DEVELOPMENT AND APPLICATION OF AN EFFICIENT METHOD TO RIVER DISCHARGE MEASUREMENT

1 INTRODUCTION There are 129 rivers in Taiwan. Most of them are short and steep with small drainage basins and rapid flows. Heavy rains and flood flows usually carry large amount of sediment. The specific peak discharge (peak discharge per unit drainage area) in Taiwan has the highest value in the world. For example, the specific peak discharge of Wu River in central Taiwan is 10.5 cms/km2, which is about 618 times that of Yangtze River in China and 35 times that of Sinno River i…     

Relationship between discharge,velocity and flow area for rills eroding loose,non-layered materials

A relationship between discharge, flow velocity and flow area in rills is established using data from four field and laboratory studies. The proposed relationship is shown to predict successfully flow velocities measured in six other studies. Although slopes range from 0.035 to 0.45 and soil materials range from stony sands over silt loams to vertisols, mean flow velocity can be well predicted from discharge alone. Thus, there is no important influence of slope and/or soil material characteristics on flow velocities in rills. The proposed relationship may be used to improve performance of deterministic flow routing models when applied to rilled catchments. Furthermore, it allows the calculation of unit stream power, which has been shown to be related to the transporting capacity of overland flow, in terms of slope and discharge.     

A fast method of flood discharge estimation

Discharge, especially during flood periods, is among the most important information necessary for flood control, water resources planning and management. Owing to the high flood velocities, flood discharge usually cannot be measured efficiently by conventional methods, which explains why records of flood discharge are scarce or do not exist for the watersheds in Taiwan. A fast method of flood discharge estimation is presented. The greatest advantage of the proposed method is its application to estimate flood discharge that cannot be measured by conventional methods. It has as its basis the regularity of open‐channel flows, i.e. that nature maintains a constant ratio of mean to maximum velocities at a given channel section by adjusting the velocity distribution and the channel geometry. The maximum velocity at a given section can be determined easily over a single vertical profile, which tends to remain invariant with time and discharge, and can be converted to the mean velocity of the entire cross‐section by multying by the constant ratio. Therefore the mean velocity is a common multiple of maximum velocity and the mean/maximum velocity ratio. The channel cross‐sectional area can be determined from the gauge height, the water depth at the y‐axis or the product of the channel width multiplied by the water depth at the y‐axis. Then the most commonly used method, i.e. the velocity–area method, which determines discharge as the product of the cross‐sectional area multiplied by mean velocity, is applied to estimate the flood discharge. Only a few velocity measurements on the y‐axis are necessary to estimate flood discharge. Moreover the location of the y‐axis will not vary with time and water stage. Once the relationship of mean and maximum velocities is established, the flood estimation can be determined efficiently. This method avoids exposure to hazardous environments and sharply reduces the measurement time and cost. The method can be applied in both high and low flows in rivers. Available laboratory flume and stream‐flow data are used to illustrate accuracy and reliability, and results show that this method can quickly and accurately estimate flood discharges. Copyright © 2004 John Wiley & Sons, Ltd.     

VELOCITY–DISCHARGE RELATIONSHIPS DERIVED FROM DYE TRACER EXPERIMENTS IN GLACIAL MELTWATERS: IMPLICATIONS FOR SUBGLACIAL FLOW CONDITIONS

Repeated dye tracer tests were undertaken from individual moulins at Haut Glacier d'Arolla, Switzerland, over a number of diurnal discharge cycles during the summers of 1989–1991. It was hoped to use the concepts of at-a-station hydraulic geometry to infer flow conditions in subglacial channels from the form of the velocity–discharge relationships derived from these tests. The results, however, displayed both clockwise and anticlockwise velocity–discharge hysteresis, in addition to the simple power function relationship assumed in the hydraulic geometry approach. Clockwise hysteresis seems to indicate that a moulin drains into a small tributary channel rather than directly into an arterial channel, and that discharges in the two channels vary out of phase with each other. Anticlockwise hysteresis is accompanied by strong diurnal variations in the value of dispersivity derived from the dye breakthrough curve, and is best explained by hydraulic damming of moulins or sub/englacial passageways. Despite the complex velocity–discharge relationships observed, some indication of subglacial flow conditions may be obtained if tributary channels comprise only a small fraction of the drainage path and power function velocity–discharge relationships are derived from dye injections conducted during periods when the supraglacial discharge entering the moulin and the bulk discharge vary in phase. Analyses based on this premise suggest that both open and closed channel flow occur beneath Haut Glacier d'Arolla, and that flow conditions are highly variable at and between sites.     

