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1.
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.  相似文献   

2.
Predicting the geometry of channels and alluvial rivers is of primary importance in river engineering science. Appropriately designing channels and predicting stable river cross‐sections can decrease costs and prevent the destruction of installations and agricultural land by rivers. Consequently, researchers have applied different empirical and regression methods to achieve relations for predicting stable channel and river geometry. In this study, Group Method of Data Handling ]GMDH) models are used to predict three geometric variables of stable channels, namely width (w), depth (h) and slope (s). The effect of different input parameters, such discharge (Q), median grain size (d50) and the Shields parameter (τ*) on the GMDH models is assessed with regard to predicting stable channel geometry. The results indicate that the GMDH model with mean absolute percentage error (MAPE) of 5.53%, 4.05% and 4.89% for channel width, depth and slope prediction respectively, exhibits good accuracy. Moreover, a comparison of the GMDH models with previous theoretical equations (based on regression analysis) indicates the superiority of GMDH model performance, with error reductions of one‐fifth, one‐eighth and one‐sixth compared with the regression equations for channel width, depth and slope prediction, respectively. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

3.
A better understanding of bedrock incision mechanisms and processes is essential to the study of long‐term landscape evolution. Yet, little is known about flow dynamics in bedrock rivers, limiting our ability to make realistic predictions of local bedrock incision rates. A recent investigation of flow through bedrock canyons of the Fraser River revealed that plunging flows, defined by the downward‐directed movement of near surface flow toward the channel bed, occur in channels that have low width‐to‐depth ratios. Plunging flows occur into deep scour pools, which are often coincident with lateral constrictions and channel spanning submerged ridges (sills). A phenomenological investigation was undertaken to reproduce the flow fields observed in the Fraser canyons and to explore morphological controls on the occurrence and relative strength of plunging flow in bedrock canyons. Our observations show that the plunging flow structure can be produced along a scour pool entrance slope by accelerating the flow at the canyon entrance either over submerged sills or through lateral constrictions. Plunging flow appears to be a function of convective deceleration into a scour pool which can be enhanced by sill height, the amount of the channel width that is constricted, pool entrance slope, discharge, and a reduction in channel width‐to‐depth ratio. Plunging flow greatly enhances the potential for incision to occur along the channel bed and is an extreme departure from the assumptions of steady, uniform flow in bedrock incision models, highlighting the need for improved formulations that account for fluid flow. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

4.
Stream network morphometrics have been used frequently in environmental applications and are embedded in several hydrological models. This is because channel network geometry partly controls the runoff response of a basin. Network indices are often measured from channels that are mapped from digital elevation models (DEMs) using automated procedures. Simulations were used in this paper to study the influence of elevation error on the reliability of estimates of several common morphometrics, including stream order, the bifurcation, length, area and slope ratios, stream magnitude, network diameter, the flood magnitude and timing parameters of the geomorphological instantaneous unit hydrograph (GIUH) and the network width function. DEMs of three UK basins, ranging from high to low relief, were used for the analyses. The findings showed that moderate elevation error (RMSE of 1·8 m) can result in significant uncertainty in DEM‐mapped network morphometrics and that this uncertainty can be expressed in complex ways. For example, estimates of the bifurcation, length and area ratios and the flood magnitude and timing parameters of the GIUH each displayed multimodal frequency distributions, i.e. two or more estimated values were highly likely. Furthermore, these preferential estimates were wide ranging relative to the ranges typically observed for these indices. The wide‐ranging estimates of the two GIUH parameters represented significant uncertainty in the shape of the unit hydrograph. Stream magnitude, network diameter and the network width function were found to be highly sensitive to elevation error because of the difficulty in mapping low‐magnitude links. Uncertainties in the width function were found to increase with distance from outlet, implying that hydrological models that use network width contain greater uncertainty in the shape of the falling limb of the hydrograph. In light of these findings, care should be exercised when interpreting the results of analyses based on DEM‐mapped stream networks. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

