A coupled sediment routing and lateral migration model for gravel‐bed rivers

We describe additions made to a multi‐size sediment routing model enabling it to simulate width adjustment simultaneously alongside bed aggradation/incision and fining/coarsening. The model is intended for use in single thread gravel‐bed rivers over annual to decadal timescales and for reach lengths of 1–10 km. It uses a split‐channel approach with separate calculations of flow and sediment transport in the left and right sides of the channel. Bank erosion is treated as a function of excess shear stress with bank accretion occurring when shear stress falls below a second, low, threshold. A curvature function redistributes shear stress to either side of the channel. We illustrate the model through applications to a 5·6‐km reach of the upper River Wharfe in northern England. The sediment routing component with default parameter values gives excellent agreement with field data on downstream fining and down‐reach reduction in bedload flux, and the width‐adjustment components with approximate calibration to match maximum observed rates of bank shifting give plausible patterns of local change. The approach may be useful for exploring interactions between sediment delivery, river management and channel change in upland settings. Copyright © 2011 John Wiley & Sons, Ltd.     

Sediment mobility and bed armoring in the St Clair River: insights from hydrodynamic modeling

The lake levels in Lake Michigan‐Huron have recently fallen to near historical lows, as has the elevation difference between Lake Michigan‐Huron compared to Lake Erie. This decline in lake levels has the potential to cause detrimental impacts on the lake ecosystems, together with social and economic impacts on communities in the entire Great Lakes region. Results from past work suggest that morphological changes in the St Clair River, which is the only natural outlet for Lake Michigan‐Huron, could be an appreciable factor in the recent trends of lake level decline. A key research question is whether bed erosion within the river has caused an increase in water conveyance, therefore, contributed to the falling lake level. In this paper, a numerical modeling approach with field data is used to investigate the possibility of sediment movement in the St Clair River and assess the likelihood of morphological change under the current flow regime. A two‐dimensional numerical model was used to study flow structure, bed shear stress, and sediment mobility/armoring over a range of flow discharges. Boundary conditions for the numerical model were provided by detailed field measurements that included high‐resolution bathymetry and three‐dimensional flow velocities. The results indicate that, without considering other effects, under the current range of flow conditions, the shear stresses produced by the river flow are too low to transport most of the coarse bed sediment within the reach and are too low to cause substantial bed erosion or bed scour. However, the detailed maps of the bed show mobile bedforms in the upper St Clair River that are indicative of sediment transport. Relatively high shear stresses near a constriction at the upstream end of the river and at channel bends could cause local scour and deposition. Ship‐induced propeller wake erosion also is a likely cause of sediment movement in the entire reach. Other factors that may promote sediment movement, such as ice cover and dredging in the lower river, require further investigation. Copyright © 2012 John Wiley & Sons, Ltd.     

River ice cover influence on sediment transportation at present and under projected hydroclimatic conditions

A large number of rivers are frozen annually, and the river ice cover has an influence on the geomorphological processes. These processes in cohesive sediment rivers are not fully understood. Therefore, this paper demonstrates the impact of river ice cover on sediment transport, i.e. turbidity, suspended sediment loads and erosion potential, compared with a river with ice‐free flow conditions. The present sediment transportation conditions during the annual cycle are analysed, and the implications of climate change on wintertime geomorphological processes are estimated. A one‐dimensional hydrodynamic model has been applied to the Kokemäenjoki River in Southwest Finland. The shear stress forces directed to the river bed are simulated with present and projected hydroclimatic conditions. The results of shear stress simulations indicate that a thermally formed smooth ice cover diminishes river bed erosion, compared with an ice‐free river with similar discharges. Based on long‐term field data, the river ice cover reduces turbidity statistically significantly. Furthermore, suspended sediment concentrations measured in ice‐free and ice‐covered river water reveal a diminishing effect of ice cover on riverine sediment load. The hydrodynamic simulations suggest that the influence of rippled ice cover on shear stress is varying. Climate change is projected to increase the winter discharges by 27–77% on average by 2070–2099. Thus, the increasing winter discharges and possible diminishing ice cover periods both increase the erosion potential of the river bed. Hence, the wintertime sediment load of the river is expected to become larger in the future. Copyright © 2015 John Wiley & Sons, Ltd.     

