Stage-discharge Relationship Research Articles

The stage-discharge relationship of a sharp-crested triangular weir pierced by square orifices

In this paper, the stage-discharge equation of a sharp-crested triangular weir pierced by square orifices is deduced applying both the classical approach of the discharge coefficient Cd and the Π- Theorem of dimensional analysis and the self-similarity theory. At first, using the experimental data by Zeinivand et al. (2024), the applicability of the expression of the discharge coefficient proposed by these authors was verified. Then, applying the dimensional analysis, a new stage-discharge relationship was deduced and calibrated using the available dataset. This theoretical equation is characterized by errors in the discharge estimate that are less than or equal to ±20 % for 98.9 % of cases and ≤ ±10 % for 87.8 % of cases, and the root mean square error is equal to 0.00071 m3 s−1. In conclusion, the stage-discharge relationship deduced by dimensional analysis is characterized by an improvement in the performances in the discharge estimate and also has the advantage of working without the need of estimating the discharge coefficient.

Discharge and sediment load modeling using rating curve-based missing data management

ABSTRACT Hydrological models are vital for water management to determine in-stream flow, irrigational water, domestic water supply, and biodiversity conservation. This study formulates a hydrological model with a novel approach for streamflow and sediment load in the QGIS-supported Soil and Water Assessment Tool for the Halda River catchment, a unique ecological habitat for natural carp spawning and freshwater sources. The daily simulation uses an innovative stage–discharge relationship technique from available 15-day interval flow data. The model evaluation parameters R2 values 0.80 and 0.62, and NS values 0.81 and 0.61 for calibration and validation of streamflow suggested excellent agreement in the seasonal cycle and most of the monsoon peak flow. The streamflow/precipitation ratio indicates a significant influence of groundwater through infiltration. The baseflow shows a decreasing trend. The sediment load based on suspended sediment concentration at a downstream location is 1,625 tons/day. On the contrary, the model prediction is 30 times lower. The scattered sediment load data support the model estimate by considering relatively lower intervention or land use change in its upstream. This model provides a baseline for daily flow and sediment load for scenario modeling (e.g., climate change, land use change) for environmental flow estimation of the fish habitat, freshwater supply, irrigation, and salinity intrusion.

Stage–discharge prediction in the multi-stage ice-covered compound channel

The multi-stage compound channel, which is a common pattern in natural alluvial rivers and the regulation projects of urban rivers, inevitably freezes in winter when it is situated in cold northern areas with high latitudes. Given that ascertaining the stage–discharge relationship for rivers is the foundation for the development of flood control schemes and water resources management, this study concentrates on proposing an analytical model for predicting the stage–discharge curves of multi-stage ice-covered compound channels. In deducing the analytical model, the cross section of the channel is first segmented into several homogeneous subregions that can be grouped into seven categories according to the geometric characteristics. Through analyzing the momentum transfer between adjacent subregions, the force balance equation for each subregion is then established to get the bulk mean velocity for the corresponding subregion, thereby obtaining the discharge by solving a tridiagonal matrix. Subsequently, measurements from two-stage and three-stage ice-covered compound channel experiments and three sets of experimental data from the literature are used to validate the performance of the proposed model. Good agreement between the predictions and the measured data suggests that the deduced model can accurately estimate the discharge for the multi-stage ice-covered compound channels when the flow depth is given. Finally, sensitivity analysis indicates that Manning's roughness coefficient of the channel bed has a more pronounced impact on the stage–discharge relationship than that of the ice cover. Moreover, when compared to the two-stage ice-covered compound channel, the multi-stage ice-covered compound channel offers greater potential for water resource utilization.

