Regular spacing of drainage outlets from linear mountain belts

Abstract Straight sections of many actively uplifting mountain belts have simple patterns of drainage, transverse to their main structural trend. Streams rising near or beyond the topographic ridgepole of these sections are spaced at seemingly regular intervals. To test whether this regularity exists, morphometric aspects of drainage networks were measured in 11 mountain belts. The spacing of drainage basins can be expressed using a spacing ratio, which in effect is the ratio of the length and the width of the catchments under consideration. Average spacing ratios for most linear mountain belts are within a narrow range of values between 1.91 and 2.23. A linear relationship exists between the spacing of catchment outlets and the distance between the main divide and the front of the mountain belt in which they have developed. The Nepalese Himalaya form an exception to this regular pattern. In this mountain belt drainage is blocked and diverted by structures that have developed in relation to the Main Boundary Thrust. Structural complications cause drainage patterns to become less regular, introducing important non trans verse components. The linear relationship between spacing of catchment outlets and half-width of the mountain belt may be expressed in an equation of the same general form as Hack's law of stream length and drainage basin area. It seems likely that the mechanism underlying Hack's law also explains the consistent regularity of drainage spacing in active mountain belts. However, no generally accepted explanation for Hack's law has been offered. The narrow range of spacing ratios found for drainage networks in active orogens may represent an optimal catchment geometry that embodies a ‘most probable state’ in the uplift-erosion system of a linear mountain belt. The linear relationship between the half-width of a mountain belt and spacing of catchment outlets has profound implications for the modelling of erosion of orogenic topography, and for the formation and filling of foreland basins.     

Investigating the surface process response to fault interaction and linkage using a numerical modelling approach

In order to better understand the evolution of rift‐related topography and sedimentation, we present the results of a numerical modelling study in which elevation changes generated by extensional fault propagation, interaction and linkage are used to drive a landscape evolution model. Drainage network development, landsliding and sediment accumulation in response to faulting are calculated using CASCADE, a numerical model developed by Braun and Sambridge, and the results are compared with field examples. We first show theoretically how the ‘fluvial length scale’, L_f, in the fluvial incision algorithm can be related to the erodibility of the substrate and can be varied to mimic a range of river behaviour between detachment‐limited (DL) and transport‐limited (TL) end‐member models for river incision. We also present new hydraulic geometry data from an extensional setting which show that channel width does not scale with drainage area where a channel incises through an area of active footwall uplift. We include this information in the coupled model, initially for a single value of L_f, and use it to demonstrate how fault interaction controls the location of the main drainage divide and thus the size of the footwall catchments that develop along an evolving basin‐bounding normal fault. We show how erosion by landsliding and fluvial incision varies as the footwall area grows and quantify the volume, source area, and timing of sediment input to the hanging‐wall basin through time. We also demonstrate how fault growth imposes a geometrical control on the scaling of river discharge with downstream distance within the footwall catchments, thus influencing the incision rate of rivers that drain into the hanging‐wall basin. Whether these rivers continue to flow into the basin after the basin‐bounding fault becomes fully linked strongly depends on the value of L_f. We show that such rivers are more likely to maintain their course if they are close to the TL end member (small L_f); as a river becomes progressively more under supplied, i.e. the DL end member (large L_f), it is more likely to be deflected or dammed by the growing fault. These model results are compared quantitatively with real drainage networks from mainland Greece, the Italian Apennines and eastern California. Finally, we infer the calibre of sediments entering the hanging‐wall basin by integrating measurements of erosion rate across the growing footwall with the variation in surface processes in space and time. Combining this information with the observed structural control of sediment entry points into individual hanging‐wall depocentres we develop a greater understanding of facies changes associated with the rift‐initiation to rift‐climax transition previously recognised in syn‐rift stratigraphy.     

