Estimation of peak streamflows through channel geometry / Estimation de pics de débit fluviatiles à l'aide de la géométrie des cours d'eau

Abstract

Knowledge of peak discharge is essential for safe and economical planning and design of hydraulic structures. In India, as in most developing countries, the majority of river basins are either sparsely gauged or not gauged at all. The gauged records are also of short length (generally 15–30 years), therefore development of robust models is necessary for estimation of streamflows. Various studies reveal that flood estimation through channel geometry is an alternative method for ungauged catchments. It is appropriate for use where flow characteristics are poorly related to catchment area and other catchment characteristics. In the present study, stream geometry parameters for 42 river sites in central-south India were used; calibration equations were developed with data for 35 stations and tested on data for the remaining seven stations. The relationships developed between mean discharge and channel geometry parameters provide an alternative technique for estimation of mean annual channel discharge.     

Regionalizing mean annual flow and daily flow variability for basin‐scale sediment and nutrient modelling

River discharges vary strongly through time and space, and quantifying this variability is fundamental to understanding and modelling river processes. The river basin is increasingly being used as the unit for natural resource planning and management; to facilitate this, basin‐scale models of material supply and transport are being developed. For many basin‐scale planning activities, detailed rainfall‐runoff modelling is neither necessary nor tractable, and models that capture spatial patterns of material supply and transport averaged over decades are sufficient. Nevertheless, the data to describe the spatial variability of river discharge across large basins for use in such models are often limited, and hence models to predict river discharge at the basin scale are required. We describe models for predicting mean annual flow and a non‐dimensional measure of daily flow variability for every river reach within a drainage network. The models use sparse river gauging data, modelled grid surfaces of mean annual rainfall and mean annual potential evapotranspiration, and a network accumulation algorithm. We demonstrate the parameterization and application of the models using data for the Murrumbidgee basin, in southeast Australia, and describe the use of these predictions in modelling sediment transport through the river network. The regionalizations described contain less uncertainty, and are more sensitive to observed spatial variations in runoff, than regionalizations based on catchment area and rainfall alone. Copyright © 2006 John Wiley & Sons, Ltd.     

Predicting wetted width in any river at any discharge

Coefficients describing at‐a‐station power‐law relationships between discharge and width were calculated by applying multilevel models to field data collected during routine hydrological monitoring at 326 gauging stations across New Zealand. These hydraulic geometry coefficients were then estimated for each of these stations using standard stepwise multiple‐linear regression models. Analysis was carried out to quantify how the relationship between width and discharge changed in relation to several available explanatory variables. All coefficients describing the at‐a‐station hydraulic geometry were found to have statistically significant relationships with catchment area. Statistically significant relationships between each of the coefficients were also found with the addition of catchment climate as an explanatory variable. Further statistically significant relationships were found when station elevation and channel slope, as well as hydrological source of flow and landcover of the upstream catchment were added to the explanatory variables. The level of confidence that can be associated with estimates of width at ungauged sites, and sites with limited data availability, was then assessed by comparing model predictions with independent paired data on observed width and discharge from 197 sites. When compared against these independent data, model predictions of width were improved with the addition of predictor variables of the hydraulic geometry coefficients. The greatest improvements were made when climate was added to catchment area as predictor variables. Minor improvements were made when all available information was used to predict width at these independent sites. Although the analysis was purely empirical, results describing relationships between hydraulic geometry coefficients and catchment characteristics corresponded well with knowledge of the processes controlling at‐a‐station hydraulic geometry of river width. Copyright © 2010 John Wiley & Sons, Ltd.     

Variation in hydraulic geometry for stable versus incised streams in the Yazoo River basin-USA

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.     

Modelling the effect of time‐dependent river dune evolution on bed roughness and stage

This paper presents an approach to incorporate time‐dependent dune evolution in the determination of bed roughness coefficients applied in hydraulic models. Dune roughness is calculated by using the process‐based dune evolution model of Paarlberg et al. ( 2009 ) and the empirical dune roughness predictor of Van Rijn ( 1984 ). The approach is illustrated by applying it to a river of simple geometry in the 1‐D hydraulic model SOBEK for two different flood wave shapes. Calculated dune heights clearly show a dependency on rate of change in discharge with time: dunes grow to larger heights for a flood wave with a smaller rate of change. Bed roughness coefficients computed using the new approach can be up to 10% higher than roughness coefficients based on calibration, with the largest differences at low flows. As a result of this larger bed roughness, computed water depths can be up to 15% larger at low flow. The new approach helps to reduce uncertainties in bed roughness coefficients of flow models, especially for river systems with strong variations in discharge with time. Copyright © 2010 John Wiley & Sons, Ltd.     