Comment on “Hydraulic characteristics of labyrinth sluice gates” by T. Hashem, A.Y. Mohammed, T.J. Alfatlawi

In this paper, the stage-discharge relationship of a labyrinth sluice gate is theoretically deduced by the Π-Theorem of dimensional analysis and the self-similarity condition. This approach was then compared with the classical approach using the discharge coefficient Cd proposed by Hashem et al. (2024). The classical stage-discharge equation (Eq. 4), with the discharge coefficient estimated by the empirical relationship (Eq. (1)) proposed by Hashem et al. (2024), resulted in errors E that are less than or equal to ±5 % for 74.3 % of the investigated cases and a mean square error MSE of 0.0078. The new stage-discharge relationship, deduced by dimensional analysis and self-similarity theory, was calibrated using the dataset by Hashem et al. (2024). The obtained stage-discharge equation (Eq. 20) is characterized by errors in the discharge estimate E that are less than or equal to ±5 % for 82.2 % of the investigated cases and a mean square error MSE of 0.0051. In conclusion, the stage-discharge relationship deduced by dimensional analysis allows for the best performance in the discharge estimate, which can be obtained without knowledge of the empirical discharge coefficient.

Comment on “the hydraulic investigation of harmonic plan weirs” by A. Yıldız, A. İhsan Marti, M. Göğüş

In this paper, the stage-discharge equation of a harmonic plane weir is deduced applying both the classical approach of the discharge coefficient Cd and the Π- Theorem of dimensional analysis and the self-similarity theory. At first, using the laboratory measurements carried out by Yildiz et al. (2024), a new relationship for estimating Cd is proposed. This new empirical expression of the discharge coefficient (Eq. (15)) allows for improving the performance of the stage-discharge equation (Eq. 13), which is characterized by errors in the discharge estimate E varying from – 7.7 to 7.7 % and a mean square error MSE of 0.214. Then, applying the dimensional analysis, a new stage-discharge relationship was deduced and calibrated using the same dataset. This theoretical equation is characterized by errors E ranging from – 7.1 to 7.4 %, and a MSE of 0.193. In conclusion, the stage-discharge relationship deduced by dimensional analysis is characterized by the best performances in the discharge estimate and has also the advantage of working without the need of estimating the discharge coefficient.

Stage–discharge relationship in an erodible compound channel with overbank floods

Due to environmental changes and anthropogenic activities, a dramatically diminished upstream sediment supply can promote riverbed erosion and alter the stage–discharge relationship in a channel with overbank flows, which can impact flood control. It is important to understand how the stage–discharge relationship in an erodible compound channel is affected and how to predict this relationship. In this study, we performed laboratory experiments in a straight compound channel with a mobile main channel under clear water scour. Stage–discharge relationships were measured before the destruction of the armor layer and after the formation of a new armor layer at the riverbed surface. The results indicated that the impact of riverbed erosion on the stage–discharge relationship cannot be ignored. Under the same discharge, the flow depth in the main channel increased, while the flow depth in the floodplains decreased after the new armor layer was formed relative to the case before armor layer destruction. Considering the impacts of the erosion depth and the variation in the bed resistance, we proposed a new method for predicting the stage–discharge relationship in an erodible compound channel after riverbed erosion. The predicted stage–discharge relationships agreed with the measurements, indicating that the proposed method could be used to precisely predict the stage–discharge relationship after riverbed erosion occurrence. The comparison of the results of the proposed method with and without considering the erosion depth supported the idea that the impact of riverbed erosion on the stage–discharge relationship must be included. Finally, the proposed method was further used to examine the influence of floodplain encroachment on flood control and riverbed erosion. Floodplain encroachment produced a larger flood flow depth on floodplains and a higher mean velocity in the main channel, suggesting that floodplain encroachment should be avoided to eliminate possible increases in flood disasters and riverbed erosion risks.

Enhancing river flow predictions: Comparative analysis of machine learning approaches in modeling stage-discharge relationship