Sediment dispersal and redistributive processes in axial and transverse deep‐time source‐to‐sink systems of marine rift basins: Dampier Sub‐basin,Northwest Shelf,Australia

Morphological scaling relationships between source‐to‐sink segments have been widely explored in modern settings, however, deep‐time systems remain difficult to assess due to limited preservation of drainage basins and difficulty in quantifying complex processes that impact sediment dispersals. Integration of core, well‐logs and 3‐D seismic data across the Dampier Sub‐basin, Northwest Shelf of Australia, enables a complete deep‐time source‐to‐sink study from the footwall (Rankin Platform) catchment to the hanging wall (Kendrew Trough) depositional systems in a Jurassic late syn‐rift succession. Hydrological analysis identifies 24 drainage basins on the J50.0 (Tithonian) erosional surface, which are delimited into six drainage domains confined by NNE‐SSW trending grabens and their horsts, with drainage domain areas ranging between 29 and 156 km². Drainage outlets of these drainage domains are well preserved along the Rankin Fault System scarp, with cross‐sectional areas ranging from 0.08 to 0.31 km². Corresponding to the six drainage domains, sedimentological and geomorphological analysis identifies six transverse submarine fan complexes developing in the Kendrew Trough, ranging in areas from 43 to 193 km². Seismic geomorphological analysis reveals over 90‐km‐long, slightly sinuous axial turbidity channels, developing in the lower topography of the Kendrew Trough which erodes toe parts of transverse submarine fan complexes. Positive scaling relationships exist between drainage outlet spacing and drainage basin length, and drainage outlet cross‐sectional area and drainage basin area, which indicates the geometry of drainage outlets can provide important constraints on source area dimensions in deep‐time source‐to‐sink studies. The broadly negative bias of fan area to drainage basin area ratios indicates net sediment losses in submarine fan complexes caused by axial turbidity current erosion. Source‐to‐sink sediment balance studies must be done with full evaluating of adjacent source‐to‐sink systems to delineate fans and their associated up‐dip drainages, to achieve an accurate tectonic and sedimentologic picture of deep‐time basins.     

Drainage spacing regularity on a fault-block: A case study from the eastern Ruahine Range

Abstract:  Recent research has indicated river basin outlets draining linear sections of large, uplifting mountain belts often show a regularity of spacing, transverse to the main structural trend. A morphometric analysis of part of the Ruahine Range, on the North Island was undertaken to test whether drainage regularity may exist in smaller, younger mountain ranges. The ratio, R , of the half-width of the mountain belt, W , and the outlet spacing, S , was used to characterize drainage networks on the eastern side of the range. The spacing ratio for the range of 1.31 is lower than R results from studies of larger mountain belts ( R  = 1.91–2.23). We suggest the cause of this lower ratio is related to eastward migration of the Ruahine drainage divide.     

River spacing and drainage network growth in widening mountain ranges

Drainage networks in linear mountain ranges always display a particular geometrical organisation whereby the spacing between the major drainage basins is on average equal to half the mountain width (distance from the mountain front to the main drainage divide), independent of climate and tectonics. This relationship is valid for mountains having different widths and is thus usually thought to be maintained by drainage reorganisation during mountain belt widening. However, such large‐scale systematic drainage reorganisation has never been evidenced. In this paper, we suggest an alternative explanation, namely that the observed drainage basin relationships are an inherent property of dendritic river networks and that these relationships are established on the undissected, lowland margins outside mountain ranges and are progressively incorporated and quenched into uplifted topography during range widening. Thus, we suggest that the large‐scale geometry of drainage networks in mountain ranges is mainly antecedent to erosion. We propose a model in which the large‐scale drainage geometry is controlled mainly by the geometrical properties of the undissected surfaces (in particular, the ratio of the regional slope to the local slope related to roughness) over which rivers are flowing before uplift, and is therefore independent of climate and tectonics.     