Total load transport in gravel bed and sand bed rivers case study:Chelichay watershed

Field experiments were conducted on total load transport in the Chelichay River Basin,a mountainous catchment (1,400 km~2) located in north eastern of Iran,to evaluate total load formulas including four gravel bed rivers and a sand bed river(Qaresoo River).Gravel bed rivers in Chelichay River Basin can be grouped into two types;steep slope rivers with high shear values(Chehelchay River and Khormaloo River) and mild slope rivers with low shear values(Narmab River and Soosara River).Two depth integrating suspended load samplers(DH-48 and D-49),and two bed load samplers(Helley-Smith and BLSH) were used to measure total load.The performance is tested of 8 total load transport formulae including 4 macroscopic and 4 microscopic methods.A systematic and thorough analysis of 59 sets of data collected from sand bed river indicate that Yang and Engelund and Hansen reach to the better results, and from four gravel bed rivers confirmed that the methods of Karim and Kennedy and Engelund and Hansen yields the best results for steep slope rivers,and the methods of Einstein and Bijker are ranked highest in gradual slope rivers.     

A study of river channel pattern information recorded by grain size parameters of fluvial sediment

River channel pattern may be regarded as the outcome of streamflow, sediment load, and channel boundary conditions, as can the grain size distribution of bed material. It may therefore be expected that connections should exist between river channel pattern characteristics and the corresponding river bed material grain size parameters. Using data from some Chinese rivers, an attempt has been made to express these connections quantitatively by using statistical methods. The work demonstrates that the river's bed load can be related to the percentage of the traction subpopulation of the bed material shown by the probabilistic plot of grain size cumulative-frequency curve. The study has also revealed some correlations between the bed material grain size parameters of rivers and their channel geometry such as channel width-depth ratio and channel sinuosity. For instance, the higher the ratio of the traction to suspension subpopulation in bed material, the more sinuous, more shallow, and wider the river channel would be. Furthermore, a discrimination function has been given to distinguish between meandering and wandering braided rivers. If the existence of these relationships can be supported by data from more rivers in other regions, then by using them we can postdict palaeoriver channel geometry and its channel pattern character from fluvial sediment grain size parameters of the palaeoriver. This would open a new way to reconstruct the physicogeographical environment in which palaeorivers developed.     

Effect of changes in fine‐grained matrix on bedload sediment transport in a gravel‐bed river

While clay and silt matrices of gravel‐bed rivers have received attention from ecologists concerned variously with the deteriorating environments of benthic and hyporheic organisms, their impact on sediment entrainment and transport has been explored less. A recent increase of such a matrix in the bed of Nahal Eshtemoa, an ephemeral river of the northern Negev, has more than doubled the boundary shear stress needed to initiate bedload, from 7 N m^‐2 (τ^* = 0.027) during the flash floods of 1991–2001 to 15 N m^‐2 (τ^* = 0.059) during those of 2008–2009. The relation between bedload flux and boundary shear stress continues to be well‐defined, but it is displaced. The matrix now contains a significant amount of silt and clay size material. The reasons for the increased entrainment threshold of bedload are explored. Large‐scale laser scanning of the dry bed reveals a reduction in grain‐scale morphological roughness, while artificial in situ tests of matrix integrity indicate considerable cohesion. The implications for adopting bed material sampling strategies that account for matrix development are assessed. Copyright © 2012 John Wiley & Sons, Ltd.     

Gravel‐bed river evolution in earthquake‐prone regions subject to cycled hydrographs and repeated sediment pulses

Sediment often enters rivers in the form of sediment pulses associated with landslides and debris flows. This is particularly so in gravel‐bed rivers in earthquake‐prone mountain regions, such as Southwest China. Under such circumstances, sediment pulses can rapidly change river topography and leave the river in repeated states of gradual recovery. In this paper, we implement a one‐dimensional morphodynamic model of river response to pulsed sediment supply. The model is validated using data from flume experiments, so demonstrating that it can successfully reproduce the overall morphodynamics of experimental pulses. The model is then used to explore the evolution of a gravel‐bed river subject to cycled hydrographs and repeated sediment pulses. These pulses are fed into the channel in a fixed region centered at a point halfway down the calculational domain. The pulsed sediment supply is in addition to a constant sediment supply at the upstream end. Results indicate that the river can reach a mobile‐bed equilibrium in which two regions exist within which bed elevation and surface grain size distribution vary periodically in time. One of these is at the upstream end, where a periodic discharge hydrograph and constant sediment supply are imposed, and the other is in a region about halfway down the channel where periodic sediment pulses are introduced. Outside these two regions, bed elevation and surface grain size distribution reach a mobile‐bed equilibrium that is invariant in time. The zone of fluctuation‐free mobile‐bed equilibrium upstream of the pulse region is not affected by repeated sediment pulses under the scenarios tested, but downstream of the pulse region, the channel reaches different fluctuation‐free mobile‐bed equilibriums under different sediment pulse scenarios. The vertical bed structure predicted by the simulations indicates that the cyclic variation associated with the hydrograph and sediment pulses can affect the substrate stratigraphy to some depth. Copyright © 2017 John Wiley & Sons, Ltd.     