Impacts of river bed gas on the hydraulic and thermal dynamics of the hyporheic zone

Despite the presence of gas in river beds being a well known phenomenon, its potential feedbacks on the hydraulic and thermal dynamics of the hyporheic zone has not been widely studied. This paper explores hypotheses that the presence of accumulated gas impacts the hydraulic and thermal dynamics of a river bed due to changes in specific storage, hydraulic conductivity, effective porosity, and thermal diffusivity. The hypotheses are tested using data analysis and modelling for a study site on the urban River Tame, Birmingham, UK. Gas, predominantly attributed to microbial denitrification, was observed in the river bed up to around 14% by volume, and to at least 0.8 m depth below river bed. Numerical modelling indicates that, by altering the relative hydraulic conductivity distribution, the gas in the river bed leads to an increase of groundwater discharge from the river banks (relative to river bed) by a factor of approximately 2 during river low flow periods. The increased compressible storage of the gas phase in the river bed leads to an increase in the simulated volume of river water invading the river bed within the centre of the channel during storm events. The exchange volume can be more than 30% greater in comparison to that for water saturated conditions. Furthermore, the presence of gas also reduces the water-filled porosity, and so the possible depth of such invading flows may also increase markedly, by more than a factor of 2 in the observed case. Observed diurnal temperature variations within the gaseous river bed at 0.1 and 0.5 m depth are, respectively, around 1.5 and 6 times larger than those predicted for saturated sediments. Annual temperature fluctuations are seen to be enhanced by around 4 to 20% compared to literature values for saturated sediments. The presence of gas may thus alter the bulk thermal properties to such a degree that the use of heat tracer techniques becomes subject to a much greater degree of uncertainty. Although the likely magnitude of thermal and hydraulic changes due to the presence of gas for this site have been demonstrated, further research is needed into the origins of the gas and its spatial and temporal variability to enable quantification of the significance of these changes for chemical attenuation and hyporheic zone biology.     

Stochastic evolution of hydraulic geometry relations in the lower Yellow River of China under environmental uncertainties

Hydraulic geometry relations comprise a classic way to understand characteristics of a river. However, environmental changes pose large uncertainties for the reliability of such relations. In the current study, on the basis of the ordinary differential equations (ODEs) formed through linear treatment of the deterministic power-law hydraulic geometry relations, a set of stochastic differential equations (SDEs) driven by Fractional white noise and Poisson noise are developed to simulate the historical dynamic probability distributions of typical hydraulic geometry variables such as slope, width, depth, and velocity with bankfull discharge variation over time in the lower Yellow River of China. One group of possible stochastic average behaviors within the next 50 years are calculated under three different design incoming water-sediment conditions (including 300, 600, and 800 million t of annual average sediment discharge). In each part of the lower reaches, after estimation of the SDE parameters using a nonparametric maximum likelihood estimation (MLE) method, the model is carefully examined using Monte Carlo simulation as compared with the deterministic control models. The results of this comparison reveal the potential responses of hydraulic geometry characteristics to environmental disturbances, and the average trends mainly agree with the measurements. Comparisons among the three different prediction results reveal the stochastic average solution generally is greater than the deterministic solution. The results also confirm the severe negative impacts that result from the condition of 300 million t of incoming sediment, thus, pointing out the need to raise the level of river evolution alert for the lower Yellow River of China in the future. Moreover, with the help of the stochastic computation, the stream power and hydraulic width/depth ratio could be representative of an effective systematic measure for river dynamics. The proposed stochastic approach is not only important to development in the field of fluvial relations, but also beneficial to the practical design and monitoring of a river system according to specified accuracy requirements.     