5.
The Forestry Commission carry out drainage work in the uninclosed portion of the New Forest which includes cutting artificial drains and deepening and straightening natural channels. This paper, based on observation of operations on 53 channels for periods up to eight years between 1962 and 1975, examines the geomorphic results of such work. Of 24,000 metres of channel inspected, 24 per cent by length showed erosion, 40 per cent deposition and 36 per cent no apparent change since the work was executed. The subsequent pattern of erosion and deposition within the channels is governed largely by channel slope, but also by the nature of the superficial material and the width: depth ratio of the excavated channel. It is suggested that the choice of some preferred width: depth ratio for a given channel slope might reduce erosion. Instances are given where erosion might be described as severe, 0.5 cubic metres of material per metre of channel per year in two cases, but it appears that after a few years channels stabilize and erosion is also arrested by growth of vegetation.  相似文献   

6.
Gravel-bed rivers characteristically exhibit shallow riffles in wide sections and deeper pools where the channel becomes constricted and narrow. While rivers can adjust to changing flow and sediment supply through some combination of adjustments of channel slope, bed-surface sorting, and channel shape, the degree to which riffle-pools may adopt these changes in response to changing flows and sediment supplies remains unclear. This article presents results from a flume experiment investigating how constant- and variable-width channels adjust their morphology in response to changing flow and increased sediment supply. Two flume geometries were used: (1) constant-width and (2) variable-width, characterized by a sinusoidal pattern with a mean width equal to that of the first channel. The variable-width channel developed bed undulations in phase with the width, representing riffle-pools. The experiment consisted of three phases for each flume geometry: (1) steady flow, constant sediment supply; (2) unsteady flow, constant sediment supply; and (3) unsteady flow, doubled sediment supply. Unsteady flow was implemented in the form of repeated symmetrical stepped hydrographs, with a mean discharge equal to that in the steady flow phase. In all phases the bed and sediment supply were composed of a sand/gravel mixture ranging from 1 to 8 mm. In both the straight and variable-width channels, transitioning from steady flow to repeated hydrographs did not result in significant changes in bed morphology. The two channel geometries had different responses to increased sediment supply: the slope of the straight channel increased nearly 40%, while the variable-width channel reduced the relief between bars and pools and decreased the variability in cross-sectional elevation with a slight slope increase. Bar-pool relief varied with repeat discharge hydrographs. Pool elevation changed twice the distance of bar elevations, emphasizing the relevance of pool scour for riffle-pool self-maintenance in channels with width variations.  相似文献   

7.
The present analysis derives a stability criterion for long‐term equilibrium channel heads. The concept of finite perturbation analysis is presented, during which the surface is subjected to perturbations of a finite amplitude and resulting changes in flow path structure and slope are computed. Based on these quantities the analysis predicts whether the perturbed location is going to erode, be filled in or remain steady. The channel head is defined geometrically as the focus point of converging flow lines at the bottom of hollows. It is demonstrated that stability at the channel head grows out of the competition between the rate of flow path convergence and the degree of profile concavity. Analytical functions are derived to compute channel head‐contributing area and ‐slope, flow path convergence and profile concavity as a function of perturbation depth, distance from the crest and the initial slope. In a numerical model these quantities point to the long‐term equilibrium channel head position, which is shown to depend also on the width to length ratio of hollows. It is also demonstrated that the equilibrium channel head position is sensitive to the base‐level lowering/non‐dimensional slope length ratio and to the slope of the initial topography. Morphometrical measurements both in the field and on simulated topographies were used to test the theoretical predictions.  相似文献   

8.
开挖岩体边坡卸荷带宽度的计算方法   总被引:1,自引:0,他引:1  
卸荷带的判别与计算,直接关系到岩体边坡的长期稳定性及致灾安全性。针对均质岩体边坡,采用弹性理论楔形体力学模型,提出了开挖岩体边坡力学模型,建立了开挖岩体边坡应力的计算方法;从开挖高度、开挖坡度、台阶宽度、岩体粘聚力、内摩擦角及岩体容重等方面,通过敏感性分析,探讨了开挖岩体边坡卸荷带宽度的变化规律,据此采用量纲分析法,建立了开挖岩体边坡卸荷带宽度的计算公式。  相似文献   

