Space–time variability of denudation rates at the catchment and hillslope scales on the Tyrrhenian side of Central Italy

Studies on denudation rates can provide insight into the influence of climate change, tectonics, and human activities on landscape evolution. Research performed in Central Italy has shown considerable spatial variability of denudation rates in the major river basins. These studies have focused mainly on the Tyrrhenian side of the Italian peninsula, where Plio-Pleistocene marine deposits filling NW–SE elongated sedimentary basins have been uplifted during the Quaternary up to several hundreds of meters above present sea level. Small sub-catchments developed on clays are affected by sharp- and/or rounded-edged badlands (i.e. calanchi and biancane), representing denudation “hot spots” in the present-day morphoclimatic framework.In this paper, we analyze the relationships between indirectly estimated denudation rates at the catchment scale and field monitoring data at the hillslope scale. We attempt to better understand and quantify all hillslope processes that contribute to seasonal variability of denudation, to help with predicting the net input from “hot spots” to the overall estimated sediment yield at the basin outlets. At the hillslope scale, we discuss, in particular, the variability of denudation rates at calanchi and biancane badlands as a function of their different morphoevolution.     

Regional relief characteristics and denudation pattern of the western Southern Alps, New Zealand

The Southern Alps of New Zealand are the topographic expression of active oblique continental convergence of the Australian and Pacific plates. Despite inferred high rates of tectonic and climatic forcing, the pattern of differential uplift and erosion remains uncertain. We use a 25-m DEM to conduct a regional-scale relief analysis of a 250-km long strip of the western Southern Alps (WSA). We present a preliminary map of regional erosion and denudation by overlaying mean basin relief, a modelled stream-power erosion index, river incision rates, historic landslide denudation rates, and landslide density. The interplay between strong tectonic and climatic forcing has led to relief production that locally attains 2 km in major catchments, with mean values of 0.65–0.68 km. Interpolation between elevations of major catchment divides indicates potential removal of l0¹–10³ km³, or a mean basin relief of 0.51–0.85 km in the larger catchments. Local relief and inferred river incision rates into bedrock are highest about 50–67% of the distance between the Alpine fault and the main divide. The mean regional relief variability is ± 0.5 km.Local relief, valley cross-sectional area, and catchment width correlate moderately with catchment area, and also reach maximum values between the range front and the divide. Hypsometric integrals show scale dependence, and together with hypsometric curves, are insufficient to clearly differentiate between glacial and fluvial dominated basins. Mean slope angle in the WSA (ψ = 30°) is lower where major longitudinal valleys and extensive ice cover occur, and may be an insensitive measure of regional relief. Modal slope angle is strikingly uniform throughout the WSA (φ = 38–40°), and may record adjustment to runoff and landsliding. Both ψ and φ show non-linear relationships with elevation, which we attribute to dominant geomorphic process domains, such as fluvial processes in low-altitude valley trains, surface runoff and frequent landsliding on montane hillslopes, “relief dampening” by glaciers, and rock fall/avalanching on steep main-divide slopes.     

Steady, balanced rates of uplift and erosion of the Santa Monica Mountains, California

Topographic change in regions of active deformation is a function of rates of uplift and denudation. The rate of topographic development and change of an actively uplifting mountain range, the Santa Monica Mountains, southern California, was assessed using landscape attributes of the present topography, uplift rates and denudation rates. Landscape features were characterized through analysis of a digital elevation model (DEM). Uplift rates at time scales ranging from 10⁴ to 10⁶ years were constrained with geological cross-sections and published estimates. Denudation rate was determined from sediment yield data from debris basins in southern California and from the relief of rivers set into geomorphic surfaces of known age. First-order morphology of the Santa Monica Mountains is set by large-scale along-strike variations in structural geometry. Drainage spacing, drainage geometry and to a lesser extent relief are controlled by bedrock strength. Dissection of the range flanks and position of the principal drainage divide are modulated by structural asymmetry and differences in structural relief across the range. Topographic and catchment-scale relief are ≈300–900 m. Mean denudation rate derived from the sediment yield data and river incision is 0.5±0.3 mm yr^?1. Uplift rate across the south flank of the range is ≈0.5±0.4 mm yr^?1 and across the north flank is 0.24±0.12 mm yr^?1. At least 1.6–2.7 Myr is required to create either the present topographic or the catchment-scale relief based on either the mean rates of denudation or uplift. Although the landscape has had sufficient time to achieve a steady-state form, comparison of the time-scale of uplift and denudation rate variation with probable landscape response times implies the present topography does not represent the steady-state form.     

