation leading to a deeper understanding of the development and recent dynamics of the landscape.