岩体准静态运动失稳的 CUSP 型突变模型

为了研究岩体在水平力(N)和垂直力(P)作用下运动的稳定性问题,本文对简化的岩体系统建立了突变理论模型,用以定量描述引起运动失稳的应力条件.文中导出了系统的总势能函数表达式,证明了该系统可由 CUSP 型突变模型描述,确定了N-P 控制空间中使系统失去稳定平衡的分叉集 B.得到的主要结果是:对 N-P 控制空间中使岩体运动保持稳定平衡和失稳的区域进行了划分;分析了作用力的渐变导致状态突变的过程,和点(N,P)在控制空间的运动途径对岩体运动稳定性的影响;讨论了势能发生突变时,所要求的应力变化量级.并根据这些初步结果,讨论了地震过程的某些现象.      

Spatial distribution of surface rock fragment on hill-slopes in a small catchment in wind-water erosion crisscross region of the Loess Plateau

The cover and size distributions of surface rock fragment in hillslopes were investigated by using digital photographing and treating technique in a small catchment in wind-water erosion crisscross region of the Loess Plateau. The results indicated that the maximal cover of rock fragment was pre-sented at mid-position in steep hillslope. Rock fragment presented a general decreasing-trend along the hillslope in gentle hillslope. Rock fragment cover was positively related to gradient, rock fragment size decreased generally along the hillslope, and the size reduced with the gradient. The mean size of rock fragment was at a range of 6―20 mm in the steep hillslope, rock fragment size > 50 mm was rarely presented. The covers of rock fragment at different positions were markedly related to the quantities of rock fragment < 40 mm. The area of rock fragment of 2―50 mm accounted for 60% or more of the total area, dominating the distribution of rock fragment in the hillslopes.     

Landscape form and millennial erosion rates in the San Gabriel Mountains,CA

It has been long hypothesized that topography, as well as climate and rock strength, exert first order controls on erosion rates. Here we use detrital cosmogenic ¹⁰Be from 50 basins, ranging in size from 1 to 150 km², to measure millennial erosion rates across the San Gabriel Mountains in southern California, where a strong E–W gradient in relief compared to weak variation in precipitation and lithology allow us to isolate the relationship between topographic form and erosion rate. Our erosion rates range from 35 to 1100 m/Ma, and generally agree with both decadal sediment fluxes and long term exhumation rates inferred from low temperature thermochronometry. Catchment-mean hillslope angle increases with erosion rate until ～ 300 m/Ma, at which point slopes become invariant with erosion rate. Although this sort of relation has been offered as support for non-linear models of soil transport, we use 1-D analytical hillslope profiles derived from existing soil transport laws to show that a model with soil flux linear in slope, but including a slope stability threshold, is indistinguishable from a non-linear law within the scatter of our data. Catchment-mean normalized channel steepness index increases monotonically, though non-linearly, with erosion rate throughout the San Gabriel Mountains, even where catchment-mean hillslope angles have reached a threshold. This non-linearity can be mostly accounted for by a stochastic threshold incision model, though additional factors likely contribute to the observed relationship between channel steepness and erosion rate. These findings substantiate the claim that the normalized channel steepness index is an important topographic metric in active ranges.     

Hillslope response to tectonic forcing in threshold landscapes

Hillslopes are thought to poorly record tectonic signals in threshold landscapes. Numerous previous studies of steep landscapes suggest that large changes in long‐term erosion rate lead to little change in mean hillslope angle, measured at coarse resolution. New LiDAR‐derived topography data enables a finer examination of threshold hillslopes. Here we quantify hillslope response to tectonic forcing in a threshold landscape. To do so, we use an extensive cosmogenic beryllium‐10 (¹⁰Be)‐based dataset of catchment‐averaged erosion rates combined with a 500 km² LiDAR‐derived 1 m digital elevation model to exploit a gradient of tectonic forcing and topographic relief in the San Gabriel Mountains, California. We also calibrate a new method of quantifying rock exposure from LiDAR‐derived slope measurements using high‐resolution panoramic photographs. Two distinct trends in hillslope behavior emerge: below catchment‐mean slopes of 30°, modal slopes increase with mean slopes, slope distribution skewness decreases with increasing mean slope, and bedrock exposure is limited; above mean slopes of 30°, our rock exposure index increases strongly with mean slope, and the prevalence of angle‐of‐repose debris wedges keeps modal slopes near 37°, resulting in a positive relationship between slope distribution skewness and mean slope. We find that both mean slopes and rock exposure increase with erosion rate up to 1 mm/a, in contrast to previous work based on coarser topographic data. We also find that as erosion rates increase, the extent of the fluvial network decreases, while colluvial channels extend downstream, keeping the total drainage density similar across the range. Our results reveal important textural details lost in 10 or 30 m resolution digital elevation models of steep landscapes, and highlight the need for process‐based studies of threshold hillslopes and colluvial channels. Copyright © 2012 John Wiley & Sons, Ltd.     

