Stage-discharge Relationship Research Articles

Prediction of stage-discharge relationship in two-stage channels

Predicting the stage-discharge relationship in two-stage channels is a significant factor, as it determines the discharge and the degree of flood accurately. There are conventional methods, in which they either do not meet the required accuracy or simplicity. In this paper, a new simple model is developed for symmetric compound channels to predict the stage-discharge relationship accurately. The method is proposed by improving the weighted divided channel method (WDCM), which includes the apparent shear force (ASF), wetted perimeters and B/b ratio. It was concluded that the improved weighted divided channel method (IWDCM) is limited to all rigid symmetric compound channels with B/b ratios greater than or equal to 3. The IWDCM led to an absolute percentage error always less than 10% for total discharges for all smooth and rough cases. The proposed IWDCM method will therefore be very helpful to hydraulic engineers to predict the stage-discharge relationship precisely due to its simplicity.

Stage-Discharge Relationships of Drawdown Plates for Denitrifying Woodchip Bioreactors

HighlightsDrawdown plates can prevent prolonged saturation in denitrifying woodchip bioreactors.Contraction coefficients for the orifice equation ranged from 0.74 to 0.76.Drawdown orifice should be sized appropriately to avoid interfering with design flow rates.Established stage-discharge relationships for drawdown orifice improve accuracy of flow monitoring.Abstract.Denitrifying woodchip bioreactors are a conservation drainage practice used to reduce nitrate loads in tile drainage water from field crops. Prolonged saturation in the woodchip media under no flow or low flow conditions can result in the production of hydrogen sulfide and methane. The US Department of Agriculture Natural Resources Conservation Service’s (NRCS) Conservation Practice Standard for denitrifying bioreactors recommends a low-level orifice at the bioreactor outlet to drain the woodchip media within 48 h to prevent prolonged stagnation. This study determined stage-discharge relationships for three drawdown configurations in an AgriDrain water level control structure (15.2 cm nominal tile size) to improve accuracy of estimating flow in field bioreactors. Tested drawdown configurations consisted of a custom-made inverted-v orifice plate currently used by the NRCS (3.6 cm2 orifice area); and a 2 and an 8 mm gap between the base of the structure and the bottom stop log (2.6 and 12.3 cm2 orifice area, respectively). The stage-discharge relationship for all three orifices was accurately described by the orifice flow equation (R2 > 0.99). Stage-discharge relationship for the inverted-v drawdown plate in combination with a stainless steel-edged v-notch weir was the sum of their respective stage-discharge relationships for orifice flow and flow over the weir. Contraction coefficients for the inverted-v, 2 mm gap, and 8 mm gap configurations were 0.74, 0.74, and 0.76, respectively. The stage-discharge relationships for the inverted-v, 2 mm gap, and 8 mm gap configurations were Q = 3.26*A*h0.5, Q = 3.29*A*h0.5, and Q = 3.38*A*h0.5, respectively, where Q is in m3 s-1, A is the orifice area in m2, and h is the water head differential in meters. Keywords: Denitrifying bioreactor, Drawdown plate, Flow monitoring, NRCS, Prolonged saturation.

Modelling of stage-discharge relationship using optimisation techniques for Jhelum River in Kashmir Valley, NW Himalayas

Modelling of stage-discharge relationship using optimisation techniques for Jhelum River in Kashmir Valley, NW Himalayas

Flow Characteristics and Bed Morphology in a Compound Channel between Two Single Channels

In mountainous areas, a river can widen from a single channel to a compound channel under the influence of geological conditions or human impacts, bringing about challenges in terms of flood control and channel regulation. This paper reports the results of tests conducted in a 26 m long flume with a uniform sediment bed (grain size = 0.5 mm), investigating the flow characteristics and bed morphology in a compound channel between two single channels. The stage‒discharge relationship in the compound channel and the longitudinal and cross-sectional bed profile in the compound channel between two single channels are presented and analyzed. The experimental results indicate that the flow characteristics and bed morphology in a compound channel between two single channels are significantly different from those in a normal compound channel. Based on the experimental data and observations, the mechanisms of flow and sediment transport in the compound channel between two single channels are illuminated.

