Stage-discharge Relationship Research Articles

A framework for detecting stage-discharge hysteresis due to flow unsteadiness: Application to France’s national hydrometry network

A generic framework is proposed to evaluate the relative discharge error made when ignoring stage-discharge hysteresis due to transient flow over large gauging station networks. The diagnosis is conducted using the Jones equation, a simple hydraulic concept relating discharge to stage and its time-gradient. The input data used for the method are the flow resistance coefficients, the temporal stage gradients, and the bed slopes. The hysteresis effect is quantified for each gauging station and mapped using the relative discharge error. The method was applied to 2618 gauging stations of France’s national hydrometry network using data extracted from the national hydrological archive and from Digital Terrain Models. The diagnostic results highly depend on slope estimates used as inputs. Substantial hysteresis effects were found at stations with low bed slope combined with a fast flood regime. The application to France shows the difficulty of drawing a firm conclusion about stations prone to hysteresis due to the slope data uncertainty. This issue is not specific to France; slope estimates over a network of hydrometric stations are difficult to obtain in many countries. The use of local bed slope estimates is recommended to approach the slopes of the reaches controlling the station stage-discharge relation.

Experimental study of discharge formulas for rectangular sharp-crested weirs under free flow condition

Laboratory experiments were carried out to investigate the discharge characteristics of rectangular sharp-crested weirs under free flow condition. The performances of available discharge formulas have been evaluated by using the experimental data sets of present and previous studies. Error statistics of our experimental data indicate that the recent stage-discharge relationships show satisfactory performances. Discharge formula in terms of weir Reynolds number proposed by Vatankhah gives the highest accuracy among the existing slit weir equations, with E±4=100.00% (i.e. percent error less than or equal to ±4) and a mean absolute error |E|m=0.88%. The full-range discharge equation presented by Bijankhan and Mahdavi Mazdeh shows the highest accuracy among the relationships in terms of weir contraction ratio, with E±4=100.00%, |E|m=0.91% for slit weirs and, E±4=94.64%, |E|m=1.60% for partially contracted weirs, respectively. The weir velocity formulae suggested by Gharahjeh et al. exhibit the relatively better performance, with E±4=98.41%, |E|m=1.34% for slit weirs and, E±4=91.07%, |E|m=1.91% for contracted weirs, respectively. Statistical results of this study confirm the weir velocity approach presented by Aydin et al. and show that, the weir velocity is a predominant quantity for rectangular sharp-crested weirs, unique characteristics of the weir velocity curves make it more suitable for expressing the discharges. Moreover, it is important to point out that the performance of weir velocity formulae can be further improved.

Development of stage-discharge rating curve using ANN

Accurate forecasting of river discharge is essential for the efficient operation of water resources systems. Therefore, researchers are consistently developing and improving various techniques to predict river discharge with relative ease and high accuracy, although traditional methods are available. This paper presents mainly three data-driven modelling techniques, namely the stage rating curve (SRC), generalised reduced gradient (GRG) solver, and an artificial neural network (ANN) to accurately model the stage-discharge relationship for local rivers in Trinidad and Tobago using only low flow data. The model that produced the overall superior results was the ANN.

Modeling of stage-discharge using back propagation ANN-, ANFIS-, and WANN-based computing techniques

The development of the stage-discharge relationship is a fundamental issue in hydrological modeling. Due to the complexity of the stage-discharge relationship, discharge prediction plays an essential role in planning and water resource management. The present study was conducted to model discharge at the Gaula Barrage site in the Uttarakhand state of India. The study evaluated adaptive neuro-fuzzy inference system (ANFIS)-, artificial neural network (ANN)-, and wavelet-based artificial neural system (WANN)-based models to estimate the discharge. The daily data of 12 years (2007–2018) were used to train and test the models. The gamma test was used to identify the best model for discharge prediction. The input data having a stage with 1-day lag and discharge with 1- and 2-day lags and current-day discharge as output was used for discharge modeling. In the case of ANN models, the back propagation algorithm and hyperbolic tangent sigmoid activation function were used. WANN used Haar, a trous-based wavelet function. In ANFIS models, triangular, psig, generalized bell, and Gaussian membership functions were used to train and test the models. The models were evaluated qualitatively and quantitatively using correlation coefficient, and root means square error, Willmott index, and efficiency coefficient. It was found that the ANFIS model performed better than ANN- and WANN-based models for discharge prediction at the Gaula Barrage.