Self-affinity dimensions of topography and its implications in morphotectonics: an example from Taiwan

This paper discusses the self-affinity dimensions of landscape surfaces at a short-range scale and the link to morphotectonic features of the young orogenic belts of Taiwan. The variogram method is adopted to estimate such parameters as the fractal dimension (D), the ordinate-intercept (γ) and the range (R) from data subsets of the digital elevation model (DEM) in a moving-window operation. The fractal morphology expressed by D and γ is found to be useful in defining geomorphic provinces that are related to tectonic features. The mountainous terrain is characterized by high gamma values and low fractal dimensions in contrast to the coastal plains where low gamma values and high fractal dimensions are found. A zone, defined by the fractal parameters (2.4<D<2.6 and 0<γ<2.4), is found to coincide with the most tectonically active zone of Taiwan. Active faults often occur at the boundary between landscapes with contrasting fractal patterns. In the flat lowlands along the western coast, the fractal morphology displays a west-facing amphitheatric pattern, which may be related to the indentation of the pre-Miocene Peikang Basement High. The fractal morphology may reflect some subtle changes in surface textures of a landscape sculpted by surface processes, which in turn are influenced by tectonic activities. The surface roughening and diffusive smoothing may concur to shape the landscape surface at the short ranges we discuss in this study.     

Remote sensing and geomorphometry for studying relief production in high mountains

Mountain topography is the result of highly scale-dependent interactions involving climatic, tectonic, and surface processes. No complete understanding of the geodynamics of mountain building and topographic evolution yet exists, although numerous conceptual and physical models indicate that surficial erosion plays a significant role. Mapping and assessing landforms and erosion in mountain environments is essential in order to understand landscape denudation and complex feedback mechanisms. This requires the development and evaluation of new approaches in remote sensing and geomorphometry. The research herein evaluates the problem of topographic normalization of satellite imagery and demonstrates the use of terrain analysis using a digital elevation model (DEM) to evaluate the relief structure of the landscape in the western Himalaya. We specifically evaluated the Cosine-correction and Minnaert-correction methods to reduce spectral variation in imagery caused by the topography. Semivariogram analyses of the topography were used to examine the relationships between relief and surface processes. Remote-sensing results indicate that the Minnaert-correction method can be used to reduce the “topographic effect” in satellite imagery for mapping, although extreme radiance values are the result of not accounting for the diffuse-skylight and adjacent-terrain irradiance. Geomorphometry results indicate that river incision and glaciation can generate extreme relief, although the greatest mesoscale relief is produced by glaciation at high altitudes. At intermediate altitudes, warm-based glaciation was found to decrease relief. Our results indicate that glaciation can have a differential influence on the relief structure of the landscape. Collectively, our results indicate that scale-dependent analysis of the topography is required to address radiation transfer issues and the polygenetic nature of landscape denudation and relief production.     

The Gunnison's prairie dog structures a high desert grassland landscape as a keystone engineer

The influence of landscape spatial structure on ecological processes has recently received much attention. Comparisons are made here between the spatial structure of grasslands, and active and extirpated Gunnison's prairie dog (Cynomys gunnisoni Hollister) towns at the Petrified Forest National Park, Arizona, U.S.A. The spatial structure of bare ground was quatified using a box-counting technique to extract landscape fractal dimensions, D, and bare-ground patch size. These landscapes are fractal, and active prairie dog towns had higher fractal dimensions, i.e. a more homogeneous spatial structure as D approaches 2, than inactive towns, which had higher fractal dimensions than unmodified grasslands. Morisita's index suggested that shrubs were more randomly distributed on prairie dog towns and more aggregated on grassland habitats. The different spatial distributions of bare ground and shrubs have the potential to influence resource distributions between these habitats for both prairie dogs and other fauna. Consequently, the presence of prairie dogs in these grasslands increases grassland landscape heterogeneity at large spatial scales, potentially enhancing beta diversity.     