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.     

Testing a theoretical resistance law for overland flow on a stony hillslope

Overland flow, sediments, and nutrients transported in runoff are important processes involved in soil erosion and water pollution. Modelling transport of sediments and chemicals requires accurate estimates of hydraulic resistance, which is one of the key variables characterizing runoff water depth and velocity. In this paper, a new theoretical power–velocity profile, originally deduced neglecting the impact effect of rainfall, was initially modified for taking into account the effect of rainfall intensity. Then a theoretical flow resistance law was obtained by integration of the new flow velocity distribution. This flow resistance law was tested using field measurements by Nearing for the condition of overland flow under simulated rainfall. Measurements of the Darcy–Weisbach friction factor, corresponding to flow Reynolds number ranging from 48 to 194, were obtained for simulated rainfall with two different rainfall intensity values (59 and 178 mm hr⁻¹). The database, including measurements of flow velocity, water depth, cross-sectional area, wetted perimeter, and bed slope, allowed for calibration of the relationship between the velocity profile parameter Γ, the slope steepness s, and the flow Froude number F, taking also into account the influence of rainfall intensity i. Results yielded the following conclusions: (a) The proposed theoretical flow resistance equation accurately estimated the Darcy–Weisbach friction factor for overland flow under simulated rainfall, (b) the flow resistance increased with rainfall intensity for laminar overland flow, and (c) the mean flow velocity was quasi-independent of the slope gradient.     

Mechanisms responsible for streamflow generation on a small,salt-affected and deeply weathered hillslope

This paper considers the contributions of overland flow, throughflow and deep seepage to the generation of streamflow in a salt-affected, deeply weathered landscape. Runoff mechanisms on a small hillslope in south-western Australia were dependent on the extent and development of variable source areas. In winter, streamflow generation was controlled by returnflow, saturation overland flow and throughflow. In summer, post-ponding, infiltration-excess and saturation overland flow dominated. The extent of the variable source area and the magnitude of streamflow were due to antecedent soil moisture, rainfall and slope morphology. Concave hillslope sections accumulated soil moisture due to both saturated and unsaturated lateral flow processes. Throughflow provided the mechanism and vehicle for solute movement from the groundwater discharge area to the stream. However, discharge from the deep aquifer was the primary mechanism responsible for soil salinity and maintaining the core of the variable source area. Estimates of throughflow which only take account of soil-water movement and disregard returnflow, will underestimate the magnitude of throughflow.     

CORRECTION FACTORS IN THE DETERMINATION OF MEAN VELOCITY OF OVERLAND FLOW

The velocity of overland flow has been conventionally measured using tracers, but it is difficult to measure the mean flow velocity directly because the centroid of the tracer plume is not easily identified. Consequently, previous investigators have measured the velocity of the leading edge of the plume and multiplied it by a correction factor α to obtain an estimate of mean velocity. An alternative method is to measure the velocity of the peak concentration in the tracer plume and multiply this velocity by another correction factor β to estimate mean velocity. To investigate the controls of α and β and develop predictive models for these correction factors, 40 experiments were performed in a flume with a mobile sand bed. Multiple regression analyses reveal that both α and β vary inversely with slope and directly with Reynolds number. The derived regression equations may be used to calculate the mean velocity of other shallow overland flows, at least within the range of slope and Reynolds number for which the equations were developed. In the experiments, slope ranged from 2.7;° to 10° and Reynolds number from 1900 to 12 600.     