9.
The Middle Reach of the Huai River (MRHR) flows northeast into the Hongzehu Lake. Before entering the Hongzehu Lake, the Huai River has a braided channel which is shallow and wide, and the riverbed has a negative slope. Based on the characteristics of the MRHR, this river reach can be divided into the following sections: a quasi-straight (or mildly curved) section, a bend section, and a braided section. The majority of the MRHR is quasi-straight. In this paper, several parameters are used to assess the geomorphology of the MRHR. Statistical analyses are performed to establish a relationship between the span length "L" and channel width "B" for different channel patterns. The relationship between the meandering length "S" and bankfull channel width "B" is also derived. Results indicate that the bankfull channel width "B", the bankfull cross sectional area "A" and the average flow depth "H" are mainly dependent on the dominant discharge in the channel. A relationship is derived that describes the denendencv of the curvature radius "R" on the dominant discharae "O". water surface slone "J"and the turning angle "α".  相似文献   

10.
The effects of basin hydrology on hydraulic geometry of channels variability for incised streams were investigated using available field data sets and models of watershed hydrology and channel hydraulics for the Yazoo River basin,USA.The study presents the hydraulic geometry relations of bankfull discharge,channel width,mean depth,cross-sectional area,longitudinal slope,unit stream power,and mean velocity at bankfull discharge as a function of drainage area using simple linear regression.The hydraulic geometry relations were developed for 61 streams,20 of them are classified as channel evolution model(CEM) Types Ⅳ and Ⅴ and 41 of them are CEM streams Types Ⅱ and Ⅲ.These relationships are invaluable to hydraulic and water resources engineers,hydrologists,and geomorphologists involved in stream restoration and protection.These relations can be used to assist in field identification of bankfull stage and stream dimension in un-gauged watersheds as well as estimation of the comparative stability of a stream channel.A set of hydraulic geometry relations are presented in this study,these empirical relations describe physical correlations for stable and incised channels.Cross-sectional area,which combines the effects of channel width and mean channel depth,was found to be highly responsive to changes in drainage area and bankfull discharge.Analyses of cross-sectional area,channel width,mean channel depth,and mean velocity in conjunction with changes in drainage area and bankfull discharge indicated that the channel width is much more responsive to changes in both drainage area and bankfull discharge than are mean channel depth or mean velocity.  相似文献   

11.
G. Kaless  L. Mao  M. A. Lenzi 《水文研究》2014,28(4):2348-2360
Downstream hydraulic geometry relationships describe the shape of alluvial channels in terms of bankfull width, flow depth, flow velocity, and channel slope. Recent investigations have stressed the difference in spatial scales associated with these variables and thus the time span required for their adjustment after a disturbance. The aim of this study is to explore the consequences in regime models considering the hypothesis that while channel width and depth adjust quickly to changes in water and sediment supply, reach slope requires a longer time span. Three theoretical models were applied. One model incorporates an extremal hypothesis (Millar RG. 2005. Theoretical regime equations for mobile gravel‐bed rivers with stable banks. Geomorphology 64 : 207–220), and the other two are fully physically based (Ikeda S, Parker G, Kimura Y. 1988. Stable width and depth of straight gravel rivers with heterogeneous bed materials. Water Resources Research 24 : 713–722; Parker G, Wilcock PR, Paola C, Dietrich W, Pitlick J. 2007. Physical basis for quasi universal relations describing bankfull hydraulic geometry of single‐thread gravel‐bed rivers. Journal of Geophysical Research 112 , DOI: 10.1029/2006JF000549). In order to evaluate the performance of models introducing the slope as an independent variable, we propose two modifications to previous models. The performance of regime models was tested against published data from 142 river reaches and new hydraulic geometry data from gravel‐bed rivers in Patagonia (Argentina) and north‐eastern Italy. Models that assume slope as a control (Ikeda et al., 1988; or Millar, 2005) predict channel depth and width reasonably well. Parker et al.'s (2007) model improved predictions because it filters the scatter in slope data with a relation slope–discharge. The extremal hypothesis model of Millar (2005) predicts comparably to the other physically based models. Millar's model was chosen to describe the recent changes in the Piave and Brenta rivers due to human intervention – mainly in‐channel gravel mining. The change in sediment supply and recovery was estimated for these rivers. This study supports the interpretation that sediment supply is the key factor guiding morphological changes in these rivers. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

