Regional analysis of bedrock stream long profiles: evaluation of Hack's SL form,and formulation and assessment of an alternative (the DS form)

The equilibrium form of the fluvial long profile has been used to elucidate a wide range of aspects of landscape history including tectonic activity in tectonic collision zones, and in continental margin and other intraplate settings, as well as other base‐level changes such as due to sealevel fluctuations. The Hack SL form of the long profile, which describes a straight line on a log–normal plot of elevation (normal) versus distance (logarithmic), is the equilibrium long profile form that has been most widely used in such studies; slope–area analysis has also been used in recent years. We show that the SL form is a special case of a more general form of the equilibrium long profile (here called the DS form) that can be derived from the power relationship between stream discharge and downstream distance, and the dependence of stream incision on stream power. The DS form provides a better fit than the SL form to river long profiles in an intraplate setting in southeastern Australia experiencing low rates of denudation and mild surface uplift. We conclude that, if an a priori form of the long profile is to be used for investigations of regional landscape history, the DS form is preferable. In particular, the DS form in principle enables equilibrium steepening due to an increase in channel substrate lithological resistance (parallel shift in the DS plot) to be distinguished from disequilibrium steepening due to long profile rejuvenation (disordered outliers on the DS plot). Slope–area analysis and the slope–distance (DS) approach outlined here are complementary approaches, reflecting the close relationship between downstream distance and downstream catchment area. Copyright © 2006 John Wiley & Sons, Ltd.     

At‐a‐station hydraulic geometry relations, 1: theoretical development

This paper, the first of two, hypothesizes that: (1) the temporal variation of stream power of a river channel at a given station with varying discharge is accomplished by the temporal variation in channel form (flow depth and channel width) and hydraulic variables, including energy slope, flow velocity and friction; (2) the change in stream power is distributed among the changes in flow depth, channel width, flow velocity, slope, and friction, depending on the boundary conditions that the channels has to satisfy. The second hypothesis is a result of the principle of maximum entropy and the theory of minimum energy dissipation or its simplified minimum stream power. These two hypotheses lead to families of at‐a‐station hydraulic geometry relations. The conditions under which these families of relations can occur in the field are discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

The relationship between throughflow generation and the solute concentration of soil and stream water

Variation in solute concentrations of soil and stream water during throughflow events was studied at Bicknoller Combe, Somerset, England. The main hydrological process acting in the catchment involves a delayed throughflow discharge pulse a day or two after the rainfall event. During the period of storm runoff, coincident with the rainfall, the solutes in the stream are diluted, but their concentration in the throughflow remains unchanged. During the delayed throughflow pulse, concentrations of both soil and stream water increase. This is due to additional leaching from the soil in hollows where saturated moisture conditions prevail. The results suggest that two distinct erosional environments may exist: on the spurs, leaching seems to be related solely to infiltration processes, whilst in the hollows, saturated throughflow also contributes to the solute removal. This contrast in erosional processes may perhaps account for the difference in slope form and development between the hollow and spur zones.     

Re‐examination of Bagnold's empirical bedload ­formulae

Bagnold developed his formula for bedload transport over several decades, with the final form of the relation given in his 1980 paper. In this formula, bedload transport rate is a function of stream power above some threshold value, depth and grain size. In 1986, he presented a graph which illustrated the strength of his relation. A double‐log graph of bedload transport rate, adjusted for depth and grain size, versus excess stream power was shown to collapse along a line having a slope of 1·5. However, Bagnold based his analyses on limited data. In this paper, the formula is re‐examined using a large data set in order to define the most consistent empirical representation, and dimensional analysis is performed to seek a rationalization of the formula. Functional analysis is performed for the final version of the equation defined by Bagnold to determine if the slope of 1·5 is preserved and to assess the strength of the relation. Finally, relations between excess stream power and bedload transport are examined for a fixed slope of 1·5 to assess the performance of various depth and grain size adjustment factors. The rational scaling is found to provide the best result. Copyright © 2000 John Wiley & Sons, Ltd.     