Lithological controls on hillslope sediment supply: insights from landslide activity and grain size distributions

The volumes, rates and grain size distributions of sediment supplied from hillslopes represent the initial input of sediment delivered from upland areas and propagated through sediment routing systems. Moreover, hillslope sediment supply has a significant impact on landscape response time to tectonic and climatic perturbations. However, there are very few detailed field studies characterizing hillslope sediment supply as a function of lithology and delivery process. Here, we present new empirical data from tectonically‐active areas in southern Italy that quantifies how lithology and rock strength control the landslide fluxes and grain size distributions supplied from hillslopes. Landslides are the major source of hillslope sediment supply in this area, and our inventory of ~2800 landslides reveals that landslide sediment flux is dominated by small, shallow landslides. We find that lithology and rock strength modulate the abundance of steep slopes and landslides, and the distribution of landslide sizes. Outcrop‐scale rock strength also controls the grain sizes supplied by bedrock weathering, and influences the degree of coarsening of landslide supply with respect to weathering supply. Finally, we show that hillslope sediment supply largely determines the grain sizes of fluvial export, from catchments and that catchments with greater long‐term landslide rates deliver coarser material. Therefore, our results demonstrate a dual control of lithology on hillslope sediment supply, by modulating both the sediment fluxes from landslides and the grain sizes supplied by hillslopes to the fluvial system. Copyright © 2017 John Wiley & Sons, Ltd.     

Numerical modelling of combined erosion and weathering of slopes in weak rock

Due to various decay processes associated with weathering, the stability of artificial slopes in weak rocks may be affected well within their envisaged engineering lifetime. Conceptually, the decay following the initial stress release after excavation can be described as a process seeking equilibrium between weathering and erosion. The extent to which such an equilibrium is actually reached influences the outcome of the weathering‐erosion decay process as well as the effects that the decay has on the geotechnical properties of the exposed rock mass, and thus ultimately the stability of slopes affected by erosion and weathering. This paper combines two conceptual models for erosion and weathering, and derives a numerical model which predicts the resulting slope development. This can help to predict the development of a slope profile excavated in a weak rock in time, and can be extended with the addition of strength parameters to the weathering profile to enable prediction of slope stability as a function of time. Copyright © 2011 John Wiley & Sons, Ltd.     

A channel head stability criterion for first‐order catchments

The present analysis derives a stability criterion for long‐term equilibrium channel heads. The concept of finite perturbation analysis is presented, during which the surface is subjected to perturbations of a finite amplitude and resulting changes in flow path structure and slope are computed. Based on these quantities the analysis predicts whether the perturbed location is going to erode, be filled in or remain steady. The channel head is defined geometrically as the focus point of converging flow lines at the bottom of hollows. It is demonstrated that stability at the channel head grows out of the competition between the rate of flow path convergence and the degree of profile concavity. Analytical functions are derived to compute channel head‐contributing area and ‐slope, flow path convergence and profile concavity as a function of perturbation depth, distance from the crest and the initial slope. In a numerical model these quantities point to the long‐term equilibrium channel head position, which is shown to depend also on the width to length ratio of hollows. It is also demonstrated that the equilibrium channel head position is sensitive to the base‐level lowering/non‐dimensional slope length ratio and to the slope of the initial topography. Morphometrical measurements both in the field and on simulated topographies were used to test the theoretical predictions.     