Estimation of discharge coefficient of the overshot gates, based on the brink depth, under free and submerged conditions

ABSTRACT Overshot gates are used as a flow measuring device to fix the upstream water level. Flow through the overshot gates under submerged conditions often has many problems, mainly due to the need to measure the tail-water depth. In this research, the application of the brink depth, instead of tail-water depth, has been selected to overcome this problem. Many experiments were conducted with nine different angles of the overshot lip under free and submerged conditions. The discharge coefficient of the gate was estimated based on the brink depth. Besides, the flow discharge through the gate was evaluated through an equation based on the energy equation and the stage-discharge relation. The results showed good consistency and high accuracy under free and submerged conditions which refers to the suitability of the proposed equations for flow discharge and water depth because of their theoretical basis.

Extent of detection of hidden relationships among different hydrological variables during floods using data-driven models.

Understanding of flood dynamics forms the basis for the leading water resource management and flood risk mitigation practices. In particular, accurate prediction of river flow during massive flood events and capturing the hysteretic behavior of river stage-discharge are among the key interests in hydrological research. The literature demonstrates that data-driven models are significant in identifying complex and hidden relationships among dependent variables, without considering explicit physical schemes. In this regard, we aim to discover the extent to which data-driven models can recognize the hidden relationships among different hydrological variables, in order to generate accurate predictions of the river flow. A secondary aim involves the detection of whether data-driven models can digest the internal features of training inputs to extrapolate severe flood records beyond the training domain. To achieve these aims, we developed a recurrent neural network (RNN) model of two hidden layers to capture the hidden relationships among the inputs, and investigated the model's predictive capability using quantitative and qualitative analyses. The quantitative analysis comprised of a comparison between model predictions, and another set of precise independent records obtained through an advanced hydroacoustic system for reference. A qualitative approach was adopted to visualize the hysteretic behavior of the stage-discharge relations of the model records, with the high-resolution records of the hydroacoustic system. The findings display the potential of data-driven models for accurately predicting river flow. Consequently, the qualitative analysis revealed moderate correlations of stage-discharge loops as compared to the reference records. Additionally, the model was tested against severe destructive flood records generated from the East Asian monsoon and tropical cyclones. Its findings suggest that data-driven models cannot extrapolate new features beyond their training dataset. Overall, this study discusses the competence of RNNs in providing reliable and accurate river flow predictions during floods.

Stabilization of the Lower Jamuna River in Bangladesh—Hydraulic and Morphological Assessment

This paper presents a hydraulic and morphological analysis of the Lower Jamuna in Bangladesh with a focus on two key bifurcations that are important for stabilization of the Lower Jamuna reach. We used ground measurements, historical data, multispectral satellite images from various sources as well as numerical models. We carried out hydraulic analyses of the changes and their peculiarities, such as flow distributions at the bifurcation and hysteresis of the stage–discharge relationships. We supplemented our analysis by using numerical models to simulate discharge distribution at the bifurcations under various flow and riverbed conditions. We developed an advanced and automated satellite image processing application for the Lower Jamuna, referred to as Morphology Monitor (MoMo), using the Google Earth Engine. MoMo was found to be an effective tool for a rapid assessment and analysis of the changes in deep-channel and sandbar areas. It is also useful for monitoring and assessing riverbank and char erosion and accretion, which is important not only for morphological but also ecological impact assessment. The application can be adapted as an operational tool as well. Furthermore, we assessed the evolution of deep channels at the bifurcations based on regularly and extensively measured bathymetry data. The analysis was carried out in complement with morphological modeling, particularly for short-term prediction. In this paper we present the major findings of the analysis and discuss their implications for adaptive river management.

Calibration of Stage–Discharge Relationship for Rectangular Flume with Central Cylindrical Contraction

The design and calibration of a simple rectangular flume with central cylindrical contraction is presented. The flume is designed based on principles of critical flow in open channels. Critical flow is created through contraction of flow cross section by installing a vertical cylindrical column at the center of a rectangular open channel. The stage–discharge relationship was calibrated using a laboratory prototype with various configurations. A previously developed model was recalibrated using the laboratory data for the proposed flume. The results of the proposed stage relationship were also compared with results from a computational fluid dynamics model (CFD). The results and analysis show that if the piezometric head is measured at midstream at the upstream side of the contracting column, then stage–discharge relationship can be developed, which is independent of the contraction ratio. The stage–discharge function developed in this paper can be used for design and calibration of the flume regardless of the flume size or contraction ratio. The stage–discharge relationship equation is also compared with another set of independently measured laboratory data.