Density effects on solute release from streambeds

Contaminants that entered the streambed during previous surface water pollution events can be released to the stream, causing secondary pollution of the stream and impacting its eco-environmental condition. By means of laboratory experiments and numerical simulations, we investigated density effects on the release of solute from periodic bedforms. The results show that solute release from the upper streambed is driven by bedform-induced convection, and that density effects generally inhibit the solute release from the lower streambed. Density gradients modify the pore water flow patterns and form circulating flows in the area of lower streambed. The formation of circulating flows is affected by density gradients associated with the solute concentration and horizontal pressure gradients induced by stream slope. The circulating flows near the bottom of the streambed enhance mixing of the hyporheic zone and the ambient flow zone.     

The distribution of solute processes on an acid hillslope and the delivery of solutes to a stream: I. Exchangeable bases

This paper aims to identify the spatial distribution of exchangeable base cations in soils on an acid hillslope and to investigate possible cation release processes from slope soils to the stream. The basic assumption underlying this research is that the amount of exchangeable cations in soils reflects the nutrient stores and cation leaching processes across the slope where vegetation and parent materials are similar. The distribution of exchangeable Ca²⁺, Mg²⁺, K⁺ and Na⁺ has been investigated on a three-dimensional hillslope on the Quantock Hills, Somerset, UK. A two-way ANOVA shows that soil depth is predominant in explaining the total variance of exchangeable bases, despite the steep slope gradient and clear podzolic catena development. Major nutrient base cations, such as Ca²⁺, Mg²⁺ and K⁺, display homogeneous topsoil storage right across the slope. This spatial pattern may indicate that the spatial distribution of major nutrient cations is tightly controlled by the soil–vegetation system in nutrient-poor heathland environments. Na⁺ is an exception to this vegetation-controlled spatial distribution, because of its small involvement in the soil–vegetation and soil exchangeable systems. In subsurface soils, cations liberated from the soil–vegetation system are subject to redistribution over the slope according to the hydrological flowpaths operating on the slope, with some eventually released into the stream. The saturated wedge developed at the base of the slope plays a key role in the storage and release processes of base cations from slope soils to the stream. Ca²⁺, Mg²⁺ and Na⁺ carried by throughflow are stored in the saturated wedge and gradually released into the stream at times of high flow. K⁺, however, shows an apparently different spatial behaviour, being deficient in the saturated wedge. Copyright © 1999 John Wiley & Sons, Ltd.     

Slope form and basal stream relationships: Some further comments

The nature and strength of the correlation between stream gradient and valley side slope angle are seen to vary according to the order of the stream segment. In addition, it is suggested that the relationship will depend on the efficiency of slope processes, and that this may contribute to tye different from of relationship obtained in different regions.     

Types of river channel patterns and their natural controls

River channel patterns are thought to form a morphological continuum. This continuum is two-dimensional, defined by plan features of which there are three (straight, meandering, branching), and structural levels of fluvial relief of which there are also three (floodplain, flood channel, low-water channel). Combinations of these three categories define the diversity of patterns. One of the most important factors in channel development is stream power, defined by water discharge and river slope. The greater the stream power, the stronger the branching tendency, but threshold values of stream power are different for the three different hierarchical levels of channel relief. The critical stream power values and hydrological regime together define the channel pattern, and analysis of the pattern type can be undertaken using effective discharge curves. © 1998 John Wiley & Sons, Ltd.     