Influence of orographic precipitation on the topographic and erosional evolution of mountain ranges

The influence of climate on mountain denudation has been the topic of an intense debate for two decades. This debate partly arises from the covariation of rainfall and topography during the growth of mountain ranges, both of which influence denudation. However, the denudational response of this co-evolution is poorly understood. Here, we use a landscape evolution model where the rainfall evolves according to a prescribed rainfall–elevation relationship. This relationship is a bell curve defined by a rainfall base level, a rainfall maximum and a width around the rainfall peak elevation. This is a first-order model that fits a large range of orographic rainfall data at the ca. 1-km spatial scale. We carried out simulations of an uplifting block with an alluvial apron, starting from an initially horizontal surface, and testing different rainfall–elevation relationships. We find that the denudation history is different from that with constant rainfall models. The results essentially depend on the ratio between the final steady-state summit elevation H_ss and the prescribed rainfall peak elevation H_p. This ratio is hard to predict because it depends on the transient coupling of rainfall and elevation. We identified three types of results according to H_ss/H_p. If H_ss/H_p > 4 (Type I), the denudation rates peak when the summits reach values close to H_p. If H_ss/H_p > 1.5 and < 4 (Type II), the denudation is strongly accelerated when the elevation of the summits approaches H_p, and then the denudation increases slowly towards the uplift rate. If H_ss/H_p < 1.5 (Type III), the denudation evolution is similar to situations with constant and homogeneous rainfall. In the Type I and II experiments, the mountain top is subjected to aridification once the summits have passed through H_p. To adapt to this reduced rainfall, the slopes increase. This can lead to a paradoxical situation where the mountain relief increases faster, whereas the denudation increases more slowly. The development of orographic precipitation may thus favour the stability of the mean denudation rate in a rising mountain. Despite the model limitations, including a constant rainfall–elevation relationship, our study suggests that the “classical” exponential increase in the denudation rate predicted by constant rainfall models is not the common case. Instead, the common case involves pulses and acceleration of the denudation even in the absence of uplift or global climate variations.     

Accordant summit heights, summit levels and the origin of the “upper denudation level” in the Serra do Mar (SE-Brazil, São Paulo): A study of hillslope forms and processes

In southern São Paulo the Serra do Mar is characterized by three distinct terrain types: 1) highly dissected areas with closely spaced ridges and accordant summit heights; 2) multiconvex hills; and 3) terrains with highly elevated watershed areas, irregular summit heights, and locally subdued relief. The development of this landscape is considered to be the result of the Cenozoic block-faulting and of the influences that are exerted by the differing lithological and structural setting of block-faulted compartments on weathering and erosion processes.In areas characterized by pronounced accordant summits the close coincidence between hillslope angle and the angle of limiting stability against landsliding points to a close adjustment of hillslope gradients and the mechanical properties of the regolith. The relative height of the hillslopes is functionally related to the spacing of the valleys and the gradient of the hillslopes. In areas with a regular spacing of v-shaped valleys and uniform rocks, this leads to the intersection of valley-side slopes in summits and ridges at a certain elevation. This elevation is determined by the length and steepness of the valley-side slopes. Therefore, the heights of the summits are geometrically constrained and are likely to indicate the upper limit of summit heights or an “upper denudation level” that is adjusted by hillslope processes to the incising streams. Accordant summit heights of this type are poor indicators of formerly more extensive denudation surfaces as it is also likely that they are a result of the long-term adjustment of hillslopes to river incision.The steep mountain flanks of block-faulted compartments on the other hand, comprise regolith-covered hillslopes that are closely adjusted to the maximum stable gradient as well as rock-slopes that are controlled by the rock-mass strength. Their summits are usually not accommodated into uniform summit levels. Highly elevated watershed areas exhibiting a subdued relief are detached from the base level response. On granitoid rocks these areas are often characterized by the rocky hills and domal rock outcrops. However, differences in the elevation of interfluves and summits between rocks of differing resistance and in the elevation of lithologically distinct individual fault-blocks imply that long-term weathering and erosion has transformed and lowered these landscapes. Therefore, these areas cannot be interpreted as a remnant of a pre-uplift topography and it appears to be unlikely that the height of the summits correlates with formerly more widespread planation surfaces in the far hinterland.The studies indicate that concepts such as the parallel retreat of hillslopes cannot account for the observed differences in the landscape. It is suggested that the Serra do Mar is consumed from the Atlantic and the inland side by spatially non-uniform developmental states. These states are determined by local differences in the coupling and distance to the regional base level and sea-level or are due to lithological and structural controls between and within the block-faulted compartments.     