Particle size distribution of bed materials in the sandy river bed of alluvial rivers

The particle size distribution of bed materials in the sandy river bed of alluvial rivers is important in the study of topics such as friction, river bed evolution, erosion, and siltation. It also can reflect the dependency relation between river bed sediment and flow intensity. In this paper, the critical pattern of sediment movement in the near-wall region of a sandy river bed was analyzed. According to the principle of momentum balance, the critical settling-rising condition of bed material in a sandy river bed was found to be instantaneous turbulent velocity equal to 2.7 times the sediment settling velocity in quiescent water. Based on a vertical instantaneous turbulent velocity with a Gaussian distribution, a theoretical relation for calculating the particle size distribution of bed materials in a sandy river bed without pre-known characteristic grain sizes was developed by solving a stochastic equation. The for-mula is verified using measured data, and the results show that the proposed formula was in accordance with the measured data. This study has theoretical significance and practical value for determining the bed material particle size distribution of the sandy bed of alluvial rivers.     

THREE DIMENSIONAL NUMERICAL MODELLING OF FLOW AND SEDIMENT TRANSPORT IN RIVERS

The 3D numerical model, ECOMSED (open source code), was used to simulate flow and sediment transport in rivers. The model has a long history of successful applications to oceanic, coastal and estuarine waters. Improvements in the advection scheme, treatment of river roughness parameterization and shear stress partitioning were necessary to reproduce realistic and comparable results in a river application. To account for the dynamics of the mobile bed boundary, a model for the bed load transport was included in the code. The model reproduced observed secondary currents, bed shear stress distribution and erosion-deposition patterns on a curved channel. The model also successfully predicted the general flow patterns and sediment transport characteristics of a 1-km long reach of the River Klar?lven, located in the north of the county of V?rmland, Sweden.     

Numerical simulation of the impact of sediment supply and streamflow variations on channel grain sizes and Chinook salmon habitat in mountain drainage networks

Climatically driven changes in streamflow and hillslope sediment supply could potentially alter stream surface grain size distribution patterns and thereby impact habitat for a number of threatened and endangered in‐stream fish species. Relatively little is known about hydrograph (shape, peak flow) influence or the relative importance of chronic and episodic hillslope inputs on channel conditions. To better understand these external drivers, we calculated sediment routing through a gravel‐bedded river network using a one‐dimensional (1D) bedload transport model. We calculated changes in grain sizes and estimated Chinook salmon habitat suitability caused by a dry year and an extreme flood hydrograph, and chronic (diffusive, overland flow) or pulse (landslide, debris flow) hillslope sediment supplies. To obtain accurate channel conditions, a relatively high reference Shields stress, representative of steep mountain streams, was needed. An extreme event flood without any hillslope sediment inputs caused widespread bed coarsening and a decrease in aquatic habitat. Chronic sediment input combined with this hydrograph eliminated any changes in grain size and habitat, although when combined with a dry year flow, caused systematic bed fining. The influence of a given hydrograph therefore highly depends on the hillslope sediment supply. Regardless of the flow hydrograph or sediment pulse timing, grain size distribution or location, pulse sediment inputs did not cause widespread grain size changes despite being 100 times the total chronic input volume. Widespread and continuous hillslope sediment inputs may influence channel grain sizes and aquatic habitat more than a single discrete sediment pulse. Depending on the magnitudes of flow hydrograph and sediment supply alterations, climate change may induce no differences in grain sizes or very dramatic changes with significant consequences for long‐term sustainability. Copyright © 2013 John Wiley & Sons, Ltd.     