The effect of urbanization on stream hydrology in hillslope watersheds in central Texas

This study examined the effect of urbanization on stream hydrology in hillslope watersheds. Ten streams (seven in hillslope and three in gentle slope watersheds) around Austin, Texas were selected for analysis. For each stream, we compared parameters of transfer function (TF) models estimated from daily rainfall and streamflow data collected in two study periods (October 1988–September 1992 and October 2004–September 2008) representing different degrees of watershed urbanization. As expected, the streams became more intermittent as the watersheds were more urbanized in all the study streams. However, the effect of urbanization on peakflow differs between hillslope and gentle slope watersheds. After watershed urbanization, peakflow increased in gentle slope watersheds, but decreased in hillslope watersheds. Based on the results of the TF models, we found that urbanization made stream not flashier but drier in hillslope watersheds. Overpumpage of aquifer has been recognized as a problem that leads to the stream dryness in the study area. However, the overpumpage alone cannot explain the differences in hydrological changes between the two types of watersheds. We attributed the reduced peakflow and stream dryness in the hillslope watersheds to land grading for construction forming stair‐stepped or terraced landscape. Compared with natural hillslope, a stair‐stepped landscape could infiltrate more stormwater by slowing down surface runoff on tread portions of the stair. Our findings suggest that a watershed management scheme should take into account local hydrogeologic conditions to mitigate the stream dryness resulting from urbanization in hillslope watersheds. Copyright © 2010 John Wiley & Sons, Ltd.     

An integral approach to bedrock river profile analysis

Bedrock river profiles are often interpreted with the aid of slope–area analysis, but noisy topographic data make such interpretations challenging. We present an alternative approach based on an integration of the steady‐state form of the stream power equation. The main component of this approach is a transformation of the horizontal coordinate that converts a steady‐state river profile into a straight line with a slope that is simply related to the ratio of the uplift rate to the erodibility. The transformed profiles, called chi plots, have other useful properties, including co‐linearity of steady‐state tributaries with their main stem and the ease of identifying transient erosional signals. We illustrate these applications with analyses of river profiles extracted from digital topographic datasets. Copyright © 2012 John Wiley & Sons, Ltd.     

Response of soil detachment rate to the hydraulic parameters of concentrated flow on steep loessial slopes on the Loess Plateau of China

Using hydraulic parameters is essential for describing soil detachment and developing physically based erosion prediction models. Many hydraulic parameters have been used, but the one that performs the best for describing soil detachment on steep slopes when the lateral expansion (widening) of rills is not limited has not been identified. An indoor concentrated flow scouring experiment was performed on steep loessial slopes to investigate soil detachment rates for different flow rates and slope gradients. The experiments were conducted on a slope‐adjustable plot (5 m length, 1 m width, 0.5 m depth). Sixteen combinations of 4 flow rates (10, 15, 20, and 25 L/min) and 4 slope gradients (17.6%, 26.8%, 36.4%, and 46.6%) were investigated. The individual and combined effects of slope gradient and flow hydraulic parameters on soil detachment rate were analysed. The results indicated that soil detachment rate increased with flow rate and slope gradient. Soil detachment rate varied linearly and exponentially with flow rate and slope gradient, respectively. Multivariate, nonlinear regression analysis indicated that flow depth exerted the greatest influence on the soil detachment rate, followed by unit discharge per unit width, slope gradient, and flow rate in this study. Shear stress and stream power could efficiently describe the soil detachment rate using a power equation. However, the unit stream power and unit energy of the water‐carrying section changed linearly with soil detachment rate. Stream power was an optimal hydraulic parameter for describing soil detachment. These findings improve our understanding of concentrated flow erosion on steep loessial slopes.     

Transporting capacity of overland flow on plane and on irregular beds

In this paper the transporting capacity of thin flows, in the laminar and transitional flow regime, is studied. Experiments were carried out on irregular as well as on plane beds, using two totally different set-ups. The results of these two types of experiment were convergent. In both cases, sediment concentration was clearly related to grain shear velocity and unit stream power, expressed as the product of mean velocity and slope (Yang, 1973). The data agreed with those of Kramer and Meyer (1969). For a sandy bed, the unit stream power relationship was able to predict reasonably well the sediment concentrations measured on a mulched surface. For laminar and transitional flows, both the unit stream power and the shear velocity are related in the same way to slope and unit discharge. The unit stream power is a parameter which in particular can be very easily measured and might therefore become useful in obtaining a quick estimate of the transporting capacity of a thin flow. However, before a sediment transport equation for thin flows can be developed, more information is needed about the influence of the flow regime and grain size and density.     