Effects of River Stage and Waste Water Discharges on the Unconfined Aquifer, Hanford, Washington

This study examined the effects of river stage and waste water discharge on the unconfined aquifer near the N nuclear reactor on the U.S. Department of Energy-operated Hanford site in Washington State. River levels were statistically correlated with water-level data from 12 wells.
During the course of this study, water table elevations declined in the study area primarily as a result of a significant decrease in discharge to waste water disposal facilities, A minor contributing factor was the regional decline of the water table caused by decreasing waste water discharges upgradient of the study area.
High-frequency river-level fluctuations (e.g., short-term daily fluctuations) had good correlation with water-level variations in a well approximately 750 feet inland. Low-frequency river-level fluctuations (e.g., long-term seasonal fluctuations) had good correlation with water-level variations in a well approximately 1000 feet from the river shore. Time lags and attenuation generally increased with distance from the river as expected, with the exception of two northern wells. These two wells were relatively more responsive to river-level fluctuations at a greater distance inland from the river. This suggests that hydraulic properties (e.g., hydraulic conductivity) are a control on the aquifer reponses.
During peak river stage in June, the river level rose above water table elevations in several wells implying a temporary reversal in ground water flow direction near the river.     

Investigation of spatially distributed braided river flows using a two‐dimensional hydraulic model

This paper reports the application of a two‐dimensional hydraulic model to a braided reach of the Avoca River, New Zealand. Field measurements of water surface elevation, depth and velocity obtained at low flow were used to validate the model and to optimize the parameterization of bed friction. The main systematic trends in the measured flow variables are reproduced by the model. However, field data are characterized by greater spatial variability than model output reflecting differences in the scale of processes measured in the field and represented by the model. Additional model runs were conducted to simulate flow patterns within the study reach at five higher discharges. The purpose of these simulations was to evaluate the potential for using two‐dimensional hydraulic models to quantify the reach‐scale hydraulic characteristics of braided rivers and their dependence on discharge. Changes in flow depth and velocity with increasing discharge exhibit trends that are consistent with the results of previous field investigations, although the tendency for the wetted area of the braidplain within particular depth and velocity categories to remain fixed as discharge rises, as has been noted for several braided rivers in New Zealand, was not observed. Modelled shear stress frequency distributions fit gamma functions that incorporate a distribution shape parameter, the value of which follows clear systematic trends with rising discharge. These results illustrate both the problems of, and potential for, using two‐dimensional hydraulic models in braided river applications. This leads to something of a paradox in that while such models provide a means of generating hydraulic information that would be difficult to obtain in the field at an equivalent spatial resolution, they are, due to the problems inherent to data collection, difficult to validate conclusively. Despite this limitation, the application of spatially distributed models to investigate relationships between discharge and reach‐scale form and process variables appears to have considerable potential. Copyright © 2003 John Wiley & Sons, Ltd.     

Hydraulic visibility: Using satellite altimetry to parameterize a hydraulic model of an ungauged reach of a braided river

What hydraulic information can be gained from remotely sensed observations of a river's surface? In this study, we analyze the relationship between river bed undulations and water surfaces for an ungauged reach of the Xingu River, a first‐order tributary of the Amazon river. This braided reach is crosscut more than 10 times by a ENVISAT (ENVironmental SATellite) track that extends over 100 km. Rating curves based on a modeled discharge series and altimetric measurements are used, including the zero‐flow depth Z ₀ parameter, which describes river's bathymetry. River widths are determined from JERS (Japanese Earth Ressources Satellite) images. Hydrodynamic laws predict that irregularities in the geometry of a river bed produce spatial and temporal variations in the water level, as well as in its slope. Observation of these changes is a goal of the Surface Water and Ocean Topography satellite mission, which has a final objective of determining river discharge. First, the concept of hydraulic visibility is introduced, and the seasonality of water surface slope is highlighted along with different flow regimes and reach behaviors. Then, we propose a new single‐thread effective hydraulic approach for modeling braided rivers flows, based on the observation scales of current satellite altimetry. The effective hydraulic model is able to reproduce water surface elevations derived by satellite altimetry, and it shows that hydrodynamical signatures are more visible in areas where the river bed morphology varies significantly and for reaches with strong downstream control. The results of this study suggest that longitudinal variations of the slope might be an interesting criteria for the analysis of river segmentation into elementary reaches for the Surface Water Ocean Topography mission that will provide continuous measurements of the water surface elevations, the slopes, and the reach widths.     

