13 Deterministic Complexity, Explanation, and Predictability in Geomorphic Systems

Increasingly, geomorphic systems are viewed as nonlinear dynamical systems (NDS) and are examined using the tools and concepts of NDS theory. Many geomorphic systems have recently been shown to exhibit the more complex traits of some NDS, including deterministic chaos and self-organization. The exercise of determining that a geomorphic system has, or may have, deterministic complexity is quite troubling to many geomorphologists, usually for one or more of four general reasons: 1. Expectations of what NDS theory can or should reveal are unrealistic. 2. Many NDS concepts and analytical techniques are imported from mathematics and physics, where the simple, abstract systems bear little resemblance to complicated real-world landscapes. 3. NDS analyses are often based on mathematical models which lack rigorous field tests. 4. Merely showing that a geomorphic system exhibits determinstic complexity, while providing a plausible explanation for unexplained real-world complexity, provides no mechanistic explanations of geomorphic process or evolution. This chapter addresses these issues. It is argued that many concepts and definitions of traditional or mainstream NDS theory are indeed inappropriate for earth sciences. There is a need for alternative concepts and definitions devised or adapted specifically for the earth sciences. This is worth doing, as there are examples of specific, testable hypotheses generated by NDS theory which suggest that the latter has some legitimate explanatory value in geomorphology. Finally, a case study of the evolution of soil landscapes is used to show that NDS theory can generate insight into mechanisms of landscape evolution. ND