Comparison of conceptual landscape metrics to define hillslope-scale sediment delivery ratio

The aim of this study was to evaluate four metrics to define the spatially variable (regionalised) hillslope sediment delivery ratio (HSDR). A catchment model that accounted for gully and streambank erosion and floodplain deposition was used to isolate the effects of hillslope gross erosion and hillslope delivery from other landscape processes. The analysis was carried out at the subcatchment (~ 40 km²) and the cell scale (400 m²) in the Avon-Richardson catchment (3300 km²), south-east Australia. The four landscape metrics selected for the study were based on sediment travel time, sediment transport capacity, flux connectivity, and residence time. Model configurations with spatially-constant or regionalised HSDR were calibrated against sediment yield measured at five gauging stations. The impact of using regionalised HSDR was evaluated in terms of improved model performance against measured sediment yields in a nested monitoring network, the complexity and data requirements of the metric, and the resulting spatial relationship between hillslope erosion and landscape factors in the catchment and along hillslope transects. The introduction of a regionalised HSDR generally improved model predictions of specific sediment yields at the subcatchment scale, increasing model efficiency from 0.48 to > 0.6 in the best cases. However, the introduction of regionalised HSDR metrics at the cell scale did not improve model performance. The flux connectivity was the most promising metric because it showed the largest improvement in predicting specific sediment yields, was easy to implement, was scale-independent and its formulation was consistent with sedimentological connectivity concepts. These properties make the flux connectivity metric preferable for applications to catchments where climatic conditions can be considered homogeneous, i.e. in small-medium sized basins (up to approximately 3000 km² for Australian conditions, with the Avon-Richardson catchment being at the upper boundary). The residence time metric improved model assessment of sediment yields and enabled accounting for climatic variability on sediment delivery, but at the cost of greater complexity and data requirements; this metric might be more suitable for application in catchments with important climatic gradients, i.e. large basins and at the regional scale. The application of a regionalised HSDR metric did not increase data or computational requirements substantially, and is recommended to improve assessment of hillslope erosion in empirical, semi-lumped erosion modelling applications. However, more research is needed to assess the quality of spatial patterns of erosion depicted by the different landscape metrics.     

Cenozoic sediment budget of West Africa and the Niger delta

Long‐term (10^6–7 yr) clastic sedimentary fluxes to the ocean provide first‐order constraints on the response of continental surfaces to both tectonic and climatic forcing as well as the supply that builds the stratigraphic record. Here, we use the dated and regionally correlated relict lateritic landforms preserved over Sub‐Saharan West Africa to map and quantify regional denudation as well as the export of main catchments for three time intervals (45–24, 24–11 and 11–0 Ma). At the scale of West Africa, denudation rates are low (ca. 7 m Myr⁻¹) and total clastic export rate represents 18.5 × 10³ km³ Myr⁻¹. Export rate variations among the different drainage groups depend on the drainage area and, more importantly, rock uplift. Denuded volumes and offshore accumulations are of the same magnitude, with a noticeably balanced budget between the Niger River delta and its catchment. This supports the establishment of the modern Niger catchment before 29 Ma, which then provided sufficient clastic material to the Niger delta by mainly collecting the erosion products of the Hoggar hotspot swell. Accumulations on the remaining Equatorial Atlantic margin of Africa suggest an apparent export deficit but the sediment budget is complicated by the low resolution of the offshore data and potential lateral sediment supply from the Niger delta. Further distortion of the depositional record by intracontinental transient storage and lateral input or destabilization of sediments along the margin may be identified in several locations, prompting caution when deducing continental denudation rates from accumulation only.     