Regular spacing of drainage outlets from linear fault blocks

Outlets of river basins located on fault blocks often show a regular spacing. This regularity is most pronounced for fault blocks with linear ridge crests and a constant half-width, measured perpendicular to the ridge crest. The ratio of the half-width of the fault block and the outlet spacing is used in this study to characterize the average shape (or spacing ratio) of 31 sets of drainage basins. These fault-block spacing ratios are compared with similar data from small-scale flume experiments and large-scale mountain belts. Fault-block spacing ratios are much more variable than those measured for mountain belts. Differences between fault-block spacing ratios are attributed to variability in factors influencing the initial spacing of channel heads and subsequent rates of channel incision during the early stages of channel network growth (e.g. initial slope and uplift rate, precipitation, runoff efficiency and substrate erodibility). Widening or narrowing of fault blocks during ongoing faulting will also make spacing ratios more variable. It is enigmatic that some of these factors do not produce similar variability in mountain belt spacing ratios. Flume experiments in which drainage networks were grown on static topography show a strong correlation between spacing ratios and surface gradient. Spacing ratios on fault blocks are unaffected by variations in present-day gradients. Drainage basins on the Wheeler Ridge anticline in central California, which have formed on surfaces progressively uplifted by thrust faulting during the last 14 kyr, demonstrate that outlet spacing is likely to be determined during the early stages of drainage growth. This dependency on initial conditions may explain the lack of correlation between spacing ratios of fault blocks and slopes measured at the present day. Spacing ratios determine the location of sediment supply points to adjacent areas of deposition, and hence strongly influence the spatial scale of lateral facies variations in the proximal parts of sedimentary basins. Spacing ratios may be used to estimate this length scale in ancient sedimentary basins if the width of adjacent topography is known. Spacing ratio variability makes these estimates much less precise for fault blocks than for mountain belts.     

Interplay between lithospheric flexure and river transport in foreland basins

ABSTRACT Foreland basins form by lithospheric flexure under orogenic loading and are filled by surface transport of sediment. This work readdresses the interplay between these processes by integrating in a 3D numerical model: the mechanisms of thrust stacking, elastic flexural subsidence and sediment transport along the drainage network. The experiments show that both crustal tectonic deformation and vertical movements related to lithospheric flexure control and organise the basin-scale drainage pattern, competing with the nonlinear, unpredictable intrinsic nature of river network evolution. Drainage pattern characteristics are predicted that match those observed in many foreland basins, such as the axial drainage, the distal location of the main river within the basin, and the formation of large, long-lasting lacustrine systems. In areas where the river network is not well developed before the formation of the basin, these lithospheric flexural effects on drainage patterns may be enhanced by the role of the forebulge uplift as drainage divide. Inversely, fluvial transport modifies the flexural vertical movements differently than simpler transport models (e.g. diffusion): Rivers can drive erosion products far from a filled basin, amplifying the erosional rebound of both orogen and basin. The evolution of the sediment budget between orogen and basin is strongly dependent on this coupling between flexure and fluvial transport: Maximum sediment accumulations on the foreland are predicted for a narrow range of lithospheric elastic thickness between 15 and 40 km, coinciding with the T _e values most commonly reported for foreland basins.     

陕北黄土高原沟道小流域形态特征分析

本文就黄土高原不同地貌类型区的小流域进行了形态量计分析。并以河网密度为地表切割程度指标,建立了河网密度与流域形态要素的复相关方程式。     

Measuring the significance of a divide to local drainage patterns

This article presents a framework for estimating a new topographic attribute derived from digital elevation models (DEMs) called maximum branch length (B _max). Branch length is defined as the distance travelled along a flow path initiated at one grid cell to the confluence with the flow path passing through a second cell. B _max is the longest branch length measured for a grid cell and its eight neighbours. The index provides a physically meaningful method for assessing the relative significance of drainage divides to the dispersion of materials and energy across a landscape, that is, it is a measure of ‘divide size’. B _max is particularly useful for studying divide network structure, for mapping drainage divides, and in landform classification applications. Sensitivity analyses were performed to evaluate the robustness of estimates of B _max to the algorithm used to estimate flow lengths and the prevalence of edge effects resulting from inadequate DEM extent. The findings suggest that the index is insensitive to the specific flow algorithm used but that edge effects can result in significant underestimation along major divides. Edge contamination can, however, be avoided by using an appropriately extensive DEM.     

A consistent framework for Horton regression statistics that leads to a modified Hack's law

A statistical framework is introduced that resolves important problems with the interpretation and use of traditional Horton regression statistics. The framework is based on a univariate regression model that leads to an alternative expression for Horton ratio, connects Horton regression statistics to distributional simple scaling, and improves the accuracy in estimating Horton plot parameters. The model is used to examine data for drainage area A and mainstream length L from two groups of basins located in different physiographic settings. Results show that confidence intervals for the Horton plot regression statistics are quite wide. Nonetheless, an analysis of covariance shows that regression intercepts, but not regression slopes, can be used to distinguish between basin groups. The univariate model is generalized to include n > 1 dependent variables. For the case where the dependent variables represent ln A and ln L, the generalized model performs somewhat better at distinguishing between basin groups than two separate univariate models. The generalized model leads to a modification of Hack's law where L depends on both A and Strahler order ω. Data show that ω plays a statistically significant role in the modified Hack's law expression.     