Coupled 1D–3D hydrodynamic modelling,with application to the Pearl River Delta

Within the hydrodynamic modelling community, it is common practice to apply different modelling systems for coastal waters and river systems. Whereas for coastal waters 3D finite difference or finite element grids are commonly used, river systems are generally modelled using 1D networks. Each of these systems is tailored towards specific applications. Three-dimensional coastal water models are designed to model the horizontal and vertical variability in coastal waters and are less well suited for representing the complex geometry and cross-sectional areas of river networks. On the other hand, 1D river network models are designed to accurately represent complex river network geometries and complex structures like weirs, barrages and dams. A disadvantage, however, is that they are unable to resolve complex spatial flow variability. In real life, however, coastal oceans and rivers interact. In deltaic estuaries, both tidal intrusion of seawater into the upstream river network and river discharge into open waters play a role. This is frequently approached by modelling the systems independently, with off-line coupling of the lateral boundary forcing. This implies that the river and the coastal model run sequentially, providing lateral discharge (1D) and water level (3D) forcing to each other without the possibility of direct feedback or interaction between these processes. An additional disadvantage is that due to the time aggregation usually applied to exchanged quantities, mass conservation is difficult to ensure. In this paper, we propose an approach that couples a 3D hydrodynamic modelling system for coastal waters (Delft3D) with a 1D modelling system for river hydraulics (SOBEK) online. This implies that contrary to off-line coupling, the hydrodynamic quantities are exchanged between the 1D and 3D domains during runtime to resolve the real-time exchange and interaction between the coastal waters and river network. This allows for accurate and mass conserving modelling of complex coastal waters and river network systems, whilst the advantages of both systems are maintained and used in an optimal and computationally efficient way. The coupled 1D–3D system is used to model the flows in the Pearl River Delta (Guangdong, China), which are determined by the interaction of the upstream network of the Pearl River and the open waters of the South China Sea. The highly complex upstream river network is modelled in 1D, simulating river discharges for the dry and wet monsoon periods. The 3D coastal model simulates the flow due to the external (ocean) periodic tidal forcing, the salinity distribution for both dry and wet seasons, as well as residual water levels (sea level anomalies) originating from the South China Sea. The model is calibrated and its performance extensively assessed against field measurements, resulting in a mean root mean square (RMS) error of below 6% for water levels over the entire Pearl River Delta. The model also represents both the discharge distribution over the river network and salinity transport processes with good accuracy, resolving the discharge distribution over the main branches of the river network within 5% of reported annual mean values and RMS errors for salinity in the range of 2 ppt (dry season) to 5 ppt (wet season).     

Two-dimensional stochastic analysis of flow in leaky confined aquifers subject to spatial and periodic leakage

This paper addresses the issue of flow in heterogeneous leaky confined aquifers subject to leakage. The leakage into the confined aquifer is driven by spatial and periodic fluctuations of water table in an overlying phreatic aquifer. The introduction of leakage leads to non-uniformity in the mean head gradient and results in nonstationarity in hydraulic head and velocity fields. Therefore, a nonstationary spectral approach based on Fourier–Stieltjes representations for the perturbed quantities is adopted to account for the spatial variability of nonstationary head fields. Closed-form expressions for the variances of hydraulic head and specific discharge are developed in terms of statistical properties of hydraulic parameters. The results indicate that the spatiotemporal variations in leakage leads to enhanced variability of the hydraulic head and of the specific discharge, which increase with distance from any arbitrary reference point. The coefficient of leakage and the spatial structure of log transmissivity field and of the amplitude of water table fluctuation are critical in quantifying the variability of the hydraulic head and of the specific discharge.     

Developing channel and floodplain dimensions with limited data: a case study in the Amazon Basin

This research builds on the concept of hydraulic geometry and presents a methodology for estimating bankfull discharge and the hydraulic geometry coefficients and exponents for a station using limited data; only stage‐discharge and Landsat imagery. The approach is implemented using 82 streamflow gauging locations in the Amazon Basin. Using the estimated values for the hydraulic geometry relations, bankfull discharge, discharge data above bankfull and upstream drainage area at each site, relationships for estimating channel and floodplain characteristics as a function of drainage area are developed. Specifically, this research provides relationships for estimating bankfull discharge, bankfull depth, bankfull width, and floodplain width as a function of upstream drainage area in the Amazon Basin intended for providing reasonable cross‐section estimates for large scale hydraulic routing models. The derived relationships are also combined with a high resolution drainage network to develop relationships for estimating cumulative upstream channel lengths and surface areas as a function of the specified minimum channel width ranging from 2 m to 1 km (i.e. threshold drainage areas ranging from 1 to 431,000 km²). At the finest resolution (i.e. all channels greater than 2 m or a threshold area of 1 km²), the Amazon Basin contains approximately 4.4 million kilometers of channels with a combined surface area of 59,700 km². The intended use of these relationships is for partitioning total floodable area (channels versus lakes and floodplain lakes) obtained from remote sensing for biogeochemical applications (e.g. quantifying CO₂ evasion in the Amazon Basin). Copyright © 2011 John Wiley & Sons, Ltd.     