Improvement of streams hydro‐geomorphological assessment using LiDAR DEMs

Hydro‐geomorphological assessments are an essential component for riverine management plans. They usually require costly and time‐consuming field surveys to characterize the spatial variability of key variables such as flow depth, width, discharge, water surface slope, grain size and unit stream power throughout the river corridor. The objective of this research is to develop automated tools for hydro‐geomorphological assessments using high‐resolution LiDAR digital elevation models (DEMs). More specifically, this paper aims at developing geographic information system (GIS) tools to extract channel slope, width and discharge from 1 m‐resolution LiDAR DEMs to estimate the spatial distribution of unit stream power in two contrasted watersheds in Quebec: a small agricultural stream (Des Fèves River) and a large gravel‐bed river (Matane River). For slope, the centreline extracted from the raw LiDAR DEM was resampled at a coarser resolution using the minimum elevation value. The channel width extraction algorithm progressively increased the centerline from the raw DEM until thresholds of elevation differences and slopes were reached. Based on the comparison with over 4000 differential global positioning system (GPS) measurements of the water surface collected in a 50 km reach of the Matane River, the longitudinal profile and slope estimates extracted from the raw and resampled LiDAR DEMs were in very good agreement with the field measurements (correlation coefficients ranging from 0 · 83 to 0 · 87) and can thus be used to compute stream power. The extracted width also corresponded very well to the channel as seen from ortho‐photos, although the presence of bars in the Matane River increased the level of error in width estimates. The estimated maximum unit stream power spatial patterns corresponded well with field evidence of bank erosion, indicating that LiDAR DEMs can be used with confidence for initial hydro‐geomorphological assessments. Copyright © 2013 John Wiley & Sons, Ltd.     

Threshold response of small streams to surface coal mining,bituminous coal fields,central Pennsylvania

Stream response to surface coal mining and reclamation was studied in 29 small (0·13 to 5·72 km²) watersheds located in the bituminous coal fields of Central Pennsylvania. These basins, up to 82 per cent mined, were selected from 176 first-order tributaries of Beech Creek with similar vegetation, soil, lithology, and basin characteristics. Measurements were made at 262 cross-sections (an average of nine cross-sections per stream) of channel cross-section area, bankfull width, mean bankfull depth, dimensions of the largest moving blocks, stream slope, valley-side slope, basin area, and mined area. Observed differences in channel morphology were related to differences in extent of mining by means of scatter plots, correlation, cluster analysis, and bivariate regression. Stream response to increased peak discharge and channel shear stress produced by increased surface runoff from regraded mine spoil takes the form of enlarged channels and increases in the size of moving blocks. Large basin areas appear to dampen the effect of mining, resulting in limited channel enlargement with greater extent of mining. In contrast, where peak discharges and associated shear stresses exceed the combined erosional resistance of floodplain vegetation, colluvial blocks, and channel banks, streams adjust extensively to higher levels of mining, causing an abrupt increase in the size of transported blocks and eroded channels. In the first-order basins studied, this stepped response occurs at approximately 0·45 km² mined area and 50 per cent of the total basin area mined. For streams that have exceeded both threshold levels, disequilibrium is demonstrated by a strong, positive correlation between local stream slope and basin area. Where both threshold levels of mining are exceeded, steep channel slopes reinforce the tendency of stream cross-sections to increase with greater disturbance by mining, necessitating that these streams rapidly adjust their morphology in order to attain a new equilibrium which is compatible with the conditions imposed by mining and reclamation.     

流域水系自动提取的方法和应用

讨论由栅格数字高程模型(DEM)自动提取流域水系的原理和方法,并以西苕溪中上游流域为研究区进行了河网生成实验. 研究表明:在山地丘陵区和平均地形坡度不小于3°的区域,所生成河网具有很高的可靠性. 为了解决在平均地形坡度小于3°的平坦区域河网生成中产生的虚拟河网与自然水系偏差较大的问题,提出了利用主干河道和平原水系数字化作为约束条件的生成河网的方法,取得了与实际情况比较接近的结果,从而使水文要素的模拟更具有实际意义.     