Seasonal vegetation and management influence overland flow velocity and roughness in upland grasslands

There is considerable interest in how headwater management may influence downstream flood peaks in temperate humid regions. However, there is a dearth of data on flow velocities across headwater hillslopes and limited understanding of whether surface flow velocity is influenced by seasonal changes in roughness through vegetation cycles or management. A portable hillslope flume was used to investigate overland flow velocities for four common headwater grassland habitats in northern England: Low-density Grazing, Hay Meadow, Rank Grassland and Juncus effusus Rush pasture. Overland flow velocity was measured in replicate plots for each habitat, in response to three applied flow rates, with the experiments repeated during five different periods of the annual grassland cycle. Mean annual overland flow velocity was significantly lower for the Rank Grassland habitat (0.026 m/s) followed by Low-density Grazing and Rushes (0.032 and 0.029 m/s), then Hay Meadows (0.041 m/s), which had the greatest mean annual velocity (examples from 12 L/min flow rate). Applying our mean overland flow velocities to a theoretical 100 m hillslope suggests overland flow is delayed by >1 hr on Rank Grassland when compared to Hay Meadows in an 18 mm storm. Thus grassland management is important for slowing overland flow and delaying peak flows across upland headwaters. Surface roughness was also strongly controlled by annual cycles of vegetation growth, decay, grazing and cutting. Winter overland flow velocities were significantly higher than in summer, varying between 0.004 m/s (Rushes, November) and 0.034 m/s (Rushes, June); and velocities significantly increased after cutting varying between 0.006 m/s (Hay meadows, July) and 0.054 m/s (Hay meadows, September). These results show that seasonal vegetation change should be incorporated into flood modelling, as cycles of surface roughness in grasslands strongly modify overland flow, potentially having a large impact on downstream flood peak and timing. Our data also showed that Darcy-Weisbach roughness approximations greatly over-estimated measured flow velocities.     

Effect of saltating sediment on flow resistance and bed roughness in overland flow

The acceleration of saltating grains by overland flow causes momentum to be transferred from the flow to the grains, thereby increasing flow resistance and bed roughness. To assess the impact of saltating sediment on overland flow hydraulics, velocity profiles in transitional and turbulent flows on a fixed sand-covered bed were measured using hot-film anemometry. Five discharges were studied. At each discharge, three flows were measured: one free of sediment, one with a relatively low sediment load, and one with a relatively high sediment load. In these flows from 83 to 90 per cent of the sediment was travelling by saltation. As a result, in the sediment-laden flows the near-bed velocities were smaller and the velocity profiles steeper than those in the equivalent sediment-free flows. Sediment loads ranged up to 87·0 per cent of transport capacity and accounted for as much as 20·8 per cent of flow resistance (measured by the friction factor) and 89·7 per cent of bed roughness (measured by the ratio of the roughness length to median grain diameter). It is concluded that saltating sediment has a considerable impact on overland flow hydraulics, at least on fixed granular beds. Saltation is likely to have a relatively smaller effect on overland flow on natural hillslopes and agricultural fields where form and wave resistance dominate. Still, saltation is generally of greater significance in overland flow than in river flow, and for this reason its effect on overland flow hydraulics is deserving of further study. © 1998 John Wiley & Sons, Ltd.     

A study on limit velocity and its mechanism and implications for alluvial rivers

Observations from field investigations showed that flow velocity greater than 3 m/s rarely occurs in nature, and high flow velocity stresses the bio-community and causes instability to the channel. For alluvial rivers without strong human disturbance, the flow velocity varies within a limited range, gen-erally below 3 m/s, while the discharge and wet area may vary in a range of several orders. This phe-nomenon was studied by analyzing hydrological data, including daily average discharge, stage, cross sections, and sediment concentration, collected from 25 stations on 20 rivers in China, including the Yangtze, Yellow, Songhua, Yalu, Daling, and Liaohe Rivers. The cross-sectional average velocity was cal-culated from the discharge and wet area using the continuity equation. For alluvial rivers, the wet cross section may self-adjust in accordance with the varying flow discharge so that the flow velocity does not exceed a limit value. In general, the average velocity increases with the discharge increase at low dis-charge. As the discharge exceeds the discharge capacity of the banks, any further increase in discharge does not result in a great increase in velocity. The average velocity approaches an upper limit as the discharge increases. This limit velocity, in most cases, is less than 3 m/s. Human activities, especially levee construction, disturb the limit velocity law for alluvial rivers. In these cases, the average velocity may be approximately equal to or higher than the limit velocity. The limit velocity law has profound morphological and ecological implications on alluvial rivers and requires further study. Rivers should be trained and managed by mimicking natural processes and meeting the limit velocity law, so as to maintain ecologically-sound and morphological stability.     