Development of partial rock veneers by root throw in a subalpine setting

Rock veneers stabilize hillslope surfaces, occur especially in areas of immature soil, and form through a variety of process sets that includes root throw. Near Westcliffe, Colorado, USA, data were collected from a 20 × 500 m transect on the east slope of the Sangre de Cristo Mountains. Ages of pit/mound complexes with rock fragments exposed at the surface by root throw ranged from recent (freshly toppled tree) to unknown (complete tree decay). Calculations based on dimensions of the pit/mound complexes, estimated time of tree toppling, sizes of exposed rock fragments, and percentage rock covers at pit/mound complexes, as well as within the transect area, indicate that recent rates of root throw have resulted in only partial rock veneering since late Pleistocene deglaciation. Weathering of rock fragments prevents development of an extensive rock veneer and causes a balance, achieved within an estimated 700 years, between the rates of rock‐fragment exposure by root throw and clast disintegration by chemical reduction. The estimated rate of rock‐fragment reduction accounts for part of the fluvial sediment yields observed for forested subalpine areas of western North America. Copyright © 2005 John Wiley & Sons, Ltd.     

Water storage dynamics in a till hillslope: the foundation for modeling flows and turnover times

Studies on hydrology, biogeochemistry, or mineral weathering often rely on assumptions about flow paths, water storage dynamics, and transit times. Testing these assumptions requires detailed hydrometric data that are usually unavailable at the catchment scale. Hillslope studies provide an alternative for obtaining a better understanding, but even on such well‐defined and delimited scales, it is rare to have a comprehensive set of hydrometric observations from the water divide down to the stream that can constrain efforts to quantify water storage, movement, and turnover time. Here, we quantified water storage with daily resolution in a hillslope during the course of almost an entire year using hydrological measurements at the study site and an extended version of the vertical equilibrium model. We used an exponential function to simulate the relationship between hillslope discharge and water table; this was used to derive transmissivity profiles along the hillslope and map mean pore water velocities in the saturated zone. Based on the transmissivity profiles, the soil layer transmitting 99% of lateral flow to the stream had a depth that ranged from 8.9 m at the water divide to under 1 m closer to the stream. During the study period, the total storage of this layer varied from 1189 to 1485 mm, resulting in a turnover time of 2172 days. From the pore water velocities, we mapped the time it would take a water particle situated at any point of the saturated zone anywhere along the hillslope to exit as runoff. Our calculations point to the strengths as well as limitations of simple hydrometric data for inferring hydrological properties and water travel times in the subsurface.     

Ten year remeasurement of chemical denudation on a magnesian limestone hillslope

Results from the measurement of microweight loss of Magnesian Limestone rock tablets placed at the soil–bedrock interface on a hillslope over 10 years (1982–1992) gave the same relative pattern of upslope increase in weight loss as did short-term measurements (1979–1981), but the absolute values were an order of magnitude lower (0·01–0·03 per cent per year long term and 0·1–0·6 per cent per year short term). Microweighed rock tablets may therefore give unreliable absolute rates and can only be used to indicate relative spatial differences rather than to give reliable data on temporal changes.     

Morphodynamics of a bedrock‐alluvial meander bend that incises as it migrates outward: approximate solution of permanent form

In meandering rivers cut into bedrock, erosion across a channel cross‐section can be strongly asymmetric. At a meander apex, deep undercutting of the outer bank can result in the formation of a hanging cliff (which may drive hillslope failure), whereas the inner bank adjoins a slip‐off slope that connects to the hillslope itself. Here we propose a physically‐based model for predicting channel planform migration and incision, point bar and slip‐off slope formation, bedrock abrasion, the spatial distribution of alluvial cover, and adaptation of channel width in a mixed bedrock‐alluvial channel. We simplify the analysis by considering a numerical model of steady, uniform bend flow satisfying cyclic boundary conditions. Thus in our analysis, ‘sediment supply’, i.e. the total volume of alluvium in the system, is conserved. In our numerical simulations, the migration rate of the outer bank is a specified parameter. Our simulations demonstrate the existence of an approximate state of dynamic equilibrium corresponding to a near‐solution of permanent form in which a bend of constant curvature, width, cross‐sectional shape and alluvial cover distribution migrates diagonally downward at constant speed, leaving a bedrock equivalent of a point bar on the inside of the bend. Channel width is set internally by the processes of migration and incision. We find that equilibrium width increases with increasing sediment supply, but is insensitive to outer bank migration rate. The slope of the bedrock point bar varies inversely with both outer bank migration rate and sediment supply. Although the migration rate of the outer bank is externally imposed here, we discuss a model modification that would allow lateral side‐wall abrasion to be treated in a manner similar to the process of bedrock incision. Copyright © 2016 John Wiley & Sons, Ltd.     