A rapid method for simulating three-dimensional fluvial terrain

A rapid, computer-based method of simulating ‘geomorphologically-sensible’ three-dimensional terrain data by modelling landform morphology is presented. For some engineering applications such an approach, even in a simple form, is preferable to the synthesis of terrain data by purely stochastic methods, and additionally can be useful where real data sets are difficult to obtain. The approach adopted utilizes a computer program which models landscape evolution by establishing a stream network on a tilted surface, with accompanying fluvial downcutting and slope adjustment. This is achieved by an iterative mechanism that combines deterministic and stochastic processes with geomorphological theory. The end-product is a matrix of high-resolution altitude data that has been used as the terrain model for a vehicle simulation exercise.     

Forecasting sediment distribution in reservoirs during unstable conditions

A method for rapid estimation of slopes of deposited sediment in reservoirs during unstable conditions is presented. As the limiting factor determining sediment load in a reservoir is the sediment carrying capacity of a current flowing through a reservoir, it is arqued that the slope of deposited sediment must be a function of the latter. After deriving an equation relating sediment slope to stream power, the latter being regarded as representative of sediment carrying capacity, a comparison between calculated and observed sediment slopes for average annual conditions in two South African reservoirs are presented. Using this equation as basic guideline, a semi-empirical graph is then presented which relates sediment slope to a factor representing average stream power in reservoirs.     

Contrasting mechanisms of salt delivery to the stream from three different landforms in South Eastern Australia

This study explores the pathways of salt and water movement from the landscape to the stream across major landforms, in dryland areas of south eastern Australia. It was conducted at the Livingstone Creek catchment (43 km²) a sub catchment of the Kyeamba catchment, NSW, Australia. An extensive stream salinity field monitoring network between major landforms was developed and data capture occurred from 2002 to 2004. Additional measurements of surface water isotopes were also taken to independently assess responses observed from the detailed monitoring network and assist in determining the sources of water. Flow and salt mass balances were calculated across four gauging stations for each event. The stream monitoring found patterns of salt delivery to streams were consistent during four monitored stream events. In the hill slope and colluvial fill, lower sloped, meta-sediment landforms, stream salinity responses showed the classical salinity response to an event: an initial increase of salinity at the beginning of an event (due to first flush) which then diminished as a consequence of dilution. The main difference between these landforms was that the colluvial fill lower sloped meta-sediments had sodic, low permeability soils near the stream edge. This lead to (1) less variation in stream salinities during event conditions and (2) during low base flow increases in stream salinity occurred as concentrated salts from the stream banks dissolved. For the flatter, alluvial landforms, the salinity response showed quite a different and contrasting temporal pattern: salinity continued to increase and vary directly with flow during events. For all the landforms, base flow salinity increases as flow diminished after a event although salinity responses were more lagged in the alluvial landform. This different salinity pattern in the alluvial landform is attributed to (1) for event flow, the increased contributions of more saline subsurface lateral flow of soil water from the alluvial landform compared to very fresh direct surface runoff sourced from hillslope landforms upstream and (2) for base flow, seepage of near stream alluvial groundwater through the stream banks that was less saline then the base flow water sourced upstream from the hillslope landforms. The stream water isotope values confirm the above findings by showing that, in the alluvial landforms soil water contributions are important during events and that direct surface runoff with little interaction of soil water occurs from the hill slope landforms during events. Conceptual models describing salt and water movement through the different landforms and under different antecedent catchment wetness conditions are presented. These conceptual models develop our understanding of water and solute (salt) pathways through the landscape to the stream. To date, this is one of the few experimental studies in Australia connecting landscape and stream salinisation.     