12.
《水文科学杂志》2012,57(15):1918-1931
ABSTRACT

In stormwater management, it is important to accurately quantify the infiltration rates to solve urban runoff-related problems. This study proposes a method to improve estimates of the infiltration rate in permeable stormwater channels. As part of the analysis, five infiltration models were evaluated: the Kostiakov, Horton, modified Kostiakov, Philip and SCS (Soil Conservation Service) models. Infiltration tests with various initial water levels were performed on channel models with differing base width and side slopes. The results show that the addition of three parameters that describe the trapezoidal cross-sectional area, i.e. the depth, side slope and base width, in the infiltration models yielded better estimates of the infiltration rate. A comparison of the infiltration capacity values obtained from the models after the three parameters were added with those that were experimentally obtained, shows that the improved modified Kostiakov model is the most suitable model to predict infiltration rates in trapezoidal permeable stormwater channels.  相似文献   

13.
A number of methods and formulae has been proposed in the literature to estimate the discharge capacity of compound channels. When the main channel has a meandering pattern, a reduction in the conveyance capacity for a given stage is observed, which is due to the energy dissipations caused by the development of strong secondary currents and to the decrease of the main channel bed slope with respect to the valley bed slope. The discharges in meandering compound channels are usually assessed applying, with some adjustments, the same methods used in the straight compound channels. Specifically, the sinuosity of the main channel is frequently introduced to account for its meandering pattern, although some methods use different geometric parameters.In this paper the stage—discharge curves for several compound channels having identical cross-sectional area, roughness and bed slope but different planimetric patterns are numerically calculated and compared, in order to identify which geometric parameter should be efficaciously used in empirical formulae to account for meandering patterns. The simulations are carried out using a 3D finite-volume model that solves the RANS equations using a k-ε turbulence model. The numerical code is validated against experimental data collected in both straight and meandering compound channels.The numerical results show that the sinuosity is the main parameter to be accounted for in empirical formulae to assess the conveyance capacity of meandering compound channels. Comparison of the stage—discharge curves in the meandering compound channels with that obtained in a straight channel having identical cross-sectional area clearly shows the reduction of discharge due to the presence of bends in the main channel. The effect of other geometric parameters, such as the meander-belt width and the mean curvature radius, results very weak.  相似文献   

14.
Taking into account a general concept of risk parameters and knowing that natural gas provides very significant portion of energy, firstly, it is important to insure that the infrastructure remains as robust and reliable as possible. For this purpose, authors present available statistical information and probabilistic analysis related to failures of natural gas pipelines. Presented historical failure data is used to model age-dependent reliability of pipelines in terms of Bayesian methods, which have advantages of being capable to manage scarcity and rareness of data and of being easily interpretable for engineers. The performed probabilistic analysis enables to investigate uncertainty and failure rates of pipelines when age-dependence is significant and when it is not relevant. The results of age-dependent modeling and analysis of gas pipeline reliability and uncertainty are applied to estimate frequency of combustions due to natural gas release when pipeline failure occurs. Estimated age-dependent combustion frequency is compared and proposed to be used instead of conservative and age-independent estimate. The rupture of a high-pressure natural gas pipeline can lead to consequences that can pose a significant threat to people and property in the close vicinity to the pipeline fault location. The dominant hazard is combustion and thermal radiation from a sustained fire. The second purpose of the paper is to present the combustion consequence assessment and application of probabilistic uncertainty analysis for modeling of gas pipeline combustion effects. The related work includes performance of the following tasks: to study gas pipeline combustion model, to identify uncertainty of model inputs noting their variation range, and to apply uncertainty and sensitivity analysis for results of this model. The performed uncertainty analysis is the part of safety assessment that focuses on the combustion consequence analysis. Important components of such uncertainty analysis are qualitative and quantitative analysis that identifies the most uncertain parameters of combustion model, assessment of uncertainty, analysis of the impact of uncertain parameters on the modeling results, and communication of the results’ uncertainty. As outcome of uncertainty analysis the tolerance limits and distribution function of thermal radiation intensity are given. The measures of uncertainty and sensitivity analysis were estimated and outcomes presented applying software system for uncertainty and sensitivity analysis. Conclusions on the importance of the parameters and sensitivity of the results are obtained using a linear approximation of the model under analysis. The outcome of sensitivity analysis confirms that distance from the fire center has the greatest influence on the heat flux caused by gas pipeline combustion.  相似文献   