Open check dams and large wood: head losses and release conditions

Abstract. Open check dams are strategic structures to control sediment and large-wood transport during extreme flood events in steep streams and piedmont rivers. Large wood (LW) tends to accumulate at such structures, obstruct their openings and increase energy head losses, thus increasing flow levels. The extent and variability to which the stage–discharge relationship of a check dam is modified by LW presence has so far not been clear. In addition, sufficiently high flows may trigger a sudden release of the trapped LW with eventual dramatic consequences downstream. This paper provides experimental quantification of LW-related energy head loss and simple ways to compute the related increase in water depth at dams of various shapes: trapezoidal, slit, slot and sabo (i.e. made of piles), with consideration of the flow capacity through their open bodies and atop their spillways. In addition, it was observed that LW is often released over the structure when the overflowing depth, i.e. total depth minus spillway elevation, is about 3–5 times the mean log diameter. Two regimes of LW accumulations were observed. Dams with low permeability generate low velocity upstream, and LW then accumulates as floating carpets, i.e. as a single floating layer. Conversely, dams with high permeability maintain high velocities immediately upstream of the dams and LW tends to accumulate in dense complex 3D patterns. This is because the drag forces are stronger than the buoyancy, allowing the logs to be sucked below the flow surface. In such cases, LW releases occur for higher overflowing depth and the LW-related head losses are higher. A new dimensionless number, namely the buoyancy-to-drag-force ratio, can be used to compute whether (or not) flows stay in the floating-carpet domain where buoyancy prevails over drag force.

Stage-discharge relationship for slide gates installed in partially full pipes

Sluice/slide gates are widely used for flow depth control and flow discharge measurements in open channels. The hydraulic behavior of the sluice gates located in the rectangular open channels is well documented in the literature. This study reports the results of an investigation conducted to establish the stage-discharge relationship for the sluice gates located in horizontal, circular open channels/pipes under free outflow conditions. Different stage-discharge models were proposed based on the Buckingham's theorem of dimensional analysis and orifice theory. A comprehensive series of laboratory experiments (729 runs) were performed to study the sluice gates located at the middle, and at the end of two circular pipes. Using the data collected from two circular open channels of nominal diameters 20 and 30 cm, the proposed models were calibrated. For the middle slide gates, the experimental results showed that the discharge prediction can be improved by introducing the Reynolds number. For the slide gates located at the middle of the channel, the best proposed model has an average error of 1.40% with a maximum error of 7.12%. For the slide gates located at the end of the channel, the Reynolds number has no significant effect and best proposed model has an average error of 2.47% with a maximum error of 6.59%. The results also showed that the flow discharge of the end slide gate (with unconfined free jet under gravity) is higher than the flow discharge of the middle slide gate for the same gate opening areas and upstream flow depths. The proposed sluice/slide gate for circular open channels offers a simple and reliable discharge measurement approach with acceptable accuracy.

Improving Stage–Discharge Relation in The Mekong River Estuary by Remotely Sensed Long-Period Ocean Tides

Ocean tidal backwater reshapes the stage–discharge relation in the fluvial-to-marine transition zone at estuaries, rendering the cautious use of these data for hydrological studies. While a qualitative explanation is traditionally provided by examining a scatter plot of water discharge against water level, a quantitative assessment of long-period ocean tidal effect on the stage–discharge relation has been rarely investigated. This study analyzes the relationship among water level, water discharge, and ocean tidal height via their standardized forms in the Mekong Delta. We found that semiannual and annual components of ocean tides contribute significantly to the discrepancy between standardized water level and standardized water discharge time series. This reveals that the long-period ocean tides are the significant factors influencing the stage–discharge relation in the river delta, implying a potential of improving the relation as long as proper long-period ocean tidal components are taken into consideration. By isolating the short-period signals (i.e., less than 15 days) from land surface hydrology and ocean tides, better consistent stage–discharge relations are obtained, in terms of improving the Pearson correlation coefficient (PCC) from ~0.4 to ~0.8 and from ~0.6 to ~0.9 for the stations closest to the estuary and at the Mekong Delta entrance, respectively. By incorporating the long-period ocean tidal height time series generated from a remotely sensed global ocean tide model into the stage–discharge relation, further refined stage–discharge relations are obtained with the PCC higher than 0.9 for all employed stations, suggesting the improvement of daily averaged water level and water discharge while ignoring the short-period intratidal variability. The remotely sensed global ocean tide model, OSU12, which contains annual and semiannual ocean tide components, is capable of generating accurate tidal height time series necessary for the partial recovery of the stage–discharge relation.