Research on stage–discharge relationship model based on information entropy

Abstract In order to improve the estimation accuracy of stage–discharge relationship model, the back propagation neural network optimized through the genetic algorithm (GA-BP) based on information entropy was proposed. Firstly, the information entropy and hierarchical clustering were used to quickly cluster the hydrological sample data and get the optimal number of clusters. Secondly, the k-nearest neighbor algorithm was used to divide the new stage data into the most appropriate clustering categories. Finally, the river daily discharge was estimated. Some measured data collected from a hydrological station were used to test the model, and the simulation results showed that the method proposed by this paper can get higher estimation accuracy than the classical analytical model, BP neural network algorithm and GA-BP neural network algorithm, which provided a new effective method for parameter estimation of the stage–discharge relationship model.

Hydrograph recession extraction algorithm (HYDRA): Minimizing influence of stage uncertainty in identification of recession events

Fine temporal resolution streamflow records offer valuable information to further our understanding of watershed function. Among the many tools to decipher watershed processes, recession analysis can be used to gain insight into storage-discharge properties and watershed storage by analyzing portions of stream hydrographs whose behavior is attributed to the relationship between aquifer structure and groundwater outflow to the steam channel. Although numerous methods have been employed to advance recession analysis methodology, no comprehensive approach to identify the cessation or continuation of recession events from fine temporal resolution data has been established. A new extraction algorithm, the HYDrograph Recession extraction Algorithm (HYDRA), is proposed to improve identification of recession events from fine temporal resolution hydrographs. HYDRA exploits site-specific stage-discharge relations to qualify the beginning or end of a hydrograph recession by accounting for stage measurement error which translates to uncertainty in the stream hydrograph. Experiments compared HYDRA to previous published methods, revealing that HYDRA led to significant improvements in identifying the continuation of recession events, resulting in superior estimation of theoretical recession parameter values. Additional case studies assert that HYDRA robustly identifies recession events across a spectrum of temporal resolution discharge records, affirming that the extraction algorithm provides a functional tool to identify recession events for further recession-based theoretical analysis.

Predictive modelling of the stage–discharge relationship using Gene-Expression Programming

Abstract Modelling the hydrologic processes is an essential tool for the efficient management of water resource systems. Therefore, researchers are consistently developing and improving various predictive/forecasting techniques to accurately represent a river's attributes, even though traditional methods are available. This paper presents the Gene-Expression Programming (GEP) modelling technique to accurately model the stage–discharge relationship for the Arouca River in Trinidad and Tobago using only low flow data. The proposed method uses the stage and associated discharge measurements at one cross-section of the Arouca River. These measurements were used to train the GEP model. The results of the GEP model were also compared to the traditional method of the Stage–Discharge Rating Curve (SRC). Four statistical paraments namely the Pearson's Correlation Coefficient (R), Root Mean Square Error (RMSE), Mean Absolute Relative Error (MARE) and Nash–Sutcliffe Efficiency (NSE) were used to evaluate the performance of the GEP model and the SRC method. Overall, the GEP model performed exceptionally well with an R2 of 0.990, RMSE of 0.104, MARE of 0.076 and NSE of 0.957.

Effect of rating curve hysteresis on flood extent simulation with a 2D hydrodynamic model: A case study of the Inner Niger Delta, Mali, West Africa

The Inner Niger Delta (IND) is a complex hydraulic system where the flood dynamics and connectivity between water bodies is the main driver for ecosystem services and economic activities. Therefore, it is of pivotal importance that hydraulic models used to assess ecosystem services and socio-economic usages in the IND are capable of capturing both the inundation and connectivity dynamics. A particularity of the IND is that a strong hysteresis effect can be observed in the stage-discharge relationships at all hydrometric stations in the area. However, existing hydrodynamic models of the IND typically use a static stage-discharge relationship as the downstream boundary condition during both the rise and recession of the flood, which leads to potential inaccuracies when trying to predict the flood extent. This paper explores how the simulation results of the flood and connectivity dynamics in the IND can be improved by using a looped rating curve at the downstream model boundary. The looped rating curve is described using the dimensionless discharges and water levels (DLRC) method. The results show that simulation with DLRC improves the accuracy in predicting floodplain extent and connectivity dynamics between the Niger river system and an important lake in the IND. The improvement in water level predictions decreased steadily with the distance from the downstream boundary of the modelled area.