15.
IINTRODUCTIONThequestfordeterminingthedesigncharacteristicsofregimechannelshasbeengoingonforalongtime.Peoplehavebeenexcavatingnewormodifyingexistingchannelstousethemforirrigation,watersupply,navigation,floodcontrolandotherpurposes.Recently,archeologistsdiscoveredwhatiscurrentlybelievedtobetheoldestman(madecanalsystem.ItwasfoundintheareawhereMesopotamiausedtoexistanditisdatedbacktoabollt4,000BC.Ifachanne]isnotproperlydesigned,erosionofitsbanksordepositionofsedimentwithinitscross-sectionw…  相似文献   

16.
An extensive survey and topographic analysis of five watersheds draining the Luquillo Mountains in north‐eastern Puerto Rico was conducted to decouple the relative influences of lithologic and hydraulic forces in shaping the morphology of tropical montane stream channels. The Luquillo Mountains are a steep landscape composed of volcaniclastic and igneous rocks that exert a localized lithologic influence on the stream channels. However, the stream channels also experience strong hydraulic forcing due to high unit discharge in the humid rainforest environment. GIS‐based topographic analysis was used to examine channel profiles, and survey data were used to analyze downstream changes in channel geometry, grain sizes, stream power, and shear stresses. Results indicate that the longitudinal profiles are generally well graded but have concavities that reflect the influence of multiple rock types and colluvial‐alluvial transitions. Non‐fluvial processes, such as landslides, deliver coarse boulder‐sized sediment to the channels and may locally determine channel gradient and geometry. Median grain size is strongly related to drainage area and slope, and coarsens in the headwaters before fining in the downstream reaches; a pattern associated with a mid‐basin transition between colluvial and fluvial processes. Downstream hydraulic geometry relationships between discharge, width and velocity (although not depth) are well developed for all watersheds. Stream power displays a mid‐basin maximum in all basins, although the ratio of stream power to coarse grain size (indicative of hydraulic forcing) increases downstream. Excess dimensionless shear stress at bankfull flow wavers around the threshold for sediment mobility of the median grain size, and does not vary systematically with bankfull discharge; a common characteristic in self‐forming ‘threshold’ alluvial channels. The results suggest that although there is apparent bedrock and lithologic control on local reach‐scale channel morphology, strong fluvial forces acting over time have been sufficient to override boundary resistance and give rise to systematic basin‐scale patterns. Copyright © 2010 John Wiley and Sons, Ltd.  相似文献   

17.
Optimal design of artificial open channels is essential for the planning and management of irrigation projects. In this paper a modified formulation is presented for the comprehensive design of open channels considering the seepage loss, evaporation loss and land acquisition cost along with the lining and excavation cost. The resulting formulation is solved using a recent meta-heuristic optimization technique namely probabilistic global search Lausanne (PGSL). The uncertainty associated with channel design parameter may lead to the failure of canals (channels). The parametric uncertainty in open channel design is modeled using first order reliability method (FORM). A bi-objective optimization model is presented in the study which minimizes the cost and minimizes the probability of overtopping considering a probabilistic cost function as the objective function. A new approach is proposed to solve the model in a meta-heuristic environment following PGSL as the solution method. Also a chance constrained optimization model which considers overtopping probability constraint and channel capacity constraint simultaneously along with the objective of minimization of cost is propounded and solved using PGSL. The solutions obtained using coupled FORM-PGSL approach is encouraging and the method can be used for optimal and reliable design of artificial open channels.  相似文献   