Rapid and long-distance channel incision in the Lower Yellow River owing to upstream damming

The operation of the Xiaolangdi Reservoir has significantly altered the flow and sediment regime of the Yellow River, which has led to rapid and long-distance channel incision in the Lower Yellow River. Variations in the channel incision depth and stage-discharge relationships were identified in the braided, transitional and meandering reaches based on the cross-sectional profiles at 91 sedimentation sections and hydrological data at hydrometric stations. The results show that the cumulative reach-scale channel incision depths in the braided, transitional and meandering reaches in response to upstream damming were 3.0 m, 2.5 m and 2.3 m, respectively. In addition, water levels at given discharges dramatically decreased at three hydrometric stations in the different reaches. The previous 5-year average incoming sediment coefficients are the key fluvial factor influencing the cumulative channel incision depth in the Lower Yellow River. The cumulative bank retreat width increased with the cumulative channel incision depth in the braided reach, and a linear function between these parameters was established. However, bank retreat occurred when the channel incision depths reached critical values in the transitional and meandering reaches. Empirical equations were established between the cumulative channel incision depth and the relative bed roughness in the braided and transitional reaches, and they indicate that the riverbed coarsening process can mitigate channel incision to some extent.

Estimation of Daily Stage–Discharge Relationship by Using Data-Driven Techniques of a Perennial River, India

Modeling the stage-discharge relationship in river flow is crucial in controlling floods, planning sustainable development, managing water resources and economic development, and sustaining the ecosystem. In the present study, two data-driven techniques, namely wavelet-based artificial neural networks (WANN) and a support vector machine with linear and radial basis kernel functions (SVM-LF and SVM-RF), were employed for daily discharge (Q) estimation. The hydrological data of daily stage (H) and discharge (Q) from June to October for 10 years (2004–2013) at the Govindpur station, situated in the Burhabalang river basin, Orissa, were considered for analysis. For model construction, an optimum number of inputs (lags) was extracted using the partial autocorrelation function (PACF) at a 5% level of significance. The outcomes of the WANN, SVM-LF, and SVM-RF models were appraised over the observed value of Q based on performance indicators, viz., root mean square error (RMSE), Nash–Sutcliffe efficiency (NSE), Pearson’s correlation coefficient (PCC), and Willmott index (WI), and through visual inspection (time variation, scatter plot, and Taylor diagram). Results of the evaluation showed that the SVM-RF model (RMSE = 104.426 m3/s, NSE = 0.925, PCC = 0.964, WI = 0.979) outperformed the WANN and SVM-LF models with the combination of three inputs, i.e., current stage, one-day antecedent stage, and discharge, during the testing period. In addition, the SVM-RF model was found to be more reliable and robust than the other models and having important implications for water resources management at the study site.

Numerical 3D Model Development and Validation of Curb-Cut Inlet for Efficiency Prediction

Green infrastructure (GI) is a decentralized stormwater management strategy that can simultaneously enhance the resilience of the urban landscape to weather-related stressors. The effectiveness of individual GI facilities is determined by the physical characteristics of the tributary area and inlet, including factors such as slope and geometry, apron configuration, roughness, and clogging, all of which have been inadequately studied. In this paper, we construct, calibrate, and validate a computational fluid dynamics (CFD) model using field survey data collected at a Bronx, NY GI facility. The validated CFD model is used to evaluate how inlet clogging and flow rate affect GI inlet performance. Seven flow rates ranging from 0.00044 to 0.00755 CMS were simulated. As the flow rate increased, the inlet efficiency dropped from 100% to 60% at one location (the SW inlet) and from 100% to 25% at another location (the NW inlet). At a fixed flow rate, the inlet efficiency dropped from 100% efficient (with no clogging) to 0% (with the inlet fully clogged). The stage-discharge relationship for the inlet based on the simulated field conditions deviated from that assumed based on normative flow and was revised. We suggest that GI facilities installed on mild- slope, or rough streets be fitted with non-clogging inlets to maintain free outfall conditions.