Accelerating shear velocity in gravel-bed channels

Abstract

The behaviour of the shear velocity along a gravel-bed channel is investigated experimentally in the presence of a negative pressure gradient (accelerating flow). Different methods of estimation of the shear velocity, derived from vertical profiles of the mean longitudinal point velocity, are examined and a new method is proposed. Results show that the proposed method of estimation is comparable to the St Venant and Clauser's methods. At a specific cross section, for constant bottom slope and relative roughness, shear velocity increases with discharge.     

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.     

Estimation of ecological high flow

Floods can destroy fish habitat. During a flood a fish has to seek shelters (refuges) to survive. It is necessary to know the maximum discharge that the fish can sustain against the strong current. Ecological and hydraulic engineers can simulate the flow condition of high flow for designing the refuge when restoring and enhancing the rivers are needed. Based on the average ratio of the mean and maximum velocities invariant with time, discharge and water level, this paper tries to introduce the concept of ecological high flow. The mean‐maximum velocity ratio can be used to estimate the mean velocity of the river. If the maximum velocity of the cross section is replaced by the maximum sustained swimming speeds of fish, the mean velocity of ecological high flow can be calculated with the constant ratio. The cross‐sectional area can be estimated by the gage height. Then the ecological high flow can be estimated as the product of mean velocity of ecological high flow multiplied by the cross‐sectional area. The available data of the upstream of the Dacha River where is the habitat of the Formosan landlocked salmon were used to illustrate the estimation of the ecological high flow. Any restoration project at Sonmou that try to improve the stream habitat can use the ecological high flow to design the hydraulic structure at suitable location to offer refuges for the Formosan landlocked salmon that is an endangered species in Taiwan Copyright © 2005 John Wiley & Sons, Ltd.     

The influence of river discharge on tidal damping in alluvial estuaries

The tidal range, the difference between high water level and low water level, along an alluvial estuary can be described by Savenije's analytical equation [Journal of Hydrology 243 (2001) 205-215] analytical equation. This equation was derived from the complete St Venant equations in a Lagrangian reference frame. In the derivation of that equation the effect of river discharge was disregarded. Measurements in the Schelde Estuary show that this assumption is only valid in the lower part of the estuary, but that in the upper part the river discharge has an influence on tidal damping. In the downstream part of the estuary, where the cross-sectional area is large compared to the cross-sectional area of the river, it is correct to disregard the river discharge. However, in the upstream part of the estuary, where the cross-sectional area approaches that of the river, the fresh water discharge gains importance over the tidal flow and affects the tidal range. In this paper, the derivation of the analytical equation is expanded to include the effect of the river discharge. It is demonstrated that the river discharge can have a considerable influence on tidal damping in the upper reach of the estuary. The river discharge affects tidal damping primarily through friction. A critical point along the estuary is the point where there is a single slack, upstream of which the fresh water velocity is larger than the tidal velocity. The location of this point varies with the river discharge. From that point onwards the effect of river discharge on damping is dominant. It is the point where the estuary becomes primarily of riverine character.     