The distribution of solute processes on an acid hillslope and the delivery of solutes to a stream: II. Exchangeable Al3+

In order to identify the distribution of aluminium (Al) within an acid hillslope and its release to a stream, the spatial distribution of acid ammonium oxalate extractable Al (Al_o) and exchangeable Al³⁺ have been investigated on a podzolized hillslope in Bicknoller Combe, Somerset, UK. The eluviated Al from topsoils is mainly deposited in the lower soil horizons forming podzolic B horizons, but some Al flows downslope carried by lateral throughflow. Al oxides may provide the main source of exchangeable Al³⁺ on the study slope due to high soil acidity. Examination of the spatial distribution of exchangeable Al³⁺ suggests that the slope hollow, where active convergent throughflow occurs, and the saturation wedge at the base of the slope are the main delivery routes of dissolved Al³⁺ to the stream. Divalent base cations (Ca²⁺ and Mg²⁺), supplied from atmospheric input and organic decomposition and carried by throughflow, exchange Al³⁺ via cation exchange reactions under high water content. Laterally illuviated Al oxides in the lower hollow adjacent to the saturation wedge probably provide a pool for continuous delivery of Al either as soluble or complexed forms to the stream via the saturated wedge. Copyright © 1999 John Wiley & Sons, Ltd.     

A modelling study of hyporheic exchange pattern and the sequence,size, and spacing of stream bedforms in mountain stream networks,Oregon, USA

Studies of hyporheic exchange flows have identified physical features of channels that control exchange flow at the channel unit scale, namely slope breaks in the longitudinal profile of streams that generate subsurface head distributions. We recently completed a field study that suggested channel unit spacing in stream longitudinal profiles can be used to predict the spacing between zones of upwelling (flux of hyporheic water into the stream) and downwelling (flux of stream water into the hyporheic zone) in the beds of mountain streams. Here, we use two‐dimensional groundwater flow and particle tracking models to simulate vertical and longitudinal hyporheic exchange along the longitudinal axis of stream flow in second‐, third‐, and fourth‐order mountain stream reaches. Modelling allowed us to (1) represent visually the effect that the shape of the longitudinal profile has on the flow net beneath streambeds; (2) isolate channel unit sequence and spacing as individual factors controlling the depth that stream water penetrates the hyporheic zone and the length of upwelling and downwelling zones; (3) evaluate the degree to which the effects of regular patterns in bedform size and sequence are masked by irregularities in real streams. We simulated hyporheic exchange in two sets of idealized stream reaches and one set of observed stream reaches. Idealized profiles were constructed using regression equations relating channel form to basin area. The size and length of channel units (step size, pool length, etc.) increased with increasing stream order. Simulations of hyporheic exchange flows in these reaches suggested that upwelling lengths increased (from 2·7 m to 7·6 m), and downwelling lengths increased (from 2·9 m to 6·0 m) with increase in stream order from second to fourth order. Step spacing in the idealized reaches increased from 5·3 m to 13·7 m as stream size increased from second to fourth order. Simulated downwelling lengths increased from 4·3 m in second‐order streams to 9·7 m in fourth‐order streams with a POOL–RIFFLE–STEP channel unit sequence, and increased from 2·5 m to 6·1 m from second‐ to fourth‐order streams with a POOL–STEP–RIFFLE channel unit sequence. Upwelling lengths also increased with stream order in these idealized channels. Our results suggest that channel unit spacing, size, and sequence are all important in determining hyporheic exchange patterns of upwelling and downwelling. Though irregularities in the size and spacing of bedforms caused flow nets to be much more complex in surveyed stream reaches than in idealized stream reaches, similar trends emerged relating the average geomorphic wavelength to the average hyporheic wavelength in both surveyed and idealized reaches. This article replaces a previously published version (Hydrological Processes, 19 (17), 2915–2929 (2005) [ DOI:10.1002/hyp.5790 ]. See also retraction notice DOI:10.1002/hyp.6350 Copyright © 2006 John Wiley & Sons, Ltd.