Flow resistance law under suspended sediment laden conditions

The uniform flow resistance equation, in the form due to Manning or Darcy-Weisbach, is widely applied to establish the stage-discharge relationship of a river cross-section. The application of this equation, namely the slope-area method, allows to indirectly measure the corresponding river discharge by measurements of bed slope, water level, cross-section area, wetted perimeter and an estimate of channel roughness. In this paper, a recently deduced flow resistance equation for open channel flow was tested during conditions of suspended sediment-laden flow. First, the flow resistance equation was determined by dimensional analysis and by applying the condition of incomplete self-similarity for the flow velocity profile. Then the analysis was developed by the following steps: (i) for sediment-laden flows characterized by known values of mean diameter and concentration of suspended sediments, a relationship (Eq. (28)) between the Γ function of the velocity profile, the channel slope and the Froude number was calibrated by the available measurements; and (ii) a relationship for estimating the Γ function (Eq. (29)) which also takes into account the mean concentration of suspended particles was also established. The theoretical flow resistance law (Eq. (26)) coupled with the relationship for estimating the Γ function (Eq. (28) or Eq. (29)), which is characterized by the applicability of a wide range of flow conditions, allowed to estimate the Darcy-Weisbach friction factor for flows with suspended-load. The analysis showed that for large-size mixtures the Darcy-Weisbach friction factor can be accurately estimated neglecting the effect of mean concentration of suspended sediments while for small-size mixtures the friction factor decreases when the mean sediment concentration increases.

Stage-Discharge Relationship for Weir–Orifice Structure Located at the End of Circular Open Channels

AbstractWeirs and orifices of different shapes are widely used as flow-measuring devices or adjusting the upstream water level. These water structures can be combined, yielding a simultaneous flow ...

Analysis of Stage–Discharge Relationship Stability Based on Historical Ratings

We explored the stability of the rating curves at six streamflow gauging sites in the state of Iowa, USA, to examine temporal variability of their stage–discharge relationships. The analyzed sites have up to 10 years of rating and shift records. Rating curve shifts reflect the alteration of channel geometry caused by scouring and sediment deposition. We studied how rating shifts are connected to the occurrence of flood events and drought periods over time. We found that most rating curve changes take place during spring and summer, which are the seasons with more precipitation in Iowa. We quantified stability in terms of standard deviation of stages for a continuous range of discharges in a rating curve, and show that most of the sites exhibit greater standard stage deviation for discharge–flood ratios smaller than 1, while for larger discharge–flood ratios, the deviation decreases. In stable rating curves, the stage deviation tends to decrease as discharge increases. Non-stable rating curves exhibit large stage deviation in the stage–discharge relationship throughout all stages.

Dimensionless Stage-Discharge Relationship for a Non-Linear Water Reservoir: Theory and Experiments

In the field of hydrology, stage–discharge relationships are commonly used to estimate the discharge at the basin outlet or by experimental plots. Many experimental efforts have been made in order to derive stage–discharge relationships, according to the Buckingham theorem and dimensional analysis, for a multiplicity of gauge geometry. However, these relationships require experimental and physical meaningless numerical coefficients, thus they need extended calibration. The latter issue merits attention, since the empirical coefficients can be applied when the experimental conditions are strictly reproduced in the field. The aim of this paper is to derive a theoretically based stage–discharge relationship of a non-linear water reservoir that requires limited calibration, by using the continuity equation and the principle of conservation of energy. An analysis was performed using a rectangular water tank with a hole at the bottom. However, the suggested approach can be similarly used for tank geometries that differ from the example used in this study. Since the proposed approach is purely hydraulic, only limited calibration of the physical meaningful discharge coefficient characteristic of the hole is needed. A tank design procedure is suggested, and different theoretical and experimental applications of the proposed methodology are performed and discussed. For the considered cases, the mass water balance was also checked.