18.
We explore the fluvial response to faulting in three low‐gradient, sand‐bed rivers in south‐eastern Louisiana, USA, that flow across active normal faults from footwall (upstream) to hangingwall (downstream). We calculate sinuosity, migration rate and migration direction in order to identify anomalies spatially associated with fault scarps. In two of the rivers we model one‐dimensional steady water flow to identify anomalies in surface water slope, width‐to‐depth ratio, and shear stress. In each of these rivers there is one location where flow modeling suggests potential channel incision through the footwall, as indicated by relatively high surface water slopes and shear stress values. In one of these footwall locations, the river straightens and width‐to‐depth ratios decrease, likely contributing to higher surface water slopes and shear stress. This is in contrast to previous studies that have proposed increased sinuosity across fault footwalls and decreased sinuosity across hangingwalls. However, in two hangingwall locations we also observe relatively less sinuous channels. Other planform changes on the hangingwall include topographic steering of channels along and towards the fault and one example of an avulsion. The most notable anomaly in migration rate occurs on the hangingwall of a fault where a river has cut off a meander loop. Although fluvial response to faulting varies here, comparatively large and small channels exhibit similar responses. Further, Pleistocene fault slip rates are orders of magnitude lower than the channel migration rates, suggesting that faulting should not be a major influence on the fluvial evolution. Nonetheless, notable channel anomalies exist near faults, suggesting that recent fault slip rates are higher than Pleistocene rates, and/or that low‐gradient alluvial channels are more sensitive to faulting than previous studies have suggested. Rivers appear to be influenced by faulting in this setting, however background rates of meander loop cutoff may be just as influential as faulting. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

19.
Recharge through intermittent and ephemeral stream channels is believed to be a primary aquifer recharge process in arid and semiarid environments. The intermittent nature of precipitation and flow events in these channels, and their often remote locations, makes direct flow and loss measurements difficult and expensive. Airborne and satellite optical images were interpreted to evaluate aquifer recharge due to stream losses on the Frio River in south-central Texas. Losses in the Frio River are believed to be a major contributor of recharge to the Edwards Aquifer. The results of this work indicate that interpretation of readily available remote sensing optical images can offer important insights into the spatial distribution of aquifer recharge from losing streams. In cases where upstream gauging data are available, simple visual analysis of the length of the flowing reach downstream from the gauging station can be used to estimate channel losses. In the case of the Frio River, the rate of channel loss estimated from the length of the flowing reach at low flows was about half of the loss rate calculated from in-stream gain-loss measurements. Analysis based on water-surface width and channel slope indicated that losses were mainly in a reach downstream of the mapped recharge zone. The analysis based on water-surface width, however, did not indicate that this method could yield accurate estimates of actual flow in pool and riffle streams, such as the Frio River and similar rivers draining the Edwards Plateau.  相似文献   

20.
Comprehensive empirical data of the response of unstable streams over a range of environmental conditions are unavailable. In this study, as a substitute for empirical data, a physically based numerical model of channel evolution is used in a range of numerical simulation experiments designed to predict the sensitivity of channel response to changes in control variables. The scope of the study is limited by the scope of the numerical model which applies to straight, sand-bed streams with cohesive bank materials that have been destabilized by sediment starvation and evolve towards equilibrium through bed degradation followed by channel widening. Results are presented for stable and unstable channel conditions. Stable channel depths are most sensitive to channel discharge, though the critical threshold shear stress for the entrainment of cohesive bank materials and discharge are both significant in determining the width. The sediment load, channel gradient, bank material cohesion, size of failed bank material aggregates and the initial bank height have sensitivities an order of magnitude smaller than discharge for both width and depth. Variations in bed material characteristics within the sand-size range are found to have little impact on simulated stable channel morphology. For unstable channels, the relative dominance of parameter sensitivities is examined in the context of an empirical-conceptual model of channel evolution proposed by Thorne and Osman (1988), to highlight the relationships between parameter dominance, time, and the processes and forms characterizing individual stages of channel evolution. Rates of change with time of width and depth sensitivity parameters for five tested independent variables (discharge, sediment supply, channel gradient, bank material cohesion and bed material size) are found to vary as a function of time, such that different stages of channel evolution are characterized by variations in the relative dominance of tested variables. The results support the hypothesis proposed by Thorne and Osman (1988) that the critical bank height required to initiate mass-wasting and widening may be regarded as a geomorphic threshold.  相似文献   

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