Sources of nonlinearity and complexity in geomorphic systems

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Abstract
Nonlinearity is common in geomorphology, though not present or relevant in every geomorphic problem. It is often ignored, sometimes to the detriment of understanding surface processes and landforms. Nonlinearity opens up possibilities for complex behavior that are not possible in linear systems, though not all nonlinear systems are complex. Complex nonlinear dynamics have been documented in a number of geomorphic systems, thus nonlinear complexity is a characteristic of real-world landscapes, not just models. In at least some cases complex nonlinear dynamics can be directly linked to specific geomorphic processes and controls. Nonlinear complexities pose obstacles for some aspects of prediction in geomorphology, but provide opportunities and tools to enhance predictability in other respects. Methods and theories based on or grounded in complex nonlinear dynamics are useful to geomorphologists. These nonlinear frameworks can explain some phenomena not otherwise explained, provide better or more appropriate analytical tools, improve the interpretation of historical evidence and usefully inform modeling, experimental design, landscape management and environmental policy. It is also clear that no nonlinear formalism (and, as of yet, no other formalism) provides a universal meta-explanation for geomorphology. The sources of nonlinearity in geomorphic systems largely represent well-known geomorphic processes, controls and relationships that can be readily observed. A typology is presented, including thresholds, storage effects, saturation and depletion, self-reinforcing feedback, self-limiting processes, competitive feedbacks, multiple modes of adjustment, self-organization and hysteresis.