Modelling stage–discharge relationships in anastomosed bedrock-influenced sections of the Sabie River system

Flow dynamics in a bedrock-influenced river system, the Sabie River, South Africa, have been found to be significantly different from those in temperate alluvial systems. The lack of lateral water connectivity leads to multiple bedrock distributaries with varying water surface elevations across a cross-section. Distributary activation is dependent on upstream breaching of bedrock barriers between distributaries by rising discharge. Where measurement of individual stage–discharge relationships in each distributary was not possible, a ‘Multiple Stage’ model was developed to predict hydraulic conditions in each distributary, using a single measured rating curve and knowledge of individual distributary water surface elevations at a low flow. Use of the ‘Multiple Stage’ model has enabled realistic prediction of channel geometry and hydraulic variables, that accounts for the different stages found in bedrock-influenced sections, yet is not prohibitively data intensive. Predicted ‘Multiple Stage’ results for maximum depth and velocity demonstrate the vast improvement on modelling flow dynamics, when compared to the conventional assumption of a single stage representing the whole cross-section. © 1998 John Wiley & Sons, Ltd.     

Uncertainty analysis of flow velocity estimation by a simplified entropy model

The velocity field in a river flow cross‐sectional area can be determined by applying entropy as done in 1978 by Chiu, who developed a two‐dimensional model of flow velocity based on the knowledge of maximum velocity, u_max, and the dimensionless entropic parameter, characteristic of the river site. This is appealing in the context of discharge monitoring, particularly for high floods, considering that u_max occurs in the upper portion of flow area and can be easily sampled, unlike velocity in the lower portion of flow area. The simplified form of Chiu's entropy‐based velocity model, proposed in 2004 by Moramarco et al., has been found to be reasonably accurate for determining mean flow velocity along each vertical sampled in the flow area, but no uncertainty analysis has been reported for this simplified entropy‐based velocity model. This study, therefore, performed uncertainty analysis of the simplified model following a procedure proposed by Misirli et al. in 2003. The flow velocity measurements at the Rosciano River section along the Chiascio River, central Italy, carried out for a period spanning 20 years were used for this purpose. Results showed that the simplified entropy velocity model was able to provide satisfactory estimates of velocity profiles in the whole flow area and the 95% confidence bands for the computed estimated mean vertical velocity were quite representative of observed values. In addition, using these 95% confidence bands, it was possible to have an indication of the uncertainty in the determination of mean cross‐sectional flow velocity as well. Copyright © 2012 John Wiley & Sons, Ltd.     

Steady flow patterns in saturated and unsaturated,isotropic soils

A comprehensive analysis of steady flow patterns in saturated and unsaturated, possibly heterogeneous, isotropic soils is presented. It is shown that, at any point, the divergence of the unit tangent vector field to the streamlines is equal to the directional derivative along the streamlines of the orthogonal cross-sectional area of an infinitesimal stream tube divided by that area and also equal to the mean curvature of the surface of constant total head. Expressions are derived for the distribution of the flux, the water content, the velocity, the hydraulic conductivity, the total head, and the pressure head along a stream line or an infinitesimal, stream tube. Among the results is a simpler derivation, further interpretation, and extension of earlier work on calculating the hydraulic conductivity distribution from detailed measurements of the total head distribution in combination with measurements of the hydraulic conductivity at a few locations. In the last section, the jumps of various quantities at an interface are discussed.     

Roughness coefficients and velocity estimation in well-inundated sheet and rilled overland flow without strongly eroding bed forms

Even with the flow of water over a soil surface in which roughness elements are well inundated, and in less erosive situations where erosional bed forms are not pronounced, the magnitude of resistance coefficients in equations such as those of Darcy–Weisbach, Chezy or Manning vary with flow velocity (at least). Using both original laboratory and field data, and data from the literature, the paper examines this question of the apparent variation of resistance coefficients in relation to flow velocity, even in the absence of interaction between hydraulics and resulting erosional bed forms. Resistance equations are first assessed as to their ability to describe overland flow velocity when tested against these data sources. The result is that Manning's equation received stronger support than the Darcy–Weisbach or Chezy equations, though all equations were useful. The second question addressed is how best to estimate velocity of overland flow from measurements of slope and unit discharge, recognizing that the apparent flow velocity variation in resistance coefficients is probably a result of shortcomings in all of the listed resistance equations. A new methodology is illustrated which gives good agreement between estimated and measured flow velocity for both well-inundated sheet and rill flow. Comments are given on the predictive use of this methodology. Copyright © 1999 John Wiley & Sons, Ltd.