Fractal dimension and fractal growth of urbanized areas

Based on a box-accounting fractal dimension algorithm (BCFD) and a unique procedure of data processing, this paper computes planar fractal dimensions of 20 large US cities along with their surrounding urbanized areas. The results show that the value range of planar urban fractal dimension (D) is 1< D <2, with D for the largest city, New York City, and the smallest city, Omaha being 1.7014 and 1.2778 respectively. The estimated urban fractal dimensions are then regressed to the total urbanized areas, Log (C), and total urban population, Log (POP), with log-linear functions. In general, the linear functions can produce good-fits for Log (C) vs. D and Log (POP) vs. in terms of R₂ values. The observation that cities may have virtually the same D or Log(C) value but quite disparate population sizes indicates that D itself says little about the specific orientation and configuration of an urban form and is not a good measure of urban population density. This paper also explores fractal dimension and fractal growth of Baltimore, MD for the 200-year span from 1792–1992. The results show that Baltimore's D also satisfies the inequality 1< D <2, with D =1.0157 in 1822 and D =1.7221 in 1992. D =0.6641 for Baltimore in 1792 is an exception due mainly to its relatively small urban image with respect to pixel size. While D always increases with Log (C) over the years, it is not always positively correlated to urban population, Log(POP).     

Post‐orogenic evolution of the southern Pyrenees: constraints from inverse thermo‐kinematic modelling of low‐temperature thermochronology data

The late‐stage evolution of the southern central Pyrenees has been well documented but controversies remain concerning potential Neogene acceleration of exhumation rates and the influence of tectonic and/or climatic processes. A popular model suggests that the Pyrenees and their southern foreland were buried below a thick succession of conglomerates during the Oligocene, when the basin was endorheic. However, both the amount of post‐orogenic fill and the timing of re‐excavation remain controversial. We address this question by revisiting extensive thermochronological datasets of the Axial Zone. We use an inverse approach that couples the thermo‐kinematic model Pecube and the Neighbourhood inversion algorithm to constrain the history of exhumation and topographic changes since 40 Ma. By comparison with independent geological data, we identified a most probable scenario involving rapid exhumation (>2.5 km Myr^?1) between 37 and 30 Ma followed by a strong decrease to very slow rates (0.02 km Myr^?1) that remain constant until the present. Therefore, the inversion does not require a previously inferred Pliocene acceleration in regional exhumation rates. A clear topographic signal emerges, however: the topography has to be infilled by conglomerates to an elevation of 2.6 km between 40 and 29 Ma and then to remain stable until ca. 9 Ma. We interpret the last stage of the topographic history as recording major incision of the southern Pyrenean wedge, due to the Ebro basin connection to the Mediterranean, well before previously suggested Messinian ages. These results thus demonstrate temporally varying controls of different processes on exhumation: rapid rock uplift in an active orogen during late Eocene, whereas base‐level changes in the foreland basin control the post‐orogenic evolution of topography and exhumation in the central Pyrenees. In contrast, climate changes appear to play a lesser role in the post‐orogenic topographic and erosional evolution of this mountain belt.     

