The general concepts generated by modern studies of geomorphological processes are examined in terms of their utility for models of long-term landform evolution. The work is summarized by four fundamental propositions of landform genesis. These include the idea that each set of environments is represented by constant processes and characteristic landforms which tend to persist over time. 'Geomorphological' time is divided into the time taken to attain this characteristic state and the time over which it persists. The systems and forms are subject, over Io2-Io5 years, to perturbations caused by high magnitude-low frequency events, environmental change and internal structural instabilities which initiate change. The responses to these impulses are complex and include damped, sustained and reinforcing changes taking place by ubiquitous, linear or diffusive propagation which reflect the sensitivity of the landscape to change. This sensitivity is dependent on the path density of the process and the strength of the coupling between the system components and has two end members, mobile-sensitive systems and slowly responding-insensitive areas. Some of the results include the concepts of (i) relief and pattern persistence; (2) stagnancy of development and the hypothesis of unequal activity; (3) convergence of form; (4) the concept of transient forms; (5) stability-instability phases and episodic landscape evolution, which together form a coherent framework for long-term landform evolution. Davis's great mistake was the assumption that we know the processes involved in the development of land forms. We don't; and until we do we shall be ignorant of the general course of their development. LEIGHLY, 1940

http://www.jstor.org/stable/pdfplus/622210.pdf

Landscape sensitivity and change

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 geomorpholo- gy, 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.

http://online.sfsu.edu/jerry/geog810/refs/Phillips2003.pdf

Sources of nonlinearity and complexity in geomorphic systems

Analogue modelling of intraplate strike-slip tectonics: A review and new experimental results

The Rate Law in Fluvial Geomorphology

Abstract Restraining- and releasing bends with similar morphology and structure have been described by many previous studies of strike-slip faults in a variety of active and ancient tectonic settings. Despite the documentation of at least 49 restraining and 144 releasing bends along active and ancient strike-slip faults in the continents and oceans, there is no consensus on how these structural features are named and classified, or how their wide range of structures and morphologies are controlled by the distinctive strike-slip tectonic settings in which they form. In this overview, I have compiled published information on the strike-slip tectonic setting, size, basin and bend type, age, and models for active and ancient releasing and restraining bends. Examples of bends on strike-slip faults are compiled and illustrated from five distinctive active strike-slip settings: oceanic transforms separating oceanic crust and offsetting mid-oceanic spreading ridges; long and linear plate-boundary strike-slip fault systems separating two continental plates whose plate-boundary kinematics can be quantified for long distances along strike by a single pole of rotation (e.g. the San Andreas fault system of western North America); relatively shorter, more arcuate indent-linked strike-slip fault systems bounding escaping continental fragments in zones of continent–continent or arc–continent collision (e.g. the Anatolian plate); straight to arcuate trench-linked strike-slip fault systems bounding elongate fore-arc slivers generated in active and ancient fore-arc settings by oblique subduction (e.g. Sumatra); and cratonic strike-slip fault systems removed from active plate boundaries, formed on older crustal faults, but acting as ‘concentrators’ of intraplate stresses. By far the most common, predictable and best-studied settings for restraining and releasing bends occur in continental-boundary strike-slip fault systems, where arrays of two to eight en échelon pull-apart basins mark transtensional fault segments and single and sometimes multiple large restraining bends mark transpressional segments; fault areas of transtension versus transpression are determined by the intersection angles between small circles about the interplate pole of rotation and the trend of the strike-slip fault system. These longer and more continuous boundary strike-slip systems also exhibit a widespread pattern of ‘paired bends’ or ‘sidewall ripouts’, or adjacent zones of pull-aparts and restraining bends—that range in along-strike-scale from kilometres to hundreds of kilometres. En échelon arrays of pull-apart basins are also observed on active ‘leaky’ or transtensional oceanic transforms, but restraining bends are rarely observed. In indent-linked strike-slip settings, strike-slip fault traces bounding escaping continental fragments tend to be more arcuate, less-continuous, and more splayed – but paired bends are common. Trench-linked strike-slip fault patterns closely mimic the trends of the subduction zone; these strike-slip faults can vary from long and continuous to short and arcuate, depending on the trace of the adjacent subduction zone. Paired bends are also observed in this setting. Bends on active, cratonic strike-slip fault form isolated, seismically active structures that act as ‘stress concentrators’ for intraplate stress. Cratonic strike-slip faults are generally not associated with pull-apart basins, and therefore paired bends are not observed in this setting. The most likely geological models for the formation of releasing, restraining bends, and paired bends along boundary and trench-linked strike-slip faults include: progressive linkage of en échelon shears within a young evolving shear zone; this model is not applicable to older strike-slip fault traces that have accumulated significant, lateral fault offsets; formation of lenticular ‘sidewall ripout’ structures at scales ranging from outcrop to regional; ripouts are thought to form as a response to adherence or sticking along an adjacent and relatively straight strike-slip fault zone; this structural concept may help to explain the large number of paired bends embedded within strike-slip systems, sinusoidal curvature along the traces of many strike-slip faults, and the episodic nature of lateral shifts in the main strike-slip fault zone; interaction of propagating strike-slip faults with pre-existing crustal structures such as ancient rift basins. Propagation of new strike-slip faults and interaction with older structures may occur on plate boundary, indent-linked, and trench-linked strike-slip faults; and concentration of regional maximum compressive stress on pre-existing, basement fault trends in stable cratonic areas can produce active restraining-bend structures; periodic release of these bend-related stress concentrations is one of the leading causes of intraplate earthquakes within otherwise stable cratons.

Global catalogue, classification and tectonic origins of restraining- and releasing bends on active and ancient strike-slip fault systems

Rivers are open systems and achieve a steady state or grow allometrically, according to the general equation y = ax b . This equation yields a straight line on double logarithmic paper and reflects a lognormal or Yule stochastic process. Horton9s laws are shown to be statements of these processes, and successive stream orders are seen to be new logarithmic cycles to the base of the bifurcation ratio for a river system. A new absolute order is suggested, derived by raising the bifurcation ratio to successive integer powers equivalent to stream order minus one.

Horton's laws justified in terms of allometric growth and steady state in open systems

The number of stream basin areas (that is, the number of Strahler stream segments) is predicted on the basis of an hexagonal model for basin areas. It is suggested that the number of orders and the number of basins per order balance opposing tendencies for minimum overland work for streams flowing in small basins and maximum work savings in large, as opposed to small, channels. In addition, the entropy of the system approaches the maximum possible. The model agrees with empirical data in cases where the land surface is reasonably uniform with regard to structure and lithology. The necessity for approximate geometric progressions of basin areas with order creates geometric progressions of other basin parameters, leading directly to the power function relationships between variables, known as allometric growth. This model is identical to one proposed to explain the numbers of market areas per order in a system of cities. In addition, the model predicts the structure of bile ducts in one bovine liver cited in this paper.

Michael J Woldenberg

Papers

Horton's laws justified in terms of allometric growth and steady state in open systems

Spatial Order in Fluvial Systems: Horton's Laws Derived from Mixed Hexagonal Hierarchies of Drainage Basin Areas