The evolution of the high‐elevated depocenters of the northern Sierras Pampeanas (ca. 28˚ SL), Argentine broken foreland,South‐Central Andes: the Pipanaco Basin

The Pipanaco Basin, in the southern margin of the Andean Puna plateau at ca. 28°SL, is one of the largest and highest intermontane basins within the northernmost Argentine broken foreland. With a surface elevation >1000 m above sea level, this basin represents a strategic location to understand the subsidence and subsequent uplift history of high‐elevation depositional surfaces within the distal Andean foreland. However, the stratigraphic record of the Pipanaco Basin is almost entirely within the subsurface, and no geophysical surveys have been conducted in the region. A high‐resolution gravity study has been designed to understand the subsurface basin geometry. This study, together with stratigraphic correlations and flexural and backstripping analysis, suggests that the region was dominated by a regional subsidence episode of ca. 2 km during the Miocene‐Pliocene, followed by basement thrusting and ca. 1–1.5 km of sediment filling within restricted intermontane basin between the Pliocene‐Pleistocene. Based on the present‐day position of the basement top as well as the Neogene‐Present sediment thicknesses across the Sierras Pampeanas, which show slight variations along strike, sediment aggradation is not the most suitable process to account for the increase in the topographic level of the high‐elevation, close‐drainage basins of Argentina. The close correlation between the depth to basement and the mean surface elevations recorded in different swaths indicates that deep‐seated geodynamic process affected the northern Sierras Pampeanas. Seismic tomography, as well as a preliminary comparison between the isostatic and seismic Moho, suggests a buoyant lithosphere beneath the northern Sierras Pampeanas, which might have driven the long‐wavelength rise of this part of the broken foreland after the major phase of deposition in these Andean basins.     

Late Cenozoic tectono‐stratigraphic sequences of the Crotone Basin: insights on the geodynamic history of the Calabrian arc and Tyrrhenian Sea

The Crotone Basin was generated in the late Cenozoic as a forearc basin of the Ionian arc‐trench system. New data are gained through detailed field mapping, high‐resolution stratigraphic analysis of a key area and examination of offshore well data and seismic reflection profiles. Major unconformities divide the basin fill into major sequences, which reveal a three‐stage internal organization thought to reflect geodynamic events of the Calabrian arc and backarc area closely. The first stage is characterized by extensional block faulting and uplift followed by rapid drowning during high subsidence and transtension in the basin along a major NNW‐ to NW‐striking fault system. This stage is interpreted to reflect resumption of rollback after an episode of slab tearing triggered by transitory docking of continental lithosphere in the trench. The initial uplift is inferred to reflect decoupling and rebound after the transitory coupling phase. The second stage is characterized by increased subsidence and continued extension/transtension. This trend presumably reflects a decreasing rate of rollback resulting from a tendency towards viscous coupling after acceleration of slab downwelling. The third stage is characterized by short‐lived transpression along major shear zones and local inversion of former basins. This is inferred to reflect entrance into the trench of buoyant continental lithosphere, resulting in significant deceleration of slab rollback and consequently a break in, or slowing of, backarc extension, and predominance of the effects of compression related to Africa–Europe convergence. Overall, the above evolution resulted in the formation of a progressively narrower and rapidly retreating slab, inducing extreme rates of backarc extension, and may have played a critical role in determining the intermittent nature of the backarc rifting.     