Thermo‐tectonic evolution of the south‐central Pyrenees from rifting to orogeny: insights from detrital zircon U/Pb and (U‐Th)/He thermochronometry

Constraining the thermal and denudational evolution of continental margins from extensional episodes to early orogenic stages is critical in the objective to better understand the sediment routing during the growth of orogenic topography. Here, we report 160 detrital zircon U/Pb ages and 73 (U‐Th)/He ages from Albian, Upper Cretaceous and Eocene sandstones from the south‐central Pyrenees. All samples show dominant zircon U/Pb age peaks at 310–320 Ma, indicating a primary contribution from Variscan granites of the central Pyrenean Axial Zone. A secondary population at 450–600 Ma documents zircon grains sourced from the eastern Pyrenees. Zircon (U‐Th)/He ages recovered from older samples document, a Triassic age peak at ca. 241 Ma, corresponding to denudation coeval with the initiation of Atlantic rifting. An Early Cretaceous cooling event at ca. 133 Ma appears consistent with rift‐related exhumation and thermal overprint on the Iberian margin. The (U‐Th)/He age peaks from ca. 80 Ma to ca. 68 Ma with decreasing depositional ages are interpreted to reflect the southward‐migrating thrust‐related exhumation on the pro‐wedge side of the Pyrenean orogen. The increase in lag times, from ca. 15 Ma in the Tremp Formation (ca. 65 Ma) to 28 Ma in the Escanilla Formation (ca. 40 Ma), suggests decreasing exhumation rates from 0.4 km Myr^–1 to 0.2 km Myr^–1. The apparent inconsistency with convergence rates is used to infer that rocks cooled at 68 Ma may have resided in the crust before final exhumation to the surface. Finally, the cooling event observed at 68 Ma provides support to the inferred acceleration of convergence, shortening and exhumation during Late Cretaceous times.     

Macrogeomorphic evolution of the post-Triassic Appalachian mountains determined by deconvolution of the offshore basin sedimentary record

A perplexing macrogeomorphic problem is the persistence of topography in mountain ranges that were initially formed by orogenic events hundreds of millions of years old. In this paper, we deconvolve the post-Triassic macrogeomorphic history of a portion of one of these ranges, the central and northern Appalachians, using a well-documented offshore isopach sedimentary record of the US Atlantic margin. Topography is an important signature of tectonic, eustatic and/or geomorphic processes that produces changes in the erodible thickness of the crust (ETC). We define ETC as the total thickness of crust that would have to be consumed by erosion to reduce the mean elevation of a landscape to sea level. We use the term ‘source flux’, designated by ν˙, to describe the rate of change in ETC attributed to deep-seated geological processes such as crustal thickening, crustal extension, magmatic intrusions or dynamic flow in the mantle. In a mountain belt, the rate of change of mean elevation with respect to a base level, designated by ? ′, can be represented as ? ′ = c(ν˙ ? k _d z ′ ?; ? _c ) ?& hairsp;l˙ , where k _d is a proportionality constant relating the mean mechanical erosion rate to mean elevation, ? _c is the mean chemcial erosion rate, c  is a compensation ratio (held constant for Airy isostasy at 0.21) and l˙  is the rate of eustatic sea-level change. This equation describes the sum of constructive source terms, two destructive erosion terms and a eustatic sea-level term. We use this simple linear equation to develop a landscape evolution model based on the concept of a unit response function. The unit response function is analogous to a unit hydrograph which describes the relationship between input (rainfall) and output (discharge) in a hydrological system. In our case, we solve for the general relationship between the source flux into the mountain belt and the erosional flux out of the belt. Offshore sediment volumes are used to determine the erosional flux. Drainage basin area is treated as either a constant (pinned drainage divide) or as increasing through time (migrating drainage divide). We use a third-order polynomial fit to a global sea-level curve to account for long-term eustatically driven changes in ETC and in drainage basin area. Chemical erosion is treated as a constant fixed at 5 m Myr^?1. We consider two end-member models. The first is a ‘tectonic’ model in which the source flux is allowed to vary while k _d is assumed to be constant over geological time and equal to its mean Pleistocene value of about 0.07 Myr^?1. The second is an ‘erodibility’ model in which k _d is allowed to vary, reflecting changes in climatic, climatic variables and rock-type erodibility, while the source flux is held constant at zero. The ‘tectonic’ model reveals four important increases in the source flux, ranging from 200 to 2000 m Myr^?1 that occur over short (<10 Myr) time spans, followed by a protracted period (>25 Myr) where ν˙ drops below zero to values of ?1000 to ?6000 m Myr^?1. The ‘erodibility’ model produces a topography that decays in a step-like fashion from an initial mean elevation that ranges between ～1800 and 2300 m. These models cannot unequivocally distinguish the relative importance of tectonic vs. climatic processes in the macrogeomorphic evolution of the post-rift Appalachians, but they do provide some first-order quantitative prediction about these two end-member options. In light of existing stratigraphic, geological and thermochronological data, we favour the tectonic model because most of the events correlate well in time and form with known syn- and post-rift magmatic events. Nevertheless, the most recent episode of increased sediment flux to the offshore basins during the Miocene remains difficult to explain by either model. Limited evidence suggests that this event may reflect asthenospheric flow-driven uplift and the development of dynamically supported topography at a time when mechanical erosion rates were increasing in response to a cooling terrestrial climate.     