Streamflow, a pivotal variable in water resources management, holds profound significance in shaping the decision-making processes of hydrologic projects. This paper tries to delve into the exploration of the stage-discharge relationship using three machine learning methods (MLMs) namely multi-layer neural networks (MLNN), radial basis neural networks (RBNN), and neuro-fuzzy systems (ANFIS) to predict and simulate mean daily stage-discharge data derived from two monitoring stations, Bulakbasi and Karaozü, Kizilirmak River, Turkey. Root mean square error (RMSE), Mean absolute percentage error (MAPE), coefficient of determination (R2), and the Developed Discrepancy Ratio (DDR) metrics were utilized to MLMs' performance assessment. The performance evaluation indices (RMSE, MAEP, R2, DDR) for the preeminent MLNN model applied to Bulakhbashi and Karasu stations were determined as (0.29, 1.57, 0.9998, 17.62) and (1.71, 6.56, 0.9980, 6.65), respectively. The MLNN model contributed to a notable enhancement in the RMSE performance index for the aforementioned stations, exhibiting improvements of 87% and 56%, respectively. These results affirm the MLNN's proficiency in accurately capturing the stage-discharge at both monitoring stations.

Modelling stage–discharge relationship of Himalayan river using ANN, SVM and ANFIS

Modelling stage–discharge relationship of Himalayan river using ANN, SVM and ANFIS

Impact of a concentrated lateral inflow and stage–discharge relation imposed at the downstream end of a finite channel for the diffusive wave model

Impact of a concentrated lateral inflow and stage–discharge relation imposed at the downstream end of a finite channel for the diffusive wave model

Remote sensing assessment of anthropogenic and climate variation effects on river channel morphology and vegetation: Impact of dry periods on a European piedmont river

AbstractRivers are subject to increasing human pressure, resulting in a loss of their natural characteristics, further enhanced by climate change. The present study focuses on a piedmont reach of the Italian Po River and combines Landsat satellite information with hydrological records to investigate changes in sandbars exposure and riparian vegetation coverage, considering the summer period of 1984–2022. Satellite data were handled via Google Earth Engine, looking at common indexes such as the Modified Normalized Difference Water Index, which was used to identify temporal variations in wetted channel area, and the Normalized Difference Vegetation Index, considered as a proxy of vegetation coverage variations. Changes in the river hydrology were analysed by looking at the annual minimum water levels, the discharge duration curve, the stage–discharge relationship and the yearly annual water volume. Results suggest that a process of oversimplification is affecting this reach of the Po River, showing how climate change can affect piedmont European watercourses. Indeed, after an initial period where bars tended to be barer and somehow stable over time, in the most recent decade a different trend appeared, with vegetation able to colonize the exposed sandbars more. Using the Po River as an exemplary case study, this work suggests that prolonged dry periods, which are more common in recent decades, might impact large and medium rivers located in temperate climates, favouring the development of vegetation on exposed sandbars, eventually resulting in a less dynamic active channel.

The effects of vegetative feedbacks on flood shape, sediment transport, and geomorphic change in a dryland river: Moenkopi Wash, AZ

Since the 1950s, Moenkopi Wash, in Arizona, United States, has been transformed from a relatively wide river at low flow, to a narrow, heavily vegetated river that is less than half of its former width. We analyzed a ~95-years-long instantaneous-discharge record, an extensive sediment-transport record, oblique and aerial photographs, historical channel surveys, and historical stage-discharge rating relations to determine the primary mechanisms responsible for this transformation.Frequent, large floods dominated the early part of the discharge record between 1926 and 1940. A dramatic ~30 % decrease in annual mean discharge, and ~27 % decrease in the mean of the partial-duration flood series occurred in 1941. This decline did not result in widespread channel change but provided an opportunity for vegetation to establish along the channel margins. Widespread channel narrowing began after a second decline in mean and peak discharge in 1956 at which time the channel banks became heavily vegetated. Between 1952 and 2019, the river channel narrowed by 57–59 %. Approximately 2–4 m of bed aggradation occurred at most study sites. As the channel narrowed and became more vegetated, large floods maintained the narrower channel width but did not cause rewidening. Suspended-sediment transport data illustrate the sediment trapping effects of vegetation that lead to channel narrowing; suspended-sand concentrations decline, thereby indicating sediment deposition, as vegetation becomes progressively inundated during floods. Furthermore, dense channel-margin and floodplain vegetation provide increased roughness, resulting in flood-peak attenuation and alteration of hydrograph shape. Vegetation expansion causes positive feedbacks whereby sediment deposition during floods is exacerbated by the roughness and sediment-trapping effects of vegetation leading to further narrowing. These positive feedbacks have reduced sediment delivery to the Little Colorado River downstream. Channel widening is not likely to occur unless there are very large floods that exceed the erosional threshold of the channel-margin vegetation, or unless large-scale vegetation removal efforts are undertaken.