Effects of vegetation channel banks and gravel size on flow structure

Vegetation on river banks and bed roughness are important factors affecting flow structure, sediment transport, erosion and geomorphology in rivers. In this experimental study, the impacts of vegetation on flume walls, grain size of bed gravels and aspect ratio on characteristics of shear stress distribution, Coles' wake parameter, the kinematic energy correction factor (α) and the momentum correction factor (β) have been assessed. Reynolds stress distribution illustrates a three-layer pattern when the aspect ratio is smaller than 2. In addition, the aspect ratio and changes of vegetation affect α, β as well as the Coles' wake parameter Π.     

Downstream fining in contrasting reaches of the sand‐bedded Yellow River

Compared to downstream fining of a gravel‐bedded river, little field evidence exists to support the process of downstream fining in large, fine sand‐bedded rivers. In fact, the typically unimodal bed sediments of these rivers are thought to produce equal mobility of coarse and fine grains that may discourage downstream fining. To investigate this topic, we drilled 200 sediment cores in the channel beds of two fine‐grained sand‐bedded reaches of the Yellow River (a desert reach and a lower reach) and identified a fine surface layer (FSL) developed over a coarse subsurface layer (CSL) in the 3‐m‐thick bed deposits. In both reaches downstream, the thickness of the FSL increased, while that of the CSL decreased. Comparison of the depth‐averaged median grain sizes of the CSL and the FSL separately in both reaches shows a distinct downstream fining dependence to the median grain size, which indicates that at a large scale of 600‐800 km, the CSL shows a significant downstream fining, but the FSL shows no significant trends in downstream variations in grain size. This result shows that fine sediment supply (<0·08 mm median grain size) from upstream, combined with lateral fine sediment inputs from tributaries and bank erosion, can cause a rapid fining of the downstream channel bed surface and can develop the FSL layer. However, in the desert reach, lateral coarse sediment supply (>0·08 mm median grain size) from wind‐borne sediments and cross‐desert tributaries can interrupt the FSL and coarsen the channel bed surface locally. Copyright © 2011 John Wiley & Sons, Ltd.     

The influence of lithology on channel geometry and bed sediment organization in mountainous hillslope-coupled streams

Sediment transport and channel morphology in mountainous hillslope-coupled streams reflect a mixture of hillslope and channel processes. However, the influence of lithology on channel form and adjustment and sediment transport remains poorly understood. Patterns of channel form, grain size, and transport capacity were investigated in two gravel-bed streams with contrasting lithology (basalt and sandstone) in the Oregon Coast Range, USA, in a region in which widespread landslides and debris flows occurred in 1996. This information was used to evaluate threshold channel conditions and channel bed adjustment since 1996. Channel geometry, slope, and valley width were measured or extracted from LiDAR and sediment textures were measured in the surface and subsurface. Similar coarsening patterns in the first few kilometres of both streams indicated strong hillslope influences, but subsequent downstream fining was lithology-dependent. Despite these differences, surface grain size was strongly related to shear stress, such that the ratio of available to critical shear stress for motion of the median surface grain size at bankfull stage was around one over most of the surveyed lengths. This indicated hydraulic sorting of supplied sediment, independent of lithology. We infer a cycle of adjustment to sediment delivered during the 1996 flooding, from threshold conditions, to non-alluvial characteristics, to threshold conditions in both basins. The sandstone basin can also experience complete depletion of the gravel-size alluvium to sand size, leading to bedrock exposure because of high diminution rates. Although debris flows being more frequent in a basalt basin, this system will likely display threshold-like characteristics over a longer period, indicating that the lithologic control on channel adjustment is driven by differences in rock competence that control grain size and available gravel for bed load transport. © 2020 John Wiley & Sons, Ltd.     