Fractal behavior in space and time in a simplified model of fluvial landform evolution

Two general approaches have been applied to understanding the fractal structure of fluvial topography: (1) deterministic, process-based models, and (2) stochastic partial differential equations (PDE). Deterministic models reproduce the fractal behavior of fluvial topography but have two limitations: they often underestimate the amount of lateral valley and ridge migration that occurs in nature, and the complexity has made it difficult to identify the precise origin of fractal behavior in fluvial landscapes. The simplicity of stochastic PDE models has made them useful for investigating fractal behavior, but they incorrectly suggest that fractal behavior is only possible with stochastic forcing. In this paper I investigate whether simplified, deterministic PDE models of landform evolution also exhibit fractal behavior and other features of complexity (i.e. deterministic chaos). These models are based on the KPZ equation, well known in the physics literature. This equation combines diffusion (i.e. hillslope processes) and nonlinear advection (i.e. bedrock or alluvial channel incision). Two models are considered: (1) a deterministic model with uniform erodibility and random initial topography, and (2) a deterministic model with random erodibility and uniform initial topography. Results illustrate that both of these deterministic models exhibit fractal behavior and deterministic chaos. In this context, chaotic behavior means that valley and ridge migration and nonlinear amplification of small perturbations in these models prevent an ideal steady state landscape from ever developing in the large-system limit. These results suggest that fractal structure and deterministic chaos are intrinsic features of the evolution of fluvial landforms, and that these features result from an inverse cascade of energy from small to large wavelengths in drainage basins. This inverse cascade differs from the direct cascade of three-dimensional turbulence in which energy flows from large to small wavelengths.     

Hypsometric Analysis of Headwater Rock Basins in the Dolomites (Eastern Alps) Using High‐Resolution Topography

Hypsometric curves and integrals are effective tools for rapid quantitative assessments of topography. High‐resolution digital terrain models derived from airborne LiDAR data have been analysed to study the hypsometry of small headwater rock basins (drainage areas up to 0.13 km²) in three study areas in the Dolomites (Eastern Alps) that have similar lithologies and climatic conditions. Hypsometric curves in the studied rocky headwaters display a variety of shapes and present remarkable differences between neighbouring basins. Hypsometric integrals show generally high values in the three study areas (>0.42, mean values between 0.51 and 0.65). The extent of the scree slopes located at the foot of rock basins in the three study areas is larger in the area with lower hypsometric integrals and indicates consistency between the development of basin erosion, which is shown by the hypsometric integral, and debris yield, represented by the extent of scree slope. No clear relations were observed between the hypsometric integrals and basin area and shape. When extending the analysis to larger basins, which encompass rocky headwaters and downslope soil‐mantled slopes, a negative correlation is found between the hypsometric integral and catchment area, suggesting that the scale independency of the hypsometric integral occurs essentially in headwater rock basins. Geomorphometric indices (residual relief and surface roughness) have contributed to interpreting the variability of surface morphology, which is related to the geo‐structural complexity of the catchments.     

