Deterministic uncertainty in landscapes

Abstract

AbstractDeterministic complexity (chaos) may be common in geomorphic systems, but traditional definitions may have limited practical utility for empirical geomorphology. These definitions are based on sensitivity to initial conditions, which in geomorphology are both unknown and unknowable. Further, chaos analysis depends on distinguishing deterministic complexity from stochastic complexity. This is problematic in geomorphology because some stochastic complexity is virtually always present in addition to any chaos that may be present. While it is important to recognize that some complex, apparently random patterns may derive from inherent non‐linear system dynamics, this is of limited use in explaining process–response relationships or mechanics of landscape evolution. A more general term, which subsumes chaos, is deterministic uncertainty, i.e. uncertainty associated with an identifiable but unknown or uncertain source. An analysis of landscape entropy shows that such underlying constraints produce spatial patterns which are apparently chaotic. For the case of geologic controls, the apparent contribution of deterministic chaos to the landscape entropy is a direct non‐linear function of the extent of geologic constraints. However, the underlying constraints and their contribution to observed spatial patterns can also be interpreted in non‐chaotic terms. Examples are given, involving geologic constraints on stream channel networks and parent material control of surface soil textures. Because both randomness and chaos may be more apparent than real, the concept of deterministic uncertainty is more useful in process geomorphology than that of chaos.