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.

Abstract. Geomorphic systems are typically nonlinear, owing largely to their threshold-dominated nature (but due to other factors as well). Nonlinear geomorphic systems may exhibit complex behaviors not possible in linear systems, including dynamical instability and deterministic chaos. The latter are common in geomorphology, indicating that small, short-lived changes may produce disproportionately large and long-lived results; that evidence of geomorphic change may not reflect proportionally large external forcings; and that geomorphic systems may have multiple potential response trajectories or modes of adjustment to change. Instability and chaos do not preclude predictability, but do modify the context of predictability. The presence of chaotic dynamics inhibits or excludes some forms of predicability and prediction techniques, but does not preclude, and enables, others. These dynamics also make spatial and historical contingency inevitable: geography and history matter. Geomorphic systems are thus governed by a combination of "global" laws, generalizations and relationships that are largely (if not wholly) independent of time and place, and "local" place and/or time-contingent factors. The more factors incorporated in the representation of any geomorphic system, the more singular the results or description are. Generalization is enhanced by reducing rather than increasing the number of factors considered. Prediction of geomorphic responses calls for a recursive approach whereby global laws and local contingencies are used to constrain each other. More specifically a methodology whereby local details are embedded within simple but more highly general phenomenological models is advocated. As landscapes and landforms change in response to climate and other forcings, it cannot be assumed that geomorphic systems progress along any particular pathway. Geomorphic systems are evolutionary in the sense of being path dependent, and historically and geographically contingent.Correspondence to: J. D. Phillips (jdp@uky.edu) Assessing and predicting geomorphic responses obliges us to engage these contingencies, which often arise from nonlinear complexities. We are obliged, then, to practice evolutionary geomorphology: an approach to the study of surface processes and landforms which recognizes multiple possible historical pathways rather than an inexorable progression toward some equilbribrium state or along a cyclic pattern.

Invasive species, often recognized as ecosystem engineers, can dramatically alter geomorphic processes and landforms. Our review shows that the biogeomorphic impacts of invasive species are common, but variable in magnitude or severity, ranging from simple acceleration or deceleration of preexisting geomorphic processes to landscape metamorphosis. Primary effects of invasive flora are bioconstruction and bioprotection, whereas primary effects of invasive fauna are bioturbation, bioerosion, and bioconstruction. Landwater interfaces seem particularly vulnerable to biogeomorphic impacts of invasive species. Although not different from biogeomorphic impacts in general, invasive species are far more likely to lead to major geomorphic changes or landscape metamorphosis, which can have long-lasting impacts. In addition, invasive species can alter selection pressures in both macroevolution and microevolution by changing geomorphic processes. However, the differing timescales of biological invasions, landscape evolution, and biological evolution complicate assessment of the evolutionary impacts of invasive organisms.

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Channel cross-sectional changes since construction of Livingston Dam and Lake Livingston in 1968 were studied in the lower Trinity River, Texas, to test theoretical models of channel adjustment, and to determine controls on the spatial extent of channel response. High and average flows were not significantly modified by the dam, but sediment transport is greatly reduced. The study is treated as an opportunistic experiment to examine the effects of a reduction in sediment supply when discharge regime is unchanged. Channel scour is evident for about 60 km downstream, and the general phenomena of incision, widening, coarsening of channel sediment and a decrease in channel slope are successfully predicted, in a qualitative sense, by standard models of channel response. However, there is no consistent channel response within this reach, as various qualitatively different combinations of increases, decreases or no change in width, depth, slope and roughness occur. These multiple modes of adjustment are predicted by the unstable hydraulic geometry model. Between about 60 km and the Trinity delta 175 km downstream of the dam, no morphological response to the dam is observed. Rather than a diminution of the dam's effects on fluvial processes, this is due to a fundamental change in controls of the fluvial system. The downstream end of the scour zone corresponds to the upstream extent of channel response to Holocene sea level rise. Beyond 60 km downstream, the Trinity River is characterized by extensive sediment storage and reduced conveyance capacity, so that even after dam construction sediment supply still exceeds transport capacity. The channel bed of much of this reach is near or below sea level, so that sea level rise and backwater effects from the estuary are more important controls on the fluvial system than upstream inputs.

In recent decades views of change, disturbance, response, and recovery in geomorphology have expanded considerably. Conceptual frameworks emphasizing single-path, single-outcome trajectories of change have been supplemented — not replaced — by multi-path, multi-outcome perspectives. Geomorphology has also seen a transition from the idea of normative standards such as characteristic, (steady-state) equilibrium, zonal, and mature forms to the recognition that some systems may have multiple potential characteristic or equilibrium forms — and that some may have no particular normative state at all. These trends are not presented as a replacement of outmoded ideas, but rather as a broadening of approaches. The single-path single-outcome frameworks can generally be viewed as special cases of the broader pluralistic analytical structures. In this context, two perspectives — an adaptation of White's hazards matrix, and the landscape sensitivity concept — are suggested which lend themselves to studies of recent and contemporary changes in earth surface systems. These perspectives can be synthesized into a framework for the assessment of geomorphic changes and responses based on the `four Rs': response (reaction and relaxation times), resistance (relative to the drivers of change), resilience (recovery ability, based on dynamical stability), and recursion (positive and/or negative feedbacks).