Rating curve development and uncertainty analysis in mountainous watersheds for informed hydrology and resource management

Accurate measurement of continuous stream discharge poses both excitement and challenges for hydrologists and water resource planners, particularly in mountainous watersheds. This study centers on the development of rating curves utilizing the power law at three headwaters of the lesser Himalayas—Aglar, Paligaad, and Balganga—through the installation of water level recorders for stage measurement and salt dilution for discharge measurement from 2014 to 2016. The stream stage–discharge relationship, crucially known as the rating curve, is susceptible to numerous factors in mountainous watersheds that are often challenging to comprehend or quantify. Despite significant errors introduced during the rating curve development, such as stemming from observations, modeling, and parameterization, they are frequently overlooked. In this study, acknowledging the inherent uncertainty, we employ the maximum-likelihood method to assess uncertainty in the developed rating curve. Our findings reveal substantial inconsistency in the stage–discharge relationship, particularly during high flows. A novel contribution of this study is introducing a weighing factor concept that correlates uncertainty with the morphological parameters of the watershed. The higher value of the weighting factor in Paligaad (0.37) as compared to Balganga (0.35) and less in the case of Aglar (0.27) will have more uncertainty. The authors contend that precise rating curves and comprehensive uncertainty analyses can mitigate construction costs, foster robust decision-making, and enhance the perceived credibility of decisions in hydrology and water resource management.

Optimizing Height Above Nearest Drainage parameters to enable rapid flood mapping in North Carolina

Surface water flooding represents a significant hazard for many infrastructure systems. For example, residential, commercial, and industrial properties, water and wastewater treatment facilities, private drinking water wells, stormwater systems, or transportation networks are often impacted (i.e., in terms of damage or functionality) by flooding events. For large scale events, knowing where to prioritize recovery resources can be challenging. To help communities throughout North Carolina manage flood disaster responses, near real-time state-wide rapid flood mapping methods are needed. In this study, Height Above Nearest Drainage (HAND) concepts are combined with National Water Model river discharges to enable rapid flood mapping throughout North Carolina. The modeling system is calibrated using USGS stage-discharge relationships and FEMA 100-year flood maps. The calibration process ultimately provides spatially distributed channel roughness values to best match the available datasets. Results show that the flood mapping system, when calibrated, provides reasonable estimates of both river stage (or corresponding water surface elevations) and surface water extents. Comparing HAND to FEMA hazard maps both in Wake County and state-wide shows an agreement of 80.1% and 76.3%, respectively. For the non-agreement locations, flood extents tend to be overestimated as compared to underestimated, which is preferred in the context of identifying potentially impacted infrastructure systems. Future research will focus on developing transfer relationships to estimate channel roughness values for locations that lack the data needed for calibration.

Research on stage–discharge relationship model based on random forest algorithm

Hydrological simulations and predictions are vital aspects of hydrological change research. Accurate predictions of hydrological factors such as stage and discharge are essential for water resources planning, reservoir dispatching and operation, shipping management and flood control. River discharge forecasting during flood seasons is an important issue in water resources planning and management. To improve the calibration accuracy and stability of the stage–discharge relationship model, the feasibility of integrated algorithms for studying the stage–discharge relationship was explored. A random forest (RF) algorithm based on a neural network (NN) was developed using a framework of integrated algorithms. First, the Levenberg–Marquardt (LM) algorithm was used to optimise the weight updating process of a back-propagation (BP) NN and improve the convergence speed. Then, the LM-BP algorithm was used as a decision tree to build an RF algorithm. The model was tested using hydrological data from Hongqi station on the Dadu River in China in the flood season. Results for the classical model, BP NN model, LM-BP NN model and optimised algorithm model were evaluated based on the mean absolute error (MAE), mean square error (MSE) and mean absolute percentage error (MAPE). The performance indicators showed that the optimised algorithm model (MAE = 3.13 m3/s, MSE = 19.28 m3/s and MAPE = 1.8%) was superior to the other models and showed high accuracy and good stability in flood-season flow forecasting.