A low‐dimensional physically based model of hydrologic control of shallow landsliding on complex hillslopes

Hillslopes have complex three‐dimensional shapes that are characterized by their plan shape, profile curvature of surface and bedrock, and soil depth. To investigate the stability of complex hillslopes (with different slope curvatures and plan shapes), we combine the hillslope‐storage Boussinesq (HSB) model with the infinite slope stability method. The HSB model is based on the continuity and Darcy equations expressed in terms of storage along the hillslope. Solutions of the HSB equation account explicitly for plan shape by introducing the hillslope width function and for profile curvature through the bedrock slope angle and the hillslope soil depth function. The presented model is composed of three parts: a topography model conceptualizing three‐dimensional soil mantled landscapes, a dynamic hydrology model for shallow subsurface flow and water table depth (HSB model) and an infinite slope stability method based on the Mohr–Coulomb failure law. The resulting hillslope‐storage Boussinesq stability model (HSB‐SM) is able to simulate rain‐induced shallow landsliding on hillslopes with non‐constant bedrock slope and non‐parallel plan shape. We apply the model to nine characteristic hillslope types with three different profile curvatures (concave, straight, convex) and three different plan shapes (convergent, parallel, divergent). In the presented model, the unsaturated storage has been calculated based on the unit head gradient assumption. To relax this assumption and to investigate the effect of neglecting the variations of unsaturated storage on the assessment of slope stability in the transient case, we also combine a coupled model of saturated and unsaturated storage and the infinite slope stability method. The results show that the variations of the unsaturated zone storage do not play a critical role in hillslope stability. Therefore, it can be concluded that the presented dynamic slope stability model (HSB‐SM) can be used safely for slope stability analysis on complex hillslopes. Our results show that after a certain period of rainfall the convergent hillslopes with concave and straight profiles become unstable more quickly than others, whilst divergent convex hillslopes remain stable (even after intense rainfall). In addition, the relation between subsurface flow and hillslope stability has been investigated. Our analyses show that the minimum safety factor (FS) occurs when the rate of subsurface flow is a maximum. In fact, by increasing the subsurface flow, stability decreases for all hillslope shapes. Copyright © 2008 John Wiley & Sons, Ltd.     

Rock damage and regolith transport by frost: an example of climate modulation of the geomorphology of the critical zone

In this article we craft process‐specific algorithms that capture climate control of hillslope evolution in order to elucidate the legacy of past climate on present critical zone architecture and topography. Models of hillslope evolution traditionally comprise rock detachment into the mobile layer, mobile regolith transport, and a channel incision or aggradation boundary condition. We extend this system into the deep critical zone by considering a weathering damage zone below the mobile regolith in which rock strength is diminished; the degree of damage conditions the rate of mobile regolith production. We first discuss generic damage profiles in which appropriate length and damage scales govern profile shapes, and examine their dependence upon exhumation rate. We then introduce climate control through the example of rock damage by frost‐generated crack growth. We augment existing frost cracking models by incorporating damage rate limitations for long transport distances for water to the freezing front. Finally we link the frost cracking damage model, a mobile regolith production rule in which rock entrainment is conditioned by the damage state of the rock, and a frost creep transport model, to examine the evolution of an interfluve under oscillating climate. Aspect‐related differences in mean annual surface temperatures result in differences in bedrock damage rate and mobile regolith transport efficiency, which in turn lead to asymmetries in critical zone architecture and hillslope form (divide migration). In a quasi‐steady state hillslope, the lowering rate is uniform, and the damage profile is better developed on north‐facing slopes where the frost damage process is most intense. Because the residence times of mobile regolith and weathered bedrock in such landscapes are on the order of 10 to 100 ka, climate cycles over similar timescales result in modulation of transport and damage efficiencies. These lead to temporal variation in mobile regolith thickness, and to corresponding changes in sediment delivery to bounding streams. Copyright © 2012 John Wiley & Sons, Ltd.     