侯马盆地冲积扇及其流域地貌发育规律

根据从DEM数据中提取的侯马盆地冲积扇及其流域的多项地貌指标,分析了各地貌指标的空间分布规律,并通过地貌指标的空间分布曲线与山前地形高程曲线形态的对比以及地貌指标相关性分析来揭示冲积扇及其流域地貌的发育规律。结果表明,在侯马盆地相对隆起部位的冲积扇及其流域的地貌指标与在盆地凹陷部位的冲积扇及其流域的地貌指标有较大差异;流域地貌指标的空间分布受到盆地边界断层构造活动性的影响;冲积扇的发育主要受到流域规模、山前构造活动以及盆地基准面等多种因素共同的影响;流域内岩性的差异不是造成研究区域内冲积扇地貌差异的主要因素。     

地貌发育阶段的定量研究

文章提出用临界侵蚀积分值作为划分流域发育阶段的定量指标,是对经典理论的发展,主要表现在:1)将地貌发育阶段纳入开放系统的概念之中;2)避免高程积分法在划分发育阶段上的不确定性;3)建立地貌发育阶段与流域物质迁移之间的定量关系;4)区分自然侵蚀和加速侵蚀。用文中的临界侵蚀方程对黄土高原丘陵沟壑区分析计算,得到临界侵蚀积分值为0.30和0.70,即当侵蚀积分值小于0.30寸,流域处于侵蚀早期;当侵蚀积分值大于0.30,小于0.70时,流域处于侵蚀中期;当侵蚀积分值大于0.70时,流域处于侵蚀晚期。对于纯自然侵蚀过程,与临界侵蚀积分值相对应的年代及侵蚀模数为7万年前,7008t/km~2·a和距今7.2万年以后,7008t/km~2·a。目前黄土高原丘陵沟壑区加速侵蚀所占比例为30％。     

Drainage, sediment transport, and denudation rates on the Nanga Parbat Himalaya, Pakistan

The Nanga Parbat Himalaya presents some of the greatest relief on Earth, yet sediment production and denudation rates have only been sporadically addressed. We utilized field measurements and computer models to estimate bank full discharge, sediment transport, and denudation rates for the Raikot and Buldar drainage basins (north slope of Nanga Parbat) and the upper reach of the Rupal drainage basin (south slope).The overall tasks of determining stream flow conditions in such a dynamic geomorphic setting is challenging. No gage data exist for these drainage basins, and the overall character of the drainage basins (high relief, steep flow gradients, and turbulent flow conditions) does not lend itself to either ready access or complete profiling.Cross-sectional profiles were surveyed through selected reaches of these drainage basins. These data were then incorporated into software (WinXSPRO) that aids in the characterization (stage, discharge, velocity, and shear stress) of high altitude, steep mountain stream conditions.Complete field measurements of channel depths were rarely possible (except at several bridges where the middle of the channel could actually be straddled and probed) and, when coupled with velocity measurements, provided discrete points of field-measured discharge calculations. These points were then used to calibrate WinXSPRO results for the same reach and provided a confidence level for computer-generated results.Flow calculations suggest that under near bank full conditions, the upper Raikot drainage basin produces discharges of 61 cm and moves about 11,000 tons day⁻¹ (9980 tons day⁻¹) of sediment through its channel. Bank full conditions on the upper portion of the Rupal drainage basin generate discharges of 84 cm and moves only about 3800 tons day⁻¹ (3450 tons day⁻¹) of sediment. Although the upper Rupal drainage basin moves more water, the lower slope of the drainage basin (0.03) generates a much smaller shear stress (461 Pa) than does the higher slope (0.12) of the upper Raikot drainage basin (1925 Pa).Dissolved and suspended sediment loads were measured from water/sediment samples collected throughout the day and night over a period of 10 days at the height of the summer melt season but proved to be a minor variable in transport flux. Channel bed loads were measured using a pebble count method of bank material and then used to generate ratings curves of bed loads relative to discharge volumes. When coupled with discharge data and basin area, mean annual sediment yield and denudation rates for Nanga Parbat are produced. Denudation rates calculated in this fashion range from 0.2 mm year⁻¹ in the slower, more sluggish Rupal drainage basin to almost 6 mm year⁻¹ in the steeper, faster flowing Raikot and Buldar drainage basins.     