Characterization of the spatial variability of channel morphology

The spatial variability of two fundamental morphological variables is investigated for rivers having a wide range of discharge (five orders of magnitude). The variables, water‐surface width and average depth, were measured at 58 to 888 equally spaced cross‐sections in channel links (river reaches between major tributaries). These measurements provide data to characterize the two‐dimensional structure of a channel link which is the fundamental unit of a channel network. The morphological variables have nearly log‐normal probability distributions. A general relation was determined which relates the means of the log‐transformed variables to the logarithm of discharge similar to previously published downstream hydraulic geometry relations. The spatial variability of the variables is described by two properties: (1) the coefficient of variation which was nearly constant (0·13–0·42) over a wide range of discharge; and (2) the integral length scale in the downstream direction which was approximately equal to one to two mean channel widths. The joint probability distribution of the morphological variables in the downstream direction was modelled as a first‐order, bivariate autoregressive process. This model accounted for up to 76 per cent of the total variance. The two‐dimensional morphological variables can be scaled such that the channel width–depth process is independent of discharge. The scaling properties will be valuable to modellers of both basin and channel dynamics. Published in 2002 John Wiley & Sons, Ltd.     

Development of spatial regression models for predicting summer river temperatures from landscape characteristics: Implications for land and fisheries management

There is increasing demand for models that can accurately predict river temperature at the large spatial scales appropriate to river management. This paper combined summer water temperature data from a strategically designed, quality controlled network of 25 sites, with recently developed flexible spatial regression models, to understand and predict river temperature across a 3,000 km² river catchment. Minimum, mean and maximum temperatures were modelled as a function of nine potential landscape covariates that represented proxies for heat and water exchange processes. Generalised additive models were used to allow for flexible responses. Spatial structure in the river network data (local spatial variation) was accounted for by including river network smoothers. Minimum and mean temperatures decreased with increasing elevation, riparian woodland and channel gradient. Maximum temperatures increased with channel width. There was greater between‐river and between‐reach variability in all temperature metrics in lower‐order rivers indicating that increased monitoring effort should be focussed at these smaller scales. The combination of strategic network design and recently developed spatial statistical approaches employed in this study have not been used in previous studies of river temperature. The resulting catchment scale temperature models provide a valuable quantitative tool for understanding and predicting river temperature variability at the catchment scales relevant to land use planning and fisheries management and provide a template for future studies.     

Geometric and structural river channel complexity and the prediction of urban inundation

Recent research modelling floodplain inundation processes has concentrated on issues surrounding the level of physical, topographical, and numerical solver complexity needed to represent floodplain flows adequately. However, during flooding episodes the channel typically still conveys the bulk of the flow. Despite this, the effect of channel physical processes and topographic complexity on model results has been largely unexplored. To address this, the impact of channel cross‐section geometry, channel long‐profile variability and the representation of hydraulic structures on floodplain inundation are explored using a coupled dynamic 1D‐2D hydraulic model (ESTRY‐TUFLOW) of the Carlisle floods of January 2005. These simulations are compared with those from a simplified 1D‐2D model, LISFLOOD‐FP. In this case, the simpler model is sufficient to simulate the far‐field peak flood elevations. However, comparison of channel dynamics suggests that the full shallow water approximation used by ESTRY‐TUFLOW gives a more robust performance when models calibrated on maximum floodplain water elevations are used to predict channel water levels. Examination of the response of ESTRY‐TUFLOW to variations in channel geometric complexity shows that downstream variations in the channel long profile are more important than cross‐section variability for obtaining a dataset‐independent calibration. The results show, in general, that as model physical complexity is increased, calibrated parameters become less ‘effective’, and as a consequence, the values of performance measures reduce less rapidly away from the optimum value. This means that often more physically complex models are less likely to yield different optimum parameter values when calibrated on different datasets resulting in a more robust numerical model. Lastly, the inclusion of bridge structures can simulate substantial local backwatering effects, but the variability in observed water and wrack marks is such that it is not possible to discern the effect of the bridges at this site in the post‐event observational dataset. Copyright © 2011 John Wiley & Sons, Ltd.     