A comparative study of wavelet and empirical mode decomposition-based GPR models for river discharge relationship modeling at consecutive hydrometric stations

Abstract The river stage–discharge relationship has an important impact on modeling, planning, and management of river basins and water resources. In this study, the capability of the Gaussian Process Regressions (GPR) kernel-based approach was assessed in predicting the daily river stage–discharge (RSD) relationship. Three successive hydrometric stations of the Housatonic River were considered, and based on the flow characteristics during the period of 2002–2006 several models were developed and tested via GPR. To enhance the applied model efficiency, two pre-processing techniques, namely Wavelet Transform (WT) and Ensemble Empirical Mode Decomposition (EEMD), were used. Also, two states of the RSD modeling were investigated. In state 1, each station's own data was used and in state 2, the upstream stations’ datasets were used as input to model the RSD downstream of the river. The single and integrated model results showed that the integrated WT- and EEMD-GPR models resulted in more accurate outcomes. Data processing enhanced the models' capability between 25% and 40%. The results showed that the RSD modeling in state 1 led to better results; however, when the station's own data were not available the integrated methods could be applied successfully for the RSD modeling using the previous stations’ data.

Combining a segmentation procedure and the BaRatin stationary model to estimate nonstationary rating curves and the associated uncertainties

Streamflow time series data are fundamental to hydrological science and water management applications, which are commonly derived from stage-discharge rating curves. The rating curves are usually nonstationary due to temporal characteristics of stream channel and human activities such as indiscriminate dig of sediment. This implies the need for an efficient method to estimate nonstationary rating curves from an adequate dataset. This study employed a shifting method to estimate the nonstationary rating curves and the associated uncertainties. The method includes two steps: a coupled algorithm PELT&CROPS was first performed to divide the gauging samples into homogeneous families by detecting the multiple change points in a time series of a residual indicator. Then, the rating curves were calibrated with the BaRatin stationary model using these homogeneous gaugings within each stationary period. The method was applied at Shijiao Hydrological Station in China. We found that: (1) Set the lower and upper limit of parameter CROPS (changepoints for arangeofpenalties) to 0 and Inf respectively, the whole range of segmentation can be calculated. (2) Parameter Minseglen (minimum segment length) is of great significance to the segmentation result. More changepoints will be detected as the value of Minseglen decreasing. An appropriate Minseglen value should be assigned to find the optimal segmentation. (3) The stage-discharge relationship in the low flow part is more sensitive to the variation of river topography. Ten segmentations are needed to produce an accurate discharge for low flow prediction, while two segmentations for calibration can produce an accurate discharge for high flow prediction. (4) Information redundancy exists in the vast amount of gaugings. The BaRatin model can reduce the use of calibration data by employing stage-discharge function with a precise exponent from the hydraulic knowledge at a hydrological station.

Discharge prediction for rectangular sharp-crested weirs by machine learning techniques

The stage-discharge relationship of a weir is essential for posteriori calculations of flow discharges. Conventionally, it is determined by regression methods, which is time-consuming and may subject to limited prediction accuracy. To provide a better estimate, the machine learning models, artificial neural network (ANN), support vector machine (SVM) and extreme learning machine (ELM), are assessed for the prediction of discharges of rectangular sharp-crested weirs. A large number of experimental data sets are adopted to develop and calibrate these models. Different input scenarios and data management strategies are employed to optimize the models, for which performance is evaluated in the light of statistical criteria. The results show that all three models are capable of predicting the discharge coefficient with high accuracy, but the SVM exhibits somewhat better performance. Its maximum and mean relative error are respectively 5.44 and 0.99%, and 99% of the predicted data show an error below 5%. The coefficient of determination and root mean square error are 0.95 and 0.01, respectively. The model sensitivity is examined, indicative of the dominant roles of weir Reynolds number and contraction ratio in discharge estimation. The existing empirical formulas are assessed and compared against the machine learning models. It is found that the relationship proposed by Vatankhah exhibits the highest accuracy. However, it is still less accurate than the machine learning approaches. The study is intended to provide reference for discharge determination of overflow structures including spillways.