Impact of model simplifications on soil erosion predictions: application of the GLUE methodology to a distributed event‐based model at the hillslope scale

In this paper, we analyse how the performance and calibration of a distributed event‐based soil erosion model at the hillslope scale is affected by different simplifications on the parameterizations used to compute the production of suspended sediment by rainfall and runoff. Six modelling scenarios of different complexity are used to evaluate the temporal variability of the sedimentograph at the outlet of a 60 m long cultivated hillslope. The six scenarios are calibrated within the generalized likelihood uncertainty estimation framework in order to account for parameter uncertainty, and their performance is evaluated against experimental data registered during five storm events. The Nash–Sutcliffe efficiency, percent bias and coverage performance ratios show that the sedimentary response of the hillslope in terms of mass flux of eroded soil can be efficiently captured by a model structure including only two soil erodibility parameters, which control the rainfall and runoff production of suspended sediment. Increasing the number of parameters makes the calibration process more complex without increasing in a noticeable manner the predictive capability of the model. Copyright © 2015 John Wiley & Sons, Ltd.     

A one‐dimensional model for simulating armouring and erosion on hillslopes: 2. Long term erosion and armouring predictions for two contrasting mine spoils

This paper investigates the dynamics of soil armouring as a result of fluvial erosion for a non‐cohesive sandy gravel spoil from the Ranger Mine, Australia, and a cohesive silt loam spoil from the Northparkes Mine, Australia, using a model for hillslope soil armouring. These long term predictions concentrate on the temporal and spatial changes of the spoil grading and erosion over 100–200 years for the flat cap regions (1–2%) and steep batter edges (10–30%) typically encountered on waste rock dumps. The existence of a significant rock fragment fraction in the Ranger spoil means that it armours readily, while Northparkes does not. For Ranger the waste rock showed reductions in (1) cumulative erosion of up to 81% from that obtained by extrapolating the initial erosion rate out 100 years and (2) the erosion/year by more than 10‐fold. For Northparkes reductions were less marked, with the maximum reduction in erosion/year being 37% after 200 years. For Ranger the reductions were greatest and fastest for intermediate gradient hillslopes. For the steepest hillslopes the armouring decreased because the flow shear stresses were large enough to mobilize all material in the armour layer. Model uncertainty was assessed with probabilistic confidence limits demonstrating that these erodibility reductions were statistically significant. A commonly used hillslope erosion model (sediment flux = β₁ discharge m₁ slope n₁) was fitted to these predictions. The erodibility, β₁, and m₁ decreased with time, which was consistent with our physical intuition about armouring. At Ranger the parameter m₁ asymptoted to 1·5–1·6 while at Northparkes it asymptoted to 1·2–1·3. At Ranger transient spatial trends in armouring led to a short term (50–200 years in the future) reduction in n₁, to below zero under certain circumstances, recovering to an asymptote of about 0·5–1. At Northparkes n₁ asymptoted to about 0·6, with no negative transients predicted. The m₁ and n₁ parameters predicted for Ranger were shown to be consistent with field data from a 10‐year‐old armoured hillslope and consistent with published relationships between erodibility and rock content for natural hillslopes. Copyright © 2007 John Wiley & Sons, Ltd.     

Spatial and temporal analysis of hillslope–channel coupling and implications for the longitudinal profile in a dryland basin

The long‐term evolution of channel longitudinal profiles within drainage basins is partly determined by the relative balance of hillslope sediment supply to channels and the evacuation of channel sediment. However, the lack of theoretical understanding of the physical processes of hillslope–channel coupling makes it challenging to determine whether hillslope sediment supply or channel sediment evacuation dominates over different timescales and how this balance affects bed elevation locally along the longitudinal profile. In this paper, we develop a framework for inferring the relative dominance of hillslope sediment supply to the channel versus channel sediment evacuation, over a range of temporal and spatial scales. The framework combines distinct local flow distributions on hillslopes and in the channel with surface grain‐size distributions. We use these to compute local hydraulic stresses at various hillslope‐channel coupling locations within the Walnut Gulch Experimental Watershed (WGEW) in southeast Arizona, USA. These stresses are then assessed as a local net balance of geomorphic work between hillslopes and channel for a range of flow conditions generalizing decadal historical records. Our analysis reveals that, although the magnitude of hydraulic stress in the channel is consistently higher than that on hillslopes, the product of stress magnitude and frequency results in a close balance between hillslope supply and channel evacuation for the most frequent flows. Only at less frequent, high‐magnitude flows do channel hydraulic stresses exceed those on hillslopes, and channel evacuation dominates the net balance. This result suggests that WGEW exists mostly (~50% of the time) in an equilibrium condition of sediment balance between hillslopes and channels, which helps to explain the observed straight longitudinal profile. We illustrate how this balance can be upset by climate changes that differentially affect relative flow regimes on slopes and in channels. Such changes can push the long profile into a convex or concave condition. © 2018 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