基于连续方程的河道水流双变量耦合演算模型

针对现有的河道水流洪水演算模型只能模拟单一变量(流量或水位)的问题,以水流连续方程和河段蓄水量的两种不同表达形式(蓄水量等于平均过水断面面积与河段长乘积,蓄水量等于河段平均流量与传播时间的乘积)为基础,对马斯京根模型进行了通用性改进,提出了双变量耦合通用演算模型.选取了四大水系(包括内陆河流和入海河流)的16个河段汛期洪水资料进行模型检验,模型验证考虑了地理范围、不同的河段特征和水力特征、洪水量级等因素,全面地检验了模型结构的合理性和模拟实际洪水的有效性.将双变量耦合通用演算模型与传统的马斯京根法进行了效果比较,结果表明双变量耦合通用演算模型的模拟精度高于马斯京根法,模拟效果比马斯京根法稳定一些,而且具有较好的通用性.     

Hydrological management strategies for the control of algal blooms in regulated lowland rivers

Reservoirs of lowland floodplain rivers with eutrophic backgrounds cause variations in the hydrological and hydraulic conditions of estuaries and low-dam reservoir areas, which can promote planktonic algae to proliferate and algal bloom outbreaks. Understanding the ecological effects of variations in hydrological and hydraulic processes in lowland rivers is important for algal bloom control. In this study, the middle and lower reaches of the Han River, China, a typical regulated lowland river with a eutrophic background, are selected. Based on the effect of hydrological and hydraulic variability on algal blooms, a hydrological management strategy for river algal bloom control is proposed. The results showed that (a) differences in river morphology and background nutrient levels cause significant differences in the critical threshold flow velocities for algal bloom outbreaks between natural river and low-dam reservoir sections; there is no uniform threshold flow velocity for algal bloom control. (b) There are significant differences in the river hydrological/hydraulic conditions between years with and without algal blooms. The average river flow, water level and velocity in years with algal blooms are significantly lower than those in years without algal blooms. (c) For different river sections where algal blooms occur and to meet the threshold flow velocities, the joint operation of cascade reservoirs and diversion projects is an effective method to prevent and control algal blooms in regulated lowland rivers. This study is expected to deepen our understanding of the ecological significance of special hydrological processes and guide algal bloom management in regulated lowland rivers.     

Velocity-discharge relationships in three lowland rivers

The use of different functional forms to describe the variation of velocity with discharge is explored for four cross-sections, nine short reaches (100-250 m), and three long reaches (2-7 km) in three lowland rivers in Lincolnshire. The traditional log-linear relationship applies to more than half the cases, the degree of correlation never falling below 0-9. Although probably more valid from a physical standpoint, the log-quadratic relationship-is only moderately successful, one problem being the position of the vertex relative to bankfull discharge. Alternative formulations based on a kinematic routing model and a partitioned log-linear model have restricted application. Rates of change of velocity with discharge are relatively high in these lowland rivers, not only at-a-station but also downstream. One explanation is that velocity becomes particularly sensitive to local slope and within-channel vegetation conditions as discharge decreases, resulting in rather low velocities at small discharges. Cross-sectional and reach-based results are compared for neighbouring stretches of river. Velocities in short reaches do not differ appreciably from those at nearby cross-sections or from those in long reaches with a length of less than 3 km. By integrating within-reach variability and avoiding the need to chose a representative cross-section, velocity measurement over short reaches is probably preferable to that at cross-sections as a basis for at-a-station hydraulic geometry.     

Bedform effect on the reorganization of surface and subsurface grain size distribution in gravel bedded channels

Quantification of river bedform variability and complexity is important for sediment transport modeling as well as for characterization of river morphology. Alluvial bedforms are shown to exhibit highly nonlinear dynamics across a range of scales, affect local bed roughness, and vary with local hydraulic, hydrologic, and geomorphic properties. This paper examines sediment sorting on the crest and trough of gravel bedforms and relates it to bed elevation statistics. The data analysed here are the spatial and temporal series of bed elevation, grain size distribution of surface and subsurface bed materials, and sediment transport rates from flume experiments. We describe surface topography through bedform variability in height and wavelength and multiscale analysis of bed elevations as a function of discharge. We further relate bedform migration to preferential distribution of coarse and fine sediments on the troughs and crests, respectively, measuring directly surface and subsurface grain size distributions, and indirectly the small scale roughness variations as estimated from high resolution topographic scans.