Experimental study on rectangular cut-throated flume: Effects of flume walls slopes and channel longitudinal slope

This research conducted to study the flow through a rectangular cut-throated flume (RCTF). The flume is simply formed by placing two vertical triangular prisms (two vertical folded plates) on either side of a rectangular open channel. Both channel and flume cross-sections are rectangular. The investigated flume is inexpensive, easy to install and does not require high maintenance. A wide experimental investigation, carried out under free outflow conditions and under upstream subcritical flow regime to investigate the effects of the channel longitudinal slope, the flume throat width, and slopes of upstream and downstream flume walls on the stage-discharge relationship. The stage-discharge relationships were deduced by applying the dimensional analysis and were calibrated using the data of this study. The proposed stage-discharge equation for horizontal channel has an average absolute relative error of 2.97% with the relative errors restricted in the range of ±10%, and 80% of the data points are in the error range of ±5%. The proposed stage-discharge equation for sloping channel has an average absolute relative error of 3.97% with the relative errors restricted in the range of ±10%, and 66% of the data points are in the error range of ±5%. The measurements indicate that slopes of upstream and downstream walls affect the stage-discharge relationship of the CTFs only in sloping channels and flow discharge is not influenced by the flume walls slopes in a horizontal channel. The proposed unified stage-discharge equation for both horizontal and sloping channels has an average absolute relative error of 3.38% with the relative errors restricted in the range of ±10%, and 74% of the data points are in the error range of ±5%. The proposed stage-discharge model demonstrates favorable accurate and convenient estimation of discharge for flows through the CTFs.

Research on stage-divided water level prediction technology of rivers-connected lake based on machine learning: a case study of Hongze Lake, China

The rivers-connected lake involved in the “River–Lake-Reservoir” hydrological complex system and it's water level fluctuations are more severe than those of other lakes, which challenges the scientific management of lakes. Therefore, to improve the accuracy of water level prediction for the rivers-connected lake, taking Hongze Lake as an example, we used the BFAST algorithm to analyze the inconsistency of the lake's inter-annual water level and selected a stable stage for water level prediction research. Next, considering the lake basin shape, based on the Stage-discharge relationship curve, the fluctuation process of the lake's inter-annual water level was divided into four periods: the discharge period, the early period of storage, the later period of storage, and the balance period. Then, the NARX model was used to build the water level prediction model for different periods. Finally, the wavelet analysis and KNN algorithm were introduced into the water level prediction model for input data pre-process and result post-processing, respectively. The result shows that: (1) There are significant differences in the mechanism of water level regime modification in different periods. The outflowing runoff is the main driving factor for the water level regime modification in most times; (2) Coupling multiple machine learning methods is an effective way to improve the accuracy of the lake water level prediction; (3) The combination of the staged-divided water level prediction method and the hybrid machine learning models can further improve the accuracy of the water level prediction.

Comments on “Overflow characteristics of streamlined weirs based on model experimentation” by Bagheri S. and Kabiri-Samani A

In this paper the stage-discharge equation of a streamlined weir is theoretically deduced applying the Π-Theorem of dimensional analysis and the self-similarity theory. The coefficients of the new stage-discharge relationship are estimated using the experimental results by Bagheri and Kabiri-Samani.

Closure to “Unsteady Stage-Discharge Relationships for Sharp-Crested Weirs” by Firouz Ghasemzadeh, Salah Kouchakzadeh, and Gilles Belaud

Closure to “Unsteady Stage-Discharge Relationships for Sharp-Crested Weirs” by Firouz Ghasemzadeh, Salah Kouchakzadeh, and Gilles Belaud

Discussion of “Unsteady Stage-Discharge Relationships for Sharp-Crested Weirs” by Firouz Ghasemzadeh, Salah Kouchakzadeh, and Gilles Belaud

Discussion of “Unsteady Stage-Discharge Relationships for Sharp-Crested Weirs” by Firouz Ghasemzadeh, Salah Kouchakzadeh, and Gilles Belaud