Hazards: singularities in geomorphic systems

Abstract

The development of landscapes is commonly interpreted as the outcome of the operation of a few simple phenomenological principles amongst which the Antagonism Principle is the most fundamental one. It states that there are two types of processes active in the formation of a landscape at the same time: the endogenic (tectonic) and the exogenic (climate-driven) processes. These two types of processes may more or less balance each other, in which case the actual aspect of a landscape corresponds to the instantaneous dynamic equilibrium between them. If one of the external parameters is changed, the equilibrium is supposed to be re-established by a corresponding continuous change of the other parameters (process–response theory). The dependences between various landscape parameters may become multivalued at junctions, cusps, etc. In that case, the system can jump from one branch of the process–response curve to another: a natural disaster occurs. However, modern views on the behavior of complex systems allow a somewhat different interpretation of the above phenomenological landscape interpretation, but also in the context of the Principle of Antagonism. However, a “stationary” landscape-state does now not correspond to a dynamic equilibrium, but to self-organized exogenic order at the edge of chaos. Under conditions of such self-organized criticality there are no natural space and time scales, so that fractal statistics are applicable; spatial and temporal correlations follow a power law. Extremely small accidental perturbations can cause the system to become unstable, leading to rapid changes in the landscape which are experienced as hazard-events. These follow a power law distribution for size versus frequency, provided the endogenic input occurs at a constant rate; they are therefore simply part and parcel of geomorphic systems.