Allometric change of landforms

Abstract

Allometry is the study of the relative rates of change of two variables of a system. In the study of landforms, or the processes acting upon them, the power function Y = a X b is useful for correlating changes in variables. Allometric analysis includes the study of dynamic interrelations during geomorphic history, or the static interrelations at a given time. Such analyses may include aspects of geomorphic open systems that are tending toward a steady state, have attained a steady state, or do not tend toward a steady state. The highly flexible allometric model can be used to demonstrate adjustment between interdependent variables of hillslopes, streams, and depositional environments. It is highly unlikely that geomorphic steady states exist, because the dependent variables of a geomorphic open system cannot attain a time-independent state where the independent variables do not remain constant. Independent variables, such as climate, uplift, base level, erodibility of surficial materials, and impact of man, are changing at rates that are sufficiently rapid as to preclude attainment of steady state, particularly for those landforms that require geologic time spans to approach steady-state configurations. For most studies of processes and landforms, a broad perspective of the interrelations of materials, processes, and landforms can be obtained by using the model of allometric change in which landscape elements and processes are changing at different rates.