River adjustments in response to human activities: A case study of the lower Beijiang River, China

AbstractIntensive human activity has caused significant changes in the river morphology and hydrological characteristics of the Pearl River Delta. Particularly, in‐channel mining and dam construction have induced remarkable levels of downward riverbed incision. Although strict control measures have been implemented for in‐channel sand mining, it remains unclear how the river has evolved since the abandonment of high‐intensity mining and its impact on flow diversion at the downstream confluence. This study presents the hydrological and morphological adjustments in the lower Beijiang River, the second largest tributary of the Pearl River, under the impacts of human interventions. A hydrodynamic model was developed to reveal the impacts of riverbed deformation on the flow diversion ratio at Sixianjiao, the confluence of the Beijaing River and the Xijiang River. The results showed that construction of cascade reservoirs upstream reach did not strongly influence run‐off, whereas incoming sediment loads were decreased. Because of upstream damming and in‐channel sand mining, a dramatic downward incision was observed in the lower Beijiang River, with a degradation volume of approximately 239.8 million m3 from 1999 to 2012. Particularly, in the upper reach, the incision depth was typically larger than 8 m. Riverbed incision caused continuous changes in the water stage–discharge relationship, and discharge increased remarkably under the same water level at the three hydrometric stations. During 2012–2020, because in‐channel sand mining was strictly controlled, rapid degradation was alleviated, deposition occurred in some cross‐sections and the deformation volume decreased by approximately 90% compared to that in the last period. A fast downward incision induced a change in flow exchange between the two rivers, and the flow diversion ratio of the Beijiang River increased from an average of 17% before 1998 to more than 21%.

ODRA2D – TWO-DIMENSIONAL CASCADE FLOOD MODELLING FOR THE ODRA RIVER – DEVELOPMENT AND APPLICATIONS

Aim of the study: Development of new hydrodynamic numerical tools for simulations of the flow in the Odra River valley for the flood hazard assessment and management Material and methods: Use of the MIKE21 software for models building. Geospatial (ArcGis) topographical data processing and analysis for model inputs and outputs. Extensive use of remote sensing data (digital terrain model and orthophoto maps) combined with traditional data sources. Results and conclusions: A cascade of twenty five MIKE21 models was developed to cover a nearly 600 km long section of the Odra River. The models were used in different studies, including: the assessment of flood hazards with regards to various scenarios, the assessment of flooding due to ice jamming and breaks in embankments, the evaluation of the effectiveness of flood mitigating works within the complex Hydrosystem of the city of Wrocław, the verification of historic flood data and stage-discharge relations, and also the verification of design discharges.

Adaptive design of tipping bucket flow meters for continuous runoff measurement

Introduction: Runoff measurement and monitoring is a laborious, time-consuming, and costly task. Additionally, common runoff monitoring usually primarily provide water level, requiring information on the stage-discharge relation. Automatic equipment such as flow meter tipping bucket (TB) is a potential option to simplify and provide continuous runoff monitoring in small catchments. However, a proper description of how to size and adapt the design under different flow conditions is still lacking.Methodology: In this paper we present a novel standardized framework for the design of TB that can be used for low-cost and real-time runoff monitoring under many different conditions. The framework consists of an estimation of the runoff peak rate using the rational equation and a volumetric capacity estimate of the cavity based on runoff rate, operation speed, and inclination angle of TB when at resting position. The proposed framework was implemented in a case study where four TBs were designed for continuous runoff monitoring from experimental plots (100 m2) with different land use (sugarcane, soybean, and bare soil).Results: During field tests (five months), the designed TBs had a recovery rate of actual runoff ranging from 61% to 81% and were able to capture features poorly studied (starting/ending time and peak flow) that have potential importance in hydrological models.Discussion: The proposed framework is flexible and can be used for different environmental conditions to provide continuous runoff data records.