Hydraulic Performance for Combined Weir-Gate Structure

Combined hydraulic structure play an important role in controlling flow in open channels. This study was based on experimental and numerical modeling investigations for combined hydraulic structure. For this purpose three physical models of combined sharp crested trapezoidal weir with bottom opening and one physical model of sharp crested trapezoidal weir separately were used and tested by running eight different flow rates over each model. In which three configurations of bottom opening were tested; the first configuration is a rectangular gate while other two configuration were trapezoidal with two different side slopes of (1V:4H) and (1V:2H). The water surface profiles passing through weir-gate system were measured for all thirty two runs of all models which show uniform flow at 2.11h from the upstream of weir. The commercial computational fluid dynamic software ANSYS CFX was used to simulate flow numerically. The verification of the numerical model was based on water surface profiles and discharge which showed acceptable agreement. Also, the results showed that discharge coefficient Cd varies from (0.52-0.58). Furthermore, it was shown that both models with trapezoidal gate pass a higher discharge of flow than the model with rectangular gate with average percentage increase of discharge (40.78% and 19.40%) for trapezoidal side slopes (1H:2V and 1H:4V) respectively. In addition, the combined system with milder trapezoidal side slopes of bottom opening had a better performance for discharging weir flow which is about 40% as compared with traditional one. Finally, the empirical equations for stage-discharge relationship were estimated for all models and discharge coefficients were estimated for all runs.

Evaluation of Stage–Discharge Relationships in Alluvial Rivers (Case Study: Shahroud River, Qazvin province, Iran)

Many rivers are classified in alluvial rivers. Stage–discharge curve of these rivers is reliable just in measured conditions and for the sections by the use of measured data. Most of the stage–discharge equations are not able to consider flow resistance, and it causes some errors in qualitative and quantitative modeling. Therefore, it seems necessary to determine the accuracy of stage–discharge curve methods in the river sections without hydrometric stations. In this study, Einstein and Barbarossa (Trans ASCE 117:1121–1132, 1952), Engelund and Hansen (A monograph on sediment transport in alluvial streams. Technical University of Denmark, Copenhagen, Denmark, 1967) and White et al. (A new general method for predicting the frictional characteristics of alluvial streams. Report No IT 187. Hydraulics Research Station, Wallingford, England, 1979) methods were investigated in four hydrometric stations in Shahroud River. To do so, after field data collection, the stage–discharge curve of studied hydrometric stations was obtained by the mentioned methods. Results revealed that effect of flow resistance factors increased in maximum discharge. Einstein and Barbarossa’s (1952) method enjoyed the most accuracy in the stations with ripple bed form and discharge less than 20 cms. By increasing discharge or changing the bed form, the accuracy of this method decreased, so in this condition Engelund and Hansen (1967) and White et al.’s (1979) methods showed reliable accuracy. In the rivers with anti-dune bed form, White et al.’s (1979) equation had the most accuracy. Additionally, evaluating the effect of bed form, discharge, bed slope and bed load sediment size indicated that all the methods are highly sensitive to discharge flow and river bed form; on the other hand, bed slope and bed load sediment size are not determining factors in choosing proper method for the development of stage–discharge curve in alluvial rivers.