Modelling of sediment dynamics in a laboratory‐scale experimental catchment

The variability of hillslope form and function is examined experimentally using a simple model catchment in which most landscape development parameters are either known or controlled. It is demonstrated that there is considerable variability in sediment output from similar catchments, subjected to the same hydrological processes, and for which the initial hillslope profiles are the same. The results demonstrate that, in the case of catchments with a linear initial hillslope profile, the sediment output is initially high but reduces through time, whereas for a concave initial profile the sediment output was smaller and relatively constant. Concave hillslope profiles also displayed reduced sediment output when compared with linear slopes with the same overall slope. Using this experimental model catchment data, the SIBERIA landscape evolution model was tested for its ability to predict temporal sediment transport. When calibrated for the rainfall and erodible material, SIBERIA is able to simulate mean temporal sediment output for the experimental catchment over a range of hillslope profiles and rainfall intensities. SIBERIA is also able to match the hillslope profile of the experimental catchments. The results of the study provide confidence in the ability of SIBERIA to predict temporal sediment output. The experimental and modelling data also demonstrate that, even with all geomorphic and hydrological variables being known and/or controlled, there is still a need for long‐term stream gauging to obtain reliable assessments of field catchment hydrology and sediment transport. Copyright © 2005 John Wiley & Sons, Ltd.     

A model that helps explain Sr-isotope disequilibrium between feldspar phenocrysts and melt in large-volume silicic magma systems

Feldspar phenocrysts of silicic volcanic rocks are commonly in Sr-isotopic disequilibrium with groundmass. In some cases the feldspar is more radiogenic, and in others it is less radiogenic. Several explanations have been published previously, but none of these is able to accommodate both senses of disequilibrium. We present a model by which either more- or less-radiogenic feldspar (or even both within a single eruptive unit) can originate. The model requires a magma body open to interaction with biotite- and feldspar-bearing wall rock. Magma is incrementally contaminated as wall rock melts incongruently. Biotite preferentially melts first, followed by feldspar. Such melting behavior, which is supported by both field and experimental studies, first contaminates magma with a relatively radiogenic addition, followed by a less-radiogenic addition. Feldspar phenocrysts lag behind melt (groundmass of volcanic rock) in incorporating the influx of contaminant, thus resulting in Sr-isotopic disequilibrium between the crystals and melt. The sense of disequilibrium recorded in a volcanic rock depends on when eruption quenches the contamination process. This model is testable by isotopic fingerprinting of individual feldspar crystals. For a given set of geologic boundary conditions, specific core-to-rim Sr-isotopic profiles are expectable. Moreover, phenocrysts that nucleate at different times during the contamination process should record different and predictable parts of the history. Initial results of Sr-isotopic fingerprinting of sanidine phenocrysts from the Taylor Creek Rhyolite are consistent with the model. More tests of the model are desirable.     

Controls on the stability and inclinations of hillslopes formed on hard rock

In identifying controls on rock slope form a distinction is made between: (1) rock slopes with joints which dip steeply out of a cliff and hence are subject to mass failure of the rock mass above a critical joint; and (2) rock slopes with inclinations which are either in equilibrium with the mass strength of their rocks, or have profiles which will develop towards strength equilibrium as cross joints open. In the first class of slope, stability results not just from the basic frictional resistance of the rock but also from the frictional roughness along the critical joint and from the normal stress acting across that joint. Stability may be reduced by weathering and loss of strength of the joint wall rock. As a result of normal stress variations with depth, induced by overburdens, high cliffs which are not undercut have a concave profile. The second group of slopes includes those with inclinations controlled at the scale of individual joint blocks, buttressed slopes and those on unjointed rock masses. Buttressed and unjointed rock masses develop towards a condition of mass strength equilibrium as cross joints open. Strength equilibrium slopes may be recognized by application of a rock mass strength classification proposed for geomorphic purposes. Eleven propositions are formulated which identify controls on rock slope development and some consequences of these controls.     