筑坝拦截对黑河河道沉积物粒度空间分布的影响

河流沉积物对流域环境变化具有敏感响应,其粒度参数能反映沉积环境中物质来源和水动力环境.本文以黑河流域上中游为研究区域,探究河流沉积物粒度对流域环境变化的响应.从黑河上中游干流22个主要控制断面采集河床沉积物样品,采用筛分法和吸管法对沉积物样品粒度参数进行测定,并分析其空间分布规律对筑坝拦截为主的环境改变响应.研究结果表明：受梯级水库建设影响,黑河上中游泥沙粒径大小差异显著.干流库区泥沙粒径较自然河段明显减小,分选很好,呈正偏或极正偏尖锐分布,而且在库区不同沉积高度上表现出分层沉积特征;坝下游河段因遭受强烈冲刷,较自然河段泥沙粒径粗化显著,分选变差,偏态趋向极正偏,峰态尖锐化;水库回水区受水库壅水及下泄清水的双重制约,泥沙粒度参数介于自然河段和坝下游河段之间,整体分选中等,呈极正偏尖锐分布;沉积环境分析表明,上游支流河段沉积物粒度特征受泥沙供给和物源特征的影响较水动力条件显著,干流河段沉积物粒度特征主要受水动力条件控制.研究结果既符合河流上中游沉积物粒度分布规律,也反映了河流环境变化对沉积物粒度组成的影响.     

Radio‐tracking gravel particles in a large braided river in New Zealand: a field test of the stochastic theory of bed load transport proposed by Einstein

Hans A. Einstein initiated a probabilistic approach to modelling sediment transport in rivers. His formulae were based on theory and were stimulated by laboratory investigations. The theory assumes that bed load movement occurs in individual steps of rolling, sliding or saltation and rest periods. So far very few attempts have been made to measure stochastic elements in nature. For the first time this paper presents results of radio‐tracing the travel path of individual particles in a large braided gravel bed river: the Waimakariri River of New Zealand. As proposed by Einstein, it was found that rest periods can be modelled by an exponential distribution, but particle step lengths are better represented by a gamma distribution. Einstein assumed an average travel distance of 100 grain‐diameters for any bed load particle between consecutive points of deposition, but larger values of 6·7 m or 150 grain‐diameters and 6·1 m or 120 grain‐diameters were measured for two test particle sizes. Together with other available large scale field data, a dependence of the mean step length on particle diameter relative to the D₅₀ of the bed surface was found. During small floods the time used for movement represents only 2·7% of the total time from erosion to deposition. The increase in percentage of time being used for transport means that it then has to be regarded in stochastic transport models. Tracing the flow path of bed load particles between erosion and deposition sites is a step towards explaining the interactions between sediment transport and river morphology. Copyright © 2001 John Wiley & Sons, Ltd.     

Development of a river delta: a case study of Cimanuk river mouth,Indonesia

This paper describes delta development processes with particular reference to Cimanuk Delta in Indonesia. Cimanuk river delta, the most rapidly growing river delta in Indonesia, is located on the northern coast of Java Island. The delta is subject to ocean waves of less than 1 m height due to its position in the semi‐enclosed Java Sea in the Indonesian archipelago. The study has been carried out using a hydrodynamic model that accounts for sediment movement through the rivers and estuaries. As an advanced approach to management of river deltas, a numerical model, namely MIKE‐21, is used as a tool in the management of Cimanuk river delta. From calibration and verification of hydrodynamic model, it was found that the best value of bed roughness was 0·1 m. For the sediment‐transport model, the calibration parameters were adjusted to obtain the most satisfactory results of suspended sediment concentration and volume of deposition. By comparing the computed and observed data in the calibration, the best values of critical bed shear stress for deposition, critical bed shear stress for erosion and erosion coefficient were 0·05 N m^?2, 0·15 N m^?2, and 0·00001 kg m^?2 s^?1, respectively. The calibrated model was then used to analyse sensitivity of model parameters and to simulate delta development during the periods 1945–1963 and 1981–1997. It was found that the sensitive model parameters were bed shear stresses for deposition and erosion, while the important model inputs were river suspended sediment concentration, sediment characteristics and hydrodynamic. The model result showed reasonable agreement with the observed data. As evidenced by field data, the mathematical model proves that the Cimanuk river delta is a river‐dominated delta because of its protrusion pattern and very high sediment loads from the Cimanuk river. It was concluded that 86% of sediment load from the Cimanuk river was deposited in the Cimanuk delta. Copyright © 2008 John Wiley & Sons, Ltd.     