Uncertainty in streamflow measurements significantly impacts estimates of downstream nitrate export

Across watershed science, two key variables emerge–streamflow and solute concentration–which serve as the basis for efforts ranging from basic watershed biogeochemistry research to policy decisions surrounding watershed management. However, we rarely account for how error in discharge (Q) impacts estimates of downstream nutrient loading. Here, we examined the impact of uncertainty in streamflow measurements on estimates of downstream nitrate export using publicly available data from the U.S. Geological Survey (USGS). We characterized how uncertainty in stage-discharge relationships impacts annual flux estimates across 70 USGS gages. Our results indicate the interquartile range of relative error in Q was 33% across these USGS sites. We documented a wide range in mean error in annual nitrate loads; some sites were underestimated (−105%), while predicted loads at other sites vastly overestimated (500%). Overall, any error in estimating Q leads to significant unpredictability of annual nutrient loads, which are often used as critical success benchmarks for governmental nutrient reduction strategies. Moreover, error in annual nitrate loads (as mass, kg) increases with mean Q; thus, as high flows become more unpredictable and intense under future climate change, error in estimates of downstream nutrient loading may also increase. Together, this indicates that error in Q may drastically influence our measures of water quality success and decrease our ability to accurately quantify progress towards algal bloom and ‘dead zone’ reduction.

Increasing spruce budworm defoliation increases catchment discharge in conifer forests

Forest insect outbreaks cause significant reductions in the forest canopy through defoliation and tree mortality that modify the storage and flow of water, potentially altering catchment runoff and stream discharge patterns. Despite a growing understanding of the impacts of insect outbreaks on the hydrology of broadleaf forests, little is known about these impacts to catchment hydrology in northern conifer-dominated forests. We measured the effects of cumulative defoliation by spruce budworm (Choristoneura fumiferana) on stream discharge and runoff in 12 experimental catchments (6.33–9.85 km2) across the central Gaspé Peninsula in eastern Québec, Canada over a three-year period (2019–2021). Six catchments were aerially treated with BtK (Bacillus thuringiensis kurstaki) insecticide to suppress the outbreak and six catchments were left untreated, leading to a defoliation gradient across the study sites. Stage-discharge relationships were established between June and October from 2019 to 2021. Stream volumetric discharge (r = 0.71, p < 0.01, t(34) = 5.85), runoff (r = 0.55, p < 0.01, t(34) = 3.81) and runoff ratios (r = 0.67, p < 0.01, t(33) = 5.19) were all strongly positively correlated with cumulative defoliation intensity, likely by reducing available water storage in the catchment and therefore enhancing runoff generation. Seasonally, volumetric discharge, runoff, and runoff ratios were more strongly correlated with defoliation in the summer than autumn months, likely because available catchment storage was more limited following the freshet. Overall, we found that insect defoliation impacts forested catchment hydrology similar to other landscape disturbances, and such consequences should be considered in forest management and the control of forest insect outbreaks.

Stage discharge relations of a trapezoidal broad-crested weir pierced by a circular culvert

The present work focusses on the stage discharge relationship of a trapezoidal broad-crested weir pierced by a circular shape culvert at its base. The objective is to evaluate the relevance of the experimental and of the predictive superposition approaches for this hydraulic structure frequently encountered at the outlet of flood prevention basins, combining a flow through the culvert and a flow over the weir. The “experimental” superposition consists of the linear sum of the experimental relations of both elementary structures. Compared to the stage discharge relation of the complete structure, this sum performs well with a difference in discharge that does not exceed 15 %. The sum of discharges through both elementary structures slightly exceeds the discharge through the complete structure for an upstream head slightly above the weir crest elevation; it slightly underestimates this discharge for a larger upstream head, as already reported in the literature. The “predictive” superposition approach consists in predicting the stage discharge relation of the hydraulic structure using the sum of the stage discharge relations, available in the literature, for the elementary structures. The predictive superposition proves to be highly accurate for our combined hydraulic structure, especially for flow conditions with an incoming head high enough, for which the flow over the weir dominates.