Variable complexity of the US Continental Divide trace

Abstract

Map-view complexity of 65 contiguous segments of the conterminous US Continental Divide trace was evaluated by the divider method, with each segment’s geometry approximated by a fractal dimension (D) value, or two D values applying to fine and coarse scales of inspection. Results support a generalization that D values in the range 1.05–1.12 are typical for drainage divides viewed at regional to national scales. However about 20% of cases reviewed in this study are smoother (D = 1.01–1.04) or more complex (D = 1.13–1.18) traces. Complexities of these watershed boundary segments show no significant correlation with physiographic province or local relief. The primary influence of bedrock lithology and surface process is seen in zones of Quaternary volcanism, where uncommonly smooth and highly complex divide trace segments are more the rule than exception. Uncommonly smooth divide traces are also found descending mountain pediments in areas of parallel drainage, and some of the most tortuous traces are associated with drainage patterns disrupted by non-fluvial processes. Divide trace segments crossing terrain with uniform lithology show decreased complexity, but traces with the broadest range of complexity, including highest D values, occur in areas with moderate, not extreme, degrees of bedrock diversity.     

Fractal analysis of tidal channels in the Bahía Blanca Estuary (Argentina)

The fractal dimension (D) was estimated for nine tidal channels depicted in thematic mapper (TM) Landsat-5 imagery to derive information about the degree of geomorphological control on a tidal channel network characteristic of the Bahía Blanca Estuary (Argentina). Two methods, box counting and contiguity, were used to estimate fractal dimensions for each tidal channel. All channels produced D values close to 1, meaning that they are self-affine fractal features. However, these fractal dimensions do not represent the meandering pattern complexity characteristic of the tidal channels analysed. Although both methods allowed for estimation of D, the contiguity method showed that three of the channels actually are not fractal but have sinusoidal characteristics, a condition that was not detected by the former method.     

Impact of hillslope-derived sediment supply on drainage basin development in small watersheds at the northern border of the central Alps of Switzerland

This paper explores the effects of hillslope mobility on the evolution of a 10-km² drainage basin located at the northern border of the Swiss Alps. It uses geomorphologic maps and the results of numerical models that are based on the shear stress formulation for fluvial erosion and linear diffusion for hillslope processes. The geomorphic data suggest the presence of landscapes with specific cross-sectional geometries reflecting variations in the relationships between processes in channels and on hillslopes. In the headwaters, the landscape displays parabolic cross-sectional geometries indicating that mass delivered to channels by hillslope processes is efficiently removed. In the trunk stream portion, the landscape is (i) V-shaped if the downslope flux of mass is balanced by erosion in channels (i.e. if mass delivered to channels by hillslope processes is efficiently removed) and (ii) U-shaped if in-channel accumulation of hillslope-derived material occurs. This latter situation indicates a non-balanced mass flux between processes in channels and on hillslopes.Information about the spatial pattern of the postglacial depth of erosion allows comparative estimates to be made about the erosional efficiency for the various landscapes that were mapped in the study area. The data suggest that the erosional potential and sediment discharge are reduced for the situation of a non-balanced mass flux between processes in channels and on hillslopes. These findings are also supported by the numerical model. Indeed, the model results show that high hillslope mobility tends to reduce the hillslope relief and to inhibit dissection and formation of channels. In contrast, stable hillslopes tend to promote fluvial incision, and the hillslope relief increases. The model results also show that very low erosional resistance of bedrock promotes backward erosion and steepening of channel profiles in headwaters. Beyond that, the model reveals that sediment discharge generally increases with decreasing erosional resistance of bedrock, but that this increase decays exponentially with increasing magnitudes of fluvial and hillslope mobilities. Very high hillslope diffusivities even tend to reduce the erosional potential of the whole watershed. It appears that besides rates of base-level lowering, factors limiting sediment discharge might be the nonlinear relationships between processes in channels and on hillslopes.