Long‐term landscape evolution: linking tectonics and surface processes

Research in landscape evolution over millions to tens of millions of years slowed considerably in the mid‐20th century, when Davisian and other approaches to geomorphology were replaced by functional, morphometric and ultimately process‐based approaches. Hack's scheme of dynamic equilibrium in landscape evolution was perhaps the major theoretical contribution to long‐term landscape evolution between the 1950s and about 1990, but it essentially ‘looked back’ to Davis for its springboard to a viewpoint contrary to that of Davis, as did less widely known schemes, such as Crickmay's hypothesis of unequal activity. Since about 1990, the field of long‐term landscape evolution has blossomed again, stimulated by the plate tectonics revolution and its re‐forging of the link between tectonics and topography, and by the development of numerical models that explore the links between tectonic processes and surface processes. This numerical modelling of landscape evolution has been built around formulation of bedrock river processes and slope processes, and has mostly focused on high‐elevation passive continental margins and convergent zones; these models now routinely include flexural and denudational isostasy. Major breakthroughs in analytical and geochronological techniques have been of profound relevance to all of the above. Low‐temperature thermochronology, and in particular apatite fission track analysis and (U–Th)/He analysis in apatite, have enabled rates of rock uplift and denudational exhumation from relatively shallow crustal depths (up to about 4 km) to be determined directly from, in effect, rock hand specimens. In a few situations, (U–Th)/He analysis has been used to determine the antiquity of major, long‐wavelength topography. Cosmogenic isotope analysis has enabled the determination of the ‘ages’ of bedrock and sedimentary surfaces, and/or the rates of denudation of these surfaces. These latter advances represent in some ways a ‘holy grail’ in geomorphology in that they enable determination of ‘dates and rates’ of geomorphological processes directly from rock surfaces. The increasing availability of analytical techniques such as cosmogenic isotope analysis should mean that much larger data sets become possible and lead to more sophisticated analyses, such as probability density functions (PDFs) of cosmogenic ages and even of cosmogenic isotope concentrations (CICs). PDFs of isotope concentrations must be a function of catchment area geomorphology (including tectonics) and it is at least theoretically possible to infer aspects of source area geomorphology and geomorphological processes from PDFs of CICs in sediments (‘detrital CICs’). Thus it may be possible to use PDFs of detrital CICs in basin sediments as a tool to infer aspects of the sediments' source area geomorphology and tectonics, complementing the standard sedimentological textural and compositional approaches to such issues. One of the most stimulating of recent conceptual advances has followed the considerations of the relationships between tectonics, climate and surface processes and especially the recognition of the importance of denudational isostasy in driving rock uplift (i.e. in driving tectonics and crustal processes). Attention has been focused very directly on surface processes and on the ways in which they may ‘drive’ rock uplift and thus even influence sub‐surface crustal conditions, such as pressure and temperature. Consequently, the broader geoscience communities are looking to geomorphologists to provide more detailed information on rates and processes of bedrock channel incision, as well as on catchment responses to such bedrock channel processes. More sophisticated numerical models of processes in bedrock channels and on their flanking hillslopes are required. In current numerical models of long‐term evolution of hillslopes and interfluves, for example, the simple dependency on slope of both the fluvial and hillslope components of these models means that a Davisian‐type of landscape evolution characterized by slope lowering is inevitably ‘confirmed’ by the models. In numerical modelling, the next advances will require better parameterized algorithms for hillslope processes, and more sophisticated formulations of bedrock channel incision processes, incorporating, for example, the effects of sediment shielding of the bed. Such increasing sophistication must be matched by careful assessment and testing of model outputs using pre‐established criteria and tests. Confirmation by these more sophisticated Davisian‐type numerical models of slope lowering under conditions of tectonic stability (no active rock uplift), and of constant slope angle and steady‐state landscape under conditions of ongoing rock uplift, will indicate that the Davis and Hack models are not mutually exclusive. A Hack‐type model (or a variant of it, incorporating slope adjustment to rock strength rather than to regolith strength) will apply to active settings where there is sufficient stream power and/or sediment flux for channels to incise at the rate of rock uplift. Post‐orogenic settings of decreased (or zero) active rock uplift would be characterized by a Davisian scheme of declining slope angles and non‐steady‐state (or transient) landscapes. Such post‐orogenic landscapes deserve much more attention than they have received of late, not least because the intriguing questions they pose about the preservation of ancient landscapes were hinted at in passing in the 1960s and have recently re‐surfaced. As we begin to ask again some of the grand questions that lay at the heart of geomorphology in its earliest days, large‐scale geomorphology is on the threshold of another ‘golden’ era to match that of the first half of the 20th century, when cyclical approaches underpinned virtually all geomorphological work. Copyright © 2007 John Wiley & Sons, Ltd.