Analytical and experimental study of flow through elliptical side orifices

Discharge estimation is important for water management. Side orifices are commonly used in irrigation and drainage networks for distributing the water. Despite the vast amount of theoretical and experimental studies published, no generally applicable discharge equations are available for elliptical sharp-crested side orifices. When the length (diameter) of the circular side orifice is not sufficient to divert the water, an elliptical side orifice is a good alternative. In this paper, the elliptical sharp-crested side orifices were studied theoretically and experimentally. Several models were developed to predict the discharge coefficient of elliptical side orifices based on the Buckingham's theorem of dimensional analysis. A series of laboratory runs (588 runs) were conducted for different values of orifice geometry. The main channel discharge used in the tests ranged from 13.8 to 39.6 l/s and the side orifice discharge ranged from 3.66 to 21.4 l/s and upstream Froude number ranged from 0.22 to 0.77. Using measurements obtained by laboratory runs carried out in this investigation the proposed models of elliptical side orifices were calibrated under free outflow conditions. The model that includes the approach Froude number had an average error of 1.74%, while other model that does not include the approach Froude number had an average error about 2.43%. Moreover, suitable models were proposed for design procedure when measurement data for flow depths above the centroid of the orifice are not available. In this case, the model that includes the approach Froude number had an average error of 1.92%, while other model that does not include the approach Froude number had an average error of 2.24%. It was found that the proposed stage-discharge relationships were in an excellent agreement with the experimental results.

Stage–discharge equation for simple flumes with semi-cylinder contractions

In this study, the outflow process of a simple flume with two semi-cylinders on either side of a rectangular channel having a zero slope was studied. This can be considered as one of the simplest form of contraction in a channel so it may have a broad applicability. From a practical viewpoint, the availability of a stage–discharge equation that can be reliably applied to a wide range of discharges would be of great practical importance. To extend the range of previous available data, new experimental runs were performed. Two new stage–discharge relationships were deduced: one general relationship by considering the contraction ratio and another relationship by neglecting the contraction ratio for a specified range of this variable. The proposed general stage–discharge relationship represents a novel equation to describe the flume outflow process. Other relationship can be used by neglecting the approaching channel width for the upstream Froude number ranges from 0.11 to 0.38. Compared with the available stage–discharge relationships, the results indicate that the proposed simple relationships can be reliably used for a wide range of discharges with acceptable accuracy.

Discharge estimation in wide meandering compound channels

ABSTRACT A model for stage–discharge relationship in two-stage wide meandering channels, devised by statistical analysis of new experimental boundary shear data and some published shear data, is presented. By evaluating the measured boundary shear percentage on floodplains of unequal length on either side along with corresponding wetted area percentage for sinuous channels, it is seen that different but particular empirical relationships exist between shear percentage and percentage flow area due to various flow mechanisms occurring on floodplains lying on either side of the bend. The empirical relationships obtained for left floodplain shear is an exponential function while that for total floodplain is a power function. Expressions for average zonal velocity and hence for zonal discharge are then estimated by 1D analysis to compute the H–Q rating curve for such channels. This method is validated through its application to different published data sets with discharge prediction error lying close to ±10% on most occasions. The method when compared with some other well-known 1D approaches is found to perform reasonably well as evident from error analysis. The method when tested for predicting flow distribution, the error percentage is again within 10% for available limited data series.

An expanded rating curve model to estimate river discharge during tidal influences across the progressive-mixed-standing wave systems.

Empirically quantifying tidally-influenced river discharge is typically laborious, expensive, and subject to more uncertainty than estimation of upstream river discharge. The tidal stage-discharge relationship is not monotonic nor necessarily single-valued, so conventional stage-based river rating curves fail in the tidal zone. Herein, we propose an expanded rating curve method incorporating stage-rate-of-change to estimate river discharge under tidal influences across progressive, mixed, and standing waves. This simple and inexpensive method requires (1) stage from a pressure transducer, (2) flow direction from a tilt current meter, and (3) a series of ADP surveys at different flow rates for model calibration. The method was validated using excerpts from 12 tidal USGS gauging stations during baseflow conditions. USGS gauging stations model discharge using a different more complex and expensive method. Comparison of new and previous models resulted in good R2 correlations (min 0.62, mean 0.87 with S.D. 0.10, max 0.97). The method for modeling tidally-influenced discharge during baseflow conditions was applied de novo to eight intertidal stations in the Mission and Aransas Rivers, Texas, USA. In these same rivers, the model was further expanded to identify and estimate tidally-influenced stormflow discharges. The Mission and Aransas examples illustrated the potential scientific and management utility of the applied tidal rating curve method for isolating transient tidal influences and quantifying baseflow and storm discharges to sensitive coastal waters.