A coupled hierarchical modeling approach to simulating the geomorphic response of river systems to anthropogenic climate change

Anthropogenic climate change is expected to change the discharge and sediment transport regime of river systems. Because rivers adjust their channels to accommodate their typical inputs of water and sediment, changes in these variables can potentially alter river morphology. In this study, a hierarchical modeling approach was developed and applied to examine potential changes in reach‐averaged bedload transport and spatial patterns of erosion and deposition for three snowmelt‐dominated gravel‐bed rivers in the interior Pacific Northwest. The modeling hierarchy was based on discharge and suspended‐sediment load from a basin‐scale hydrologic model driven by a range of downscaled climate‐change scenarios. In the field, channel morphology and sediment grain‐size data for all three rivers were collected. Changes in reach‐averaged bedload transport were estimated using the Bedload Assessment of Gravel‐bedded Streams (BAGS) software, and the Cellular Automaton Evolutionary Slope and River (CAESAR) model was used to simulate the spatial pattern of erosion and deposition within each reach to infer potential changes in channel geometry and planform. The duration of critical discharge was found to control bedload transport. Changes in channel geometry were simulated for the two higher‐energy river reaches, but no significant morphological changes were found for a lower‐energy reach with steep, cohesive banks. Changes in sediment transport and river morphology resulting from climate change could affect the management of river systems for human and ecological uses. Copyright © 2015 John Wiley & Sons, Ltd.     

Bed material transport estimate in large gravel‐bed rivers using the virtual velocity approach

This paper reports on a first attempt of using the virtual velocity approach to assess sediment mobility and transport in two wide and complex gravel‐bed rivers of northern Italy. Displacement length and virtual velocity of spray‐painted tracers were measured in the field. Also, the thickness of the sediment active layer during floods was measured using scour chains and post‐flood morphological changes as documented by repeated survey of channel cross‐sections. The effects of eight and seven floods were studied on the Tagliamento and Brenta Rivers, where 259 and 277 spray‐painted areas were surveyed, respectively. In the Tagliamento River 36% of the spray‐painted areas experienced partial transport, whereas in the Brenta River this accounted for 20%. Whereas, full removal/gravel deposition was observed on 37% and 26% of these areas on the Tagliamento and Brenta Rivers, respectively. The mean displacement length of particles, the thickness of the active layer and the extent of partial transport are well correlated with the dimensionless shear stress. The virtual velocity approach allowed calculation of bed material transport over a wide range of flood magnitudes. Annual coarse sediment transport was calculated up to 150 for the Tagliamento, and 30 × 10³  m³ yr^?1 for the Brenta. The outcomes of this work highlight the relevance of partial transport condition, as it could represent more than 70% of the total bed material transported during low‐magnitude floods, and up to 40% for near‐bankfull events. Results confirm that bed material load tends to be overestimated by traditional formulas. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical simulation of hydrodynamic characteristics and bedload transport in cross sections of two gravel-bed rivers based on one-dimensional lateral distribution method

Accurate evaluation and prediction of bedload transport are crucial in studies of fluvial hydrodynamic characteristics and river morphology.This paper presents a one-dimensional numerical model based on the one-dimensional lateral distribution method(1 D-LDM) and six classic bedload transport formulae that can be used to simulate hydrodynamic characteristics and bedload transport discharge in cross sections.Two gravel-bed rivers,i.e.the Danube River located approximately 70 km downstream from Bratislava in Slovakia and the Tolten River in south of Chile are used as examples.In the 1 D-LDM,gravity,bed shear stress,turbulent diffusion,and secondary flow are included to allow for accurate predictions of flow velocity and consequently bed shear stress in the cross sections.Six classic formulae were applied to evaluate the non-dimensional bedload transport rate,and the bedload transport discharge through a river cross section is obtained by integrating the bedload transport rate over the width of the cross section.The results show that the root mean square error(RMSE) and mean absolute error(MAE) of velocity and water discharge were less than 8% of the observed magnitude,while the correlation coefficient between model predictions and observations was close to unity.The formulae proposed by Ashida and Michiue(1972),in which particle collision with the bed is taken into account,and by Camenen and Larson(2005),which allows for yielding a non-zero bedload transport rate even when the bed shear stress is smaller than the critical bed shear stress value,appeared to be more appropriate for predicting the observed bedload transport rate in the studied cross sections of two gravel-bed rivers.If non-uniform sediment mixtures were considered,the bedload transport discharge through a cross-section could change considerably by up to 22.5% of the observed magnitude.The relations proposed by Ashida and Michiue(1972) and Egiazaroff(1965) for parameterizing the hiding factor yielded more realistic model predictions in comparison with observations for the measured data set collected for the Tolten River,while the one proposed by Wilcock and Crowe(2003) performs the best for the data set measured for the Danube River.