Synclinal-horst basins: examples from the southern Rio Grande rift and southern transition zone of southwestern New Mexico, USA

In areas of broadly distributed extensional strain, the back‐tilted edges of a wider than normal horst block may create a synclinal‐horst basin. Three Neogene synclinal‐horst basins are described from the southern Rio Grande rift and southern Transition Zone of southwestern New Mexico, USA. The late Miocene–Quaternary Uvas Valley basin developed between two fault blocks that dip 6–8° toward one another. Containing a maximum of 200 m of sediment, the Uvas Valley basin has a nearly symmetrical distribution of sediment thickness and appears to have been hydrologically closed throughout its history. The Miocene Gila Wilderness synclinal‐horst basin is bordered on three sides by gently tilted (10°, 15°, 20°) fault blocks. Despite evidence of an axial drainage that may have exited the northern edge of the basin, 200–300 m of sediment accumulated in the basin, probably as a result of high sediment yields from the large, high‐relief catchments. The Jornada del Muerto synclinal‐horst basin is positioned between the east‐tilted Caballo and west‐tilted San Andres fault blocks. Despite uplift and probable tilting of the adjacent fault blocks in the latest Oligocene and Miocene time, sediment was transported off the horst and deposited in an adjacent basin to the south. Sediment only began to accumulate in the Jornada del Muerto basin in Pliocene and Quaternary time, when an east‐dipping normal fault along the axis of the syncline created a small half graben. Overall, synclinal‐horst basins are rare, because horsts wide enough to develop broad synclines are uncommon in extensional terrains. Synclinal‐horst basins may be most common along the margins of extensional terrains, where thicker, colder crust results in wider fault spacing.     

1960-2007年中国地表潜在蒸散发敏感性的时空变化(英文)

Potential evapotranspiration (E0), as an estimate of the evaporative demand of the atmosphere, has been widely studied in the fields of irrigation management, crop water demand and predictions in ungauged basins (PUBs). Analysis of the sensitivity of E0 to meteorological factors is a basic research on the impact of climate change on water resources, and also is important to the optimal allocation of agricultural water resources. This paper dealt with sensitivity of E0 over China, which was divided into ten drainage systems, including Songhua River basin, Liaohe River basin, Haihe River basin, Yellow River basin, Yangtze River basin, Pearl River basin, Huaihe River drainage system, Southeast river drainage system, Northwest river drainage system and Southwest river drainage system. In addition, the calculation method of global radiation in Penman-Monteith formula was improved by optimization, and the sensitivities of Penman-Monteith potential evapotranspiration to the daily maximum temperature (STmax), daily minimum temperature (STmin), wind speed (SU2), global radiation (SRs) and vapor pressure (SVP) were calculated and analyzed based on the long-term meteorological data from 653 meteorological stations in China during the period 1960-2007. Results show that: (1) the correlation coefficient between E0 and pan evaporation increased from 0.61 to 0.75. E0 had the decline trends in eight of ten drainage systems in China, which indicates that "pan evaporation paradox" commonly exists in China from 1960 to 2007. (2) Spatially, Tmax was the most sensitive factor in Haihe River basin, Yellow River basin, Huaihe River drainage system, Yangtze River basin, Pearl River basin and Southeast river drainage system, and VP was the most sensitive factor in Songhua River Basin, Liaohe River basin, Northwest river drainage system while Rs was the most sensitive factor in Southwest river drainage system. For the nation-wide average, the most sensitive factor was VP, followed by Tmax, Rs, U2 and Tmin. In addition, the changes in sensitivity coefficients had a certain correlation with elevation. (3) Temporally, the maximum values of STmax and SRs occurred in July, while the maximum values of STmin, SVP and SU2 occurred in January. Moreover, trend analysis indicates that STmax had decline trends, while STmin, SU2, SRs and SVP had increasing trends.     

长江上游输沙尺度效应研究

利用长江上游DEM、降雨、土地利用、土壤类型数据库,计算出通用土壤流失方程中代表影响侵蚀产沙的各因子,建立这些因子以及流域面积与长江上游268个水文站以上流域输沙模数回归关系,探讨上游侵蚀输沙的尺度效应。结果显示长江上游输沙模数与流域面积之间呈负幂函数单元回归关系,而且这一关系主要产生于降雨侵蚀力因子和土壤可蚀性因子随流域面积的变化。长江上游输沙模数随流域面积增大而降低主要发生在大约1×10⁴~1.58×10⁵km²之间。在考虑了影响侵蚀产沙因子对输沙模数的作用后,输沙模数与流域面积之间呈正幂函数相关,反映出上游输沙近源沉积的特征。分析还发现长江上游各主要支流输沙模数变化与流域尺度大小的关系和原因有明显不同。